<i>Kwasu</i> Function: A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Amoloye, Taofiq O.

doi:10.2514/6.2018-1288

Cited by 4 publications

(92 citation statements)

References 19 publications

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“…Amoloye [1,2] explores a viscous-potential function, κ, that satisfies the physical relationship between the scalar pressure field and the velocity field in…”

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

“…as a realistic closed-form solution of the incompressible NSE [1,16]. The existence of such a function is well-known and has been researched by many [1,2,11,14,16,31,32,41].…”

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

“…as a realistic closed-form solution of the incompressible NSE [1,16]. The existence of such a function is well-known and has been researched by many [1,2,11,14,16,31,32,41]. Although, widely considered an oxymoron, the idea of a viscous potential flow or function is not new [2,32].…”

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

“…That function is a stream function and a velocity potential simultaneously. This is the central idea to the Kwasu function [1,2]. Fig.…”

Section: Conservation Of Momentummentioning

confidence: 99%

“…At the 2018 American Institute of Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting in Florida, United States (US), the current author presented a work in progress on the analytical solution to the complete Navier-Stokes equations (NSE) [1]. This formed the basis for the current author's doctoral research at the Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, US that was completed in 2020 [2].…”

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Amoloye

2021

Preprint

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The three main approaches to exploring fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics. Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author embarked on a doctoral research on the refinement of CPT. He introduced the Refined Potential Theory (RPT) that provides the Kwasu function as a physically consistent solution to the NSE problem. The Kwasu function is a viscous scalar potential function that captures known and observable unsteady features of experimentally observed wall bounded flows including flow separation, wake formation, vortex shedding, compressibility effects, turbulence and Reynolds-number-dependence. It is appropriately defined to combine the properties of a three-dimensional potential function to satisfy the inertia terms of the NSE and the features of a stream function to satisfy the continuity equation, the viscous vorticity equation and the viscous terms of the NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere and spheroid. It is concluded that the Kwasu function is a physically consistent and closed-form analytical solution to the NSE problem.

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“…Amoloye [1,2] explores a viscous-potential function, κ, that satisfies the physical relationship between the scalar pressure field and the velocity field in…”

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

“…as a realistic closed-form solution of the incompressible NSE [1,16]. The existence of such a function is well-known and has been researched by many [1,2,11,14,16,31,32,41].…”

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

Section: Literature Review On Extant Solutions and Modelsmentioning

confidence: 99%

“…That function is a stream function and a velocity potential simultaneously. This is the central idea to the Kwasu function [1,2]. Fig.…”

Section: Conservation Of Momentummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Amoloye

2021

Preprint

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Modeling the unsteady wake of an impulsively started circular cylinder using refined potential flow theory

Amoloye

2024

Phys. Scr.

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Cylindrical structures find usage in many engineering applications including tethered oil drums and engine canisters slung beneath helicopters in flight. The motion of air around such circular cylindrical structures and the helicopter presents interesting phenomena including flow separation, wakes and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes equations. Therefore, their studies are not only important in mathematics and physics, but they are also required for efficient helicopter operations. In practice, reduced-order models of these operations that take in aerodynamics models of the tethered loads are utilized for stability analysis, flight certification and pilot training because of the prohibitive cost of experimentation and computational analyses of these configurations. However, there is a dearth of realistic analytical models of finite cylinder flows because of the Navier-Stokes problem. Classical potential flow theory provides an avenue to develop such models, but the extant gaps in its predictions significantly preclude its usage for engineering applications. Attempting to bridge these gaps, this article introduces refined potential flow theory in which the governing equations and boundary conditions are satisfied. Viscous effects, fluctuations of the mean flow and three-dimensional effects are also incorporated. For characterization, refined potential flow theory is employed on an incompressible flow over an impulsively started circular cylinder for Reynolds numbers and non-dimensional times in the range 30 < Re < 10^4 and 0.2 ≤ T≤ 77, 047 respectively. There is an excellent prediction of 0.209 for the Strouhal number at Re = 3, 900. At this transitional Reynolds number, the harmonics of the Strouhal frequency are also captured, and the characteristic irregular fluctuations at sub-Strouhal frequencies are discernible in the velocity spectra. As the flow becomes more turbulent, these become more pronounced at Re = 9, 500 when the predicted Strouhal number is within 10% of experimental result. In the fully developed stage, spectra analyses of the wake velocity components at some downstream locations also display Kolmogorov’s Five-Thirds law of homogeneous isotropic turbulence. The present model can thus aid the development of reduced-order models of helicopter operations that feature tethered cylindrical loads.

show abstract

A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

Amoloye

2021

Preprint

View full text Add to dashboard Cite

The three main approaches in fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics.Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author refined CPT. He introduced refined potential theory (RPT) that provides a viscous potential/stream function as a physically consistent solution to the NSE problem. This function captures observable unsteady flow features including separation, wake, vortex shedding, compressibility, turbulence, and Reynolds-number-dependence. It appropriately combines the properties of a three-dimensional potential function that satisfy the inertia terms of NSE and the features of a stream function that satisfy the continuity equation, the viscous vorticity equation, and the viscous terms of NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere, and spheroid.

show abstract

Kwasu Function: A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Cited by 4 publications

References 19 publications

A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Modeling the unsteady wake of an impulsively started circular cylinder using refined potential flow theory

A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

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