scholarly journals Experimental verification of an Oseen flow slender body theory

2010 ◽  
Vol 654 ◽  
pp. 271-279 ◽  
Author(s):  
E. CHADWICK ◽  
H. M. KHAN ◽  
M. MOATAMEDI ◽  
M. MAPPIN ◽  
M. PENNEY
Keyword(s):  
Cross Section ◽  
Semimajor Axis ◽  
Major Axis ◽  
The Body ◽  
Slender Body ◽  
Radius Of Curvature ◽  
Slender Body Theory ◽  
Elliptical Cross ◽  
Oseen Flow ◽  
Body Theory

Consider uniform flow past four slender bodies with elliptical cross-section of constant ellipticity along the length of 0, 0.125, 0.25 and 0.375, respectively, for each body. Here, ellipticity is defined as the ratio of the semiminor axis of the ellipse to the semimajor axis. The bodies have a pointed nose which gradually increases in cross-section with a radius of curvature 419 mm to a mid-section which then remains constant up to a blunt end section with semimajor axis diameter 160 mm, the total length of all bodies being 800 mm. The bodies are side-mounted within a low-speed wind tunnel with an operational wind speed of the order 30 m s−1. The side force (or lift) is measured within an angle of attack range of −3° to 3° such that the body is rotated about the major axis of the ellipse cross-section. The lift slope is determined for each body, and how it varies with ellipticity. It is found that this variance follows a straight line which steadily increases with increasing ellipticity. It is shown that this result is predicted by a recently developed Oseen flow slender body theory, and cannot be predicted by either inviscid flow slender body theory or viscous crossflow theories based upon the Allen and Perkins method.

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.

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.

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.

scholarly journals Slender-body theory for transient heat conduction: theoretical basis, numerical implementation and case studies

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150494 ◽  
Author(s):  
Koenraad F. Beckers ◽  
Donald L. Koch ◽  
Jefferson W. Tester
Keyword(s):  
Heat Transfer ◽  
Case Studies ◽  
Circular Cross Section ◽  
Transient Heat Conduction ◽  
The Body ◽  
Slender Body ◽  
Numerical Implementation ◽  
Discrete Elements ◽  
Slender Body Theory ◽  
Body Theory

Slender-body theory (SBT) for transient heat transfer from bodies whose lengths are much larger than their radius into a conductive medium is derived. SBT uses matched asymptotic expansions of inner and outer solutions. An analytical inner solution for heat transfer from a circular cross section is matched to an outer solution obtained using Green’s functions. An efficient numerical implementation is obtained based on a judicious choice of the discrete elements used to represent the body and implementation of the fast multipole method (FMM). The SBT requires a one-dimensional spatial discretization only along the axis of the body in contrast to the three-dimensional discretization for finite-element models. Two case studies, heat transfer from two parallel cylinders and heat transfer from a slinky-coil heat exchanger, are used to show the speed and accuracy of the SBT model and its ability to model interacting slender bodies of finite length and bodies with centreline curvature and internal advective heat flow.

On the Unsteady Motion of a Slender Body through a Compressible Fluid

1955 ◽  
Vol 6 (1) ◽  
pp. 59-80 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Rigid Body ◽  
Integral Transforms ◽  
Unsteady Motion ◽  
The Body ◽  
Slender Body ◽  
Variable Velocity ◽  
Cross Sectional ◽  
Slender Body Theory ◽  
Trailing Edges ◽  
Body Theory

SummaryWard's slender-body theory is extended to examine the unsteady motion of a slender body through a fluid at rest. The cross-sectional area and shape of the body, its forward velocity and its lateral motion are all arbitrary functions of time, but are subject to the restrictions of small disturbances. The length of the body is fixed. An approximate velocity potential is obtained by the joint use of two integral transforms, and the accuracy of this potential is discussed in some detail. General expressions for the aerodynamic forces acting on the body are derived in terms of a co-ordinate system which moves forward with the body in the mean direction of motion, but is fixed laterally. These expressions are then transformed, for the particular case of an oscillating rigid body moving forward with variable velocity, to expressions in terms of co-ordinates referred to the body axes. (The former co-ordinate system makes possible a fairly compact general treatment, whereas the latter is more convenient if the solution of a particular rigid-body problem is required.) Finally, arguments are advanced to justify the application of the slender-body theory to wings of slender plan form whose trailing edges are perpendicular to the direction of motion, and results are given for an oscillating wing moving forward with variable velocity.

A generalized slender-body theory for fish-like forms

1973 ◽  
Vol 57 (4) ◽  
pp. 673-693 ◽  
Author(s):  
J. N. Newman ◽  
T. Y. Wu
Keyword(s):  
The Body ◽  
Slender Body ◽  
Slender Body Theory ◽  
Vortex Sheets ◽  
Flow Past ◽  
Longitudinal Orientation ◽  
Trailing Edges ◽  
Lifting Surfaces ◽  
Axisymmetric Bodies ◽  
Body Theory

A consistent slender-body approximation is developed for the flow past a fish- like body with arbitrary combinations of body thickness and low-aspect-ratio fin appendages, but with the fins confined to the plane of symmetry of the body. Attention is focused on the interaction of the fin lifting surfaces with the body thickness, and especially on the dynamics of the vortex sheets shed from the fin trailing edges. This vorticity is convected by the (non-lifting) flow past the stretched-straight body, and departs significantly from the purely longitudinal orientation of conventional lifting-surface theory. Explicit results are given for axisymmetric bodies having fins with abrupt trailing edges, and calculations of the total lift force are presented for bodies with symmetric and asymmetric fin configurations, moving with a constant angle of attack.

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.

Sign in / Sign up

Export Citation Format

Share Document