Determination of Number, Sizes, Locations, and Shapes of Coolant Flow Passages

During the past dozen years, the author’s research team has been developing a unique inverse shape design methodology and accompanying software which allows a thermal system designer to determine the minimum number and correct sizes, shapes, and locations of coolant passages in arbitrarily-shaped internally-cooled configurations |238]-(255| The designer needs to specify

boih the desired temperatures and heat fluxes on the hot surface, and either temperatures or con­vective heat coefficients on the guessed coolant passage walls. The designer must also provide an initial guess of the total number, sizes, shapes, and locations of the coolant flow passages. Af­terwards. the design process uses a constrained optimization algorithm to minimize the differ­ence between the specified and computed hot surface heat fluxes by automatically relocating, resizing, reshaping and reoncnting the initially-guessed coolant passages. All unnecessary’ cool­ant flow passages arc automatically reduced to a very small size and eliminated while honoring the specified minimum distances between the neighboring passages and between any passage and the thermal barrier coating if such exists.

This type of computer code is highly economical, reliable and geometrically flexible if it utilizes the boundary element method (BBM) instead of finite clement or finite difference method for the thermal field analysis. The В EM docs not require generation of the interior grid and it is non-itcrativc (238). (239). Thus the method is computationally efficient and robust. The resulting shapes of coolant passages arc smooth,- and easily manufacturable.

The methodology has been successfully demonstrated on 2-D coated and non-coatcd turbine blade airfoils (240)-{249). scramjet combustor struts (252). and 3-D coolant passages in the walls of 3-D rocket engine combustion chambers (253) and 3-D turbine blades (254). [2551.

Nonlinear BEM algorithms are the best choice for the thermal analysis because of their computational speed, reliability (due to their non-iterative nature) and accuracy with elliptic type problems. A simple method for escaping local minima has been implemented and involves switching the objective function when a stationary point is achieved |245). An accurate method, based on cxponcntal spline fitting and interpolation of the cost function values, has been devel­oped for finding the value of optimal search step parameter during gradient search optimization (244). It is also possible to develop a version of the 3-D inverse shape design code that will allow for multiple realistically shaped coolant flow passages with an arbitrary – number of fins or ribs in each of the passages (252) and prespecified locations of struts (242). In addition, this ver­sion of the 3-D inverse design code could allow for a variable thickness, segmented and non – segmented thermal barrier coatings with temperature-dependent thermal conductivities.

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