40
Yuguo Li
1 ij3 = −C3 Fij − ij Fkk 3 3 3 uk um nk nm ij − uk ui nk nj − uk uj nk ni ijw = C1 k 2 2 3 3 + C2 km2 nk nm ij − ik2 nk nj − kj2 nk ni 2 2 3 k2 3 + C2 km3 nk nm ij − ik3 nk ni 2 Cl xn
(1.137)
(1.138)
The above model is only one of few other Reynolds stress models developed in the literature. Launder et al. (1975) referred to the above model as the Basic Reynolds Stress Model. The closure coefficients Cs = 0 22" C1 = 1 8" C2 = 0 6" C3 = 0 6" C1 = 0 5" C2 = 0 3" C3 = 0 0" Cl = 0 15" C = 0 15" C1 = 1 44" C2 = 1 92
(1.139)
Examples of application and evaluation of the Reynolds stress models in building ventilation can be found in Chen (1996). 1.4.6 Large eddy simulation If we try to solve the complete time-dependent solution of the Navier– Stokes and continuity equations, we have to deal with the so-called direct numerical simulation (DNS). In principle, the computational domain must be sufficiently large to accommodate the largest turbulence scales, and the grid must also be sufficiently fine to resolve the smallest eddies whose size is of the order of the Kolmogorov length scale #, and similarly, the time step should be at least of the same order as the Kolmogorov time scale . If we compute only the large eddies and those small eddies not resolved or modeled, we have the so-called large eddy simulation (LES). It is believed that the large eddies contain most of the turbulence energy, and they are directly affected by the boundary conditions. The small-scale turbulence has nearly universal characteristics and is more isotropic. Thus, the small eddies are easier to be modeled than large eddies. It should be noted that both methods require significant computer resources. Wilcox (1993) summarized the required number of grid points for a turbulent channel flow with DNS and LES, when a stretched grid is used. 9
NDNS ≈ 3Re 4 0 4 NDNS NLES ≈ Re 1/4
(1.140) (1.141)