Singularity Superposition BEM/inverse
Technique For Reconstruction Of Heat Flux
Distributions Within Film Cooling Holes
Author(s)
M. Silieti, E.Divo & A. J. Kassab
Abstract
A hybrid singularity superposition/boundary element-based inverse problem
method for the reconstruction of multi-dimensional heat flux distributions is developed.
Cauchy conditions are imposed at exposed surfaces that are readily reached
for measurements while convective boundary conditions are unknown at surfaces
that are not amenable to measurements such as the walls of the cooling holes. The
purpose of the inverse analysis is to determine the heat flux distribution along the
cooling hole surfaces. This is accomplished in an iterative process by distributing
a set of singularities (sinks) inside the physical boundaries of the cooling hole
(usually along cooling hole centerline) with a given initial strength distribution.
A forward steady-state heat conduction problem is solved using the boundary element
method (BEM), and an objective function is defined to measure the difference
between the heat flux measured at the exposed surfaces and the heat flux predicted
by the BEM under the current strength distribution of the singularities. A Genetic
algorithm (GA) iteratively alters the strength distribution of the singularities until
the measuring surface heat fluxes are matched, thus satisfying Cauchy conditions.
The distribution of the heat flux at the walls of the cooling hole is determined in
a post-processing stage after the inverse problem is solved. The advantage of this
technique is to eliminate the need for meshing the surfaces of the cooling holes,
which requires a large amount of effort to achieve a high quality mesh. Moreover,
the use of singularity distributions significantly reduces the number of parameters
sought in the inverse problem, which constitutes a tremendous advantage in
solving the inverse problem, particularly in the application of film cooling holes.
Keywords
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