Numerical modelling of swept and crossing shock-wave turbulent boundary-layer interactions

Two configurations that have received a great deal of attention in the last decades are namely the single-fin and double-fin. In these interactions, deflected un-swept sharp fins are used to generate single-swept and double-crossing oblique shock-waves that interact with a supersonic/hypersonic turbulent boundary-layer developing over a flat plate. Following the swept-shock interaction, the study of crossing-shock interaction represents a logical progression in the general study of shock- wave / turbulent boundary-layer interactions (SWTBLIS). These rather simple geometries allow isolating the inherent flow physics which can be applied to more complex configurations. Besides having fundamental importance, swept- and crossing-shock interactions also have important engineering applications. Research findings on single-fin can be applied, for example, in the design of wing/tail fuselage juncture, and in high incidence flows on swept delta wings and slender bodies. The double-fin, on the other hand, could represent a simplification of a high-speed inlet of vehicles employing air-breathing propulsion. Such an inlet geometry concepts employ side- wall compression to increase, in reasonable short distance, the air pressure prior combustion. The side-wall compression surfaces (i.e. fins) generate an oblique shock-wave that crosses one another and interacts with the boundary-layer developing on the windward of the fiJselage. The nature of such complex 3-D interactions can affect the performance of the inlet as well as the engine. If the physical principles governing these interactions are well determined and understood, then an active control system can be developed so that to reduce the risk of engine fail and optimise its performance. Note that the findings of this investigation are crucial for the design of effective thermal protection systems since these interactions produce high peaks of heating which can damage materials severely around concentrated areas where shock-waves hit surfaces. The main objective of this thesis is to predict accurately secondary separation flows and wall heat transfer under conditions of turbulent and separated flow, which has represented a challenging problem for computational fluid dynamists for the past thirty years. Steady RANS modelling has been carried out for a symmetrical double-sharp-fin configuration with an inclination angles from 7 degrees to 21 degrees, Mach 3.92 and Reynolds number RC5 = 3.08X105, aiming for comparison and improvement of wall heat transfer predictions. Grid refinement and turbulence modelling studies have been carried out carefully in order to improve previous numerical predictions against experimental measurements. Overall, current steady Reynolds Averaged Navier-Stokes computations with co-based Reynolds Stress Model (RANS-RSM) outperformed one- and two-equation conventional turbulence models as well as other numerical investigations carried out over the last three decades. My original contribution to knowledge focuses primarily on improving numerical prediction of wall heat transfer in supersonic/hypersonic side-wall compression inlets and deflected aerodynamic surfaces. Different methods of evaluation of the wall heat transfer, to improve the comparison with available experiments, have been proposed for both single- and double-fin configurations. Results are compared with experimental measurements and previous numerical studies. The most challenging numerical prediction of wall heat transfer coefficient in strong pressure gradient flows has been largely improved, for the first time, by adopting three approaches: (1) choosing a suitable turbulence model - the wall heat transfer coefficients peaks computed by RANS-RSM are in fact closer to experimental peaks (50% improvement) in comparison with other conventional two- equation eddy-viscosity turbulence models; (2) increasing the wall turbulent Prandtl number in region of high shear strain; (3) and finally, adopting a pressure-based correlation formula. The latter appeared to be the most effective method of predicting wall heat transfer coefficient, provided accurate wall pressure distributions being obtained by numerical simulations. Within the scope of this original research, complex flow structures are also numerically investigated in detail to verify and further examine, existing conclusions on the nature of incipient and secondary separation evolution at monotonic increasing shock strengths, for the single-fin configurations at Mach numbers 3, 4 and 5 and at beta fin's deflection angles [if ranging from 9 degrees to 30.6 degrees. The nature of secondary separation will be explained at different regimes III-VI in condition of subsonic and supersonic transverse conical cross-flow. Computational Fluid Dynamics (CFD) analyses using conventional two-equation turbulence models are unable to capture secondary flow separations at moderate interaction strength - a phenomenon observed in experiments and believed to be associated with a 'weakly-turbulent' boundary-layer separation. I investigated this aspect in further details. In fact, RANS-RSM, due to its capability of reproducing correct level of turbulence kinetic energy (TKE), confirmed the presence of such a 'weakly-turbulent' state of transverse cross-flow in the near-wall regions underneath the main cross-flow vortex at moderate interaction strength (regime 111/] V). Computations revealed that the development of the secondary separation at early stage (regime III) is caused by the interaction of (1) the 'conically-subsonic' (Mn < 1) flow region of the transverse cross-flow developed from the primary reattachment (R[sub 1]) line with (2) the subsonic (M < 1) region of the near-wall secondary cross-flow which forms within the primary separation zone. Turbulence behaviour was also analysed, for the first time, in the reverse cross-flow in order to investigate the influence of the (laminar or turbulent) flow state in evolution of secondary separation phenomenon at increasing shock strengths. Remarkably, computed results are in good agreement with the conclusions of experimentalists. In fact, the secondary separation (S[sub 2]) cross- flow gradually disappears in transitional (laminar-to-turbulent) supersonic conical cross-flow regions (regimes IV and V), except at the regime VI, where S[sub 2] reappears, accompanied by a secondary reattachment (R[sub 2]) line, once the supersonic conical cross-flow becomes fully-developed turbulent. At this stage, the embedded normal shock-wave reaches the critical shock strength (xi[sub i]- 1.56) which is typically required to force turbulent separation. This study demonstrated numerically that the critical value xi[sub i]= 1.5 corresponds to the incipient secondary separation condition which is typical for the separated turbulent flows (regime V). A careful quantitative and qualitative analysis on the developments of the turbulence kinetic energy across the 3-D domain excitingly also confirms these findings. Thus, it was concluded that evolution of the secondary separation phenomenon at increasing shock strengths is influenced not only by the acceleration of the transverse cross-flow to conically-supersonic regime but also by some physical mechanisms that amplify the turbulence levels in the near-wall reverse cross-flow. One unique feature of the crossing-shock interaction at regime III; i.e. the secondary separation phenomenon, initially observed in the single-fin flow, has been successfully reproduced in a double-fin configuration by numerical computation using RANS-RSM. CFD predicted 3-D flow stream-surfaces showed that the initially weak secondary separation has been further strengthened in span-wise direction towards the central separated zone. Additional flow topology at stronger crossing-shock interactions has been also presented showing the evolution of surface flow-pattems at increasing shock strengths. To the author's knowledge, the present study represents the first attempt to predict the evolution of secondary separation phenomenon in single- and double-fin configurations at different interaction regimes. Findings suggest that the classification originally made by Zheltovodov er al. for single- fin flows (hence for Swept-Shock-Wave/Turbulent Boundary-Layer Interaction, S-SWTBLI) can be also applied to double-fin configurations (thus for Crossing-Shock-Wave/Turbulent Boundary- Layer Interaction, C-SWTBLI).