Subsonic Compressible Flow Past Bluff Bodies

1954 ◽  
Vol 5 (3) ◽  
pp. 144-162 ◽  
Author(s):  
A. L. Longhorn
Keyword(s):  
Correction Factor ◽  
Fluid Velocity ◽  
Analytic Form ◽  
Prolate Spheroid ◽  
The Body ◽  
Inviscid Fluid ◽  
Bluff Bodies ◽  
Legendre Functions ◽  
Slender Body Theory ◽  
Axis Ratio

SummaryIn this paper the Janzen-Rayleigh method is used to calculate the velocity potential for the steady subsonic flow of a compressible, inviscid fluid past a prolate spheroid. The fluid velocity at a point on the body is calculated. The analytic form obtained for this velocity differs, from that giving the velocity which an incompressible fluid would possess at the same point on the body, by a correction factor. The factor is an infinite series of first derivatives of Legendre functions of the first kind and odd order. The first three coefficients in this series are computed for bodies of certain axis ratios, and graphs of the values of these coefficients against axis ratio are plotted. The behaviour of the nth coefficient for large values of n is given. Results for slender ellipsoids, considering these as a limiting case of the family of ellipsoids just referred to, are obtained and are found to agree with the usual slender-body theory. Using these an attempt is made to continue the graphs of the first three coefficients in the correction factor series for the whole range of axis ratios of the ellipsoids in the system, namely zero to unity. The results obtained for the bluff-nosed ellipsoids may be used to estimate the effects of compressibility on the pressure distribution over the front of a general bluff-nosed body in steady flow.

Optimal Self-Propulsion of a Deformable Prolate Spheroid

1983 ◽  
Vol 27 (02) ◽  
pp. 121-130
Author(s):  
T. Miloh
Keyword(s):  
Kinetic Energy ◽  
Surface Deformation ◽  
Deformable Body ◽  
Large Degree ◽  
Prolate Spheroid ◽  
The Body ◽  
Deformation Pattern ◽  
Inviscid Fluid ◽  
Periodic Surface ◽  
Deformation Velocity

The problem of self-propulsion of an elongated deformable body moving in an infinite medium of inviscid fluid is considered in some detail. A prolate spheroid is chosen as a model shape, and a particular deformation pattern which maximizes the Froude efficiency is sought. The Froude efficiency in this context is defined by the ratio of the kinetic energy of the body to the total kinetic energy of the system comprising the body and the fluid. It is demonstrated that a body can propel itself from rest in a persistent manner even for a periodic surface deformation with zero mean which preserves both the volume and the location of its centroid. Under these constraints the induced forward velocity of the body is of 0(ε2) where ε is the amplitude of the deformation velocity. It is also demonstrated that for a persistent self-propulsion to exist the body should develop a large degree of skewness, resulting from the interaction between the two deformation components—one with fore-and-aft symmetry and one without. It is also essential that the symmetric and asymmetric deformation components should be out of phase.

The motion of long slender bodies in a viscous fluid. Part 2. Shear flow

1971 ◽  
Vol 45 (4) ◽  
pp. 625-657 ◽  
Author(s):  
R. G. Cox
Keyword(s):  
Shear Flow ◽  
Viscous Fluid ◽  
Fluid Velocity ◽  
Axial Rotation ◽  
Axisymmetric Body ◽  
The Body ◽  
Total Force ◽  
Axis Ratio ◽  
Linear Flow ◽  
Slender Bodies

A long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis. Formulae for the total force and torque on the body are found as an expansion in terms of a small parameter κ defined as the radius-to-length ratio of the body. These general results are used to determine the resistance to axial rotation of the body and also the equivalent axis ratio of the body for motion in a shear flow.

