On the scaling and unsteadiness of shock induced separation

Abstract

Shock wave boundary layer interactions (SWBLI) are a common phenomenon in transonic and supersonic flows. The presence of shock waves, induced by specific geometrical configurations, causes a rapid increase of the pressure, which can lead to flow separation. Examples of such interactions are found in amongst others rocket engine nozzles and on aerospikes, on re-entry vehicles, in supersonic and hypersonic engine intakes, and at the tips of compressor and turbine blades in jet engines. The interactions are important factors in vehicle development. Both the separated flow and the induced shock have been shown to be highly unsteady, causing pressure fluctuations and thermal loading. This generally leads to a degraded performance and possibly structural failure. The current work therefore aims to improve the physical understanding of the mechanisms that govern the interaction, with a special attention for the flow organisation and for the sources of the unsteadiness of the induced shock. In particular, the case of a reflecting incident shock is investigated, but the results find their application more generally in other configurations. Additionally, it is verified whether the interaction can be controlled by means of upstream fluid injection. To attain these aims, experiments were performed, comparing systematically several interactions for a range of shock intensities (producing incipiently separated and well separated flows) and under a number of flow conditions (Mach numbers of 1.7 and 2.3 and Reynolds numbers of 5,000 (‘low’) and 50,000 (‘high’)). This was done using the latest developments in the field of measurement techniques. A large amount of data was obtained for multiple interactions by means of a range of flow diagnostic techniques, yielding highly consistent results. A full field determination of the characteristic time scales by means of dual plane particle image velocimetry (Dual-PIV) has shown that the unsteadiness frequencies in the high Reynolds number incipient interaction span almost three orders of magnitude, demonstrating additionally the existence of low frequency dynamics of the reflected shock. The effect of control by means of air jet vortex generators (AJVGs) was thoroughly characterised, putting in evidence the generation of pairs of counter-rotating vortices of unequal strength that induce streaks of low and high speed fluid. These in their turn modify the separation bubble size without suppressing it. There is an inversely proportional relation between the reflected shock frequency and the bubble size. A scaling analysis was made, aimed at reconciling the observed discrepancies between interactions documented in literature. As part of this analysis, a separation criterion has been formulated that depends on the free-stream Mach number and the flow deflection angle only. In addition, a scaling approach has been derived for the interaction length based on the mass and momentum conservation. A conditional analysis has been performed based on the instantaneous separation bubble size. The generation and successive shedding of large coherent structures was found to be present also in absence of instantaneous flow separation. For the incipient cases, a link has been put into evidence between the separation region and the state of the upstream boundary layer. For the separated interactions, this link was absent and the shock unsteadiness seems to be mainly related to the separation bubble pulsation. The separation criterion in combination with the normalised interaction length represents a single trend line onto which all data for a large scope of documented interactions fall together with only a moderate scatter. This trend line predicts that the only way to effectively eliminate a separation bubble (without massive separation) by means of upstream control is by decreasing the displacement thickness of the incoming boundary layer. A scaling for the wall normal coordinate has been defined based on the interaction length with a correction for Mach number effects, producing a large resemblance in the geometric organisation of the mean and turbulent flow fields within the considered interactions. It can be concluded that multiple unsteadiness mechanisms are at work within the interaction, irrespective of the Mach number and the Reynolds number. It is proposed that the relative importance of the different mechanisms shifts with the imposed shock intensity. It seems that weak interactions without instantaneous flow separation should be governed by upstream effects only, with rather high shock frequencies. For incipient interactions, downstream effects start to occur; the region of high turbulence intensities displays mainly a lifting motion, producing a shock foot of varying strength and a shock unsteadiness that involves a time scales which can differ by at least one decade. Interactions with significant flow separation show mainly a translating motion, producing a low frequency unsteadiness and a shock foot of constant strength, which is in accordance with a free interaction behaviour. Concerning the Reynolds number and Mach number effects, it is concluded that for turbulent boundary layers, the onset of separation is Reynolds number independent. The interaction length is however governed by both the Reynolds number and the Mach number.