The characterisation of the compressible shear layer is fundamental towards the understanding of the mixing of supersonic fluids. The density and velocity ratio across the layer as well as the Kelvin-Helmholtz Instabilities (KHI) that develop play an important role in the growth and shape of the mixing zone. Of particular interest for this study are shear layers occurring in a pseudosteady Mach reflection.
A large scale shock tube facility was utilised with a 450 by 100 mm rectangular cross-section. Three Mach numbers were selected for testing, namely Ms = 1.26, 1.37, 1.45. This range was chosen in order to extend work by Rubidge and Skews [1] and Rikanati et al. [2] in the weak shock (Ms < 1.5) domain. The scale of the experiment is much larger than previous work. A 30 degree mild steel wedge was used to obtain a single-Mach Reflection (SMR) [3]. A shadowgraph image is shown in Figure 1. A clear braided structure resembling the KHI is visible along the shear layer as well as an increase in shear layer thickness from the triple point.
A comparison to Papamoschou and Roshko [4] visual growth rates is undertaken in the pseudosteady reference frame. The theoretical density (s) and velocity (r) ratios across the shear layer are obtained from Three Shock Theory (3ST), with the triple point trajectory angle (χ) and reflected shock angle (ωir) measured experimentally. The compressibility parameter Mc [5] can be calculated using the values of r and s mentioned previously. The convective velocity Uc of the KHI structures is difficult to measure due to curvature of the shear layer.
Due to the large cross-section of the tube and uneven bursting of the diaphragm, transverse waves occur in the test section due to small steps between the driven sections. A 40 degree wedge is to be manufactured and tested to investigate the effect of the boundary layer proximity and the interaction with the shear layer. Further experimental work will utilise the large scale of the test section and shadowgraph images will be obtained with Mach stem heights in excess of 70mm. The self-similarity of the shear layer is being investigated for the Mach number range prescribed.
Figure 1: Kelvin-Helmholtz Instability forming on Mach reflection shear layer with a wedge angle of 30 degrees. Ms = 1.37
References
- Rubidge, S. R., Skews B. W.: Shear-layer instability in the Mach reflection of shock waves. Shock Waves. 24, 479-488 (2014)
- Rikanati, A., Sadot, O., Ben-Dor, G., Shvarts, D., Kuribayashi, T., Takayama, K.: Shock-wave Mach-reflection slip-stream instability: a secondary small-scale turbulent mixing phenomenon. Phys. Rev. Lett. 96, 174503 (2006)
- Ben-Dor, G.: Shock Wave Reflection Phenomena. Springer, Berlin (2007)
- Papamoschou, D., Roshko, A.: Observations of supersonic free shear layers. Sadhana. 12, 1-14 (1988)
- Papamoschou, D.: Structure of the Compressible Turbulent Shear Layer. In: 27th Aerospace Science Meeting, Nevada, (January 1989)
