Modeling and Simulation of an Air-cooling Condenser under Transient Conditions

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1 Availale online at.sciencedirect.com Procedia Engineering 3 (202) International Conference on Advances in Computational Modeling and Simulation Modeling and Simulation of an Air-cooling Condenser under Transient Conditions Xing Xue a,xianming Feng a*,junmin Wang a,fang Liu a a Guilin University of Electronic TechnologyNo. Jinji Road,Guilin 54004China Astract Condenser is a major component of the refrigeration and air conditioning system, the performance of the condenser ill have a direct influence on the system efficiency. In practice, the condenser alays orks in varying conditions. So it is essential to investigate its transient response for system design and control strategy. In this paper, a dynamic mathematical model of an air-cooling condenser ased on the moving-oundary model has een developed for control strategy, using the zone model. Customary moving-oundary approach applied in heat exchanger simulation alays focuses on the refrigerants side ut neglect the air side. In order to study the actual ehavior of the condenser, oth sides of the condenser coil are fully considered in the model for this ork. Moreover, to avoid iterative operation, state parameters of the mathematical modelare expressed as the functions of the temperature in this paper. Depending on this model, several types of transient conditions such as step changes of the compressor speed, air temperature and air quality flo rate are studied. The simulation results sho satisfactory predictions hich indicate that this model can e used to formulate a control algorithm. 20 Pulished y Elsevier Ltd. Selection and/or peer-revie under responsiility of Kunming University of Science and Technology Open access under CC BY-NC-ND license. Keyords: Condenser; Moving-oundary; Transition simulation Introduction Condenser is a major component in refrigeration system and air conditioning system, its performance has a direct effect on the system efficiency, such as the effect of service life and energy consumption. At present, due to its energy saving, frequency conversion air conditioning is gradually recognized y people. * Corresponding author. Tel.: ; address:myisfxm@26.com Pulished y Elsevier Ltd. doi:0.06/j.proeng Open access under CC BY-NC-ND license.

2 88 Xing Xue et al. / Procedia Engineering 3 (202) Its compressor isnt frequent start and stop, so the study should focus on short transient changes, namely the transient response of various oundary conditions, so as to provide optimization control strategy for frequency conversion air conditioning. Here, a dynamic mathematical model of an air-cooling condenser ased on the moving-oundary Nomenclature density (kg/m 3 ) A area (m 2 ) h enthalpy (kj/kg) L length (m) p pressure (Pa) Superscripts t time (s) mean value convective heat transfer coefficient (W/(m 2 k)) T temperature () D diameter of heat transfer tue (m) C all specific heat (J /(kg K)) Suscripts,2,3 regions of condenser i, o inner, outer 2,23 regions interface f o outer area of condenser per meter of pipe length in, out inlet, outlet o fin tue efficiency r refrigerant void fraction of to-phase flo a air m mass flo rate (kg/s) g, l saturated gas, saturated liquid u velocity (m/s) saturation T degree of superheat () pipe all model has een developed, using the zone model in this paper. Moving-oundary model is frequently used to track the phase change of the refrigerants fluid in the heat exchanger, as to the condenser, it is the length change of the phase region, namely the superheated region, the to-phase region and the su-cooled region. Moving-oundary method used in simulation of heat exchangerhas een presented in many literatures[-4], hoever, they rarely considered the time-variant void fraction, time-variant heat transfer coefficient together,moreover, they rarely discussed the heat exchange eteen the pipe and the air side[5]. Hence, the time-variant mean void fraction of the to-phase and the time-variant mean heat transfer coefficient of each region are taken into account simultaneously in the model in this paper, as ell as the heat exchange eteen the pipe and the air side. In order to avoid the iterative calculation, all state parameters of the mathematical model are expressed as the functions of the temperature. The zone model constructed here ill ell predict the transient response of the condenser, hen the compressor speed, air temperature and air quality flo are changed separately.

