PLANE UNSTEADY FLOWS IN NOZZLES WITH DOUBLE RESTRICTIONS
Keywords:
unsteady flow, double-constriction nozzle, transonic flow, Laval nozzle, Weierstrass elliptic functions, sonic line, velocity potential, gas dynamicsAbstract
This article is devoted to the development of an analytical method for solving a plane initial-boundary value problem for unsteady transonic ideal gas flow in a Laval nozzle with two constrictions. The mathematical model is based on the classical nonlinear velocity potential equation for unsteady flows. The authors propose a method of separation of variables, which reduces the original problem to a system of ordinary differential equations whose solutions are expressed in terms of Weierstrass elliptic functions and Bessel functions. Various flow regimes are analyzed: the transition from subsonic to supersonic flow, the formation of local supersonic zones, and the occurrence of Taylor-Meyer flows in critical sections. Graphical dependences of the stream functions and pressure distributions are presented, confirming the adequacy of the model as time tends to infinity.
References
1. Tomotika S., Tamada K. Studies an two-dimensional transonic flows of сompressible fluids.-Qurt. Of Apple. Mathem., 1950, vol №4, part I, P.381-391.
2. Чечейбаев Б. Исследование околозвуковых пространственных течений газа в сопле с двумя сужениями и в слабовогнутой трубе. Вестник КНУ им. Ж.Баласагына, 2004.-С.76-81.
3. Цзянь Х.Ш., Лин П.П., Рейснер Г. О двумерном неустановившемся движении тонкого крыла в сжимаемой жидкости. Газовая динамика. М.: Изд-во иностр.лит., 1950.С.183-196.
4. Ахиезер Р.И. Элементы теории эллипт. функций. – М.: Наука,1970. -304с.
5. Пирумов У.Г., Росляков Г.С. Течения газа в соплах.-М.:Изд-во Москов.Университета, 1978.-352с.
