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Miniature Pipe Bundle Heat Exchanger for Thermophoretic Deposition ofUltrafine Soot Aerosol Particles at High Flow VelocitiesA. Messerer a; R. Niessner a; U. Pöschl a

a Technical University of Munich, Institute of Hydrochemistry, Munich, Germany

First Published on: 01 May 2004

To cite this Article Messerer, A., Niessner, R. and Pöschl, U.(2004)'Miniature Pipe Bundle Heat Exchanger for ThermophoreticDeposition of Ultrafine Soot Aerosol Particles at High Flow Velocities',Aerosol Science and Technology,38:5,456 — 466

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Aerosol Science and Technology, 38:456–466, 2004Copyright c© American Association for Aerosol ResearchISSN: 0278-6826 print / 1521-7388 onlineDOI: 10.1080/02786820490449449

Miniature Pipe Bundle Heat Exchanger for ThermophoreticDeposition of Ultrafine Soot Aerosol Particles atHigh Flow Velocities

A. Messerer, R. Niessner, and U. PoschlTechnical University of Munich, Institute of Hydrochemistry, Munich, Germany

The deposition of submicrometer soot aerosol particles in aminiature pipe bundle heat exchanger system has been investi-gated under conditions characteristic for combustion exhaust fromdiesel engines and oil or biomass burning processes. The system hasbeen characterized for a wide range of aerosol inlet temperatures(390–510 K) and flow velocities (1–4 m s−1), and particle depositionefficiencies up to 45% have been achieved over an effective deposi-tion length of 27 cm. Thermophoresis was the dominant depositionmechanism, and its decoupling from isothermal deposition was con-sistent with the assumption of independently acting processes. Themeasured deposition efficiencies can be described by simple linearparameterizations based on an approximation formula for ther-mophoretic plate precipitators. The results of this study supportthe development of modified heat exchanger systems with enhancedcapability for filterless removal of combustion aerosol particles.

INTRODUCTIONUltrafine combustion aerosol particles pose a potential threat

to human health since they can enter the alveolar system ofhuman lungs. Therefore, public authorities and industry aimto reduce particle emissions by means of combustion processdevelopment and exhaust gas treatment. In many applications,conventional filter systems lead to an undesired increase of pres-sure drop and are prone to clogging by soot and oil ashes (Neeftet al. 1996). Electrostatic filtration has found wide applicationto remove combustion particles; however, this method imposes

Received 17 September 2003; accepted 19 February 2004.This work is part of the project “Katalytisches System zur filter-

losen kontinuierlichen Rußpartikelverminderung fur Fahrzeugdiesel-motoren,” supported by the Bavarian Research Foundation, Mu-nich. Additional funding from the Max-Buchner-Forschungsstiftungand technical support by Sebastian Wiesemann are gratefullyacknowledged.

Address correspondence to Reinhard Niessner, Technical Univer-sity of Munich, Institute of Hydrochemistry, Marchioninistrasse, 17,Munich D-81377, Germany. E-mail: [email protected]

high investment and running costs. Due to the limitations of par-ticle loading by their size, small particles between 10 and 30 nmcannot be removed reliably. Furthermore, electrostatic precip-itators can generate undesired gaseous components, especiallywhen operated with negative voltage (Yehia et al. 2000). Turbu-lent precipitators showed particle deposition efficiencies of upto 35% with significantly reduced removal of particles in therange between 80 and 300 nm (van Gulijk et al. 2001). Shi andHarrison (2001) report on thermophoretic deposition of dieselsoot in a water-cooled fluidized bed. In diesel processes (Shiet al. 1999) nearly all particles are in the submicrometer sizerange based on particle mass; in the case of biomass burning(Baumbach 1993) it is more than 80%. Messerer et al. (2003)could show that the thermophoretic coefficient of ultrafine sootagglomerate particles exhibits no significant dependency on ag-glomerate size. Therefore, thermophoretic soot particle removalcan provide a reliable solution for filterless combustion aerosoldeposition in the submicrometer size range. Sufficient tempera-ture gradients for particulate removal can be established in heatexchangers, so that future engineering could focus on the paral-lel optimization of heat transfer and submicrometer particulateremoval in one device.

