Topology optimization, introduced by Bendsoe and Sigmund in 1988 has been a topic of research in the structural mechanics field for several decades. This technique is commonly used to optimize system performance of structural components with minimum material usage by varying the distribution of materials in a given domain. Fluid dynamic topology optimization, a relatively new research topic uses a method of adding or subtracting materials to a given flow domain to obtain an optimal flow-path for a given objective function. While the structural TO creates a solid structure by introducing holes into the domain, fluid TO introduces solid into a flow domain by creating flow blockage. From a numerical standpoint, by introducing a permeability penalty parameter into the Navier-Stokes equations, a blockage can be simulated, with each individual cell possessing a value for permeability. The group of cell with maximum values of the permeability penalty will resemble an impervious solid. This opens up the entire computation domain as the design space. The number of cells in the design space is equal to the number of design parameters, which creates a higher degree of freedom optimization problem when compared to other existing optimization approaches. With the recent advancements in additive manufacturing techniques, possibilities have been opened up for fabrication of unconventional geometries. The aim of the current study is to analyze the application of TO to turbulent flow problems. Many real-world cooling problems such as those related to electronic circuits and aerospace/power engine components fall in the category of turbulent flow related heat transfer, due to the high requirements in temperature. It is key to prevent failure of components while maintaining a high efficiency of cooling. The first part of this thesis works on establishing the mathematical equations which govern the optimization problem along with the flow physics. A Lagrangian multiplier method combines the objective functions and constraints in a single equation using adjoint multipliers. A modified version of AdjointshapeoptimizationFOAM solver in OpenFOAM with added flow-thermal capabilities has been used. This method is applied to serpentine ducts and a straight rectangular duct with high aspect ratio. These ducts are commonly found in gas turbine blade internal cooling circuits and other heat exchanger geometries. Due to the lack of turbulence model permeability corrections, it is necessary to re-run the CFD simulation with extracted flow-paths and body-fitted meshes. The post-processing was performed in STAR-CCM+, with the flow path extracted using PARAVIEW. Some post-processed optimum shapes were compared to traditional turbulator geometries from literature, to understand the degree of improvement in thermal efficiency. Another application was carried out on a U-bend baseline, with the final shape being experimentally validated using an ABS 3D printer. This is also compared to a channel shape designed using parametric surrogate model-based optimization from the same baseline. The pressure reduction from TO was 20% higher. The 2020 release of STAR-CCM+ has a level set based TO capability, which has been used in the current study to compare with the OpenFOAM results from the simplified U-bend case and high aspect ratio duct. The lessons learnt were finally used to optimize a GE-E3 airfoil internal cooling passage.


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Graduation Date





Kapat, Jayanta


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Mechanical and Aerospace Engineering

Degree Program

Mechanical Engineering




CFE0008840; DP0026119





Release Date

December 2021

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)