In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine–Hugoniot equations are applied to provide a relationship between the disturbances field of two sides of the shock. To incorporate real gas effects in the formulation, real gas relations and equilibrium air curve-fits are used in the resulting system of equations. The general formulation presented here may be simplified to derive Morkovin's formulation by the perfect gas assumption. The magnitudes of downstream disturbances field resulting from different types of upstream disturbances field (entropy wave and fast/slow acoustic waves) with the shock are expressed by appropriate analytical relations. Results for different disturbance variables are presented for a wide range of upstream Mach number considering real gas effects and compared with those of the perfect gas and some conclusions are made. The effects of the presence of body are also studied theoretically and the analytical relations for the magnitude of the pressure disturbance at the body for different types of upstream disturbances field considering real gas effects are provided and their results are presented and discussed.
An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 2, 2017; final manuscript received May 25, 2018; published online June 27, 2018. Assoc. Editor: Daniel Livescu.
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Hejranfar, K., and Rahmani, S. (June 27, 2018). "An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects." ASME. J. Fluids Eng. January 2019; 141(1): 011201. https://doi.org/10.1115/1.4040446
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