A direct shape design method for thermo-fluid engineering problems

Abstract

A design method for thermo-fluid engineering problems is proposed in which the desired distribution of pressure, for example, is specified on the boundary, and the dependent variables in the equations of motion are the boundary coordinates that define the boundary shape, and the field variables (e.g. pressure and velocity). When the surface (boundary) shape is unknown, the problem is called a shape design problem. The final discretized form of the governing equations, obtained by the proposed method and called the unified formulation, can be used for solving both analysis and shape design problems.

The method, at its current stage of development, is applied to some steady two-dimensional thermal and fluid flow problems. Shape design problems in the context of inviscid. irrotational flow in ducts (formulated with the secondary variables) and conduction heat transfer problems are directly solved to achieve a prescribed pressure or heat flux distribution along the boundaries.

An integral boundary layer analysis method is modified and used together with the proposed direct shape design method to design short ducts. Short ducts are defined as ducts in which the flow is hydrodynamically developing and the boundary viscous layers remain thin along the duct.

A simple one dimensional flow model which uses primitive variables (pressure and velocity) is used to discuss some new ideas regarding the pressure-velocity coupling and advection modeling and also to implement the proposed direct shape design method in the context of primitive variable formulation.