A Simulation Model for the Application of Nanofluids as Condenser Coolants in Vapor Compression Heat Pumps

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1 Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2012 A Simulation Model for the Alication of Nanofluids as Condenser Coolants in Vaor Comression Heat Pums José Alberto Reis Parise arise@uc-rio.br Follow this and additional works at: htt://docs.lib.urdue.edu/iracc Parise, José Alberto Reis, "A Simulation Model for the Alication of Nanofluids as Condenser Coolants in Vaor Comression Heat Pums" (2012). International Refrigeration and Air Conditioning Conference. Paer htt://docs.lib.urdue.edu/iracc/1335 This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact eubs@urdue.edu for additional information. Comlete roceedings may be acquired in rint and on CD-ROM directly from the Ray W. Herrick Laboratories at htts://engineering.urdue.edu/ Herrick/Events/orderlit.html

2 2531, Page 1 A Simulation Model for the Alication of Nanofluids as Condenser Coolants in Vaor Comression Heat Pums José Alberto Reis PARISE 1 *, Ricardo Fernando Paes TIECHER 2 1 Pontifícia Universidade Católica do Rio de Janeiro, Deartment of Mechanical Engineering, , Rio de Janeiro, RJ, Brazil Phone: , Fax: , arise@uc-rio.br 2 Pontifícia Universidade Católica do Rio de Janeiro, Deartment of Mechanical Engineering, , Rio de Janeiro, RJ, Brazil Phone: , Fax: , ricardo.tiecher@aluno.uc-rio.br ABSTRACT A simulation model was develoed for the erformance rediction of a vaor comression heat um using nanoscale colloidal solutions (nanofluids) as condenser coolants. The model was intended for a liquid-to-liquid heat um, with recirocating comressor, thermostatic exansion valve and counter-flow double-tube condenser and evaorator. The comressor is characterized (inut data) by its swet volume, shaft seed and isentroic and volumetric efficiencies curves, and the exansion device, by the evaorator suerheat. The condenser is divided into three zones, desuerheating, condensing and subcooling. Likewise, the evaorator is divided into the boiling and suerheating zones. The heat exchangers are characterized (inut data) by their geometry (inner and outer tube diameters and length). Oerational inut data also include condenser subcooling and heat transfer fluids (condenser and evaorator) mass flow rates and inlet thermodynamic states. A comutational rogram was develoed to solve the resulting non-linear system of algebraic equations. Solution of the system rovides the cycle overall thermal erformance, as well as condensing and evaorating ressures and the thermodynamic states of refrigerant and heat transfer fluids at all oints of the cycle. Preliminary results were obtained for the simulation of a 19 kw nominal caacity water-to-water/(h 2 O-Cu nanofluid) heat um. A 5.4% increase in the heating coefficient of erformance, for a tyical oerating condition, was redicted for a nanoarticle volume fraction of 2%. 1. INTRODUCTION This aer studies the alication of nanofluids as condenser coolants of vaor comression heat ums. Nanofluids are nanoscale colloidal solutions, consisting of nanoarticles (with sizes of the order of 1 to 100 nm) disersed in a base fluid (Choi, 1995; Cheng et al, 2008). If comared to their corresonding base-fluid, nanofluids resent an uncontested enhancement in thermal conductivity, viscosity and density, as now reorted in a number of research aers and reviews (e.g., Khanafer and Vafai, 2011). Heat transfer in nanofluids (laminar or turbulent flow; natural or forced convection; single hase, ool boiling, nucleate boiling or critical heat flux) has also been investigated worldwide. For the urose of the resent simulation, i.e., single-hase forced convective flow, literature results conclude that, in general, conventional ressure dro correlations still aly to nanofluids, whereas new correlations for the Nusselt number, or even new heat transfer mechanisms (such as from Buongiorno, 2006), must be sought (see, for examle, Sarkar, 2011). Paers on alications of nanofluids are found in smaller numbers and, more secifically, the study on their use as heat transfer fluids in vaour comression cycles is still inciient. An exloratory simulation was carried out by Loaiza et al (2010), who numerically studied the use of nanofluids as secondary fluids (i.e., heat transfer fluids exchanging heat with the refrigerant in the evaorator) in vaour comression refrigeration systems. The resent aer imroves the model from Loaiza et al. (2010) by allowing more realistic situations to be redicted (for examle, variable condensing and evaorating ressures, to be determined as a result of oerational and fluid conditions, including nanofluid characteristics).