Incipient Separation Near Corners

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Corner Point ◽  
Analytic Form ◽  
The Body ◽  
Recirculation Region ◽  
Body Contour ◽  
Concave Corner ◽  
Attached Flow ◽  
Surface Deflection ◽  
Interaction Problem ◽  
Incipient Separation

Chapter 4 analyses the transition from an attached flow to a flow with local recirculation region near a corner point of a body contour. It considers both subsonic and supersonic flow regimes, and shows that the flow near a corner can be studied in the framework of the triple-deck theory. It assumes that the body surface deflection angle is small, and formulates the linearized viscous-inviscid interaction problem. Its solution is found in an analytic form. It also presents the results of the numerical solution of the full nonlinear problem. It shows how, and when, the separation region forms in the boundary layer. In conclusion, it suggests that in the subsonic flow past a concave corner, the solution is not unique.

scholarly journals The approach of a vortex pair to a plane surface in inviscid fluid

1979 ◽  
Vol 92 (3) ◽  
pp. 497-503 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Approximate Calculation ◽  
Plane Surface ◽  
Vortex Pair ◽  
Plane Wall ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Axis Ratio ◽  
Local Rate

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

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.

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018 ◽  
Vol 860 ◽  
pp. 465-486 ◽  
Author(s):  
Nimish Pujara ◽  
Greg A. Voth ◽  
Evan A. Variano
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Inertial Range ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Scaling Exponents ◽  
Slender Body Theory ◽  
Velocity Statistics ◽  
Rigid Rods ◽  
Dissipation Range

We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

scholarly journals Trapping of waves by a submerged elliptical torus

2002 ◽  
Vol 456 ◽  
pp. 277-293 ◽  
Author(s):  
M. McIVER ◽  
R. PORTER
Keyword(s):  
Fluid Velocity ◽  
Three Dimensional ◽  
Mode Frequency ◽  
The Body ◽  
Necessary Condition ◽  
Numerical Evidence ◽  
Side Condition ◽  
Trapped Mode ◽  
Specific Geometry ◽  
The Time Domain

An investigation is made into the trapping of surface gravity waves by totally submerged three-dimensional obstacles and strong numerical evidence of the existence of trapped modes is presented. The specific geometry considered is a submerged elliptical torus. The depth of submergence of the torus and the aspect ratio of its cross-section are held fixed and a search for a trapped mode is made in the parameter space formed by varying the radius of the torus and the frequency. A plane wave approximation to the location of the mode in this space is derived and an integral equation and a side condition for the exact trapped mode are obtained. Each of these conditions is satisfied on a different line in the plane and the point at which the lines cross corresponds to a trapped mode. Although it is not possible to locate this point exactly, because of numerical error, existence of the mode may be inferred with confidence as small changes in the numerical results do not alter the fact that the lines cross.If the torus makes small vertical oscillations, it is customary to try to express the fluid velocity as the gradient of the so-called heave potential, which is assumed to have the same time dependence as the body oscillations. A necessary condition for the existence of this potential at the trapped mode frequency is derived and numerical evidence is cited which shows that this condition is not satisfied for an elliptical torus. Calculations of the heave potential for such a torus are made over a range of frequencies, and it is shown that the force coefficients behave in a singular fashion in the vicinity of the trapped mode frequency. An analysis of the time domain problem for a torus which is forced to make small vertical oscillations at the trapped mode frequency shows that the potential contains a term which represents a growing oscillation.

An Investigation of the Forces on Three Dimensional Bluff Bodies in Rough Wall Turbulent Boundary Layers

1977 ◽  
Vol 99 (3) ◽  
pp. 503-509 ◽  
Author(s):  
B. E. Lee ◽  
B. F. Soliman
Keyword(s):  
Three Dimensional ◽  
The Body ◽  
Bluff Bodies ◽  
Drag Forces ◽  
Pressure Distributions ◽  
Mean Pressure ◽  
Flow Phenomena ◽  
The Mean ◽  
Building Ventilation ◽  
Group Density

A study has been made of the influence of grouping parameters on the mean pressure distributions experienced by three dimensional bluff bodies immersed in a turbulent boundary layer. The range of variable parameters has included group density, group pattern and incident flow type and direction for a simple cuboid element form. The three flow regimes associated with increasing group density are reflected in both the mean drag forces acting on the body and their associated pressure distributions. A comparison of both pressure distributions and velocity profile parameters with established work on two dimensional bodies shows close agreement in identifying these flow regime changes. It is considered that the application of these results may enhance our understanding of some common flow phenomena, including turbulent flow over rough surfaces, building ventilation studies and environmental wind around buildings.

