Line source distributions and slender-body theory

1963 ◽  
Vol 17 (2) ◽  
pp. 285-304 ◽  
Author(s):  
John P. Moran
Keyword(s):  
Potential Flow ◽  
Line Source ◽  
The Body ◽  
Successive Approximations ◽  
External Disturbances ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Plane Flow ◽  
Body Theory

A systematic procedure is presented for the determination of uniformly valid successive approximations to the axisymmetric incompressible potential flow about elongated bodies of revolution meeting certain shape requirements. The presence of external disturbances moving with respect to the body under study is admitted. The accuracy of the procedure and its extension beyond the scope of the present study—e.g. to problems in plane flow - are discussed.

Calculation of Subsonic Normal Force and Centre of Pressure Position of Bodies of Revolution Using a Slender Body Theory – Boundary Layer Method

1980 ◽  
Vol 31 (1) ◽  
pp. 1-25
Author(s):  
K.D. Thomson
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Normal Force ◽  
The Body ◽  
Slender Body ◽  
Centre Of Pressure ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Slender Bodies ◽  
Body Theory

SummaryThe aim of this paper is to present a method for predicting the aerodynamic characteristics of slender bodies of revolution at small incidence, under flow conditions such that the boundary layer is turbulent. Firstly a panel method based on slender body theory is developed and used to calculate the surface velocity distribution on the body at zero incidence. Secondly this velocity distribution is used in conjunction with an existing boundary layer estimation method to calculate the growth of boundary layer displacement thickness which is added to the body to produce the effective aerodynamic profile. Finally, recourse is again made to slender body theory to calculate the normal force curve slope and centre of pressure position of the effective aerodynamic profile. Comparisons made between predictions and experiment for a number of slender bodies extending from highly boattailed configurations to ogive-cylinders, and covering a large range of boundary layer growth rates, indicate that the method is useful for missile design purposes.

A Combination of the Quasi-Cylinder and Slender Body Theories

1955 ◽  
Vol 59 (532) ◽  
pp. 305-308 ◽  
Author(s):  
C. H. E. Warren ◽  
L. E. Fraenkel
Keyword(s):  
Point Of View ◽  
The Body ◽  
Slender Body ◽  
Maximum Diameter ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Pressure Distributions ◽  
Simple Body ◽  
Body Theory ◽  
Supersonic Flow Past Bodies

The Quasi-Cylinder and slender body theories for the supersonic flow past bodies of revolution have been much used in recent years because, for reasonably simple body profiles, these theories permit a simple and rapid calculation of the first-order pressure distributions and aerodynamic forces. It is assumed in both theories that the body profile slope is small; in the quasi-cylinder theory it is also assumed that the body radius is nearly constant, whereas in the slender body theory it is assumed that the thickness ratio of the body (maximum diameter/length) is small.In the present note these two theories are combined completely. From a strictly mathematical point of view nothing is gained by this combination, and, furthermore,application of the combined theory to a particular case is in general a little more laborious than application of either of the original theories.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Application of Slender-Body Theory

1957 ◽  
Vol 1 (04) ◽  
pp. 40-49
Author(s):  
Paul Kaplan
Keyword(s):  
Slender Body ◽  
Vertical Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Surface Theory ◽  
Surface Ship ◽  
Submerged Body ◽  
Dynamic Forces ◽  
Body Theory

The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow concepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Has-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also included.

An analytical solution for two slender bodies of revolution translating in very close proximity

2007 ◽  
Vol 582 ◽  
pp. 223-251 ◽  
Author(s):  
Q. X. WANG
Keyword(s):  
Body Length ◽  
Present Model ◽  
The Body ◽  
Attraction Force ◽  
Bodies Of Revolution ◽  
Plane Flow ◽  
Lateral Forces ◽  
Close Proximity ◽  
Slender Bodies ◽  
Two Bodies

The irrotational flow past two slender bodies of revolution at angles of yaw, translating in parallel paths in very close proximity, is analysed by extending the classical slender body theory. The flow far away from the two bodies is shown to be a direct problem, which is represented in terms of two line sources along their longitudinal axes, at the strengths of the variation rates of their cross-section areas. The inner flow near the two bodies is reduced to the plane flow problem of the expanding (contracting) and lateral translations of two parallel circular cylinders with different radii, which is then solved analytically using conformal mapping. Consequently, an analytical flow solution has been obtained for two arbitrary slender bodies of revolution at angles of yaw translating in close proximity. The lateral forces and yaw moments acting on the two bodies are obtained in terms of integrals along the body lengths. A comparison is made among the present model for two slender bodies in close proximity, Tuck & Newman's (1974) model for two slender bodies far apart, and VSAERO (AMI)–commercial software based on potential flow theory and the boundary element method (BEM). The attraction force of the present model agrees well with the BEM result, when the clearance, h0, is within 20% of the body length, whereas the attraction force of Tuck & Newman is much smaller than the BEM result when h0 is within 30% of the body length, but approaches the latter when h0 is about half the body length. Numerical simulations are performed for the three typical manoeuvres of two bodies: (i) a body passing a stationary body, (ii) two bodies in a meeting manoeuvre (translating in opposite directions), and (iii) two bodies in a passing manoeuvre (translating in the same direction). The analysis reveals the orders of the lateral forces and yaw moments, as well as their variation trends in terms of the manoeuvre type, velocities, sizes, angles of yaw of the two bodies, and their proximity, etc. These irrotational dynamic features are expected to provide a basic understanding of this problem and will be beneficial to further numerical and experimental studies involving additional physical effects.