3 2531, Page 2 2. MATHEMATICAL MODEL The mathematical model here emloyed has already been outlined in Parise (2010) and Loaiza et al (2010). It was udated to meet the secific obectives of the resent study. 2.1 Control Volumes Figure 1a deicts a tyical vaor comression heat um cycle oerating with liquid circuits at both the evaorator (secondary fluid) and condenser (coolant). Seven control volumes comrise the system, namely: comressor (c), condenser s desuerheating (ds), condensing (cs) and subcooling (sc) zones, exansion device (xd) and evaorator s zones, boiling (bo) and suerheating (sh). The P-h diagram of the cycle, with corresonding control volumes and refrigerant thermodynamic states, is resented in Figure 1b. 5x P [kpa] C 4 3 sc cs ds 5 40 C 2 xd -7.8 C 12.7 C 6 7 bo 1 kj/kg-k c 1 sh 2x R134a h [kj/kg] Figure 1: a) Vaor comression heat um system with secondary fluid and condenser coolant; b) Control volumes and refrigerant states deicted in the P-h diagram. Refrigerant states: 1 comressor suction; 2 comressor discharge; 3 start of condensation (or dew oint, for mixtures); 4 condenser saturated liquid or, for mixtures, bubble oint; 5 condenser outlet; 6 evaorator inlet; 7 evaorator dry-out oint. 2.2 Comressor A simle efficiency-based model is emloyed for the comressor. In order to determine the refrigerant state at comressor discharge, an emirical curve (e.g., Brown et al., 2002) is rovided for the isentroic efficiency, which is related to comressor suction and discharge thermodynamic states as follows: ( s ) ( ) h h P η = ; s = s ; η = b + b θ ; θ = s, c 2s 1 s, c 1 2 c c h2 h1 P1 (1) With an emirical equation for the volumetric efficiency (Brown et al., 2002), written in terms of the ressure ratio and secific heat ratio, the refrigerant mass flow rate is determined by: 2 π D 1 N c γ m rf = ηvv1v c = ηv v1 n s ; ηv, c a a 2 θc 1 = ; γ = 4 60 (2) cv Finally, comressor adiabatic work and ower consumtion are determined from: W = m w η ; w = h h (3) c rf c em c 2 1

4 2531, Page Condenser Heat transfer: Each zone of the condenser, Figure 2, is treated as an indeendent heat exchanger, with its own refrigerant and cooling fluid energy balance equations, as well as the heat transfer rate and effectiveness equation (e.g., Martins Costa and Parise, 1993). Overall counter-flow is assumed. T 5 sc T 4 T T co, in co, a cs T 3 T co, b (a) (b) (c) ds T 2 T co, out Figure 2: Control volumes for the condenser (desuerheater, ds, condensing zone, cs, and subcooler, sc). Equations (4) and (5) describe the gas-to-gas and liquid-to-gas single-hase heat exchange in the desuerheating and subcooling zones, resectively. Equations (6) and (7) rovide the zones effectiveness (counter-flow single-hase heat transfer) equations. ( ); ( ); ε ( ) Q = m c T T Q = m h h Q = C T T (4) ds co, co co, out co, b ds rf 2 3 ds min, ds ds 2 co, b ( 4 5 );, (,, ); min, ε ( 4, ) Q = m h h Q = m c T T Q = C T T (5) sc rf sc co co co a co in sc sc sc co in * ( ) ( ) 1 ex NTU 1 C NTU ε = or ε = = * * 1 C NTU 1 C NTU + 1 *, if C 1 (6) * Cmin U A Cmin, ds = min ( m coc, co; m rf c, v, ds ); Cmin, sc = min ( m coc, co; mrf c, l, sc ); C = ; NTU = (7) C C The condensing control volume (cs), given the variation of the refrigerant-side heat transfer coefficient with the local vaor quality, was further divided into a number of small control volumes of equal secific enthaly increment, Figure 3, for which the following equations aly: max min T 4 h rf, + 1 h rf, T 3 cs T co, + 1 T co, T co, b T co, a Figure 3: Heat transfer element in the condenser two-hase zone (cs). ( + ); ( + ); ε ( + ) Q = m h h Q = m c T T Q = m c T T (8) cs, rf rf, rf, 1 cs, co, co co, co, 1 cs, co, co cs, 3 co, 1

