POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell’Informazione

Corso di Laurea Magistrale in Energy Engineering

Optimization of a Cascade Phase Change Regeneratorfor Heat Recovery from a Real Batch Drying Process

Relatore: Prof. Gianluca VALENTICo-relatore: Dott. Abdullah BAMOSHMOOSH

Tesi di Laurea Magistrale di:Camilla Nicol BONACINA Matr. 892329

Anno Accademico 2018-2019

L’espressione attiva della virtuaffina anche la piu acuta intelligenza.

− Sri Yukteswar

Dedicato alla mia famiglia.

III

Ringraziamenti

Lo sviluppo di una tesi e un percorso lungo e travagliato, ma, una volta con-cluso, ne deriva una soddisfazione indescrivibile, perche e rappresentazionedi te stessa e della tua passione messa in atto. Per questo, devo ringrazia-re il Prof. Gianluca Valenti che mi ha guidato e dato fiducia. Per me harappresentato e rappresenta tuttora un modello da seguire sia in ambito pro-fessionale, per la passione e ambizione che accompagna ogni suo progetto,che personale, per i valori che mi ha trasmesso. Alla fine di questo percorso,posso dirlo: un professore, ma soprattuto una persona, come pochi.

Ringrazio molto Abi, il cui aiuto e stato fondamentale in questo percorsoe che mi ha incoraggiato nei momenti in cui mi serviva l’appoggio di unamico e collega speciale. Ringrazio Officine Meccaniche Deca S.r.l., i titolari,per la disponibilita, e tutti i colleghi con cui ho condiviso molti momenti,sorrisi e caffe. Un ringraziamento speciale anche ai titolari della lavanderiaBorromeo e a Mauro, che mi hanno permesso gentilmente di compiere lemisure e hanno dato un importante contributo allo svolgimento della miatesi. Inoltre, ringrazio Marco e Ferdinando per l’aiuto durante la campagnasperimentale. Ringrazio anche i Prof. Luigi Colombo e Stefano De Antonellisper la loro disponibilita e per l’appoggio tecnico riguardante rispettivamenteil modello di condensazione e gli scambiatori. Infine, un grazie a Michele pergli spunti da puro ingegnere matematico riguardanti l’ottimizzazione.

Ora devo ringraziare le persone che per me ci sono state per una vita erappresentano la mia forza piu grande. Grazie papa, perche sei sempre statoun esempio di virtu, di determinazione e sacrificio, perche semplicemente mihai fatto capire come in molti aspetti vorrei essere da grande. Grazie mam-ma, perche con il tuo appoggio in tutti i momenti difficili, le tue attenzioni,preoccupazioni, il tuo amore incondizionato, mi hai reso la persona che sonoora. Grazie perche mi hai dato una felicita in tutti questi anni che solo unamamma come te sa dare. Con voi ho capito cosa e davvero importante nel-la vita e quanto la nostra famiglia sia ineguagliabile. Grazie sorelle! Comeavrei fatto senza di voi? Il nostro completarci a vicenda mi lascia sempreimpressionata. Tutti i momenti che abbiamo passato insieme rimangono frai piu indimenticabili per me. Franci, da te ho imparato che sorridere un po’

V

di piu rende felice anche gli altri e che, alcune volte, lasciarsi andare rendeliberi. Ale, da te ho imparato ad essere piu generosa e ad apprezzare tantilati della vita che prima non volevo osservare. Voi ci siete sempre state perme e, cosı, saro io per voi. Dedico questa tesi a tutti voi, perche mi aveteaccompagnato in questi anni, sopportandomi, sostenendomi e migliorandomigiorno per giorno.

Ringrazio tanto i miei nonni: Luciano, una delle persone piu intelligentiche conosca, perche mi ha trasmesso la sua voglia di inventare, progettare econoscere, e Lola, perche, diciamocelo, una nonna unica come te non esiste innessun angolo della terra. Grazie ai nonni Anna e Mario, che mi hanno sem-pre regalato un sorriso. Ringrazio poi tutti i parenti che mi hanno pensato,hanno creduto in me e sostenuto.

Un grazie davvero speciale e per te, Tecli. Un’amica vera, con cui hocondiviso momenti belli e momenti bui, viaggi, avventure e tant’altro, dallesuperiori fino ad ora. Ti ringrazio per il tuo appoggio incondizionato e perchesei sempre stata una persona con cui poter ridere, piangere e condividere cioche pensavo. Infine, ringrazio tutti i miei amici e tutti i miei compagnidi universita che hanno reso il mio percorso in tutti questi anni unico, chemi hanno fatto imparare sempre qualcosa di nuovo e che mi hanno dato lapossibilita di migliorare come persona e come collega.

VI

Contents

Sommario XV

Summary XVII

Extended Summary XIX

1 Introduction 11.1 Context and Motivation . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Bibliography Review 92.1 Related Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Experimental Analysis . . . . . . . . . . . . . . . . . . . . . . 102.3 Phase Change Materials . . . . . . . . . . . . . . . . . . . . . 102.4 Drying Processes . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Optimization algorithms . . . . . . . . . . . . . . . . . . . . . 132.6 Thermophysical properties of the flow . . . . . . . . . . . . . . 142.7 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Case Study Measurements 173.1 Instrumentation and Measurements . . . . . . . . . . . . . . . 17

3.1.1 Temperature and Velocity Measurements . . . . . . . . 173.1.2 Air Mass Flow Rate . . . . . . . . . . . . . . . . . . . 223.1.3 Air Absolute Humidity Prediction . . . . . . . . . . . . 23

3.2 Measurement Uncertainties . . . . . . . . . . . . . . . . . . . . 24

4 Phase Change Materials 274.1 Energy Storage Technologies . . . . . . . . . . . . . . . . . . . 274.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

VII

Contents

4.4 Market Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 304.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 304.4.2 Selected Products . . . . . . . . . . . . . . . . . . . . . 30

5 Implementation 335.1 New Convergence Method . . . . . . . . . . . . . . . . . . . . 33

5.1.1 Film Method . . . . . . . . . . . . . . . . . . . . . . . 335.1.2 Convergence Method . . . . . . . . . . . . . . . . . . . 34

5.2 High Level Function New Structure . . . . . . . . . . . . . . . 355.3 Low Level Function Improvements . . . . . . . . . . . . . . . . 37

6 Optimization 436.1 Optimization Problem Review . . . . . . . . . . . . . . . . . . 436.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.3 Local Search and Simulated Annealing . . . . . . . . . . . . . 476.4 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 49

7 Case Study Results 537.1 Case Study Description . . . . . . . . . . . . . . . . . . . . . . 53

7.1.1 Flow Specifications . . . . . . . . . . . . . . . . . . . . 537.1.2 Stove Specifications . . . . . . . . . . . . . . . . . . . . 54

7.2 Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . 557.2.1 Energy and Economic Indexes . . . . . . . . . . . . . . 557.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.4 Analysis of the Optimal Configuration . . . . . . . . . . . . . 62

7.4.1 Hot Blow . . . . . . . . . . . . . . . . . . . . . . . . . 637.4.2 Cold Blow . . . . . . . . . . . . . . . . . . . . . . . . . 647.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.4.4 Further Improvements . . . . . . . . . . . . . . . . . . 67

8 Comparison with a Recuperator 698.1 Problem Review . . . . . . . . . . . . . . . . . . . . . . . . . . 698.2 Chevron Plate Heat Exchanger Model . . . . . . . . . . . . . . 70

8.2.1 Geometrical Parameters . . . . . . . . . . . . . . . . . 718.2.2 Mathematical Model . . . . . . . . . . . . . . . . . . . 728.2.3 Heat Transfer and Pressure Drop . . . . . . . . . . . . 73

8.3 Case Study of the Chevron Plate Heat Exchanger . . . . . . . 768.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 768.3.2 Preliminary Design . . . . . . . . . . . . . . . . . . . . 778.3.3 Results and Discussion . . . . . . . . . . . . . . . . . . 81

VIII

Contents

9 Conclusions 83

10 Future Work 85

Bibliography 87

IX

List of Figures

1 Dryer exhaust measurements and uncertainty intervals . . . . . XXI2 Parametric analysis results . . . . . . . . . . . . . . . . . . . . . XXVII3 Temperature profiles during the hot blow . . . . . . . . . . . . . XXVIII4 Temperature profiles during the cold blow . . . . . . . . . . . . XXVIII

1.1 Scheme of the regenerator comprised of the two stoves with hor-izontal rod bundles filled with phase change materials, the hotand cold blows, and the switching mechanism. . . . . . . . . . . 4

3.1 Temperature of the dryer inlet air, the exhausts from the dryerand the fabric . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Back view of the instrument . . . . . . . . . . . . . . . . . . . . 193.3 Front view of the instrument . . . . . . . . . . . . . . . . . . . . 203.4 Exhaust temperature measurements over the whole drying cycle

with uncertainty intervals . . . . . . . . . . . . . . . . . . . . . 213.5 Exhaust velocity measurements over the whole drying cycle with

uncertainty intervals . . . . . . . . . . . . . . . . . . . . . . . . 213.6 Examples of the velocity profiles in a circular duct for turbulent

flow with different n coefficients, in the case of fully developedconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.7 Exhaust mass flow rate profile over the whole drying cycle withuncertainty intervals . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Classification of phase change materials . . . . . . . . . . . . . . 29

5.1 Flowchart of the convergence method for the iterative solutionof Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2 Flowchart of the high level functions of the program . . . . . . . 385.3 Flowchart of the “stove.m” function . . . . . . . . . . . . . . . . 405.4 Flowchart of the “row stove.m” function . . . . . . . . . . . . . 41

6.1 Scheme of the bed matrix divided in 4 sectors . . . . . . . . . . 456.2 Example of the formation of a population in the sector 4 of the

stove . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

XI

List of Figures

6.3 Flowchart of the local search algorithm . . . . . . . . . . . . . . 486.4 Flowchart of the genetic algorithm . . . . . . . . . . . . . . . . 506.5 Example of the pairing with the binary vector [1100010] . . . . 51

7.1 Specific energy recoveries in function of the number of cylindersper row and their diameter . . . . . . . . . . . . . . . . . . . . . 58

7.2 Saving per year in function of the number of cylinders per rowand their diameter . . . . . . . . . . . . . . . . . . . . . . . . . 58

7.3 Energy recovery in function of the pressure drop for differentstove configurations . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.4 Energy recovery in function of the height of the stove for theoptimal configuration . . . . . . . . . . . . . . . . . . . . . . . . 60

7.5 Annual saving in function of the height of the stove for theoptimal configuration . . . . . . . . . . . . . . . . . . . . . . . . 61

7.6 Energy recovered in function of the number of sectors of thestove for their corresponding optimal configuration . . . . . . . 62

7.7 Temperature of the hot blow in the regenerator for diverse in-stants of the drying cycle . . . . . . . . . . . . . . . . . . . . . . 65

7.8 Temperature of the cylinders during the hot blow over time forthe first, middle and last rows of the stove . . . . . . . . . . . . 66

7.9 Temperature of the cold blow in the regenerator for diverse in-stants of the drying cycle . . . . . . . . . . . . . . . . . . . . . . 66

7.10 Temperature of the cylinders during the cold blow over time forthe first, middle and last rows of the stove . . . . . . . . . . . . 67

8.1 Scheme of the heat recovery system adopting a heat exchanger . 708.2 Scheme of single pass counter-flow plate heat exchangers [1] . . 708.3 Types of corrugation of plate heat exchangers: (a) washboard;

(b) zigzag; (c) chevron; (d) protrusions and depressions; (e)washboard with secondary corrugations; (f) oblique washboard [2] 71

8.4 Main geometrical parameters of a chevron plate heat exchanger [1] 728.5 Effect of the number of plates on the heat transfer and pressure

drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788.6 Effect of the plate width on the heat transfer and pressure drop 788.7 Effect of the plate gap on the heat transfer and pressure drop . 798.8 Effect of the port diameter on the pressure drop . . . . . . . . . 798.9 Annual savings in function of the plate gap . . . . . . . . . . . . 81

XII

List of Tables

3.1 Technical data of the instrument “Testovent 4000” . . . . . . . . 20

4.1 Values of the material properties of PCM Products Ltd’s prod-ucts [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Values of the material properties of Rubitherm GmbH’s prod-ucts [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7.1 Main parameters for the preliminary economic analysis . . . . . 567.2 Main parameters for the investment cost analysis . . . . . . . . 577.3 Optimal set of phase change materials obtained through the

local search and genetic algorithms for a regenerator divided indiverse numbers of sectors . . . . . . . . . . . . . . . . . . . . . 63

XIII

Sommario

La crescita del consumo di energia a livello globale ha reso il recupero ter-mico una delle principali strategie per la realizzazione di sistemi a crescenterisparmio energetico. Il presente lavoro affronta l’analisi sperimentale, lostudio numerico e la fattibilita economica di un rigeneratore con materialia cambiamento di fase per il recupero termico nell’industria degli essiccatoiindustriali. Il rigeneratore opera in modo discontinuo con un flusso caldo ver-so il basso e uno freddo verso l’alto, i quali attraversano in modo alternatodue camere verticali. Il primo flusso e l’aria calda e umida in uscita dal-l’essiccatoio, che scambia energia con la matrice del rigeneratore. Il secondoflusso e aria in condizioni ambiente, che si preriscalda scambiando energiacon la matrice precedentemente attraversata dal flusso caldo. Il processo ereso continuo dall’utilizzo di due matrici. La matrice e composta da fascitubieri cavi e riempiti di materiali a cambiamento di fase commerciali.

Lo scopo di questo processo e quello di massimizzare la temperatura del-l’aria preriscaldata in ingresso all’essiccatoio, ossia massimizzare l’energiarecuperata dal flusso freddo e minimizzare l’energia usata dall’essiccatoio.Quindi, un processo di ottimizzazione e utilizzato per trovare quale sia laconfigurazione del rigeneratore e l’insieme di materiali industriali che garan-tiscano lo scambio termico piu efficiente. Un’analisi parametrica e due metodidi ottimizzazione, di cui un modello basato sulla ricerca locale e un algorit-mo genetico, sono utilizzati. Inoltre, le condizioni operative del rigeneratoresono ottenute attraverso un’indagine sperimentale.

La configurazione ottimale ottenuta per il caso studio del rigeneratoree caratterizzata da un recupero di energia del 61.5%, che corrisponde adun’energia recuperata pari a 52 MJ e a risparmi annuali nell’ordine di 3340 e.Confrontando il rigeneratore con uno scambiatore a piastre, si nota che ilrigeneratore ha delle caratteristiche operative e di manutenzione promettentirispetto al recuperatore. In particolare, il problema dello sporcamento e lapossibilita di migliorare lo scambio termico del rigeneratore sono considerati.

Parole chiave: recupero termico; materiali a cambiamento di fase;processi di asciugatura

XV

Summary

The increase of the worldwide energy consumption makes waste heat recoveryone of the most interesting strategies for the realization of effective energysaving systems. The present work deals with the experimental analysis, nu-merical study and economic feasibility of a cascade phase change regeneratorfor heat recovery in the textile dryer industry. The regenerator operates ina batch mode with a downward hot blow and an upward cold blow flowingalternatively in two vertical stoves. The former is the hot and humid airexiting the dryer, that transfers energy to the bed matrix. The latter is theambient air that preheats while exchanging energy with the stove previouslycrossed by the hot blow. The blows are switched between the two beds eachcycle to make the process continuous. The bed matrix is made of hollow rodbundles filled with phase change materials available on the market.

The aim of this process is to maximize the temperature of the preheatedair at the inlet of the dryer, that is equivalent to maximizing the energyrecovered during the cold blow and minimizing the use of energy for drying.An optimization process is performed in an extended numerical model tofind the stove configuration and set of commercial materials that lead tothe most efficient heat exchange process. Both a parametric analysis andtwo optimization methods, i.e. local research and genetic algorithms, areperformed. Moreover, the inlet and boundary operating conditions of theregenerator are found through an experimental analysis.

The optimal configuration obtained for the case study of the regeneratoris characterized by an energy recovery of 61.5%, corresponding to 52 MJ ofsaved energy. On their turn, the annual savings are in the order of 3340 e.The comparison of the regenerator with a plate heat exchanger shows that theformer is promising in terms of operating and maintenance aspects. Specif-ically, the issue of fouling and the possibility to enhance the heat transfermechanism in the regenerator are considered.

Key words: heat recovery; phase change materials; drying process

XVII

Extended Summary

Introduction

The dryer industry is characterized byhighly energy-intensive processes andwaste heat recovery represents one ofthe major strategies to decrease its en-ergy consumptions. Many heat recov-ery technologies applied to continuousprocesses are available in literature, e.g.heat exchangers and heat pumps. Thepresent case study deals with a naturalgas fired batch dryer, thus a regener-ator is chosen because it is inherentlydiscontinuous. The system is made oftwo vertical stoves with horizontal rodbundles. The rods are hollow and filledwith phase change materials available onthe market. Among different types of re-generators, this configuration is chosento avoid structural and cleaning issues.A cycle is characterized by a downwardhot blow and an upward cold blow. Theformer comes from the dryer outlet andtransfers energy to the bed matrix. Thelatter is ambient air that is preheated bythe bed matrix and enters the burner ofthe dryer. The blows are switched be-tween the two beds each cycle to makethe process continuous.

The aim of this thesis is to performan accurate analysis of a cascade phasechange regenerator. From an experi-mental point of view, measurements of

the exhaust temperature, velocity andmass flow rate, and prediction of the hu-midity are performed for a dryer presentin an industrial laundry in Milan. Froma numerical point of view, a MATLABcode is corrected and advanced mainlyby the introduction of two optimizationalgorithms and a convergence method.The best set of industrial phase changematerials with sliding transition temper-ature, that maximizes the energy recov-ered during the cold blow, is computed.Moreover, the regenerator performancesare compared to that of a system adopt-ing a plate heat exchanger as heat recov-ery device.

Hence, the present thesis aims to im-prove the regenerator analysis in 5 fieldsof study: experimental analysis, numer-ical model, market investigation, deter-mination of the optimal configurationand evaluation of the economical feasi-bility of the regenerator.

Case Study

Measurements

This section deals with the measure-ments and uncertainty calculation of thetemperature, velocity, mass flow rateand humidity of the dryer exhausts, i.e.the inlet conditions of the hot blow.

XIX

Extended Summary

Instrumentation andMeasurementsThe exhaust outlet temperature and ve-locity are directly measured with thetemperature and impeller probe of theinstrument “Testovent 4000”. The mea-sures are performed in the squared ductof the dryer exhausts. The instrument isplaced as far as possible from the dryerexit to consider fully developed condi-tions of the flow. A hole is made in theduct, and the instrument is held by anarm and fixed with a magnetic base ona tube close to the exhaust duct. In-deed, the instrument must be well fixedto avoid deviations of the velocity dueto the rotation of the impeller itself.

The mass flow rate of the air enter-ing the regenerator mair (kg/s) is re-trieved through the mean velocity in thecross section of the duct as [5]

mair = ρairvmAc (1)

where vm (m/s) is the mean velocity,Ac (m2) the cross section area of theduct, and ρair (kg/m3) the air densitycalculated with the ideal gas law, asfunction of the measured temperatureprofile. Assuming incompressible flowand constant cross section, the velocityis independent on the position along theaxial direction of the duct, but it variesover the cross section. In the presentwork, fully developed conditions are as-sumed. Moreover, correlations for circu-lar ducts are employed adopting the hy-draulic diameter Dh (m) as characteris-tic length [2]. As suggested by Fang [6],the calculation of vm is retrieved as

vmvc

=2n2

(n+ 1) (2n+ 1)(2)

where vc (m/s) is the velocity at the cen-ter of the duct, and n the power law co-efficient that depends on the Reynolds

number. Figg.1a and 1b show the ex-perimental analysis results. Specifically,the exhaust temperature and mass flowrate are depicted, respectively.

Then, a preliminary prediction ofthe absolute humidity of the air at theinlet of the regenerator is obtained di-viding the evaporated water mass flowrate mevap (kg/s) by the mean exhaustmass flow rate. The value of mevap iscalculated from the mass of water con-tained in the fabric, known from experi-ence in the laundry. The value obtainedis of about 0.04 kgwater/kgdry,air.

