1、 VOLUME 13, NUMBER 6 HVAC accepted August 29, 2007Air distribution in enclosed environments is crucial to thermal comfort and air quality. Compu-tational fluid dynamics (CFD) has played an important role in evaluating and designing variousair distribution. Many factors can influence the applications
2、 of CFD for studying air distribu-tion. The most critical factors are the selection of an appropriate CFD approach and a turbu-lence model. Recent advances in CFD approaches and turbulence models provide greatpotential for improving prediction accuracy of air distribution in enclosed environments. T
3、hispaper summarizes recent progress in CFD turbulence modeling and its application to somepractical indoor environment studies. Also described are turbulence models that either are com-monly used or have been proposed and used recently for indoor environment modeling. Finally,this study further iden
4、tifies a few turbulence models that show great potential for modeling air-flows in enclosed environments. A companion paper presents the evaluation of the selected mod-els by using experimental data from the literature. INTRODUCTIONEnclosed environments, such as commercial, institutional, and reside
5、ntial buildings; health-care facilities; sport facilities; manufacturing plants; animal facilities; and transportation vehi-cles, are confined spaces with certain functionalities. It is essential to control air distribution inthe enclosed environments. The parameters of air distribution include, but
6、 are not limited to, airvelocity, temperature, relative humidity, enclosure surface temperature, air turbulence intensity,and concentrations of airborne gaseous, particulate, and liquid droplet contaminants in theenclosed environments. The air distribution control is to create and maintain a comfort
7、able andhealthy environment required by occupants and/or thermofluid conditions for industrial pro-cesses in the enclosed environments.Air distribution in an enclosed environment can be driven by different forces, for instance,natural wind, mechanical fan, and/or thermal buoyancy. The combination of
8、 these flow mecha-nisms (forced, natural, and mixed convection) creates complex indoor airflow characteristicswith impingement, separation, circulation, reattachment, vortices, buoyancy, etc., as illustratedin Figure 1. Most indoor environments have a low mean air velocity of less than 0.2 m/s, and
9、theZhiqiang (John) Zhai is an assistant professor in the Department of Civil, Environmental, and Architectural Engineer-ing, University of Colorado, Boulder. Zhao Zhang is a graduate research assistant, Wei Zhang is an affiliate, andQingyan (Yan) Chen is a professor of mechanical engineering in the
10、School of Mechanical Engineering, Purdue Uni-versity, West Lafayette, IN. 2007, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC Chen et al. 2005). Li et al.(2005) further applied this zero-equation model for outdoor thermal environm
11、ent simulations,which also provided reasonable predictions when compared with the measured data. Airpak(Fluent 2002), commercial CFD software for HVAC applications, has adopted this model as itsdefault. This model is the most popular zero-equation model for enclosed environments.One-Equation Eddy-Vi
12、scosity Models. The turbulent viscosity correlations of zero-equa-tion models may sometimes fail due to the inherent physical deficiencies, such as not consider-ing nonlocal and flow-history effects on turbulent eddy viscosity. One-equation turbulencemodels use additional turbulence variables (such
13、as the turbulent kinetic energy, ) tocalculate eddy viscosity, , such as follows: (2)where is obtained by solving a transport equation, is a turbulence length scale, and is aconstant coefficient. The one-equation models need to prescribe the length scale, , in a similarmanner as that for the zero-eq
14、uation models. Most one-equation models solve the transport equation for turbulent kinetic energy, . Someone-equation models derive transport equations for other turbulent variables, such as the turbu-lent Reynolds number (Baldwin and Barth 1990). Spalart and Allmaras (1992) proposed todirectly solv
15、e a transport equation for eddy viscosity (the S-A model). Unlike most otherone-equation models, the S-A model is local so that the solution at one point is independent ofthe solutions at neighboring cells and thus compatible with grids of any structure. This model ismost accurate for free-shear and
16、 boundary-layer flows. The literature review shows that the S-Amodel, among very few one-equation models used for indoor environment simulation, is a rela-tively popular and reliable one-equation model at present. Torao et al. (2006) simulated venti-lation in tunnels and galleries with the constant
17、turbulent eddy viscosity model, the model,and the S-A model. The comparison of simulation results with detailed experimental data showsgreat performance of the and the S-A models. In addition, the S-A model has been incorpo-rated by one of the newest turbulence modeling methodsdetached eddy simulati
