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Applied Thermal Engineering 50 (2013) 868e876

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Heat transfer and pressure drop in spacer-filled channels formembrane energy recovery ventilators

Jason Woods*, Eric KozubalNational Renewable Energy Laboratory, Jason Woods, 52/213-17, 1617 Cole Blvd, Golden, CO 80401, USA

h i g h l i g h t s

< We investigated support spacers for membrane energy recovery ventilators (ERVs).< We calculated and measured heat transfer and pressure drop for several spacers.< New spacer designs show improved performance over simple spacers common in ERVs.< Tests showed a transition to unsteady flow for velocity ranges expected in ERVs.< We evaluated the use of common heat transfer performance metrics for ERV spacers.

a r t i c l e i n f o

Article history:Received 23 February 2012Accepted 8 June 2012Available online 23 August 2012

Keywords:Membrane spacersHeat transferMass transferEnhancementPolarizationEnergy recovery ventilator

* Corresponding author. Tel.: þ1 303 384 6189.E-mail address: jason.woods@nrel.gov (J. Woods).

1359-4311/$ e see front matter � 2012 Published byhttp://dx.doi.org/10.1016/j.applthermaleng.2012.06.05

a b s t r a c t

This article investigates various support spacers for airflow through membrane-bound channels inenergy recovery ventilators (ERVs) to enhance heat and mass transfer. Although liquid flow throughmembrane-bound channels has been extensively investigated, little work has looked at airflow throughthese channels. This article presents theoretical pressure drop and heat transfer for an open channel andfor simple triangular corrugation (or plain-fin) spacers, which are common in heat exchangers and insome ERVs. It then presents the experimental pressure drop and heat transfer for two new corrugatedmesh spacers, with one spacer in three orientations. Results indicate that these can improve heat transferwith little pressure-drop penalty compared to the triangular corrugation spacers. Results also show thatunsteady flow occurs in the mesh spacers once a certain flow rate is reached. The optimal spacer dependson the application, which is shown with a cost savings estimate for a hypothetical ERV. Simplerperformance metrics that do not require cost estimates can be used to compare two spacers, as long astheir limitations are considered.

� 2012 Published by Elsevier Ltd.

1. Introduction

We investigated spacers for enhancing heat and mass transferfor airflow in membrane-bound channels of heating, ventilation,and air conditioning (HVAC) devices. A common device is themembrane energy recovery ventilator (ERV) [1e4], which iscommercially available from several manufacturers (e.g., ConsERV,RenewAire, NuAire, Fantech). Membrane ERVs consist of alter-nating channels of exhaust air and ventilation air separated by flat-sheet membranes, which are permeable to water vapor but nearlyimpermeable to air. During the winter, the ventilation air recoverssensible and latent energy from the exhaust air and returns it to the

Elsevier Ltd.2

space; in the summer the exhaust air removes this energy from theventilation air.

ERVs require support spacers to maintain air channel geometry,because the pressure on the exhaust side at one location is not, ingeneral, the same as that of the ventilation air on the other side ofthe membrane. Another application requiring support spacers isliquid desiccant dehumidification using membranes, wherea hygroscopic salt solution (liquid desiccant) absorbs moisture fromthe air through the membrane [5]. A support spacer maintainsconsistent air channel geometry while several forces act on themembrane.

We are interested in these spacers for two reasons: (1) the spacerincreases the pressure loss of the airflow, which requires higher fanpower and operating cost; and (2) the spacer influences the airsideheat and mass transfer coefficients between the membrane surfaceand the bulk flow. If the spacer increases mixing, and therefore heatand mass transfer, it reduces the ERV size and initial cost, because

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876 869

the overall energy transfer is dominated by these airside resistances.Zhang [6] showed that the airside boundary layers were roughly99% of the heat transfer resistance for laminar flow through open 2-mmchannels. Formass transfer, the improved vapor permeability ofpolymer membranes compared to paper cores [2,7e9] has reducedthe membrane mass transfer resistance. Zhang [6] estimated thatthe airside resistance is about 25% of the mass transfer resistance,while Min and Su [10] estimated the airside resistance at 10e35%.Using the membrane resistance from [11], this would increase toroughly 75%. So, although the membrane is still a significant part ofthe mass transfer resistance, the airside resistance is becomingmore important.

