Classical Potential Flow Theory Research Articles

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

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<104 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 yaw stability analysis for stratospheric airships in float situation

When a stratospheric airship free floats at pressure altitude, the sideslip angle of the airship is neither random nor against the wind, but is stable on certain values. According to classical potential flow theory, a simplified two-dimensional ellipse and three-dimensional ellipsoid are firstly analyzed respectively, which implied that the airship could present crosswind orientation. The numerical investigations (CFD) on the yaw stability based on a bare hull and a finned airship are employed for verifying the theory conclusion. It is found that the finned airships can remain stable when its sideslip Angle is 55–70°, which is less than 90° of the stable angle of the ellipsoid and bare hull, but statically unstable at low sideslip angles, its static instability is similar to that of dynamic flight. Then the fight data of three stratospheric airships is analyzed. The yaw stability in flight data generally agrees with expectations drawn of theoretical and numerical simulation. These investigations serve to provide references for yaw control and configuration design of airships.

Predicting modal characteristics of a cluster of cylinders in axial flow: From potential flow solutions to coupled CFD–CSM calculations

External fluid flow has a number of effects on the dynamics of a submersed structure: e.g., a solitary cylinder exposed to an external flow experiences added mass and damping due to the presence of the surrounding fluid. At high axial flow velocities relative to the stiffness of the cylinder, coupled instabilities such as flutter and divergence occur. Compared to a solitary cylinder, a cluster of cylinders also experiences inter-cylinder coupling: pressure perturbations in the fluid due to the movement or acceleration of one cylinder force another cylinder to move. Consequently, the different cylinders can move in organized patterns.In this contribution, modal characteristics of a 7-rod bundle will be predicted by linear theory as well as by coupled CFD–CSM (Computational Fluid Dynamics — Computational Structure Mechanics) calculations. In the first part, fluid forces which lead to coupling of motion are computed with classical potential flow theory and URANS (Unsteady Reynolds-Averaged Navier–Stokes). Those forces are divided in a contribution in phase with the acceleration and a contribution in phase with the velocity of a cylinder. In the second part, modal characteristics of a 7 cylinder bundle are computed with coupled CFD–CSM simulations. The initial perturbations, which are required for the time-domain simulations come from a simplified structural model, with potential flow coupling between cylinders. The results are compared to linear theory. In the final part, approximations are proposed to predict upper and lower bounds of eigenfrequencies and damping, using calculations with only one cylinder.

Vibration characteristics of fluid-conveying FGM cylindrical shells resting on Pasternak elastic foundation with an oblique edge

The flow-induced vibration characteristics (natural frequency and critical flow velocity) of FGM cylindrical shells partially resting on elastic foundation are investigated by an analytical method. These shells are completely filled with fluid or subjected to a flowing fluid. The cylindrical shells are partially surrounded by an elastic foundation with an oblique edge which is represented by the Pasternak model. The boundary edge of an elastic foundation lies in a plane that is oblique at an angle with the shell axis. The effective material properties of FGM models are predicted based on two homogenization methods such as Voigt and Mori-Tanaka models. Material properties vary continuously through the thickness according to a four-parameter power law distribution in terms of volume fraction of the constituents. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The fluid is described by the classical potential flow theory. The governing equation for eigenvalue problem is obtained using the Rayleigh-Ritz method. To validate the present method, numerical examples are presented and compared with the available existing results.

Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells

The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear deformation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh–Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method. The free vibration of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations is investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. Shell motion is represented by first-order shear deformation theory. The governing equation is obtained using the Rayleigh–Ritz method. The fluid is described by classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.

