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The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.

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In the present paper we extend our earlier work on the finite-difference shock-capturing essentially non-oscillatory (ENO) scheme for a non-uniform grid. The design of the ENO scheme is based on the methodology for uniform grids. We provide the analysis of the different variations of the limiter functions for the developed algorithm to define the optimal function producing the smallest spread of the solution. The effect of the limiter choice on the mixing layer dynamics was studied for the non-uniform grid. The numerical experiments revealed that the nonoptimal choice of limiter can result in the overgrowth of the mixing layer, that is important for the numerical modeling of the combustion.

In the present paper the third order finite-difference shock-capturing essentially non-oscillatory (ENO) scheme for a non-uniform grid has been developed. The design of the ENO scheme is based on the methodology for uniform grids. To construct the essentially non-oscillatory piecewise polynomial, the Newtoninterpolant of the third order degree is adapted for the non-uniform grid. Also, the implementation of the symmetrical form of the slope limiters on non-uniform meshes is examined. The efficiency of the developed algorithm is demonstrated by the numerical experiments on the simulation of the three-dimensional turbulent steady flowfield generated by the transverse hydrogen injection into the supersonic air cross-flow. The comparison with results on the uniform grid using the coordinate system transformation is done.