Traditional heat transfer enhancements protrude from the walland are difficult to implement when the wall is a membrane.Support spacers do not attach to the membrane and can bedesigned to produce these heat and mass transfer enhancements.Many researchers have investigated spacers for liquid flows inmembrane-bound channels, focusing on how these spacers affectpressure drop and mass transfer in pressure-driven processes [12e24], and heat transfer in membrane distillation [25e28]. Littleresearch has been done on heat and mass transfer for airflows inspacer-filled channels of membrane modules. While the fluidmechanics between liquid flows and airflows is similar, thedifferent pressure requirement necessitates a different spacerdesign. ERV fans provide 100e300 Pa, which is orders of magnitudeless than the pressure provided by liquid pumps.

Our objectives are to determine: (1) the relative performance ofvarious airside spacers for membrane HVAC applications; (2) thetransport mechanisms (e.g., unsteady flowor turbulence) that mustbe included in any computational fluid dynamics (CFD) simulationsto accurately model the flow around these spacers; and (3) theapplicability of commonly used heat and mass transfer enhance-ment metrics to ERV spacers. The article presents theoretical andexperimental results for heat transfer and pressure drop for threespacers over a range of Reynolds numbers (Re). We compare simpletriangular corrugation spacers commonly used in ERVs, withalternative, more complicated spacers. The comparison is based ontheir Darcy friction factors (f) for pressure drop and Colburn jfactors (j) for heat transfer. When thermal conduction througha spacer is near zero, invoking the heat and mass transfer analogyenables the extension of heat transfer results to mass transfer. Wethen compare the spacers using heat and mass exchanger metricsfrom the literature based on the tradeoff between pressure drop(parasitic energy use) and heat transfer (reduced size or largercapacity). Finally, we evaluate these metrics with a more realistic,yet simple, calculation of energy-related cost savings for a hypo-thetical ERV.

2. Methods

Three spacers were considered (Table 1 and Fig. 1). Spacer 1 isa triangular (plain-fin) corrugation that is common in membrane

Table 1List of spacers and their properties. Filament size and pitch are indicated in Fig. 1. Forspacer 1, we consider three conductivities: zero, polypropylene (typical for an ERV),and infinite.

Spacer 1 Spacer 2 Spacer 3

Supplier n/a AIL Research PermatronMaterial Varies Aluminum AluminumThickness (mm) 3 3 3.175Corrugation pitch (mm) 8 6 9Porosity (open volume) 0.89 0.98 0.95Filament size, df (mm) 0.2 0.2 0.9

ERVs and heat exchangers. These spacers are typically madefrom a polymer, such as polypropylene. We consider poly-propylene and also hypothetical materials of zero conductivityand infinite conductivity. The simple geometry of spacer 1enables j and f to be calculated with equations from the litera-ture, and they are not measured experimentally. Spacers 2 and 3are alternative designs for HVAC devices. Their complex geom-etries require experimental measurements. To validate the testsetup, we also measured the performance of an open channelwith no spacer.

The factors, j and f, were calculated (no spacer, spacer 1) andmeasured (no spacer, spacers 2 and 3) as a function of the channelRe, which is defined as:

Re ¼ rairVdhmair

(1)

with rair and mair the air density and dynamic viscosity, dh thechannel hydraulic diameter, and V the superficial velocity. Thisvelocity is:

V ¼ _mairrairAx-sec

(2)

where _mair is the air mass flow rate and Ax-sec the empty-channelcross-sectional area. Tests were performed for 300 < Re < 800,which is a typical ERV operating range. As defined, Re is the inde-pendent variable (independent of spacer geometry) and f and j thedependent variables (dependent on spacer geometry and Re). Thisenables easier comparison between f and j of different spacers forthe same mass flow rate.