Measurement UncertaintiesThis section deals with the calculationof the uncertainty of the measurementsof velocity, temperature and mass flowrate. The uncertainties of the firsttwo parameters are retrieved from theinstrument technical specifications pro-vided by the manufacturers. While thecalculation of the combined uncertaintyis necessary for the latter.

Considering vm and Tair as the onlysource of uncertainty, the mass flow raterelative uncertainty Um/mair (-) is ob-tained as follows

Ummair

=

√(Uvmvm

)2

+

(UTairTair

)2

(3)

Adopting this equation, the mean rel-ative uncertainty of the mass flow rateturns out to be 7%. This result is ac-ceptable for the present case study, be-cause an indicative value of the flow rateis needed. Indeed, each cycle is char-acterized by different operating condi-tions, depending on the type of cottonfabrics that are dried. Hence, a moreprecise result is not necessary.

XX

Extended Summary

(a) Exhaust temperature (b) Exhaust mass flow rate

Figure 1. Dryer exhaust measurements and uncertainty intervals

Phase Change

Materials

This section deals with phase changematerials as energy storage technolo-gies. First, their fundamentals, prop-erties and classification are described.Then, a market analysis is performed toselect commercial products.

Energy Storage TechnologiesDifferent storage technologies are avail-able and well known in the industry,i.e. electrical, chemical, mechanical andthermal storage [7]. Phase change ma-terials are comprised in the latter cat-egory. They are considered promisingtechnologies because a high energy perunit volume can be stored when theirlatent heat is exploited. Generally, theycan store an amount of energy in the or-der of 5 -15 times than that of sensibleonly storage materials [8].

PropertiesMany features must be considered whendesigning a system that adopts phasechange materials. Phase change tem-perature, latent heat of fusion and ther-

mal conductivity play a major role inthe effectiveness of the heat exchangeprocess. Phase equilibrium, density,volume change and vapor pressure areimportant physical properties to con-sider. They mainly affect the stabilityof the transition phase, the bulk volumeand the sealing issues, respectively. Interms of kinetics, supercooling and in-congruent melting can occur when us-ing specific classes of phase change ma-terials such as salts. It is very impor-tant to consider also chemical stability,non-toxicity, non-flammability and non-corrosiveness. Moreover, widely avail-able, abundant and cost effective phasechange materials should be chosen to de-sign an economically feasible system [8].

ClassificationPhase change materials can be classifiedin solid-solid, solid-liquid and liquid-gasPCMs [7]. Especially solid-liquid phasechange materials are suitable for regen-erators because of their low specific vol-ume change [9]. It is possible to fur-ther classify this category in organic, in-organic and eutectic materials [8]. Or-ganics are divided in paraffins and non-

XXI

Extended Summary

paraffins. Salt hydrates and metals arein the class of inorganics. While eutec-tics are present in a wide variety of prop-erties. These PCMs have very differentcharacteristics, thus their selection mustbe performed carefully.

Market analysisA market analysis is performed to findmaterials available in the industry thatare suited for the present case study.The research focuses on organic mate-rials, i.e. waxes, because of their low ornull corrosiveness, their easy handlingand low cost. Transition temperaturesin the range of the operating tempera-tures of the regenerator are selected, i.e.between 40 ◦C and 133 ◦C. The mate-rials must be non-corrosive, non-toxic,non-hazardous and non-flammable in allthe operating conditions of the regen-erator. The products of PCM Prod-ucts Ltd are selected mainly because oftheir wide range of transition tempera-tures and their high flash temperatures.

Implementation

The physical and numerical modelsadopted in this thesis are implementedin a MATLAB code to obtain the perfor-mances of the heat recovery system. Inthis chapter a new convergence methodis depicted, and the main functionscalled in the MATLAB script are de-scribed. Moreover, some corrections ofthe MATLAB code are reviewed.

New Convergence MethodThe film method is implemented toconsider condensation of vapor in non-condensable gases, and the overall heattransfer coefficient that considers the la-

tent contribution is found as explainedextensively by Seveso [10]. The finalenergy balance obtained between thecylinders and the bulk flow, separatedby a boundary layer interface, is

m′′vhlv + α∗s(Tb − Ti) = · · ·

· · · = αc(Ti − Tcln)(4)

where m′′v (kg/(s m2)) is the mass flux of

condensate, α∗s (W/(m2 K)) the sensibleheat transfer coefficient modified by theAckermann’s number, αc (W/(m2 K))the heat transfer coefficient on the cylin-der side, and Tb (K) and Ti (K) thebulk and interface temperatures, respec-tively. The left side of Eq.4 repre-sents the heat flux between the inter-face and the bulk flow Q

′′flw (W/m2),

while the right side the heat fluxbetween the cylinders and the inter-face Q

′′cln (W/m2).

The calculation of the heat fluxesin Eq.4 is straightforward once the in-terface temperature is found. Then,the total and sensible only heat trans-fer coefficients, αtot (W/(m2 K)) andαs (W/(m2 K)), are computed as

αtot =Q′′flw

(Tflw − Tcln)(5)

αs =Q′′flw − m

′′vhlv

(Tflw − Tcln)(6)

These two parameters are used to calcu-late the temperature change of the cylin-ders and that of the flow, as well as theenergy exchanged row by row over eachtime-step of the drying cycle.

However, the interface temperatureis unknown, thus an iterative method isperformed to solve the energy balancein Eq.4. In this thesis, a more robustmethod is implemented to reach conver-gence. First, a bisection approach is

XXII

Extended Summary

adopted till a tolerance εbis (-) in theorder of 10−2 is reached. Once a moreprecise solution of Ti is obtained, theNewton method utilizes this solution asinitial guess, and it is performed untila tolerance εnewt (-) of about 10−4 isreached. The error considered for theconvergence is calculated as follows

err =Q′′flw − Q

′′cln

Q′′flw

(7)

In terms of iterative methods, theupdating of the interface temperaturefor each iteration step “n” is per-formed for the bisection and the New-ton method as depicted by the followingequations, respectively

Ti,n+1 =Tmin,n + Tmax,n

2(8)

Ti,n+1 = Ti,n −err(Ti,n)

d err(Ti,n)(9)

where Tmin,n (K) and Tmax,n (K) are theinitial temperature guesses for the bisec-tion method, err (-) is calculated as inEq.7, n is the number of the iterationand d err the derivative of the error cal-culated numerically. More details of thisprocedure are shown in the chapter re-garding the implementation.

High Level FunctionNew StructureThe code consists of a main script“CALL generic.m” comprised of threefunctions named “regenerator input.m”,“regenerator ss.m” and “regenera-tor output.m”. In “CALL generic.m”the user sets the main geometrical pa-rameters of the stove, the inlet andboundary conditions, the models of theflow and of the cylinders, and the dis-cretization grid. The function “regener-ator input.m” retrieves inputs from the

user and elaborates them to make themready to be used in the main functionof the code, “regenerator ss.m”. Thelatter function performs a parallel andcyclic analysis that is concluded un-til steady-state conditions are reachedin the two stoves. Diverse child func-tions are called in this latter functionof the code and they will be describedin the following section. Finally, “re-generator output.m” displays the resultsand the plots useful for the quantitativeanalysis of the whole process.

Low Level FunctionImprovementsThe function “stove.m” retrieves the ini-tial and inlet conditions of the stovefrom “regenerator.m” and performs aprogressive analysis through the Nt

time-steps and the Ns rows. The func-tion “row stove” is called for each time-step and for each row. The properties ofthe flow and the heat transfer coefficientare calculated with the model chosen bythe user. The functions for the calcu-lation of the temperature distributionin the cylinders are called depending onthe material and the model adopted.

Specifically, the function “cylin-der lumped” calculates the evolution ofthe temperature of the cylinders with a0D approach. This model is valid onlyfor Biot numbers Bi (-) lower than 0.1.However, this constraint is not fulfilledfor the present case study, because ofthe low conductivity of paraffins. Hence,a correction is applied to decrease thevalue of the heat transfer coefficient, ob-taining αnew (W/(m2 K)) as follows

αnew =

(1

α+Rc

)−1

(10)

where α (W/(m2 K)) is the heat transfer

XXIII

Extended Summary

coefficient before performing the correc-tion, and Rc ((m2 K)/W) a characteris-tic resistance of the cylinders. Eq.10 isapplied for both αtot and αs. Then, theformer is used to calculate the energy ex-changed between the cylinders and theflow, while the latter is adopted to calcu-late the outlet temperature of the flow ineach row. Indeed, the former considersthe total heat exchanged, while the lat-ter takes into account the sensible onlycontribution. More details of this anal-ysis are depicted in Chapter 5.

Optimization

To exploit in the best possible way thelatent heat of fusion of phase changematerials, a cascade regenerator is stud-ied: diverse sectors are filled with phasechange materials with sliding transitiontemperatures to decrease the temper-ature difference between the cylindersand the flow. Optimization algorithmsare adopted to maximize the energy re-covered. First, a review of optimizationtechniques is shown. Then, the appli-cation to the present case study is de-picted and the algorithms selected aredescribed in detail.

Optimization Problem ReviewAn optimization problem can be formu-lated as the research of a variable x ofa set X ⊆ <n that minimizes the valueof a function f : Y → Z ⊆ <n [11].Focusing the attention on integer pro-gramming, different analytical optimiza-tion methods can be adopted. However,most of the practical problems are toodifficult to be solved with these meth-ods, hence heuristic or approximated al-gorithms can be a useful tool to simplify

the problem. Among this latter cate-gory, natural optimization methods arewidely used in practice.

MethodologyThe regenerator is divided in a num-ber of sector nsector filled with the phasechange materials selected in the previ-ous section. These PCMs represent theparameters that are analyzed in the op-timization problem. Moreover, phasechange materials with decreasing tran-sition temperature should be positionedfrom the inlet to the outlet of the stoveduring the hot blow, and viceversa forthe cold blow. From the numerical pointof view, the objective function that mustbe maximized is the energy recoveredduring the cold blow. Thus, the prob-lem is non-linear, due to the structureof the code implemented. These char-acteristics of the problem make heuris-tic methods the most suitable modelsfor this case study. Specifically, localsearch and the genetic algorithm are im-plemented.

Local Search andSimulated AnnealingIn a local research approach, an initialsolution S is set and neighbor solutionsS′ are created. The objective functionf to be maximized is calculated for eachneighbor. The set of parameters thatgives the maximum value of f(S′) is se-lected as initial solution for the next it-eration [12]. The implementation stopswhen the relative difference between theenergy calculated in the current and inthe previous iteration is lower than atolerance εconv (-) of 10−3. The neigh-bor creation mechanism works as fol-lows: each iteration of the model corre-sponds to the change of the material of

XXIV

Extended Summary

one single sector, starting from the topto the bottom of the regenerator. Oncethe last sector is reached, the processstarts again from the first sector on thetop. In this way, sector by sector thematerials selected are adjusted to fit inthe best possible way the heat exchange.

Moreover, to avoid problems of localminima, simulated annealing is imple-mented in particular cases to check thevalidity of the code.

Genetic AlgorithmIn a genetic algorithm the fitness func-tion f(x) is defined as the function thatmust be minimized. When a maximumis searched, the algorithm is set suchthat min(−f(x)) is found. The variablex is called individual or chromosome,and it is comprised of nvar parameters.In the present case study, x is the setof materials in the regenerator and theparameters are the diverse PCMs thatfill each sector. First, an ensemble ofindividuals is chosen to form a popu-lation. Once a population is set, theobjective function is calculated for eachindividuals and only the best solutionsare kept for each iteration. Secondly,couples formed by the individuals previ-ously selected are created, and two off-springs are formed combining the chro-mosomes of the parent functions. Then,random mutations are performed in or-der to modify a small percentage of thenew individuals. Finally, a new set of xis obtained and a new generation is set.This iterative process usually continuesuntil convergence is reached [13].

In the present case study, the func-tion “ga” available in MATLAB isadopted. The genetic algorithm is com-pletely based on a probabilistic ap-proach, differently from the local re-

search algorithm that is implemented.Indeed, the latter is thought specificallyconsidering the physics of the system.

Case Study Results

This chapter deals with the simulationof the MATLAB code developed in thepresent work for the case study. Theoperating conditions of the dryer are re-trieved mainly from the experimentalanalysis. Moreover, the methodologyfollowed to find the optimal configura-tion and the results are discussed.

Case Study DescriptionA regenerator for heat recovery in anindustrial tumble dryer for cotton flatfabrics is studied in the present work.The regenerator is characterized by twofeeds: a cold blow at ambient condi-tions, and a hot blow, whose conditionsare described in the experimental anal-ysis. The frontal area of the stove is setequal to 0.250 m2 to have a flow witha velocity of about 5 m/s. Thus, thewidth and depth of the stove result tobe 500 mm, assuming a square-shapedcross section. The maximum height ofthe system is set to 3 m, according tothe size of the industrial building. Addi-tional consideration will be discussed toexamine the possibility to decrease theheight of the system. Different numbersof cylinders per row Ncln (-) and dif-ferent cylinder diameters Dcln (m) arestudied in a parametric analysis.

Regarding materials, a cascade of di-verse PCMs found on market is consid-ered. The first configuration guess is setby experience and inspection of the op-erating temperatures of the regenerator.Specifically, the initial materials selected

XXV

Extended Summary

to fill the whole regenerator, from thetop to the bottom, are: A95, A70, A58Hand A48 of Tab.4.1.

Parametric StudyThis section deals with the paramet-ric study applied to the case study de-scribed above. The range of Ncln andDcln is 11-27 and 9-18 mm, respectively.The aim is to find the configuration ofthe stoves characterized by the highestperformances and saving per year. Therecovery (-) is the main index that de-picts how the regenerator is performingin terms of energy transfer, and its valueis calculated as follows

Recovery =ErecoveredEmax,flw

(11)

where Erecovered (J) is the energy recov-ered in the cold blow and Emax,flw (J)the maximum energy that could be ide-ally exchanged in the hot blow.

In their turn, the energy indexesused in the analysis are the mass specificenergy recovered Espec,mass (J/kg) andthe pumping work specific energy recov-ered Espec,pmp (J/J), that are the ratiosof the energy recovered with respect tothe total mass of the stove mstv (kg)and to the pumping energy Epmp (J), re-spectively. In addition, the annual sav-ing Csaving (e/year) considers two con-tributes: the avoided costs due to theenergy recovered by the system, and thepumping costs related to the energy con-sumed by the two fans adopted for thehot and cold blows.

Among these parameters, the spe-cific energy recoveries and the savingper year are plotted in function of thenumber of cylinders per row and theirdiameter, as shown in Figg.2a and 2b.The former depicts the behavior of the

mass and pumping work specific ener-gies. The plot is characterized by asharp change in slope, because of the dif-ferent increase rates of the efficiency andthe pumping work spent for the fans.The latter highlights that an optimal an-nual saving is found and it represents thebest configuration from an economicalpoint of view. Specifically, this configu-ration is characterized by a diameter of9 mm and a number of cylinders per rowequal to 26. Overall, a mass specific en-ergy recovered of 442 kJ/kg is obtained,corresponding to savings of about 3300euros per year. For this configuration,the height that ensures the highest effi-ciency, while observing the constraint ofspace, is equal to 3 m.

OptimizationThe last step to find the best configura-tion is the optimization of the materialdistribution in the diverse sectors of theregenerator. The local search and ge-netic algorithm are computed, and theirbehavior is compared. The number ofsectors for which the procedure is re-peated goes from 1 to 10.

From this analysis, it is noticed thatthe optimal configuration is that corre-sponding to 8 sectors, in which only 5different materials are used, without af-fecting considerably the complexity ofthe structure. Moreover, increasing thenumber of sectors from 1 to 8, the re-covery increases of 6 percentage points.In terms of optimal configurations, thetwo algorithms gives equal or very simi-lar results. However, the former resultsto be faster than the latter, because it isimplemented considering the physics ofthe problem.

XXVI

Extended Summary

(a) Specific energies (b) Annual savings

Figure 2. Parametric analysis results

Analysis of the OptimalConfigurationThe optimal configuration retrievedfrom the optimization process is ana-lyzed in detail for both the hot and coldblows. Specifically, the flow tempera-ture is plotted in function of the numberof the row for diverse instants of the dry-ing cycle, as in Figg.3a and 4a. Whilethe cylinder temperature is plotted infunction of time for diverse sections ofthe stove, as in Figg.3b and 4b.

Two main characteristics of the tem-perature profiles are noticed. First, theflow temperature difference between theinlet and outlet of the regenerator de-creases from the beginning to the end ofthe cycle. Indeed, the heat exchange isless efficient in the last instants of thecycle, because the temperature differ-ence between the cylinder and the flowdecreases. Secondly, the phase changetransition zones are depicted by the hor-izontal temperature distribution, high-lighting the sliding melting tempera-tures of the diverse materials.

Overall, the outlet temperature ofthe regenerator represents how much is

possible to preheat the cold air at theinlet of the burner. The regenerator en-sures an efficiency in the order of 61.5%,corresponding to a recovered energy,mass of the stove and pressure drop inthe order of 52 MJ, 117 kg and 1.4 kPa,respectively. Thus, the mass and pump-ing work specific energies turn out to be444 kJ/kg and 38 kJ/kJ, respectively. Interms of economical profits, the annualsaving is of about 3340 euros.

Moreover, a preliminary analysis toincrease the regenerator efficiency isstudied. Qureshi et al. [14] show thatthe heat conductivity of paraffins simi-lar to that studied in this thesis can in-crease of about 25 times with inclusionsof extended graphite. Thus, the regen-erator behavior is studied increasing theconductivity from about 0.22 to about5.5 W/(m K). The optimization pro-cess previously described is performedfor the enhanced paraffins. The analy-sis shows that the recovered energy in-creases of about the 5%, leading to anannual saving in the order of 3800 e.

XXVII

Extended Summary

(a) Flow temperature (b) Cylinder temperature

Figure 3. Temperature profiles during the hot blow

(a) Flow temperature (b) Cylinder temperature

Figure 4. Temperature profiles during the cold blow

XXVIII

Extended Summary

Comparison with

Recuperators

This section aims to compare the regen-erator studied in this thesis with a com-mon heat recovery device, such as a heatexchanger. First, a review of the systemadopting the heat exchanger is shown.Secondly, the heat exchanger model isdepicted. Finally, the economic resultsare discussed and compared to that ob-tained for the regenerator.

Problem ReviewThe economic indexes previously calcu-lated are compared to that of heat ex-changers, to understand if the regener-ator is economically interesting. Hence,the recovered energy and the pressuredrop of this system are calculated to ob-tain the annual saving, as for the regen-erator. In the case of recuperators, theheat is transferred directly from the hotto the cold blow. The recuperator stopsthe operation when the drying cycle iscompleted, and restarts when the nextcycle begins.

In textile drying applications, gas-ket plate heat exchangers are commonlyadopted [15]. Specifically, this type ofstructure is chosen because of its sim-plicity and ease of cleaning the accumu-lated dust [16]. Moreover, a counter-flow arrangement is selected to ensurehigh efficiencies, for a single pass con-figuration with chevron plates selectedfrom a literature review.

Heat Exchanger ModelThis section depicts the model imple-mented in MATLAB to study the be-havior of a chevron plate heat ex-changer. The geometrical parameters,

the ε-NTU method, and the heat trans-fer and pressure drop correlations aredescribed in detail. For the present casestudy, the relation between ε and NTUis simplified [5] as follows

ε =NTU

NTU + 1(12)

where NTU (-) is the number of transferunits and is defined [5] as

NTU =UAtotCmin

(13)

where U (W/(m2 K)) is the overall heattransfer coefficient, Atot (m2) the to-tal heat transfer area and Cmin (W/K)the heat capacity. The unknown inthe NTU equation is the overall heattransfer coefficient, that depends on theheat transfer coefficient α (W/(m2 K)).The definition of the Nusselt numberNu = CRemPrn is used to calculatethe latter, where C, m, and n are coeffi-cients that depend on the plate geome-try, Re and Pr. Once the Nusselt num-ber, heat transfer coefficient and overallheat transfer coefficient are calculated,the effectiveness and the actual heat ex-changed are found from their definitions.From these values, the energy recoveredover the whole drying cycle is found.

