Figure 7a. Flow in a pump: boundaries of the computational domain.

Figure 7b. Flow in a pump: Top view of the pressure field.
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Figure 7c. Flow in a pump: Bottom view of the pressure field.
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The DSD/SST formulation and the SSMUM approach have been used to simulate a flow in a centrifugal blood pump. The pump is modeled after a KP305 ventricular assist device being developed at Baylor College of Medicine. The computational domain, shown in Figure 7a, consists of a cylindrical chamber with diameter 40.00 mm, housing the impeller with six large vanes and two small ones, and of the inflow and outflow tubes. The shear-slip layer is an axisymmetric shell with exterior diameter of 37.5 mm, and a mostly uniform thickness of 0.5 mm. The shell is closed, except for the opening at the base of the rotor. To accommodate the close spacing between the top of the fuselage and the rotor blades, the thickness of the layer in that area is reduced to 0.04 m.

The mesh consists of 172,152 space-time nodes and 488,689 tetrahedral elements. The regular shear-slip layer, which is one element thick, has 96 segments in the circumferential direction and 45 segments in the radial direction. This layer goes through shear deformation during each time step, and at the end of the time step re-connects to the new nodes belonging to the rotating interior disk. The unstructured meshes in both the inner (rotating) and the outer (stationary) rigid regions of the domain were generated using an automatic mesh generator.

The structured mesh which fills the shear-slip region was generated manually. The impeller is assumed to be rotating at a unoform radial velocity of 3000 rpm. The unsteady flow is computed for 768 time steps with a time step size of 0.000052 s. Figures 7b and 7c illustrate the evolution of the pressure field on the impeller and the housing, with Figure 7c also showing the outer (stationary, blue) and inner (rotating, red) surfaces of the slip layer.

This computation has been carried out on the IBM SP (Nighthawk nodes). At every time step the coupled, nonlinear equations are solved with 4 Newton-Raphson iterations. The coupled, linear equations that need to be solved at each Newton-Raphson step are solved also iteratively, with the GMRES update techniques with a Krylov space size of 100. More information on the SSMUM approach and on this simulation can be found in Behr and Tezduyar (1999a) and (1999b).