2.1. Theory

2.1.1. Pressure dropFor the open channel, f ¼ C0/Re, where C0 is 96 for parallel

plate channels. The channels used in the experiments havea height of 3 mm and width of 250 mm, which leads to C0 ¼ 94.8[29]. For spacer 1, f was calculated with theoretical correlationsfor laminar flow through triangular channels [30]. The triangularchannel friction factor (ftri) is C0/Retri, where Retri is the Reynoldsnumber based on the triangle hydraulic diameter, and C0 dependson the angles of the triangle (C0 ¼ 51.7 for spacer 1). The ftri wasconverted to the friction factor for spacer 1 (f1) based on thechannel Re (Eq. (1)) by equating the pressure drops for bothcases:

f12rV2 L

dh;channel¼ ftri

2rV2

triL

dh;tri(3)

where L is the channel length. Some algebra leads to:

f1 ¼ ftridh;channelV

2tri

dh;triV2 (4)

2.1.2. Heat transferThe j factors for an open channel and for spacer 1 were calcu-

latedwith constant-temperature Nusselt number (Nu) correlations.For the open channel, we used a developing flow correlation fromBejan [31]. For spacer 1, we used relations from Zhang [32] tocalculate the Nu for adiabatic fins (non-conductive), fins of a typicalspacer (polypropylene, 0.15 W m�1 K�1), and assumed isothermalfins (infinitely conductive). These were derived as follows. The

Fig. 1. Schematics of the three spacers with their flow directions: (a) spacer 1, (b) spacer 2, (c) spacer 3.

flow straightenerheader

(channel-to-tube adapter)

test fixture inlet airair

pressure taps

Tout

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876870

triangular-based isothermal Nu from Zhang [32] is defined asNutri,max. This was then converted to j, based on the channel Re, byequating the two heat transfer rates:

Nu1;maxkairAdh;channel

¼ Nutri;maxkairAtri

dh;tri(5)

where Nu1,max is the Nu based on the channel Re, kair is the airthermal conductivity, A the surface area of the channel walls, andAtri the surface area of the triangle channels (A plus spacer surfacearea). Rearranging and using the definition of j leads to the Colburnj factor for spacer 1 with infinite conductivity:

j1;max ¼ Nu1;max

RePr1=3¼ Nutri;max

RePr1=3dh;channelAtri

dh;triA(6)

where Pr is the air Prandtl number. For spacer 1, Atri ¼ 2.2A. The jfactor for the non-conductive material and for polypropylene arethen calculated with j1 ¼ j1,max*Nutri/Nutri,max, where Nutri is takenfrom the tabulated data in Zhang [32] for fins of different thermalconductivities.

LFE

P

vacuum pump

discharge air70 psi air

Manometer

25 mm x 3 mm strip to set channel thickness

Fig. 2. Experimental setup for pressure-drop tests. LFE ¼ laminar flow element.

2.2. Experimental

2.2.1. Pressure dropPressure-drop experimentsmeasured f for the open channel and

for spacers 2 and 3. A vacuum pump pulled ambient air througha narrow channel made from 20-mm thick aluminum plates(Fig. 2). The channel length (L) is 500mm andwidth (W) is 250mm.

Two 25-mm wide aluminum strips at the edges of the plate wereclamped tight to set the 3-mm channel thickness. Two pressuretaps 250mm apart were machined into the top plate. A manometer(Dwyer Model 1430, �0.062 Pa) measured the pressure differencebetween these two pressure taps. A differential pressure transducer(MKS 220DD,�0.75%) measured the pressure across a laminar flowelement (Meriam 50MH10, �0.8%) to measure the volumetricairflow rate. This was then converted to a mass flow rate withtemperature and absolute pressure measurements (temperature:type-T thermocouples, �0.25 �C; absolute pressure: OMEGAPX2760, �0.63 kPa).

The manometer differential pressure measurements (DP) wereconverted to f with the equation:

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876 871

fexper ¼ dhL

112rV2

DP (7)

A power-law function was fit to the plotted fexper data:

f ¼ C0Rem

(8)

2.2.2. Heat transferA similar test setup was used for the heat transfer experiments,

except that the flow length is only 80 mm (Fig. 3). It is shorter toensure measurable differences between spacers. Very long chan-nels would provide air at the same temperature as the water,regardless of spacer.

In each experiment, dry air at 40 �C was provided to the channelinlet. A pump circulated 20 �C water at 1.5 L min�1 from a refrig-eration bath to internal channels in the aluminum plates, whichkept the plates’ temperature nearly constant. The air exitedbetween 22 and 25 �C. These near-ambient exit temperatures,along with 2 inches of foam insulation around the test fixture,reduced heat gains and losses from ambient.

