exergy analysis of an isothermal heat pump dryer

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Energy 36 (2011) 4616e4624

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Energy

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Exergy analysis of an isothermal heat pump dryer

Will Catton*, Gerry Carrington, Zhifa SunDepartment of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016, New Zealand

a r t i c l e i n f o

Article history:Received 12 November 2010Received in revised form9 March 2011Accepted 12 March 2011Available online 12 April 2011

Keywords:DryingHeat pumpIsothermalExergyEnergy efficiency

* Corresponding author. Tel.: þ64 3 4797796; fax:E-mail address: [email protected] (W. C

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.03.038

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A numerical simulation of a plate contact-type isothermal heat pump dryer (HPD) is used to examine theenergy efficiency improvement obtainable from this system compared with a conventional HPD. Whilewe consider this system design to be entirely feasible, we are not aware of any existing practicalapplications of the design. The simulation incorporates a detailed plate, product and air flow model,solving the mass, momentum and energy balances within the drier, into a pre-existing model of theremaining HPD components. The accuracy of an idealised drier-duct model used in a previous analysis isassessed. Although the accuracy of the idealised model is found to be sensitive to local systemtemperature variations, this is found not to lead to significant error when it is integrated into the whole-system HPD model. The energy efficiency benefit associated with the isothermal contact HPD isconfirmed to be a factor of between 2 and 3. An exergy analysis is used to determine the causes of thisperfomance gain. Contact heat transfer in isothermal HPD is found to reduce irreversibility within therefrigerant cycle by roughly the same amount as that occurring in heat transfer from the condenser to theproduct.

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1. Introduction

The present work centers on a simple idea for increasing theenergy efficiency of heat pump dryers (HPDs) [1,2]. The idea arisesnaturally from consideration of the Gouy-Stodola law [3]. Ina standard (adiabatic) heat pump drying system, recycled heat isreturned to the drying process by heating the dehumidifiedairstream as it is recycled to the product. But from a second-lawviewpoint, this approach e using air for heat transfer e appearswasteful. Heat transfer both to the air and from the air to the dryingprocess is responsible for a large part of the entropy creation insuch a system [4,5]; so are irreversible losses owing to the air flowresistance of the system, and fan losses [6]. Jonassen et al. [7, 8]have successfully reduced the effect of these irreversibilities byconstructing a two-stage non-adiabatic HPD e a full cycle of theenergy efficiency work-flow discussed by Asprion [9]. The ideabehind the present work is that these irreversibilities could befurther reduced by providing heat directly to the drying process,through a conductive plate connecting the refrigerant and theproduct (condenser plates labelled CD2 in Fig. 1). This configura-tion, which wewill refer to as the ‘isothermal contact HPD’ (ICHPD)mode, would be most applicable to the drying of products that canbe spread into thin layers, especially those that can be dried under

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high-humidity conditions [10]. The system depicted in Fig. 1becomes equivalent to a standard adiabatic HPD if the refrigerantbypasses the condenser plates (dotted line 2e20).

The idea of ICHPD has itself been advanced in the literaturepreviously [11], but the modelling of ICHPD is not straightforward,because of the tightness of the linkage between the refrigerantcircuit, the drying process, and the air circuit. Perhaps partly for thisreason, no detailed modelling has apparently been reported priorto the work described here. Nor has there been any reportedattempt to build and test a prototype system. A previous prelimi-nary assessment of ICHPD previously indicated that such a systemconfiguration offers the potential for energy performance benefitsof 2e3 times compared with an adiabatic HPD [10]. However, thatassessment was based on a highly idealised model of the HPDsystem. The heat pump heating COP was simply assumed to bea constant percentage (50%) of the Carnot COP. Also the modelassumed that the temperatures of the product surface (Ts) and ofthe bulk duct air (Tb) were everywhere equal to that at the drierinlet, i.e. location D in Fig. 1, an assumption we call the idealisedisothermal case. Thus although the analysis was able to satisfac-torily match measured data in the adiabatic case, substantialuncertainty remained in its predictions for the isothermal mode.

In the present work we corroborate and extend the previousanalysis, by developing a detailed physical model of a stack of drierducts with embedded refrigerant condenser tubes, and incorpo-rating this model into a detailed model of the remainder of an HPDsystem, previously established by Carrington and Bannister [12].

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gospinaaldana

Highlight

gospinaaldana

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Fig. 1. Schematic of HPD system being modelled. Locations on the air cycle are denoted by letters, and on the refrigerant cycle are denoted by numbers.

Table 1Baseline values of key system parameters. Entries marked by asterisks are subject tovariation in the whole-system model.