Byers and Calvert (1969) were the first to perform exper-iments and analyses of thermophoretic deposition of particlesin a hot turbulent gas stream from the aspect of air cleaning.Nishio et al. (1974) investigated the thermophoretic depositionof aerosol particles in a heat exchanger pipe, in particular theinfluence of fouling on the long-term heat exchange behaviorof the tube. Further studies of thermophoretic particle deposi-tion in externally cooled tubes include Stratmann and Fissan(1989), Chang et al. (1990), Montassier et al. (1991), Sasse andNazaroff (1994), Chang et al. (1995), and Lin and Tsai (2003).Sasse and Nazaroff (1994) performed a numerical simulationof a tobacco smoke particle filter based on thermophoretic de-position from natural convection flow. They emphasize the ne-cessity for a proof-of-principle experiment for the validation oftheir simulation results. Up to now little information about the

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THERMOPHORETIC DEPOSITION IN A HEAT EXCHANGER 457

thermophoretic deposition of submicrometer aerosol particlesat high flow velocities in the temperature gradient field aroundinternally cooled tubes is available.

Thermophoretic particle motion can be described by (Talbotet al. 1980)

vth = −Kthµg∇T

ρgTp, [1]

where Kth is the thermophoretic coefficient, vth is the ther-mophoretic particle velocity, and ∇T represents the temperaturegradient in the vicinity of the particle. µg is the gas dynamic vis-cosity, Tp is the particle temperature, and ρg is the gas density.For the free molecular regime (Kn � 1), Waldmann and Schmitt(1966) derived a thermophoretic coefficient that is independentof particle size: Kth = 0.55. For the transition (Kn ≈ 1) and con-tinuum (Kn � 1) regimes, however, the thermophoretic coeffi-cient generally depends on particle size, and different formulaefor the calculation of Kth as a function of the Knudsen num-ber have been derived (e.g., Brock 1962; Derjaguin et al. 1976;Kousaka et al. 1976; Talbot et al. 1980). In accordance with atheoretical study by Rosner and Khalil (2000), we demonstratedthat the thermophoretic coefficient of agglomerate soot parti-cles in the transition regime can be approximated by Kth ≈ 0.55(Messerer et al. 2003). For the simple case of a constant tem-perature gradient along a flown-through rectangular channel inthermophoretic plate precipitators, the thermophoretic deposi-tion efficiency εth can be efficiently approximated by (Tsai andLu 1995; Messerer et al. 2003)

εth = vth L

vx,0 H= Kth

L µg,0 �T

ρg,0 vx,0 H 2 T, [2]

where H and �T are the distance and temperature differencebetween the plates, respectively; and µg,0, ρg,0, and vx,0 are thegas properties (dynamic viscosity, density, and axial velocity) atthe average temperature in the precipitator.

Miniaturized heat exchanger systems provide a high surface-to-volume ratio and therefore lead to high heat transfer rateseven under laminar flow conditions. The heat transfer behaviorin these devices has been investigated by a number of researchersover the last decade, e.g., Peng et al. (1995). Due to high tem-perature gradients thermophoresis is expected to be significantlyhigher than in conventional heat exchangers for particle-loadedflows. To our knowledge this is the first study on the removalof aerosol particles in the external flow around cooling tubes ina miniature heat exchanger under experimental conditions rele-vant for modern combustion exhaust systems with aerosol flowvelocities between 1 and 4 m s−1.

METHODS

High Temperature Gradient Pipe Bundle Heat ExchangerFigure 1 shows the cross-sectional area of the miniature pipe

bundle heat exchanger that has been designed and used to inves-

tigate particle deposition at high gas flow rates and temperaturegradients. Twenty seven stainless steel tubes with an inner diam-eter of 0.99 mm and an outer diameter of 1.59 mm are arrangedin a near-quadratic area of 10.4 · 10.5 mm such that the axes ofall tubes are near-equidistant. At their ends 5 mm of each tubeare fitted into 10 mm stainless steel blocks, which are insertedinto a stainless steel channel. The top of the channel can be re-moved to control the alignment of the tubes as well as the sootdeposition (Figure 2). The 2 mm viton sealing in the top wasfound to be leak proof for the experimental conditions of thisstudy. Along the 300 mm effective length of the tubes betweenthe two blocks the bottom area of the channel as well as the topwere formed in a way that reduces the free space towards thetubes, simulating half-perimeter tubes directly mounted at thebottom and top plate.