The operating costs of the fans arecalculated as it is explained in the modelof the regenerator. While, the totalpressure drop is calculated as functionof the friction and port losses, as sug-gested by Imran et al. [17]. The fric-tion pressure drop ∆Pf (Pa) is calcu-lated with the correlations for the fric-tion factor f (-) implemented in “AS-PEN EDR” [18] to obtain good predic-tions for different ranges of the Reynoldsnumber. On its turn, the port pressuredrop ∆Pp (Pa) depends on the flux atthe manifolds.

XXIX

Extended Summary

Case StudyThe recuperator annual savings arecompared to that of the regeneratorand calculated performing the numeri-cal analysis, fixing the geometrical pa-rameters obtained imposing the pressuredrop and capital cost. A combination ofsimulations of “ASPEN EDR” and themodel implemented in MATLAB is per-formed to rate the recuperator. Specifi-cally, the effect of the change of the num-ber of plates, plate width, plate gap andport diameter is studied while fixing theother geometrical parameters.

The number of plates obtained fixingthe capital costs is equal to 127, corre-sponding to a plate width and height of660 and 1188 mm, respectively. More-over, the plate gap is increased to de-crease the channel velocity and to limitthe pressure drop. A maximum of theannual savings is found for b equal toroughly 10 mm. The computation showsa recovered energy of 57 MJ, with pres-sure drops of 1260 Pa, corresponding to3900 e of annual saving.

Comparing the recuperator resultswith that of the regenerator, it is pos-sible to notice that the savings per yearof the former are slightly higher. How-ever, two important aspects should beconsidered: the fouling issues and thepossibility to improve the regeneratordesign. Indeed, the high quantity of cot-ton residues can damage the recuperatorconsiderably, while the simple structureof the regenerator can be easily cleanedby blowing compressed air during theperiod between two cycles. The otheraspect to consider is that the regener-ator is in a first stage of research, andother major improvements can be per-formed to increase its efficiency, such asthe conductivity enhancement describedin the section regarding the case study.

Conclusions

The analysis performed in this thesisleads to the following conclusions:

1. From the experimental and mar-ket analysis, the operating condi-tions of the hot blow and the se-lection of 14 suitable PCMs areobtained.

2. The optimization process leads toan optimal configuration charac-terized by an efficiency, recov-ered energy and annual saving inthe order of 61.5%, 52 MJ and3340 euros, respectively.

3. Fixing the investment costs andpressure drop, the annual savingof the heat exchanger investigatedis about 500 euros higher thanthat of the regenerator. How-ever, the problem of fouling forthe recuperator and the possi-bility to enhance the regeneratorperformances, make this secondtechnology the most promising interms of operating and mainte-nance conditions.

Future Work

The work developed in the present the-sis can be refined by theoretical and nu-merical improvements. The main fieldsof study that can be investigated toperform these developments are as fol-lows: the implementation of the “en-thalpy method” to study phase changematerials, the analysis of conductivityenhancement techniques, the investiga-tion of the fouling issue, the design ofthe system and the calculation of moreprecise investment costs.

XXX

Nomenclature

In this chapter the nomenclature adopted is introduced. Specifically, the di-mensionless groups, Greek and Roman letters, subscripts, apexes and acronymsare depicted. A brief description for each item is included.

Dimensionless groups

Bi Biot number

Nu Nusselt number

Pr Prandtl number

Re Reynolds number

Greek letters

α Convective heat transfercoefficient, W/(m2K)

ε Tolerance, −Effectiveness, −

η Efficiency, −λ Thermal conductivity,

W/(mK)

µ Dynamic viscosity, Pa s

Φ Plate enlargement factor, −ρ Density, kg/m3

τ Characteristic energy, J

Roman letters

A Area, m2

a Plate aspect ratio, −Duct width, m

b Vertical pitch, −Plate gap, mDuct height, m

C Cost, eHeat capacity, W/K

c Specific heat capacity,J/(kgK)

cp Specific heat capacity atconstant pressure, J/(kgK)

Dh Hydraulic diameter, m

Dp Port diameter, m

Dpt Depth of a stove, m

Dt Time-step, s

E Energy, J

err error, −f Generic function, −

Friction factor, −G Mass flux, kg/(m2s)

XXXI

Extended Summary

H Height of the stove, m

h Specific enthalpy, J/kg

I Investment, e

kt Turbulent coefficient, −L Length, m

Lv Effective vertical length, m

Lh Effective horizontal length, m

m Mass, kg

m Mass flow rate, kg/s

m′′

Mass flux, kg/(m2s)

Ncln Number of row cylinders, −Nc Number of channels, −Np Number of plates, −Ns Total number of rows, −Nt Total number of temporal

discretization steps, −Nturn Number of corrugation turn, −n Iteration, −

Generic number, −Generic coefficient, −

P Pressure, Pa

p Probability, −pc Corrugation pitch, m

par Generic parameter, −Q Thermal power, W

Q′′

Heat flux, W/m2

R Radius, mResistance, (m2K)/W

Rg Specific gas constant, J/(kgK)

r Cooling factor, −Interest rate, −Generic radial coordinate, −

S Generic set of solutions, −S′ Generic set of neighbors, −

Scln Cylinder external surface, m2

T Temperature, K

t Time, sPlate thickness, m

U Overall heat transfercoefficient, W/(m2K)Uncertainty

V Volume flow rate, m3/s

v Velocity, m/s

W Power, W

Wdt Width of a stove, m

Wc Characteristic width, m

X Generic set of variables x, −x Generic variable, −

Generic coordinate, −Y Generic set of variables y, −

Subscripts and apexes

b Bulk

bis Bisection

brn Burner

c Condensation, Cold,Cross section, Center,Characteristic

ch Channel

cln Cylinder

conv Convergence

el Electric

f Final, Fouling, Friction

flw Flow

fus Fusion

h Hot

hx Heat exchanger

XXXII

Extended Summary

i Initial, Interface, Iteration

in Inlet

j Generic neighbor

l Liquid, Laminar

lat Latent

lv Latent liquid-vapor

m Mean, Mass

min Minimum

max Maximum

newt Newton

out Outlet

oper Operative

p Plate

pmp Referred to the pumping

q Generic spatial position

row Row

s Generic row, Sector

st Steel

spec Specific

stv Stove

t Turbulent

th Thermal

tot Total

v Vapor

var Generic variable

x Generic individual

∗ Modified

Acronyms

NA Not available

NTU Number of transfer units

PCM Phase Change Material

XXXIII

Chapter 1

Introduction

This chapter deals with the context and motivation of the present work.Specifically, an overview on heat recovery from dryer processes is described,and the main characteristics of the technology adopted are discussed. Then,the goals and the novelties that represent the core of the present thesis aresummarized. Finally, the structure of this work is introduced and the subdi-vision in the diverse chapters is shown.

1.1 Context and Motivation

The increase of the worldwide energy consumption made waste heat recov-ery one of the most interesting strategies for the development of efficientenergy saving systems. The ”Efficient World Strategy”, published by theInternational Energy Agency, shows that the increase of the minimum en-ergy performance standards may be one of the major measures to decreasethe energy consumption in the industrial sector. Specifically, they show thatit would be possible to double the production value per unit of energy in2040 with respect to the current value. Moreover, energy savings up to 70%can be achieved in the light industry if the strategy of the ”Efficient WorldScenario” is put in place [19]. Thus, the study and installation of efficientenergy systems are becoming more and more valuable in the industry sector.

Specifically, industrial dryer systems are very energy-intensive processesbecause of the high latent heat supplied for the evaporation of water [20].An efficient and effective waste heat recovery is necessary to achieve moreand more energy saving technologies in this sector. Many heat recoverytechnologies applied to the dryer industry are present in literature. However,they focus mainly on continuous processes.

Heat exchangers are the most common devices used for heat recovery inthe dryer industry, because of their simplicity and low cost [21]. Generally,

1

Chapter 1

they are of the crossflow plate-type when adopted in the textile industry [15].Jokiniemi et al. [16] perform a theoretical study and an experimental set-upfor a parallel plate heat exchanger applied to a scaled-down batch graindryer. They obtain an 18% recovery and they specify possible improvementsin the design of the recuperator. In their turn, heat pumps ensure higherefficiencies, but are characterized by higher electric energy consumptions, asdescribed by Anderson and Westerlund [21]. Minea [22] studies a wood dry-ing heat pump operating in three different modes: all-electric, hybrid andconventional. The latter configuration is comprised of a natural gas burneras single energy source, while the second one utilizes the burner as back-upthermal source. The reduction of the total energy consumption is between42% and 48%. Krokida and Bisharat [23] make a further step comparinga heat exchanger, a heat pump and their combination. All the configura-tions achieve recoveries up to 40%. Moreover, Anderson and Westerlund [21]compare a heat exchanger, a heat pump and an open absorption system forsawmill dryers. They find out that the latter technology represents a goodcompromise between energy consumptions and energy recoveries. Indeed,the heat demand is reduced by the 67.4% with an increase of the annualelectric consumption of 49.2 GWh. On the contrary, the heat pump systemis characterized by a higher energy demand in the order of 1 TWh, while theheat exchanger achieves very low heat recoveries. It is possible to understandfrom the previous examples that there is not a specific technology that suitsall the possible applications. Hence, it is important to match the technologyadopted with the specific nature of the process that is studied.

Specifically, the present case study deals with a natural gas fired batchdryer for cotton flat fabrics. A fixed-bed regenerator is chosen because itworks inherently in a discontinuous mode. The heat recovery system, shownin Fig.1.1, is made of two stoves with horizontal rod bundles. Among differ-ent types of regenerators, this configuration is chosen to avoid structural andcleaning issues. Indeed, the flow exiting the dryer can cause fouling due tothe presence of cotton residues. Moreover, this architecture ensures the pos-sibility to adopt a modular design and construction. A cycle is characterizedby a downward hot blow and an upward cold blow. The former comes fromthe dryer outlet and transfers energy to the matrix. The latter is ambient airthat is preheated by the matrix and enters the dryer burner. The blows areswitched between the two beds each cycle to make the process continuous.This idea was initially developed by Bernardelli [24], that modeled a regener-ator with steel rod bundles. Later, Seveso [10] introduced the phase changematerial inside the rods and the condensation model of the air flow. Thephysical model developed in the previous thesis is based on mass and energybalances between the fluid and each row of the beds. The heat transfer coef-

2

Introduction

ficient and the pressure drop are calculated by way of correlations based onRe, Pr, Nu and Eu, the Reynolds, Prandtl, Nusselt and Euler dimensionlessnumbers, respectively. More details can be found in the work of Seveso [10].Further improvements in this analysis can be performed, and their detailsare depicted in the following chapters.

1.2 Objectives

This thesis aims to improve the analysis of the Master’s thesis introducedin the previous section. First, a more robust convergence method for thecondensation model and some corrections are implemented in the numericalcode. Secondly, an experimental analysis is performed to measure the realoperating conditions of the regenerator. Then, an optimization is performedto maximize the energy recovered. This analysis is computed for a cascaderegenerator divided in sectors that can be filled with diverse phase changematerials found in the industry. Therefore, a market analysis is performedto find commercial products that suit the case study of the present work.Finally, an optimal configuration of the regenerator for the present case studyis found. Moreover, its performances and economic indexes are compared tothat of a system adopting a plate heat exchanger as heat recovery device.Specifically, the objectives of the present work are as follows:

• A more robust convergence method applied to the model of condensingvapor in air is performed. In the numerical approach, a combinationof the bisection and Newton method is computed.

• An experimental analysis is performed in an industrial laundry in Milanto measure the operating temperatures, air mass flow rate and humidityof the air exiting the dryer studied in the present work.

• An extensive study of phase change materials is developed. Moreover,a market analysis is performed to find the most suitable materials avail-able in the industry.

• A numerical optimization is studied to maximize the energy recoveredduring the cold blow. Specifically, the regenerator is divided in diversesectors filled with diverse phase change materials to exploit in the bestpossible way their latent heat of fusion. Two heuristic methods areimplemented: a local search improved by simulating annealing and agenetic algorithm.

• The best configuration of the regenerator in terms of performance andeconomic aspects is found. Specifically, a parametric analysis as well

3

Chapter 1

Figure 1.1. Scheme of the regenerator comprised of the two stoves with horizontalrod bundles filled with phase change materials, the hot and cold blows, and theswitching mechanism.

4

Introduction

as the optimization tools are used to obtain the most efficient structureof the regenerator for the specific case study of the present thesis.

• The behavior of the regenerator is compared to that of a recuperator.Specifically, a model is implemented in MATLAB to retrieve the energyrecovered and the annual savings of a system in which a chevron plateheat exchanger is adopted.

1.3 Methodology

The practical procedure adopted in the present thesis can be divided in fivemain steps. These steps are dependent one each other by a cause and effectrelation. First, a critical review of the literature and the numerical modeladopted to study the behavior of the regenerator is performed. Simulationsand tests of the code are performed in order to understand all the variablesincluded in the model as well as their effects on the recovery and economicalindexes. This procedure is performed in order to find which are the majorimprovements that should be implemented to go towards a more and more ef-fective system in terms of both energetic and economical aspects. Moreover,improvements in the MATLAB code are performed, e.g. a new convergencemethod for the condensation model is introduced, and the structure of thecode is advanced. Secondly, an experimental analysis is developed to findthe real conditions of the flow exiting the dryer, that represent also the inletconditions of the regenerator. Then, phase change materials available in themarket are investigated. These materials must have a transition temperaturein the range of the inlet temperatures of the regenerator. An optimizationprocess based on heuristic approaches is studied, once the operating con-ditions of the regenerator are obtained and the commercial materials areselected. The regenerator is divided in sectors and the set of materials thatis characterized by the maximum energy recovered is selected. Then, thistools together with a parametric analysis are used to obtain the configura-tion of the regenerator that ensures the highest performances. Finally, theoptimal configuration is compared to that of a chevron plate heat exchangerto evaluate the feasibility of the regenerator studied in this thesis.

1.4 Novelty

The work developed in this thesis starts from two Master’s thesis, as previ-ously explained. First, Bernardelli [24] introduced the adoption of a discon-tinuous system comprised of two stoves operating in an alternating mode.Later, Seveso [10] decided to introduce a model that studies the behavior of

5

Chapter 1

phase change materials as energy storage systems. The latter work considershypothetical initial and boundary operating conditions of the regenerator, aswell as a bed matrix made of one single hypothetical material.

The present thesis aims to improve this work in 5 fields of study: ex-perimental analysis, numerical model, market investigation, determinationof the optimal configuration, and evaluation of the economical feasibility ofthe regenerator. The experimental analysis is performed because only thecharacteristics of the cold blow entering the regenerator are well known, i.e.ambient air conditions. However, the operating conditions of the air at theinlet of the regenerator during the hot blow are unknown, and they needto be measured to use them as input of the numerical analysis. Moreover,two optimization algorithms are implemented to find the set of materialsthat exploits in the best way the energy exchanged in the regenerator. Theinteger programming performed for the optimization includes phase changematerials available in the market as input parameters. Therefore, a marketinvestigation is performed to find commercial products readily available inthe industry. The retrievement of the best configuration of the regenerator isa core aspect in this thesis. Indeed, the whole procedure is explained in de-tail in the last chapters. Finally, it is important to compare the regeneratorwith common heat recovery devices, to evaluate the feasibility of the formerin terms of economic indexes.

1.5 Thesis Structure

This section depicts the structure of the present thesis. The subdivision inthe main chapters is as follows:

• Chapter 2: Bibliography Review. This chapter presents a reviewof the main literature adopted to develop the present work. The relatedthesis, the works regarding the experimental analysis, phase changematerials, drying processes, linear programming and heat exchangersare cited and briefly described.

• Chapter 3: Case Study Measurements. This chapter explainsthe measurements of the dryer exhaust temperature, velocity, massflow rate and absolute humidity. Hence, the real operating inlet condi-tions of the regenerator are obtained. Moreover, the calculation of themeasurement uncertainties is discussed.

• Chapter 4: Phase Change Materials. The fundamentals, proper-ties and classification of phase change materials are shown. Moreover,a market analysis is performed and commercial materials suitable forthe present case study are selected.

6

Introduction

• Chapter 5: Implementation. This chapter deals with the structureof the numerical model implemented in the MATLAB code. The mainfunctions are described, the implementation of the convergence methodfor the condensation model is depicted, and some corrections appliedto the code are reviewed.

• Chapter 6: Optimization. This chapter shows a review of optimiza-tion algorithms and their application to the present case study. Then,the two optimization methods selected are described in detail.

• Chapter 7: Case Study Results. The specifications of the presentcase study are shown. Then, the procedure to optimize the structureof the stoves is explained in detail. Moreover, the parametric analysisand the optimization results are shown. Finally, the behavior of theregenerator for the optimal configuration selected is discussed in detail.

• Chapter 8: Comparison with a Recuperator. This chapter com-pares the performances of the regenerator with that of common heat re-covery devices, e.g. plate heat exchangers. The methodology adopted,as well as the geometry and the numerical model of a chevron plate heatexchanger are explained in detail. Finally, the results of the analysisare discussed.

• Chapter 9: Conclusions. This chapter summarizes the conclusionsachieved with the development of the present work. Specifically, theoutcomes regarding performances and efficacy of the system are shown.

• Chapter 10: Future Work. The last chapter suggests some outlinesfor the development of future works related to this thesis.

7

Chapter 2

Bibliography Review

This chapter deals with the bibliography review of the main sources adoptedfor the investigation performed in the present work. First, the Master’s thesisrelated to this work are described. Then, the critical review related to the ex-perimental analysis, phase change materials, drying processes, optimizationalgorithms, thermophysical properties and heat exchangers is summarized.

2.1 Related Thesis

The present work aims to improve and extend two previous thesis. Theformer is developed by Bernardelli in 2018. The latter is developed by Sevesoin 2019 and it continues the work carried out by Bernardelli. The more recentwork is selected as the starting point of the present thesis.

Bernardelli, 2018Bernardelli studies an innovative system for heat recovery from drying pro-cesses. A fixed-bed regenerator is selected because it is inherently discon-tinuous, and rod bundles made of steel are analyzed. A theoretical analysisregarding the heat transfer models for both the fluid and the bundle matrixis performed. The model is based on mass and energy balances betweenthe rows of the tube bundles and the blows, as well as on empirical corre-lations. Then, a numerical model is implemented in MATLAB to analyzethe behavior of the regenerator. The case studied is limited by unknownoperating conditions of the dryer. Though, the input parameters are basedon a literature analysis of the drying technologies.

Seveso, 2019Seveso extended the work of Bernardelli introducing two main advancements.First, a phase change material is adopted in order to increase the effective-ness of the system in terms of bulk mass and economical aspects. Secondly,

9

Chapter 2

a condensation model based on the film method is introduced. In terms ofnumerical analysis, a lumped parameter approach is performed for the phasechange material rods. Instead, mass and energy balances as well as empiricalcorrelations are adopted for the condensation model. A parametric analysisis performed to find the best configuration of the regenerator matrix. Finally,a preliminary economic analysis is performed to have an insight of the feasi-bility of the system in terms of profitability. Similarly to Bernardelli’s work,the real operating conditions of the regenerator are unknown. Though, datafrom a literature analysis are used to perform the calculations. Moreover,ideal phase change materials are studied and adopted in the models.

2.2 Experimental Analysis

During the experimental analysis, the fundamentals of fluid mechanics inducts are studied to estimate the value of the air mass flow rate from themeasurements of velocity and temperature. Moreover, the calculation ofuncertainties is analyzed.

Incropera, 2006This book is adopted to understand the basics of the development of velocityboundary layers in the case of internal flows. Specifically, the case of fullydeveloped turbulent flow is studied. Moreover, a general idea of the behaviorof the fluid flow in the duct is depicted.

