Numerical Simulation of Supersonic Jet

Turbulent under-expanded jet is an important fundamental flow, involving interactions between supersonic shock-wave and turbulent compressible flow. Jets have practical applications, like exhaust plumes of propulsion vehicles, investigations on supersonic combustion, reduction of noise emissions like screech tones which are a particular interest because acoustic equipment and materials properties can be affected and gaseous fuel injection system. Bearing in main this considerations, a under-expanded supersonic jet of air was simulated during the present work using LES method. The main reason to do this work is because measurements of the structure of under-expanded jets are limited, due to difficulties caused for variation of static pressures, velocities, and shock waves at the time of introducing equipment.

There is a complicated structure inside of the jet which has some remarkable features. First, the jet boundary oscillates as the supersonic jet periodically expands and converges in zones where expansion fans and shock-waves take place. These shocks waves (red color) alternate with expansions fans (blue color). The supersonic jet expands and cools as it flows through the expansion fans and is compressed and heats as it flows through the shock wave. If the supersonic jet is circular, then the axisymmetric shock wave and fans have conical shape.

Shock-wave cells of Supersonic Jet


Number of nodes nx=155, ny=109, nz=109

Solution for Cartesian Navier-Stokes equations.

Boundary condition for compressible Navier-Stokes equations [1]

Sixth-order finite differences scheme (spatial discretization).

Third-order Runge-Kutta method (time discretization)

Wave radation Ma=1.4 of supersonic Jet


Transient velocity vectors indicating the pressure field.

Isosurfaces of criterion Q which represent physically speaking, the development of turbulence.


[1] Poinsot and Lele “Boundary Conditions for Direct Simulations of Compressible Viscous Flow “. Stanford 1991.



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