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Building and Environment 46 (2011) 1292e1302

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Building and Environment

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A virtual supply airflow rate meter for rooftop air-conditioning units

Daihong Yu*, Haorong Li, Mo YangDepartment of Architectural Engineering, University of Nebraska-Lincoln, PKI Room 245 1110 S, 67th Street, Omaha, NE 68182, United States

a r t i c l e i n f o

Article history:Received 18 August 2010Received in revised form14 December 2010Accepted 14 December 2010

Keywords:Virtual sensing technologyVirtual calibration methodologyRooftop air-conditioning unitsAirflow rateFault detection and diagnosis

* Corresponding author. Tel.: þ1 402 554 2074.E-mail addresses: dyu@mail.unomaha.edu, daisy.y

0360-1323/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.buildenv.2010.12.017

a b s t r a c t

A proper amount of supply airflow is critical in all kinds of air-based HVAC systems to maintain desiredcontrol effectiveness, energy efficiency and indoor air quality (IAQ). Although knowledge of supply airflowrate (SCFM) is certainly very important, measuring andmonitoring SCFM in rooftop air-conditioning units(RTUs) by using the conventional SCFMmetering devices are very costly and more than often problematic.This paper proposes a low-cost but accurate virtual SCFM meter to solve the dilemma for RTUs. The SCFMvalues are indirectly derived from a first-principle model in combination with accurate measurements oflow-cost virtual or virtually calibrated temperature sensors. Modeling, uncertainty analysis and experi-mental evaluation through a wide range of laboratory testing for both cooling- and heating-basedapproaches are performed respectively in the development. The study reveals that the heating-basedmethod surpasses the other in terms of its simplicity, accuracy (uncertainty is �6.9% vs �13.8%) andreliability and is chosen to be the virtual SCFM meter in RTUs. This cost-effective application is promisingwith a number ofmerits, such as easy to implement, economical for use, and generic in RTUswith the sameconstructed gas furnaces. For applications, it could be applied as a permanently installedmonitoring tool toindicate the SCFM and/or to automatically detect and diagnose improper quantity of SCFM for RTUs.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

RTUs are widely used for air-conditioning retail, residential andindustrial premises, covering from small to medium sizes of spaces.The U.S. Department of Energy estimates that RTUs includingunitary air-conditioning equipments account for about 1.66 quadsof total energy consumption for commercial buildings in the UnitedStates [1]. Knowledge of SCFM through RTUs is certainly of greatimportance for a number of reasons. For instance, low SCFMdirectly impairs temperature distribution and causes poor IAQ.ASHRAE standard 62.1-2007 [2] specifies ventilation and circula-tion airflow rate based on the occupancy and floor area. In somecases, low SCFM across the RTUs makes the heating equipment torun on the high temperature limit, leading to intensive heatingcycling and energy losses.

In the last two decades, a number of studies have focused onfinding good solutions for measuring SCFM [3e10]. In terms ofphysical airflow measuring and monitoring devices, the mostpopular techniques are based on air dynamic pressure measure-ments by using a pitot traverse or on air velocity by vane anemom-eter. However, in general

u926@gmail.com (D. Yu).

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� A physical airflow monitoring meter (PAFM) is fragile

The main disadvantage of PAFM is its flimsy reliability. Period-ical calibration is required but rarely followed in real applications.Credibility of measurements would be compromised dramaticallyafter long-term use in adverse duct work surroundings.

� Implementing and maintaining a PAFM are expensive

PAFMs are costly in the regards of procurement and installation,ranging from hundreds to thousands dollars. Much more expensesemerge along for maintenance, repair or rebuild, due to the hostileoperating environment.

� Additional pressure loss is incurred

In order to get accurate measurement, a high air velocity acrossthe instrument is desired for a spread of different airflow rate. Toachieve this, a piece of duct work is throttled and it causes addi-tional pressure loss to the fan.

Besides, installing PAFMs in RTUs is even more unrealistic,

� It is hard to install a PAFM in RTUs.

RTUs usually have compact structure and duct work. The orig-inally efficient configuration leaves barely any space for a physical

Nomenclature

A area, ft2 (m2)C capacity rate, Btu/(h �F) (kW/K) or specific heat, Btu/

(lbm �F) (kJ/(kg K))Cmin the smaller of Cg and Ca, Btu/(h �F) (kW/K)Cmax the bigger of Cg and Ca, Btu/(h �F) (kW/K)Cr a capacity ratio as Cmin/Cmax

D duct diameter, in (m)e offset error, �F (�C) or relative erroreC,eva relative error between _VC;meas and _VC;model in cooling

modeeH,eva relative error between _VH;meas and _VH;model in heating

modeh heat transfer coefficient, Btu/(h ft2 �F) (kW/(m2 K))h1 enthalpy of air before the thermal equipment Btu/lbm

(kJ/kg)h2 enthalpy of air after the thermal equipment Btu/lbm

(kJ/kg)k thermal conductivity, Btu/h ft �F (kW/(mK))L duct length, ft (m)_m mass flow rate, lbm/h (kg/s)MAT mixed air temperature, �F (�C)MATwb

0 critical point of the mixed air wet bulb temperature, �F(�C)

MOAT measurement of the manufacturer-installed OATsensor, �F (�C)

MRAT measurement of the manufacturer-installed RATsensor, �F (�C)

MSAT measurement of the manufacturer-installed SATsensor, �F (�C)

NTU number of transfer unitsNu Nusselt numberOADst outside air damper positionOAT ambient temperature or outside air temperature, �F

(�C)Pr Prandtl number_Q rate of heat flow, Btu/h (kJ/s)RAT return air temperature, �F (�C)Re duct Reynolds numberSAT supply air temperature, �F (�C)T temperature, �F (�C)U heat transfer coefficient, Btu/(h �F ft2) (kW/(m2 K))

v specific volume of air, ft3/lbm (m3/kg), kinematicviscosity, ft2/s (m2/s)

V linear velocity, ft/s (m/s)_V supply airflow rate, cfm (m3/s)DTfan supply fan temperature rise, �F (�C)

Greek symbolsb outside fresh air ratio3 heat exchanger effectivenessm absolute viscosity, lbm/ft s (N s/m2)r density, lbm/ft3 (kg/m3)

Subscriptsa airC coolingcal calibrationd designeva evaluationfan supply air fang flue gasH heatingi inletmax maximummeas measuredmfr manufacturermin minimumO outletP constant pressurer ratiosens sensiblevir virtualwb wet bulb

AbbreviationsCAV constant air volumeDX direct expansionFDD fault detection and diagnosesHstage heating stage statusHVAC heating, ventilation and air-conditioningIAQ indoor air qualityPAFM physical airflow meterRTU rooftop air-conditioning unitsSCFM supply airflow rateSHR sensible heat ratio

D. Yu et al. / Building and Environment 46 (2011) 1292e1302 1293

meter. PAFMs require more space than is available to measure thetrue value of SCFM.