Fang, 2019This recent source provides an extensive review of fluid mechanics. Specifi-cally, the velocity profiles in ducts are of interest for the present thesis. Thesimplified correlation to calculate the mean velocity in the exhaust channelis selected from this work for the case of fully developed turbulent flow.

Doebelin, 2008This masterpiece provides an overview of instruments and methods of mea-sure. Specifically, the calculation of the combined uncertainty for indi-rect measures is of importance for the present thesis. Moreover, a generaloverview of the characteristics of the instruments to measure velocity andtemperature is considered.

2.3 Phase Change Materials

Phase change materials are relatively new energy storing technologies. How-ever, an extensive literature is available, especially for their fundamentals

10

Bibliography Review

and classification. The principles, properties and characteristics of the dif-ferent materials are studied in the present work to choose PCMs suitablefor the specific case study. Moreover, the adoption of cascade phase changeregenerators is discussed.

Fleisher, 2015The work developed by Fleisher deals with an overview of the basics, advan-tages, properties as well as classification of phase change materials. It showsdifferent applications of phase change materials from solar to space systems.A fundamental thermal model based on the Stefan problem is investigatedand it is developed with an advanced phase change material analysis. Thisextensive work is fundamental in the development of this thesis because itoffers a wide overview of phase change materials and, especially, because itoffers a practical outline of possible design issues related to the adoption ofPCMs. Moreover, enhancement techniques of the thermal conductivity aswell as containment issues are described in detail.

Sharma et al., 2007This work provides a concise as well as clear description of phase change ma-terials. Especially their classification and properties are of great importancein the present work. The authors provide information about the advantagesand disadvantages of the different types of materials. These information arefundamental to choose the most suitable materials for the present case study.This work deals also with the adoption of phase change materials in solarand building applications. Moreover, a mathematical review based on the socalled “enthalpy method” is discussed in detail.

Zalba et al., 2003This work deals with a review of the properties and classification of phasechange materials. Long therm stability, heat transfer theory and simulation,as well as applications of PCMs, are also described. This study is importantfor the present thesis because it gives a through idea of the quantitativefeatures of diverse phase change materials. Though, a comparison betweenthe properties of different real PCMs can be performed. Indeed, this thesisaims to find accurate values of the material properties, in order to make afurther step towards the design and construction of the regenerator.

Shamseldin et al., 2017This work introduces phase change materials in the context of the energystoring technologies available in the industry. Their principles, classificationand main properties are depicted extensively. Moreover, the problem of longterm stability is assessed. Specifically, corrosion, thermal cycling and encap-

11

Chapter 2

sulation of phase change materials are discussed. Finally, diverse techniquesof thermal enhancement are shown in detail. Overall, this article outlinesthe main features of phase change materials, underlying their advantages aswell as the issues that may arise while adopting PCMs.

Khor et al., 2018The authors perform a study on cascade phase change regenerators for twodiverse applications: low grade and high grade energy storage. Materialswith diverse transition temperature are selected for the two systems. Amathematical model is described and validated. Moreover, improvements tosolve overcharging of the regenerator are discussed. This work confirms theimportance of selecting PCMs according to their phase change temperature,as it is investigated in the present work.

Yang et al., 2013A multiple-type and a single-type packed bed phase change regenerator forsolar storage applications are compared. The authors underline that theformer ensures higher recoveries. Moreover, an exergy analysis is performed,and the effect on the temperature variations is depicted. Specifically, thesolar collector is made of spherical capsules filled with phase change materialswith sliding transition temperatures. This work represents another evidenceof the efficacy of cascade regenerators. Indeed, a portion of the phase changematerial matrix does not melt in the case of the single-type packed bedregenerator. Moreover, the maximum temperature achieved with the cascaderegenerator results to be much higher than that of the single phase changetype structure.

2.4 Drying Processes

This section describes the literature adopted to understand the major char-acteristics of the drying technologies, their current status, as well as heatrecovery strategies in this industrial sector.

Mujumdar, 2006This work comprises an extensive review of the drying technologies. In partic-ular, the main principles of the drying devices, the different types of dryersused in the industry, as well as the criterion to select them, are depicted.Different applications of the dryers are described in detail. The chapter re-garding the dryer adoption in the textile industry is considered as the mainsource for the present thesis.

12

Bibliography Review

Krokida and Bisharat, 2004Heat exchangers, heat pumps and their combinations are studied by the au-thors for heat recovery purposes in industrial drying applications. The workoutlines the advantages and disadvantages of these technologies, highlightingalso the economical aspects.

Ogulata, 2004The author underlines the importance of heat recovery in the dryer industry,focusing the attention on the textile sector. Specifically, the mathematicalformulation of a system with a heat exchanger adopted as recuperator isdeveloped. It is also explained that these technologies are most suited forconvection-type drying machines.

Anderson and Westerlund, 2014The most commonly used heat recovery technologies in the dryer industry areheat exchangers and heat pumps. However, the authors perform a study onan open absorption system for heat recovery in samwill dryers. This systemturns out to be the best in terms of compromise between energy consumptionand efficiency. Though, this work underlines the importance of matching thetechnology adopted with the specific case study to deal with.

2.5 Optimization algorithms

In this section the books regarding integer programming and heuristic meth-ods are described. These references are adopted to understand the basis ofoptimization programming. Moreover, the different algorithms that can beused to maximize a particular objective function are described and classifieddepending on the problem structure.

Integer Programming, 1998This work deals with the formulation of integer programming and diversealgorithms to solve optimization problems with integer variables. In the classof heuristic methods, local search and simulated annealing are particularlyinteresting for the case study considered. Their formulation is well describedand represents the basis of the implementation performed in this thesis.

Practical genetic algorithms, 1998This work focuses on a particular heuristic method: the genetic algorithm.The introduction to natural optimized methods, as well as the comparisonwith natural selection, gives an idea of the approach on which the geneticalgorithm is based. Moreover, the different techniques and statistical meth-ods adopted are described in detail from the beginning to the end of the

13

Chapter 2

algorithm structure. The description of the pairing, mating and mutationapproaches is particularly interesting for the scope of this thesis.

2.6 Thermophysical properties of the flow

In this section the reference for the calculation of the thermophysical prop-erties of the air blows is described.

Bamoshmoosh, 2019The MATLAB program “ThermoPhysProps” developed by Bamoshmooshis adopted in the present work to calculate the thermodynamic and trans-port properties of both dry and humid air. Bamoshmoosh’s work gives thepossibility to choose different models and methods to perform the numericalanalysis. Moreover, a resolution method was developed in parallel to thepresent thesis to decrease the computational time in the case of dry air. Theadoption of “ThermoPhysProps” is of great importance in the present workbecause it is a reliable and useful tool to calculate the properties of the fluidflows that cross the regenerator.

2.7 Heat Exchangers

A general overview of heat exchanger rating and design is necessary to com-pare the behavior of common devices, such as recuperators, with that ofthe regenerator studied in the present work. Diverse sources are adopted torange from general understanding of heat exchangers to some of their specificapplications, e.g. heat recovery in drying processes.

Rosenhow et al., 1998This masterpiece provides a general overview of heat transfer. The mainchapter of interest for this thesis is that dealing with heat exchangers. Specif-ically, their classification, selection, heat transfer and friction behavior is ex-plained. Moreover, diverse correlations are provided to model both the heattransfer and pressure drop.

Spalding, 1983This handbook of heat exchangers is a fundamental source for this thesis,because it provides a very detailed description of the main type of recu-perators adopted in the market. Their selection, rating and design is welldepicted. Diverse methods to design heat exchangers is provided. Moreover,the characteristic values of their main geometrical parameters are shown.

14

Bibliography Review

Imran et al., 2017This paper is useful for the development of this work, because it deals with avery schematic and concise description of the model adopted to study chevronplate heat exchangers. The ε-NTU method, heat transfer and pressure dropequations are described for the specific case study. Moreover, typical geo-metrical parameters are shown.

Kumar et al., 2018This paper is adopted to understand the effect of the main geometrical pa-rameters of chevron plate heat exchangers on the efficiency and pressuredrop. The trends and results are compared with that developed in this the-sis to validate the recuperator model implemented in MATLAB. Moreover,the typical values of the main geometrical parameters are shown.

Raja et al., 2018This work provides an effective list of the main equations needed to modelchevron plate heat exchangers. The authors underline the importance ofoptimization algorithms to design this type of recuperator, due to the highquantity of variables involved in the problem. The trends obtained duringthe optimization are represented and discussed in detail. Moreover, typicalupper and lower bounds of the main design variables are depicted.

15

Chapter 3

Case Study Measurements

This chapter deals with the experimental analysis of the operating conditionsof the drying process studied in the present thesis. First, the main tempera-ture distributions of the dryer are shown. Secondly, the temperature and ve-locity of the exhausts at the outlet of the dryer are directly measured. Then,the corresponding air mass flow rate is retrieved from the direct measure-ments stated above. Moreover, the value of the exhaust absolute humidityis calculated using data from experience in the laundry. These measures arefundamental to know the operating conditions of the present work and tostudy the regenerator relying on real data. Finally, the uncertainties of themeasurements are discussed.

3.1 Instrumentation and Measurements

This section deals with temperature and velocity direct measurements, as wellas the air mass flow rate and absolute humidity calculation. The procedureand instrumentation adopted as well as the results are described in detail.

3.1.1 Temperature and Velocity MeasurementsInitially, three temperature distributions are retrieved from the dryer controlpanel in the industrial laundry during the whole drying cycle. These valuesare reported each 30 seconds. Fig.3.1 shows the temperature at the inletof the dryer Tdryer,in (◦C), the temperature of the fabric Tfabric (◦C) andthe temperature of the exhausts at the outlet of the dryer Tdryer,out (◦C)as function of the cycle instants. The latter is the one used as input inthe numerical analysis. Indeed, it is the temperature at the inlet of theregenerator and is directly linked to the maximum energy exploitable fromthe dryer exhausts. It is possible to notice that the drying cycle is dividedin three phases: the pre-heating, drying and after-cooling period. Thus, the

17

Chapter 3

Figure 3.1. Temperature of the dryer inlet air, the exhausts from the dryer andthe fabric

exhaust temperature is higher than 120 ◦C only between the minutes 4 and13 of the drying cycle.

The exhaust outlet temperature and velocity are also measured over thecycle period with the impeller and temperature probe of the instrument“Testovent 4000”, provided by Officine Meccaniche DECA S.r.l.. The NiCr-NiAl thermocouple allows to measure the instantaneous temperature. On itsturn, the velocity measurement is performed by means of impeller probes.The flow moves the impeller, whose rotary movement is converted in anelectrical signal. An inductive proximity switch scans the impeller bladesand processes the impulses. The systematic error related to the frictioneffects is corrected electronically. It is possible to compute the instantaneousand mean values over a specific period of time. However, the current valuesof temperature and velocity are selected for this analysis.

In terms of operating mode, the measures are performed in the squaredduct of the dryer exhausts, that are conveyed outside the industrial building.The instrument is placed as far as possible from the dryer exit section toconsider fully developed conditions of the flow, regardless the rather limitedavailable space in the laundry. A hole is made in the duct, and the instrumentis held by an arm and fixed with a magnetic base on a tube close to theexhaust duct, as shown in Fig.3.2. Indeed, the movements of the instrument

18

Case Study Measurements

Figure 3.2. Back view of the instrument

must be avoided to have a flow parallel to the axis of the impeller. Deviationsof the velocity may be measured because the rotation of the impeller isdependent on the direction of the flow. The deviations depend on the typeof probe used, specifically on its diameter. Figg.3.2 and 3.3 show the textbench and the installation of the instruments in the laundry.

It is also fundamental to ensure the durability of the probes. In particular,exceeding the permissible operating temperatures and velocities, as well asthe presence of aggressive mediums and electromagnetic fields, may damagethe probe. Tab.3.1 shows the technical data of the instrument “Testovent4000”. It is important to underline that the values of the uncertainties areselected from instruments of the same brand with characteristics similar tothat used in the present work. This assumption is considered due to lack ofdocumentation of the instrument used.

Once the experimental analysis is performed, the values of temperatureand velocity at the center of the duct are known, as shown in Fig.3.4 and 3.5,respectively. The former depicts the three phases of the drying cycle: pre-heating, drying and after-cooling. On its turn, the latter highlights the de-creasing trend of the velocity profile over the cycle. Indeed, the velocity goesfrom about 5 to 2.5 m/s from the pre-heating to the after-cooling period.While the middle phase is characterized by velocities in the order of 4 m/s.

19

Chapter 3

Figure 3.3. Front view of the instrument

Table 3.1. Technical data of the instrument “Testovent 4000”

Characteristic Value

Velocity range 0.4 · · · 40 m/sVelocity resolution 0.1 m/sVelocity uncertainty ±(0.2 m/s + 1.5% m.v.)Temperature range −30 · · ·+140 ◦CTemperature resolution 0.1 ◦CTemperature uncertainty ±(0.5 ◦C + 0.3% m.v.)Measuring rate 2/secondImpeller probe diameter 25 mm

20

Case Study Measurements

Figure 3.4. Exhaust temperature measurements over the whole drying cycle withuncertainty intervals

Figure 3.5. Exhaust velocity measurements over the whole drying cycle with un-certainty intervals

21

Chapter 3

3.1.2 Air Mass Flow RateThe mass flow rate of the air entering the regenerator is retrieved throughthe direct measures of the exhaust velocity and temperature. Specifically, itis necessary to adopt the mean velocity in the cross section of the duct [5] tocalculate the mass flow rate of the air mair (kg/s) as follows

mair = ρairvmAc (3.1)

where vm (m/s) is the mean velocity, Ac (m2) the cross section area of theduct, and ρair (kg/m3) the air density calculated with the ideal gas law,as function of the measured temperature profile. Assuming incompressibleflow and constant cross section, the velocity is independent on the positionalong the axial direction of the duct x. On its turn, the velocity varies overthe cross section of the duct. Thus, the mean velocity is calculated fromthe velocity profile over the cross section Ac. In the present work, fullydeveloped conditions are assumed. This means that the radial component ofthe velocity and the gradient of the axial velocity component are everywhereequal to zero. This statement can be considered valid if x/Dh>10 [5], whereDh (m) is the hydraulic diameter.

An analytical solution of the velocity profile should be performed solvingthe x-momentum equation. However, many examples are present in litera-ture to simplify the problem using correlations retrieved from experimentalanalysis. In the present work, the duct that conveys the exhausts from theexit of the dryer is characterized by a squared cross section area. Correla-tions for circular ducts are employed as suggested by Rosenhow [2], adoptinga hydraulic diameter as characteristic length as follows

Dh =4ab

a+ b(3.2)

where a (m) and b (m) are the width and height of the duct, respectively.For a squared section, the width and height are equal. Though, the hydraulicdiameter equation is further simplified as Dh = 2a. As suggested by Fang [6],it is convenient to adopt the power law equation to study the velocity profilev(r) (m/s) in the cross section of a circular duct as

v(r)

vc=

(1− 2r

d

)1/n

(3.3)

where r (m) is the radial coordinate, d (m) the duct diameter, vc (m/s) themean velocity at the center of the duct, and n the power law coefficient. Thelatter is a function of the Reynolds number, Rec (-), calculated as functionof vc. Specifically, n can be calculated as follows

n = −1.7 + 1.8 logRec (3.4)

22

Case Study Measurements

Figure 3.6. Examples of the velocity profiles in a circular duct for turbulent flowwith different n coefficients, in the case of fully developed conditions

This correlation is retrieved from experimental analysis and it is valid forRec > 2 · 104. From Eqq.3.3 and 3.4, the calculation of vm is found as

vmvc

=2n2

(n+ 1) (2n+ 1)(3.5)

As the Reynolds number increases, turbulence increases and the velocity pro-file tends to be flatter. Fig.3.6 shows examples of the velocity profiles v(r)/vcin a circular duct for turbulent flow characterized by diverse n coefficients,in the case of fully developed conditions.

Though, the value of vm is calculated from the measurements of vc, oncethe value of the n coefficient is computed. Then, the mass flow rate ofthe exhausts is calculated as in Eq.3.1, and the profile of mair over time isobtained, as shown in Fig.3.7.

3.1.3 Air Absolute Humidity PredictionThe absolute humidity of the air at the inlet of the regenerator is a keyparameter when dealing with the model that considers the condensation ofvapor. The mass of water contained in the cotton fabric is known to be 0.4times that of the dry fabric itself. Moreover, the load mfabric (kg) of thedryer is known from experience in the laundry, and it is equal to 80 kg. Inthis preliminary approach, the exhaust humidity is assumed to be constantover the whole drying cycle. Though, the mass flow rate of the evaporated

23

Chapter 3

Figure 3.7. Exhaust mass flow rate profile over the whole drying cycle with un-certainty intervals

water mevap (kg/s) is calculated as follows

mevap =0.4mfabric

∆tcycle(3.6)

where ∆tcycle (s) is the cycle duration. Finally, the absolute humidity isevaluated with a preliminary approach dividing the mass flow rate of thewater evaporated from the fabric by the mean mass flow rate of the airpreviously calculated in Eq.3.1. The value of this parameter turns out to beabout 0.04 kgwater/kgdry,air.

3.2 Measurement Uncertainties

This section deals with the calculation of the uncertainty of the measure-ments of velocity, temperature and mass flow rate. The first two parame-ters are retrieved from direct measurements performed with the instrument“Testovent 4000”. Though, their uncertainties are that found in the instru-ment technical specifications provided by the manufacturers, as in Tab.3.1.It is possible to notice from Fig.3.4 and Fig.3.5, that the value of uncertaintyof the velocity is much higher than that of the temperature. This is mainlydue to the low values of velocity of the exhausts. On its turn, the latter is

24

Case Study Measurements

measured indirectly by the simple model described in Eq.3.1. The densityis calculated with the ideal gas law. Though, the mass flow rate equationbecomes

mair =PairRgTair

vmAc (3.7)

where Rg (J/(kg K)) is the specific gas constant. It is straightforward thatthe mass flow rate is a function of the velocity and the temperature measured.Though, the calculation of the combined uncertainty is necessary.

In general, the combined uncertainty Uf of a function f(x1, . . . , xpar)depends on the uncertainties of the xi variables involved in the model. Itsvalue is calculated as shown by Doeblin [25] as follows

Uf =

√√√√npar∑i=1

(∂f(xi)

∂xiUxi

)2

(3.8)

where npar is the number of parameters x.Considering v and T as the only source of uncertainty, Eq.3.8 becomes

Um =

√(PairAcRgTair

Uvm

)2

+

(−PairvmAc

RgT 2air

UTair

)2

(3.9)

Multiplying and dividing the first term on the right by vm and rearrangingthe equation, Eq.3.9 becomes

Um =

√(PairvmAcRgTair

Uvmvm

)2

+

(−PairvmAc

RgTair

UTairTair

)2

(3.10)

Explicating the definition of the mass flow rate and dividing by mair, therelative uncertainty Um/mair (-) is obtained as follows

Ummair

=

√(Uvmvm

)2

+

(UTairTair

)2

(3.11)

Eq.3.11 shows that the relative uncertainty of the mass flow rate can be easilycalculated from the relative uncertainty of the velocity and temperature.Adopting this procedure, the mean relative uncertainty of the mass flow rateturns out to be of the 7%. Indeed, it is possible to notice in Fig.3.7 thatalso the absolute uncertainty interval is rather high. This is mainly dueto the high uncertainty of the velocity, that is characterized by rather lowabsolute values of measurement, as shown in Fig.3.5. However, the result isacceptable for the present case study, because an indicative value of the massflow rate is needed. Indeed, each cycle is characterized by different operatingconditions, depending on the type of cotton fabrics that are dried. Though,a more precise result is not necessary for this work.

25

Chapter 4

Phase Change Materials

This chapter depicts the main characteristics of phase change materials.First, their fundamentals are shown. Specifically, the reason why PCMs areconsidered interesting energy storage technologies is explained. Secondly,their main properties are analyzed and described in detail. Then, a conve-nient classification for phase change materials is proposed. Finally, a marketanalysis is performed to select materials available in the industry.