Parameter (unit) Baseline value

Condenser face area Aco (m2) 1.0Evaporator face area Aev (m2) 1.0Number of ducts ND 10Product air flow _ma;co(kg s�1) 1.0Drier maximum temperature TD (�C) 55.0Relative humidity at drier inlet fD (%)* 30.0Tray drier length L (m) 5.0Tray drier width w (m) 1.0Air duct depth d (m) 20.0� 10�3

Product thickness d (m) 1.0� 10�3

Heating plate condenser tube diameter D (m) 10.0� 10�3

Heating plate condenser tube midline depth xp (m) 6.0� 10�3

Refrigerant circuits per plate nb (e) 3Passes through plate per circuit p (e) 5Total refrigerant mass flow rate _mr (kg s�1)* 1.0Refrigerant saturated condensing temperature Trsat,3 (�C)* 60.0

W. Catton et al. / Energy 36 (2011) 4616e4624 4617

We present and discuss results from the resulting comprehensivewhole-system model, including an exergy audit comparing theadiabatic and isothermal modes, and clarifying the system-leveleffects of contact heat transfer. The detailed model also enables usto assess the impact on predicted system performance of deviationsfrom several of the idealisations that were used in the preliminaryassessment, in particular (1) deviations from the isothermal andadiabatic duct idealisations, and (2) an additional pressure dropthat arises when refrigerant passes through the condenser plateslabelled CD2 in Fig. 1.

We now briefly discuss the range of potential applications forICHPD technology. The modelling work presented in this paperconfirms that ICHPD promises an increase in drying energy effi-ciency that could yield significant operational cost reductions,especially in HPD applications with large product throughput. Onthe other hand, the relative capital cost of ICHPD is presentlyunknown. An ICHPD of a given drying capacity would requirea significantly smaller compressor than its adiabatic HPD counter-part (see below); however, the technology would employ a signifi-cantly larger heat transfer area at the condenser than the adiabaticHPD. Furthermore, the energy performance gain offered by ICHPDis highly sensitive to the acceptable relative humidity at theproduct, and to product thickness. These sensitivities restrict therange of products towhich ICHPD is likely to be applicable, andmayalso impact on ICHPD capital costs. In Section 3, we presenta tentative economic analysis of ICHPD in a hypothetical filter-cakesludge drying case study. The analysis shows, in particular, that theviability of ICHPD as a substitute for adiabatic HPDmay be sensitiveto electricity and waste disposal price trends.

The dimensions of the batch-operation tray drier configurationconsidered throughout this paper are specified in Table 1. ICHPDcould of course be implemented under a range of different dryerconfigurations. For instance an internal-drum contact dryer, oper-ating continuouslywith product throughputmaintained by rotatingwipers [13], could offer steady-state operation allowing the systemto be held near to optimal operating conditions [14], and alsowouldoffer a mechanism for maintaining a thin product layer with goodthermal contactwith the heat transfer surface. Such varying designswould diverge in the specifics of their performance, but our broadconclusions are unlikely to require significant modification.

2. Theory

Here we describe the detailed drier-duct model and, briefly, thewhole-system model. In the detailed duct model, discretisedcontrol-volume conservation equations are numerically solved ina 1-D plug-flowmodel of a drier duct (between locations D and E inFig. 1), using the staggered-grid SIMPLER algorithm described byPatankar [15], subject to boundary conditions given by the inlet airflow velocity and psychrometric state, the outlet air pressure pE,and the refrigerant inlet enthalpy hr,2, outlet pressure pr,20, andmassflow rate _mr. Employing Fick’s and Fourier’s laws, and the New-tonian model of viscous stress, and adopting a 1-dimensional plug-flow model, the steady-state (species-k) mass, momentum andenergy balance equations can be expressed for the air-side controlvolume depicted in Fig. 2, as follows [16e18]:

ZSw

�rky� rDva

vuk

vx

�dS ¼

ZSe

�rky� rDva

vuk

vx

�dS� _mðmÞ

k (1)

Fig. 2. Close-up of a single duct. Temperature gradient from refrigerant to air is shown.Surfaces (Sw, Se, Sn, Sm) of an air-side control volume are indicated.

