1、2009 ASHRAE 463ABSTRACTThis study experimentally and numerically examines the 3D effect on the performance of an open refrigerated display cases (ORDC). Three dimensional simulation model with k-E turbulence model incorpating the buoyancy effect is carried out to compare with the results by 2D simul
2、ation model. It is found that the infiltration rate of 3D simulation is significantly larger than that of 2D simulation, indicating the importance of 3D flow field, and it should not be neglected in CFD analysis of an ORDC. The simulation also suggests that turbulence intensity cast a considerable i
3、nfluence on the performance of ORDC. When the turbulence intensity is reduced from 25% to 5%, the temperature difference between the first and the sixth shelf can be reduced from 11C to 5C (19.8F to 9F) and the infiltration rate can be reduced by 25 percent. The 3D compu-tations in terms of temperat
4、ure distribution inside the shelves were compared with the measurements, and good agreement are reported.INTRODUCTIONOpen refrigerated display cases (ORDC) are common used in supermarkets to maintain the food products at setting temperatures. In typical design of ORDC, having a correct temperature s
5、etting and an appropriate controlling entrain-ment or infiltration rate are the most crucial deign parameters as far as energy saving is concerned. The suitable design parameters can be obtained either numerically or experimen-tally. As far as cost is concerned, CFD is regarded as the best design to
6、ol because it is generally fast and reliable. Hence, there were many researchers adopt CFD tools to optimize the design parameters and to improve the performance of open display cases 1, 3-6, 8-14. Amid the CFD examinations of relevant design parame-ters under vertical design situation, most of them
7、 were performed in two-dimensional conditions 1, 3-5, 9-14, and only very few literatures (DAgaro et al. 2006; Foster et al. 2005) were using three-dimensional simulation. The simula-tions 1, 5-6, 8-14 were generally compared with experimen-tal tests but its agreement with the experimental data was
8、usually qualitative rather than quantitative. For the horizontal refrigerated display cases, the simulation by Cui and Wang (2004) is the only one that is in line with measured temperature profile at the outlet of the air curtain. For the vertical refriger-ated display cases, unfortunately, none of
9、the existing litera-tures can provide a quantitative agreement with the experimental data. Notice that in vertical refrigerated display case the momentum force of air jetting from DAG and buoy-ancy force counteracts with each other, resulting in imbalance during simulations. Yet the importance of bu
10、oyancy force can be made clear from the numerical simulation carried out by Bhattacharjee and Loth (2004) and was confirmed experimen-tally by Field and Loth (2006). Without considering the influ-ence of buoyancy force, it was not surprised that the simulation results 9-14 were not consistent with t
11、he measurements.There were some studies associated with the influence of buoyancy force. Cortella et al. (2001, 2002) included the buoy-ancy force in the simulation but the simulation was unable to extend to 3D situation for the model was based on stream-vorticity formulation. DAgaro et al. (2006) c
12、onsidered both buoyancy force and 3D effects, and showed that the cabinet performance was highly dependent on 3D flow structures. However, they mentioned that it was quite difficult to achieve full agreement with experimental data due to the uncertainty in the experimental boundary conditions, espec
13、ially in the A Comparative Study of the Effect of Initial Turbulence on the Performance of an Open Vertical Refrigerated Multi-DeckA Numerical Study and its Experimental ValidationY.F. Chen, PhD H.W. Lin, PhD W.D. Hsieh, PhDJ.Y. Lin, PhD C.C. WangMember ASHRAE Fellow ASHRAEY.F. Chen and H.W. Lin are
14、 researchers, W.D. Hsieh is an engineer, J.Y. Lin is a senior researcher, and C.C. Wang is a senior lead researcher in the Department of Energy and Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan.LO-09-043 2009, American Society of Heating, Refrigerating
15、and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.464 ASHRAE Transacti
16、onsvelocity distribution at the curtain outlets, small imperfection in the actual cabinet geometry, or modeling issues in radiative heat transfer. The forgoing survey suggests that a 3D simulation model taking into account the effect of buoyancy force accompanied with and the exact boundary conditio
17、ns would resolve the present inaccurate agreements between simulations and experiments. Hence it is the purpose of this study to include these effects for simulation. The simulation is made in a typi-cal ORDC having six decks (Fig. 1). In addition, the experi-mental verification is also carried out