3 Xing Xue et al. / Procedia Engineering 3 (202) Condenser Model An air-cooling condenser of finned tue is discussed in this paper. Due to the complexity of physical model and dynamic process, the primary assumptions for condenser are as follos: The refrigerant is one-dimensional flo and compressile fluid. The air is one-dimensional flo and incompressile fluid. The refrigerant and the air flo are regarded as a counter-current form[6]. The pressure drop in the condenser and the axial heat conduction of pipe all are neglected. The specific heat of air is constant. The energy storage in the air is neglected. There are three zones in the condenser at the very start..m in,t rin, in,t aout Superheat region To-phase region Su-cooled region air fluid 2.m,T r,t,,t a refrigerant m 2,T r2,t 2,T a2 4.m 2, T, T 2, 2,T a2 L L2 L3 5.m 23,T r23,t 23,T a23 6.m 3,T r3,t 3, 3,T a3 Figure : Schematic of the condenser model 7.m out,t rout,t ain There is the heat exchange eteen the refrigerant and pipe all, as ell as heat exchange eteen the air and pipe all. According to aove assumptions, the governing equations of the refrigerant flo for mass and energy can e expressed as follos[7]: ( u) 0 t x () h p uh 4 i( T Tr) t t x Di (2) The energy equation for pipe all and fins is: CA T i Di( Tr T) ofoo( Ta T) t (3) Given of the small mass and specific heat of the air, the mass and energy storage in the air can e neglected. Therefore, air side can use steady state equation hich descries as elo: dha ma Doo( Ta T) dx (4) hen the refrigerant in the condenser is to-phase region,the and h in the aove equations can express as follos: g ( ) l h ghg ( ) lhl (5) is the average void fraction in the to-phase region, it can reference the literature []. [ ( 2/3 / ) (2/3ln( / ) )]/[( 2/3 2 / ) ] (6) 3. Numerical Resolution g l g l g l ()- (4) are the asic equation of the dynamic model of the condenser. Simultaneous equations should e

4 820 Xing Xue et al. / Procedia Engineering 3 (202) applied in each region of the condenser. Integration of the simultaneous equations over the superheated region, the to-phase region and the sucooled region are along the flo direction, from 0 to L, from L to L 2, from L 2 to L 3, respectively. Leinizs rule is employed on the simultaneous equations in each region. The Integral results of the superheated region give as elo. And the computational detail of the other to regions is omited, due to its similar method to the superheated region. 2 ( dt dtrin dl m min ) L ( g ) 0 T 2 T dt 2 T dt dt Ai L h h p dt dl g g T 2T T 2T T dt dt [ L ( ) L h( ) L ] ( h h ) g h dt minh in g m2 L Li T Tr i 2 i i h 4 ( ) A T dt A D dt dl 2 i i r o o a C A ( T T ) L D( T T ) L D ( T T ) (9) dt dt mc a a ( Taout Ta 2) Lo Do ( Ta T ) (0) In the aove equation T Trin T, f( T, T), h f( T, T), Tr ( Trin T)/2, Ta ( Taout Ta 2)/2.Integral calculation of the three regions contains 2 equations ith 7 state variales: ( L, L 2, T, T rout, T, T 2, T 3 ). The dependent variale ( T aout ) can e calculated from the state variales through the equations. To solve the equations, initial conditions and oundary conditions must e added. Initial conditions of the dynamic model can e calculated y the steady-state simulation. Boundary conditions at the inlet of the condenser is set as the outlet of the compressor, and at the outlet of the condenser, the mass flo rests ith the TEV. At the outside of the condenser coil, there is the air hich acts as the cooling medium of the aircooling condenser. Hence the oundary conditions on the heat exchanger surface depend on the air conditions hich are artificial hypothesis in this paper. The oundary condition can e descried as: x0, hin hcpo, min mcpo ; xl, L2 L3 mout mv ; The ma and Tain are set to e some value. 4. Simulation and Discussions The condenser is a tin circuit air-cooling coil ith 52 tues, the pipe length is 800 mm, inner diameter is 6.75 mm and the outer diameter is 7mm.The numer of aluminum flat fin is 570.Rotor speed of the scroll type compressor is 2820rpm, and compressor cavity volume is 4.8cm 3. The coefficient of thermal expansion valves is E-007. Based on the aove structure parameter model, performance of fin and tue condenser ith R22 as simulated to achieve a stale state first, and then changed the oundary conditions. These transient conditions include the compressor speed, the air inlet temperature and the air inlet flo rate. When the simulation as doing, one of the aove conditions as changed and the other to conditions remain unchanged. At t=9 s the compressor speed as increased y 63, at (7) (8)

