ALGORITHM FOR THE CONJUGATION OF TWO-DIMENSIONAL IN THE PLAN OF UNIFORM AND RADIAL FLOWS

The algorithm of the theoretical method proposed by the authors using the speed hodograph plane and simple waves for solving the problem of coupling a two-dimensional flow in terms of flow is considered. This technique allows you to determine the boundaries of the free flow of a turbulent flow and its parameters in the flow area. it is revealed that using both planes physical OXYZ and hodograph G (,) it is possible to solve the problem uniquely analytically. All verification calculations were performed in the MathCad package. The calculation results showed a satisfactory convergence of model and experimental parameters in the free flow model, which does not exceed 10 % by error before the flow expansion within  = 7;  = B/b.

Separated Flow in Bends of Arbitrary Turning Angles, Using the Hodograph Method and Kirchhoff’s Free Streamline Theory

The problem of separated flow in bends of arbitrary turning angles has been examined. The method of analysis is based on the inviscid flow theory coupled with Kirchhoff’s separation model. The physical flow problem is first transformed to the hodograph domain, and then into a rectangular computational region using properly selected flow parameters. The solution is first established in the hodograph plane. The final flow pattern including the inner and outer walls of the bend, the separation streamline, and other flow properties in the physical plane are subsequently obtained through direct integration. The results of the present analysis are compared with those of Lichtarowicz and Markland as well as Mankbadi and Zaki.

Jet-Plate Interaction for Wedge-Shaped Plates of Arbitrary Angles

An investigation has been undertaken to study the problems of jet-plate interaction through the method of hodograph transformation. The physical flow field is first transformed to a hodograph domain. By using properly selected flow parameters, the solution is established through numerical computations with rectangular grid in the hodograph plane. The resulting plate configuration, the free streamlines, and the flow properties in the physical plane are subsequently obtained through direct numerical integration. Jet flows toward wedge-shaped plates of arbitrary angles are solved to demonstrate the ability of the method. To verify the solutions, momentum principle has been employed in the physical plane for all test cases. It is found that the results obtained through this method are satisfactory.

The Hodograph and the Balancer of any Frequency Term of the Shaking Force of Spatial Mechanisms

It is proved in this paper that the hodograph of a frequency term (for example the kth frequency term) of the shaking force of spatial mechanisms is an ellipse. Furthermore, expressions are provided for the lengths and attitudes of the semi-axes of this ellipse in terms of Fourier coefficients of the shaking force. Accordingly, a pair of counterweights, contra-rotating at k times of cycle frequency with their axes parallel to the unit normal vector of the hodograph plane, can be installed for eliminating the frequency term of the shaking force of spatial mechanisms. An example of a seven-link 7-R spatial linkage is included.

The Interaction Between a Jet and a Flat Plate—An Inviscid Analysis

The problem of jet-plate interaction has been examined. It is shown that the problem of this type is governed by the mechanisms of inviscid interaction. The method of hodograph transformation has been employed to formulate the problem, and the solution is obtained from numerical computations in the hodograph plane. The flow pattern in the physical plane is produced from additional integrations. Extensions to the compressible flow regime with practical applications have also been mentioned.

Steady compressible vortex flows: the hollow-core vortex array

We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M∞ = q∞/c∞, and the speed ratio, a = q∞/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M∞, is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.