18、on (DES)discussed below. Two-Equation Eddy-Viscosity Models. In addition to the -equation, two-equationeddy-viscosity models solve a second partial differential transport equation for torepresent more turbulence physics. Different and values form various kinds of two-equa-tion models. Two-equation m
19、odels are generally superior to zero- and one-equation modelsbecause they do not need prior knowledge of turbulence structure. The eddy viscosity can becalculated from the and the length scale, . Table 1 lists some typical two-equation models.Table 1. Typical Forms of z Variable in Two-Equation Eddy
20、-Viscosity Modelsz = k1/2/l k3/2/l k/l2k/lSymbol W klReference Kolmogorov (1942) Chou (1945) Spalding (1972) Rodi and Spalding (1984)tU Lvt0.03874 UL=k12-uiui=vtvtCk12l=k l Clkk-k-kz zkl=() k l858 HVAC Menter 1994) have also received increasing attention in many industrial applica-tions in the last
21、decade. In the models, is the ratio of over . Compared to the models, the models are superior in predicting equilibrium adverse pressure flows (Wilcox1988; Huang et al. 1992), while less robust in wake region and free-shear flows (Menter 1992).This led to the development of an integrated model that
22、takes advantage of both models, a fairlyk- k-k-k-k-k-k- k-k- k-k-k-k-k-k-k-k-k- k-k-k-k-k-k-k- k k-k-860 HVAC Lien and Durbin 1996; Davidson et al. 2003; and Laurence et al. 2004).The v2f model, as one of the most recently developed eddy-viscosity models, has a more solidtheoretical ground than LRN
23、models but is less stable for segregated solvers. Choi et al. (2004)tested the accuracy and numerical stability of the original v2f model (Durbin 1995) and a modi-fied v2f model (Lien and Kalitzin 2001) along with a two-layer model (Chen and Patel 1988) fornatural convection in a rectangular cavity.
24、 The study found the original v2f model with the alge-braic heat-flux model best predicted the mean velocity, velocity fluctuation, Reynolds shearstress, turbulent heat flux, local Nusselt number, and wall shear stress. The predicted resultsagreed with the measurements fairly well. However, this mod
25、el exhibits the numerical stiffnessproblem in a segregate solution procedure, such as the SIMPLE algorithm, which requires rem-edy. Davidson et al. (2003) discovered that the v2f model could overpredict in regions faraway from walls. They analyzed the equation in isotropic condition and postulated a
26、 simplebut effective way to limit in nearly isotropic flow regions. With this restriction function, thev2f model can improve the accuracy in regions far away from walls. The v2f model brings moreturbulence physics, especially for low-speed near-wall flows, which are critical in enclosedenvironments.
27、 However, the model has not been well tested and evaluated for indoor environ-ment modeling under different flow conditions. A comprehensive and quantitative evaluation isinevitable before the model can be recommended.Other than the v2f models, some other multiple-equation eddy-viscosity models can
28、be foundin literature. For instance, Hanjalic et al. (1996) proposed a new three-equation eddy-viscositymodel by introducing a transport equation for RMS temperature fluctuation, , for highRaleigh number flows. However, all these models become more complicated and have not beenwell accepted and appl
29、ied for predicting air distributions in enclosed environments. RANS Reynolds Stress Models Most eddy viscosity models assume isotropic turbulence structures, which could fail for flowswith strong anisotropic behaviors, such as swirling flows and flows with strong curvatures.RSMs, instead of calculat
30、ing turbulence eddy viscosity, explicitly solve the transport equationsof Reynolds stresses and fluxes. However, the derivation of the Reynolds stresses transportequations leads to higher-order unsolved turbulence correlations, such as , which needbe modeled to close the equations. The development a
31、nd application of Reynolds stress models can be traced back to the 1970s.Studies directed toward three-dimensional flows, however, began to appear in the 1990s. Earlyapplications of the RSM in room airflow computation include those by Murakami et al. (1990)and Renz and Terhaag (1990). They computed
32、airflow patterns in a room with jets. The resultsshowed that the Reynolds stress model is superior to the standard model because anisotro-pic effects of turbulence are taken into account. The same conclusions were reached recentlyby Moureh and Flick (2003), who investigated the characteristic of air
33、flow generated by a walljet within a long and empty slot-ventilated enclosure. Dol and Hanjalic (2001) predicted theturbulent natural convection in a side-heated near-cubic enclosure. They found that the sec-ond-moment closure is better at capturing thermal three-dimensional effects and strongstream
