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.

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.

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.

Researchers and the energy industry are currently focusing their efforts on optimizing the effectiveness of vertical-axis wind turbines (VAWT) to cut down on the reliance on energy supply from fossil fuels which releases gases that are toxic to the environment. As such, several methods have been applied, including increasing the velocity and modification of both the trailing and leading edges of the aerofoil. In the present investigation, numerical studies of the flow on the wind turbine blades with a NACA0015 airfoil section equipped with and without tubercles on the trailing edge were conducted using ANSYS Fluent. A computational domain of 2000mm by 35000mm was employed with the turbulence model. This two-dimensional computational fluid dynamics (CFD) analysis was performed with Ilorin, Kwara State, Nigeria wind data that was received from the Nigeria Meteorological Agency (NIMET). The modified blade with a wavelength of 0.09m and an amplitude of 0.004m is seen to have a better thrust than the unmodified blade. It produced a thrust of 118N for a tip-speed ratio (TSR) of 4.0 compared to 109N of the unmodified blade at the same TSR and that of the modified blade (1) which attains 107N. Also, its coefficient of performance is 5% and 6% higher than that of the straight and modified blades (1) respectively,suggest that an increase in the tubercle’s wavelength and amplitude increased the maximum thrust.

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.