5 Xing Xue et al. / Procedia Engineering 3 (202) Tale : Steady-state results steady-state results L =2.62 L 2=7.37 L 3=2.7 C =385 =8960 i =623 i2 T ain =34 r m ain =0.233 T =80 T r 2 =5 T r3 =45 =455 i3 =426 o =59 o2 =60 o3 =60 P =.9965E+6 60 Q= m in =0.029 t=200s the air inlet temperature as increased y 35.7and at t=400s the air inlet flo rate as increased y kg/s. The transient response of condenser pressure and heat exchange quantity isshon in Fig.2 and Fig.3, respectively. The Fig.2 shos that other parameters are constants : (a) When the compressor speed is increased, the refrigerant storage in the tue increases, so that the pressure of the condenser rises. () When the air inlet temperature is increased, the pressure of the condenser rises due to the reduction of heat exchange.(c) When the air inlet flo rate is increased, the pressure of the condenser reduces for the enhancement of heat transfer. The Fig.3 shos that other parameters are constants : (a) An Figure 2: Pressure in the condenser Figure 3: Heat exchange in the condenser increase of compressor speed as ell as an increase of air inlet flo rate result in more heat exchange.()an increase of air inlet temperature results in less heat exchange. These simulation results otain the right trends comparing ith other related literature. 5. Conclusions A zone transient model for predicting air-cooling condenser performance has een developed in this paper. Ne features of the model include the heat transfer eteen the air and fin, the air and tue are took into accounted and considered into the steady state, state parameters are all expressed as the functions of the temperature.the response of the condenser to varying the compressor speed, the air inlet temperature and the air inlet flo rate is studied and yields expected trends using this model. The simulation speed and rationality of the model ill provide certain reference value for the optimization design of the control strategy in the refrigeration and air conditioning system.

6 822 Xing Xue et al. / Procedia Engineering 3 (202) References [] Jensen J.M.,Tummescheit H. Moving oundary models for dynamic simulations of to-phase Flos. 2nd International Modelica Conference,Proceedings,2002,p [2] Nan Liang, Shuangquan Shao,Changqing Tian,Yuying Yan. Dynamic simulation of variale capacity refrigeration systems under anormal condictions. Applied Thermal Engineering,30(200) [3] Thomas L. McKinley, Andre G. Alleyne. An advanced nonlinear sitched heat exchanger model for vapor compression cycles using the moving-oundary method. International Journal of Refrigeration, 3(2008) [4] Weijiang Zhang. Chunlu Zhang. A generalized moving-oundary model for transient simulation of dry-expansion evaporators under larger disturances. International jounal of refrigeration;29(2006)927. [5] M. Willatzen, N. B. O. L. Pettit and L. Ploug-Sørensen. A general dynamic simulation model for evaporators and condensers in refrigeration, Part I: moving-oundary formulation of to-phase flos ith heat exchange. Int.J.Refrig. (998),p, [6] Guoliang Ding. Simulation technology for refrigeration and air conditioning appliances. Chinese Science Bulletin, Vol. 5 No. 6 August (2006) [7] R.N.N. Koury, L. Machado, K.A.R. Ismail. Numerical simulation of a variale speed refrigeration system. International Journal of Refrigeration, 24(200)

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