Uniform asymptotic solutions for potential flow about a slender body of revolution

1975 ◽  
Vol 67 (4) ◽  
pp. 817-827 ◽  
Author(s):  
James Geer
Keyword(s):  
Potential Flow ◽  
The Body ◽  
Slender Body ◽  
Linear Integral Equation ◽  
Body Of Revolution ◽  
Uniform Asymptotic Expansion ◽  
Arbitrary Potential ◽  
Linear Integral ◽  
Special Case ◽  
Slender Body Of Revolution

The general problem of potential flow past a slender body of revolution is considered. The flow incident on the body is described by an arbitrary potential function and hence the results presented here extend those obtained by Handels-man & Keller (1967 α). The part of the potential due to the presence of the body is represented as a superposition of potentials due to point singularities (sources, dipoles and higher-order singularities) distributed along a segment of the axis of the body inside the body. The boundary condition on the body leads to a linear integral equation for the density of the singularities. The complete uniform asymptotic expansion of the solution of this equation, as well as the extent of the distribution, is obtained using the method of Handelsman & Keller. The special case of transverse incident flow is considered in detail. Complete expansions for the dipole moment of the distribution and the virtual mass of the body are obtained. Some general comments on the method of Handelsman & Keller are given, and may be useful to others wishing to use their method.

Dynamic Analysis of a Slender Body of Revolution Berthing to a Wall

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Q. X. Wang ◽  
S. K. Tan
Keyword(s):  
Practical Importance ◽  
Lateral Force ◽  
The Body ◽  
Slender Body ◽  
Body Of Revolution ◽  
Dynamic Features ◽  
Slender Body Theory ◽  
Quay Wall ◽  
Angle Of Yaw ◽  
Slender Body Of Revolution

A slender body of revolution berthing to a wall is studied by extending the classical slender body theory. This topic is of practical importance for a ship berthing to a quay wall. The flow problem is solved analytically using the method of matched asymptotic expansions. The lateral force and yaw moment on the body are obtained in a closed form too. The translation and yawing of the body are modeled using the second Newton law and coupled with the flow induced. Numerical analyses are performed for the dynamic lateral translation and yawing of a slender spheroid, while its horizontal translation parallel to the wall is prescribed at zero speed, constant speed, and time varying speed, respectively. The analysis reveals the interesting dynamic features of the translation and yawing of the body in terms of the forward speed and starting angle of yaw of the body.

Experimental investigations of the asymmetric vortex formation over a slender body of revolution at high angles of attack

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040089
Author(s):  
Yiding Zhu
Keyword(s):  
Vortex Formation ◽  
The Body ◽  
Slender Body ◽  
Experimental Investigations ◽  
Initial Growth ◽  
Body Of Revolution ◽  
Momentum Exchange ◽  
Time Resolved ◽  
High Angles Of Attack ◽  
Slender Body Of Revolution

This paper describes an experimental investigation of the initial growth of flow asymmetries over a slender body of revolution at high angles of attack with natural and disturbed noses. Time-resolved particle image velocimetry (PIV) is used to investigate the flow field around the body. Flow visualization clearly shows the formation of the asymmetric vortices. Instantaneous PIV shows that the amplified asymmetric disturbances lead to Kelvin–Helmholtz instability appearing first on one side, which increases the momentum exchange crossing the layer. As a result, the separation region shrinks which creates the initial vortex asymmetry.

The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone

1977 ◽  
Vol 79 (3) ◽  
pp. 499-524 ◽  
Author(s):  
J. F. Clarke ◽  
Y. L. Sinai
Keyword(s):  
Linear Theory ◽  
The Body ◽  
Slender Body ◽  
Wave System ◽  
Body Of Revolution ◽  
Relaxation Length ◽  
Relaxation Effects ◽  
Mode Energy ◽  
Relaxing Gas ◽  
Slender Body Of Revolution

The results of the linear theory for the flow of a supersonic relaxing gas past a slender body of revolution are analysed in regions where its predictions of wavelet position begin to break down. In this way new variable systems can be found which make it possible to discuss the correct nonlinear wave behaviour far from the body. The situation depends upon three especially important parameters, namely the thickness ratio ε of the body, the ratio δ of relaxing-mode energy to thermal energy and the ratio λ of a relaxation length to a typical body length. After establishing general results from the linear theory, the conical body is treated in some detail. This makes it possible to demote λ as an important parameter, although its restoration does prove useful at one point in the analysis, and results are derived for shock-wave behaviour when ord 1 [ges ] δ > ord ε4, δ = ord ε4and δ < ord ε4. In the first range of δ fully dispersed waves are essential, although they are fully established only at great distances from the cone; in the second range of δ partly dispersed waves seem to be the most likely to appear, and in the third range relaxation effects are second-order modifications of a basically frozen-flow field. Practical situations may well fall into the first of these categories.

