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Instability of supersonic compression ramp flow.

R P Logue¹, J S B Gajjar², A I Ruban³

¹School of Mathematics, University of Manchester, Manchester M13 9PL, UK j.gajjar@manchester.ac.uk.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|June 18, 2014

Summary

Investigating supersonic compression ramp flow instability at high Reynolds numbers reveals no singularities for increasing ramp angles. Numerical simulations show growing wavepacket disturbances, though results vary with grid size.

Keywords:

compression ramp instability shock-wave boundary layer interaction transition triple-deck

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Area of Science:

Fluid dynamics
Aerodynamics
Computational fluid dynamics

Background:

Supersonic flows over compression ramps are critical in aerospace applications.
Understanding flow instability is key to predicting aerodynamic performance and stability.
High Reynolds number flows present unique challenges due to viscous effects.

Purpose of the Study:

To investigate the instability of supersonic compression ramp flow.
To analyze flow behavior under high Reynolds number conditions using unsteady triple-deck equations.
To determine the impact of ramp angles on flow stability.

Main Methods:

Solving steady triple-deck equations to calculate mean flow for various ramp angles.
Employing two stability analysis approaches: linearized unsteady equations for global modes and numerical simulations with varied initial conditions.
Assessing the influence of grid size on numerical simulation accuracy.

Main Results:

No singularities were found for increasing ramp angles in the mean flow calculations.
No globally unsteady modes were detected within the studied range of ramp angles.
Numerical simulations demonstrated the development of wavepacket disturbances that grow and convect to large amplitudes.
Significant grid size dependency was observed in the numerical results.

Conclusions:

Supersonic compression ramp flow does not exhibit singularities with increasing ramp angles.
While global instability modes were not found, localized wavepacket disturbances can emerge and grow.
Further research is needed to refine numerical methods and address grid dependency for accurate instability prediction.