4.1 Energy Storage Technologies

Different storage technologies are available and well known in the industry,i.e. electrical, chemical, mechanical and thermal storage. The latter canbe further classified in sensible energy storage and latent energy storage,as explained by Shamseldin et al. [7]. In the latter category, phase changematerials are considered promising materials for energy storage applications.Indeed, the latent heat is exploited when the material undergoes a phasechange transition, leading to stored energies per unit volume in the order of5 -15 times than that of sensible only storage materials [8]. Moreover, theheat exchange with sources at constant temperature is efficient during thephase transition, and they can store a relatively high amount of energy evenwhen the temperature difference with the heat source is small [7].

Phase change materials are characterized by both sensible and latent heattransfer. Considering the melting process, sensible only heat transfer occursfrom the initial temperature Ti (K) to the transition temperature Tfus (K),and continues from the end of the phase transition to the final temperatureTf (K). Thus, the energy exchanged E (J) in case of solid-liquid transition,considering constant specific heat capacity c (J/(kg K)), is modeled as

E =

∫ Tfus

Ti

mcdT +mf∆hfus +

∫ Tf

Tfus

mcdT (4.1)

27

Chapter 4

where m (kg) is the mass of the phase change material, ∆hfus (J/kg) thespecific latent heat of fusion and f (-) the melted fraction.

4.2 Properties

Phase change materials are available in a very wide range of transition tem-peratures. Hence, they can suit a large number of different sectors in theindustry, from low to high temperature applications. However, many prop-erties must be considered when designing a system with phase change materi-als. Sharma et al. [8] clearly define and classify these characteristics. Amongthermal properties, a proper phase change temperature is fundamental tomatch the material and the process in which it is utilized. At the same time,a high latent heat of fusion and a high thermal conductivity are preferred toensure high heat stored and heat transfer coefficient.

Phase equilibrium, density, volume change and vapor pressure are themain physical properties to be considered. The former helps maintainingstability during the transition phase; a high density decreases the volume ofbulk phase change material required; low volume change and vapor pressurelimit sealing problems in the structure of the heat storage system. Anothervery important feature to consider is the kinetic behavior of the differentmaterials. Indeed, problems of supercooling and incongruent melting canoccur. The former occurs when the phase transition is detected at a tem-perature that is lower than the nominal transition temperature [26]. Thisbehavior is due to low nucleation rate and difficulties in the crystallizationof the solid phase. The latter occurs in phase change materials such as salts.Specifically, it is due to the incomplete solubility of hydrates in their waterat melting conditions. The compatibility with other materials and the reli-ability of PCMs is related mainly to the chemical properties. Among themchemical stability, non-toxicity, non-flammability and non-corrosiveness arethe major properties to be considered.

Finally, it is necessary to take into account the economic aspects. Hence,widely available, abundant and cost effective phase change materials shouldbe chosen to design an economically feasible system.

4.3 Classification

A first classification divides phase change materials in solid-solid, solid-liquidand liquid-gas PCMs [7]. Tabrizi and Sandrameli [9] state that especiallysolid-liquid phase change materials are suitable for regenerators because oftheir low specific volume change. Among this category, Sharma et al. [8] give

28

Phase Change Materials

PhaseChangeMaterials

Organic

Eutectic

Inorganic

Paraffin

Non-paraffin

Salt-hydrate

Inorganic-organic

Metal

Inorganic

Organic

Figure 4.1. Classification of phase change materials

an effective classification of phase change materials, that are divided intoorganic, inorganic and eutectic, as in Fig.4.1.

Paraffins and non-paraffins are organic materials. The formers are chainsof n-alkanes, with a latent heat that increases while increasing the chainlength. They do not lead to kinetic issues, they are predictable, reliable,non-corrosive, stable and with low volume change. On the other hand, theirconductivity is rather low and they may be flammable at rather low temper-ature conditions. Esters, glycols, fatty acids and alcohols are non-paraffins.They are available in a large variety of properties. However, they are 2 -2.5times more costly than paraffins. Inorganics are classified in salt hydrates andmetallics. The formers are advantageous for their high latent heat of fusion,high thermal conductivity and small volume change. On the other hand, theyare not suitable for all the applications because of corrosion, supercooling andmelting problems. Especially, incongruent melting is a characteristic of salthydrates. Indeed, salts settle down once solidified and their recombinationwith water is no more possible during liquefaction. Available techniques toovercome this problem are mechanical stirring, encapsulation, addition ofthickening agents, utilization of excess water for preventing supersaturation,and modification of the hydrates chemical composition. Metallics may bepreferred substantially for their high thermal conductivity, but they are lessadopted as phase change materials due to their weight and cost. The lastclass of PCMs are the eutectics. They are minimum-melting combinationsof more components that work in a wide range of properties. However, onlyfew data are available in literature for this category.

Finally, the less effective properties of phase change materials should be

29

Chapter 4

improved by way of thermal enhancement techniques. Diverse options forheat conductivity enhancement are studied by Qureshi et al. [14]. Generally,the most effective strategies are inclusion of metallic fins and graphite foams.This latter technology can lead to heat conductivity enhancement ratios upto 45. Fleischer [27] performes a detailed description of both macro-scale andnano-scale carbon inclusions. Moreover, the author describes many applica-tions of thermal enhancement techniques for different case studies.

4.4 Market Analysis

This section introduces the industrial materials found in the market. First,the methodology used to choose the phase change materials is shown. Sec-ondly, the selected industrial materials are described. These commercialproducts will be used in the MATLAB implementation, as well as in theoptimization process.

4.4.1 MethodologyThe research focuses on organic materials, i.e. waxes, because of their low ornull corrosiveness, their easy handling and low cost. The transition tempera-tures are chosen according to the operating temperatures of the regenerator,thus materials with point of fusion between 40 ◦C and 133 ◦C are selected.The materials need to be non-corrosive, non-toxic, non-hazardous and witha flash temperature such that no problems of ignition could occur in theregenerator for all the operating conditions of the present case study. Theoperative maximum temperature of the cylinders is considered to be roughly133 ◦C, that is a conservative value of the maximum temperature of the hotflow at the inlet of the regenerator. Another important factor that mustbe considered is the ease in purchasing and getting ready for use the phasechange materials. Indeed, they must be readily available for the design andconstruction of a real prototype. Thus, European companies are preferredrather than American or Asian ones.

4.4.2 Selected ProductsNowadays many companies sell phase change materials, but most of themprovide low transition temperature materials, not suitable for the applica-tion studied in this thesis. Four companies meet the criteria described in theprevious section: PCM Products Ltd situated in the United Kingdom [3], Ru-bitherm GmbH in Germany [4], PureTemp LLC in the US [28] and Ichembuyin China [29]. The first and the second companies are European and, hence,they are preferred and prioritized according to the reasons previously dis-cussed. The main properties of the materials are listed in Tabb.4.1 and 4.2

30

Phase Change Materials

for the two companies selected: PCM Products Ltd and Rubitherm GmbH,respectively. The available material characteristics are not the same for allthe companies because of different data available on the net. Nevertheless,the most important properties are provided by each firm.

It is important to pay attention on the maximum operating tempera-ture of the phase change material. In particular, the flash temperature isfundamental when dealing with paraffins, as explained by Fleisher [27] in adetailed study of phase change material applications. In Tab.4.2, it is visiblethat Rubitherm GmbH’s technologies are characterized by maximum oper-ating temperatures Toper (K) lower than that reached in the case study ofthis thesis. Thus, the most suitable supplier is PCM Products Ltd, whoseproducts are characterized by flash temperatures Tflash (K) far above the op-erating conditions of the present case study. In Tabb.4.1 and 4.2 the acronym“NA” stands for not available. Specifically, it is used for the unknown con-ductivity λ (W/(m K)), whose value is assumed to be similar to that of theother paraffins.

31

Chapter 4

Table 4.1. Values of the material properties of PCM Products Ltd’s products [3]

Material Tfus hfus λ cp ρ Tflash(K) (kJ/kg) (W/(m K)) (kJ/(kg K)) (kg/m3) (◦C)

A42 315 140 0.21 2.22 905 250A43 316 280 0.18 2.37 780 250A46 319 155 0.22 2.22 910 250A48 321 230 0.18 2.85 810 250A50 323 190 0.18 2.15 810 250A52 325 220 0.18 2.15 810 250A53 326 155 0.22 2.22 910 250A58 331 215 0.22 2.22 910 250

A58H 331 240 0.18 2.85 820 200A62 335 205 0.22 2.2 910 250A70 343 225 0.23 2.2 890 250A82 355 170 0.22 2.21 850 250A95 368 260 0.22 2.2 900 300A118 391 285 NA 2.7 1450 200A133 406 125 0.23 2.2 880 250

Table 4.2. Values of the material properties of Rubitherm GmbH’s products [4]

Material Tfus hfus λ cp ρ Toper(K) (kJ/kg) (W/(m K)) (kJ/(kg K)) (kg/m3) (◦C)

RT64 HC 337 250 0.2 2 880 95RT65 338 150 0.2 2 880 85

RT69 HC 342 230 0.2 2 940 100RT70 HC 343 260 0.2 2 880 100

RT82 355 170 0.2 2 880 100RT80 HC 353 220 0.14 2 900 NART90 HC 363 170 NA 2 950 120

RT100 373 124 0.2 2 880 120RT100 HC 373 180 0.2 2 1000 130

32

Chapter 5

Implementation

The physical and numerical models adopted in this thesis are implementedin a MATLAB code to obtain the main parameters of the heat recoverysystem. In this chapter, the introduction of a new convergence method isdepicted, and the main functions called in the MATLAB script are described.Flowcharts are shown to better understand the evolution of the most impor-tant functions. Moreover, some corrections applied to the code are discussed.

5.1 New Convergence Method

A model for the humid air can be selected to consider condensation of va-por in non-condensable gases. This section briefly describes this model andintroduces a new method for convergence to obtain the desired solution.

5.1.1 Film MethodIn the case of condensation, it is not straightforward to calculate the heattransfer coefficient. Specifically, the model adopted is based on the filmmethod, that computes an energy balance between the cylinders and the flowseparated by a boundary layer interface. Seveso [10] describes extensively thismodel in his Master’s thesis and explains the main equations in detail. Thefinal energy balance obtained is as follows

m′′

vhlv + α∗s (Tb − Ti) = αc (Ti − Tcln) (5.1)

where m′′v (kg/(s m2)) is the mass flux of condensate, α∗s (W/(m2 K)) the

sensible heat transfer coefficient modified by the Ackermann’s coefficient,αc (W/(m2 K)) the heat transfer coefficient, and Tb (K) and Ti (K) the bulkand interface temperatures, respectively. The left side of Eq.5.1 representsthe heat flux between the interface and the bulk flow Q

′′

flw (W/m2), and itis comprised of both sensible and latent heat transfer contributes. While the

33

Chapter 5

right side of Eq.5.1 represents the heat flux between the cylinders and theinterface Q

′′

cln (W/m2).The calculation of the contribution of the heat fluxes in Eq.5.1 is straight-

forward once the interface temperature is found. Then, it is possible to com-pute both the total and sensible only heat transfer coefficients, αtot (W/(m2 K))and αs (W/(m2 K)), in the case of condensing vapor as follows

αtot =Q′′

flw

(Tflw − Tcln)(5.2)

αs =Q′′

flw − m′′vhlv

(Tflw − Tcln)(5.3)

It is possible to notice that the sensible heat transfer coefficient is calculatedas the latent one, but decreasing the heat exchanged by the contribution ofthe latent heat of the condensing vapor. These two parameters are used tocalculate the temperature change of the cylinders and that of the flow, as wellas the energy exchanged row by row over each time-step of the drying cycle.The equations involved to calculate these parameters are briefly explained atthe end of this chapter.

5.1.2 Convergence MethodThe interface temperature is unknown, thus an iterative method is performedto solve the energy balance in Eq.5.1 and find the heat transfer coefficient.In this thesis, a more robust method is implemented to reach convergence.First, a bisection approach is adopted till a tolerance εbis (-) in the order of10−2 is reached. Once a more precise solution is found, the Newton method isperformed to make the computation faster, till a tolerance εnewt (-) of about10−4 is reached. The error err (-) considered for the convergence is calculatedas follows

err =Q′′

flw − Q′′

cln

Q′′flw

(5.4)

In the bisection method, two initial guesses of Ti must be selected andtheir error is calculated as in Eq.5.4. Their value must be in accordance tothe physical constraints of the cylinder and the flow temperatures Tcln (K)and Tflw (K), respectively. Indeed, the interface temperature must be inbetween these temperatures for physical consistency. The two initial guesstemperatures Tmin (K) and Tmax (K) are set as follows{

Tmin = 1.05 Tcln (5.5)

Tmax = 1.05 Ti (5.6)

where the interface temperature is initially set as Ti=0.995Tdew. If the errorsare concordant, the bisection method can’t be performed. Hence, the left and

34

Implementation

right guess of Ti are adjusted to obtain errors with different signs. When thenew Tmin and Tmax are selected, Ti is calculated as follows

Ti =Tmin + Tmax

2(5.7)

Then, the error is computed as in Eq.5.4 as function of the new interfacetemperature calculated in Eq.5.7. Moreover, Tmin or Tmax are updated toset the starting guesses of the next iteration. This process is performed todecrease the distance to the solution for the following iteration. The bisec-tion method continues until the error calculated as function of the interfacetemperature is lower than the set tolerance εbis.

The interface temperature obtained in the bisection method is used asinitial guess of the Newton method. This method is based on the followingequation to calculate the interface temperature at the iteration step n+ 1

Ti,n+1 = Ti,n −err(Ti,n)

d err(Ti,n)(5.8)

where err (-) is calculated as in Eq.5.4, n is the number of the iteration,while the derivative of the error d err is calculated numerically as follows

d err(Ti,n) =err(Ti,forward)− err(Ti,backward)

2(Ti,forward − Ti,backward)(5.9)

where Ti,forward = Ti + ∆T , Ti,backward = Ti − ∆T and ∆T = 10−5Ti. Theiteration stops and the solution of Ti is obtained when the error err(Ti,n+1)is lower then the tolerance εnewt. The iterative procedure described in thissection is shown in the flow diagram of Fig.5.1.

5.2 High Level Function New Structure

The code consists in a main script “CALL generic.m” comprised of threefunctions named “regenerator input.m”, “regenerator ss.m” and “regenera-tor output.m”. In “CALL generic.m” the user sets the main geometrical pa-rameters of the stove, the inlet and boundary conditions, the models of theflow and of the cylinders, and the discretization grid. The geometrical pa-rameters required are the width Wdt (m) and the depth Dpt (m) of the stove,the height of the stoves, and the dimensionless vertical pitch b (-). Eitheraligned or staggered configuration can be studied. The boundary conditionsare the conditions of the flow entering the stoves and of the cylinders, i.e.temperature distributions, pressure, composition and mass flow rate of thefeeds. The user can choose to perform an analysis with either dry air orhumid air models, and the cylinders can be modeled both for steel and phase

35

Chapter 5

Retriveuserinput fromrow_stove.m

Ti,minandTi,maxcalculation

START

err(Ti,min)anderr(Ti,max)calculation

err(Ti,min)*err(Ti,max)<0?

YES

NO

Ticalculation

err(Ti)calculation

err(Ti)<tolerancebis?NO

UpdateTi,minandTi,max

Ti,forwardandTi,backwardcalculation

err(Ti,forward)anderr(Ti,backward)calculation

Ticalculation

err(Ti)<tolerancenewt?NO

YES

UpdateTi,minandTi,max

STOP

YES

Figure 5.1. Flowchart of the convergence method for the iterative solution of Ti

36

Implementation

change materials. In the first case a conduction only approach is studied,in the second case a lumped parameter approach is performed. Moreover, aproper discretization scheme for the time-steps must be set in order to obtainresults with suitable precision. Specifically, time-steps in the order of 0.1 sensure accuracy in the energy balances calculated.

The function “regenerator input.m” retrieves inputs from the user andelaborates them to make them ready to be used in the main function ofthe code. Some geometrical parameters are calculated, e.g. the number ofrows Ns, the frontal area, the dimensionless pitches and the external surfaceof the cylinders. Moreover, a check on the user geometrical inputs is per-formed to control the structural feasibility of the stove configuration. Thefunction “regenerator input.m” retrieves also the cylinder properties from alibrary of materials. Specifically, PCM Product’s phase change materialsare chosen for the present case study, as described in the previous chapter.Moreover, the disposition of these materials along the regenerator is set.

The function “regenerator ss.m” is the main engine of the code. Theanalysis is cyclic and the implementation of a dryer cycle is performed tilla steady-state condition is reached in the stoves. Indeed, in the first cycleafter the shut-down of the process the stoves are at ambient temperature andno energy is recovered by the first cold blow. The function “regenerator.m”works with a parallel approach for the two stoves in order to half the com-putational time. The child functions to perform the core of the computationare called inside “regenerator.m” and they are described in the following sec-tion. Once the steady-state condition is reached, the regenerator recovery,temperature distributions and other main parameters are calculated.

Finally, “regenerator output.m” displays the results and the plots use-ful for the quantitative analysis of the whole process. The main programdescribed above is summarized in the flowchart in Fig.5.2.

5.3 Low Level Function Improvements

The function “stove.m” retrieves the initial and inlet conditions of the stovefrom “regenerator.m” and performs a progressive analysis through the time-steps Nt and the rows Ns. The function “row stove” is called for each time-step and for each row. Its results are retrieved and used to update the inletand initial conditions for the next row and the next time-step, respectively.The pressure drop is calculated for each time-step. On the other hand,the heat transfer coefficient is performed row-by-row by specific correlations.When the results implemented in “row stove” are calculated, the error in theenergy balance is checked. Specifically, the program compares the energiestransferred by the rows and the cylinders, that are calculated separately and

37

Chapter 5

Retriveuserinput frommainscript 

Retriveresultsfromparallelcomputing

Parallelcomputing

HOTBLOWstove.mfunction

COLDBLOWstove.mfunction

Prepareinputsforthefunctionregenerator_ss.m

Updateinitialcondition fornextcycle

relativeerror<tolerance

Displayresults

STOP

START

YES

NO

Figure 5.2. Flowchart of the high level functions of the program

38

Implementation

can differ less than a certain tolerance. The flowchart in Fig.5.3 depicts themain structure of “stove.m”.

The function “row stove”, represented in Fig.5.4, is the real core of thecomputational analysis. The properties of the flow and the heat transfercoefficient are calculated with the chosen model. The functions for the cal-culation of the temperature distribution in the cylinders are called dependingon the material and the model adopted.

Specifically, the function “cylinder lumped” calculates the evolution ofthe temperature of the cylinders with a 0D approach. Thus, the temperatureloses its spatial discretization along the radius of the cylinder. This model isvalid only for Biot numbers Bi (-) lower than 0.1. However, this constraintis not fulfilled for the present case study, because of the low conductivityof paraffins. Thus, a correction is applied to decrease the value of the heattransfer coefficient, obtaining αnew (W/(m2 K)) as follows

αnew =

(1

α+Rc

)−1

(5.10)

where α (W/(m2 K)) is the heat transfer coefficient before performing thecorrection, and Rc ((m2 K)/W) a characteristic resistance of the cylinders.

Eq.5.10 is applied for both αtot and αs, calculated through the film methodpreviously described. In this way, both the outlet conditions of the flow andthe energy exchanged by the rows are calculated by way of energy balances,considering the correction of the lumped parameter approach. These equa-tions are performed for each row and each time-step. Hence, the energyexchanged Eflw (J) during the time-step Dt (s) is calculated performing anenergy balance between the inlet and outlet of the row “s” as follows

Eflw = αtot,newSclnDt (Tcln − Tflw,in) (5.11)

where Scln (m2) is the total external surface of the cylinders in the row“s”, and the subscript “in” stands for the inlet of the row. On its turn, thetemperature at the outlet of the row “s” Tflw,out (K) is calculated consideringthe sensible heat transfer coefficient as follows

Tflw,out = Tflw,in +αs,newScln(Tcln − Tflw,in)

maircp(5.12)

39

Chapter 5

Displayerror

Retriveuserinput fromregenerator.m

Updateparametersfornextrow

nt<Nt

Pressuredropfunction

Initializeparameters

error<tolerance

STOP

START

ns<Ns

row_stove.mfunction

Updateparametersfornexttime-step

Energyandtotalpressuredropcalculation

YES

NO

NO

NO

YES

YES

Figure 5.3. Flowchart of the “stove.m” function

40

Implementation

Retriveuserinput fromstove.m

Heattransfercoefficientcalculation

Flowmodel

PERFECTGASThermoPhysProp.m

IDEALMIXThermoPhysProp.m

START

Sensibleheattransferfunction

Condensationheattransferfunction

Condensationconditionreached?