5 2531, Page 4 ( NTU ) 1 ex ; NTU cs, cs, ε cs, = cs, cs, = m co c, co U A (9) The condenser total ower outut, condenser heat and total heat transfer area are, resectively: ( ) ;, ( 2 5 ) ; (, ) Q = Q + Q + Q q = h h A = A + A + A (10) cd ds cs sc cd cd ds cs sc Pressure dro: The ressure dro at each control volume defines the ressure levels along the condenser. The ressure at the start of condensation, P 3, is adoted as the nominal condensing ressure. ( ) ( ) (11) P = P ; P = P + P ; P = P P ; P = P P P cd ds 4 3 cs, 5 3 cs, sc Degree of subcooling: The rescribed condenser outlet degree of subcooling rovides: T = T T (12) sc Exansion Device An adiabatic thermostatic exansion valve, roviding constant degree of suerheat, was assumed. Therefore, h = h T = T + T (13) 6 5; 1 7 sh 2.5 Evaorator The evaorator is treated similarly to the condenser. Two control volumes, Fig. 4, are established, and the boiling zone is further divided into elements, to coe with local variation of the vaor quality. T sf, out bo T, T sf m sf, T + 1 sf, h T rf,, h rf + T sh (a) (b) T sf, in T 1 Figure 4: Control volumes for the evaorator (suerheater, sh, and boiling, bo, zones), also showing the heat transfer element in the two-hase zone Heat transfer: The energy balances, heat transfer rate, effectiveness equations and overall heat transfer coefficient for the heat transfer element of the boiling zone are as follows: ( + ); ( + ); ε ( + ) Q = m h h Q = m c T T Q = m c T T (14) bo, rf rf, 1 rf, bo, sf, sf sf, 1 sf, bo, sf, sf bo, sf, 1 rf, ( NTU ) 1 ex ; NTU bo, bo, ε bo, = bo, bo, = m sf c, sf U A (15) For the suerheating zone, one has: ( 1 7 );, (,, ); min, ε (, 7 ) Q = m h h Q = m c T T Q = C T T (16) sh rf sh sf sf sf in sf m sh sh sh sf i