34、line curvature in the corners, while the model still provides reasonable predictionsof the first moments away from the corners.Chen (1996) compared three RSMs with the standard model for natural convection,forced convection, mixed convection, and impinging jet in a room. He concluded that theRSMs ar
35、e only slightly better than the model and have a severe penalty in computingtime. Based on a large number of applications for engineering flows, Leschziner (1990) con-cluded that RSMs are appropriate and beneficial when the flow is dominated by a recircula-v2fv22uiujukk-k-k-k-862 HVAC Lilly 1992) ca
36、lculates thewith the information from resolved scales of motion as follows:(6)k- k-lij13-kkij2tSij=Sijkkptcs()2S=S 2SijSij= CsCsCsCsCs()2LijMijMijMij-=VOLUME 13, NUMBER 6, NOVEMBER 2007 863where and are the resolved stress tensors and is an average operation on a homoge-neous region. Without the ave
37、rage, the dynamic model has been found to yield a highly variableeddy-viscosity field with negative values, which causes the numerical instability. However, theaverage operation is difficult to implement when the flow field does not have statistical homoge-neous direction. Meneveau et al. (1996) pro
38、posed the Lagrangian dynamic model in which aLagrangian time average was applied to Equation 6. Zhang and Chen (2000) proposed the appli-cation of an additional filter to Equation 6, which improved the simulation of indoor airflows.Other, more complex models have been proposed to improve accuracy, s
39、uch as the dynamicmodels as reviewed by Meneveau and Katz (2000).In the last decade, LES has been increasingly applied to model airflows in enclosed environ-ments due to its rich dynamic details as compared to RANS models. Some representative applica-tions include forced convection flow in a room (D
40、avidson and Nielsen 1996; Emmerich andMcGrattan 1998) or an airliner cabin (Lin et al. 2005), fire-driven air and smoke flows (McGrat-tan et al. 2000), natural ventilation flow in buildings (Jiang and Chen 2001), particle dispersion inbuildings (Jiang and Chen 2002; Bghein et al. 2005; Chang et al.
41、2006; Zhang and Chen 2006). Chow and Yin (2004) indicated that, due to the short computing time and less knowledgedemand of users, the turbulence model is still a practical approach (the first choice) for simu-lating fire-induced airflows; although, the LES approach would give more detailed informat
42、ionthat is important for understanding dynamic fire and smoke behaviors. Tian et al. (2006) com-pared the predictions of indoor particle dispersion and contaminant concentration distribution in amodel room with LES and the standard model and the RNG model. Their study showedthat all three of the tur
43、bulence model predictions were in good agreement with the experimentaldata, while the LES model yielded the best agreement. Their paper thus concluded that the LESprediction can be effectively employed to validate various models that are widely applied inbuilding simulations. Musser and McGrattan (2
44、002) evaluated LES for indoor-air-quality model-ing and smoldering fires and indicated that LES can, in general, predict the experimental datarea-sonably well; however, care mustbe taken in defining convection from heated surfaces andgridresolution. As indicated by most studies, the LES model provid
45、es more detailed and accurate pre-diction of air distributions in enclosed environments, which could be important for understandingthe flow mechanism; however, the high demand on computing time and user knowledge makesLES still viable mainly for research and RANS model development purposes.Detached-
46、Eddy Simulation Models The DES method presents the most recent development in turbulence modeling, which cou-ples the RANS and LES models to solve problems where RANS is not sufficiently accurateand LES is not affordable. The earliest DES work includes Spalart et al. (1997) and Shur et al.(1999), in
47、 which the one-equation eddy-viscosity model (Spalart and Allmaras 1992) was usedfor the attached boundary layer flow, while LES was used for free-shear flows away from thewalls. Since the formation of eddy viscosity in RANS and LES models is similar, the S-A andLES models can be coupled using this
48、similarity. In the near-wall region, the wall distance, d,of a cell is normally much smaller than the stream-wise and span-wise grid size. In the regionsfar away from the wall, the wall distance is usually much larger than the cubic root of the cellvolume, . Hence, the switch between the S-A and LES
49、 models can be determined by compar-ing d and . When d is much larger than , LES is performed; otherwise, the RANS (S-A)model is executed. In practice, the switch between the RANS and LES models requires more programming andcomputing effort than simply changing the calculation of the length scale. In fact, manyimplementations of the DES approach allow for regions to be explicitly designated as RANSor LES regions, ove
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