W. Catton et al. / Energy 36 (2011) 4616e46244618

ZSw

�ry2 þ p� 2m

vy

vx

�dS ¼

ZSe

�ry2 þ p� 2m

vy

vx

�dS�Ff (2)

ZSw

�r�hþ1

2y2�y�k

vTvx

�dS¼

ZSe

�r

�hþ1

2y2�y�k

vTvx

��dS� _Q

� _QðmÞ

(3)

In Eqs. (1)e(3), the following definitions have been used:

_mðmÞk ¼

ZSm

�ðukryÞsþh$m�rk;s � rk;b

�dS (4)

Ff ¼ �Z

Sm;n

C$f12ry2dS (5)

_Q ¼Z

Sm;n

h$ðTs � TbÞdS (6)

_QðmÞ ¼

Xk¼a;y

hk _mðmÞk (7)

In Eqs. (1)e(7), the bounding surface of the control volume isdivided into the entrance-surface Sw, the exit-surface Se, the masstransfer (product) surface Sm, and the duct top surface Sn, as shownin Fig. 2. In Eqs. (4)e(7), h$m, C$

f and h$ are the local mass transfercoefficient, friction factor and heat transfer coefficient, respectively,all adjusted for high mass transfer rates by the method of Bird et al.[18, p. 661]. These have been calculated using the DittuseBoelterequation [19] and the ChiltoneColburn analogy [18]. The steady-state product surface temperature for each control volume isevaluated by solving the energy balance at this surface [20, p. 222],using

at ¼ ðTr � TsÞ ¼ nvDhvap þ h$ðTs � TbÞ (8)

Eq. (8) states that, per unit area at the product surface, the rate ofheat delivery from the refrigerant, at(Tr� Ts), equals the heatconsumed by vaporization, nvDhvap, plus the heat lost at the productsurface to the air above, h$(Ts� Tb). The term at¼ (1/a1þ1/a2þ1/a3)�1 is the overall plate-product heat transfer coefficient,a1¼ arpD/l is an effective heat transfer coefficient from the refrig-erant to the inside surface of the tubes, a2 ¼ ð2pkp=lÞOln½ð2l=pDÞsinhð2pxp=lÞ� is the effective heat transfer coefficientthrough the plate, and a3¼ kd/d is the effective heat transfer coeffi-cient through the product [10]. Eq. (8) is also valid for the adiabaticmode, which can be simulated by setting the plate thermalconductivity, kp, to zero. Considering only the constant-activityperiod of drying, the humidity ratio at the product surface, us, is thesaturated value at Ts. The mean refrigerant heat transfer coefficientar is evaluatedusing themethodof Fischer andRice [21, p. 51],wherethe local refrigerant heat transfer coefficient a(hr,pr)is evaluatedusing the method of Cavallini et al. [22].

The idealised drier model, which was used in the previousanalysis, plays an important role in the validation of the detailedduct model. The idealised model is based on the followingexpression for the drier outlet humidity ratio uE, using theisothermal assumption Ts¼ TD [10] or the adiabatic assumptionTs¼ Twb,D, i.e. in the adiabatic case, product surface temperature Tsgiven by the wet-bulb temperature at D [23]:

uE ¼ usatðTsÞ þ ½uD � usatðTsÞ�exp�� hmraNDw

_maL�

(9)

Eq. (9) can be derived (for the present geometry) using theconstant Ts assumptions described above, together with theassumptions of constant mass transfer coefficient hm; constant dry-air density ra; and the approximation uv�ua, which allowsconvective enhancement of mðmÞ

y to be neglected. The pyschro-metric state at E is obtained using uE and the inlet wet-bulbtemperature Twb,D (in the adiabatic case), or the inlet temperatureTD in the isothermal case [10]. Varying L in Eq. (9) allows thevariation of air state within the duct to be evaluated.

The whole-systemmodel used in the present work, which is themodel of Carrington and Bannister [12] modified to include thedetailed drier-duct model described above, incorporates the isen-tropic and volumetric efficiencies of the ZR61K2-TFD scrollcompressor with R134a characterised by [24]. The New-toneRaphson method is applied to the state vector x¼ (x1, x2, x3),where, in terms of the locations shown in Fig. 1:

x1 ¼ Trsat;1 (10)

x2 ¼ Trsat;3 (11)

x3 ¼ uD (12)

Using the compressor model and assuming isenthalpic throt-tling, the two saturated refrigerant states Trsat,1 and Trsat,3 aresufficient to specify the refrigerant thermodynamic cycle and massflow rate _mr. The pressure drop over each refrigerant flow branchwithin the heating plates (in CD2) is evaluated by the method ofTraviss et al. [25]. The remaining refrigerant pressure drops areevaluated using the correlations of Carrington and Bannister [12].Subcooling is assumed negligible, and the thermostatic expansionvalve is assumed set to a 5 �C superheat at location 1. A constant fanefficiency of 50% is assumed. The air pressure at E is assumed equalto ambient: pE¼ 101,325 Pa. The air pressure drop within the drieris evaluated using the SIMPLER algorithm; other air pressure dropsare estimated using correlations developed by Turaga et al. [26] and

Fig. 3. Psychrometric paths predicted by the detailed duct model. Tin¼ 63 �C,uin¼ 0.069, _ma;in ¼ 0:75 kg s�1 (circles) and 2.25 kg s�1 (diamonds).


the dynamic loss coefficients (k-factors) determined by Carringtonet al. [6]. Venting is assumed to be controlled to maintain TD fixed.Thus the air state at D is specified by uD, pD. Air states around thesystem are obtained using the driermodel and energy andmoisturebalances across the HP components.