Gas interchange between bubble and emulsion phases in a 2D fluidized bed as revealed by two-fluid model simulations

Using two-fluid model simulations, the present work aims at characterizing the interchange due to gas advection between the emulsion phase and bubbles in fully bubbling beds of Geldart group B particles that are fluidized with air. In the studied beds the bubbles are slow, which means that the advection transport of gas through the bubble boundary is the main mechanism of gas interchange. In an initial verification step, the pressure distribution and the gas interchange coefficient for isolated bubbles obtained in the two-fluid simulation are compared with the classical potential flow theory of fluidized beds, providing concordant results. In a second step, the work analyzes the gas interchange in fully bubbling beds and the effects of the superficial velocity, bed height, and particle diameter on the interchange coefficient and the crossflow ratio. The results indicate that both the interchange coefficient and the crossflow ratio in bubbling beds are about two times those predicted by the potential theory of isolated bubbles. A corrected model for the gas interchange is proposed based on the introduction of the gas throughflow into the classical potential flow theory. As a consequence, the gas interchange coefficient in the corrected model is a function of the superficial gas velocity instead of the minimum fluidization velocity.

부분 탄성지지된 유체 저장 원통셸의 자유진동

The free vibration characteristics of fluid-filled cylindrical shells on partial elastic foundations are investigated by an analytical method. The cylindrical shell is fully or partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The motion of shell is represented by the first order shear deformation theory to account for rotary inertia and transverse shear strains. The steady flow of fluid is described by the classical potential flow theory. The fluid-structure interaction is considered in the analysis. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. To validate the present method, the numerical example is presented and compared with the available existing results.

중간 지지된 유체 유동 외팔형 원통셸의 임계유속

The critical fluid velocity of cantilevered cylindrical shells subjected to internal fluid flow is investigated in this study. The fluid-structure interaction is considered in the analysis. The cantilevered cylindrical shell is supported intermediately at an arbitrary axial position. The intermediate support is simulated by two types of artificial springs: translational and rotational spring. It is assumed that the artificial springs are placed continuously and uniformly on the middle surface of an intermediate support along the circumferential direction. The steady flow of fluid is described by the classical potential flow theory. The motion of shell is represented by the first order shear deformation theory (FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with existing results.

유체 유동을 고려한 경사기능재료 원통셸의 연성진동

The coupled fluid-structure interaction problem is analyzed using the theoretical method to investigate the coupled vibration characteristics of functionally graded material(FGM) cylindrical shells conveying an incompressible, inviscid fluid. Material properties are assumed to vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The steady flow of fluid is described by the classical potential flow theory. The motion of shell represented by the first order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with exiting results.

Shape Optimization of Surface Ships in Potential Flow Using an Adjoint Formulation

A numerical method for shape optimization of surface ships is presented. The classical potential flow theory is used, and the free surface boundary conditions are linearized using Dawson's method. Objective functionals for wave resistance minimization and inverse problems are considered. An important contribution of this work is the formulation of a continuous adjoint approach for computing the gradients of these objective functionals. The potential flow problem is solved with an existing panel code (SWAN-v2.2). Like the velocity potential function, the adjoint function is governed by Laplace's equation; however, the adjoint radiation condition demands that waves may exist only upstream. The adjoint problem is also solved using the same code (SWAN-v2.2) after some modifications are introduced to handle the respective boundary conditions. Geometric characteristics, wave resistance, and surface wave patterns of optimized hull forms are presented

Vibration of prestressed thin cylindrical shells conveying fluid

A general approach to modelling the vibration of prestressed thin cylindrical shells conveying fluid is presented. The steady flow of fluid is described by the classical potential flow theory, and the motion of the shell is represented by Sanders’ theory of thin shells. A strain–displacement relationship is deployed to derive the geometric stiffness matrix due to the initial stresses caused by hydrostatic pressure. Hydrodynamic pressure acting on the shell is developed through dynamic interfacial coupling conditions. The resulting equations governing the motion of the shell and fluid are solved by a finite element method. This model is subsequently used to investigate the small-vibration dynamic behaviour of prestressed thin cylindrical shells conveying fluid. It is validated by comparing the computed natural frequencies, within the linear region, with existing reported experimental results. The influence of initial tension, internal pressure, fluid flow velocity and the various geometric properties is also examined.