6 2531, Page 5 Equations (9), for the determination of the effectivenesses of the condenser single-hase zones, also aly to the evaorator suerheating zone. The total refrigeration caacity, refrigerant effect and evaorator total heat transfer area are, resectively: ( ) ; Q ev Q = Q ;, + Q q = A = ( A, ) + A ev bo sh ev ev bo sh mrf (17) Pressure dro: Likewise, the nominal evaorating ressure is taken as the ressure at the evaorator entrance, and the ressure dros are ( ) P = P ; P = P P ; P = P P (18) ev bo, 1 7 sh 2.6 Heat Transfer Coefficients and Friction Factors Overall heat transfer coefficients: It is assumed, for all control volumes, that (i) heat exchangers resent no fouling; (ii) the thermal resistance due to conduction across the inner tube wall is negligible; (iii) the overall heat transfer coefficients are based on the inner heat transfer area of the inner tube of the heat exchanger and (iv) refrigerant flows in the annular assage of both heat exchangers. The overall heat transfer coefficients for the singlehase control volumes, (sh), (ds) and (sc), and for the two-hase flow control volumes, (cs,) and (bo,) are, resectively: U 1 D 1 1 D 1 = + ; U = + io, ev/ cd io, ev/ cd sh/ ds/ sc bo/ cs, αsf / co Dii, ev/ cd αsh/ ds/ sc αsf / co Dii, ev/ cd αbo/ cs, (19) Heat transfer and friction factor correlations: Table 1 summarizes the correlations used for all ossible flow conditions in the heat exchangers. In both condenser and evaorator, chosen to be of the double-tube tye, refrigerant was assumed to flow in the annular assages. This left the nanofluid, either as secondary fluid in the evaorator or condenser coolant, to flow in the circular conduit, a geometry for which nanofluid ressure dro and heat transfer studies are more readily available. For laminar single-hase internal flow of the base-fluid through a circular tube, the Fanning friction factor and the Nusselt number, Nu = α D k, were calculated assuming fully develoed flow, with Re ( m D) ( A µ ) =. For turbulent regime, equally assuming fully develoed flow and c uniform wall temerature, the friction factor and Nusselt number correlations from Bhatti and Shah (1987) and Pethukov and Poov (1963), resectively, were adoted. The Nusselt number in the transition regime is calculated from a linear interolation between the Nusselt number values at the laminar and turbulent limits of the Reynolds number that are 2000 and 8000, resectively. For the Fanning friction factor, these limits vary slightly, to 2100 and 4000, resectively (Bhatti and Shah, 1987). As far as single-hase internal flow of a nanofluid through a circular tube is concerned, recent reviews from Kakaç and Pramuanaroenki (2009) and Godson et al. (2010) conclude that further theoretical and exerimental work is needed to comrehensively understand the heat transfer mechanism. It is believed that the Dittus-Boelter (1930) correlation tends to underredict the heat transfer (Yu et al., 2008). Godson et al. (2010) list convective heat transfer correlations for nanofluids from five investigations, three of which (Pak and Cho, 1998; Maïga et al., 2005; Maïga et al., 2006) make direct use of the traditional Dittus-Boelter (1930) correlation format, with different values for coefficient and exonents. In the resent model, the correlation from Pak and Cho (1998), Nu = Re Pr, and the two-comonent nonhomogeneous equilibrium model from Buongiorno (2006) were equally tested. Pressure dro on the nanofluid side was calculated in the same way as for any other fluid (Xuan and Roetzel, 2000). For the refrigerant side, adequate correlations were chosen for single and two-hase flow in annular assages. 2.7 Refrigerant Proerties Equations (20) to (23) reresent the refrigerant thermodynamic functions here emloyed, taken, in the resent work, directly from the libraries of the EES (Engineering Equation Solver) latform.

7 cd sat cd (, ); (, ); (, ) , Page 6 h = h T P v = v T P s = s T P (20) ( ) ( ) h, ;, s = h s s P T = T h P (21) ( ); ( 1, ); ( 0, ); ( 0, ); (, ) T = T P h = h x = P = P T = T x = P h = h x = P = P T = T h P (22) ( 1, ); ( 1, ) T = T x = P = P h = h x = P = P (23) Table 1: Choices of friction factor and heat transfer correlations for different control volumes Control Volume CD Fluid Flow Friction Factor Correlation Base-fluid Heat Transfer Correlation laminar f Re = 16 Nu = turbulent Bhatti and Shah (1987) Pethukov and Poov (1963) Nanofluid laminar f Re = 16 Nu = Conduit Geometry turbulent Bhatti and Shah (1987) Pak and Cho (1998) Xuan and Li (2003) Circular laminar f Re = 16 Nu = EV Base fluid turbulent Bhatti and Shah (1987) Pethukov and Poov (1963) laminar f Re = 16 Nu = Nanofluid turbulent Bhatti and Shah (1987) Two-comonent nonhomogeneous equilibrium model, Buongiorno (2006) BO two-hase Shah (1982) CS DS SC SH Refrigerant Shah and two-hase Shah (1979) Sekulic (2003) laminar and turbulent Bhatti and Shah (1987) Laminar: Nu = Turbulent: Gnielinski (1976) Annular 2.8 Nanofluid Characterization Thermal conductivity: The thermal conductivity was calculated following the comrehensive work of Buongiorno et al. (2009), which reorts measurements taken from identical samles of nanofluids by over 30 institutions worldwide. An imortant finding was that Maxwell s model (1881), equation (24), for sherical and well-disersed articles, generalized by Nan et al. (1997), to include article geometry and finite interfacial thermal resistance, would rovide thermal conductivity redictions in good agreement with exerimental data. ( ) ( ) k k + 2 k + 2φ k k nf ξk = = k k + 2k φ k k n bf n n bf bf n bf n n bf (24)