The error vector D that is used in the NewtoneRaphson methodis:

D1 ¼ _Qev � fev�yev; Twb;E; T4

�(13a)

D2 ¼ _Qco � fco�yco; TC; Trsat;3

�(13b)

D3 ¼ uD � uC (13c)

where fev and fco are specified by Eqs. (4) and (7) of [12]. These areempirical component heat transfer correlations based on theincoming flows. Each iteration of the NewtoneRaphson methodoccurs as follows. From the current estimate of the state vector, x,a current estimate of the states throughout the system is formed,and the error vector D is evaluated. An estimated value J of theJacobian matrix for the system is then used to update the state-vector estimate using

x1 ¼ x0 � r$J�1D (14)

where r represents the relaxation that is applied, and x1 is the newestimate of the system state, as obtained from the previous esti-mate x0.

The convergence criterion for the whole-system model is thatthe maximum error function, across all submodels of the whole-system model, must be less than a threshold, which is typically setto 10�5. Each updated variable is used to generate an error functionfor that variable. In the duct model these are the control volumesource terms that arise from the SIMPLER algorithm. For thewhole-system model, these are the magnitudes of the error vectorcomponents D1, D2, and D3. For the remaining system variables, theerror function is the relative change in the variable in the latestiteration. Since fev and fco represent the heat transfer from thecondenser and evaporator that was measured as a function of theincoming refrigerant and air flow conditions [12], the componentsof the error vector D approach zero only if the heat transfer at theseheat exchangers is consistent with these empirical correlations. Inaddition, the global convergence criterion requires that the mass,momentum and energy balances within the drier ducts be satisfied.Thus on convergence the model is guaranteed to satisfy mass andenergy balances across all system components.

3. Results and discussion

3.1. Drier-duct model e comparison with previous results

Before discussing the validation of the detailed drier-ductmodel, we examine representative outputs showing key differ-ences between the adiabatic and isothermal modes. Fig. 3 showsa set of psychrometric paths obtained from the detailed modelunder the air inlet condition TD¼ 63 �C, uD¼ 0.069 (kg/kg-dry),corresponding to a relative humidity of 44%. Two dry-air mass flowrates are considered: _ma ¼ 0:75 kg s�1, and _ma ¼ 2:25 kg s�1. Thedrier geometry is as specified in Table 1. Locations 0, 1, 2, 3, 4 and5 m into the duct are indicated using circles for the low flow ratescenarios and diamonds for the high flow rate scenarios. Variationof the dashed lines from the idealised isothermal case (whichwould yield vertical psychrometric paths) is evident. With contactheat transfer, a lowair flow rate enables the air to receivemore heatas it passes over the product, resulting in a greater air temperature

at a given humidity. In contrast, in the adiabatic case the humidityratio and the temperature are functionally related by way of theconstant wet-bulb temperature of the air, and the psychrometricpath traced by the air is unaffected by the air flow rate, although theduct location at which a given state is attained is affected by the airflow rate. The isothermal moisture extraction rates (MERs) arelarger than those in the corresponding adiabatic cases.

The low-flow case described in the previous paragraph wasselected to match the steady-state inlet condition that occurs in thefirst ten hours of the timber-drying situation modelled by Sun et al.[17], which itself was tested against measured data [27,28]. Theadiabatic timber kiln modelled had similar duct dimensions(5.76 m� 0.02 m as seen from the side) and an inlet air velocity of4 m s�1. With an inlet velocity of 4.0 m s�1, the present detailedduct model predicts a change in the vapour mass fraction of0.0041 kg kg�1, which is in fair agreement with the value of0.0045 kg kg�1 that can be read from Fig. 2 of [17]. The low-flowcase leads to a pressure drop in the isothermal mode of 33 Pa. In theadiabatic mode with the same inlet condition, the pressure drop is28 Pa. This latter value is also in fair agreement with the pressuredrop of 20e25 Pa found by Sun et al. [17]. The disagreementbetween the predictions of the present model in the adiabaticmode and Sun et al.’s model can be attributed to the differenttransfer correlations employed in the two models, and to theabsence of evaporation from the duct ceiling (Sn in Fig. 2).