YES

NO

Cylindermodel

LUMPEDAPPROACH

cylinder_lumped.mCONDUCTIONcylinder_solid.m

Retriveresultsfromcylindermodelfunctions

Computecondition fornextrow

error<tolerance Displayerror

STOP

Energybalancecalculation

NO

YES

Figure 5.4. Flowchart of the “row stove.m” function

41

Chapter 6

Optimization

Chapter 4 shows that thermophysical, chemical, kinetic and economic as-pects must be considered when selecting a phase change material. However,it is rather difficult to meet all the criteria previously explained to choosethe most suitable material, because a very high number of properties shouldbe taken into account, e.g. transition temperature, latent heat, conductivity,density and many others. Moreover, also the heat transfer characteristicsof the specific application must be considered [30], e.g. temperature distri-butions along the regenerator and properties of the heat transfer fluid. Inaddition, the storage capacity and design of the system itself have effects onthe selection criterion of the energy storage materials [31].

It is possible to notice that many features must be considered to maximizethe heat transfer efficiency. Thus, a numerical approach based on linearprogramming should be performed. The next sections aim to explain thistype of optimization problems. First, a review of optimization problems isdepicted. Secondly, this chapter shows the methodology adopted and thereasons why heuristic algorithms are selected. Finally, a detailed descriptionof the local search algorithm as well as the genetic model is provided.

6.1 Optimization Problem Review

An optimization problem can be formulated as the research of a variable xof a set X ⊆ <n that minimizes a function f : Y → Z ⊆ <n [11]. Optimiza-tion is different from root finding in a mathematical point of view, becauseit aims to find the zeros of a function derivative rather than the zeros ofthe function itself. Finding the derivative of a function is not always aneasy task and problems of local minimum selection may occur [13]. Thereare different types of optimization categories. In the present section, few ofthem are cited. First, we can distinguish linear and non-linear programming,

43

Chapter 6

that are characterized by linear and non-linear functions of the unknowns,respectively [32]. Secondly, constrained and unconstrained as well as contin-uous and integer problems may be distinguished. The latter class is difficultto deal with, thus these problems are usually linearized when it is feasible.Then, there is another class of algorithms that start from an initial guessof parameters and move towards an optimal solution through probabilisticcalculations [13]. This latter class of optimization may give problems of localminimum, but it is usually characterized by lower computational time.

Focusing the attention on integer programming, different analytical opti-mization methods can be adopted. However, most of the practical problemsare too difficult to be solved with these methods, hence heuristic or approx-imated algorithms can be a useful tool to simplify the problem. Heuristicmethods are usually adopted when the function to be optimized is too com-plicated, a rapid approach is desirable and the problem is physically knownby inspection or experience. Among this latter category, natural optimiza-tion methods are widely used. As implied by the name, they are based onthe concept of natural selection: if we set the survivability of a populationas the objective function, the organisms of the natural world will be theparameters on which the function depends, the environment as well as theinteraction between species will be part of the constraints, and the evolutionprocess will be the algorithm that governs the objective function behavior.The combination of genes will produce new individuals that may lead to anincrease or a decrease of the value of survivability. If the new individuals leadto a strong decrease of the objective function, they may not survive to matein the next combination of population. After a certain time, the populationshould be more or less adapted to the natural world [13].

6.2 Methodology

From the structural point of view, the regenerator is divided in a number ofsector nsector between 1 and 10. An example of this structure is schematizedin Fig.6.1, where 4 sectors of the regenerator are filled with diverse materials.Few case studies dealing with cascade phase change material regeneratorsare present in literature. Khor et al. [33] recently studied a packed bedregenerator for cold energy storage. They divided the system in 3 sectors,obtaining an increase in the energy recovery of more than the 10%. A similarsubdivision of the regenerator is studied by Yang et al. [34] as well as byMichels and Pitz-Pall [35] for solar collector applications. Also in these cases,energy recovery improvements are obtained. In the present case study alsoa higher number of sectors is studied because the regenerator is much longerthan the ones available in literature. On the other hand, nsector doesn’t exceed

44

Optimization

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

22 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

33 3 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

44 4 4 4 4

4 4 4 4 4

4 4 4 4 4

4 4 4 4 4

Sector1

Sector4

Sector3

Sector2

HotBlow

ColdBlow

Figure 6.1. Scheme of the bed matrix divided in 4 sectors

10, because it is unpractical to design a system with too many phase changematerials. Indeed, the manufacturing of the regenerator may be characterizedby higher possibility to make mistakes during the assembling, as well as byincreased cost due to the presence of many different materials. Moreover,the higher nsector the better is the optimization, but, at the same time, thehigher is the computational complexity.

The materials that can fill the sectors are the parameters that are ana-lyzed and interchanged in the present optimization problem. They are cho-sen among the 14 materials selected and described in Chapter 4. Then, itis straightforward that these parameters are intrinsically integers. It is alsopossible that the same material is used in different sectors. Indeed, thereare few material properties other than the transition temperature that canaffect the value of the energy recovered, e.g. the thermal conductivity andthe latent heat of fusion. Thus, if a material is particularly performing interms of heat transfer, it is probable that it is chosen rather than anotherone, even if the transition temperature of the latter would be optimal for theconditions of the flow on equal conductivity and latent heat.

45

Chapter 6

From the process point of view, the temperature at the inlet of the re-generator during the hot blow is not constant in the present case study, asdepicted in Chapter 3. Moreover, the decreasing flow temperature of the hotblow and the increasing flow temperature of the cold blow along the regen-erator make less effective the energy exchange in the last rows. Hence, it isdesirable to adopt paraffins with different transition temperatures in differentrows to better exploit the latent heat during the phase change. Specifically,phase change materials with decreasing transition temperature should be po-sitioned from the inlet to the outlet of the stove during the hot blow, andviceversa for the cold blow, i.e. the phase change temperature is decreasingfrom material 1 to 4 in Fig.6.1. This method is adopted in order to exploitin the best possible way the latent heat during the phase change and to in-crease the saturation of each stove. Indeed, imagining to deal with one singlephase change material during the hot blow, if the transition temperature istoo high, only the first rows will undergo the transition phase, because thenext ones will be characterized by a lower cylinder temperature.

From the numerical point of view, the objective function that must bemaximized is the energy recovered during the cold blow. Its calculation is per-formed progressively over the whole regenerator for each time-step, throughthe implementation of diverse correlations and energy balances. Hence, theobjective function of the present case study is intrinsically non-linear. Onthe contrary, in another solar application studied by Yang et al. [36], therecovery efficiency is maximized by calculating its derivative with respect tothe transition temperatures of the phase change materials, and performingan iterative procedure. In that case, an explicit function of the efficiency isavailable, thus an analytical solution can be found.

The main features of the present case study are summarized as follows:

• The number of phase change materials with transition temperature be-tween 40 and 133 ◦C is 14. Hence, performing a parametric analysisthat calculates the objective function for each combination of materialsand sectors is too costly in terms of computational time. An optimiza-tion tool is desirable, especially for a relatively high number of sectors.

• The parameters that should maximize the objective functions are inte-ger and the problem is non-linear. Thus, the solution of the optimiza-tion can’t be easily obtained by way of analytical methods.

• The physics behind the process is well known by inspection of theoperating conditions of the process. Hence, the utilization of heuristicmodels is suggested.

These characteristics of the problem make heuristic methods the mostsuitable models for the present case study. Specifically, local research and

46

Optimization

genetic algorithm are implemented. These models start from an initial setof parameters and search new points applying operators and statistical tech-niques. An intelligent search is performed without making derivatives andit is applied to discrete and non-continuous objective functions [13]. At thesame time, these methods are stochastic and do not ensure to find the bestsolution as for the analytical integer programming algorithms. However, theyare considered advisable methods for problems similar to that of this thesis.These algorithms will be described in detail in the next sections.

6.3 Local Search and Simulated Annealing

In a local research heuristic approach, an initial solution S is chosen andneighbor solutions S ′ are created. The objective function f to be maximizedis calculated for each neighbor. Then, the set of parameters that gives themaximum value of f(S ′) is selected as initial solution for the next itera-tion [12]. The neighbor creation mechanism can be chosen depending on thespecific problem structure. In the present case study, each iteration of themodel corresponds to the change of the material of one single sector, start-ing from the top to the bottom of the regenerator. Once the last sector isreached, the process starts again from the first sector on the top. In this way,sector by sector the materials selected are adjusted to fit in the best possibleway the heat exchange. Moreover, the solution of the optimization is refinedgoing over again the whole regenerator.

The upper limit for a sector “s” is chosen to be the material with a tran-sition temperature immediately higher than that of the sector “s -1”. Thelower limit for a sector “s” is chosen to be the material with a transitiontemperature immediately lower than that of the sector “s +1”. In this way,a wide range of physically reasonable neighbors is selected to form a popula-tion. Fig.6.2 shows an example of the formation of the population for sector4, in which the materials with decreasing transition temperature are labeledwith the numbers from 1 to 14, respectively. In the initial set of materials,sectors 3,4 and 5 are filled with PCMs number 5,6 and 7, respectively. Thepopulation is comprised of diverse neighbors in which only the material insector 4 changes. Specifically, this sector is filled with phase change mate-rials from “5 -1” to “7+1”. The implementation stops when convergence isreached, i.e. when the relative difference between the energy calculated inthe current and in the previous iteration is lower than a tolerance εconv (-) of10−3. However, also a simple time limit could be set as stopping criterion [37].The model described above is shown in the flowchart of Fig.6.3.

If the best fitting solution of the iteration “i +1” is the same as thatof iteration “i”, the algorithm stops according to the flowchart in Fig.6.3.

47

Chapter 6

1 3 5 6 7 10 12

1 3 5 4 8 10 12

1 3 5 5 8 10 12

1 3 5 8 8 10 12

1 3 5 7 8 10 12

1 3 5 6 8 10 12

Sector4

Sector4

InitialSet

Population

Figure 6.2. Example of the formation of a population in the sector 4 of the stove

CALL_generic.mforeachneighbor

Initialcascadematerialsguess

STOP

START

Creationoftheneighborsofiteration"i"

Retrievementofthemaximum energyEi(J)amongtheneighbors

Convergence?NOUpdatetheinitialsolutionfor

iteration"i+1"YES

Figure 6.3. Flowchart of the local search algorithm

48

Optimization

However, the problem of local minimum may occur with heuristic problems.Thus, simulated annealing is implemented in particular cases to check thevalidity of the code. Specifically, in the case in which the best solutionSi+1 = Si, the starting solution of the next iteration “i +1” is chosen ran-domly among the neighbors with a probability that is proportional to thedifference in the goal values, i.e. the recovered energy. The probability p (-)of the neighbor “j” is calculated according to the procedure suggested byWolsey [12], and it is adapted to the present case study as follows

pj =e−∆Ej/τ∑e−∆Ej/τ

(6.1)

where ∆Ej (J) is the difference between the energy recovered for the bestsolution obtained in the previous iteration “i -1” and the one of the neighbor“j” in the current iteration “i”, while τ (J) is a characteristic energy set to106 J. The value of τ is chosen according to the characteristic values of ∆Ejin the previous iterations. In each iteration, τ is reduced by a cooling factorr (-) set to 0.9. Once a neighbor is selected randomly through a probabilisticapproach, the initial solution of the next iteration is updated and it is possibleto escape from local minima.

6.4 Genetic Algorithm

In a genetic algorithm the function that must be minimized is defined asthe fitness function f(x). When a maximum is researched, the algorithm isset such that min(−f(x)) is found. The variable x is called individual orchromosome, and it is defined as follows

x = [par1, par2, · · · , parnvar ] (6.2)

where par are the parameters that can change to optimize f(x) and nvar isthe number of genes that can be interchanged. In the present case study, x isthe set of materials that fill the regenerator, while par are the diverse phasechange materials of the different sectors. It is straightforward that nsectorcoincides with nvar.

An ensemble of individuals forms a population, represented by a matrixwith dimensions nx × nvar, where nx is the number of individuals created.Once a population is set, the objective function is calculated for each indi-vidual and the best solutions only are kept for each iteration. Then, pairingand mating is performed: couples formed by the individuals previously se-lected are created and two offsprings are formed combining the chromosomesof the parent functions. Different pairing approaches can be implemented,e.g. weighted random pairing, in which individuals are coupled assigning

49

Chapter 6

CALL_generic.mforeachchromosomeofP

Definitonof: parameters,objectivefunctionandinitialsolutionguess

START

CreationofthepopulationP

RetrievementoftheenergyEi(J)recoveredinthecoldblowfor

each chromosomeofP

NOConvergence?

YES

Mutuation

STOP

Paringandmating

Figure 6.4. Flowchart of the genetic algorithm

probabilities according to the fitness of their objective function. After themating process, random mutations are performed in order to modify a smallpercentage of the new individuals. Finally, a new set of x is obtained anda new generation is set. This iterative process continues until convergenceis reached [13], as in the case of the local research algorithm. The geneticalgorithm flow diagram is briefly explained in Fig.6.4.

The function “ga” available in the MATLAB optimization toolbox isadopted in the present case study. The fitness function is set as the energyrecovered in the cold blow, implemented in the MATLAB code explained inChapter 5. An initial set of materials is set in order to start the iteration froma physically reasonable solution. This starting condition, as well as the valueof the tolerance for convergence, is set equal to that of the local research algo-rithm to compare the behavior and performance of the two different methods.The pairing or crossover is performed with a “scattered” approach: a binaryvector is created and the chromosomes where the vector is a 1 are takenfrom the first parent, while that where there is a 0 are taken from the second

50

Optimization

1 3 5 6 7 10 12

1 3 7 9 10 10 14

Parent1

2 5 7 9 10 12 14

Parent2

Child

Figure 6.5. Example of the pairing with the binary vector [1100010]

parent. Then, a child is formed from combination of the genes selected. Thisprocess is performed for diverse couples of parents among the chromosomesselected in the previous iteration. Fig.6.5 shows an example of the pairingto form a chromosome with the binary vector [1100010]. In their turn, themutations are performed with a “Gaussian” approach: a random numbertaken from a Gaussian distribution with mean equal to 0 is added to eachentry of the parent vector. In this way, small random changes are applied tothe child individuals previously created.

It is possible to notice that the genetic algorithm is completely basedon a probabilistic approach, differently from the local research algorithmthat is implemented. Indeed, the latter is a model thought and adaptedspecifically for the present case study. Moreover, the physics of the problemis considered, and the approach is based on the knowledge of the behavior ofthe regenerator in the operating conditions of the selected case study.

51

Chapter 7

Case Study Results

This chapter deals with the simulation of the MATLAB code for the casestudy developed in the present work. The specifications of the present casestudy are depicted. In terms of implementation, the methodology followedto find the optimal configuration is discussed in detail. The choices andsetting of a particular step of this procedure have an effect on the followingones. Thus, it is fundamental to choose the best approach to find an optimalstructure of the regenerator for the present case study. Finally, the resultsof the optimization are discussed.

7.1 Case Study Description

The case study developed in the present thesis is an industrial tumble dryerfor cotton flat fabric applications. In this section, the characteristics of theflow as well as that of the stoves of the regenerator are discussed. The flowspecifications are mainly retrieved from the experimental analysis. While thestove specifications are found from inspection of the problem as well as fromthe constraints of the system in terms of space.

7.1.1 Flow SpecificationsThe cold and hot blows are different in terms of thermodynamic behavior.The former, i.e. the fluid flow that is preheated by the matrix and enters theboiler, is assumed to be dry air at constant ambient conditions. Specifically,the temperature and pressure are set equal to 20 ◦C and 1 atm, respectively.On its turn, the hot blow, i.e. the air from the dryer outlet that transfersenergy to the regenerator matrix, is humid and hot air, whose conditionschange over the period of the drying cycle. Specifically, the temperature,mass flow rate and humidity are retrieved from the experimental analysis.Their values are that described in Chapter 3 and shown in Figg.3.4 to 3.7.

53

Chapter 7

7.1.2 Stove SpecificationsThe frontal area of the stove is calculated from the inlet mass flow rate andtemperature. Specifically, the frontal area is calculated such that the meanvelocity considering undisturbed condition of the flow is about 5 m/s. Inthis way, a compromise between heat transfer efficiency and friction lossesis achieved. The value of the frontal area Astv turns out to be 0.250 m2.For sake of simplicity, a squared cross section is studied, resulting in a shapefactor SF (-) equal to 1. This parameter is defined as SF = Wdt/Dpt, thusthe width and depth of the stoves result to be 500 mm.

In terms of height, the maximum vertical length is set to 3 m. The rea-son behind this constraint is the fact that the tumble dryer is fixed to theroof of the industrial building, whose height is approximately 4.5 m, anda space below the equipment is required for ease of movement. Additionalconsideration will be discussed once the parametric analysis is completed.Specifically, the behavior of the best configuration retrieved from the para-metric analysis is studied while changing the height of the regenerator. Avalue of the height lower than 3 m is chosen if the computation shows thatthe efficiency doesn’t increase or increases slowly while increasing the heightover that specific value. This means that an asymptote is reached in terms ofperformance. Thus, an increase of the height would lead to same efficiencies,but higher costs in terms of pumping power. Indeed, in the present casestudy, the total pressure drop is proportional to the height of the stoves.

Different combinations of the number of cylinders per row Ncln (-) andcylinder diameter Dcln (m) are studied in the parametric analysis, whoseoutput represents the best configuration in terms of energy recoveries andannual savings. For fixed Ncln and Dcln, the calculation of the number of rowsin the stoves is straightforward and it is performed directly in the MATLABcode, assuming a dimensionless vertical pitch b (-) equal to 2.

Regarding materials, the present case study deals with phase change ma-terials found in the industry after a comprehensive market analysis, whosedetails are depicted in Chapter 4. Moreover, a cascade of diverse PCMs isconsidered, as said in the chapter of the linear programming. The set ofmaterials selected to develop the parametric analysis represents a first guessas well as the starting point of the optimization process. This first configu-ration is set by experience and inspection of the operating temperatures ofthe regenerator. Specifically, the number of sectors nsector is initially set to 4,and the materials that fill the whole regenerator are the ones denoted withthe following names: A95, A70, A58H and A48, from the top to the bottomof the stoves. Their specifications are available in Tab.4.1.

54

Case Study Results

7.2 Parametric Study

This section deals with the parametric study applied to the case study de-scribed above. As previously said, the number of cylinders per row and theirdiameter are the parameters to be analyzed and interchanged. Specifically,the range of Ncln is 11-27 and that of Dcln is 9-18 mm. On the other hand,the operating conditions described in the previous chapter are fixed. The aimis to find the configuration of the stoves characterized by the highest perfor-mances and savings per year. Hence, this section is divided in two parts: theformer introduces the main energy and economic indexes; the latter dealswith the results and the outcomes of the parametric analysis.

7.2.1 Energy and Economic IndexesThe recovery (-) and the saturation (-) are the two main indexes that depicthow the regenerator is performing in terms of heat exchange. Their valuesare calculated when a stationary condition is reached as follows

Recovery =ErecoveredEmax,flw

(7.1)

Saturation =ErecoveredEmax,stv

(7.2)

where Erecovered (J) is the energy recovered during the cold blow, Emax,flw (J)the maximum energy that could be ideally exchanged during the hot blowand Emax,stv (J) the maximum energy that the stove could ideally absorbduring the hot blow. These parameters are calculated as follows

Emax,flw = mflw∆tcyclecpflw(Tmean,in − Tamb) (7.3)

Emax,stv = mstv [cPCM (Tmax,in − Tamb) + ∆hlat] (7.4)

where ∆tcycle (s) is the cycle duration, Tmean,in (K) the mean inlet temper-ature of the hot blow, Tmax,in (K) the maximum inlet temperature of thehot blow, Tamb (K) the ambient temperature, ∆hlat (J) and cPCM (J/(kgK)) the mean latent heat of fusion and specific heat of the selected phasechange materials, respectively. On its turn, the mass of the stove mstv (kg)is calculated as follows

mstv =Ns∑s=1

ρPCM,sπR2clnLclnNcln (7.5)

where ρPCM,s (kg/m3) is the phase change material density of row “s”, andRcln (m) and Lcln (m) the radius and the length of the rods, respectively.