Six type-T thermocouples inserted into the fluid streamsmeasured the temperature differences between the inlet and outletair, and the inlet and outlet water for both the top and bottomplates. After calibration in a water bath, the thermocouple uncer-tainty for measuring temperature differences was �0.05 �C. Athermocouple was also added on the outside of the polycarbonateoutlet header, which was then insulated. Steady state was assumedto be reached when its temperature was constant. For each test,10 min of steady-state data were taken at 5-s intervals.

The steady-state data were used to calculate j based on numberof transfer units (NTU)-effectiveness relations. First, the heatexchange effectiveness was calculated from the measuredtemperatures:

3 ¼ Tair;out � Tair;inTwater � Tair;in

(9)

where Tair,out and Tair,in are the air inlet and outlet air temperatures,and Twater the average of the four water temperatures, both inletsand outlets. Because of the high water flow rate, the heat capacity

LFE

Pabs

test fixture

vacuum pump

discharge air 70 psi air

inlet air, Tin

refrigerating bath

water

Tw2

Tw1

Tw3

Tw4

Tout air

pump

flow straightener header (channel-to-tube adapter)

Fig. 3. Experimental setup for heat transfer tests. LFE ¼ laminar flow element.

rate ratio (Cr) between water and air is less than 0.01, and weestimated NTU with the equation for Cr ¼ 0 (see e.g., [31]):

NTU ¼ �lnð1� 3Þ (10)

The overall heat transfer coefficient based on the airside, Uair,was then calculated from the NTU definition:

Uair ¼ NTU_maircp;air

A(11)

where cp,air is the air specific heat capacity and A the total heatexchange area, which includes the top and bottom plates:

A ¼ 2LW (12)

The heat transfer resistances of the water boundary layer andaluminum plate were estimated to be 0.8% of the overall resistancefor the open channel case and 2.3% for a hypothetical spacer withthree times higher heat transfer. Therefore, Uair is a reasonableapproximation for the airside heat transfer coefficient:

hairzUair ¼ NTU_maircp;air

A(13)

The dimensionless heat transfer coefficient (Nu) is then:

Nu ¼ hairdhkair

(14)

Note that cp,air and kair are assumed constant at the average airtemperature. Finally, j is:

jexper ¼ Nu

RePr1=3(15)

A power-law function was fit to the plotted jexper data:

j ¼ C1Rex

(16)

2.3. Mass transfer

The mass transfer of the spacers was not measured, but theanalogy between heat and mass transfer can be used to estimate itfrom the heat transfer results. The dimensionless mass transfercoefficient (Sherwood number), is related to Nu with:

Sh ¼ Nu�ScPr

�1=3(17)

where Sc is the Schmidt number. Themass and thermal diffusivitiesof air, and therefore Sc and Pr, are the samewithin 5%, whichmakesSh and Nu differ by about 1%. The mass transfer is thus nearly thesame as the heat transfer, but only if the boundary conditions arethe same. This is not true for spacers with high conductivity, whereheat transfer occurs by conduction through the spacer and into theair. There is no analogous phenomenon of mass transfer throughthe solid spacer.

Using this analogy, the mass transfer for an open channel will bethe same as the heat transfer. We consider different conductivitiesfor spacer 1: zero conductivity, polypropylene conductivity, andinfinite conductivity. Zero conductivity mimics the mass transferboundary conditions for spacer 1. For spacers 2 and 3, the effect ofconduction through the spacer is difficult to quantify from theexperiments. The contact area between the spacers and the plates isonly 1% of the total plate area, but the spacer thermal conductivity is3 orders of magnitude higher than that of air. This relationshipbetween heat and mass transfer is further discussed in Section 3.2.

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876872

2.4. Performance metrics

The performance of each spacer depends on pressure drop andheat transfer, and therefore on f and j (or Nu). Two extremeapproaches are possible: (1) a simple, but limited approach thatcompares the spacers based solely on pressure drop and heattransfer; and (2) a complex approach that attempts to find the cost-optimal spacer for a particular device by simulating the device’sperformance over a range of expected inlet air conditions, and thencalculating the ERV life cycle cost.We consider the former approachwith two simple performance metrics from the literature, but thelatter approach is outside the scope of this article. We insteadcalculate an approximate cost metric, with several simplifyingassumptions, based on the ERV energy savings. This is not meant tobe amethod for calculating anERV’s actual life cycle cost, but insteadillustrates the suitability of the simplermetrics for ERV applications.

