Unsteady Flow Evolution in Porous Chamber with Surface Mass Injection, Part 1: Free Oscillation

Unsteady  ow evolution in a porouschamberwith surfacemass injection simulatinga nozzleless rocketmotorhas been investigated numerically. The analysis is based on a large-eddy-simulation technique in which the spatially Ž ltered and Favre averaged conservation equations for large, energy-carrying turbulent structures are solved explicitly. The effect of the unresolved scales is modeled semi-empirically by considering adequate dissipation rates for the energy present in the resolved scale motions. The  owŽ eld is basically governed by the balance between the inertia force and pressure gradient, as opposed to viscous effects and pressure gradient corresponding to channel  ows without transpiration. It accelerates from zero at the head end and becomes supersonic in the divergent section of the nozzle. Three successive regimes of development, laminar, transitional, and fully turbulent  ow, are observed. Transition to turbulence occurs away from the porous wall in the midsection of the motor, and the peak in the turbulence intensity moves closer to the wall farther downstream as the local Reynolds number increases. Increase in pseudoturbulence level at the injection surface causes early transition to turbulence. As the  ow develops farther downstream, the velocity proŽ le transits into the shape of a fully developed turbulent pipe  ow with surface transpiration. The compressibility effect also plays an important role, causing transition of the mean velocity proŽ les from their incompressible  ow counterparts as the local Mach number increases. The  ow evolution is characterized primarily by three nondimensional numbers: injection Reynolds number, centerline Reynolds number, and momentum  ux coefŽ cient.