Two-dimensional subsonic and sonic flow past thin bodies

1957 ◽  
Vol 3 (1) ◽  
pp. 93-109 ◽  
Author(s):  
J. B. Helliwell ◽  
A. G. Mackie
Keyword(s):  
Complex Analysis ◽  
Free Stream ◽  
Present Theory ◽  
The Body ◽  
Sonic Velocity ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past ◽  
Sonic Flow

Hodograph methods are applied to determine the flow at high subsonic and sonic velocities past two-dimensional, thin, symmetrical bodies. The boundary value problem for the determination of the stream function Ψ, which in the present theory is a solution of Tricomi's equation, is simplified by the assumption of a free stream breakaway at sonic velocity from the shoulder of the body. A solution is obtained in terms of Bessel functions.In § 2 and 3 the flow past a wedge of small angle is discussed and expressions are obtained for the pressure on the nose, the drag coefficient and the width of the wake. A comparison with the corresponding results in the case of sonic velocity derived by the more complex analysis of Guderley & Yoshihara (1950) shows that the present simpler theory yields very similar values for the pressure over the nose.In § 4 the flow at sonic velocity past a profile which is a first-order perturbation upon a wedge profile is analysed on the basis of the same free streamline theory. The flow pattern is obtained past an arbitrarily specified body by an application of the Hankel inversion theorem and an expression is deduced for the drag.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

The flow past a rapidly rotating circular cylinder

1957 ◽  
Vol 242 (1228) ◽  
pp. 108-115 ◽  
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Present Theory ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Rotating Circular Cylinder ◽  
Flow Past ◽  
Separating Flow ◽  
Two Dimensional Flow ◽  
Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

Second-order boundary-layer effects in hypersonic flow past axisymmetric blunt bodies

1964 ◽  
Vol 20 (4) ◽  
pp. 593-623 ◽  
Author(s):  
R. T. Davis ◽  
I. Flügge-Lotz
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Free Stream ◽  
Practical Interest ◽  
Second Order ◽  
The Body ◽  
Specific Flow ◽  
Flow Past ◽  
Free Stream Mach Number ◽  
Stability And Accuracy

First- and second-order boundary-layer theory are examined in detail for some specific flow cases of practical interest. These cases are for flows over blunt axisymmetric bodies in hypersonic high-altitude (or low density) flow where second-order boundary-layer quantities may become important. These cases consist of flow over a hyperboloid and a paraboloid both with free-stream Mach number infinity and flow over a sphere at free-stream Mach number 10. The method employed in finding the solutions is an implicit finite-difference scheme. It is found to exhibit both stability and accuracy in the examples computed. The method consists of starting near the stagnation-point of a blunt body and marching downstream along the body surface. Several interesting properties of the boundary layer are pointed out, such as the nature of some second-order boundary-layer quantities far downstream in the flow past a sphere and the effect of strong vorticity interaction on the second-order boundary layer in the flow past a hyperboloid. In several of the flow cases, results are compared with other theories and experiments.

Added Mass and Damping of Rectangular Bodies Close to the Free Surface

1984 ◽  
Vol 28 (04) ◽  
pp. 219-225
Author(s):  
John Nicholas Newman ◽  
Bjørn Sortland ◽  
Tor Vinje
Keyword(s):  
Hydrodynamic Force ◽  
Standing Waves ◽  
Present Theory ◽  
Added Mass ◽  
The Body ◽  
Simple Explanation ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Calm Water ◽  
Heave Motion

A submerged two-dimensional rectangle in calm water with infinite depth is studied. The rectangle is oscillating in a heave motion. Negative added mass and sharp peaks in the damping and added-mass coefficients have been found when the submergence is small and the width of the shallow region on top of the rectangle is large. Resonant standing waves will occur in this area. A linear theory is developed to provide a relatively simple explanation of the occurrence of negative added mass for submerged bodies. The vertical hydrodynamic force is associated only with the flow in the shallow region, and the resulting pressure which acts on the top face of the rectangle. The results from this theory are compared with numerical results from the Frank method. The importance of the interaction effect between the top and the bottom of the body, which is neglected in the present theory, is discussed.

Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature

2007 ◽  
Vol 592 ◽  
pp. 89-115 ◽  
Author(s):  
A. MILIOU ◽  
A. DE VECCHI ◽  
S. J. SHERWIN ◽  
J. M. R. GRAHAM
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
Axial Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
The Body ◽  
Vertical Extension ◽  
Flow Past

Three-dimensional spectral/hp computations have been performed to study the fundamental mechanisms of vortex shedding in the wake of curved circular cylinders at Reynolds numbers of 100 and 500. The basic shape of the body is a circular cylinder whose centreline sweeps through a quarter section of a ring and the inflow direction lies on the plane of curvature of the quarter ring: the free stream is then parallel to the geometry considered and the part of the ring that is exposed to it will be referred to as the ‘leading edge’. Different configurations were investigated with respect to the leading-edge orientation. In the case of a convex-shaped geometry, the stagnation face is the outer surface of the ring: this case exhibited fully three-dimensional wake dynamics, with the vortex shedding in the upper part of the body driving the lower end at one dominant shedding frequency for the whole cylinder span. The vortex-shedding mechanism was therefore not governed by the variation of local normal Reynolds numbers dictated by the curved shape of the leading edge. A second set of simulations were conducted with the free stream directed towards the inside of the ring, in the so-called concave-shaped geometry. No vortex shedding was detected in this configuration: it is suggested that the strong axial flow due to the body's curvature and the subsequent production of streamwise vorticity plays a key role in suppressing the wake dynamics expected in the case of flow past a straight cylinder. The stabilizing mechanism stemming from the concave curved geometry was still found to govern the wake behaviour even when a vertical extension was added to the top of the concave ring, thereby displacing the numerical symmetry boundary condition at this point away from the top of the deformed cylinder. In this case, however, the axial flow from the deformed cylinder was drawn into the wake of vertical extension, weakening the shedding process expected from a straight cylinder at these Reynolds numbers. These considerations highlight the importance of investigating flow past curved cylinders using a full three-dimensional approach, which can properly take into account the role of axial velocity components without the limiting assumptions of a sectional analysis, as is commonly used in industrial practice. Finally, towing-tank flow visualizations were also conducted and found to be in qualitative agreement with the computational findings.

Density and velocity fields in collisionless flow past a diffusely reflecting cone

1970 ◽  
Vol 48 (13) ◽  
pp. 1628-1631
Author(s):  
James Parker Elliott
Keyword(s):  
Flow Field ◽  
Free Stream ◽  
Angle Of Attack ◽  
Velocity Fields ◽  
Circular Cone ◽  
Two Dimensional ◽  
Transition Flow ◽  
Flow Past ◽  
Monatomic Gas

Results of flow field calculations for the collisionless flow of a neutral, monatomic gas past a diffusely reflecting right circular cone at zero angle of attack with the free stream are presented. Singularities at the vertex and at the shoulder of the base are illustrated and discussed. Comparison is made with similar results for spheres and two-dimensional polygonal bodies and with results for transition flow past sharp cones. Methods for improving the analysis are suggested.

scholarly journals Prandtl–Batchelor flow past a flat plate with a forward-facing flap

1984 ◽  
Vol 143 ◽  
pp. 351-365 ◽  
Author(s):  
P. G. Saffman ◽  
S. Tanveer
Keyword(s):  
Flat Plate ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Two Dimensional ◽  
Rear Edge ◽  
Flow Past ◽  
Range Of Values ◽  
Streamline Method

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.

Two-Dimensional Boat-Tailed Bases in Supersonic Flow

1974 ◽  
Vol 25 (3) ◽  
pp. 210-224 ◽  
Author(s):  
P R Viswanath ◽  
R Narasimha
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Free Stream ◽  
The Body ◽  
Base Pressure ◽  
Two Dimensional ◽  
Sharp Corner ◽  
Boundary Layer Effect ◽  
Pressure Distributions ◽  
Layer Effect

SummaryBoat-tailing of aft bodies may affect the base pressure through two mechanisms: firstly by changing the angle between the approaching flow at separation and the reattachment surface, and secondly by distorting the boundary layer through the favourable pressure gradient (which can be particularly severe in the presence of a sharp corner on the body). The first effect is isolated here by tests on inclined backward-facing steps with a fully developed turbulent boundary layer at separation, at free-stream Mach numbers of 1.75 and 2.4. It is found that the base pressure increases significantly with boat-tail angle; the data have been correlated taking explicit account of the boundary layer effect, modifying and extending the approach adopted by Nash. Charts are provided for quick estimation of base pressure in engineering calculations. Some of the earlier data on boat-tailed bases, on re-examination in the light of the present correlation, suggest that strongly distorted boundary layers at separation affect the base pressure appreciably. Several features of the measured reattachment pressure distributions, including their internal similarity, are also discussed.

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