scholarly journals Viscoplastic slender-body theory

2018 ◽  
Vol 856 ◽  
pp. 870-897 ◽  
Author(s):  
D. R. Hewitt ◽  
N. J. Balmforth
Keyword(s):  
Yield Stress ◽  
Numerical Approach ◽  
The Body ◽  
Constitutive Law ◽  
Slender Body ◽  
Viscoplastic Fluid ◽  
Slender Body Theory ◽  
Local Flow ◽  
Flow Around A Cylinder ◽  
Body Theory

The theory of slow viscous flow around a slender body is generalized to the situation where the ambient fluid has a yield stress. The local flow around a cylinder that is moving along or perpendicular to its axis, and rotating, provides a first step in this theory. Unlike for a Newtonian fluid, the nonlinearity associated with the viscoplastic constitutive law precludes one from linearly superposing solutions corresponding to each independent component of motion, and instead demands a full numerical approach to the problem. This is accomplished for the case of a Bingham fluid, along with a consideration of some asymptotic limits in which analytical progress is possible. Since the yield stress of the fluid strongly localizes the flow around the body, the leading-order slender-body approximation is rendered significantly more accurate than the equivalent Newtonian problem. The theory is applied to the sedimentation of inclined cylinders, bent rods and helices, and compared with some experimental data. Finally, the theory is applied to the locomotion of a cylindrical filament driven by helical waves through a viscoplastic fluid.

Ambient Supercavities of Slender Bodies of Revolution

1986 ◽  
Vol 30 (03) ◽  
pp. 215-219
Author(s):  
William S. Vorus
Keyword(s):  
Cavitation Number ◽  
Slender Body ◽  
Surface Velocity ◽  
Body Of Revolution ◽  
Cavity Pressure ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Specific Analysis ◽  
Slender Bodies ◽  
Body Theory

Slender-body theory is applied in an analysis of the flow about the general supercavitating streamlined body of revolution. The formulation is specialized to the case of ambient cavity pressure (zero cavitation number) for the specific analysis conducted. Numerical procedures are outlined. The methodology is demonstrated in calculating the cavity shapes, surface velocity distributions, and cavity form drag coefficients for three idealized bodies. These are the convex paraboloid, the conical frustrum, and the concave paraboloid. Characteristic differences in the flows in each of the cases are discussed.

The Drift Force and Moment on Ships in Waves

1967 ◽  
Vol 11 (01) ◽  
pp. 51-60 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Horizontal Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Kochin Function ◽  
Field Velocity ◽  
Drift Force ◽  
The Waves ◽  
Body Theory

The second-order steady horizontal force and vertical moment are derived for a freely floating ship in regular waves. The fluid is assumed to be ideal and the motion is linearized. Momentum relations are used to derive general results for an arbitrary ship or other body, in terms of the Kochin function or far-field velocity potential of the body. Explicit results are derived for slender ships, based upon the assumptions of slender body theory. Computations are made for a Series 60 hull and are compared with experiments. The analysis of the vertical moment permits the prediction of stable heading angles in oblique waves, and it is shown that unless the waves are very short, the ship will be stable only in beam waves.

The wave drag at zero lift of slender delta wings and similar configurations

1956 ◽  
Vol 1 (3) ◽  
pp. 337-348 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Uniform Distribution ◽  
Present Method ◽  
Wave Drag ◽  
The Body ◽  
Slender Body ◽  
Trailing Edge ◽  
Slender Body Theory ◽  
Edge Angle ◽  
Finite Wing ◽  
Body Theory

Ward's slender-body theory of supersonic flow is applied to bodies terminating in either (i) a single trailing edge at right angles to the oncoming supersonic stream, or (ii) two trailing edges at right angles to one another as well as to the oncoming stream, or (iii) a cylindrical section with two or four identical fins equally spaced round it. The wave drag at zero lift, D, is given by the expression $\frac {D}{\frac {1}{2}\rho U^2} &=& \frac {1}{2\pi}\int^l_0 \int^l_0 log\frac{1}{|s-z|}S^{\prime \prime}(s)S^{\prime \prime}(z)dsdz - \\ &-& \frac{S^\prime (l)}{\pi}\int^l_0 log \frac {l}{l-z}S^{\prime \prime}(z)dz + \frac{S^{\prime 2}(l)}{2\pi} \{ log \frac{l}{(M^2-1)^{1|2}b}+k \} $ where l is the length of the body, b the semi-span of the trailing edge (or length of trailing edge of a single fin), and S(z) is the cross-sectional area of the body at a distance z behind the apex. The constant k depends on the distribution of trailing-edge angle along the span for each trailing-edge configuration. In case (i) it is 1·5 for a uniform distribution of trailing-edge angle and 1·64 for an elliptic distribution. In case (ii) it is 1·28 for a uniform distribution and 1·44 for an elliptic distribution. Study of case (iii) indicates that interference effects due to the presence of the body reduce the drag of the fins. For example, with a uniform distribution of trailing-edge angle, k for two fins falls from 1·5 in the absence of a body to 1·06 when the body radius equals the trailing-edge semi-span, while k for four fins falls from 1·28 to 0·45 under the same conditions.Where ordinary finite-wing theory is applicable, the present method must agree with it for small $(M^2-1)^{1|2}b|l$, and this is confirmed by two examples (§3), but within the limit imposed by slenderness the present method is of course more widely applicable, as well as simpler, than finite-wing theory.It is not known experimentally whether slender-body theory gives accurate predictions of drag at zero lift, for the shapes here discussed, under the conditions for which on theoretical grounds it might be expected to do so. It should be noted that, although tests have not yet been made on ideally suitable bodies, no clear the drag is therefore twice that of a wing made up of two of them. The final stages of the process cannot be represented by slender-body theory, but the initial trend may well be indicated fairly accurately.

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