2.4.1. Simple performance metricsFor liquid flows through membrane channels, researchers often

compare Sh at a given dimensionless power number (Pn) [13,33e36], which represents fan power requirements:

Pn ¼ Re3f (18)

For two spacers with the same initial cost and Pn, the preferredspacer has the higher Sh (or Nu).

A similar metric is used for heat exchangers, which researcherscall a performance evaluation criterion (PEC) [37]:

PEC ¼ j=j0ðf =f0Þ1=3

(19)

This PEC combines three terms: fan power, heat transfer area,and heat transfer rate. To compare two spacers, two of the threeterms should be the same from one spacer to the other.

The limitation of these twometrics is that they can compare onespacer to another only when several parameters are held constant.

2.4.2. A cost metricThe life cycle cost of an ERV considers all first costs, recurring

energy costs, and recurring energy savings from the ERV. Tosimplify this analysis, we assume a hypothetical ERV and calculatea cost metric that we can compare with the simple metrics.

We assume an ERV with an airflow rate of 170 m3 h�1

(100 ft3 min�1) and a membrane area of 5 m2. We consider designsbetween onewith 250 stacked channels of 0.1-m length to onewith50 stacked channels of 0.5-m length (see Fig. 4). Because wemeasured only heat transfer, we ignore latent energy recovery forthis article and look at sensible heat recovery only. We assumea 10 �C temperature difference between incoming and outgoing air

Fig. 4. Range of hypothetical ERV designs for 5 m2 of membrane are

(DTmax). With these assumptions, summarized in Table 2, thespacers can be compared based on a cost savings rate (CSR):

CSR ¼ CthermalQERV � CelecPfan (20)

where Pfan is the fan power (kW), QERV the energy transfer rate(kW), Celec the cost of electricity ($ kWh�1), and Cthermal the thermalenergy cost for winter heating or summer cooling ($ kWh�1). Theresults will change whenmass transfer is included, as QERV will alsoinclude latent energy recovery.

To calculate the CSR, we use the empirical fits for j and f forspacers 2 and 3 and the theoretical equations for an open channeland for spacer 1. For QERV, we use j to calculate the heat transfercoefficient for the hypothetical ERV:

hair;ERV ¼ jRePr1=3kairdh

(21)

While not exact, Zhang [38] showed that heat transfer witha constant-temperature boundary condition, which we measuredin the experiment, is a reasonable approximation for a membraneERV, and it is acceptable for this illustrative case. With negligiblemembrane heat transfer resistance, the two airside boundary layersresult in an overall heat transfer coefficient:

UERV ¼ hair;ERV2

(22)

which is used to calculate NTUERV by rearranging Eq. (11). With thisNTUERV and for Cr ¼ 1 based on equal mass flow rates for the twoairstreams, the effectiveness for a cross-flow ERV can be estimatedwith [39]:

3ERV ¼ 1� exp�NTU0:22

Cr

�exp

��CrNTU0:78

�� 1

��(23)

The energy transfer rate is then:

QERV ¼ �_maircp;airDTmax

3ERV (24)

where _mair is the mass flow rate of one airstream.For Pfan, we use f to find pressure drop for each airstream:

DPERV ¼ f2rairV

2 Ldh

(25)

There are two airstreams, so the fan power is:

Pfan ¼ 2_mair

hfanrairDPERV (26)

a. Left: tall with short channels; right: short with long channels.

0.1

1

10a

b

100 1000Re

f

sp. 2

no spacer (theory)

no spacer

sp. 1 (theory)

0.1

1

10

100 1000Re

f sp. 3 (0o)

sp. 3 (90o)

no spacer (theory)

sp. 3 (45o)

sp. 2 power law fit

Fig. 5. Measured friction factors vs. Reynolds number with power-law fits tomeasurements (d). (a) Theory for spacer 1 ($$�$$) and for no spacer (e e e).Measured for no spacer (�) and spacer 2 (>). (b) Theory for no spacer (e e e). Power-law fit for spacer 2 for comparison (/). Measured for spacer 3 at 0� (,), 45� (6), and90� (B) orientation. Uncertainty (not shown) is small: for measured f w 2%, formeasured Re w 1%.