Axially symmetric potential flow around a slender body

1967 ◽  
Vol 28 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Richard A. Handelsman ◽  
Joseph B. Keller
Keyword(s):  
Potential Flow ◽  
Slenderness Ratio ◽  
Strength Distribution ◽  
Point Sources ◽  
The Body ◽  
Linear Integral Equation ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Symmetric Rigid Body ◽  
Linear Integral

Axially symmetric potential flow about an axially symmetric rigid body is considered. The potential due to the body is represented as a superposition of potentials of point sources distributed along a segment of the axis inside the body. The source strength distribution satisfies a linear integral equation. A complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio ε½, which is the maximum radius of the body divided by its length. The expansion contains integral powers of ε multiplied by powers of log ε. From it expansions of the potential, the virtual mass and the dipole moment of the body are obtained. The flow about the body in the presence of an axially symmetric stationary obstacle is also determined. The method of analysis involves a technique for the asymptotic solution of integral equations.

Stokes flow past a slender body of revolution

1976 ◽  
Vol 78 (3) ◽  
pp. 577-600 ◽  
Author(s):  
James Geer
Keyword(s):  
Stokes Flow ◽  
Slenderness Ratio ◽  
Slip Boundary Condition ◽  
The Body ◽  
Slender Body ◽  
Total Force ◽  
Body Of Revolution ◽  
Flow Past ◽  
Special Cases ◽  
Slender Body Of Revolution

The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed.

Axial Evolution of Asymmetric Vortical Flow Around Slender Body of Revolution at High Incidence

2010 ◽  
Author(s):  
Xiaorong Guan ◽  
Song Fu ◽  
Cheng Xu
Keyword(s):  
Mach Number ◽  
The Body ◽  
Slender Body ◽  
Vortical Flow ◽  
Computational Results ◽  
Body Of Revolution ◽  
Evolution Law ◽  
Side Force ◽  
High Incidence ◽  
Slender Body Of Revolution

For studying the axial evolution of the flow around slender body of revolution at high incidence under different conditions, numerical simulations are performed. Based on the computational results, several conclusions and deductions are obtained. When the flow is asymmetric and whether the asymmetry is remarkable or not, downstream axially it always presents itself in the structure of leeside vortices forming, rising and shedding alternately from opposite sides of the body and induces the sectional side force of waving sinusoidally. Based on the idea of vortex dividing, a forming mode of shed and new leeside vortices is put forward, which is composed of two idiographic manners. The axial evolutions on the forming manner can be reduced to three idiographic laws. The global asymmetry degree of the flow lies on both the axial evolution law on the forming manner and the intensity of leeside vortex. The influences of incidence, freestream Mach number and nose-perturbation location on the axial evolution of the asymmetric vortical flow are achieved as well.

Supersonic scattering of a wing-induced incident shock by a slender body of revolution

2007 ◽  
Vol 585 ◽  
pp. 305-322 ◽  
Author(s):  
A. V. FEDOROV ◽  
N. D. MALMUTH ◽  
V. G. SOUDAKOV
Keyword(s):  
Shock Wave ◽  
Lift Force ◽  
Numerical Solutions ◽  
Asymptotic Methods ◽  
The Body ◽  
Slender Body ◽  
Body Of Revolution ◽  
Leading Order ◽  
Wide Range ◽  
Slender Body Of Revolution

The lift force acting on a slender body of revolution that separates from a thin wing in supersonic flow is analysed using Prandtl–Glauert linearized theory, scattering theory and asymptotic methods. It is shown that this lift is associated with multi-scattering of the wing-induced shock wave by the body surface. The local and global lift coefficients are obtained in simple analytical forms. It is shown that the total lift is mainly induced by the first scattering. Contributions from second, third and higher scatterings are zero in the leading-order approximation. This greatly simplifies calculations of the lift force. The theoretical solution for the flow field is compared with numerical solutions of three-dimensional Euler equations and experimental data at free-stream Mach number 2. There is agreement between the theory and the computations for a wide range of shock-wave strength, demonstrating high elasticity of the leading-order asymptotic approximation. Theoretical and experimental distributions of the cross-sectional normal force coefficient agree satisfactorily, showing robustness of the analytical solution. This solution can be applied to the moderate supersonic (Mach numbers from 1.2 to 3) multi-body interaction problem for crosschecking with other computational or engineering methods.

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

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