# Research

**PUBLICATIONS**

**Pathak, U.**, Roy, S., & Sinha, K. (2017), “A phenomenological model for turbulent heat flux in high-speed flows with shock-induced flow separation”, Journal of Fluids Engineering **(ASME)**, 140(5).

Roy, S., **Pathak, U.**, & Sinha, K. (2017), “Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction”, **AIAA Journal**, 1-14.

Vemula, J., **Pathak, U.** & Sinha, K. (2017), “Comparative analysis of ramp-type and Busemann intakes for hypersonic air-breathing engine”, 1st National Aerospace Propulsion Conference, Kanpur, India.

**NUMERICAL MODELING OF TURBULENT FLOWS**

**“Variable turbulent Prandtl number model for Shock-Boundary Layer Interaction (SBLI) flows”**

SBLIs are characterized by high localized heat transfer rates at the point of shock wave impingement. The standard turbulence models such as the k-epsilon and k-omega models, though highly popular due to low computation cost (compared to LES/DNS), tend to over-predict the amplification of turbulent kinetic energy across the shock wave in SBLIs, resulting in incorrect prediction of surface heat flux and shock topology.

By studying the unsteadiness effect of shock on the downstream turbulence, we are able to predict the separation region size accurately. The turbulent Prandtl number is identified as an important parameter for accurate prediction of the surface heat flux. Turbulent Prandtl number is a flow dependent quantity which is generally assumed as a constant for the ease of computation. Based on experiments and DNS data, a mathematical model is developed for the variation of turbulent Prandtl number in flows with Shock-Boundary Layer Interaction (SBLI), to be used in conjunction with the standard k-omega turbulence model. The proposed model is easy to implement due to its algebraic nature and provides an improvement in the prediction of surface heat flux in SBLI flows with a negligible addition to the cost of computation. Applications of this research work include external aerodynamics of supersonic vehicles.

**DEVELOPMENT OF A RANS BASED FLUID FLOW SOLVER**

Finite volume method is utilised to develop a RANS (Reynolds-Averaged Navier Stokes) equations based solver for fluid flows on unstructured triangular grids, from scratch. Grid generation is done through Gmsh, and ParaView is used for flow visualisation. The solver employs HLLC scheme and Green-Gauss method for flux and gradient calculations respectively. Code development is in C, for portability, performance and simplicity of implementation.

**DESIGN OF EXTERNAL COMPRESSION INTAKES FOR SCRAMJETS**

Scramjets are used for propulsion in the cases where freestream Mach number is beyond 4.5 because of high specific impulse. The compression of atmospheric air is achieved, not through turbomachinery, but through shock waves that are formed at the intake of the scramjet. Thus, the intake is arguably the most important component of the Scramjet. External compression intake is the most common among Scramjet intakes.

Design and analysis of an external compression scramjet intake is done with an in-house CFD code (written in Fortran and parallelized using MPI) for understanding the flow structure and the engine un-start problem.

The design and analysis of the external compression intake (double ramp configuration) acts as a precursor to the design of streamline traced intakes which are more efficient (designed for Isentropic compression, before a conical shock is encountered by the flow).

**DESIGN OF STREAMLINE TRACED INTAKES**

Streamline-traced Busemann intakes produce even loads on the intake walls and a relatively uniform flow for the combustor, which is necessary for efficient propulsion. The designing of these intakes is done using the numerical integration of Taylor-Maccoll equation, where the incoming supersonic flow is assumed to be conically symmetric.

The flow encounters a single conical shock (as opposed to the external compression intake where there are 2 ramp shocks and a shock-train in the isolator). This ensures that the flow is uniform and the loads are even on all sides of the geometry. The pressure recovery is significantly high compared to the ramp type intakes.

Early truncation of the geometry keeps the pressure recovery sufficiently high while considerably reducing the length of the intake.

Notched Busemann intakes have a higher range of working freestream Mach numbers and thus are a good counter to the engine-unstart problem.

The streamline traced circumscribed square Busemann inlet is a widely used configuration. More complex configurations exist such as square to elliptic, square to rectangle etc.

Following are the notched Busemann intakes which are produced with circumscribing of intake cross-sections.

**DEPTH ADAPTIVE DIFFUSION**

Algorithm described in “Pock, T., Schoenemann, T., Graber, G., Bischof, H., & Cremers, D. (2008, October). A convex formulation of continuous multi-label problems. In *European conference on computer vision* (pp. 792-805). Springer, Berlin, Heidelberg.” is used to get the depth map of an image based on the disparity map of two rectified images, and then gradient diffusion is implemented on the background. This is done by reformulating a non-convex variational problem as a convex variational problem via embedding in a higher dimensional space. CUDA library is used with NVIDIA GeForce GTX 1050 Ti (768 CUDA cores) for parallelising the algorithm.

Rectified images are taken as shown below. The slight disparity can be clearly observed between the two images because of different ‘depth’ of different objects. The lamp is the object nearest to the observer, while the cupboard is the farthest.

Based on the algorithm proposed in the paper, we are supposed to obtain the following disparity map.

Comparison between ground truth disparity and the disparity map obtained is shown below.

Based on the disparity map, we do gradient diffusion for the pixels that have a higher ‘depth’, and therefore we get an image in which the background is blurred while the foreground is sharp.

Algorithm, when applied to other images produces the following results.

A speed-up of approximately one thousand is observed when compared to serial implementation using Matlab. Capabilities developed in this project can be utilized in efficient parallelisation of multi-physics solvers.