Unsteady Potential Flow Research Articles

Analysis of swimming three-dimensional waving plates

The three-dimensional waving plate theory is developed to investigate the swimming performance of fish undulatory motion. In particular, the propulsive effectiveness is discussed. The unsteady potential flow over model rectangular and triangular flexible plates performing a motion which consists of a progressing wave with variable amplitudes is calculated by the vortex ring panel method. It is found that the undulatory motion can reduce three-dimensional effects. It is this important hydrodynamic phenomenon that may be one of the main reasons why such undulation is widely used as the swimming method by a large number of aquatic animals. When the span of the undulating plate is nearly unchanged and the wave amplitude is constant or increases slightly along the chord, and the wavelength is close to the body length, theoretical results show that the swimming performance is best and the flow around the plate has a quasi-two-dimensional property. This swimming method may be observed in many fishes, especially those with an anguilliform mode of propulsion. The modification of the anguilliform mode of propulsion to the carangiform mode is also discussed. It is confirmed that the pronounced necking of the body anterior to the tail, which acts to improve the propulsive performance, is a major morphological adaptation of fishes using the carangiform mode, in which the characteristic nature of flexural movement confined to the rear part of the body is that the amplitude of undulation increases posteriorly and no complete wavelength is at any time apparent.

Kernel function occurring in supersonic unsteady potential flow

Kernel function occurring in supersonic unsteady potential flow

Kernel function occurring in subsonic unsteady potential flow

We deal with the Kernel function of the integral equation relating the pressure to the normal-wash distribution in unsteady potential subsonic flow. Exact solutions of the involved integrals of the Kernel function are given in terms of new functions. Efficient and accurate numerical evaluation of these functions are described.

Unsteady Forces on a Slender Body of Revolution in a Tube. (Effect of Tube and/or Body Deformation).

The problem under consideration is the axisymmetric unsteady potential flow past a slender body of revolution capable of arbitrary radial deformations in a tube which also performs wavy deformation, where the mean radius of the tube wall is the same order as that of the body. In the analysis, the Stokes stream function is introduced and the method of matched asymptotic expansions is used. The flow is examined for two different time parameters. As a result, unsteady contributions to the flow generated by a deformable slender body and tube are obtained up to the second-order approximation, and effects of various parameters on the axial force coefficients are examined in two cases.

A study on the inertial effective length of two-dimensional centrifugal impeller flow channel.

The inertial effective length of centrifugal impeller flow channel is defined based on a two-dimensional unsteady potential flow analysis. It is shown that the effective length is not dependent on the average flow rate, impeller rotation and the time dependence of the flow rate. Theoretical values are given for logarithmic impellers. The effects of the mode of circumferential flow distribution are also studied. Making use of the nature of the effective length, simple experiments are carried out to experimentally determine the effective length. It is found that the agreements between theoretical and experimental values are fair and discussions are made on the real flow effects found in the experiments.

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Triple-wave potential flows of a polytropic gas

A system of equations describing triple-wave solutions for unsteady isentropic potential flows of a polytropic gas was derived in /1/. A family of exact triple-wave solutions of the equations of gas dynamics with three arbitrary functions of one argument was constructed in /2/ for 1 < γ < 2. Some applications and properties of this family were studied. In this paper we show that the triple-wave equations of /1/ are a system in involution and depend on one arbitrary function of two arguments.

Boundary integral equation for wave equation with moving boundary and applications to compressible potential aerodynamics of airplanes and helicopters

This work presents a general boundary-integral-equation methodology for the solution of the wave equation around objects moving in arbitrary motion, with applications to compressible potential aerodynamics of airplanes and helicopters. The paper includes the derivation of the boundary integral equation for the wave equation, in a frame of reference moving in arbitrary motion (in particular, in translation and in rotation). The formulation is then applied to study unsteady potential compressible aerodynamic flows around streamlined bodies, such as airplanes and helicopters. The formulation is given in terms of the velocity potential, for which an explicit treatment of the wake is required; a discussion of the formulation for the wake transport is included. The advantages of the velocity-potential formulation over the acceleration-potential formulation are discussed. The boundary-element algorithm used for the computational implementation is briefly outlined. Validation of the formulation is presented for airplane wings and helicopter rotors in hover. The test cases fall into two categories. prescribed-wake and free-wake analyses. The validation of the prescribed-wake analysis is presented for compressible flows, subsonic for helicopter rotors, transonic for airplanes. The numerical validation of the free-wake analysis of helicopter rotors is presented for incompressible flows.