0.01

0.1

100 1000Re

j

sp. 3 (90o)

no spacer (theory)

sp. 2

no spacer

sp. 3 (45o)

sp. 3 (0o)

sp. 1, adiabatic

sp. 1, isothermal

sp. 1, PP

Fig. 6. Colburn j factors vs. Reynolds number. Theory for spacer 1 with conductivity ofzero ($$�$$), 0.15 Wm�1 K�1 for polypropylene, PP ($�$), and infinity ($$$$). Theory forno spacer (e e e). Measured for no spacer (�), spacer 2 (>), and for spacer 3 at 0� (,),45� (6), and 90� (B) orientation. Power-law fits to measurements are also shown (d).Vertical bars show propagated uncertainty. Uncertainty in Re (w1%) not shown.

Table 2Specifications of hypothetical ERV.

Parameter Value Units

Flow length, L 0.1e0.5 mMembrane area 5 m2

Flow rate 170 m3 h�1

Channel thickness 3 mmTemperature difference, DTmax 10 �CHeat rate, QERV Calculated kWFan power, Pfan Calculated kW

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876 873

where hfan is the fan efficiency, assumed to be 50%. We then useQERV, Pfan and a range of assumed costs for electricity and thermalenergy to calculate CSR.

3. Results and discussion

This section shows the results for f (pressure drop) and j (heattransfer). It discusses the relationship between the heat transferresults and mass transfer, as well as unsteady flow. It thencompares the spacers using the performance metrics discussed inSection 2.4.

3.1. Pressure drop

Fig. 5a shows fexper vs. Re for an open channel (no spacer) and forspacers 1 and 2. For the open channel case, fexper is 1e8% higherthan laminar theory. We theorize that surface irregularities causedthis difference, which is consistent with the larger discrepancies athigher Re, where surface roughness is more important.

For spacer 1, f is roughly 200% higher than f with no spacer.Spacer 2 is also roughly 200% higher than no spacer at low Re androughly 300% higher at Re ¼ 500. The Re dependence for spacer 2changes near Re¼ 500, which is likely the transition from steady tounsteady flow. This transition occurs at a filament-based Re (Ref) of29, where Ref is defined based on the actual air velocity and thefilament diameter. While the flow around the spacer filament islikely affected by the presence of the wall, this Ref matches theexpected transition to unsteady flow for flow around a cylinder(10 < Ref < 100) [40]. Similar phenomena have been observedduring experiments [33] and computer simulations [19,22] forliquid flows through membrane channels, and in heat exchangers[41].

Fig. 5b shows fexper for spacer 3 for 0�, 45�, and 90� orientations.For comparison, the fitted equation for fexper for spacer 2 is re-plotted in Fig. 5b. Spacer 3 show a transition point similar tospacer 2, but at slightly lower channel Re: 500 for 0�, 375 for 45�,and 325 for 90�, which correspond to Ref of 92, 71, and 62.

3.2. Heat transfer

Fig. 6 shows jexper for an open channel and for spacers 2 and 3,and the theoretical j for the open channel and for spacer 1 withthree different materials. The theoretical and measured openchannel results agree within 9%. Similar to fexper, the discrepancy ishigher at higher Re.

When spacer 1 is non-conductive, it provides 57% less heattransfer than an open channel. Typically, spacer 1 would be madefrom a polymer, such as polypropylene. In this case, the Nu numberis 39% below the Nu for an open channel. If spacer 1 is assumed tobe isothermal (infinitely conductive), it provides 32% more heattransfer than an open channel, which shows the importance of thespacer thermal conductivity for the triangular corrugation spacers.The non-conductive case was used to illustrate the mass transfer

Pn = Re3f

Nu

sp. 3 (90o)

sp. 1, adiabatic

sp. 1, isothermal

no spacer

sp. 3 (45o)

sp. 3 (0o)

107 108 109 106

1 10

sp. 2

Fig. 7. Tradeoff between heat transfer (Nu) and fan power (Pn). Theory for spacer1 with zero conductivity ($$�$$) and infinite conductivity ($$$$), and for no spacer(e e e). Measured for spacer 2 (>), and for spacer 3 at 0� (,), 45� (6), and 90�

(B) orientation. Vertical bars show propagated uncertainty.

1.2

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876874

performance of a triangular corrugation spacer for any material.Because the thermal conductivity does not affect mass transfer,spacer 1 provides 57% less mass transfer than an open channelregardless of spacer material (see Section 2.3).