The hot aerosol was led into the channel by a 8 mm di tube atan angle of 35◦ as a compromise between engineering require-ments and a high fluid impulse in axial direction to minimizeturbulences in the entry region of the tube channel (Figure 3). Theaerosol outlet was designed symmetrically. The cooling fluid—in the study presented here pressurized air—was added by 8 mmdi tubes through the top plate and by a smooth 90◦ curvaturedirected into the steel blocks supporting the 27 heat exchangertubes. The pipe inlets were conical to minimize pressure build upby the inflowing cooling gas. The outlet was symmetrical. Thewhole heat exchanger was thermally insulated to reduce heattransfer to and from the channel. Therefore the aerosol flow-ing between the outer tubes and the walls of the heat exchangerheated up the channel walls, and so no significant undesiredthermal gradients that would increase thermophoretic deposi-tion towards a cooler channel wall were established. The wallsof the upper and lower plate were adopted to the void spaceto reduce the aerosol flow between the channel walls and theouter tubes. At the same time there was still space between theouter tubes and the channel walls to avoid direct thermal con-tact and conductive heat transfer between the wall and tubes.According to the cross-sectional areas (Figure 1) only about10% of the aerosol flow passed between the outer tubes and thewall. Therefore, the particle deposition effects observed in thisstudy were not significantly influenced by these boundary phe-nomena. The internal cooling of the 27 tubes lead to a smallerthermal axial expansion of the tubes in comparison to the channelhousing the steel blocks. Therefore the tubes were equidistantlydistributed over the whole heat exchanger length. The effectivedeposition length can be calculated from the tube length betweenthe stainless steel blocks, the distance between the blocks, andthe axial position where the inflowing aerosol comes in contactwith the cooling tubes: L = 300 − 2 · (15) = 270 mm. Therelative error in the determination of the deposition length re-sulting from the diameter of the inflowing aerosol tube (8 mm) is±3%.

Temperatures of the system were measured with four K-type thermocouples (accuracy ±0.1 K). The thermocouples forthe aerosol inlet and outlet were placed in the center of the


458 A. MESSERER ET AL.

Figure 1. Cross-sectional area of the miniature pipe bundle heat exchanger. Pipe inner diameter di = 0.99 mm, outer diameterdo = 1.59 mm. Aerosol flow around the cooling tubes flown through by cooling air.

8 mm tubes about 2 mm before the tube bundle. The ther-mocouples for the cooling gas inlet and outlet were mountedin the center of the tube blocks at a distance of about3 mm.

Figure 2. Photograph of the pipe bundle heat exchanger inletsection.

Experimental Setup and Measurement ProcedureThe complete experimental setup applied in this study is

outlined in Figure 4. The test aerosol particles were producedby a spark discharge between graphite electrodes (Alfa Aesar,Karlsruhe, Germany, purity 99.9995%) in a 3.7 l min−1 argonflow (Messer Griesheim, Krefeld, Germany, purity 4.6). Theprimary carbon particles produced with the applied spark dis-charge aerosol generator are known to have a diameter of ∼5 nm(PALAS GfG 1000, Karlsruhe, Germany; Evans et al. 2003). Af-ter passing through an agglomeration reservoir (2 l glass flask),the aerosol flow was diluted with 4.4 l min−1of filtered nitro-gen and led through a Kr 85 aerosol neutralizer (10 mCi). Theaerosol flow through the pipe bundle heat exchanger was con-trolled by venting the excess through an outlet valve into the ex-haust line. Before entering the heat exchanger system the aerosolwas heated to the desired inlet temperature.

The symmetric sampling setup at ambient temperature andequal flow conditions enabled near-identical aerosol samplingconditions before and after the heat exchanger. Thus the signifi-cant thermophoretic losses which are known to occur upon cool-ing of a hot aerosol flow to ambient temperature in a sampling



Figure 3. Longitudinal section of the pipe bundle heat exchanger. Note the symmetrical design of the deposition device.

line (Berger et al. 1995) could be avoided. Other potential ef-fects of the sampling process on the aerosol properties can beassumed to cancel out and were neglected in the measurementdata analysis.

