Numerical Simulations of Complex Three-Dimensional Viscous Flows

Four issues related to accurate numerical simulations of three-dimensional, viscous, compressible flows in complex -shaped geometries are addressed. First, a new formulation of the "compressible" Navier-Stokes equations for rotating reference frames was developed, which can easily be implemented into existing computer codes. The equations developed have the same form as the governing equations for inertial reference frames except for source terms that account for the effects of the rotation of the reference frame. The governing equations were tested by simulating the flow of air through a coolant passage inside a radial turbine blade. Second, new techniques were developed to enhance control over grid-point distribution in algebraic grid generation. These techniques are (a) a modified way to control orthogonality of the grid at boundaries, (b) a new interpolation function based on tension splines that improves control over grid-line curvature, and (c) multidimensional stretching functions that allow arbitrary clustering of grid points. Also, compatibility conditions were identified, which must be satisfied by the data that define the geometry and control grid-point distribution. The new techniques were used to generate a grid system for a complex-shaped coolant passage geometry with U-bends and pin fins. Third, several iterative techniques were developed for reducing or eliminating approximate-factorization errors in implicit finite-difference and finite-volume methods. The convergence of the iteration processes was analyzed. Also analyzed was the stability of the techniques when used with the ADI three-factored scheme. The techniques were tested by applying them to stabilize and accelerate convergence in the ADI three-factored scheme for the linear advection equation. Finally, three flux-vector splitting schemes were tested in a simulation of complex, low Mach number, viscous flow. The artificial dissipation created by these schemes at low Mach numbers was analyzed. Of the schemes, one was found to be unconditionally unstable, and two were found to be too dissipative at low Mach numbers. This indicates that additional research is needed in developing robust and efficient schemes for low Mach number flow problems.