Spacer 2 and spacer 3 at 0� provide higher heat transfer thanspacer 1 with infinite conductivity for Re > 350. The differencebetween mass transfer and heat transfer for spacers 2 and 3 is lesscertain. The spacer acts as a fin, but to a lesser extent than spacer 1with infinite conductivity, which has morematerial and is assumedto be isothermal. This implies that some of the increased heattransfer from spacers 2 and 3 is due to increased mixing andtherefore increased heat transfer at the wall.

Spacers 2 and 3 show a transition to unsteady flow at Re of 550and 500, respectively, consistent with the transitions in f. There isno discernible transition in spacer 3 for the 45� and 90� orienta-tions. The lowest tested Re for these two spacers was around 350,which is near the transition observed with the pressure-dropmeasurements. Thus, the flow is likely in the unsteady regime forall the heat transfer tests for these two spacers. It is difficult tomeasure heat transfer at lower Re for the 90� and 45� orientations,as indicated by the greater uncertainties at lower Re. The low flowrates result in lower exit air temperatures, increasing heat gainsfrom ambient; heat gains that have a larger impact at low flowrates. Thus, the measured heat transfer for the 90� spacer forRe < 450 is likely slightly lower than the actual heat transfer.

Lines were fit to fexper and jexper, which give the coefficients forEqs. (8) and (16) for 300 < Re < 800 (Table 3). If used for channelsizes other than 3mm, the equations are still valid if the ratio of thespacer dimensions to the channel height are the same. However,the transition points could change.

3.3. Tradeoff between heat transfer and pressure drop

The theoretical and experimental results were used to esti-mate performance metrics for each spacer (for spacer 1, weshow only results for materials with zero and infinite conduc-tivity). Fig. 7 shows the tradeoff between heat transfer (Nu) andtotal parasitic fan power (Pn). The lines are plotted for the rangeof Re (and Pn) for the ERV designs between the two extremes inFig. 4, so the lines should not be extrapolated. This plot clearlyillustrates which spacer is better at a given Pn (e.g., a spacerwith minimal flow obstruction (“no spacer” in Fig. 7) forPn < 2 � 107, and spacer 3 at 90� for Pn > 108) or which spaceris better at a given Nu. The drawback is that this metric doesnot show the tradeoff between fan power and heat transferwhen neither the Pn nor the Nu are the same between twospacers.

Table 3Coefficients for power-law equations for each measured spacer. Recrit is critical Re atthe transition from steady to unsteady flow. Heat transfer for Re < Recrit was notmeasured for spacer 3 at 45� and 90� .

Spacer 2 Spacer 3-0� Spacer 3-45� Spacer 3-90�

Recrit 500e550 500 375 325

f ¼ Co/Rem

Re < Recrit Co 60.2 87.2 35.0 31.0m 0.71 0.77 0.49 0.38

Re > Recrit Co 3.8 5.6 16.0 13.1m 0.26 0.32 0.36 0.24

j ¼ C1/Rex

Re < Recrit C1 0.81 0.71 n/a n/ax 0.54 0.51 n/a n/a

Re > Recrit C1 0.22 0.30 0.38 0.41x 0.34 0.38 0.37 0.33

To compare two such spacers, a specific application must beassumed with appropriate cost and economic conditions. Fig. 8shows CSR for different channel flow lengths for the hypotheticalERV of Section 2.4. The ratio of thermal to electricity costs isassumed to be 0.3, which is the approximate ratio of natural gascost to electricity cost. The CSR for each spacer is normalized by theCSR of an ERV with laminar, fully developed channel flow (nospacer). The figure shows that a module with long flow channelsshould use spacers with minimal flow obstructions, or low mixing,while a module with short flow channels should use high-mixingspacers.

The appropriate spacer also depends on the relative costs ofsaved thermal energy and parasitic fan power, which is illustratedin Fig. 9 for a fixed module length of 300 mm. When the thermalenergy is inexpensive relative to electricity, a low-mixing spacer isappropriate, whereas for higher thermal energy costs, a high-mixing spacer is appropriate.