3.2. Drier-duct model e comparison with analytical case

Since the idealised model represents a limiting case to which ananalytic solution exists, it can contribute to the validation of thedetailed duct model. Fig. 4 and Table 2 provide illustrativecomparison between outputs from the two models. The output ofthe detailed air flowmodel, shown in Fig. 4(b), is seem to be in goodagreement with the idealised case, Fig. 4(a). Once again, themodelled situation involves the drier geometry specified in Table 1.Air and refrigerant inlet conditions are as specified in Table 1. Thedetailed model incorporates several physical effects not accountedfor in the idealised model. The most important, which is visible in

Fig. 4. Example profiles (from D to E) (a) idealised model, (b) detailed model. 1: Tb (ISO); 2: Ts (ISO); 3: Tb (ADI); 4: u (ISO); 5: Ts (ADI); and 6: u (ADI).


Fig. 4, is that the product surface and bulk air temperatures mayvary substantially from their idealised values. The detailed modelshows a dip in the air temperature (line 1) due to a relatively lowproduct surface temperature at the inlet (line 2). This is due toevaporation being most intense near the air inlet, where theairstream is least humid. The product surface temperatureincreases with position in the drier, and between 3 and 4 m into thedrier the surface temperature can be seen to exceed the airtemperature. Beyond this location the bulk air temperatureincreases with position. Another effect visible in Fig. 4(b) is a flat-tening of the humidity ratio curve (line 4) compared with itscounterpart in Fig. 4(a). Since the humidity ratio gradient isproportional to the local drying rate, this implies that the dryingrate predicted by the detailed model is more uniform throughoutthe drier than predicted by the simple model. This effect can beunderstood as follows. The driving force for evaporation in theisothermal mode is approximately proportional to the verticalseparation between lines 2 and 4 in Fig. 4, since line 2, whichrepresents the product surface temperature, also provides a first-approximation measure of the surface vapour density. The positivegradient of line 2 thus has the effect of reducing the variation in thedriving force for drying along the length of the drier, which isreflected in the reduced curvature of line 4.

The MERs and air outlet temperatures estimated by the detailedand simple models are summarized in Table 2 for a range of inlet airtemperatures and relative humidities. In the isothermal mode theoutlet air temperatures do not deviate markedly from the inlettemperatures, but the MERs do in some cases vary significantlyfrom those predicted by the simple model. The key reason for these

Table 2Estimates of system behaviour. _ma ¼ 1.

Idealised model Detailed model Detailed with Tideal

ISO fin¼ 30% MER¼ 199.3 kg h�1 MER¼ 179.4 kg h�1 MER¼ 200.3 kg h�1

Tin¼ 55 �C Tout¼ 55.0 �C Tout¼ 53.9 �C Tout¼ 54.4 �CADI fin¼ 30% MER¼ 21.2 kg h�1 MER¼ 19.3 kg h�1 MER¼ 20.0 kg h�1

Tin¼ 55 �C Tout¼ 41.8 �C Tout¼ 42.4 �C Tout¼ 42.4 �CISO fin¼ 60% MER¼ 50.4 kg h�1 MER¼ 73.8 kg h�1 MER¼ 50.4 kg h�1




Tin¼ 70 �C Tout¼ 70.0 �C Tout¼ 68.0 �C Tout¼ 68.6 �C

variations again appears to be that the product surface temperaturemay deviate significantly from the air inlet temperature. Thishypothesis has been tested by forcing the product surfacetemperatures to equal the air inlet temperature (in the adiabaticcase, the inlet wet-bulb temperature) in the detailed model, withresults shown in the third column of Table 2. These show closeagreement, within a few percent for all the scenarios tabulatedhere, with theMER predicted by the idealised model. In addition, inthe isothermal case the curvature of the bulk relative humiditymatches the idealised model, which supports the discussion in theprevious paragraph.

The above analysis has shown that deviation of the productsurface temperature from its idealised ‘isothermal’ value, as used inthe simple model, may have a significant effect on the drying rate.At moderate drying rates the idealised and detailed models are ingood agreement; however at very high and very low drying rates,correspondingly depressed and elevated surface temperatures(respectively) may have a substantial effect on evaporation withinthe dryer, as is shown by Table 2. Taken all together, these resultsindicate the following: (1) the idealised model provides a reason-able first-order approximation; (2) the detailed model may berequired in order to obtain accurate predictions of HPD perfor-mance, because of significant temperature effects that occur at lowand high drying rates; and (3) the other additional physical effectsthat have been included in the detailed model can be regarded asminor corrections, rather than as primary aspects of the situationbeing modelled.

