Combining methods for end-to-end calculation of gas flow in a Laval nozzle

Abstract

The paper solves the problem of selecting optimal methods and combining them when performing a complex calculation of all sections of the Laval nozzle. The problem is significant, since different flow modes are realized in different areas of the nozzle and it is impossible to use a single method for the full calculation. Solving the direct problem, parameters in the flow of gas are determined. Solving the reverse problem determine the profile of the Laval nozzle. Profiling is an important applied task for calculating the nozzles of rocket and aircraft engines, or designing experimental turbines. In this paper, we consider a two-dimensional plane axisymmetric flow of an inviscid perfect gas (on the example of dry air). The problem is solved starting with an accelerating subsonic flow via using methods of establishing and finite elements. For subsonic flow found an exact solution (Prandtl-Mayer flow). Solving the problem in a supersonic flow via using proximate methods (the method of characteristics and interpolation for the grid normalization). The solution is supplemented by a method that allows taking into account the features of axisymmetric flow in the nozzle to expand the applicability of the solution for real nozzles. The results obtained – the gas velocity field and the coordinates of nodes. Results allows estimation of the optimal size of the Laval nozzle for the given conditions, its shape, and obtain a flow profile depending on its initial characteristics defined in the previous section of the nozzle. The results of flow simulation can be applied to calculate the flow in circular sections, which are the most common in the current application. The results are confirmed by the solution using the finite element method, and the convergence of the solution in the diffuser is described in the current work. Theoretically, the solution can be applied to a mixture of gases, if peculiarities of physical and chemical transformations and the participation of combustion products are taken into consideration. In this case instead of parameters in the pre-chamber, the parameters of the combustion chamber and the products in it should be used as initial conditions. This calculation will be carried out in future studies of the authors.