8 2531, Page Viscosity: In the absence, at the time of writing, of a generalized correlation for viscosity of nanofluids (Kole and Dey, 2010), secific correlations for each nanofluid had to be emloyed, such as the examles in equations (25), for H 2 0-Al 2 O 3, from Pak and Cho (1998), and H 2 0-Cu, from Chen et al. (2007). Note that these correlations allow for an asymtotic value equal, or close, to that of the base fluid when φn tends to 0. µ µ ξ = = + φ + φ ξ = = + φ + φ (25) 2 2 ( n n ); ( n n ) nf ( H2O Al2O3 ) nf ( H2O Cu ) µ µ µ bf ( H2O) µ bf ( H2O) Other roerties: Density and secific heat are determined based on mass and energy balances, resectively, assuming for the latter that nanoarticle and base fluid are in thermal equilibrium (Khanafer and Vafai, 2011). ( 1 ) φn ρn c, n + φn ρbf c, bf ρnf = ρnφn + ρbf ( 1 φn ); c, nf = (26) ρ nf 3. NUMERICAL SOLUTION The resulting non-linear system of algebraic equations was solved in the EES (Engineering Equation Solver) latform. The boiling (BO) and condensing (CS) control volumes required, as mentioned earlier, their division into small elements, of equal enthaly increments, to coe with the variation of the local heat transfer coefficient. Since the two zones act as ure counter flow heat exchangers, sequential iterative rocedures had to be established. Basically, the algorithm of these rocedures starts with a guessed value of the heat transfer fluid outlet temerature. x = f x, were carried out after each sequence. Moreover, since the boiling Convergence check and correction, ( ) i+ 1 i heat transfer coefficient deends on the Boiling number, which, by its turn, deends on the still unknown heat flux of the element, an additional inner loo had to be inserted. Convergence of the rogram deended mostly on the robustness of the heat um inut data. For this urose, an additional EES rogram was develoed to test or to roduce coherent inut values. Grid tests carried out with tyical inut data indicated a variation in the cooling caacity of a refrigeration system below 0.5% for an increase from 20 to 50 elements er two-hase zone. Inut data for the simulation included the rotational seed and geometry of the comressor (swet volume or, if recirocating, bore and stroke), geometry of the heat exchangers (inner and outer diameters of both inner and outer cylinders, and length), refrigerant tye, nanofluid characteristics (base fluid and nanoarticle material, size and volume fraction), mass flow rates and inlet states of condenser and evaorator heat transfer fluids, evaorator degree of suerheating and condenser degree of subcooling. Simulation main results included: (i) comressor refrigerant mass flow rate, ower consumtion and discharge temerature; (ii) condenser and evaorator thermal caacities, heat transfer fluids and refrigerant outlet states, condensing and evaorating temeratures, refrigerant ressure dros and area distribution amongst heat exchanger zones; (iii) system coefficient of erformance and its enhancement factor, each one defined as follows: ( ); ξ (,, ) COP = Q W = COP COP (27) h cd c COPh h nf h bf 4. RESULTS Figures 5a and 5b show reliminary results obtained with the simulation model for a liquid-to-liquid 19kW-nominal caacity heat um. One observes that the heating coefficient of erformance, deicted by the enhancement factor, increases with the volume fraction. Imroved heat transfer conditions within the condenser resulted in a reduced condensing ressure thus imroving the heating coefficient of erformance. Note that the thermal conductivity enhancement of 6.1%, for a volume concentration of 2%, imacts the heat um coefficient of erformance in 5.4%. This difference is exlained by the fact that viscosity also increases with nanoarticle volume fraction, while secific heat decreases, and that other thermal resistances in the condenser (redominantly refrigerant-side convection) come into lay, all of them somehow affecting the overall heat transfer mechanism.

