ASHRAE IJHVAC 16-6-2010 HVAC&R Research.pdf

1、Volume 16, Number 6, November 2010An International Journal of Heating, Ventilating,Air-Conditioning and Refrigerating ResearchAmerican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.Volume 16, Number 6, November 2010HVAC accepted March 11, 2010This paper is based on findings r

2、esulting from ASHRAE Research Project RP-1271.Airflows in an enclosed environment are a wall-bounded unstable flow, which is difficult to sim-ulate using either a RANS or an LES model. The hybrid RANS/LES simulation, which uses aRANS model for the near-wall attached boundary layers to avoid an exces

3、sively fine grid, andan LES for the separated turbulence region to resolve unstable eddies, is promising for this typeof flow. However, the available hybrid RANS/LES models have not performed well for indoorairflows due to the RANS model they used. This investigation developed a new RANS/LES modelfo

4、r indoor airflow modeling using a semi-v2f model. This model correctly predicted near-wallflows by taking into account the wall normal stress, which was calculated by an algebraic equa-tion. By applying the new model to a mixed-ventilation flow in a room and a strongbuoyancy-driven flow with a high

5、temperature gradient in a room, the predicted results areaccurate and the model seems robust.INTRODUCTIONAirflow in enclosed spaces can be complicated due to complex flow features such as flowtransition and lack of stability. Many indoor airflows are transitional when the Reynolds numberbased on the

6、 supply air grille is in the region of 2000 Re 3500. Turbulence is generated atthe grille where the fluctuating component of velocity is a fraction of the mean velocity. As theair travels further into the room, the fluctuating component may decay gradually due to thedecrease in the mean flow gradien

7、t and damping effect of the solid surfaces. Therefore,relaminization may occur within the occupied space, and the flow is transitional. In addition toflow transition, in many indoor environments, airflow with relatively high air change rates(between 5 to 20 ach) can be unstable under the transitiona

8、l Reynolds number. One reason forthis is that the transitional phenomenon makes the flow unstable. In the transitional region, theinertial force is approximately balanced by the viscous force. A random small impact from themain stream can break down this balance and lead to transitional flow. This m

9、echanism resultsin instability of the main flow.Another reason for unstable flow is the interaction between different flow features. Manyenclosed environments are mechanically ventilated. However, the air can also be driven bybuoyancy in the occupied zone, where the thermal plume can be as strong as

10、 the flow from themechanical ventilation system. The two flows interact, and result in instability. The complex geometry of the indoor environment can also lead to unstable flow. Furniture inan indoor environment can generate flow separation, which is usually unstable. As discussedMiao Wang is a doc

11、toral candidate and Qingyan (Yan) Chen is a professor at the Ray W. Herrick Laboratories, Schoolof Mechanical Engineering, Purdue University, West Lafayette, IN.01_Wang.fm Page 731 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

12、 (www.ashrae.org). Published in HVAC therefore, the number of time steps should be in the order of 106. However, it is not feasibleto perform this simulation on a personal computer or a moderate computer cluster in the nearfuture.A more realistic and widely used approach for indoor airflow simulatio

13、ns is by Reynolds-Averaged Navier-Stokes (RANS) equation modeling. The RANS simulation solves thetime-averaged N-S equation and models the additional Reynolds stresses. This modelingapproach can significantly reduce the grid resolution requirement, and can be performed assteady-state. Many studies h

14、ave used different RANS models for indoor airflow simulation(Yuan et al. 1999; Holmes et al. 2000; Gadgil et al. 2003; Hsieh and Lien 2004; Zhang et al.2007) and found mixed results of the model performance. Zhang et al. (2007) tested eight popu-lar turbulence models for different indoor airflows an

15、d concluded that no model was superior tothe others. Wang and Chen (2009) further tested these eight models using a set of experimentalcases with gradually added flow features and found that the RANS models failed to predict flowseparation. This conclusion was supported by Costa et al. (1999) to som

16、e extent, who found thatthe low-Reynolds-number model suffered from a problem, leading to the prediction of an unre-alistic local minimum of the wall heat transfer near points of flow reattachment. The failure ofthe RANS models to predict a separated flow could have resulted from the time-averaginga