3.3. Whole-system model

Wenowconsider an illustrative output from the detailedwhole-system model produced by integrating the detailed dryer-ductmodel into the HPDmodel established by Carrington and Bannister[12], as described in the theory section above. In the case that weconsider, the two modes again have identical specifications(Table 1) aside from plate heat transfer and plate refrigerant pres-sure drop, both of which are zero in the adiabatic case. Fig. 5 showsthe refrigerant thermodynamic state-cycle, for the isothermal andadiabatic modes. The corresponding psychrometric cycles areshown in Fig. 6. The resulting system performance is summarizedin Table 4. In the isothermal mode the total refrigerant pressuredrop in the condenser (between the locations labelled 2 and 3 inFig. 5) is somewhat greater than that for the adiabatic mode, owingto the pressure drop within the condenser plates. Despite this

Fig. 5. Thermodynamic cycle of R134a in the isothermal and adiabatic modes.

Table 3Specific exergy destruction by component; key performance indicators.

(�10�3), kWh kg�1 Adiabatic Isothermal D

Condenser and product 103.7 17.5 �86.2Compressor 62.4 21.2 �41.2Evaporator 31.1 22.4 �8.7Throttle 26.6 4.3 �22.3Fan friction 3.1 1.5 �1.6Venting and condensate 14.1 5.8 �8.3


additional pressure drop, the isothermal mode can be seen toenable the system to operate over a significantly narrower pressurerange, which contributes to an enhancement of the specific mois-ture extraction rate (SMER). Thus the model predicts that therefrigerant-side tradeoff between heat- and momentum-transferirreversibilities does not significantly impact on performance in theisothermal mode. The nominal power rating of the compressor is5 kW, but the compressor power varies with operating condition(Table 4). Despite this fact, and despite some deviation from theidealised temperatures, the psychrometric cycles shown in Fig. 6are in good agreement with the _WP ¼ 5 kW psychrometriccycles of the preliminary analysis [10].

Fig. 6. Psychrometric chart showing air property paths in baseline scenario for adia-batic and isothermal dryers.

Table 3 shows the exergy destroyed per kg of moisture removedfrom the product in key system processes and components, and thedifference in this quantity, for each component, between HPDmodes. In evaluating the exergies (and the effect of venting), theenvironment has been taken to be moisture-saturated at 10 �C.About half of the irreversibility-avoidance achieved by theisothermal mode is seen to be associated with the condenser andthe drying process. Since most of the exergy destruction in thecondenser and product is associated with the transfer of heat [4,5],this portion of the avoided irreversibility can be attributed chieflyto the isothermal mode’s avoidance of heat transfer through airthermal boundary layers. Most of the rest of the energy efficiencygain is at the compressor and throttle, and can be attributed to thenarrower temperature and pressure range of the refrigerant cyclefor the isothermal mode. Most of this temperature-range narrow-ing is due to the avoidance of air cooling in the drier ducts, and alsoto the high humidity that prevails in the isothermal mode, as can beseen by examining the cycles shown in Fig. 6. We can thereforeassociate most of this latter improvement with the fact that theisothermal mode avoids using air (with its small specific heat

Table 4Performance of adiabatic and isothermal HPD.

Adiabatic Isothermal_Qco, kW 27.8 43.5_Wt , kW 5.1 4.0MER, kg h�1 21.2 55.4SMER, kg kWh�1 4.2 13.7

Fig. 7. Relationship between d, SMER and MER.


capacity) as a heat carrier, and with the isothermal mode’s highhumidity.

In summary: (1) in the adiabatic mode, condenser and productirreversibilities contribute much of the overall work requirement;(2) the isothermal mode greatly reduces this irreversibility, byabout six-fold per kgmoisture removed; (3) a significant part of theoverall reduction of irreversibility nevertheless occurs at thecompressor and the throttle. This last result highlights the syner-gistic nature of a HPD, and also implies that the exergy destructionin the condenser and product of an adiabatic HPD does not set anupper bound on the SMER gain associated with ICHPD. (Indeed if itdid, then from the first column of Table 3 the isothermal SMERcould not exceed 7.3 kg kWh�1.)

We now consider an interesting feature of the impact of theproduct thickness on ICHPD SMER. Fig. 7(a) shows the effect thatproduct thickness has on the energy performance of the isothermaland adiabatic modes. Since we are considering the constant-activity drying period, and convective heat transfer to the productis not affected by its thickness, the adiabatic performance is unaf-fected by product thickness. In contrast, a thick product layerrepresents a significant thermal resistance, which nullifies thebenefit of the isothermal mode. As has already been discussed, therequirement that the product must be able to be spread thinly(together with the typically very high humidities in the isothermalmode) limits the products for which isothermal drying will beappropriate; a glance at Fig. 7(a) suggests that the contact HPDsystem being modelled would yield a significant performanceadvantage only in the drying of products that can be spread into

Table 5Economics of adiabatic HPD and ICHPD.