9 2531, Page 8 (a) (b) Figure 5: Variation with nanoarticle volume fraction of (a) condensing and evaorating temeratures and COP h enhancement factor; (b) viscosity and thermal conductivity enhancement factors. 5. CONCLUSIONS The following conclusions can be drawn from the resent work: Thermal conductivity, viscosity and density of the nanofluid increase with volume fraction; The thermal conductivity enhancement of the condenser coolant may imact ositively the heat um coefficient of erformance, although other thermal resistances in the condenser, as well as the viscosity enhancement, may attenuate such an increase; Although not shown in this work, the choice of the heat transfer correlation does affect the final results; Nanofluid increased uming ower (due to enhanced viscosity), degrading stability and fouling may become oerational issues and have not been addressed, of course, in the resent model; Exerimental work should be carried out, to verify the findings of the resent simulation. NOMENCLATURE A area, m 2 A cross sectional area, m 2 c a i coefficients of volumetric efficiency eqn. b i coefficients of isentroic efficiency equation Bo Boiling number, - C maximum caacity rate, kw K -1 max C minimum caacity rate, kw K -1 min COP heating coefficient of erformance, - h * C caacity rate ratio, - c secific heat at constant ressure, kj kg -1 K -1 c v secific heat at constant volume, kj kg -1 K -1 D diameter, m D hydraulic diameter, m D h iston diameter (recirocating), m f fanning friction factor, - h secific enthaly, kj kg -1 h secific enthaly function h lv latent heat, kj/kg k thermal conductivity, kw m -1 K -1 ṁ mass flow rate, kg s -1 N ` comressor rotational seed, rm n number of istons (recirocating) NTU number of transfer units, - Nu Nusselt number, - P ressure, kpa Pr Prandtl number, - q heat flux, kw m -2 Q heat transfer rate, kw Re Reynolds number

10 2531, Page 8 s secific entroy, kj kg -1 K -1 s secific entroy function comressor stroke (recirocating), m s T temerature, K T temerature function T saturation (dew oint) temerature function sat U overall heat transfer coefficient, kw m -2 K -1 UA conductance, kw K -1 v secific volume, m 3 kg -1 v secific volume function V c comressor dislacement rate, m 3 s -1 w c comressor work, kj kg -1 W c comressor ower, kw x vaour quality, - Greek symbols α heat transfer coefficient, kw m -2 K -1 α zone averaged heat transf. coeff., kw m -2 K -1 γ secific heat ratio, - P ressure dro, kpa T sc degree of subcooling, K T sh degree of suerheating, K ε effectiveness, - φ n volume fraction, - η em electric motor efficiency, - η s isentroic efficiency, - η v volumetric efficiency, - µ dynamic viscosity, kg m -1 s -1 ξ enhancement factor, - θ ressure ratio, - ρ density, kg m -3 Subscrits a b cond. coolant state leaving sub-cooling zone cond. coolant state leaving condensing zone bf bo cd co c cs ds eq ev i f ii io in l m nf n out rf s sc sf sh v base fluid boiling condenser condenser coolant comressor condensing desuerheating equivalent evaorating friction relative to zone i inner tube inner surface inner tube outer surface inlet relative to element liquid secondary fluid state at boiling zone inlet nanofluid nanoarticle outlet refrigerant isentroic subcooling secondary fluid suerheating vaour 1 comressor suction 2 comressor discharge 3 vaour (dew oint) in CD 4 sat. liquid (bubble oint) in CD 5 subcooled liquid outlet of CD 6 evaorator inlet 7 saturated vaour (dew oint) in EV REFERENCES Bhatti, M. S., and R. K. Shah, 1987, Turbulent and transition convective heat transfer in ducts, in Handbook of Single-Phase Convective Heat Transfer, S. Kakaç, R. K. Shah, and W. Aung, eds., Wiley, New York, Cha. 4. Brown, J. S., Yana-Motta, S. F., Domanski, P.A., 2002, Comarative analysis of automotive air conditioning systems oerating with CO2 and R134a, International Journal of Refrigeration, vol. 25, Buongiorno, J., 2006, Convective Transort in Nanofluids, J. Heat Transfer ASME, vol. 128, Buongiorno, J., et al., 2009, A benchmark study on the thermal conductivity of nanofluids, Journal of Alied Physics, 106,

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