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The single-expansion ramp nozzle (SERN) is intensely over-expanded and leads to a large separation zone. The flow separation is the central phenomenon causing a reduction in thrust, and shock waves lead to a drop in the flow stagnation pressure and increase the energy loss. In this study, the unsteady compressible flow in a SERN was studied by employing the  k - kl - ω  transition turbulence model with high ability in separation flow prediction. In this regard, the finite volume code with the pressure-implicit with the splitting of operators algorithm and the adaptive mesh refinement technique were applied. Firstly, the results were compared with published data and it is revealed that the numerical methodology was capable of detecting the exact structure of lambda shock and wall pressure. Then, the influences of harmonic inlet and outlet conditions were evaluated on the flow behavior. The results showed that for harmonic inlet pressure conditions the value of friction coefficient in the case with wavelength of 0.3 is greater than the cases with the wavelength of 0.15 and 0.6. Also, it is found that the shock train did not form for the case with wavelength of 0.6. Furthermore, for the harmonic condition in outlet pressure, the minimum wall shear stress was obtained for the case with the wavelength of 015, and the shock strength, in this case, is more than the cases with wavelength of 0.6 and 0.3.

Numerical analysis of shock wave train in single-expansion ramp nozzle under harmonic inlet and outlet conditions