Compressible Wall-Injection Flows in Laminar, Transitional, and Turbulent Regimes: Numerical Prediction

Abstract

Numerical simulations of compressible rocket flows are conducted in laminar, transitional, and turbulent regimes. The laminar simulation is carried out on a planar rocket flow without nozzle using the unsteady two-dimensional Navier-Stokes system. The transitional and turbulent flows are performed in three-dimensional on an extended rocket geometry with a divergent outlet using compressible large eddy simulation (LES) models. In both cases, the compressibility effect plays an important role. In the laminar case, pressure oscillation is forced at the outflow boundary. The time-averaged part of the solution is compared with the inviscid theory of compressible rocket flow of Balakrishnan et al. (Balakrishnan, G., Linan, A., and Williams F. A., Compressibility Effects in Thin Channels with Injection, AIAA Journal, Vol.29, No. 12, 1991, pp. 2149-2154) and the oscillatory part with the acoustic layer model of Majdalani and Van Moorhem (Majdalani, J., and Van Moorhem, W. K., Improved Time-Dependent Flowfield Solution for Solid Rocket Motors, AIAA Journal, Vol. 36, No. 2, 1998, pp. 241-248). The mean flow from the present numerical result is in better agreement with the compressible theory than the conventional Taylor's profiles (Taylor, G. I., Fluid Flow in Regions Bounded by Porous Surfaces, Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 234, 1956, pp. 456-475), as expected. The oscillatory part of the flow agrees well in the first quarter of the axial extent, near the head end. Farther downstream, the discrepancies develop rapidly between the numerical result and the acoustic-layer model. Possible causes of the difference are the effect of compressibility, which alters the local speed of sound, hence, acoustic properties, and the interference of hydrodynamic instabilities. In the transition and turbulent regimes, the dynamic LES model is applied on different resolutions. The measurements data of Traineau et al. (Traineau, J. C., Hervat, P., and Kuentzmann, P., Cold Flow Simulation of a Two Dimensional Nozzleless Solid Rocket Motor, AIAA Paper 86-1447, June 1986) are employed for comparison purposes. The refinement study by comparison with the measurement data suggests the importance of resolving the laminar and transition region for a reliable application of LES in transitional flows. With the consideration of this aspect, LES with efficient grid size can produce resonable accuracy. Forcing hydrodynamic instabilities and a more realistic injection fluctuations model are recommended.