SUMMARYThe axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite-difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two-dimensional lattice Boltzmann equation. Present hybrid scheme was firstly validated by simulations of Taylor-Couette flows between two concentric cylinders. Then the benchmark problems of melt flow in Czochralski crystal growth were studied and accurate results were obtained. Numerical experiment demonstrated that present axisymmetric D2Q9 model is more stable than the previous axisymmetric D2Q9 model (J. Comp. Phys. 2003; 186(1):295-307). Hence, compared with the previous model, present numerical method provides a significant advantage in simulation melt flow cases with high Reynolds number and high Grashof number.

The current investigation is aimed to simulate the complex internal flow in a centrifugal pump impeller with six twisted blades by using a three-dimensional Navier-Stokes code with a standardk-εtwo-equation turbulence model. Different flow rates were specified at inlet boundary to predict the characteristics of the pump. A detailed analysis of the results at design load,Qdesign, and off-design conditions, Q = 0.43Qdesignand Q = 1.45Qdesign, is presented. From the numerical simulation, it shows that the impeller passage flow at design point is quite smooth and follows the curvature of the blade. However, flow separation is observed at the leading edge due to nontangential inflow condition. The flow pattern changed significantly inside the volute as well, with double vortical flow structures formed at cutwater and slowly evolved into a single vortical structure at the volute diffuser. For the pressure distribution, the pressure increases gradually along streamwise direction in the impeller passages. When the centrifugal pump is operating under off-design flow rate condition, unsteady flow developed in the impeller passage and the volute casing.

Abstract:A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended model is used to govern the flow in the porous medium region. At its interface, a shear stress jump was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux is considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configurations are presented. The modeling is suitable for problems which have complex interface boundary conditions coupling between two flow domains.

SUMMARYThe ow ÿelds in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2-0.6 and spacing ratios of 1, 2, 3, 4 and ∞. In this study, it has been further veriÿed that in the laminar ow region, the numerical predictions by k-! turbulence model matched those by the laminar-ow modelling very well. This suggests that the k-! turbulence model is capable of the prediction of the laminar ow as well as the prediction of the turbulent stenotic ow with good accuracy. The extent of the spreading of the recirculation region from the ÿrst stenosis and its e ects on the ow ÿeld downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c 1 = 0:5 with c 2 6c 1 , the peak value of wall vorticity generated by the second stenosis is always less than that generated by the ÿrst stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the ÿrst stenosis. In contrast, for c 1 = 0:5 with c 2 = 0:6, the maximum values at the second stenosis are much higher than those at the ÿrst stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic ows.