55

Chapter 7

Table 7.1. Main parameters for the preliminary economic analysis

ncycles,year Cel Cth ηbrn ηfan(e/kWh) (e/kWh) (-) (-)

6000 0.7 0.047 0.9 0.7

On the other hand, the energy indexes used in the analysis are the massspecific energy recovered Espec,mass (J/kg) and the pumping work specific en-ergy recovered Espec,pmp (J/J), that are the ratios of the energy recovered withrespect to the total mass of the stove and to the pumping energy Epmp (J),respectively. In addition, the first economic index adopted is the annualsaving Csaving (e/year) calculated as follows

Csaving = ncycles,year

(ErecoveredCth

ηbrn− 2EpmpCel

ηfan

)(7.6)

where ncycles,year is the number of cycles performed in a year, Cel (e/J) theelectricity cost, Cth (e/J) the natural gas cost, ηbrn (-) and ηfan (-) thereference burner and fan efficiencies, respectively. The cost of the pumpingwork is multiplied by 2 because two fans are necessary, while only the energyrecovered in the stove crossed by the cold blow is exploited. Specifically, thepumping work of the fans Epmp (J) is computed as follows

Epmp =V∆P∆tcycle

ηpmp(7.7)

where V (m3/s) is the volumetric flow rate, ∆P (Pa) the maximum pressuredrop, ∆tcycle (s) the cycle duration and ηpmp (-) the efficiency of the fan.

On their turn, the reference burner and fan efficiencies consider the ther-mal and electric energy losses, respectively. Moreover, the number of cyclesper year is calculated considering 300 working days, comprised of 50 Satur-days and 250 midweek days. The dryer is operative 8 hours per day except onSaturday, in which it works for 6 hours. The duration of a cycle lasts about20 minutes considering the loading and discharge at the beginning and atthe end of the cycle, respectively. Tab.7.1 shows the main parameters usedto perform the preliminary economic analysis.

The calculation of the capital cost of the regenerator is also includedin this section, even though it is used exclusively in the chapter dealingwith the comparison with a recuperator. The investment is retrieved from apreliminary analysis, because of the unavailability of a detailed design of the

56

Case Study Results

Table 7.2. Main parameters for the investment cost analysis

CPCM,kg Ccln,m Cst,kg Dcln,int tcln Lcasing,int tcasing Hcasing

(e/kg) (e/m) (e/kg) (mm) (mm) (mm) (mm) (mm)

6.5 0.93 8 9 1 550 2 3000

system. Specifically, the total cost Ctot (e) is calculated asCtot = 1.5 (CPCM + Ccln + Ccasing)

CPCM = CPCM,kgmPCM

Ccln = Ccln,m LclnNcln,tot

Ccasing = Cst,kgmcasing

(7.8)

where CPCM , Ccln and Ccasing (e) are the costs of the phase change materi-als, stainless steel cylinders containing the PCMs and casing of the regener-ator, respectively. While, CPCM,kg (e/kg) is the cost of PCMs per kilogram,Ccln,m (e/m) the cost of the cylinders per meter, and Cst,kg (e/kg) thecost of manufactured stainless steel per kilogram. Moreover, the parameterm (kg) stands for mass, while Lcln (m) is the length of the Ncln,tot cylinders.The total investment is incremented of the 50% to include extra costs. Itis important to notice that, in the present case study, a safety factor of 1.5overestimates the cost of the regenerator, because the manufacturing costsof the system components are already considered in the specific costs de-scribed above. Hence, a reliable and safe range of predictions is ensured.The specific costs and main geometrical parameters considered to calculatethe investment cost are summarized in Tab.7.2. In this table, the subscript“int” stands for internal, while t, L and H are the thickness, length andheight, respectively.

7.2.2 ResultsThe main parameters described in the previous section are utilized to find theoptimal configuration of the parametric analysis. In particular, the specificenergy recoveries and the savings per year are plotted in function of thenumber of cylinders per row and their diameter, as shown in Figg.7.1 and 7.2.

The former depicts the behavior of the mass and pumping work specificenergy recovered. The plot is characterized by a sharp change in slope,because of the different increase rates of the efficiency and the pumpingwork spent for the fans. Indeed, the higher is the mass of the stove, thehigher is the energy recovered. However, also the pressure drop increases.Thus, an optimal compromise between efficiency and pressure drop should

57

Chapter 7

Figure 7.1. Specific energy recoveries in function of the number of cylinders perrow and their diameter

Figure 7.2. Saving per year in function of the number of cylinders per row andtheir diameter

58

Case Study Results

Figure 7.3. Energy recovery in function of the pressure drop for different stoveconfigurations

be computed through the economic index previously introduced. Fig.7.1shows also that the same Espec,mass can be obtained for diverse combinationsof the number of cylinders per row and cylinder diameter. However, smallerdiameters ensure higher performances. This is valid in the present case studybecause of the low heat conductivity of paraffins. On its turn, the sameEspec,pmp can be obtained for two diverse numbers of rows for a fixed diameter.Indeed, the presence of a maximum value depicts the possibility to determinean optimal configuration that considers both the heat transfer efficiency andpumping work. This behavior can be clarified by plotting the recovery versusthe total pressure drop as in Fig.7.3. This graph shows that increasing thenumber of rows is desirable until a certain point. Indeed, after the first sharpincrease in the recovery, the total pressure drop tends to increase faster thanin the left side of the graph.

It is also possible to notice that, while high mass specific energy recoveriesare obtained with small diameters, high pumping work specific energy recov-eries are obtained with large diameters. Hence, it is necessary to consider thecontribute of the energy recovered together with that of the pressure drop.Specifically, an economic analysis is needed to find the optimal configura-tion, balancing avoided and operational costs. Hence, the annual savings infunction of the number of cylinders per row for diverse cylinder diameters

59

Chapter 7

Figure 7.4. Energy recovery in function of the height of the stove for the optimalconfiguration

are analyzed, as in Fig.7.2. An optimal value is found, as predicted. Thismaximum represents the best configuration from an economic point of view.Specifically, it is characterized by a diameter of 9 mm and a number of cylin-ders per row of 26. Overall, a mass specific energy recovered of 442 kJ/kg isobtained, corresponding to savings of 3300 euros per year.

Then, it is desirable to understand if the stove is oversized, as previouslyexplained. Thus, the best configuration is studied while varying the heightof the stove H (m). If the efficiency increases for heights higher than 3 m, His set equal to the constraint of 3 m. Otherwise, the configuration with theheight that leads to the highest Csaving is selected. In Figg.7.4 and 7.5, therecovery and the annual saving are plotted for a range of heights between2 and 5 m to have an overall view of the behavior of the performances whileincreasing H. It is possible to notice that the height that ensures the highestefficiency and saving, while observing the constraint of space, is equal to 3 m.Indeed, only at heights above 4 m the rate of efficiency increase starts gettingsmaller. Moreover, the configuration with the maximum annual saving is thatcorresponding to 4 m of height, above the limit of space.

60

Case Study Results

Figure 7.5. Annual saving in function of the height of the stove for the optimalconfiguration

7.3 Optimization

The main characteristics of the stoves, i.e. height, cylinder diameter andnumber of rows, are selected with the parametric investigation. The laststep to find the best configuration is represented by the optimization of thematerial distribution in the diverse sectors of the regenerator. The procedureof this computation is depicted in Chapter 6. Thus, this section describesand compare the results of the two algorithms implemented in this thesis.Specifically, the two different algorithms take the same set of materials asstarting guess. Moreover, the number of sectors for which the procedure isrepeated goes from 1 to 10.

Fig.7.6 shows the energy recovered in function of nsector for the corre-sponding optimal configuration obtained with the two algorithms. It is possi-ble to notice that the configuration that ensures the highest energy recoveredis that corresponding to 8 sectors. However, only 5 different materials areused, without affecting considerably the complexity of the structure. More-over, increasing the number of sectors from 1 to 8, the recovery increasesof about 6 percentage points, that corresponds to an increase of the energyrecovered of about 5 MJ.

In terms of optimal configurations, the two algorithms gives equal or very

61

Chapter 7

Figure 7.6. Energy recovered in function of the number of sectors of the stove fortheir corresponding optimal configuration

similar results. Hence, the local research approach is validated by compar-ing its results with the genetic algorithm available in MATLAB. Moreover,in terms of computational time, the local search is faster than the geneticalgorithm. Indeed, the local research algorithm is implemented consideringthe physics behind the problem, while the genetic algorithm operates mainlywith a random approach, as previously said. The configurations obtainedthrough the implementation of the two optimization algorithms for a num-ber of sectors between 1 and 10 are reported in Tab.7.3. The materials inthe squared brackets are disposed in order from the top to the bottom of theregenerator. Tab.7.3 highlights also that some materials are always preferredto others. This is related to the properties of each material itself. Indeed,there are parameters other than the transition temperature that affect theefficiency of the heat transfer, e.g. the latent heat of fusion and the conduc-tivity. Thus, materials with better properties may be preferred even if thetransition temperature wouldn’t be optimal on equal other properties.

7.4 Analysis of the Optimal Configuration

This section deals with the detailed analysis of the optimal configuration ofthe regenerator, that is retrieved from the whole optimization process. First,

62

Case Study Results

Table 7.3. Optimal set of phase change materials obtained through the local searchand genetic algorithms for a regenerator divided in diverse numbers of sectors

nsector Optimal Solution

1 [A118]2 [A95 A58H]3 [A95 A70 A48]4 [A95 A70 A58H A46]5 [A95 A70 A70 A58H A48]6 [A95 A95 A70 A58H A58H A43]7 [A95 A95 A70 A70 A58H A58H A43]8 [A95 A95 A70 A70 A58H A58H A48 A43]9 [A95 A95 A70 A70 A58H A58H A58H A48 A43]10 [A95 A95 A70 A70 A70 A58H A58H A48 A48 A43]

the distributions of the flow and cylinder temperatures are shown for boththe hot and cold blows. Specifically, the former is plotted in function of thenumber of the row for diverse instants of the drying cycle. While the latter isplotted in function of time for diverse sections of the stove, i.e. first, middleand last row of the bed. Finally, the overall results are depicted.

7.4.1 Hot BlowThe flow temperature profiles of the hot blow are shown in Fig.7.7. It ispossible to notice that the temperature decreases along the regenerator be-cause the flow transfers energy to the bed matrix. Specifically, during thedrying phase, the temperature difference between the inlet and outlet of theregenerator decreases from the beginning to the end of the cycle. Indeed, theheat exchange is less efficient in the last instants of the cycle, because thetemperature difference between the cylinders and the flow tends to decrease.

Moreover, the inlet temperature changes over time, as already introducedin the experimental analysis. Specifically, the particular trend of the lasttime-steps is due to the sharp decrease of the inlet temperature that char-acterizes this part of the process: the flow temperature becomes lower thanthat of the cylinders; thus, the air heats up in the first rows rather thanmaintaining the decreasing profile that characterizes the whole hot blow.This consideration is important because it arises the possibility to deviatethe flow and avoid the air to enter the regenerator during this final phase.The same concept is shown in Fig.7.8, where the cylinder temperature of thefirst row during the last time-steps decreases instead of increasing because ofthe lower temperature of the flow.

63

Chapter 7

As soon as the phase change of the cylinders occurs, the flow temperatureprofiles show changes in slope and the efficacy of the heat exchange increases.Indeed, during the phase transition the flow temperature decreases more withrespect to the areas in which sensible only heat transfer occurs. Moreover,the difference in the slope in the diverse sectors of the regenerator is relatedto the different phase change materials that fill the stove. Indeed, their prop-erties change the heat transfer mechanism and lead to diverse heat transfercoefficients along the regenerator. The effect of condensation is not visiblebecause of two reasons: the absolute humidity of the hot air is rather low, andthe changes in slope of the flow temperature makes difficult to distinguishthe condensation phenomena in the air.

The cylinder temperature profiles are plotted in Fig.7.8. The phasechange transition zones are evident and depicted by the horizontal tempera-ture distribution. On the other hand, sensible only heat transfer occurs whenthe temperature changes over time. Moreover, the different melting tempera-tures of the diverse phase change materials are visible along the regenerator.Specifically, the flow crosses the materials from that with higher transitiontemperature to that with lower transition temperature. It is interesting tounderline the increasing time required to complete the phase change from thefirst to the last rows, because of the decrease of the heat exchange efficiency,as previously discussed.

7.4.2 Cold BlowFig.7.9 shows that the ambient air flow temperature increases along the re-generator. Indeed, the energy is transferred from the cylinders, previouslyheated by the hot blow, to the cold air entering the regenerator. Moreover,the cold blow is characterized by constant temperature conditions at the inletof the regenerator. Hence, the curves do not show particular profiles at theend of the cycle, differently from that of the hot blow.

Despite the different inlet conditions of the flow, the cold blow processbehaves similarly to that of the hot blow. Indeed, the difference betweenthe inlet and outlet temperatures of the flow decreases over time. Moreover,the changes of the slope and the increase in the heat transfer efficiency aredetected during the phase change transition. The transition temperature ofthe cylinders are different along the regenerator, similarly to the hot blow,as shown in Figg.7.10. However, their disposition is opposite to that of theprevious case, because the cold air enters the stove from the opposite side,i.e. from the bottom to the top. Then, the blow meets at first the materialswith lower transition temperature, as shown in Fig.6.1.

Overall, the temperature distribution at the outlet of the regenerator is afundamental parameter to understand the performances of the whole system.

64

Case Study Results

Figure 7.7. Temperature of the hot blow in the regenerator for diverse instants ofthe drying cycle

Indeed, it represents how much is possible to preheat the cold air at the inletof the burner. Hence, it is strictly related to the energy recovered and thesaving in terms of fuel consumption.

7.4.3 ResultsThe results obtained through the investigation and numerical analysis ofthe process are synthesized in this section. Specifically, the behavior of theregenerator for the optimal configuration is depicted.

The regenerator ensures an efficiency in the order of 61.5%, correspondingto a recovered energy in the order of 52 MJ. The mass of the stove andmaximum pressure drop are 117 kg and 1.4 kPa, respectively. Thus, the massand pumping work specific energies turns out to be 444 kJ/kg and 38 kJ/kJ,respectively. In terms of economic profits, the annual energy saving is in theorder of 3340 euros. From Eq.7.8 the preliminary calculation of the capitalcost is performed, obtaining an investment of about 9000 euros and a PayBack Time of about 3 years. This calculation is performed assuming constantsavings per year, initial investment cost only and interest rate equal to 0.

65

Chapter 7

Figure 7.8. Temperature of the cylinders during the hot blow over time for thefirst, middle and last rows of the stove

Figure 7.9. Temperature of the cold blow in the regenerator for diverse instantsof the drying cycle

66

Case Study Results

Figure 7.10. Temperature of the cylinders during the cold blow over time for thefirst, middle and last rows of the stove

7.4.4 Further ImprovementsOne of the major improvements to advance the heat transfer efficiency ofthe regenerator is the adoption of enhancement techniques to increase theheat conductivity of paraffins. Qureshi et al. [14] show that the heat con-ductivity of paraffins similar to that studied in this thesis can increase ofabout 25 times with inclusions of extended graphite. Thus, a preliminaryanalysis of the regenerator is computed increasing the conductivity fromabout 0.22 to 5.5 W/(m K). In this way, a rough idea of the advancementof the performances achievable can be depicted. Hence, the optimizationprocess previously described is performed for the enhanced paraffins. Anoptimal configuration characterized by 21 cylinders per row, with a diame-ter of 12 mm, is found. It is noticed that, increasing the conductivity, theoptimal solution goes towards bigger diameter, differently from the behaviorof paraffins with low conductivity. The analysis shows that the recoveredenergy increases of about the 5%, leading to an annual saving in the order of3800 e. It is possible to notice that, even with the implementation of minoradvancements, the heat transfer efficiency of the regenerator, as well as theeconomic savings, can be considerably increased. Then, a detailed analysisof heat transfer enhancements is suggested for future works.

67

Chapter 8

Comparison with aRecuperator

A regenerator is selected in the present case study to exploit the batch dryerexhausts, mainly because it works inherently in a discontinuous mode, aspreviously said. Most of the studies present in literature deal with continu-ous applications, in which recuperators are adopted as heat recovery devices.This chapter aims to compare the regenerator studied in this thesis with acommon technology, such as heat exchangers. First, a review of the systemadopting the recuperator is shown. For the design and investigation of the de-vice, a model is implemented in MATLAB. Then, the methodology adoptedis discussed and the economical results are compared to that obtained forthe regenerator.

8.1 Problem Review

This chapter aims to verify if the regenerator adopted in the present work iseconomically interesting. Though, it is desirable to compare the economicalindexes previously calculated with that of a heat exchanger. In the case ofrecuperators, the system is slightly different from that of the regenerator,as shown in Fig.8.1. The heat is transferred directly from the hot to thecold blow. The recuperator stops the operation when the drying cycle iscompleted, and restarts when the next cycle begins. Though, it does notwork in a continuous mode.

The type of recuperator is selected from a literature review. In textiledrying applications, gasket plate heat exchanger are commonly adopted, asexplained by Ogulata [15]. Specifically, this type of structure is chosen be-cause of its simplicity and ease of cleaning the accumulated dust, that is amajor issue in this type of applications [16]. Moreover, a counter-flow ar-

69

Chapter 8

RecuperatorBurner

NGInletair

Exhausts

Dryer

Figure 8.1. Scheme of the heat recovery system adopting a heat exchanger

Figure 8.2. Scheme of single pass counter-flow plate heat exchangers [1]

rangement is chosen, because it ensures higher efficiencies than parallel orcross-flow patterns. Gasket plate heat exchangers are made of several thinrectangular metal plates. They are packed together, and the path of theflow is determined by the disposition of gaskets on the four ports placedon the corners of the plates [2]. In the flow pattern of a counter-flow plateheat exchanger with single pass, the ports are closed alternatively in adja-cent channels [38], as shown in Fig.8.2. Different configurations of the floware available in literature, e.g. U-shape and multi-pass patterns. However,in the present thesis, a single pass configuration is selected for simplicity.Moreover, diverse types of corrugation are shown in Fig.8.3. In the presentwork, chevron plate heat exchangers are considered.

8.2 Chevron Plate Heat Exchanger Model

This section depicts the model implemented in MATLAB to study the be-havior of a chevron plate heat exchanger. First, the geometrical parametersare depicted. Secondly, the ε-NTU method, as well as the heat transfer andpressure drop correlations are described.

70

Comparison with a Recuperator

Figure 8.3. Types of corrugation of plate heat exchangers: (a) washboard; (b)zigzag; (c) chevron; (d) protrusions and depressions; (e) washboard with secondarycorrugations; (f) oblique washboard [2]

8.2.1 Geometrical ParametersThe main geometrical parameters of the plates are represented in Fig.8.4.The Np plates are characterized by an effective length Lp (m), an effectivewidth Lw (m), a plate thickness t (m) and a plate gap b (m). Though, thetotal heat transfer area Atot (m2) [17], and the cross section of the chan-nel Ach (m2) [39] are calculated as follows

Atot = Np Lp Lw (8.1)

Ach = b Lw (8.2)

An important characteristic length is represented by the hydraulic diam-eter Dh (m), whose simplified definition is suggested by Imran et al. [17] as

Dh =2b

Φ(8.3)

where Φ (-) is the enlargement factor. This parameter is calculated as ex-plained by Kumar et al. [40] as follows

Φ =1

6

1 +

[1 +

(π

2sinβ

)2

a2

]1/2

+ 4

[1 +

(π

2√

2sinβ

)2

a2

]1/2 (8.4)

where β (rad) is the corrugation angle. The channel aspect ratio a (-) iscalculated dividing 2b by pc, where pc (m) is the corrugation pitch in themain flow direction. Finally, the number of channels Nc (-) is

Nc =Np − 1

2(8.5)

71

Chapter 8

Figure 8.4. Main geometrical parameters of a chevron plate heat exchanger [1]

8.2.2 Mathematical ModelThe calculation of the pressure drop and energy recovered over the wholedrying cycle is performed through the implementation of a MATLAB code.In this numerical model, the time is discretized in Nt (-) time-steps, in whichthe inlet conditions of the flows change over time. For each time-step Dt (s),the energy and pressure drop is retrieved for a fixed geometry of the heat ex-changer. Though, a theoretical approach to model the regenerator is needed.

