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X. D. Niu et al. / Adv. Appl. Math. Mech., 5 (2010), pp. 564-572 567 where x = x(x, y) is the spatial vector. The weight coefficients wα and the sound speed cs are determined by the discrete velocity models and for the D2Q9 model they are (0,0), eα = (±1,0),(0,±1), (±1, ±1), 94, α=1, wα=91, α=2,···,5, 1, α=6,···,9, 36 c2s = 13. The relaxation parameters τf and τg in Eqs. (2.2a) and (2.2b) are determined by the (2.5a) (2.5b) (2.6) viscosity η and the diffusivity D, respectively, as τf = η +0.5, ρ c 2s δ t The density ρ, velocity u and temperature T are calculated by 9199 ρ = ∑ fα, u = ρ ∑ eα fα, T = ∑ gα. α=1 α=1 α=1 3 Problem defination and numerical simulations ρ c 2s δ t τg = D +0.5. We consider a horizontal channel as shown schematically in Fig. 2. The domain of interest is two-dimensional with dimensions of length L=200.0mm and height d=20.0mm. The computational geometry is bounded on the top and bottom by solid walls, which are assumed to be subjected to constant heat fluxes. The left and right surfaces are specified as inlet and outlet, respectively. We consider the case where the flow convection due to pump driving the supercritical CO2 fluid. The flow is consid- ered to be a developing flow with constant inlet velocity. In numerical simulations, three inlet Reynolds numbers of Rein=210, 420 and 840 and three constant heat flux conditions of q=400, 600 and 800[W/m] are investigated. In order to model accurately the solution variables with large gradients in the near- wall region and capture adequately the flow into and out of the channel, structured non-uniform grid systems are generated in the computational domain and the Taylor- series-expansion & least-square-based lattice Boltzmann scheme [8] is employed to solve the Eqs. (2.2a) and (2.2b). The grid is finer close to the wall, inlet and outlet (see Fig. 3). Grid independence of results is established by employing various grid (2.4a) (2.4b) (2.4c)PDF Image | Study of Forced Convection Heat Transfer of Supercritical CO2 in a Horizontal Channel by Lattice Boltzmann Method
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