Figs. 8 and 9 illustrate the difficulty of using a single perfor-mance metric to compare spacers. Plotting Nu against Pn visually

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5Module length (m)

CSR

/ C

SRno

spa

cer

sp. 3 (90o)

sp. 1, adiabatic

sp. 1, isothermal

no spacer (baseline)

sp. 3 (45o)

sp. 3 (0o)

sp. 2

Fig. 8. Cost savings rate for hypothetical ERV for different module lengths (formfactors). Cthermal/Celec ¼ 0.3.

Fig. 9. Cost savings rate for hypothetical ERV for different ratios of thermal to elec-tricity costs. L ¼ 0.3 m.

J. Woods, E. Kozubal / Applied Thermal Engineering 50 (2013) 868e876 875

indicates which spacers are better at the same fan power (Pn) or thesame heat transfer performance (Nu), but it does not capture thetradeoff between fan power and heat transfer when neither ofthese are constant. Considering that CSR does not include theeffects of membrane costs or the time value of money, a metric thatconsiders all the necessary variables to find the cost-optimal spacerwill clearly be much more complicated than the Pn metric and willdepend on the application.

3.4. Future work

The experimental results from this study can be used to validatea CFD model, which can then be used to investigate other spacerdesigns. The experiments show a transition to unsteady flow for Reexpected in HVAC applications, so the simulations must considerunsteady flow. While some CFD research has been performed forheat and mass transfer enhancement in membrane ERVs [42,43],none has been performed for spacer-filled channels.

In addition to f and Nu measured here, Sh is required for ERVmodeling. The mass transfer results will be similar to the heattransfer, but the heat and mass transfer analogy cannot be used forthermally conductive spacers, which act as fins. Thus, we expect theresult to show lower Sh than the heat and mass transfer analogycalculation would indicate. The CFD simulations can quantify theeffect from thermal conduction, but experiments directlymeasuring mass transfer will also indicate its importance.

4. Conclusions

We calculated and measured f and j for several support spacersfor membrane channels. The results indicate that:

(1) The triangular corrugation (plain-fin) spacers common in heatexchangers and some ERVs are detrimental to ERV perfor-mance compared to a channel with no spacer. Triangularchannels reduce heat transfer and increase pressure lossescompared to an open channel when the spacer is of lowconductivity, and will reduce mass transfer regardless of spacerconductivity. Spacers 2 and 3 increase heat transfer, and toa lesser extent mass transfer, at moderately increased pressureloss. Alternatively, they could be used to reduce ERV size fora fixed heat and mass transfer rate.

(2) Similar to studies on liquid flows through membrane channels,a transition from steady to unsteady flowwas observed as flow

rate increased. The transition occurred at Re between 325 and550 (Ref between 29 and 92).

(3) The tradeoff between f and j depends on the application. Nogeneral performance metric applies to all applications, butpreviously developed metrics are useful for preliminarycomparisons as long as their limitations are considered.

Acknowledgements

This work was supported by the U.S. Department of Energyunder Contract No. DE-AC36-08-GO28308 with the NationalRenewable Energy Laboratory.

List of symbols

A area available for heat transfer (m2)Ax-sec cross-sectional area (m2)Celec electricity costs ($ kWh�1)Cthermal thermal energy costs ($ kWh�1)C0 constant used in friction factor equationC1 constant used in Coburn j factor equationCr heat capacity rate ratiocp specific heat (J kg�1 K�1)CSR cost savings rate ($ per hour of operation)df spacer filament size (m)dh hydraulic diameter (m)f Darcy friction factorh heat transfer coefficient (W m�2 K�1)j Colburn j factorL length (m)_m mass flow rate (kg s�1)NTU number of transfer unitsNu Nusselt numberRe Reynolds number (Re ¼ rVdh/m)Recrit critical Reynolds number (transition to unsteady flow)Ref filament-based Reynolds number (Ref ¼ rV0df/m)p pressure (Pa)Pabs absolute pressure (Pa)Pn power numberPr Prandtl numberSc Schmidt numberT temperature (�C)Uair overall heat transfer coefficient based on the airside

(W m�2 K�1)V superficial velocity (m s�1)Vtri velocity through triangular channels (m s�1)V0 actual velocity (m s�1)

Subscriptsair property of airERV calculated for hypothetical ERVexper experimentally measured value

Greek symbols3 heat exchange effectivenessm dynamic viscosity (kg m�1 s�1)r density (kg m�3)

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