Particle number size distributions were measured with a scan-ning mobility particle sizer (SMPS) system consisting of anelectrostatic classifier (TSI 3071) and a condensation particlecounter (TSI 3025) operated with a sample flow of 1 l min−1, asheath air flow of 10 l min−1, and a scan time of 120 s (measure-

Figure 4. Schematic flow diagram of the experimental setup for counterflow heat exchanger particle deposition measurements.

ment range 20–300 nm). Before the SMPS, the particle con-centration in the sample flow was reduced by a ratio of 1:20in a dynamic dilution system (TOPAS DDS 560) to minimizesoiling and transient particle deposition in the measurement de-vice. The particle size spectra were analyzed with a resolutionof 16 particle size classes i per decade, providing sufficient in-formation on the size distribution of the sparkdischarge sootaerosol and maintaining a high signal-to-noise level at the sametime.



Table 1Experimental parameters for the investigation of the particle deposition mechanisms in the miniature pipe bundle heat exchanger

Exp.Vh,out

[l min−1]vx,hot,in

[m s−1]Th,in

[K]Th,out

[K]Tc,in

[K]Tc,out

[K]�T log,mean

[K] ReVc,in

[l min−1]

I a 3 1.31 403.5 301.9 300.5 329.5 18.30 64.8 5I b 3 1.41 436.0 302.8 301.0 338.8 23.92 63.1 5I c 3 1.49 460.5 303.5 301.4 346.5 28.02 62.0 5I d 3 1.58 489.0 304.1 301.5 356.0 33.14 60.8 5II a 4 1.73 400.2 301.1 300.0 333.1 16.04 86.7 5II b 4 1.79 414.0 303.5 299.5 342.5 23.40 85.4 5II c 4 2.05 474.8 303.3 300.1 363.2 30.60 81.8 5II d 4 2.16 499.0 300.4 297.8 373.0 32.80 81.0 5III a 5 2.17 401.5 301.3 300.5 330.4 15.64 108.2 10III b 5 2.37 440.1 301.6 300.7 341.0 20.87 105.0 10III c 5 2.55 473.0 302.8 301.7 352.5 25.42 102.5 10III d 5 2.74 507.9 304.4 303.0 364.5 30.69 100.1 10IV a 6 2.55 393.5 302.4 297.6 344.7 18.97 130.5 5IV b 6 2.64 407.3 303.7 302.3 339.8 17.06 128.8 10IV c 6 2.86 442.5 304.9 303.2 352.1 22.32 125.2 10IV d 6 3.03 468.0 300.8 298.9 359.0 26.45 123.8 10IV e 6 3.2 494.7 301.0 299.3 367.1 29.23 121.6 10V a 8 3.35 387.5 302.3 300.3 339.9 14.36 174.9 10V b 8 3.86 447.0 303.8 300.7 366.5 23.77 166.7 10V c 8 4.16 482.1 304.0 300.2 381.0 29.63 162.8 10

Volumetric flow rates at ambient temperature and pressure: 300 K, 950 mbar

The parameters describing flow and temperature propertiesof the different experiments are summarized in Table 1. Afterevery experiment the pipe bundle heat exchanger was flushedwith pressurized air at flow velocities of about 40 m s−1 to reli-ably remove soot deposits on the tubes, which influence particledeposition and heat transfer properties.

The spark-discharge soot aerosol exhibited an approximatedlog-normal size distribution with a median particle diameter ofabout 82 nm, a geometric standard deviation of 1.64, and a num-ber concentration between 6 and 9 · 106 cm−3. It is similar tothose encountered in the exhaust of modern heavy duty dieselengines (Shi et al. 1999). The average particle size distributionbefore and after the heat exchanger for experiment Id is givenin Figure 5.

For each set of parameters the heat exchanger system washeated up by the aerosol flow until thermal equilibrium wasreached. Then 12 consecutive particle size distribution mea-surements were taken, alternatingly before and after the heatexchanger. For every switching, the particle concentration dif-ference was divided by the particle concentration measured be-fore the precipitator. The arithmetic mean of the 11 values perparticle size class i obtained by this procedure was taken as the(size-dependent) total deposition efficiency, εtot,i . The measuredtotal deposition efficiency can be split into an isothermal con-tribution εiso,i caused by diffusion, impaction, and interceptionunder isothermal flow conditions and a thermophoretic contri-

bution εth,i . εiso,i is the deposition efficiency measured whenthe heat exchanger was operated under isothermal but other-wise unchanged conditions. It was generally in the range of2–20%.