17、pproach. In the separation region, flow is very unstable, and the velocity magnitude and direc-tion change rapidly. Therefore, it may not be meaningful to have a time-averaged solution forthis case since the information contained by the mean value of flow variables is too limited todescribe the rapi

18、dly varying unstable flow. Thus, the RANS models may not be capable of cor-rectly predicting unstable airflow features in enclosed spaces, such as the separation caused byfurniture, impingement flow, and unsteady plumes.With the advancement of computing power, large eddy simulation (LES) is becoming

19、increasingly popular for engineering applications due to its ability to solve unstable separatedflow. LES solves the filtered N-S equation for the energy-containing eddies (large eddies) andmodels the subgrid-scale flow motions (small eddies). The turbulence model for LES is not asimportant as that

20、for a RANS model (Wang and Chen 2009). In other words, LES relies more onfundamental flow physics than on modeling assumptions. As a result, LES is more accurate andinformative than RANS models for airflow modeling, especially for a separated and unstableflow. Since LES solves only the large-scale e

21、ddies, the computing cost is much lower than thatof DNS. The cell size required by LES could be much larger than the Kolmogorov length scale.Therefore, LES uses significantly less computational time than DNS. For example, to calculate a01_Wang.fm Page 732 Monday, September 27, 2010 5:34 PM 2010 Amer

22、ican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC Kawai and Fujii2005). Many other studies adopted multi-equation RANS models with LES, such as k- model(Strelets 2001; Davidson and Peng 2003), k- model (Hamba 2001, 2003), and k-l model(Tu

23、cker and Davidson 2004). After reviewing the RANS/LES hybrid models, our effort was todevelop a new hybrid model, the semi-v2f/LES model, for modeling airflows in an enclosedenvironment. The new model used transport equations for k and , and an algebraic equation forthe normal stress near a wall to

24、model turbulence viscosity in the RANS region and subgrid tur-bulence viscosity for the LES region. The new model was tested by applying it to a mixed con-vection flow in a model room, and to a strong buoyancy-driven flow with a high temperaturegradient in a room.MODEL DEVELOPMENTHybrid RANS/LES Sim

25、ulation for Indoor AirflowIndoor airflow is governed by the N-S equation together with the energy equation for the fluidphase (FLUENT 2003). Since it is not feasible to use DNS for solving such a flow, the N-Sequation should be approximated in order to make it solvable with the present capacity of c

26、om-puters. By using Reynolds-averaged approach, flow variables can be written as(1)where is the mean value of flow variables, and is the fluctuating part of flow variables. Onthe other hand, LES uses a filter to obtain large-scale flow variables:(2)where the overbar denotes filtered variables, and i

27、s a filter function.The two methods can transform the N-S equation into a single form:(3)+= x, t() x, t()Gx, x,t()xdV=Guixi- 0=01_Wang.fm Page 733 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HV

28、AC Strelet 2001; Tucker and Davidson 2004). One can explicitlyreplace the in the DES-SA model with the turbulence length scale, or implicitly involveother RANS models. Strelet (2001) developed a RANS/LES hybrid model based on the shearuit- ujuixj-+1-Pxi- v2uixjxj-ijxj-+=ijijuiuj=ijuiujuiuj=tuit- uju

29、ixj-+1-Pxi-xjt+()uixj-+=tt- ujxj-+ cb1Scw1fwl-21-xk+()xk-cb2-xk-xk-+=cb1, cb2, cw1lmin dwCDES,()= max x y z,=ldwCDESCDES ldw01_Wang.fm Page 734 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC

30、Wang and Chen 2009).Therefore, our effort was to identify an appropriate RANS model for indoor airflow simulationsand to develop a new hybrid model with the RANS model.Identification of a Suitable RANS Model for Hybrid SimulationAs discussed above, the accuracy of the RANS model is essential to the

31、performance of ahybrid model. Some studies have evaluated different RANS turbulence models for indoor air-flow, which could be helpful for choosing a suitable RANS model. Zhai et al. (2007) identified17 models that may be appropriate for calculating indoor airflows. Wang and Chen (2009) testedsix of

32、 them that are most promising for indoor airflows and concluded that the v2f, RNG k-,and Reynolds stress models were the best. This conclusion was consistent with that from Zhanget al. (2007) for forced, natural, and mixed convection flows.The RNG k- model uses a wall function near solid boundaries,

