Engineering Transactions, 5, 2, pp. 243-268, 1957

O Metodach Obliczenia Wzajemnego Oddziaływania Fali Rozrzedzeniowej i Fali Uderzeniowej

A. Rościszewski
Instytut Podstawowych Problemów Techniki PAN

In the first part of the paper the author gives a physical analysis of the wave interaction problem in a one-dimensional non-steady flow.
The flow in the interaction region is «multhisentropic», i. e. the value of the entropy is constant along the path of every particle in the at plane and different for each particle.
The solution of the fundamental equations in this region is indefinite; the solution depending on the boundary conditions along the shock waves lines which cannot be determined before the solution is obtained. The solution methods consist in replacing the fundamental differential equations by finite difference equations, or disregarding the entropy rise along the shock line. In the first case, the solution is obtained by using the auxiliary plane ua in which the line representing the state of the gas just behind the shock wave is determined in advance. The second method gives good approximations for small shock intensity (the entropy rise is proportional to the third power of shock strength). This method was introduced by Friedrichs who disregarded the reflected or transited rarefraction wave. The author of the present paper shows that disregarding the transited waves in the case of head collision of shock and rarefraction waves, we
are in contradiction to the fundamental laws of mechanics (the laws of conservation of mass momentum and energy). He proposes a modification of the Friedrichs method taking the transited simple rarefraction wave into consideration. The solution is obtained in a closed form. Finally, H Geiringer's method based on the Lagrangian representation as well as the Neuman's mechanical model are discussed.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


P. Courant a. K. Friedrichs, Supersonic Flow and Shock Waves, New York 1948.

K. Friedrichs, Formation and Decay of Shock Waves, Communic. Pure Appl. Math., t. 1, 1948.

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J. Rościszewski, Aerodynamika stosowana, MON, 1957.