Iterative methods for calculating parameters of fluid flows in throttling windows, valve clearances, channels and pipelines of steering actuators in rocket stages

The paper presents results of developing iterative methods for calculating instantaneous values for parameters of fluid flows in throttling windows of slide valves, in clearances of safety valves and overflow valves, in channels and pipelines of steering actuators of rocket stages. Obtaining instantaneous values for parameters of fluid flows in the above elements is required at each step during numerical integration of differential equations of a steering actuator math model when calculating dynamic characteristics, and after each iteration in iterative methods of calculating its static characteristics. The difficulty in determining precise values for flow rates and other parameters at each step of integration or at each iteration consists in a certain indeterminacy caused by the fact that values for flow rates and dimensionless flow parameters are indirectly (via Reynolds number) expressed, in the final analysis, through themselves. Solving systems of nonlinear algebraic and transcendent equations with the methods in question is possible using a modified iterative Seidel method.