18、to compare with the simulation result. PHYSICAL MODELING AND MATHEMATICAL FORMULATIONThe present 3D formulations of the mathematical model-ing consist of equations of mass, momentum, and energy conservation with turbulence being expressed by the k-E model. The Boussinesq approximation for the buoyan
19、cy force is adopted in momentum equation. Schematic of the front view and side view of open refrigeration display cabinet is shown in Fig. 1, and the computational domain is shown in dashed purple line.The simulation is conducted via a commercially available CFD package (CFD-ACE+2007 from ESI group)
20、. Details of the formulation are described as follows.GOVERNING EQUATIONSThe governing equations of turbulence flow with heat transfer are solved by the mass conservation, averaged momentum equation, and averaged energy equation with the k-E two-equations turbulence model which is based on the Bouss
21、inesq eddy viscosity assumption. the mass conservation equation,(1)the averaged momentum equation,(2)Fbuoyancyis the buoyancy force from the difference in density subject to temperature change.the averaged energy equation (3)k- modelTwo-equation k- model are used. Turbulence kinetic energy k and dis
22、sipation rate are computed through trans-port-diffusion equation:(4)(5)Figure 1 The schematic of (a) the front view and (b) the side view of open refrigeration display cabinet (unit: mm in.). The purple dashed line is the computational domain, and positions S1-S6 are the locations of thermocouple se
23、nsors inside the shelves. The anemometer and thermocouple sensors are also put on the middle of DAG and RAG.(a) (b)xj- uj()0=xj- uiuj()pxi-xj- uixj-ujxi-+xj- uiuj()Fbuoyancy+=xj- ujT()xj- Txj-xj- uj()+=xj- ujk()xj-tk-kxj-tuixj-ujxi-+uixj- +=xj- uj()xj-t-xj-C1tk-uixj-ujxi-+uixj- C22k-+=ASHRAE Transac
24、tions 465The generalized Boussinesq eddy viscosity is adopted to represent the Reynolds stress equation, , and the Reyn-olds heat flux equation, as shown in Eq. (2) and (3). Thus, the Reynolds stress ( ) and the Reynolds heat flux ( ) are modeled on the basis of the eddy viscosity and eddy diffusivi
25、ty models, respectively. In this model, the Reynolds stress and the Reynolds heat flux can be written as:(6)(7)where is the turbulent eddy viscosity and is turbulent eddy thermal diffusivity, and can be expressed as(8)(9)Where Prt, ranging from 0.8 to 1.3 in this study, is the turbulent Prandtl numb
26、er. The five empirical constants of Eqs. (4-9) are(10)THE BOUSSINESQ APPROXIMATION FOR BUOYANCY FORCEFor problem having small or medium density gradient, the governing equations can be simplified by invoking the Boussinesq approximation (Chen and Jaw, 1998). The Bouss-inesq approximation for buoyanc
27、y force Fbuoyancyin Eq. (2)takes the form (11)In Eq. (11), is the volume expansion coefficient and can be expressed as(at constant p) (12)As is well known, the Reynolds number (Re) is the most important dimensionless parameter for forced convection whereas the Grashof number characterizes the natura
28、l convec-tion condition. The Grashof number represents the ratio of the buoyancy force to the viscous force and is termed as(13)The Reynolds number is defined as(14)In mixed convection both modes may be comparable to each other. The relative importance of each mode of heat transfer is determined by
29、the value of Gr/Re. The width of the DAG (w = 70 mm 2.8 in., in Fig. 1a) is chosen as the characteristic length (Lc).BOUNDARY CONDITIONThe velocity of DAG is prescribed using the same measured velocity profile, yet the turbulent kinetic energy (k) of DAG can be estimated from:(15)Where TI is the tur
30、bulence intensity, and it is defined as the ratio of the root-mean-square of the fluctuation velocity, , to the mean flow velocity, u(16)The dissipation energy of DAG is initially guessed as 0.01k. Except the door region in Fig. 1(b), the adiabatic (ambient temperature T = 298K 76.7F) and no-slip bo
31、undary condi-tions (u = v = w = 0) are given on the wall surfaces that are shown in purple dashed line in Fig. 1 Fixed pressure (p = pa) and the ambient temperature T = 298K (76.7F) are given at the outlet boundary of the door region. In this study, the air channel from the evaporator to the dischar
32、ge air grill (DAG) is neglected. To amend this minor difference, a negative pressure is given at the outlet of the RAG (Fig. 1b). The magnitude of the pressure is then calculated when the flow rate is balance between the DAG and RAG.THE PERFORMANCE OF THE OPEN REFRIGERATED DISPLAY CASEFor the open r