Scenario 1 2 3

Electricity cost, $/kWh 0.1 0.1 0.1Disposal costs, $/kg 0.05 0.05 0.15Relative capital cost (ISO) 1 3 1

Value added, $/dayADI 16.1 16.1 77.6ISO 26.3 26.3 87.8

Payback time, yearsADI 7.2 7.2 1.2ISO 4.0 18.1 1.1

Net present value, k$ADI 53.4 53.4 384.5ISO 108.1 41.6 439.2

layers less than about 1e2 cm thick. However, Fig. 7(b) showsa significant potential benefit of the ICHPD mode, where it isapplicable. As the figure indicates, ICHPD may enable energyperformance (SMER) and MER to be maximised simultaneously (byusing a thin product layer). This absence of a tradeoff betweenSMER and throughput contrasts with adiabatic HPD systems, whichmust be operated at relatively low drying rates to obtain goodenergy performance [10].

3.4. Economic case study

Finally, we use the system performance values presented aboveto conduct a tentative analysis of the relative economics of ICHPD.We consider an operation that produces 1000 kg of waste sludgedaily, with an initial moisture content of 0.65 kg/kg (dry-massbasis). A waste sludge drying operation has been selected for thefollowing reasons. (1) Adiabatic HPD of filter-cake sludge is usedtoday. (2) The value that is added to the product by drying is typi-cally not large compared with the energy cost involved. (3) Wastesludges could be dried under ICHPD conditions that are set tooptimize energy performance. This sludge is to be dried to a finalmoisture content of 0.1 kg/kg, corresponding to a required dryingcapacity of 25.625 kg/h, in order to reduce transport and landfillingcosts [29]. Using the rule of thumb that the capital cost of adiabaticHPD is approximately $1 perwatt of heat provision at the condenser,we estimate a capital cost of $33,250 for the adiabatic case. Weassume that this cost is financed at an annualized rate of 7%.

Table 5 shows the value added per day (after electricity costshave been met), the payback time, and the net present value (NPV)of installation, for adiabatic and isothermal HPD systems, overa range of scenarios. We do not consider any costs associated withdepreciation, servicing or labour, and in evaluating the NPV weassume a long project lifetime. The parameters that are varied arethe cost per unit of electricity, the cost of sludge transport andlandfilling, and the relative capital cost of an ICHPD system,compared with adiabatic HPD. In each scenario each independentparameter is either ‘high’ or ‘low’. Scenarios 1e4 reflect currentelectricity prices of roughly 10c kWh�1. Scenarios 5e8 correspondto a significantly higher electricity price of 30c kWh�1, and couldrepresent a future scenario characterised by energy shortages and/or a strong CO2-emission price signal [30,31]. Scenario 6 (in whichelectricity is expensive, sludge disposal is cheap, and ICHPD iscostly to install) is the only scenario inwhich neither adiabatic HPDnor ICHPD is economically feasible. ICHPD appears to be a sensibleinvestment in scenarios 1, 3, 5, 7, and 8. Both scenarios 3 and 4 havehigh disposal costs. The economics favour adiabatic HPD somewhatin 3, and isothermal HPD somewhat in 4. In all of the high-elec-tricity cost scenarios 5e8, ICHPD is strongly favoured. In particular,

4 5 6 7 8

0.1 0.3 0.3 0.3 0.30.15 0.05 0.05 0.15 0.153 1 3 1 3

77.6 �13.2 �13.2 48.3 48.387.8 17.3 17.3 78.8 78.8

1.2 e e 2.0 2.03.5 6.6 e 1.2 4.0

384.5 �104.2 �104.2 226.9 226.9372.7 59.8 -6.7 390.9 324.4


in scenario 5 ICHPD is a sensible investment while adiabatic HPDyields a negative net value, and in scenario 8 ICPHD is preferable toadiabatic HPD despite its much higher up-front cost. Electricity andwaste disposal costs vary with region, while the relative capital costof ICHPD is currently unknown. Our results indicate that at presentthe economic viability of ICHPD strongly depends on its capital costbeing less than three times that of adiabatic HPD, but that thisdependency could be lessened or reversed by increases in the costsof sludge disposal or of electricity. Viewed alternatively, Table 5shows that the isothermal mode’s high energy efficiency makesits economics relatively less sensitive to the price of electricity,a result which may be significant in a time of energy-priceuncertainty.

4. Conclusions

This paper has described the development and testing ofa flexible finite-volume drier-duct model, which solves the mass,momentum and energy balances for the flowwithin a stack of drierducts. This detailed model has been used to examine in detail thedrying process in quasi-isothermal and adiabatic driers. The modelhas shown that the idealisation of purely isothermal conditionswithin a contact HPD is the most severe restriction applying to theidealised drier-duct model that was used in a previous analysis ofisothermal contact heat pump dehumidifiers (ICHPD). Otherassumptions have been shown to make a much smaller differenceto the accuracy of the idealised model predictions.