The small volume of the heat exchanger necessitates a macro-scopic description of the thermal gas properties by measuringtemperatures at the hot aerosol inlet, Th,in, the aerosol outlet,Th,out, the cooling gas inlet, Tc,in, and the cooling gas outlet,Tc,out. The logarithmic mean temperature difference, �T log,mean

which is generally used to describe heat transfer characteristics,is given by

�Tlog,mean

= �Tinlet − �Toutlet

ln(

�Tinlet�Toutlet

) = (Th,in − Tc,out) − (Th,out − Tc,in)

ln(

Th,in−Tc,out

Th,out−Tc,in

) .

[3]

RESULTS AND DISCUSSIONIn Figure 6 the measured εtot,i and εiso,i are displayed for the

conditions of experiment series I with average aerosol flow ve-locities vx,0 between 1.15 and 1.28 m s−1. Small particles in thesize range of 34 to 70 nm are found to exhibit significant particledeposition up to 20% in the case of small aerosol flows throughthe heat exchanger when no temperature gradients are estab-lished. This observation can be attributed to diffusion processes



Figure 5. Soot-particle size distributions measured before and after the heat exchanger in experiment Ia (arithmetic mean ±standard deviation of 6 measurements each).

Figure 6. Total particle deposition efficiencies εtot,i and isothermal losses εiso,i in the pipe bundle heat exchanger for experimentsIa–Id. Data points with error bars represent the arithmetic mean ± standard deviation of 11 differential measurement values.



occuring in the heat exchanger, leading to an increased particledeposition with decreasing dp. Increasing Th,in leads to signif-icantly enhanced particle deposition εtot,i , indicating that ther-mophoretic deposition occurs.

To investigate the contribution of thermophoresis to the totalparticulate deposition εtot,i , the different deposition mechanismshave to be decoupled. The first step in decoupling the ther-mophoretic deposition component εth,i is to determine how themechanisms couple together. A general expression for combin-ing the mechanisms occuring in this study is given by

εtot,i = εiso,i + εth,i + fiso,th, [4]

where fiso,th is a function of the mechanisms involved in the de-position process describing the interaction between the differentdeposition mechanisms. A detailed description of the differentmethods of decoupling thermophoresis from other depositionmechanisms is given in Romay et al. (1998). Still, the determi-nation of fiso,th is a matter worthy of discussion. For their studieson the contribution of thermophoresis to particle deposition intubes, Nishio et al. (1974) and Romay et al. (1998) simply addedεiso,i and εth,i with fiso,th = 0. On the other hand, Brockmann(2001) proposed fiso,th = −εiso,i · εth,i for independently act-ing deposition processes. The experimental data of this studyallow the testing different coupling approaches. Figure 7 shows

Figure 7. Total particle deposition efficiencies εtot,i , isothermal losses εiso,i , and thermophoretic deposition efficiencies εth,i

calculated with f (iso,th) = −εth,i · εiso,I and f (iso,th) = 0, respectively, for experiment Ia. Data points with error bars representthe arithmetic mean ± standard deviation of 11 differential measurement values; dashed line illustrates εth,avg calculated withf (iso,th) = −εth,i · εiso,i .

εtot,i and εiso,i measured in experiment Ia and thermophoreticcontribution εth,i calculated from Equation (4) for the differentassumptions outlined above. With fiso,th = −εiso,i · εth,i , εth,i

exhibits no significant size dependency, as expected from ear-lier experimental results and theory calculations (Messerer et al.2003). With fiso,th = 0, on the other hand, εth,i exhibits a pro-nounced decrease towards smaller particle size at dp < 100 nm,which is not consistent with earlier investigations (Messereret al. 2003). Similar effects were observed for all experimentsperformed in this study (more pronounced at low and less pro-nounced at high aerosol flow rates). Therefore, all further valuesof εth,i presented in this study have been calculated from

εth,i = (εtot,i − εiso,i )/(1 − εiso,i ). [5]

Particle removal efficiencies representative for the investigatedsize range were calculated by concentration-weighted averaging,

εtot,avg =19∑

i=1

ci

cintεtot,i , [6]

εth,avg =19∑

i=1

ci

cintεth,i , [7]

where ci represents the particle number concentration per sizeclass averaged over the 12 consecutive SMPS measurements,



and cint is the particle number concentration integrated over theinvestigated size range.

