Stokes Flow Past a Thin Oblate Body of Revolution: Axially Incident Uniform Flow

1984 ◽  
Vol 44 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Richard N. Barshinger ◽  
James F. Geer
Keyword(s):  
Stokes Flow ◽  
Uniform Flow ◽  
Body Of Revolution ◽  
Flow Past ◽  
Oblate Body

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.

scholarly journals Steady Stokes flow past dumbbell shaped axially symmetric body of revolution: An analytic approach

2012 ◽  
Vol 39 (3) ◽  
pp. 255-289
Author(s):  
Kumar Srivastava ◽  
Ram Yadav ◽  
Supriya Yadav
Keyword(s):  
Stokes Flow ◽  
Closed Form Expression ◽  
Body Of Revolution ◽  
Axially Symmetric ◽  
Moment Coefficient ◽  
Flow Past ◽  
Flow Situation ◽  
Axis Of Symmetry ◽  
Singularity Distribution ◽  
The Relationship

In this paper, the problem of steady Stokes flow past dumbbell-shaped axially symmetric isolated body of revolution about its axis of symmetry is considered by utilizing a method (Datta and Srivastava, 1999) based on body geometry under the restrictions of continuously turning tangent on the boundary. The relationship between drag and moment is established in transverse flow situation. The closed form expression of Stokes drag is then calculated for dumbbell-shaped body in terms of geometric parameters b, c, d and a with the aid of this linear relation and the formula of torque obtained by (Chwang and Wu, part 1, 1974) with the use of singularity distribution along axis of symmetry. Drag coefficient and moment coefficient are defined in various forms in terms of dumbbell parameters. Their numerical values are calculated and depicted in respective graphs and compared with some known values.

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.

Axisymmetric Stokes flow past a spherical cap

1976 ◽  
Vol 75 (2) ◽  
pp. 273-286 ◽  
Author(s):  
J. M. Dorrepaal ◽  
M. E. O'neill ◽  
K. B. Ranger
Keyword(s):  
Vortex Ring ◽  
Stokes Flow ◽  
Concave Surface ◽  
Local Velocity ◽  
Oncoming Flow ◽  
Spherical Cap ◽  
Stream Surface ◽  
Flow Past ◽  
Mainstream Flow

The axisymmetric streaming Stokes flow past a body which contains a surface concave to the fluid is considered for the simplest geometry, namely, a spherical cap. It is found that a vortex ring is attached to the concave surface of the cap regardless of whether the oncoming flow is positive or negative. A stream surface ψ = 0 divides the vortex from the mainstream flow, and a detailed description of the flow is given for the hemispherical cup. The local velocity and stress in the vicinity of the rim are expressed in terms of local co-ordinates.

scholarly journals Stokes flow past three spheres

2013 ◽  
Vol 245 ◽  
pp. 302-316 ◽  
Author(s):  
Helen J. Wilson
Keyword(s):  
Stokes Flow ◽  
Flow Past

The behaviour of supersonic flow past a body of revolution, far from the axis

1950 ◽  
Vol 201 (1064) ◽  
pp. 89-109 ◽  
Keyword(s):  
Supersonic Flow ◽  
General Theory ◽  
Body Of Revolution ◽  
Flow Past ◽  
Physical Importance ◽  
Special Case ◽  
Pointed Body ◽  
Asymptotic Forms

A theory is developed of the supersonic flow past a body of revolution at large distances from the axis, where a linearized approximation is valueless owing to the divergence of the characteristics at infinity. It is used to find the asymptotic forms of the equations of the shocks which are formed from the neighbourhoods of the nose and tail. In the special case of a slender pointed body, the general theory at large distances is used to modify the linearized approximation to give a theory which is uniformly valid at all distances from the axis. The results which are of physical importance are summarized in the conclusion (§ 9) and compared with the results of experimental observations.

Potential Flow Around a Thin Oblate Body of Revolution

1983 ◽  
Vol 43 (1) ◽  
pp. 212-224 ◽  
Author(s):  
Richard N. Barshinger ◽  
James F. Geer
Keyword(s):  
Potential Flow ◽  
Body Of Revolution ◽  
Oblate Body
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