# Nozzle Flow

Copyright: © Fraunhofer ILTThe flow of compressible gases with friction and heat transfer is described by the Navier-Stokes equations (conservation of mass, momentum and energy). Cartesian Methods and the Discontinuous Galerkin (DG) approach are applied to simulate boundary layers due to friction of the main gas/vapor flow with ambient gases and with component boundaries at elevated temperatures.

The flow of compressible, frictionless gases with heat transfer is described by the Euler equations. The Euler equations represent a system of nonlinear hyperbolic partial differential equations. Nonlinear hyperbolic conservation equations produce discontinuous solutions. A Godunov type finite volume method is applied for the solution of Euler equations for the gas flow. This method solves the finite volume Riemann problems for calculation of the numerical flows at the cell boundaries. The Riemann problems are solved approximatively by a modified Harten-Lax-Leer method.

In the following example, a gas flow from a Laval nozzle is simulated using the Euler equations. The gas flow within the Laval nozzle is accelerated to supersonic speed and leaves the nozzle with ambient gas pressure. After a short free-expansion phase, the gas stream encounters a solid surface with a depression. First, a pressure wave is reflected at the surface. Then the gas stream encounters the depression and is reflected by the base of the depression. The reflected gas stream interacts with the stream from the nozzle. The pressure distribution within the gas is shown. Different pressure values are depicted by different colour values. The colour and pressure scale ranges from blue at 1 bar to red at 3 bar.