A detailed mathematical model of particle deposition in thepipe bundle heat exchanger would require solving a complexset of differential equations describing fluid flow, heat trans-fer, and particle motion by extensive numerical calculations forevery relevant set of experimental conditions. To find a sim-ple semiempirical parameterization of deposition efficiency asa function of temperature and flow conditions, we tested theapplicability of the plate precipitator formula in Equation (2).

In Figure 8 the average total particle deposition efficienciesεtot,avg from all experiments are plotted against the dimensionless“precipitator number” (Lµ0�Tlog,mean)/(vx,0ρ0TH2

ch). µ0, vx,0

and ρ0 are the arithmetic mean values of the gas properties cal-culated for the temperatures of the aerosol flow at the inlet andoutlet of the heat exchanger (Th,in, Th,out), respectively. L and�Tlog,mean are the effective deposition length and logarithmicmean temperature difference as defined above. Hch is the char-acteristic distance for particle deposition along the temperaturegradient perpendicular to the gas flow. In a plate precipitator itis the distance between the hot and cold plates. For the minia-ture pipe bundle heat exchanger it was calculated as the arith-metic mean of vertical and horizontal half-distances between theouter surfaces of the cooling pipes: Hch = 0.25 · (0.51 mm +1.88 mm) = 0.60 mm (Figure 1). This is assumed to be a char-acteristic average for the varying distances between maximum

Figure 8. Total particle deposition efficiency εtot,avg plotted against the dimensionless precipitator number calculated from averageflow parameters, (Lµ0�Tlog,mean)/(v0ρ0T0 H 2

ch). The lines are linear least-squares fits to the data sets with different cooling air flowrates (5 l min−1 dotted; 10 l min−1 dashed). Error bars represent the standard deviation (±1 s.d.) of the averaged values εtot,i .

temperatures in the middle of the flow channels and minimumtemperatures at the cooling pipe surfaces.

For each of the investigated cooling air flow rates (5 L min−1

and 10 L min−1), εtot,avg exhibits a near-linear increase with theprecipitator number. The increase is steeper for the higher cool-ing air flow, but the linear least-squares fits to both measure-ment data sets intercept the y axis (�T = 0 K) at εtot ≈ 4%,which is consistent with the particle deposition observed underisothermal conditions averaged over all experiments (εiso,avg =4.5 ± 2.5%).

Figure 9 shows the average thermophoretic deposition effi-ciencies, εth,avg, plotted against the precipitator number. Again, anear-linear increase is observed for each of the cooling air flows.The linear least-squares fits intercept the y axis (�T = 0 K) atεth,avg ≈ 0, as expected for isothermal conditions. The slopesof the fit lines (0.42 and 0.34, respectively) are fairly close tothe value of 0.55, which can be observed in plate precipitatorsand equals the thermophoretic coefficient applicable for sootagglomerates in the investigated range of particle size and ex-perimental conditions (Tsai and Lu 1995; Messerer et al. 2003).

If the dimensionless precipitator numbers were calculatedwith characteristic distances of Hch,1

∗ = Hch sqrt (0.55/0.32) =0.79 mm and Hch,2

∗ = Hch sqrt (0.55/0.42) = 0.69 mm, whichare well within the range of different half-distances occurringbetween the outer surfaces of the cooling pipes in heat exchanger(0.26–0.94 mm), the slopes of the linear least-squares fit would



Figure 9. Thermophoretic particle deposition efficiency εth,avg plotted against the dimensionless precipitator number calculatedfrom average flow parameters, (Lµ0�Tlog,mean)/(v0ρ0T0 H 2

ch). The lines are linear least-squares fits to the data sets with differentcooling air flow rates (5 l min−1 dotted; 10 l min−1 dashed) and the theoretical relation for a plate precipitator (solid). Error barsrepresent the standard deviation (±1 s.d.) of the averaged values εth,i .

Figure 10. Thermophoretic particle deposition efficiency εth,i plotted against the dimensionless precipitator number calculatedfrom effective flow parameters at the hot inlet, (L∗µh,in�Th,in)/(vh,inρh,inTh,in H 2

ch). The line is the theoretical relation for a plateprecipitator. Error bars represent the standard deviation (±1 s.d.) of the averaged values εth,i .



be identical to Kth ≈ 0.55. The results confirm that plate pre-cipitator formula can be regarded as a physically reasonableand a consistent basis for simple semiempirical parameteriza-tions of εth,avg as a function of temperature and flow conditionsin miniature pipebundle heat exchangers. For a given geome-try and cooling gas flow the characteristic distance, H∗

ch canbe determined from a few measurements and used to estimatedeposition efficiencies for varying thermal conditions.

