Turbulence Modeling for Predicting Flow Separation in Rocket Nozzles
Abstract
ConvergentDivergent (CD) nozzles are used in rocket engines to produce thrust as a reaction to the acceleration of hot combustion chamber gases in the opposite direction. To maximize the engine performance at high altitudes, large area ratio, bellshaped or contoured nozzles are used. At lower altitudes, the exit pressure of these nozzles is lower than the ambient pressure. During this overexpanded condition, the nozzleinternal flow adapts to the ambient pressure through an oblique shock. But the boundary layer inside the divergent portion of the nozzle is unable to withstand the pressure rise associated with the shock, and consequently flow separation is induced.
Numerical simulation of separated flows in rocket nozzles is challenging because the existing turbulence models are unable to correctly predict shockinduced flow separation. The present thesis addresses this problem. Axisymmetric, steadystate, ReynoldsAveraged NavierStokes (RANS) simulations of a conical nozzle and three subscale contoured nozzles were carried out to numerically predict flow separation in overexpanded rocket nozzles at different nozzle pressure ratios (NPR). The conical nozzle is the JPL 45◦15◦ and the contoured nozzles are the VACS1, the DLRPAR and the VACS6short. The commercial CFD code ANSYS FLUENT 13 was first validated for simulation of separated cold gas flows in the VACS1 nozzle. Some modeling issues in the numerical simulations of flow separation in rocket nozzles were determined. It is recognized that compressibility correction, nozzlelip thickness and upstreamextension of the external domain are the sources of uncertainty, besides turbulence modeling.
In highspeed turbulent flows, compressibility is known to affect dissipation rate of turbulence kinetic energy. As a consequence, a reduction in the spreading rate of supersonic mixing layers occurs. Whereas, the standard turbulence models are developed and calibrated for incompressible flows and hence, do not account for this effect. ANSYS FLUENT uses the compressibility correction proposed by Wilcox [1] which modifies the turbulence dissipation terms based on turbulent Mach number. This, as shown in this thesis, may not be appropriate to the prediction of flow separation in rocket nozzles. Simulation results of the standard SST model, with and without the compressibility correction, are compared with the experimental data at NPR=22 for the DLRPAR nozzle. Compressibility correction is found to cause underprediction of separation location and hence its use in the prediction of flow separation is not recommended.
In the literature, computational domains for the simulation of DLR subscale nozzles have thick nozzlelips whereas for the VAC subscale nozzles they have no nozzlelip. Effect of nozzlelip thickness on flow separation is studied in the DLRPAR nozzle by varying its nozzlelip thickness. It is found that nozzlelip thickness significantly influences both separation location and postseparation pressure recovery by means of the recirculation bubbles formed at the nozzlelip.
Usually, experimental values of free stream turbulence are unknown. So conventionally, to minimize solution dependence on the boundary conditions specified for the ambient flow, the computational domain external to the nozzle is extended in the upstream direction. Its effect on flow separation is studied in the DLRPAR nozzle through simulations conducted with and without this domain extension. No considerable effect on separation location and pressure recovery is found.
The two eddyviscosity based turbulence models, SpalartAllmaras (SA) model and Shear Stress Transport (SST) model, are well known to predict separation location better than other eddyviscosity models, but with moderate success. Their performances, in terms of predicting separation location and postseparation wall pressure distribution, were compared with each other and evaluated against experimental data for the conical and two contoured nozzles. It is found that they fail to predict the separation location correctly, exhibiting sensitivity to the range of NPRs and to the type of nozzle.
Depending on NPR, the SST model either underpredicts or overpredicts Free Shock Separation (FSS). Moreover, it also fails to capture Restricted Shock Separation (RSS). With compressibility correction, it underpredicts separation at all NPRs to a greater extent. Even though RSS is captured by using compressibility correction, the transition from FSS to RSS is overpredicted [2]. Early efforts by few researchers to improve predictions of nozzle flow separation by realizability corrections to turbulence models have not been successful, especially in terms of capturing both the separation types.
Therefore, causes of turbulence modeling failure in predicting nozzle flow separation correctly were further investigated. It is learnt that limiting of the shear stress inside boundary layer, due to Bradshaw’s assumption, and overprediction of jet spreading rate are the causes of SST model’s failure in predicting nozzle flow separation correctly. Based on this physical reasoning, values of the a 1 parameter and the two diffusion coefficients σk,2 and σω,2 were empirically modified to match the predicted wall pressure distributions with experimental data of the DLRPAR and the VACS6short nozzles. The results confirm that accurate prediction of flow separation in rocket nozzles indeed depends on the correct prediction of spreading rate of the supersonic separationjet. It is demonstrated that accurate RANS simulation of flow separation in rocket nozzles over a wide range of NPRs is feasible by modified values of the diffusion coefficients in turbulence model.
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