� Relative price of PAFMs over RTUs is high

The majority of light commercial RTUs fall in the range of 5e15tons of cooling capacity and only cost several thousand dollars.However, a decent airflow station plus installation could cost up toone thousand dollars per unit and eat up the cost advantage ofRTUs.

Despite the importance of SCFM, it is tough to justify installationof PAFMs in RTUs. To beat the costly and vulnerable PAFMs, a low-cost but accurate virtual SCFM meter is highly needed to solve thedilemma for RTUs. In fact, the SCFM values by indirectly usingequipment capacity in combination with temperature changeacross equipment (an energy balance) has been of great concernover the past decades [11]. However, this method is known to beproblematic. For gas furnaces, erratic temperature measurement

errors in the supply plenum exist due to non-uniform temperaturedistribution and intensive thermal radiation, with the resultingestimate of SCFM having a big potential spread [12,13]. Instead, thispaper describes the virtual SCFM meter which utilizes newly dev-eloped low-cost virtual or virtually calibrated temperature sensorsto access accurate SCFM values. The primary merit of the proposedvirtual SCFM meter is its cost-effectiveness and long-standingaccuracy and stability.

By definition, a virtual sensor uses low-cost measurements andmathematical models to estimate a difficult to measure or expen-sive or new quantity [14]. Virtual sensors have been widely dev-eloped and applied in other fields within the past two decades andhave enabled many intelligent features that would otherwise notbe possible or economical [15e23]. Recently, in buildings, Li andBraun [24,25] proposed about ten virtual sensors for a vaporcompression cycle equipment in order to reduce the cost ofimplementation and systematically improve the real-time moni-toring, control and diagnosis of the system.

D. Yu et al. / Building and Environment 46 (2011) 1292e13021294

Utilizing the virtual SCFM meter as an innovative automatedFDD application to enhance the real-time monitoring, control anddiagnosis of RTUs is promising. Badly maintained, degraded, andimproperly controlled equipment wastes about 15e30% of energyused in commercial buildings [26]. Based on economic evaluations[27] by applying the automated FDD technique for RTUs to anumber of California sites, significant savings: around 70% of theoriginal service cost savings and $5e$51/kW$year operating costsavings, were observed. What is more, the payback period of theautomated FDD technique mainly derived from low-cost temper-ature sensors is less than one year [24,28].

The study is organized as follows: the basic mechanism ofa virtual SCFM meter is briefly described at first. Modeling, uncer-tainty analysis and experimental evaluation are then systematicallyconducted for both cooling- and heating-based approaches byusing a wide span of laboratory testing data. Comparisons of thetwo approaches are made based on the involved measurementsand calculations. It reveals that the latter one excels the former onein several aspects. After that, detailed implementation issuesincorporating measuring and processing the parameters and agraphical implementation flowchart of the heating-based virtualSCFM meter are provided. The study concludes that the non-intrusive virtual SCFM meter can accurately predict the SCFM forRTUs with high robustness.

2. Development of a virtual SCFM meter

The supply airflow in RTUs accompanies energy transmissionfrom thermal components to the air. According to ASHRAE hand-book of fundamental 2009 [29], for a typical air-conditioningprocess shown in Fig. 1, an energy balance exists across an air-handling unit in steady-flow conditions:

_Q ¼ _mðh2 � h1Þ (1)

where _Q ¼ rate of heat flow in Btu/h (kJ/s), _m ¼ mass flow ratein lbm/h (kg/s), h1, h2¼ enthalpy of air before and after the thermalequipment in Btu/lbm (kJ/kg).

With constant specific volume of conditioned air, SCFM can becalculated out based on the mass flow rate:

_V ¼ _mv (2)

where _V ¼ supply airflow rate in cfm (m3/s), v¼ specific volumeof air in ft3/lbm (m3/kg).

By combining Eqs. (1) and (2), the value of SCFM can be obtainedas,

_V ¼_Q

h2 � h1v (3)

To avoid using expensive measurements such as relativehumidity, only sensible capacity across the cooling or heating coil isadopted in the development of a virtual SCFM meter. Eq. (3) thuscan be represented by and a virtual SCFM meter prototype isobtained as,

Fig. 1. Typical air-conditioning process.

_V ¼_Q sens

Cp � jSAT�MATj v (4)

where _Q sens ¼ sensible capacity in Btu/h (kJ/s), SAT¼ supply airtemperature in �F (�C), and MAT¼mixed air temperature in �F (�C)

For a typical RTU, cooling and heating are two opposite energytransmissions related to SCFM and air status change. Accordingly,there are two approaches (cooling mode- and heating mode-basedapproaches) to obtain the sensible capacity in Eq. (4). The reliablevalues of _Q sens, which may involve other implicit variables, andSAT, MAT are needed in the cooling or heating process to make thevirtual SCFM meter work.

The remaining challenge is to evaluate the two candidates(cooling mode- and heating mode-based approaches) and developan implementation method which satisfies the following featuresof a feasible virtual SCFM meter: (1) using a simple while reliablemechanism; (2) characteristic of small uncertainty and robust againstfaults; (3) easy-to-obtain parameters or measurements.

Without the presence of simultaneous cooling and heating,individual cooling mode- and heating mode-based approaches arestudied in the next two subsections. The inputs and basic mea-surements are verified and adopted from the referred literature. Thecritical measurements are reiterated in detail in the section ofimplementation issues.