To investigate the influence of deposited soot on the depo-sition efficiency, experiment Ic was extended over a time spanof 13 h. εtot,avg was near-constant at (37 ± 1)%. After the long-term experiment the isothermal deposition efficiencies εiso,i werefound to be 5–10% higher than at the beginning. Apparentlythe deposited soot led to enhanced nonthermophoretic deposi-tion and reduced the contribution of thermophoresis, while theoverall deposition efficiency remained near-constant. Substan-tial blackening of the heat exchanger tubes was observed uponvisual inspection after the long-term experiment. The blacken-ing was most intense at the beginning of the heat exchanger andstrongly decreased along the flow direction, indicating that theparticle removal was dominated by deposition over the first fewcentimeters of the heat exchanger, where the highest temperaturegradients and thermophoretic forces occur.

The dominant influence of the conditions at the aerosol inletwas confirmed by test calculations in which the inlet temperatureand flow parameters (�Th,in, µh,in, vx,h,in, Th,in) instead of theaverage parameters (�Th,0, µh,0, vx,h,0, Th,0) and an effectivedeposition length L∗ = 0.1 · L = 30 mm were inserted inEquation (2). The assumption L∗ = 0.1 · L = 30 mm is basedon observed deposition patterns and is consistent with basictemperature profile calculations. With these parameters the datapoints plotted against the precipitator number converged towardsthe theoretical line for a simple plate precipitator with Kth ≈ 0.55(Figure 10).

CONCLUSIONSThe results of this study demonstrate the applicability of

miniature pipe-bundle heat exchangers for efficient particle de-position under typical combustion exhaust conditions. At aerosolinlet temperatures of 390–510 K, flow velocities of 1–4 m s−1,and cooling air inlet temperatures around 300 K, deposition ef-ficiencies of up to 45% have been achieved for submicrometerspark discharge soot aerosol particles.

Thermophoresis was the dominating particle depositionmechanism, and its decoupling from isothermal mechanismswas consistent with the assumption of independently acting pro-cesses (Brockmann 2001).

Simple parameterizations derived from plate-precipitator the-ory and experiments (Tsai and Lu 1995; Messerer et al. 2003)were found to be suitable for the description of particle deposi-tion efficiencies as a function of inlet temperatures, flow rates,and geometric parameters without solving the complex set ofdifferential equations describing fluid flow, heat transfer, andparticle motion in the pipe-bundle heat exchanger.

Overall, the results of our study confirm the high potential ofminiature pipe bundle heat exchangers for combustion exhausttreatment systems combining efficient heat recovery and aerosolparticle deposition.

NOMENCLATUREAHE Cross-sectional area of heat exchanger (m2)cp Particle number concentration (cm−3)dp Particle diameter (nm)Dh Hydraulic diameter,4AHE/PHE

fiso,th Coupling term of deposition mechanismsHch Characteristic distance (m)H∗

ch Modified characteristic distance (m)HP Plate distance (m)Kn Knudsen number, 2λ/dp

Kth Thermophoretic coefficientL Deposition length (m)L∗ Modified deposition length (m)PHE Perimeter of heat exchanger (m)Re Heat exchanger Reynolds number, vh,0 Dhρg,h,0/

µg,h,0

T Gas temperature (K)Tp Particle temperature (K)vth Thermophoretic velocity (m s−1)vx Axial velocity (m s−1)

Greek Letttersεiso Isothermal particle depositionεth Thermophoretic particle deposition efficiencyεtot Measured particle deposition efficiency�Tlog,mean Mean logarithmic temperature difference (K)λ Mean free path of gas molecules (m)µ Dynamic viscosity of the gas (kg m−1 s−1)ρg Density of the gas (kg m−3)∇T Temperature gradient in the heat exchanger

(K m−1)

Additional Subscriptsi Particle size classavg Weighted average over particle spectrum0 Arithmetic mean of inlet and outlet aerosol proper-

tiesh Hot aerosolc Cooling air

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