Solution Of Non Isoenergetic Supersonic Flows By Method Of Characteristics Volume 3

A theoretical and experimental study has been conducted of a flow field about a hemisphere-cylinder at zero incidence in the transonic and low supersonic Mach number range (M = 0.7 to 2.0). For M less than or equal to 1, the method used is a combination of the time-dependent solution for the hemispherical nose portion and the method-of-characteristics solution for the cylindrical body portion. The relaxation method has been used for Mach numbers from 0.7 to 1.3. Experimental results indicate a strong interaction of the shock and boundary layer for M approximately equal to 0.8.

Compressibility is a property inherent in any material, but it does not always manifest itself. Experience suggests that it affects the medium motion only at velocities comparable to the speed of sound. Why do we study compressibility? It turns out that in order to calculate the aircraft streamlining or the internal flow in its engine, or the shell muzzle velocity, or the dynamic load of a shock wave from an accidental blast on a structural element, and in many other cases it is necessary to know and understand the laws of the Dynamics of Compressible Media (DCM) and be able to apply them in practice. This textbook is designed to help readers achieve this goal and learn the basics of DCM. This field of knowledge is high-tech and always focuses on the future: modern developments of hypersonic aircraft, designing more advanced structural elements for airplanes and helicopters, calculating the car aerodynamics, etc. Paradoxes have always given impetus to the search for new technological devices. Unusual effects in DCM include the flow chocking in supersonic outflow from reservoirs (Sect.2.2); the shock wave formation inside an initially smooth flow (Sect.5.3); the generation of a "spallation saucer" of armor inside a tank when a shell hits it (Sect.5.5); the dog-leg of a plane discontinuity surface at shockwave reflection from a rigid wall (Sec.8.1). The way to understand these and other effects is through the creation of quantitative models of a moving compressible fluid.

A new method of characteristics numerical scheme for three- dimensional steady flow was developed which has second-order accuracy. Heretofore all such schemes for three-dimensional flow have had accuracies less than second-order. A complete numerical algorithm for computing internal supersonic flows of the type encountered in ramjet, scramjet or rocket propulsion systems was developed and programmed for both the IBM 7094 and CDC 6500 computers. The method was tested for order of accuracy using the exact solution for source flow and Prandtl-Meyer flow. The results of these tests verified the second-order accuracy of the scheme. Additional accuracy tests using existing methods for solution of two-dimensional axisymmetric flows showed that the scheme produces accuracies comparable to that of the two-dimensional method of characteristics. The computer program was used to generate the flow field for several three-dimensional nozzle contours and for nonsymmetric flow into an axisymmetric nozzle. These results reveal the complex nature of three- dimensional flows and the general inadequacy of quasi-three-dimensional analyses which neglect crossflow. An operationally convenient computer program was produced. The program has the capability to analyze nonisoenergetic and nonhomentropic flows of a calorically perfect gas or homentropic flows of a real gas in chemical equilibrium. The initial-value surface options include uniform flow, source flow or axisymmetric tabular data. The nozzle boundary options include conical nozzles, axisymmetric contoured nozzles and super-elliptical nozzles.

Progress in Aeronautical Sciences