2.1. Modeling and evaluation of cooling-based approach

2.1.1. Modeling of cooling-based approachTo simplify the analysis of air-conditioning components and

reduce the cost for model implementation in practice, certainstudies have attempted to develop generic models by using ratingdata from manufacturers. For example, a general model of adj-ustable throat-area expansion valves [30], was derived by emp-loying manufacturers’ data. Yang and Li [31] proposed a genericrating-data-based direct-expansion (DX) coil model with fourparameters (mixed air wet bulb temperature MATwb, MAT, outsideair temperature OAT and SCFM). Since this generic DX coil modelas shown in Eq. (5) has been demonstrated to be very simple andaccurate, it is utilized in this study for obtaining the coolingcapacity.

where _QC is the gross cooling capacity in Btu/h (kJ/s), _QC;sens isgross sensible cooling capacity in Btu/h (kJ/s), _VC is supply airflowrate in cooling mode in Btu/h (kJ/s), SHR is sensible heat ratio,MATwb

0 is critical point of the mixed air wet bulb temperature in �F(�C) [31].

The model can be rearranged as one expression for the grosssensible cooling capacity:

_QC;sens ¼ _QC � SHR ¼ f�OAT;MAT;MATwb;

_VC�

(6)

Besides, considering the effect of supply fan heat loss in coolingmode, the energy balance expressed in Eq. (4) can be reduced to

Fig. 2. Illustration of machine layout in the lab [12].

D. Yu et al. / Building and Environment 46 (2011) 1292e1302 1295

_VC ¼_QC;sens

Cp ��MATþ DTfan � SAT

�v (7)

where ΔTfan¼ supply fan temperature rise in �F (�C).By combining Eq. (6) and Eq. (7), the cooling-based approach

formulation for a virtual SCFM meter can be expressed as

_VC;model ¼ f�OAT;MAT;MATwb; SAT;DTfan

�(8)

Observed from Eq. (8), to develop a cooling-based SCFM meter_VC;model, four dry bulb temperatures (OAT, MAT, SAT, ΔTfan) and onewet bulb temperature (MATwb) should be used.

2.1.2. Evaluation of cooling-based SCFM meter2.1.2.1. Experiment preparation of cooling-based SCFM meter

2.1.2.1.1. System description. Experiments for evaluating thecooling-base virtual SCFM meter were performed in a 7.5 ton RTUequipped with two constant speed compressors in an environ-mental chamber. Cited Fig. 2 illustrates the basic setting [12] inthe lab. The nominal supply airflow rate is 2400 cfm (1.13 m3/s)with standard speed option. Together with another RTU outside ofthe building, artificial indoor and outdoor air physical conditionscan be created and maintained.

2.1.2.1.2. Experimental designs. Data used for evaluation hereare adopted from the study by Yang and Li [31]. About 110 sets oftests plotted in Fig. 3 were performed with OADst at 30%, coolingrunning stage at 2, and a wide span of OAT (70.0e110.0 �F[21.1e43.3 �C]) and measured SCFM _Vmeas (about 1800e2600 cfm[0.76e1.23 m3/s]) to cover the most real operation combinations.Each test was conducted around 20 min preparation, followed by10e15 min steady-status data. Average readings of each test werecollected and utilized in the evaluation. All temperature sensorshave been tuned within �1.0 �F (0.6 �C) accuracy in the lab.

2.1.2.1.3. Experimental results. The involved direct measure-ments and indirect results for evaluating the cooling-based SCFMmeter are elaborated below.

Fig. 3. Experimental settings in the cooling mode.

� Direct measurements

Outside air temperature (OAT). It is found, the manufacturer-preinstalled OAT (MOAT) sensor in Fig. 4 is fixed beside the evap-orator coils, and themeasurements are not reliable due to improperheat gain and poor temperature distribution. To supplement it foran accurate OAT, another air temperature sensor with �0.1 �F(0.6 �C) uncertainty is mounted at the RTU outside air inlet (Fig. 4).In this experiment, average reading of the lab-installed OAT sensorinstead of MOAT sensor is used.

Supply air temperature (SAT). Based on the study by Yu et al.[12], an manufacturer-preinstalled SAT (MSAT) sensor (Fig. 4) inRTUs could predict the true values in cooling mode. Therefore,average reading of the MSAT sensor with �0.1 �F (0.6 �C) uncer-tainty is adopted here.

Return air temperature (RAT). In order to calculate MAT accu-rately, obtaining the true value of RAT is also important. In the lab,a RAT sensor with �0.1 �F (0.6 �C) uncertainty installed right atthe return air duct outlet (Fig. 4) is utilized to verify the accuracy ofthe manufacturer-preinstalled RAT (MRAT) sensor. And in the case,average reading of the lab-installed RAT sensor is proved trustableand then used.

Outside air relative humidity (OARH), zone air relativehumidity (ZARH) and zone air temperature (ZAT). Besides, in anattempt to calculate the parameter of MATwb, average readings oflab-installed OARH sensor in the outdoor chamber (Fig. 2), ZARHand ZAT sensors in the indoor chamber are collected accordingly.

Measured SCFM ( _Vmeas). An airflow station offering �1% fullscale accuracy is permanently mounted in supply air duct in thelab. The airflow stationwas calibrated by themanufacturer before itwas installed. It serves as the airflow reference _Vmeas in this study.

� Indirect results

Virtual mixed air temperature (MATvir). Since there is no pre-installed physical MAT sensor available in our study, we adoptedthe method proposed by Yang and Li [32] with an acceptableuncertainty of �1.0 �F (0.6 �C). The specific details are provided inthe Section 3.1.2 about measuring and processing MAT.

Fig. 4. Lab sensors’ layout.

Table 1Uncertainty analysis of cooling-based SCFM meter.

Variables Inputs Output

OAT,�F (�C)

MATvir,�F (�C)

MATwb,vir,�F (�C)

SAT,�F (�C)

ΔTfan,�F (�C)

_VC;model

Uncertainty �1.0 (0.6) �1.0 (0.6) �1.0 (0.6) �1.0 (0.6) �0.2 (0.1) �13.8%

Table 2Experimental evaluation of cooling-based SCFM meter.

eC,eva Maximum Minimum Absolute average Standard deviation

16.4% �16.2% 7.8% 8.9%

D. Yu et al. / Building and Environment 46 (2011) 1292e13021296

Virtual mixed air wet bulb temperature (MATwb,vir). Sincemixed air wet bulb temperature could not be metered directly, anmass balance equation by using the direct measurements ofOAT, OARH, ZAT, ZARH and a correlated virtual outside air ratiosensor b [32] is computed to obtain the values, namely, MATwb,virwith an uncertainty of �1.0 �F (0.6 �C) in this study.