Unsteady Potential Flow Past a Circular Cylinder with Permeable Surface

AbstractEs wird ein neues mathematisches Modell für die instationäre ebene Potentialströmung einer reibungslosen inkompressiblen Flüssigkeit um einen Kreiszylinder mit poröser Oberfläche angegeben. Für den Fall eines linearen Filtrationsgesetzes mit konstantem Koeffizienten wird das Problem auf eine komplexe partielle Differentialgleichung erster Ordnung zurückgeführt, welche für grundlegende Anfangsbedingungen mit Hilfe einer Riccatischen Differentialgleichung gelöst werden kann.

Bubbling at high flow rates in inviscid and viscous liquids (slags)

The behavior of gas discharging into melts at high velocities but still in the bubbling regime has been investigated in a laboratory modeling study for constant flow conditions. Air or helium was injected through a vertical tuyere into water, zinc-chloride, and aqueous glycerol solutions. High speed cinematography and pressure measurements in the tuyere have been carried out simultaneously. Pressure fluctuations at the injection point were monitored and correlated to the mode of bubble formation. The effects of high gas flow rates and high liquid viscosities have been examined in particular. Flow rates were employed up to 10-3 m3/s and viscosity to 0.5 Ns/m2. In order to attain a high gas momentum, the tuyere diameter was only 3 x 10-3 m. The experimental conditions and modeling liquids were chosen with special reference to the established practice of submerged gas injection to treat nonferrous slags. Such slags can be highly viscous. Bubble volume is smaller than that calculated from existing models such as those given by Davidson and Schuler10,11 due to the effect of gas momentum elongating the bubbles. On the other hand, viscosity tends to retard the bubble rise velocity, thus increasing volumes. To take elongation into account, a mathematical model is presented that assumes a prolate ellipsoidal shape of the bubbles. The unsteady potential flow equations for the liquid are solved for this case. Viscous effects are taken into account by noting that flow deviates from irrotational motion only in a thin boundary layer along the surface of the bubble. Thus, drag on the bubble can be obtained by calculating the viscous energy dissipation for potential flow past an ellipse. The time-dependent inertia coefficient for the ellipsoid is found by equating the vertical pressure increase inside and outside the bubble. This pressure change in the bubble is obtained by assuming that gas enters as a homogeneous jet and then calculating the stagnation pressure at the apex of the bubble.

An entropy correction method for unsteady full potential flows with strong shocks

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

Unsteady Aerodynamic Measurements on a Rotating Compressor Blade Row at Low Mach Number

An experiment was conducted on a heavily instrumented isolated model compressor rotor to study the unsteady aerodynamic response of the blade row to a controlled pitching oscillation of all blades in an undistorted flow, and to a circumferential inlet flow distortion with nonoscillating blades. To accomplish this, miniature pressure transducers were embedded in the blades and the unsteady pressure time histories were recorded. Both phases of the experiment were performed over a wide range of flow coefficient, from Cx/Um = 0.6 to 0.95 in 0.05 steps, and data were taken at each condition for sinusoidal disturbances characterized by one, two, and four per revolution waves. Steady-state data were acquired for flow coefficients from 0.55 to 0.99 in 0.05 steps. In this paper the steady and unsteady results of the portion of this experiment dealing with oscillating blades are compared with analytical predictions, and the steady results are compared with experimental data from previous work. Although the model blades were instrumented at five spanwise stations, only the midspan measurements will be presented herein. The measured pressures for nonoscillating blades were in good agreement with the steady potential flow predictions (and with previous steady experimental data) when the measured exit angle was imposed as the downstream boundary condition for the analysis. It was found that a quasi-steady approach yielded marginally acceptable agreement with the experimental results for the lowest frequency tested. For the higher reduced frequencies, the experimental data could not be modeled in this manner. In contrast, a comparison of the measurements with the Verdon–Caspar unsteady potential flow theory produced generally good agreement except near the leading edge at high mean incidence (i.e., at low flow coefficient). At high incidence the blades in this experiment had very high steady pressure gradients near the leading edge and it is suspected that this may be responsible for the lack of agreement. The agreement was somewhat better at the higher frequencies.

