Browsing by Author "Taofiq O. Amoloye"

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    Analysis of an Unsteady Incompressible Cross􀂧ow on a Stationary Circular Cylinder at Reynolds number 3,900 Using Re􀂦ned Potential Flow Theory
    (Research Square, 2022-06-03) Taofiq O. Amoloye
    The motion of a fluid around a circular cylinder presents interesting phenomena including flow separation, wake and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes Equations (NSE). Therefore, their studies are important in mathematics and physics. They also have engineering applications. These studies can either be carried out experimentally, computationally, or theoretically. Theoretical studies of a cylinder flow using classical potential flow theory (CPT) have some gaps when compared to experiments. Attempting to bridge these gaps, this article introduces refined potential flow theory (RPT) and employs it on a stationary circular cylinder incompressible crossflow at Reynolds number 3, 900. It leverages experimental observations, physical deductions and some agreements between CPT and experiments in the theoretical development. This results in the incompressible Eulerian Kwasu function which is a quasi-irrotational stream function that satisfies the governing equations and boundary conditions. It captures vorticity, boundary layer, shed wake vortices, three-dimensional effects, and static unsteadiness. The Lagrangian form of the function is exploited for the flow pathlines that are used to incorporate dynamic unsteadiness. A gravity analogy is used to predict the separation, transition, and reattachment points. The analogy introduces the perifocal frame of fluid motion. The forces are obtained in this frame with a change of variable. The drag prediction is within the error bound of measured data. The RPT pressure distribution, separation point and Strouhal number are also within acceptable ranges. Energy spectra analyses of the wake velocity display Kolmogorov’s Five-Thirds law of homogeneous isotropic turbulence.
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    Kwasu Function: A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation
    (American Institute of Aeronautics and Astronautics, 2018-01-07) Taofiq O. Amoloye
    An attempt is made to re ne the classical potential theory of the flow over a circular cylinder by introducing a viscous sink-source-vortex sheet on the surface of the cylinder. These singularities introduced into the flow are modeled as concentric at every location. The vortices are modeled as variations of Lamb-Oseen, Batchelor and 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 potential function named the Kwasu function which provides a closed form analytic solution to the complete three dimensional unsteady compressible Navier-Stokes equation. Preliminary results of the work show that the theory presented captures important features of a bluff body flow includin flow separation, wake formation, vortex shedding as well as compressibilty effects. The condition at a viscous wall is shown to be transient from slip towards a complete no-slip for a steady freestream flow. It is the hope that the present theory will shed more light on the important phenomenon of turbulence in planned future work in which quantitative analysis of the theory will be carried out.