Supply fan temperature rise (ΔΔTfan). Additionally, the supplyfan temperature rise ΔTfan is calculated using the heat loss from thefan and checked with actual measurements using the methodpresented by Wichman and Braun [33] under conditions whereneither mechanical cooling nor heating is operating. The result ofit in the lab is 1.7 �F (0.9 �C) with an uncertainty of �0.2 �F (0.1 �C).Since it is a CAV RTU, the uncertainty of the fan temperature riseis relatively small.

Based on the experimental results acquired from the extensivelaboratory testing, uncertainty analysis is thereby performed atthe first place and then experimental evaluation is conducted toevaluate the effectiveness of the cooling-based approach.

2.1.2.2. Uncertainty analysis of cooling-based SCFM meter. The rootsum square method of uncertainty calculation is applied to thevariables of OAT, MATvir, MATwb,vir, SAT and ΔTfan. The randomuncertainty is expressed as Eq. (9):

d _VC;model ¼"�

v _VvOAT

dOAT�2

þ�

v _VvMATvir

dMATvir

�2

þ

v _VvMATwb;vir

dMATwb;vir

!2

þ�

v _VvSAT

dSAT�2

þ

v _VvDTfan

dDTfan

!2#1=2(9)

Fig. 5. Heat transfer of a heat exchanger.

Where dOAT, dMATvir, dMATwb,vir, dSAT and dΔTfan are inputsuncertainties.

The 110 sets of extensive laboratory tests for a 7.5 ton RTU incooling mode collected by Yang and Li [31] are used in the analysis.Table 1 summarizes the uncertainties of independent variables asinputs, as well as the calculated uncertainties of _VC;model as outputs.Uncertainties of temperature measurements are �1.0 �F (0.6 �C). Itis found that, due to the complex cooling process and multiplevariables, the absolute uncertainty of _VC;model can be up to 13.8%.

In field applications, the best practice of a physical airflowmetercould have a theoretical accuracy close to �1%, but the actualuncertainty of the meter might be enlarged to some extent, owingto a variety of practical factors, such as uneven air distribution,gradual drifting, faulty installation, or adverse duct worksurroundings. In general,�10% uncertainty of airflowmeasurementcan be regarded good for most thermal control applications inHVAC, while a better uncertainty is always desired. The uncertainty(�13.8%) of a cooling-based virtual SCFM meter is slightly high.

2.1.2.3. Experimental evaluation of cooling-based SCFM meter.Direct SCFM measurements acquired from the 110 sets of coolingtests [31] are also used to evaluate the accuracy of the cooling-based SCFM meter. The relative error eC,eva between the measuredSCFM _Vmeas and _VC;model is defined as follows,

eC;eva ¼_VC;model � _Vmeas

_Vmeas(10)

In Table 2, results show that the maximum relative error is ashigh as 16.4%, and theminimum low to�16.2%. Absolute average ofthese errors is 7.8% with a standard deviation 8.9%. It can be seenthat these actual errors are a little bit higher than those valuesobtained from prior uncertainty analysis, which is fully anticipated,because in the prior uncertainty analysis, the uncertainty fromthe model regression of gross sensible cooling capacity in Eq. (5)which is about 5% [31], was not considered. These factors lead tocertain difficulty (complex cooling process and multiple variables)and slight inaccuracy (uncertainty is �13.8% and relative erroris �16.2 to 16.4%) in developing the virtual SCFM meter for coolingmode.

2.2. Modeling and evaluation of heating-based approach

In heating mode, gas burnt in furnace transmits heat intoconditioned air and causes air temperature to increase. An obviousadvantage of utilizing heating energy transmission is that theprocess generally doesn’t have mass transfer involved across thefurnace. The measurement of conditioned air energy change reliespurely on the air dry bulb temperature. The modeling and evalua-tion of heating-based approach are explored in the followingsubsections.

2.2.1. Modeling of heating-based approachReferring to ASHRAE handbook of fundamental 2009 Chapter 4

[29], for heat exchangers, to calculate the heating transfer rate,mean temperature difference analysis and number of transfer units

D. Yu et al. / Building and Environment 46 (2011) 1292e1302 1297

(NTU)-effectiveness (3) analysis are used. The former methodinvolves trial-and-error calculations unless inlet and outlet fluidtemperatures are known for both fluids. NTU-3 method is adoptedin the study.

Fig. 5 shows the configuration of a counterflow heat exchanger.Ti,a and To,a are the air temperature at the inlet and outlet of heatexchanger respectively. Ti,g and To,g are the flue gas temperatures ofinlet and outlet of heat exchanger. The maximum possible heattransfer rate _QH;max occurs when the hot fluid enters at Ti,g andleaves at the entering temperature of the cold fluid Ti,a:

_QH;max ¼ Cmin � �Ti;g � Ti;a�

(11)

where Cmin¼min(Cg,Ca), Cmax¼max(Cg,Ca), wherein Cg½ð _m� CPÞg�and Ca½ð _m� CPÞa� are fluid capacity rates, Btu/(hr F) (kW/K).

The actual heating capacity _QH can be calculated as:

_QH ¼ _QH;max � 3 ¼_QH;d

3d� 3 (12)

According to NTU-3 method, in a counterflow heater, 3 isdetermined by,

3 ¼ 1� exp½ � NTUð1� CrÞ�1� Cr � exp½ �NTUð1� CrÞ� ðCr < 1Þ (13)

where Cr¼ Cmin/Cmax as a capacity ratio.Therefore, by combining Eqs. (12) and (13), _QH can be expressed

as,

Table 3Calculation of NTU of a heat exchanger [29].

Symbo

A¼ area, ft2 (m2)C¼ heat air capacity rate, Btu/(h �F) (kW/K)D¼ duct diameter, in (m)h¼ heat transfer coefficient, Btu/(h ft2 �F) (kW/(m2 K))k¼ thermal conductivity, Btu/(h ft �F) (kW/(mK))L¼ duct length, ft (m)NTU¼ number of transfer unitsNu¼Nusselt number

_QH ¼_QH;d

3d� 1� exp½ � NTUð1� CrÞ�1� Cr � exp½ �NTUð1� CrÞ� (14)

Observed from Eq. (14), the intermediate variables Cr and NTUare required to make _QH work. The following four steps are thusneeded in order to analyze the heating capacity and capture theheating-based virtual SCFM meter. Data from a 7.5 ton RTU isadopted for illustration purposes.