A FINITE ELEMENT METHOD FOR MODELLING THE VIBRATION OF INITIALLY TENSIONED THIN-WALLED ORTHOTROPIC CYLINDRICAL TUBES CONVEYING FLUID

This paper presents a method for the dynamic analysis of initially tensioned orthotropic thin-walled cylindrical tubes conveying steady fluid flow, based on Sanders' non-linear theory of thin shells and the classical potential flow theory. The method is relatively straightforward, using a hydrodynamic pressure formulation derived from the velocity potential, a dynamic coupling condition at the fluid–structure interface and two-noded frustum elements to assess the dynamic behaviour of these tube/fluid systems accurately. A non-linear strain–displacement relationship is also deployed to derive the geometric stiffness matrix due to the initial stresses and hydrostatic pressures. The equations of motion for the tube and fluid are solved by a finite element method, and this is validated by comparing the natural frequencies obtained with other published results. The influence of material properties, fluid flow velocities and initial axial tensions on the natural frequencies is then illustrated and discussed.

Vibration and stability analysis of toroidal shells conveying fluid

Abstract A general theory is presented to account for both the in-plane and out-of-plane motions of uniformly thin toroidal shells conveying fluid. Love’s general thin shell equations and a classical potential flow theory are used for the structure and fluid respectively. A general solution for the natural frequency is obtained and numerical results are presented. The effects of flow velocity on the natural frequency are discussed. It is shown that when the flow angular velocity exceeds a certain value, the shell becomes subject to buckling-type instability. The influences of various parameters upon the natural frequencies and the critical angular velocity are also clarified at the end of the paper.

The influence of separation on the collection efficiencies of obstacles

A mathematical investigation of the mechanism of collection of aerosol particles based on the principle of wide-stream impaction on various collection surfaces has been considered. The systems analysed were infinitely long cylinders of circular, concave or flat shapes placed in aerosol streams and are based on the assumption of potential flow both with and without separation. The results presented in terms of collection efficiency as a function of the generalized Stokes number enable the basic features of the variation of the collection efficiency with particle size, freestream velocity and width of the collection surface to be identified. Comparisons with the experimental results show that the inclusion of separation into the model for the fluid flow past an obstacle placed in a stream of aerosols offers, in general, a better approximation for the collection efficiency of a sampler based on the principle of wide-stream impaction than does the classical potential flow theory without separation.

Incremental force and moment coefficients for a parallel blade-vortex interaction

Blade-vortex interactions occur in helicopter rotors when a rotor blade passes close to or through a tip vortex trailing from the same or another blade. An unsteady, parallel blade-vortex interaction model was developed using a discrete free-vortex method and classical potential flow theory. The tip vortex was modeled by a simple vortex and, for a close encounter, by a cluster of vortices.

Free vibration of clusters of cylinders in liquid-filled channels

This paper presents two methods for the calculation of the virtual masses of clusters of parallel cylinders in liquid contained by an outer channel. The first method is based on classical potential flow theory, and its applicability is limited to circular cylinders in circular cylindrical channels; the second, using fluid finite elements, may be applied to more general geometries. Illustrative examples compare the two methods, the classical one being shown to be computationally more efficient—whenever applicable. The eigenvalues and modal shapes are calculated for clusters in still fluid, in channels of circular and rectangular cross-section, showing the effect of proximity on the natural frequencies. Some distinctive patterns in the coupled motions of the cylinders are seen to occur, some not intuitively evident. The effect of viscous hydrodynamic coupling is also discussed.

Influence of a uniform magnetic field on the hydroelastic instability of a ferromagnetic plate

The static hydroelastic instability of a two-dimensional ferromagnetic panel in a uniform oblique magnetic field, one side of which is exposed to a high velocity flow of a non-conducting incompressible fluid is investigated. The elastic panel is considered to be thin, of infinite width, simply supported along its edges and composed of soft linear magnetic material. The analysis is based on the small bending theory of thin plates, a simple model of the magnetoelastic interaction and classical potential flow theory. Galerkin's method and Fourier transforms are used. The divergence velocity is determined for various values of the magnetic field. It is found that there exists a critical angle, βcr, of the oblique magnetic field at which the effect of the magnetic field on the divergence velocity vanishes. For β βcr, the divergence velocity increases with an increase in the magnetic field.