By comparing the isothermal drying behaviour as predicted bythe detailed model with the idealised model used in the previousanalysis, we have tested the air flow model against a limiting casewhich admits of analytical solution techniques. By comparingmodel outputs in the adiabatic mode with those of the modeldeveloped by [17], which itself was tested directly againstmeasured data, we have indirectly tested the air flowmodel againstexperimental observations. These tests justify our confidence thatthe model robustly represents drying within a duct-stack. Ourinvestigation has confirmed that under moderate drying conditionsthe idealised model used previously provides a satisfactory first-approximation model of the drying process. However it has alsoprovided insight into several ways in which a contact drier, oper-ated as part of an ICHPD system, would deviate from the idealisedisothermal case.

A whole-system HPD model has been produced by combiningthe detailed dryer-duct model with models of the remaining heatpump components. The systemmodel has been used to confirm theprevious finding that isothermal contact dehumidification dryingcan increase drying energy efficiency by 2e3 times compared withconventional adiabatic dehumidification HPDs. Deviation frompurely isothermal behaviour has been found to influence the MERand SMER that is predicted by the whole-system model by onlya few percent, suggesting that the idealised duct model can legit-imately be used in assessments of ICHPD performance.

An exergy analysis of the system has been performed for boththe isothermal and adiabatic modes. This has shown that theisothermal mode derives its relative energy efficiency partially, butby no means entirely, from a reduction in the irreversibility asso-ciated with the transfer of heat to the drying process. Significantcontributions to the SMER improvement also occur at thecompressor and throttle, and have been attributed mainly to thehigh humidity throughout the ICHPD system and to the avoidanceof air as the primary path for heat transfer to the product.

We have examined the relationship between the ICHPD SMER,the product thickness d, and the product throughput as indicated bythe MER. Our results indicate that ICHPD provides an opportunityto avoid the adiabatic mode’s tradeoff between drying rate and

energy efficiency by using a thin product layer. Thus obtaining goodperformance from an ICHPD system boils down to the materials-handling problem of maintaining a sufficiently thin product layerthat has good thermal contact with the heat transfer surface.

We have presented a case study of the economics of ICHPD.Since we are not yet in a position to assess the likely capital cost ofan effective ICHPD system,we are currently unable to further assessits economic viability. However, we have shown that the viability ofICHPD would become substantially less sensitive to capital costs ifeither waste disposal or electricity prices increase significantly, andthat isothermal HPD provides an opportunity to minimize risks dueto uncertain electricity prices.

References

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Symbols (units)

A: area (m2)ADI, ISO: adiabatic, isothernalCf: friction factor (1/m2)COP: coefficient of performance (e)D: diffusivity (m2/s)d: air duct depth (m)D: heating plate refrigerant tube internal diameter (m)Ff : friction force (N)Dhvap: latent heat of vaporization (J/kg)h: specific enthalpy of moist air (J/kg dry-air), product

surface heat transfer coefficient (W/m2 K)hm: product surface mass transfer coefficient (m/s)k: thermal conductivity (W/Km)l: heating plate condenser tube spacing (m)L: heating plate length (m)_m: mass flow rate (kg/s)MER, SMER: moisture extraction rate (kg/s),

specific moisture extraction rate (kg kWh)n: mass flux (kg/m2$s), refrigerant circuits per plateND: number of ducts (e)p: pressure (Pa), passes through plate per circuit_Q: heat flow rate (W)S: surface

T: temperature (K)y: speed (m/s)w: heating plate width (m)_W: power input (W)x: distance through kiln (m)xp: heating plate refrigerant tube centerline depth (m)z: distance along refrigerant flow in CD2 (m)a: heat exchange coefficient (W/m2 K)d: product thickness (m)f: relative humidity (e)r: density (kg/m3)m: dynamic viscosity of fluid (N s/m2)u: humidity ratio (kg vapour/kg dry-air)D: change

Subscripts and superscripts0: environment1, 2, 20 , 3, 4: locations on refrigerant cycleA, B, C, D, E, F: locations on air cycleb: bulkco, ev: condenser, evaporatorD, F, P: ducts, fan, compressorin, out: inlet, outletk, a, v, w: species-k, dry-air, water-vapour, liquidewatern, w, s, e: north, west, south, east (control volume boundaries)m: mass exchangep: heating plater: refrigerantS, s: surfacesat: saturation conditiont: Total, effectivewb: wet-bulb�: modified for high mass transfer ratesd: products

exergy analysis of an isothermal heat pump dryer

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