2.2.1.1. Step 1: determination of Cr. To determine Cr, the knowns andassumptions are listed below:

� The design heating capacity and design heat exchanger effec-tiveness are: _QH;d ¼ 130;000 Btu=h (38.1 kW); 3d¼ 80%.

� The design airflow rate and design flue gas flow rate are:_Va;d ¼ 144;000 ft3=h (2400 cfm; 1.13 m3/s), _Vg ¼ 1800 ft3=h(30.0 cfm; 0.014 m3/s).

� The density and specific heat of air are: ra¼ 0.070 lb/ft3

(1.200 kg/m3); CP,a¼ 0.240 Btu/(lbm �F) (1.005 kJ/(kg K)).� It is a sufficient combustion process in the gas furnaces. Thedensity and specific heat of flue gas are: rg¼ 0.077 lb/ft3

(1.240 kg/m3); CP,g¼ 0.295 Btu/(lbm �F) (1.230 kJ/(kg K)).

Since with similar specific heat on both sides the flow rate onthe air side is several degrees of magnitude higher than that on theflue gas side, Cg� Ca, then according to Cmin and Cmax definition,we have Cmin equals Cg and Cmax equals Ca.

ls

Pr¼ Prandtl numberRe¼ duct Reynolds numberU¼ heat transfer coefficient, Btu/(h �F ft2) (kW/(m2 K))v¼ kinematic viscosity, ft2/s(m2/s)V¼ linear velocity, ft/s(m/s)_V ¼ flow rate, ft3/s (m3/s)r¼ density, lbm/ft3(kg/m3)m¼ absolute viscosity, lbm/ft s ((N s)/m2)

D. Yu et al. / Building and Environment 46 (2011) 1292e13021298

(1) Cmin¼ Cg. With flue gas flow rate known, the value of Cg can beobtained as,

Cg ¼ rg � CP;g � _Vg (15)

In this case, Cg is 40.36 Btu/(h �F) (0.021 kW/K) as calculated.

(2) Cmax¼ Ca. With design airflow rate known, Ca can be derivedfrom Eq. (16):

Ca ¼ ra � CP;a � _Va;d (16)

The result is Ca¼ 2419 Btu/(h �F) (1.423 kW/K) under designconditions.

Since Ca is significantly greater than Cg, the assumption holdsfor wide range airflow rate and we have,

Cr ¼ CminCmax

¼ CgCa

(17)

2.2.1.2. Step 2: correlating NTU. As shown in Table 3, based onASHRAE handbook of fundamental 2009 [29], with the knowns of_Va and _Vg, the NTU of a heat exchanger can be applied throughEqs. (18)e(27).

2.2.1.3. Step 3: obtaining _QH. With the intermediate parametersCr(Cg,Ca) and NTU obtained, for different operations, _QH then can becalculated through Eq. (14). However, observed from the calcula-tion of Cg (Eq. (15)), Ca (Eq. (16)) and NTU, it is found that _QH isessentially derived from and mainly effected by two parameters,the air side flow rate _Va and the flue gas flow rate _Vg. Therefore,fundamentally, we determine the _QH as Eq. (28) in this study,

_QH ¼ f�_Va; _Vg

�(28)

2.2.1.4. Step 4: modeling heating-based virtual SCFM meter_VH;model. Besides, considering the effect of supply fan heat loss inheating mode and no moisture related mass change in the air, theenergy balance expressed in Eq. (3) can be reduced to Eq. (29) inheating mode,

_VH ¼_QH

CP ��SAT�MAT� DTfan

� v (29)

Table 4Experimental designs and results of heating-based SCFM meter.

Scenario ID Running mode Hstage OADst OAT, �F (�C) RAT, �F (�

H-1 Heating 2 0% 36.0(2.2) 59.1(15.1H-2 Heating 2 0% 42.9(6.1) 63.9(17.7H-3 Heating 2 0% 44.1(6.7) 58.4(14.7H-4 Heating 2 0% 50.0(10.0) 59.4(15.2H-5 Heating 2 30% 34.4(1.3) 55.5(13.1H-6 Heating 2 30% 44.3(6.8) 60.7(15.9H-7 Heating 2 30% 43.3(6.3) 57.0(13.9H-8 Heating 2 30% 49.1(9.5) 58.6(14.8H-9 Heating 1 0% 35.6(2.0) 65.6(18.7H-10 Heating 1 0% 45.9(7.7) 65.0(18.3H-11 Heating 1 0% 44.4(6.9) 65.3(18.5H-12 Heating 1 0% 49.2(9.6) 65.6(18.7H-13 Heating 1 30% 34.1(1.2) 63.1(17.3H-14 Heating 1 30% 42.9(6.1) 62.9(17.2H-15 Heating 1 30% 43.1(6.2) 63.8(17.7H-16 Heating 1 30% 48.4(9.1) 64.4(18.0

Combining Eqs. (28) and (29), we could formulate the heating-based SCFM meter as follows,

_VH;model ¼ f�_Vg;DTfan; SAT;MAT

�(30)

It can be seen from Eq. (30) that the heating-based approachrequires reliable values of _Vg and three air temperature inputs toget SCFM, wherein _Vg and DTfan are nearly constant. _Vg possessesa low uncertainty of �1% because the natural gas regulator holdsa high accuracy of pressure control [29]. DTfan has also a lowuncertainty of �0.2 �F (0.1 �C) in a constant air volume (CAV) RTU[12]. Therefore, the uncertainty of _VH;model is mainly determined bythe uncertainty of two temperature measurements (SAT and MAT).

2.2.2. Evaluations of heating-based SCFM meter2.2.2.1. Experiment preparation of heating-based SCFM meter

2.2.2.1.1. System description. Experiments for evaluating theheating-base virtual SCFMmeterwere also performed in the 7.5 tonRTU in Fig. 2 equipped with two-stage gas heating. The design totalheating capacity is 130,000 Btu/h (38.1 kW) and the first stage is84,500 Btu/h (24.8 kW).

2.2.2.1.2. Experimental designs. Data used for evaluation hereare adopted from the study by Yu et al. [12]. Table 4 collectsexperimental configurations and results. Sixteen tests named withdifferent scenario ID were performed with different heatingrunning stages (1 and 2), OADst (0% and 30%), a wide span of OAT(34.1e50.0 �F [1.3e10.0 �C]) and measured SCFM (1829e2272 cfm[0.86e1.07 m3/s]) to cover the most real operation combinations.Similarly to the cooling mode, each test was conducted around20 min preparation, followed by 10e15 min steady-status data.Average readings of each test were collected and utilized in theevaluation. All temperature sensors have been tunedwithin�1.0 �F(0.6 �C) accuracy.

