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Doctor of Philosophy with a Major in Aerospace Engineering

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Author: Amoloye, Taofiq Omoniyi × End date: 2023 × Start date: 2020 ×

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    A Refined Potential Theory for the Incompressible Unsteady Subcritical-Reynolds number Flows on Canonical Bluff Bodies
    (Georgia Institute of Technology, 2020-11-19) Amoloye, Taofiq Omoniyi
    The three main approaches to exploring fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. In classical potential theory, the steady inviscid incompressible flow over a body can be obtained by the superposition of elementary flows with known analytical solutions. Analytical solutions can offer huge advantages over numerical and experimental solutions in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, the classical potential theory falls short of reconciling the actions of viscosity in an experimentally observed flow with the theoretical analysis of such a flow. As such, it is unable to resolve the boundary layer and predict the especially important flow separation phenomenon that results in the pressure drag experienced by a body in the flow. This has relegated potential theory to idealized flows of little practical importance. Therefore, an attempt is made in this thesis to refine the classical potential theory of the flow over a circular cylinder to bridge the gap between the theory and experimentally observed flows. This is to enhance the ability to predict and/or control the flows' aerodynamic quantities and the evolution of the wake for design purposes. The refinement is achieved by introducing a viscous sink-source-vortex sheet on the surface of the cylinder to model the boundary layer. These vortices, sources and sinks introduced at the cylinder surface are modeled as concentric at every location. The vortices are modeled as Burgers' vortices, and analytic expressions for their strengths and those of the sinks/sources are obtained from the classical theory. These are employed to obtain a viscous and time-dependent stream function that captures critical qualitative features of the flow including flow separation, reattachment, wake formation, and vortex shedding. After that, a viscous potential function, the Kwasu function, with which the pressure field is obtained from the Navier-Stokes equation, is derived from the stream function. It is obtained by defining the viscous stream function on a principal axis of the flow about which the vorticity vector is identically zero. Strategies have also been developed to account for the finite extent of the cylinder and dynamic unsteadiness of the flow, and to predict the points of separation/reattachment/transition and the boundary layer thickness. Additionally, the strategies are used to obtain forces and apply the solution to arbitrary geometries focusing on spheres and spheroids. These strategies include the gravity analogy that considers a fluid element-cylinder scenario to be like a two-body problem in orbital mechanics. This analogy introduces the perifocal frame of fluid motion and exploits it to resolve the d'Alembert's Paradox. The perifocal frame is also used to predict flow separation/reattachment/transition and explain the observation of sign changes in the shear stress distribution at the rear of a circular cylinder in a crossflow. The refined potential theory is verified against experimental and numerical data on the cylinder in an incompressible crossflow at freestream Re∞=3,900. Its drag prediction is within the error bound of measured data and tHRLES (transitional Hybrid Reynolds-averaged Navier-Stokes Large Eddy Simulation) prediction. The predictions of the pressure distribution, separation point and Strouhal number are also within acceptable ranges. Its prediction of the force coefficients over the range 25≤Re∞<300,000 is validated against experimental and theoretical data on the cylinder in crossflow. There is a good agreement in the magnitude and trend for Re∞>100. For Re∞<100, there is a disparity in magnitude that is unsafe for design purposes. Similarly, it under-predicts the coefficient of drag in some of the explored axial flow configurations. However, at Re∞=96,000 and an aspect ratio of 2, the RPT drag prediction falls within 1.2% of validated computational result. The energy spectra of the wake velocity display the Kolmogorov's Five-Thirds law of homogeneous isotropic turbulence. This verifies and validates the unsteadiness in refined potential theory as turbulent in nature. The drag coefficient of a sphere for 25≤Re∞< 300,000 is explored to demonstrate the application of refined potential theory. Additionally, the flow over a sphere at Re∞=100,000 is explored in detail. A generally good agreement is observed in the prediction of the experimental trend for Re∞≥2,000. The transitional incompressible flows over a 6:1 prolate spheroid at an angle of attack β=45° for Re∞=3,000$ and Re∞=4,000 are also explored. The present theoretical pressure distribution has a close agreement with the DNS (direct numerical simulation) result in the starboard rear of the spheroid. However, the magnitude of the predicted force coefficients are generally less than five times the corresponding DNS results. The asymmetry of the DNS pressure distribution in the meridian plane is not captured. Therefore, further analyses of the spheroid flow including the separation locations are recommended for further studies. It is concluded that the refined potential theory can be used to resolve, explore and/or control the aerodynamic quantities of the flows around canonical bluff bodies as well as the evolution of their wakes.