33、efrigerated display case, the cold air is provided through an inlet jet called the discharge air grille (DAG) located at the top front of the unit as appeared in Fig. 1b. The cold air jet, termed as air curtain, acts as an invisible barrier between cabinet and outside warm air. The continuous flow o
34、f outside warm air into the air curtain and its subsequent mixing with cold air is called entrainment, and some of the warm air becomes infiltrated. When outside warm air has infil-trated through the return air grill (RAG), it will increase the air temperature and impose a cooling load on the refrig
35、eration system. Obviously, to keep a minimum infiltrated rate from outside warm air is a critical issue in energy conservation. The infiltration rate, e, was usually used to indicate the perfor-mance of the open refrigerated display case, and is defined as (Bhattacharjee and Lothe, 2004; Navaz et ak
36、, 2005; DAgaro et al., 2006) (17)where . In the ideal air curtain, the uiujujuiujujuiuj tuixj-ujxi-+23-ijk=ui tTxi-=tttCk2-=tCPrt-k2-=C0.09 C1, 1.44 C2, 1.92 k, 1.0 , 1.3=FbuoyancygT Tamb()ij=1-T-1-ambTambT-=Grg TTamb()Lc3v2-=RevLc-=k32- TI u()2=uTI u u=eTcaptureTDAG()TambTDAG()=TcaptureTx()xd0xcapt
37、urexcapture-=466 ASHRAE Transactionsinflitration rate would be zero (ae= 0).EXPERIMENTAL SETUPThe vertical open fronted chilled multi-deck cabinet is used for experimental verification. The size is 0.91 m (2.99 ft) L 0.6 m (1.97 ft) W 1.9 m (6.23 ft) H. Tests were conducted accord-ing to the EN441 S
38、tandard requirements. An environment chamber (5 3.6 2.8 m 16.4 11.81 9.19 ft in size) main-tains the ambient conditions at 25C (77F) and at a relative humidity of 60%. The corresponding air curtain velocities are measured by a Sierra-600 hot wire anemometer having an accu-racy of 1% of the measured
39、value in the range of 0-2 m/s (0-6.56 ft/s). The air curtain temperature is measured by T-type thermo-couple (accuracy of 0.1C 0.18F) with calibrated range from -20C to 50C (-4F to 122F).Figure 1 is the schematic of the side view and the front view of the open cabinet. A thermocouple and an anemom-e
40、ter are installed in the middle of discharge air grill (DAG) to record the time history diagram of temperature and velocity. Six thermocouples are also installed in the middle of each shelf, and the positions are shown designated as S1 to S6 in Fig. 1.SIMULATION RESULTS AND DISCUSSIONSThe computatio
41、nal domain and grid system in x-y plane, x-z plane, and y-z plane are plotted in Fig. 2(a)-(c). The total cells number is 174864. The effect of evaporator area and the air channel are neglected in simulation, so that the cold air is provided from the discharge air grille (DAG) located at the top fro
42、nt of the unit (Fig. 1b), and the inlet velocity profile of DAG is given from experimental measurement. The measured velocity profile along the x-direction is shown in Fig. 3 and this is adopted as the entrance velocity profile for calculation input with z-direction being assumed uniformly. The aver
43、age velocity is 1.3 m/s (4.27 ft/s) and the Reynolds number Re is equal to 6314. The temperature of the measured cold air of DAG is 0C (32F) and the Grashof number is near 3.5106.THE EFFECT OF TURBULENCE INTENSITYFigure 4a is the temperature distribution on the media vertical section (x-y plane at z
44、 = 0.42 m 1.38 ft) with turbu-lence intensity being 5%, 10%, and 25%, respectively. By checking the temperature distribution from the different Figure 2 The computational grid system in (a) x-y plane, (b) x-z plane, and (c) y-z plane (unit: m ft).Figure 3 The input velocity distribution at the DAG.A
45、SHRAE Transactions 467shelves, it is found that a significant rise of temperature accompanied with higher turbulence intensity (Fig. 4a). The width of the cold air curtain becomes thicker as the turbulence intensity is increased from 5% to 25% (Fig. 4b). Figure 4c illustrated the velocity magnitude
46、distribution of the x-z plane at y = 0.62 m (2.03 ft) from the bottom, which is located near the sixth shelf. It is obvious that the air is infiltrated or entrain-ment from the outside of the cabinet, even though the turbu-lence intensity is as low as 5%. The infiltrated or entrainment is increased
47、with the turbulence intensity further increased, so that the infiltration rate is increased from 0.4 to 0.5 as turbu-lence intensity is increased from 5% to 25% (Fig. 5). 3D EFFECTSAs mentioned in the introduction, the three dimensional effect may play a decisive role. Hence, it is interesting to ex
48、amine the qualitative difference amid the two-dimension (2D) and three-dimension (3D) simulation. The relevant comparisons for the temperature and velocity along the open front of DAG to RAG (position L1 to L6) associated with different turbulence intensities are plotted in Fig. 6. The y (0 m 0 ft) to 1.2 m 3.94 ft) is the distance from