2.2.2.1.3. Experimental results. Experimental results for evalu-ating the heating-based virtual SCFMmeter are collected in Table 4respectively. The methods to obtain the direct measurements (OAT,RAT, and _Vmeas) and the indirect results (MATvir and ΔTfan) are thesame as the cooling mode, excepting the SAT values:

Calibrated MSAT (SATmfr,cal). Based on the study by Yu et al.[12], direct measurements of an MSAT sensor are incorrect inheating mode with gas furnaces equipped in RTUs. There existunacceptable erratic measurement errors (e.g., in a 7.5 ton RTU, theerrors are from 1.0 �F [0.6 �C] to 12.6 �F [7.0 �C]) due to severetemperature stratification and high thermal radiation. The tradi-tional calibration method can hardly overcome the defect. Themethodology of virtual calibration of an MSAT sensor is innovated

C) _Vmeas, cfm (m3/s) SAT, �F(�C) SATmfr,cal, �F(�C) MATvir, �F(�C)

) 1848(0.87) 120.1(48.9) 108.0(42.2) 54.2(12.3)) 2045(0.97) 120.0(48.9) 108.3(42.4) 59.5(15.3)) 1857(0.88) 121.5(49.7) 108.9(42.7) 55.4(13.0)) 1829(0.86) 124.0(51.1) 111.8(44.3) 57.4(14.1)) 2076(0.98) 99.9(37.7) 93.0(33.9) 44.9(7.2)) 2269(1.07) 104.5(40.3) 96.7(35.9) 52.5(11.4)) 2037(0.96) 106.1(41.2) 99.2(37.3) 50.2(10.1)) 2040(0.96) 109.9(43.3) 102.7(39.3) 53.8(12.1)) 1853(0.87) 99.4(37.4) 94.7(34.8) 59.3(15.2)) 2051(0.97) 98.1(36.7) 93.2(34.0) 61.0(16.1)) 1849(0.87) 100.8(38.2) 96.4(35.8) 60.9(16.1)) 1831(0.86) 102.6(39.2) 99.6(37.6) 63.7(17.6)) 2081(0.98) 82.6(28.1) 80.4(26.9) 48.6(9.2)) 2272(1.07) 83.2(28.4) 82.1(27.8) 52.9(11.6)) 2059(0.97) 87.5(38.3) 85.5(29.7) 53.4(11.9)) 2046(0.97) 90.8(32.7) 88.7(31.5) 56.4(13.6)

Table 5Uncertainty analysis of heating-based SCFM meter.

Independent variables Inputs Uncertainty

Flue gas flow rate, _Vg,cfm (m3/s)

30.0 (0.014) �1%

Supply fan temperature rise,DTfan, �F (�C)

1.7 (0.9) �0.2(0.1)

Supply air temperature,SATmfr,cal, �F (�C)

The results of SATmfr,cal

in Table 4�1.2(0.7)

Mixed air temperature,MATvir, �F (�C)

The results of MATvirin Table 4

�1.0(0.6)

Dependent variable Uncertainty of heating-based approach, _VH;model

Scenario ID H-1 H-2 H-3 H-4 H-5 H-6 H-7 H-8

Uncertainty �3.6% �4.0% �3.7% �3.6% �4.1% �4.4% �4.0% �4.0%Scenario ID H-9 H-10 H-11 H-12 H-13 H-14 H-15 H-16Uncertainty �5.7% �5.8% �6.3% �6.9% �6.3% �6.3% �5.7% �5.8%

D. Yu et al. / Building and Environment 46 (2011) 1292e1302 1299

with good accuracy by Yu et al [12]. This method is adopted in thisstudy and MSAT is calibrated as SATmfr,cal in Table 4 with uncer-tainty �1.2 �F (0.7 �C). For more information about the virtualcalibration of an MSAT sensor in RTUs, please refer to the Section3.1.1.

Based on the experimental results in the 7.5 ton RTU in theheating mode, uncertainty analysis and experimental evaluationare thereby conducted to evaluate the effectiveness of the heating-based approach.

2.2.2.2. Uncertainty analysis of heating-based SCFM meter. Based onEq. (30), uncertainty of heating-based approach calculation isconducted with the independent variables of _Vg, DTfan, SATmfr,caland MATvir. The root sum square is used as Eq. (31):

d _VH;model ¼"

v _VH;model

v _Vgd _Vg

!2

þ v _VH;model

vDTfandDTfan

!2

þ

v _VH;model

vSATmfr;caldSATmfr;cal

!2

þ v _VH;model

vMATvirdMATvir

!2#1=2(31)

where d _Vg, dDTfan, dSATmfr,cal and dMATvir are inputs uncertainties.The results of sixteen experiments in heating mode preformed

in the 7.5 ton RTU are used to analyze the uncertainty of heating-based approach. As shown in Table 5, _Vg is 30.0 cfm (0.014 m3/s)for the testing RTU with an uncertainty of �1%. DTfan is 1.7 �F(0.9 �C) obtained in the CAV RTU with an uncertainty of �0.2 �F(0.1 �C). The uncertainties of SATmfr,cal and MATvir are �1.2�F (0.7 �C) and �1.0 �F (0.6 �C), respectively. It is found thatuncertainty of heating-based SCFM meter is within �6.9%. Thismeans we are 93.1% confident with the true value of SCFM inheating mode.

2.2.2.3. Experimental evaluation of heating-based SCFM meter.Experimental evaluation of the heating-based virtual SCFM meterby using the sixteen sets of lab tests is given in this section. The

Table 6Experimental evaluation of heating-based SCFM meter.

Scenario ID _VH;model, cfm(m3/s) _Vmeas, cfm(m3/s) eH,eva

H-1 1854(0.87) 1848(0.87) 0.3%H-2 2076(0.98) 2045(0.97) 1.5%H-3 1866(0.88) 1857(0.88) 0.5%H-4 1834(0.87) 1829(0.86) 0.3%H-5 2174(1.03) 2076(0.98) 4.7%H-6 2399(1.13) 2269(1.07) 5.7%H-7 2125(1.00) 2037(0.96) 4.3%H-8 2132(1.01) 2040(0.96) 4.5%

relative error eH,eva between themeasured SCFM _Vmeas and _VH;modelis defined as follows,

eH;eva ¼_VH;model � _Vmeas

_Vmeas(32)

As shown in Table 6, it is found the maximum absolute relativeerror eH,eva is 7.6%. This demonstrates the virtual SCFM meter inheatingmode accurately predicts the true value of SCFM in the RTU.

