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.

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.

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.

Supersonic Flow Past Bodies of Revolution with Thin Wings of Small Aspect Ratio

1951 ◽  
Vol 3 (1) ◽  
pp. 61-79 ◽  
Author(s):  
P. M. Stocker
Keyword(s):  
Supersonic Flow ◽  
Aspect Ratio ◽  
The Body ◽  
Supersonic Stream ◽  
List Type ◽  
Body Of Revolution ◽  
Small Aspect Ratio ◽  
Flow Past ◽  
Special Cases ◽  
Ratio Set

SummaryThe method developed by G. N. Ward for the treatment of slender pointed bodies in a uniform supersonic stream is applied to three special cases. (i)Supersonic flow past a body of revolution with thin wings of symmetrical section and of small aspect ratio at zero incidence.(ii)Supersonic flow past a body of revolution with plane wings of small aspect ratio set at incidence to the body, the whole being at incidence to the stream.(iii)Supersonic flow past a body of revolution with a plane fin of small aspect ratio set at incidence, the whole being at incidence to the stream.The pressure distribution on the wing has been calculated for a special case of (i) and is given in the Appendix.

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.

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