Improvements on a Green's function method for the solution of linearized unsteady potential flows

On introduit une formulation de surface portante et le concept de jonction de variables fonctionnelles dans la methode de Morino. Application a l'analyse aeroelastique de configurations complexes. Exemples numeriques

Lateral Fluid Forces on Whirling Centrifugal Impeller (1st Report: Theory)

Lateral fluid forces acting on a rotating centrifugal impeller in whirling motion are analyzed using unsteady potential flow theory. Impellers operating in diffusers with and without vanes are modeled and the fluid forces calculated for different whirl speeds and flow rates. The influences of these parameters are clarified by parametric calculations. The results for whirling impellers operating in vaneless diffusers show that the fluid forces exert a damping effect on the rotor whirling motion at all operating conditions. The results for impellers operating in vaned diffusers or guide vanes show that the time averaged values of fluid forces remain almost unchanged, while there are significant instantaneous fluctuations due to the impeller/guide vane interactions.

Study of wall-effect on two-dimensional airfoils in an unsteady flow.

A numerical method is presented for calculating the pressure, forces and moments on arbitrary-shaped airfoils in an unsteady potential flow between two parallel walls. Airfoils and walls are represented by vorticity distributions and mirror images respectively. Vortex movements are determined by discrete vortex method. Our method does not have the restrictions on the height of walls and the location of airfoils between walls. The calculations are carried out for two cases of starting flow and accelerating flow. It is found that when walls come closer, the steady lifts, moments and apparent mass become greater, and the unsteady lifts and moments reach the steady values faster, and that the pressure center of airfoils moves notably under the influence of the flow acceleration.

Nonlinear interaction of unsteady two-dimensional potential flow for multi-aerofoils. 2nd Report. The case of two foils.

It is important to study the nonlinear interaction of forces on foils and of wake patterns in the flow around cascade of fluid machinery, helicopter rotors, and flaps. In this paper, we tried to solve the unsteady incompressible flow around two two-dimensional oscillating foils by using both the discrete vortex approximation and the surface-singularity method. A numerical analysis has been developed for the wake configuration, the lift and drag on the aerofoils. The effect of the distance between two foils, the stagger angle, and the phase difference of the two oscillating foils is discussed by the numerical results.

Nonlinear interaction of unsteady two-dimensional potential flow for multi-airfoils. (1st report The case of single foil)

Nonlinear interaction of unsteady two-dimensional potential flow for multi-airfoils. (1st report The case of single foil)

An approach for reducing computational requirements in modal identification

References ^unningham, H. J. and Desmarais, R. N., Generalization of the Subsonic Kernel Function in the S-Plane, with Applications to Flutter Analysis, NASA TP 2292, March 1984. Vepa, R., On the Use of Fade Approximants to Represent Unsteady Loads for Arbitrary Small Motions of Wings, AIAA Paper 76-17, Jan. 1976. Jones, W. P., Aerodynamic Forces on Wings in Non-Uniform Motion, ARC R&M 2117, Aug. 1945. Hounjet, M. H. L., ARSPNS: A Method to Calculate Steady and Unsteady Potential Flow about Fixed and Rotating Lifting and Nonlifting Bodies, NLR TR 85114 L, Sept. 1985.

The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

An inviscid model of unsteady aerofoil flow with fixed upper surface separation

AbstractPresented in this paper is a new method for the prediction of unsteady, incompressible separated flow over a two‐dimensional aerofoil. The algorithm was developed from an existing unsteady potential flow model1 and makes use of an inviscid formulation for the flow field. The aerofoil is represented by vortex panels of linearly varying strength which are piecewise continuous at the corners. Discrete vortices with finite cores are used to model the separating shear layers.Following a brief summary of unsteady separation modelling, the theoretical framework is presented and the subsequent numerical implementation is discussed in detail.Results are given for flows which tend asymptotically to the steady state and conclusions are drawn regarding the usefulness of the method.