A hybrid-grid scheme has been developed to afford a computationally efficient means for numerically solving equations of both (1) coupled flows of heat and mass in a fluid and (2) conduction of heat in a body or bodies that bound the fluid. The scheme should prove especially beneficial in analyzing aerodynamic, thermal, and structural effects in turbomachinery.
Among grid methods now in use, the chimera-overset-grid method offers the most flexibility and computational efficiency in representing flows bounded by complexly shaped bodies. A chimera grid is a set of overlapped structured grids that are generated independently and fitted to the body or bodies of interest. A chimera overset grid is a chimera grid that includes (1) a major grid generated about a main body element and (2) minor grids superimposed on the major grid to resolve interesting features of the configuration.
The unstructured-grid method facilitates the solution of problems pertaining to solid bodies (e.g., strain problems). However, the unstructured-grid method does not offer computational efficiency for solving flow and heat-transfer problems.
The present hybrid scheme is intended to take advantage of the strengths of the chimera-overset-grid and unstructured-grid methods. The scheme involves the use of a chimera overset grid in the flow volume, coupled to an unstructured grid or grids for modeling conduction of heat in the bounding body or bodies.
Unlike in older grid schemes and associated numerical-solution methods, in the present scheme, one need not assume physically unrealistic prescribed heat fluxes (e.g., zero heat flux in the traditional adiabatic-wall assumption) or constant temperatures at fluid/solid interfaces. Instead, the heat fluxes in the fluid and solid are treated more realistically as unknowns that are coupled to each other; following a conjugate-analysis approach, the temperatures and heat fluxes are required to be continuous across fluid/solid interfaces. In this scheme, one performs a conjugate analysis, wherein the mass flow and the heat fluxes are treated as parts of an integral system, the equations of which can be efficiently solved together to obtain aerodynamic, thermal, and structural effects.
The scheme has been tested by using it to compute flows about, and distributions of temperature within, a cooled flat plate and a turbine cascade with 10 cooling holes per blade (see figure). The results of these computations are in substantial agreement with results of experiments. In the foregoing computations and in other computations for a simplified drum/disk structure, conduction of heat in solid bodies has been shown to affect surface temperatures in that these temperatures differ from those computed with the adiabatic-wall assumption.
This work was done by Meng-Sing Liou of Lewis Research Center and Kai-Hsiung Kao of the Institute for Computational Fluid Mechanics in Propulsion. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category, or circle no. 162 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).
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