33、 which makes it unsuitable fora hybrid model. The Reynolds stress model can resolve the near-wall region, but it has six scalartransport equations that are too computationally expensive. The v2f model can be used for thehybrid model, since it can resolve the near-wall viscous region at a reasonable

34、computationalcost (three scalar transport equations) and accounts for anisotropic behavior near the wall. How-ever, studies from the literature (Durbin 1991; Davidson et al. 2003) and our preliminaryresearch show that the transport equation for the wall normal stress and the elliptic equationfor the

35、 relaxation function make the model numerically unstable. Therefore, it is essential tosimplify the v2f model before implementing it in a hybrid simulation.The Semi-v2f/LES ModelOur effort to develop the v2f model further was to introduce an algebraic equation for the nor-mal stress :(12)to replace

36、the transport equation for and the elliptic equation for , which have been prob-lematic. The procedure was first to derive new equations for and turbulence viscosity. Theconstant in the equations was then determined through curve fitting of the flow data obtained forindoor airflow. The detailed proc

37、edure was as follows.DRANSkk32l=lmin lk-CDES,()=CDESv2fv2v2fk, y ()=v2fv201_Wang.fm Page 735 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC the other was a 110 77 101 grid (fine). The v2f mod

38、el mod-ified by Davidson (2003) (v2f-Dav), the LES dynamic Smagorinsky-Lilly (LES-DSL) model,and the DES realizable k- model were also included in this study to evaluate the performance ofthe new model. The LES-DSL and DES realizable k- models used a 110 77 101 grid, andthe v2f-Dav model used a 44 4

39、4 44 grid. The comparison was based on the velocity, temper-ature, and turbulence kinetic energy at 10 positions, as shown in Figure 2b. The results shown inthis paper were at the positions where turbulence models had the best, worst, and average perfor-mances. For definition of the three categories

40、, please see Wang and Chen (2009).Figure 3 depicts the four models air velocity predictions. In general, all the models predictedvery similar, acceptable results. The new model slightly underpredicted the velocity at position(6) with a fine grid. The realizable k- had a similar prediction at this po

41、sition. However, the dis-crepancy was very small. At position (5), where the flow was separated, all the models underpre-dicted the velocity. However, the new model with the fine grids and the DES realizable k- modeldid better than the other models. The v2f-Dav model failed primarily because Reynold

42、s averag-ing may not be appropriate for separated flow. The LES-DSL model failed to provide goodresults because it requires a finer grids than DES. This also reflects the advantage of the DESmodels. At position (3), all the models gave similar results, though with small discrepancies.Figure 4 shows

43、the temperature prediction by the models. At position (8), the new model withcoarse grids surprisingly predicted better results compared with the other models. The newmodel with fine grids also predicted slightly better results than the realizable k- and v2f-Davmodels. The results of the LES-DSL mod

44、el were comparable with those of the new model withfine grids. At position (4), the results of the new model with the two grid distributions were bet-ter than those from the other models. At position (5), the new model with the fine grids predictedone of the best profiles. The new model with coarse

45、grids predicted an incorrect peak at Y/L =0.6. The grid distribution of 44 44 44 was not fine enough for the new model to capture theseparated flow.Figure 5 shows the turbulence kinetic energy profiles predicted by the four models. The newmodel with fine grids predicted the best result at position (

46、1). The DES realizable k- modelFigure 3. Air velocity profiles predicted by the semi-v2f/LES model for mixed convectionflow.01_Wang.fm Page 739 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC

47、it is indeed difficult to capture fluctuating, highly separatedflow. At position (10), where most models showed average performance, the LES-DSL modelwas slightly better.Strong Buoyancy-Driven FlowThe second case tested was a strong buoyancy-driven flow in a fire room. This case, chosen totest the n

48、ew models robustness, was designed by Murakami et al. (1995), who measureddetailed fluctuating velocity using two-component laser doppler velocimetry (LDV), and theFigure 4. Air temperature profiles predicted by the semi-v2f/LES model for mixed con-vection flow.Figure 5. Turbulence kinetic energy pr

49、ofiles predicted by the semi-v2f/LES model formixed convection flow.01_Wang.fm Page 740 Monday, September 27, 2010 5:34 PM 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC bottom: I-P.01_Wang.fm Page 742 Monday, September 27, 2010 5:34 PM 2010 America