Four basic methods have been studied to calculate the effectiveness of theheat exchanger: the ε-NTU, P-NTU, LMTD and Φ-P methods. The first isadopted in the present work, because it is the most direct and fast methodaccording to the known variables of the problem. The effectiveness ε (-),the maximum and actual thermal power exchanged, Qmax (W) and Q (W)respectively, are defined [41] as follows

ε =Q

Qmax

(8.6)

Q = Ch(Th,in − Th,out) (8.7)

Qmax = Cmin(Th,in − Tc,in) (8.8)

where the subscripts “h” and “c” stand for hot and cold, respectively. Theheat capacity C (W/K) is the product between the mass flow rate and thespecific heat of a fluid flow. In the present case study, the capacities of thehot and cold blow are assumed to be equal. Though, Cmin is equal to either

72

Comparison with a Recuperator

the hot or cold capacity, and the value of C∗ = Cmin/Cmax (-) turns outto be 1. Assuming constant capacities along the recuperator, their values,as well as that of the inlet temperature, are known from the experimentalanalysis. The only unknown of the problem to find the energy recovered isthe outlet temperature of both the hot and cold fluid flow. Though, it isnecessary to introduce a new equation through the ε-NTU method. For theflow arrangement selected in this work and for C∗ equal to 1, the relationbetween ε and NTU is simplified [5] as follows

ε =NTU

NTU + 1(8.9)

where NTU (-) is the number of transfer units and is defined [5] as

NTU =UAtotCmin

(8.10)

where U (W/(m2 K)) is the overall heat transfer coefficient, whose calculationis explained in the following section. From the number of transfer units, theeffectiveness of the heat exchanger is retrieved as in Eq.8.9. Then, the actualheat exchanged Q is found from the definition of the effectiveness.

8.2.3 Heat Transfer and Pressure DropThe only unknown in Eq.8.10 is the overall heat transfer coefficient, whosedefinition according to Zlatkovic et al. [42] is as follows

1

U=

1

αh+

1

αc+Rp +Rf,h +Rf,c (8.11)

whereRp ((m2 K)/W) is the heat transfer resistance of the plate andRf ((m2 K)/W)the fouling factor. The former is defined as the ratio between the thick-ness t (m) of the plate and its conductivity λp (W/(m K)). While the latteris neglected for consistency, because the fouling effects are neglected also inthe model of the regenerator. The heat transfer coefficient α (W/(m2 K)) iscalculated from the definition of the Nusselt number Nu, that depends onthe Reynolds and Prandtl numbers. Their definitions are

Nu = αDh

λ

Re = GDh

µ

Pr = ρcpλ

(8.12)

where λ (W/(m K)) and µ (Pa s) are the heat conductivity and viscosityof the fluid, respectively. While G (kg/(s m2)) is the mass flux, and itsdefinition is depicted by Imran et al. [17] as follows

G =mflw

Nc b Lw(8.13)

73

Chapter 8

The unknown of the heat transfer problem is the Nusselt number only, be-cause all the other variables can be obtained from geometrical parametersand boundary conditions. Though, the correlations for chevron plate heat ex-changers with Φ=1.16-1.17 and β=30◦, summarized by Gulenoglu et al. [43],are adopted as follows

Nu = 0.329 Re0.529Pr0.33 if 23 ≤ Re ≤ 468

Nu = 0.113 Re0.719Pr0.33 if 468 ≤ Re ≤ 2000

Nu = 0.074 Re0.074Pr0.33 if 2000 ≤ Re ≤ 25000

(8.14)

Once the Nusselt number, heat transfer coefficient and overall heat trans-fer coefficient are calculated, the effectiveness as well as the actual heat ex-changed are found from their definitions. From these values, the energyrecovered Erecovered (J) over the whole drying cycle is found as follows

Erecovered =Nt∑1

QDtDt (8.15)

where Nt is the number of time-steps Dt (s). It is important to notice thatthe thermal power exchanged in each time-step QDt (W) changes over thedrying period because the inlet temperature of the hot blow changes eachinstant, as described in the experimental analysis.

The energy recovered is not enough to perform an economical analysis.Though, operating costs of the fans are calculated as it is explained in themodel of the regenerator. Specifically, the decrease of pressure in the re-cuperator is due to losses related to friction and port effects, as well as toacceleration and change of elevation of the fluid. However, only the firsttwo contributions are considered, because are the ones that mainly affect thepressure drop calculation, as suggested by Imran et al. [17].

The friction pressure drop ∆Pf (Pa) is calculated as follows

∆Pf =4fL∗pG

∗2

2ρD∗h(8.16)

where the apex “*” stands for modified. Indeed, the length L∗p (m), mass fluxG∗ (kg/(m2 s)) and hydraulic diameter D∗h (m) are modified in this modelto consider the effect of corrugation as follows

L∗p = Lp

sinβ

G∗ = Gsinβ

D∗h = 2(b+t)Φ

(8.17)

74

Comparison with a Recuperator

The correlations for the friction factor f (-) are the same as that imple-mented in “ASPEN EDR” [18] to obtain good predictions for a wide rangeof Reynolds numbers. The hydrodynamic model is based on the investigationof the flow that forms zigzag patters in the subchannels of the corrugations.In all these parallel subchannels, the pressure drop is equal and the flowmakes flips from a corrugation path to that of the adjoining plate. Though,the overall friction factor f (-) considers two main contributions. The formeris the loss related to the straight portion of the channels, and the correspond-ing friction factor fch (-) is calculated as follows

fch = (f 2l + f 2

t )1/2

fl = 16Re∗

ft = kt 0.0791Re∗ −0.25

(8.18)

where the subscripts “l”, “t” and “c” stand for laminar, turbulent and chan-nel, respectively. The coefficient kt (-) is an empirical constant that considersthe swirl effects, and is set to 9. While the Reynolds number Re∗ (-) is calcu-lated as function of G∗ and D∗h. From the value of fch, the change in pressuredrop over the flow direction z is calculated as follows

dP

dz=

fchG∗2

ρ (b+ t)(8.19)

The second contribution to the friction pressure drop is that related to theturns that the flow is subjected to in a given corrugation. The behavior ofthe flow is modeled as two angle bends connected in series, and the resultingpressure drop ∆Pturn (Pa) is as follows

∆Pturn = 2G∗2

2ρ(8.20)

The overall friction factor f (-) is calculated considering the two contributionsdescribed above as follows

f = ρ (b+ t)L∗p

dPdz

+ ∆PturnNturn

G∗2L∗p(8.21)

where Nturn (-) is the number of turns of the corrugations, and is evaluatedas function of the characteristic plate width Wc (m) as follows

Nturn =L∗p

Wc tanβ− 1 (8.22)

Wc =Lw2

(8.23)

75

Chapter 8

On its turn, the port pressure drop ∆Pp (Pa) depends on the flux at themanifolds Gp (kg/(m2 s)), and it is calculated as

∆Pp =1.5 G2

p

2ρ(8.24)

Gp =mflw

π/4D2p

(8.25)

where Dp (m) is the port diameter. Then, the total pressure drop ∆P (Pa)is simply the sum of the port and friction pressure drop.

8.3 Case Study of the Chevron Plate Heat

Exchanger

This section deals with the description of the methodology adopted to ratethe heat exchanger. Moreover, the results obtained from the investigationand numerical modeling of the problem are discussed.

8.3.1 MethodologyThe comparison between the regenerator and the recuperator is performedin terms of the annual savings defined in Eq.7.6. Indeed, a trade-off be-tween hydraulic and thermal behavior should be accomplished, as explainedby Raja et al. [1]. The authors underline also the importance of optimizationalgorithms to find the best configuration of plate heat exchangers, becausemany variables are involved in the rating and design of this type of device. Inthe present case study, optimization algorithms are not adopted for recuper-ators, because it is beside the point of this thesis. Instead, a combination ofsimulations with “ASPEN EDR” and the model implemented in MATLAB,described in the previous section, is performed to rate the recuperator.

In a preliminary analysis, the program “ASPEN EDR” is used to simulatethe behavior of the heat exchanger in terms of energy recovery and investmentcost for the given input data, i.e. air operating conditions and geometricalvariables. In terms of air conditions, the inlet temperature and mass flowrate are assumed to be the mean of the real operating values that changeover the whole drying cycle. Then, the model implemented in MATLAB isvalidated comparing the energy recovered and the pressure drop with thatobtained with “ASPEN EDR” for fixed geometry and air inlet conditions.Finally, the numerical model is used to retrieve the overall heat transferredand pressure drop over the whole drying cycle, imposing the real boundaryconditions of the present case study and the geometrical parameters discussedin the following section. On their turn, the main geometrical variables must

76

Comparison with a Recuperator

be fixed in an appropriate way. To do that, it is necessary to perform asensitivity analysis to understand which geometrical variables affect mostlythe heat exchanger performances. Specifically, the effect of the change of thenumber of plates, plate width, plate gap and port diameter is shown whilefixing the other geometrical parameters.

The first parameter to be considered is the number of plates. Indeed, thehigher Np, the higher is the efficiency and the lower the pressure drop, asshown in Fig.8.5. This is due to the increase of the overall heat exchangearea and the decrease of the velocity in each channel for a fixed air mass flowrate, respectively. Though, the upper limit of the number of plates is usuallyconstrained by the maximum investment cost allowed. At the same time,space and weight constraints should be fulfilled. A similar consideration isdone for the plate width, whose behavior is represented in Fig.8.6. On itsturn, the effective length is found as 1.8 times the value of the width, assuggested by Spalding [44]. Another important parameter is the plate gap b.Its contribution to the heat transfer is not that significant as it is for theparameters discussed above. On the other hand, its effect on the pressuredrop is relevant when the number of plates is below a certain value, as shownin Fig.8.7. This behavior is due to the increase of the channel mass flux whiledecreasing the number of plates. The corrugation angle is fixed to 30◦ to meeta trade-off between pressure drop and heat transfer effects. On its turn, thecorrugation pitch is calculated from Eq.8.4, to obtain an enlargement factorbetween 1.16 and 1.17 to meet the constraint of the correlation adopted inthe numerical model. The port diameter, shown in Fig.8.8, is fixed by thevelocity at the ports. Indeed, the velocity shouldn’t exceed a certain value,because high velocities result in high pressure drops as. To limit these losses,a lower bound in the diameter of the ports is set.

From this preliminary analysis, it is clear that many variables are in-volved in the rating of the heat exchanger. Though, a fair methodology tocompare the recuperator with the regenerator must be chosen. After diverseanalysis, the best way to compare the recuperator with the regenerator isfound. Specifically, the systems are compared fixing the same pressure dropand the same investment cost. While the annual savings of the recuperatorare calculated performing the numerical analysis, fixing the geometrical pa-rameters obtained imposing the pressure drop and capital cost. The detailsof the overall procedure are depicted in the following section.

8.3.2 Preliminary DesignThe program “ASPEN EDR” allows to design and simulate the behavior ofchevron plate heat exchangers. In the design mode, only the inlet conditionsof the flow are fixed. While the simulation mode allows to change the ge-

77

Chapter 8

Figure 8.5. Effect of the number of plates on the heat transfer and pressure drop

Figure 8.6. Effect of the plate width on the heat transfer and pressure drop

78

Comparison with a Recuperator

Figure 8.7. Effect of the plate gap on the heat transfer and pressure drop

Figure 8.8. Effect of the port diameter on the pressure drop

79

Chapter 8

ometry of the recuperator as desired. In both the cases, the inlet conditionsof the flow are the mean values of temperature and mass flow rate of theexhausts from the dryer. Specifically, an average temperature of 114 ◦C anda mean mass flow rate of 1 kg/s are set.

The design mode of “ASPEN EDR” is initially used to retrieve some maingeometrical parameters. Specifically, the port diameter is set to 250 mm.This parameter depends on the pressure drop limit. While fixing Dp, theminimum width of the plate turns out to be 610 mm. Then, it is necessary tofix the number of plates. To do that, the investment cost is set equal to thatestimated for the regenerator. Thus, the number of plates are changed tillthe investment cost reaches that of the regenerator. Indeed, the investmentof the recuperator is affected by its overall heat transfer area. On its turn,Atot depends on the area of each single plate and the number of plates itself.In the present case study, to decrease the pressure drop and enhance theheat transfer as much as possible, Np is set as high as possible. Hence, thewidth of the plate is set as low as possible, and specific dimensions availablein the library of “ASPEN EDR” are used for the values of both the widthand height of the plates. The number of plates obtained fixing the capitalcosts is equal to 127, corresponding to a plate width and height of 660 and1188 mm, respectively. These values are obtained for an investment cost ofthe regenerator and recuperator of approximately 9000 e.

The decrease of the number of plates does not affect significantly theheat transfer, because a fixed heat transfer area is set, and the change of thechannel velocity does not affect considerably the heat transfer in the oper-ating conditions of the present case study. However, fixing the geometricalparameters described above and the inlet conditions of the flows, the pres-sure drop calculated is too high. This behavior is due to the increase of themass flux in the channels while decreasing the number of plates. The onlyfree parameter left is the plate gap b, that should be increased to decreasethe velocity of the air in each channel. A parametric analysis is performedin MATLAB, in which the annual savings and pressure drop are consideredwhile changing the plate gap. Fig.8.9 shows that a maximum of the annualsavings is reached for b of about 10 mm. Moreover, the limit of the totalpressure drop of 1300 Pa is not exceeded for this configuration. Though, aplate gap of 10 mm is selected. This configuration is also preferred becauseof the high fouling rate of the system.

From this preliminary analysis, all the geometrical parameters are set.Though, it is now possible to perform the analysis of the recuperator, settingthe real operating conditions of the present case study in the MATLAB code.

80

Comparison with a Recuperator

Figure 8.9. Annual savings in function of the plate gap

8.3.3 Results and DiscussionThe MATLAB computation is performed with the inlet conditions describedin Chapter 3 and the geometry described in the previous section. A recoveredenergy of 57 MJ and a pressure drops of 1260 Pa are obtained. Though,the corresponding annual saving is in the order of 3900 e. Comparing therecuperator results with that of the regenerator, it is possible to notice thatthe savings per year of the former are slightly higher.

However, two important aspects should be considered: the fouling issuesand the possibility to improve the regenerator. Indeed, the aspect of foulingis a major issue of dryers. The high quantity of cotton residues can damagethe recuperator considerably after few days of operation. On the other hand,the simple structure of the regenerator can be easily cleaned by blowing com-pressed air during the period between two cycles, in which the operation ofthe dryer is stopped. Moreover, the compressed air is readily available in thelaundry, because it is a fundamental utility for the operation of the dryer.The other aspect to consider is that the regenerator is in a first stage ofresearch, and other major improvements can be performed to increase its ef-ficiency. On the other hand, the recuperator has reached a well consolidatedstate of the art. Among the main improvements for the regenerator, conduc-tivity enhancement techniques result to be highly recommended to increasethe heat transfer efficiency of the system, as demonstrated in Chapter 6.

81

Chapter 9

Conclusions

This work assesses a rod bundle regenerator with industrial phase changematerials for the waste heat recovery from the exhaust gases of a real batchindustrial dryer. The objective is the prediction of the best configuration ofthe stoves, on the base of the energy recovery and annual saving. Specifically,the operating conditions of the regenerator are retrieved through an exper-imental analysis. The numerical implementation is performed in MATLABwith an extended and improved model. Then, a parametric analysis and twooptimization algorithms are developed to optimize the main geometrical andstructural parameters of the stove matrix. In the whole process, an economicand a market analysis are included. Finally, a comparison with common heatrecovery devices, i.e. recuperators, is performed.

The development of this work leads to the following conclusions:

1. From the experimental analysis, the operating conditions of the hotblow at the inlet of the regenerator are obtained as follows:

• Temperature between 40 and 133 ◦C• Mean mass flow rate in the order of 1 kg/s• Absolute humidity of about 0.04 kgwater/kgdry,air.

2. The phase change materials of the company PCM Products Ltd are se-lected on the market. Specifically, 14 paraffins with different transitiontemperature are considered for the present case study and inserted inthe MATLAB library.

3. From the parametric analysis, the optimal configuration in terms ofannual savings is found. Specifically, the main geometrical parametersobtained are as follows:

• Frontal area equal to 0.25 m2

• Height of the stove equal to 3 m

83

Chapter 9

• Diameter of the cylinders equal to 9 mm• Number of cylinders per row equal to 26

4. From the optimization algorithms, the set of materials that ensures thehighest performances is found, and it is characterized by the followingparaffins: A95, A95, A70, A70, A58H, A58H, A48, A43.

5. The overall optimal configuration is characterized by an efficiency inthe order of 61.5%, corresponding to a recovered energy in the order of52 MJ. In terms of economic profits, the annual saving is in the orderof 3340 euros.

6. The regenerator performances are compared to that of a chevron plateheat exchanger. Fixing the investment costs and pressure drop, theannual saving of the heat exchanger is about 500 euros higher than thatof the regenerator. However, the problem of fouling for the recuperatorand the possibility to enhance the performances of the regenerator,make this second technology the most promising in terms of operatingand maintenance issues.

7. Overall, the feasibility study for the use of a cascade phase changeregenerator leads to promising results. However, advancements of thesystem are advised to enhance the heat transfer and performances ofphase change materials.

84

Chapter 10

Future Work

In the present thesis, multiple fields of study are considered: numerical, ex-perimental and market analysis, as well as optimization programming. How-ever, some improvements should be considered to increase the effectiveness ofthe heat exchange process as well as that of the numerical model. Moreover, afurther step towards the construction of a first prototype can be investigated.The main suggestions to refine this work are as follows:

• The phase change material behavior can be studied by more refinednumerical methods. The main suggestion is the implementation of theso called “enthalpy method”, whose models are described by variousauthors. Among the main papers available in literature, the ones de-veloped by Sharma et al. [8], Tabrizi and Sandrameli [9], and Xu etal. [45] are suggested.

• The introduction of new pressure drop and heat transfer coefficientcorrelations is suggested. Indeed, more precise correlations can be im-plemented to check and improve the ones implemented in MATLAB.

• An extensive study regarding thermal enhancement techniques can beuseful. Specifically, thermal conductivity improvements can lead toincreasing efficiencies of the heat transfer mechanism. Indeed, ratherhigh increases in the energy recovered can be achieved, as shown in thecase study of the present thesis. Only recent studies are available forthis field of study, e.g. the works developed by Fleischer [27] in 2015and Qureshi [14] in 2018.

• The problem of fouling must be considered in this particular applica-tion because the heat transfer fluid is characterized by a large amountof cotton fabric residues. Thus, an accurate analysis of the effects of

85

Chapter 10

fouling should be considered to ensure high effectiveness and the tech-nical feasibility of the regenerator. Moreover, solutions to prevent thisissue should be discussed in detail.

• A vectorization of the numerical problem should be considered to de-crease the computational time. Indeed, the present MATLAB codeperforms the energy balances with a progressive approach, computingthe calculations for each time-step and each row sequentially.

• A detailed design of the system should be investigated. Among themain devices, the stove structure, fans, ducts and switching mecha-nisms must be considered.

• The investment costs to manufacture the regenerator should be con-sidered to optimize the overall system considering both operating andcapital costs. In this way, also a more extensive comparison with heatexchangers can be performed.

86

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