Flow Past Bluff Bodies Research Articles

Theory of Inviscid Shear Flow over Bluff Bodies Attached to a Plane Wall : Part 2, Application to Semielliptical Projection and Arbitrary-Shaped Body

As a continuation to the preceding paper in which a general method of analysis of the separated flows past bluff bodies attached to a plane wall was presented within the framework of the free-streamline theory, the present paper applies the method to the cases of semielliptical projection and bluff bodies of arbitrary shapes. The theoretical pressure distribution on the wetted surface of the semielliptical projection is found to show good agreement with an experimental measurement. An analytical solution for arbitrary bluff bodies is obtained by assuming an inverse power series for mapping functions. Numerical calculations showed that reasonable pressure distributions could be obtained for a few profiles which were arbitrarily chosen.

Viscous shear flow past small bluff bodies attached to a plane wall

Numerical solutions of the Navier-Stokes equations are presented for two-dimensional viscous flow past semicircular and semielliptical projections attached to a plane wall on which a laminar boundary layer has developed. Since the major axis is in the direction normal to the wall and is chosen to be twenty times as long as the minor axis in the present case, the flow around the semielliptical projection will approximately correspond to that around a normal flat plate. It is assumed that the height of each obstacle is so small in comparison with the local boundary-layer thickness that the approaching flow can be approximated by a uniform shear flow. Numerical solutions are obtained for the range 0·1-100 of the Reynolds number, which is defined in terms of the undisturbed approaching velocity at the top of the obstacle and its height. The geometrical shapes of the front and rear standing vortices, the drag coefficients and the pressure and shear-stress distributions are presented as functions of the Reynolds number. The computed results are discussed in connexion with the data already obtained in the other theoretical solutions and an experimental observation.

The relationship between the base pressure on a bluff body and the velocity at separation

In the modified free-streamline theory for the separated flow past bluff bodies due to Roshko, the velocity on the separated free streamlines is expressed asUv=kU0,where U0 is the velocity of the undisturbed stream and k is a constant. If it is assumed that the pressure on the base of the body is uniform and equal to the pressure on the free streamline, then application of Bernoulli's equation leads to;k =(1-Cpb)½,… (1)where Cpb is the base pressure coefficient.

Wall effects on flow past bluff bodies

The effects of wall interference on the drag force for two-dimensional cylinders and equilateral prisms are reported. Test bodies were of single- and multiple-body (single row) configurations. For the former, the models were mounted in the test section with and without eccentricity. In each case, an estimate of the contracted jet velocity uj was obtained from pressure distribution data. Using uj as the reference velocity, it was possible to get a drag coefficient which was nearly independent of the wall interference. In particular, for centrally mounted cylinders (subcritical) and prisms at 60°, the drag coefficient based upon the mean gap velocity u1 was also found to be constant. Consequently, the contraction coefficient is nearly constant for these shapes. The forebody pressure distributions invalidate the earlier concept of interpreting wall interference as an increase in stream velocity.

A free-streamline theory for bluff bodies attached to a plane wall

A free-streamline theory is presented for the separated flow past two-dimensional bluff bodies attached to a long plane wall on which a turbulent boundary layer has developed. The non-uniform velocity profile in the turbulent boundary layer which would be measured if the bluff bodies were absent has been replaced by a hypothetical inviscid parallel shear flow which has a constant vorticity. This model admits analytical solutions and automatically yields closed streamlines in front of the bluff bodies such as the normal plate and the semicircular projection, which are geometrically very similar to observed front separation bubbles. The present theory involves three or four parameters which must be determined on the basis of experimental information, the number of parameters depending upon the shape of bluff bodies. Two typical examples of bluff bodies, i.e. the normal plate and the semicircular projection, are worked out. Pressure distributions around these bodies predicted by the present theory are found to give a good agreement with experimental measurements.

Closure to “Effect of Side Walls on Flow Past Bluff Bodies”

Closure to “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Discussion of “Effect of Side Walls on Flow Past Bluff Bodies”

Vortex shedding from a turbulent jet in a cross-wind

Measurements in the wake behind turbulent jets exhausting from a solid surface into a cross-wind indicate that vortex shedding occurs as in the case of flow past solid bluff bodies. The Strouhal numbers for flow past a circular and a blunt jet are in qualitative agreement with those for corresponding solid bodies, provided that the width of the spreading jet some distance from the surface is used rather than the jet exit plane dimension.

Effect of Side Walls on Flow Past Bluff Bodies

The bluffness of a body is reflected in the steady drag that it experiences in an infinite stream, but this force is increased when the body is in the restricted flow of a channel or duct. The writer seeks to demonstrate a relationship for the drag force between the infinite and laterally restricted flow conditions. Various two-dimensional bluff bodies have been studied experimentally, and the results are compared with earlier analytical studies carried out by the writer. The main parameters relating forces in the restricted flow case to the better documented infinite-stream values are considered, and suggestions are made as to how the results could be applied to other two-dimensional forms. Specific applications are also considered, in particular, the significance of incorrect geometrical modeling for studies in this field.

Field Computations in Engineering and Physics.

The author’s object in this book is to describe, by means of theory and example, the method of “squares” for the solution of boundary-value problems in twodimensional partial differential equations. This method has been developed and applied by Professor Thom .and his colleagues (including, more recently, Dr Apelt) during the last thirty years. For example, we are indebted to Professor Thorn’s valuable work for much of our knowledge of steady viscous flow past bluff bodies in the range of Reynolds number below that at which a periodic wake develops. The method of squares differs from the “relaxation” method in that the former is a straightforward iterative method, whereas in relaxation the individual worker uses his experience and skill to determine the precise step to take at a given stage of computation. For this reason the authors emphasize that the method of squares is far more suitable than the relaxation method for use with a digital computer. This is certainly an important factor in a comparison of the two methods, but it should be borne in mind that much of the work described in the book was done with a desk machine. After two useful chapters on finite differences, several chapters of the book are devoted to the solution of Laplace’s equation for various boundary conditions. Following are chapters on the solution of Poisson’s equation, fourth-order linear equations, the Navier-Stokes equations of viscous flow, and the equations of compressible fluid flow. The book is liberally illustrated and has many examples, mostly taken from the fields of fluid motion and elasticity theory. It is recommended to those interested in the numerical solution of partial differential equations.