High speed flows encountered in many of the aerodynamic applications involve flow features such as turbulent boundary layers, free shear layers and their interactions with shock waves. Engineering predictions of such flows are generally done using Reynolds-averaged Navier-Stokes (RANS) equations along with an appropriate turbulence model for closure. The choice of turbulence model plays a significant role in determining the accuracy of results for such flows. It is imperative that the turbulence model is able to accurately resolve the turbulent boundary layers, free shear layers and can accurately predict shock-boundary layer interactions (SBLI) and shock-free shear layer interactions.

Generally, 2-equation turbulence models are used for such applications and the standard k-epsilon and k-omega models are the most popular choices. The standard k-omega model is known to perform better for boundary layer flows however the standard k-epsilon model predicts the spreading rates more accurately in case of free-shear layers. Also, it is known that the standard k-omega model has a very strong sensitivity to the arbitrary freestream values specified for omega outside the boundary layer. The turbulent eddy viscosity in boundary layers and free shear layers can be changed by more than 100 % by simply reducing the freestream value of omega. The standard k-epsilon model does not suffer from this deficiency. Thus, the desired choice of a turbulence model would be to use the standard k-omega model near the wall in the boundary layer and standard k-omega model away from the wall and in the free-shear layers.

The SST k-omega model of Menter utilizes the desired features of a standard k-omega model near the wall in the boundary layer and standard k-epsilon everywhere else in the flowfield. Thus, SST can be regarded as a zonal model. However, in contrast to the classical zonal approach, it does not require an a priori knowledge of flowfield in order to define zonal boundaries where different models are to be used. The change between different sub-models is achieved by 'smart' functions that can distinguish between the different zones. However, the zonal model in itself is not able to predict flows with adverse pressure gradient boundary layers as its predictions are similar to the standard k-omega model.

Menter's analysis of the standard 2-equation turbulence models showed that the classical formulation of the eddy viscosity violates Bradshaw's relation that the principal turbulent shear stress is proportional to the turbulent kinetic energy in a boundary layer. This shortcoming was attributed to the failure of standard 2-equation models in case of adverse pressure boundary layers. Menter modified the definition of eddy-viscosity so as to enfore Bradshaw's relation even in case of adverse pressure gradient boundary layer flows. A modification to mu_T that forces the principal turbulent shear stress to be proportional to TKE simulates the transport effect of the principal turbulent shear stress. Hence the resulting model is called SST k-omega model.

The standard SST k-omega model gives excellent predictions for incompressible and low speed subsonic and transonic flows with adverse pressure gradient and separation. However, in case of the high speed supersonic and hypersonic flows, SST model significantly overpredicts the shock induced separation. In this work, we analyse and explore the possible reasons of failure of the SST model in case of high speed flows with shock-induced separation. Several modifications to the standard SST model are proposed based on the shock physics so as to improve its performance in SBLIs. The main objective of this part of work is to come up with a modification to the SST model which can accurately predict shock-induced separation so that surface properties like skin friction and pressure are predicted accurately.

Multi-jet interaction is another application of interest where SST model is a better choice as the flow involves boundary layers, free shear layers and their complex interactions with shock waves. The flow field for such flows can be highly three-dimensional and hence 3D simulations are carried out for this case. The complex nature of the flowfield makes the grid generation complicated and the simulations a computationally intensive task. In this work, we have selected a case of multi-jet interaction for which experimental data and simulations from a different research group are already available in the literature. The objective is to validate our results with the available experimental data and simulation results for this case.

1. Raje, P., Saikia, B. and Sinha, K., "Numerical investigation of axisymmetric underexpanded supersonic jets" Proceedings of 1st National Aerospace Propulsion Conference NAPC-2017, IIT Kanpur, March 15-17, 2017.

2. Vemula, J. B., Raje, P., Singh, R., Roy, S. and Sinha K., 10-11 August 2016, "Parametric study of the performance of two-dimensional Scramjet Intake", 18th Annual AeSI CFD Symposium, CSIR-National Aerospace Laboratories, Bangalore, India.

3. Raje, P. and Sinha, K. "A physically consistent and numerically robust k-ε model for computing turbulent flows with shock waves", Computers & Fluids, Volume 136, pp. 35-47, September 2016.

B.E. : Mechanical Engineering (Nagpur University) - 2011
M.Tech : Applied and Computational Mechanics, Academy of Scientific and Innovative Research (AcSIR) - 2014

2 years Research experience as Trainee Scientist at CSIR-Central Mechanical Engineering Research Institute, Durgapur (2012-2014)

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