The flow structure in the lee of an inclined 6:1 prolate spheroid

1994 ◽  
Vol 269 ◽  
pp. 79-106 ◽  
Author(s):  
T. C. Fu ◽  
A. Shekarriz ◽  
J. Katz ◽  
T. T. Huang
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Structure ◽  
Incidence Angle ◽  
Prolate Spheroid ◽  
The Body ◽  
Boundary Layer Transition ◽  
Primary Vortex ◽  
Vortex Sheets ◽  
Vorticity Distribution

Particle displacement velocimetry is used to measure the velocity and vorticity distributions around an inclined 6: 1 prolate spheroid. The objective is to determine the effects of boundary-layer tripping, incidence angle, and Reynolds number on the flow structure. The vorticity distributions are also used for computing the lateral forces and rolling moments that occur when the flow is asymmetric. The computed forces agree with results of direct measurements. It is shown that when the flow is not tripped, separation causes the formation of a pair of vortex sheets. The size of these sheets increases with increasing incidence angle and axial location. Their orientation and internal vorticity distribution also depend on incidence. Rollup into distinct vortices occurs in some cases, and the primary vortex contains between 20 % and 50 % of the overall circulation. The entire flow is unsteady and there are considerable variations in the instantaneous vorticity distributions. The remainder of the lee side, excluding these vortex sheets, remains almost vorticity free, providing clear evidence that the flow can be characterized as open separation. Boundary-layer tripping causes earlier separation on part of the model, brings the primary vortex closer to the body, and spreads the vorticity over a larger region. The increased variability in the vorticity distribution causes considerable force fluctuations, but the mean loads remain unchanged. Trends with increasing Reynolds number are conflicting, probably because of boundary-layer transition. The separation point moves towards the leeward meridian and the normal force decreases when the Reynolds number is increased from 0.42 × 106 to 1.3 × 106. Further increase in the Reynolds number to 2.1 × 106 and tripping cause an increase in forces and earlier separation.

A Nonlinear Method for Predicting Unsteady Sheet Cavitation on Marine Propellers

1983 ◽  
Vol 27 (01) ◽  
pp. 56-74
Author(s):  
Frederick Stern ◽  
William S. Vorus
Keyword(s):  
Complete Solution ◽  
Near Field ◽  
Fluid Velocity ◽  
Far Field ◽  
Static Potential ◽  
Nonlinear Method ◽  
Slender Body Theory ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Dynamic Potential

A method is presented which provides a basis for predicting the nonlinear dynamic behavior of unsteady propeller sheet cavitation. The method separates the fluid velocity potential boundary-value problem into two parts, static and dynamic, which are solved sequentially in a forward time stepping procedure. The static potential problem is for the cavity fixed instantaneously relative to the propeller and the propeller translating through the nonuniform wake field. This problem can be solved by standard methods. The dynamic potential represents the instantaneous reaction of the cavity to the static potential field and thus predicts the cavity's deformation and motion relative to the blade. A solution is obtained for the dynamic potential by using the concepts of slender-body theory to define near-and far-field potentials which are matched to form the complete solution. In the far field, the cavity is represented by a three-dimensional spanwise line distribution of sources. In the near field, the cavity is approximated at each cross section as a semi-ellipse with unknown axes a(t), b(t), and position l(t) along the chord of the foil section. Conditions are derived that determine (a, b, l) by minimizing the square error in satisfying the dynamic boundary condition. These conditions yield the equations of motion of the cavity in the form of three coupled nonlinear second-order ordinary differential equations with time as the independent variable. The theory is presented for the general foil and not specifically for propellers. However, the method incorporates features in its formulation which facilitate its application to marine propellers. The method is demonstrated by using the steady noncavitating potential for the two-dimensional half-body as an approximation to the static potential. Both fixed and unsteady cavities are calculated. The unsteady cavities are calculated by varying the hydrostatic pressure in the half-body pressure field sinusoidally.

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