To here, both cooling- and heating-based approaches to developa virtual SCFM meter are presented. Finally, the comparisons andconclusions of the two approaches are explored in the nextsubsection.

2.3. Comparisons and conclusions of cooling- and heating-basedapproaches

Comparing the cooling- and heating-based approaches, wecould reach the following conclusions:

� Uncertainty of _VC;model is much higher than the uncertainty of_VH;model

_VH;model is correlated with the inputs of _Vg, DTfan, SATmfr,cal andMATvir, wherein _Vg and DTfan are quite stable with very low uncer-tainties. Uncertainty of _VH;model is low, within �6.9%. In contrast,_VC;model is calculated by five parameters of OAT, MATvir, MATwb,vir,SAT and DTfan with more difficulties of implementation andhigher risk of uncertainties (�13.8%, in this case). The heating-basedSCFM meter, with the feature of “less uncertainty”, is consideredsimple, stable and could accurately predict the SCFM in RTUs.

� The relative error eC,eva between _Vmeas and _VC;model is high, whileeH,eva in heating mode is low

Owing to the uncertainty generated by the model regression of_QC;sens in Eq. (5), as well as the uncertainty associated with themultiple measurements of _VC;model in Eq. (8), the relative errorseC,eva between _Vmeas and _VC;model are high (�16.2 to 16.4%, in thiscase). However, _VH;model, with simple and reliable inputs, is muchclose to _Vmeas as evaluated through laboratory tests.

� Robustness of _VH;model is better than _VC;model

Although the manufacturer-data based cooling capacity modelproposed by Yang and Li [31] could work well when the systemoperates normally or only air side faults are present (e.g. improper

Scenario ID _VH;model, cfm(m3/s) _Vmeas, cfm(m3/s) eH,eva

H-9 1896(0.89) 1853(0.87) 2.3%H-10 2123(1.00) 2051(0.97) 3.5%H-11 1890(0.89) 1849(0.87) 2.2%H-12 1969(0.93) 1831(0.86) 7.6%H-13 2204(1.04) 2081(0.98) 5.9%H-14 2443(1.15) 2272(1.07) 7.5%H-15 2181(1.03) 2059(0.97) 5.9%H-16 2164(1.02) 2046(0.97) 5.7%

Fig. 6. An implementation flowchart of a virtual SCFM meter in RTUs.

D. Yu et al. / Building and Environment 46 (2011) 1292e13021300

supply airflow rates), it could not work in the presence of thefaults developed at refrigerant side (e.g. low refrigerant charge).However, it is notorious that the refrigerant side of RTUs is plaguedby various common degraded faults due to its complexity[24,25,34e36]. This fact causes more difficulties and limitationswhen implementing and accurately monitoring the cooling-basedSCFM meter in practice. However, in heating mode, the gas side issimple and its gas flow rate is accurately controlled by a sophisti-cated gas regulator. Although the gas side could fail occasionally,degraded faults associated with the gas side have been rarelyreported. It is easy to identify complete failure and thus to avoidusing the flow meter. With the good-fault free property, heating-based SCFM meter performs robustly most of the time.

� Relative humidity measurement of inlet air is required for coolingmode, but not for heating mode

According to Eq. (8), MATwb is critical to calculate the SCFMfor cooling mode. Installing relative humidity sensor is needed tocollect the measurement of wet bulb temperature. However, nomeasurement on the air humidity is required in the heating-basedapproach. Only easy-to-obtain measurements (dry bulb tempera-tures) are left in Eq. (30) as unknown dependent variables. Aswe know, RTUsmay not have relative humidity sensorsmounted bymanufacturers. Comparing to temperature sensors, relative hum-idity sensors are costly. Additional costs entail with procurement,installation and maintenance of relative humidity sensors. More-over, a relative humidity sensor is notorious for its accuracy driftingand saturation under high humidity levels.

The above comparisons between cooling- and heating-basedapproaches reveal that utilizing heating mode to develop a virtualSCFM meter is worthy of confidence. Therefore, the implementa-tion issues of a heating-based virtual SCFMmeter, covering detailedmeasuring and processing the parameters and an implementationflowchart, are introduced in the following section. It is dedicated toprovide an instruction of using this virtual SCFM meter in practice.

3. Implementation process

3.1. Measuring and processing parameters

Except for the stable input of _Vg and ΔTfan, measuring andprocessing two temperature measurements SAT and MAT, aredescribed.

To ensure the robustness and reliability of this virtual meter,firstly a steady-status detector presented by Li and Braun [37] isreferred to filter out the transient data of all temperaturemeasurements related to Eq. (30).

3.1.1. Measuring and processing SATAccurate SAT measurements would directly influence the

performance of the virtual SCFM meter. In RTUs, there is an MSATinstalled right after gas furnaces and it is not difficult to collect thereadings. However, Yu et al. [12] pointed out that a direct mea-surement of SAT would not work to get the true value in heatingmode. The evaluation results of direct measurements (both MSATsensor- and measuring grid-based measurements) were presented.It was found that there were various measurement errors becauseof serious thermal radiation from gas furnaces in addition to poortemperature distribution in the compact housing of RTUs. Forexample, in a 7.5 ton RTU, the errors are in a wide range from 1.0 �F(0.6 �C) to 12.6 �F (7.0 �C).

To settle the problem which could not be solved by traditionalsensor calibration method, a methodology of virtual calibration[38,12] based on statistical and modeling methods was proposed.

