Numerical simulation of cryogenic flows in rocket combustion chambers

Kurzfassung

The accurate numerical simulation of combustion and atomization processes in rocket combustion chambers is a key element for the design of future space transportation vehicles. The main challenges include the consistent approximation of thermodynamic effects within a broad range from cryogenic temperatures at the injection to high temperature within the flame. This broad temperature range combined with high-pressure conditions is challenging for the stability of the numerical method. Another numerical challenge is to resolve and/or model the disimilar length scales: First to mention is the accurate prediction of the jet breakup of the propellants (e.g. cryogenic oxygen and/or cryogenic hydrogen) and the cryogenic mixture. Second to mention are disimilar length scales between the liquid injection conditions (e.g. liquid oxygen) and the gaseous gases in the flame. In literature the numerical prediction of cryogenic injection processes is an open question how cryogenic sub- and supercritical injection process can be modeled (see e.\,g. the discussion in Oefelein and Bellan) and which physical processes are important to characterize the breakup and the evaporation processes correctly. At these conditions, as found e.\,g. in rocket combustion chambers, all fluid properties have a strong sensitivity to changes in the (non-linear) equation of state. One major challenge is the strong discontinuity in the flow field due to the phase boundary. Another open question is which are the main physical processes that have to be modeled for Reynolds Averaged Navier-Stokes (RANS) based ap proaches, similar to the single-phase turbulence modeling. These turbulence models are of practical importance as they are used to design and assure rocket combustion chambers with many design-type calculations. Detailed numerical simulations (Large Eddy or Direct Numerical Simulations) are still too expensive for those simulations and are used to understand the fundamental flow physics in detail, even the computational resources increased significantly in the last years. In this talk we discuss the numerical methodology to handle cryogenic flows in combustion chambers using a RANS based method. The numerical development is based on the DLR flow solver TAU for which some extensions are proposed that handle the mixture of cryogenic fluids. This includes the numerical framework for an efficient evaluation of cryogenic mixture states as well as state of the art mixture rules for viscosity and heat transfer coefficients. A double-f lux based numerical method is included to prevent spurious numerical oscillations in cryogenic mixture states as proposed by Ma et al. for trans-critical flows. The framework is validated with experimental results for a lab-scale combustion chamber experiment conducted at the DLR branch in Lampoldshausen. During the BKC test campaign a single-injector cryogenic combustion chamber was fired at several combustion chamber pressures ranging from sub- to supercritical conditions. The combustion chamber was fully equipped with OH* and shadowgraphic imaging aiming to provide extensive validation data for numerical meth ods. In addition wall temperature and pressure measurements on the outer combustion chamber walls are available.