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Description
INTRODUCTION
The companion paper (Zhai et al. 2007) reviewed the recent development and applications of computational fluid dynamics (CFD) approaches and turbulence models for predicting air motion in enclosed spaces. The review identified eight prevalent and/or recently proposed turbulence models for indoor airflow prediction. These models include the indoor zero-equation model (0-eq.) by Chen and Xu (1998), the RNG k-[epsilon] model by Yakhot and Orszag (1986), a low Reynolds number k-[epsilon] model (LRN-LS) by Launder and Sharma (1974), the SST k-[omega] model (SST) by Menter (1994), a modified v2f model (v2f-dav) by Davidson et al. (2003), a Reynolds-stress model (RSM-IP) by Gibson and Launder (1978), the large eddy simulation (LES) with a dynamic subgrid scale model (LES-Dyn) (Germano et al. 1991; Lilly 1992), and the detached eddy simulation (DES-SA) by Shur et al. (1999). This paper evaluates and compares the selected turbulence models for several indoor benchmark cases that represent the primary flow mechanism of air movement in enclosed environments.
All of the turbulence model equations mentioned above can be written in a general form as follows:
[rho][[[partial derivative][[bar].[phi]]/[[partial derivative]t]] + [[rho][bar].[u.sub.j]][[[partial derivative][bar].[phi]]/[[partial derivative][x.sub.j]]][[partial derivative]/[[partial derivative][x.sub.j]]][[[GAMMA].sub.[phi],eff][[partial derivative][bar.[phi]]]/[[partial derivative][x.sub.j]]] = [S.sub.[phi]] (1)
where [phi] represents variables, [[GAMMA].sub.[phi],eff] represents the effective diffusion coefficient, and [S.sub.[phi]] represents the source term of an equation. Table 1 briefly summarizes the mathematical expressions of the eight turbulence models selected. In Table 1, [u.sub.i] is the velocity component in i direction, T is the air temperature, k is the kinetic energy of turbulence, [epsilon] is the dissipation rate of turbulent kinetic energy, [omega] is the specific dissipation rate of turbulent kinetic energy, P is the air pressure, H is the air enthalpy, [[mu].sub.t] is the eddy viscosity,[G.sub.[phi]] is the turbulence production for, [phi] and is the rate of the strain. The other coefficients are case-specific, and only some of those introduced here are important.
[TABLE 1 OMITTED]
For the 0-eq. model, V is the velocity magnitude and l is the wall distance. The [G.sub.B] is the buoyancy production term for the RNG k-[epsilon] model. For the LRN-LS model,[f.sub.[mu]], [C*.sub.[epsilon]1], and, [C*.sub.[epsilon]2] are the three modified coefficients (i.e., damping functions) to the standard k-[epsilon] model, and D and E are two additional terms. These five major modifications to the LRN model are responsible for improving model performance near the wall. In the SST model, Y is the dissipation term in the k and [omega] equations, [F.sub.1] and [F.sub.2] are blending functions that control the switch between the transformed k-[epsilon] model and the standard k-[omega] model, and [D.sub.[omega]] is produced from the transformed k-[epsilon] model, so it vanishes in the k-[omega] model when the blending function [F.sub.1] equals one. In the v2f-dav model (Davidson et al. 2003),[[bar].v'.sup.2] is the fluctuating velocity normal to the nearest wall. The variable f is part of the [[bar].v'.sup.2] source term that accounts for nonlocal blocking of the wall normal stress. The variable f is implicitly expressed by an elliptical partial differential equation. So the scalar f in principle can be solved by the same partial-differential-equation solver as the other variables. Note that T in the v2f-dav model also represents the turbulence time scale. In the RSM model, the [[phi].sub.lm] is the pressure-strain term and requires further modeling. In the present study, a liner pressure-strain model by Gibson and Launder (1978) is used.
In the LES model, the overbar represents the filtering. Expressions [[tau].sub.ij.sup.S] and [h.sub.j.sup.S] represent the subgrid-scale (SGS) stress and heat flux. Lilly's (1992) SGS model adopts the Boussinesq hypothesis and derives methods to calculate the coefficient, [C.sub.S], in the eddy-viscosity expression automatically. The presented DES model (Shur et al. 1999) couples the LES model with a one-equation RANS model (Spalart and Allmaras 1992). This one-equation model directly solves a modified eddy viscosity rather than the turbulence kinetic energy as most one-equation models do. The d variable is wall distance and [f.sub.v1] and [f.sub.v2] are the damping functions. Due to space constraints for this paper, a more detailed description of these models is not possible. Since many of the models are available in some commercial software, one could also refer to a user manual (e.g., FLUENT [2005]) for detailed model descriptions.
NUMERICAL METHOD
This study used commercial CFD software, FLUENT version 6.2 (FLUENT 2005) to conduct all the numerical investigations discussed in the next section. Most of the models shown in Table 1 are available in FLUENT except for the modified v2f-dav model. We applied user-defined scalar (UDS) transport equations and coded user-defined functions (UDF) to describe the governing equations of the k, [epsilon], and [[bar].v'.sup.2], as well as the elliptical partial differential equation for f. The RANS models used the second-order upwind scheme for all of the variables except pressure. The discretization of pressure is based on a staggered scheme, PRESTO! (FLUENT 2005). The SIMPLE algorithm was adopted to couple the pressure and momentum equations. If the sum of absolute normalized residuals for all of the cells in flow domain became less than [10.sup.-6] for energy and [10.sup.-3] for other variables, the solution was considered converged. Grid dependence of each case was checked using two to four different grids to ensure that grid resolution would not have a notable impact on the results.
RESULTS AND ANALYSIS
This study evaluated the performance of the eight selected models by simulating the distributions of airflow, air temperature, and... |
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