Virtual calibration method is an extension and complementationof traditional sensor calibration method. In traditional calibration(e.g. manufacturer supplied manual calibrations), benchmark iseither read by a reference sensor or a known value in certain cali-bration environment. Differently, in virtual calibration, the criticalvalues of the benchmark are correlated by multifarious statisticand/or modeling methods. Compared with the traditional calibra-tion, this innovative technology has a number of merits, such ashigh cost-effectiveness, handling a huge amount of measurementsacquired from both physical and/or virtual sensors and achievingreal-time, self calibration. Yu et al. [12] applied this virtual cali-bration methodology to calibrate SAT sensors as follows,

SATmfr;cal ¼ SATmfr;meas � ecal (33)

ecal ¼ aþ b�Hstageþ c� Hstage2 þ d� OADstþ f � OADst2

þ g � Hstage� OADst

(34)

where SATmfr,meas¼ direct measurement of an MSAT sensor in �F(�C), SATmfr,cal¼ virtual calibrated MSAT measurement in �F (�C);ecal¼ calibrated offset error of an MSAT sensor in �F (�C), Hsta-ge¼ heating stage status (e.g. 1, 2), OADst¼ outside air damperposition (e.g. 0%, 30%).

D. Yu et al. / Building and Environment 46 (2011) 1292e1302 1301

Whereas ecal denotes a varying offset model at different opera-tion conditions to calibrate MSAT sensor errors. Its correlation isfitted with independent variables of Hstage and OADst, and dep-endent variable of a calculated temperature residual betweenpredicted theoretical true value of SAT and measured MSAT. Thedevelopment of the correlated model ecal is needed only once andgeneric for all RTUs with similar constructed gas furnaces. Eqs. (33)and (34) jointly constitute themodel of virtual calibratedMSAT thatcan be served as part of a permanently installed control or moni-toring system to ensure accuracy of anMSATmeasurement in RTUs.

Additional experimental evaluation for this virtual calibrationmethod and uncertainty analysis of the calibrated MSAT wasprovided. The results indicated that the virtual calibration meth-odology could accurately predict the true value of SAT in RTUs[uncertainty is 1.2 �F (0.7 �C) or less]. This virtual calibrationmethod for a SAT sensor in RTUs is adopted in the development ofa virtual SCFM meter.

3.1.2. Measuring and processing MATAccurate direct MAT measurements are notoriously difficult

to obtain in RTUs due to space constraints and the use of smallchambers for mixing outdoor and return air [39]. In the pastdecade, a number of investigators have found that highly non-uniform temperature and velocity distributions at the inlet to theevaporator cause significant bias errors when employing single-point or averaging temperature sensors [40e42]. Recently, Lee andDexter [43] and Tan and Dexter [44,45] proposed a method bycorrecting the bias error associatedwith a single-point sensor usingCFD simulations. However, it is costly and difficult-to-implement inpractice. Wichman [46] suggested that a measurement grid ofmulti-point sensors mounted symmetrically in the duct centerlineprovides reasonable estimates in most cases. However, this is alsoan expensive approach.

Wichman and Braun [33] proposed and demonstrated a schemefor adjusting a single-point measurement of MAT (a smart MATsensor) in RTUs that is based on in situ measurements and selfcalibration. The approach is achieved by correlating the bias error interms of OADst and temperature difference between outdoor andreturn air. Extensive lab testing demonstrates that the smart mixedair temperature sensor performs very well and the overall root-mean-squared error is 0.57 �F (0.3 �C). The smart MAT sensor

Fig. 7. A scheme of deployme

proposed overcomes a typical technical barrier of using costlymeasurement grids or simulation software.

However, a physical MAT sensor is not typically installed in lightcommercial RTUs due to its bad performance. So this smart MATsensor cannot be implemented without adding a new MAT sensor.To further simplify this technique, Yang and Li [32] proposed analternative method which eliminates the need of a physical MATsensor and instead constructs a virtual MAT sensor to estimateMAT using OAT, RATand a correlated virtual outdoor air ratio sensorb as follows,

MAT ¼ b� OATþ ð1� bÞ � RAT (35)

Both laboratory and field testing demonstrate an acceptableuncertainty of �1.0 �F (0.6 �C). Since there is no pre-installedphysical MAT sensor available in our study, we adopted thismethod.

With accurate parameters accomplished, a graphical flowchartis explored accordingly to sum up the implementation proceduresof a virtual SCFM meter in RTUs.

3.2. Implementation flowchart

A virtual SCFM meter in RTUs can be implemented through thefollowing procedures in Fig. 6:

Step 1: Check the steady-status;Step 2: Check the heating and cooling status;Step 3: Check the availability of direct MSAT, OAT and RAT

measurements;Step 4: Virtually calibrate MSAT measurement; compute virtual

MAT values;Step 5: Run the virtual SCFM meter in Eq. (30).

4. Conclusions and discussion

The importance and necessity of monitoring SCFM for RTUs areobvious for control effectiveness, energy conservation and IAQ.Its accuracy and reliability critically influence system performanceand diagnostics. Using direct SCFM meters in RTUs has long beenretarded due to the relatively high price and practical problems. An

nt a virtual SCFM meter.

D. Yu et al. / Building and Environment 46 (2011) 1292e13021302

innovative virtual SCFM meter in RTUs only using noninvasivetemperature measurements is then presented in this study.

Modeling and evaluations of both cooling- and heating-basedapproaches are studied before selecting the algorithm. Accordingto the guiding principles for developing a virtual SCFM meter asthe authors suggested, it is found that heating-based SCFM meterpossesses the following features: (1) using a simple while reliablemechanism; (2) characteristic of small uncertainty and robust againstfaults; (3) easy-to-obtain parameters or measurements. The other-wise hard-to-measure SAT and MAT are solved by using existingresearch results.

As shown in Fig. 7, the modeling procedure for a virtual SCFMmeter in RTUs is needed only once and generic for all RTUs withthe same constructed gas furnaces. Once the one-time develop-ment is conducted, the implementation of the virtual SCFM meterfor long-term use is ready and easy with the otherwise unpre-dictable SCFM measurements in RTUs.

In conclusion, the innovative methodology demonstrates thatthe virtual SCFM meter in RTUs:

� Is robust enough against multi-variable operating conditions� Has very good performance in terms of accuracy (uncertaintyis �6.9%)

� Is easy to implement and economical for use (only using mathe-matic models and low-cost inputs)

� Is generic in RTUs with the same constructed gas furnaces

As for applications, the virtual SCFM meter can facilitate main-tenance and real-time automated FDD in RTUs:

1. Systematically, serving as part of permanently installed controlor monitoring system to indicate the real-time SCFM and aut-omatically detect and diagnose improper readings

2. Specifically, detecting RTU air side faults such as dirty indoorfilters and slipping supply fan belt, which lead to decreasedSCFM in RTUs

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