A parametric study of multiple shock wave boundary layer interactions is presented in this paper. All results were obtained using the computational fluid dynamics solver of Glasgow University. Such interactions often occur in high-speed intakes, depending on the state of the upstream boundary layer, and can adversely affect the performance of the intake. First, RANS simulations with a Reynolds-stress based turbulence model of multiple shock wave boundary layer interaction in a rectangular duct were performed and compared to the experiments followed by simulations at different Mach and Reynolds numbers and flow confinement levels. The results showed that Reynolds-stress based turbulence models can predict the interaction well. The employed explicit algebraic Reynolds stress model showed good agreement for the corner and centreline separations and resulted only in a small underprediction of the wall pressure. Flow distortion and total pressure recovery efficiency metrics were defined and evaluated for each interaction. Lower upstream Mach number and/or lower levels of flow confinement were required to achieve higher total pressure recoveries and lower flow distortion levels.

Within the framework of the NATO Science and Technology Organization Applied Vehicle Technology Task Group AVT316 calculations have been made of the supersonic flow around a slender body with wings and fins. In this paper a synthesis of the results obtained using the Reynolds Averaged Navier-Stokes equations are presented. The results show significant sensitivity to the choice of turbulence model. Whilst the gross features of the flow are similar, details of the development of the leeward wake are different. Simple linear eddy viscosity models predict vortices that rapidly decay, resulting in weak interactions with the downstream fins and relatively small rolling moments. This is attributed to an over production in turbulence quantities that results in excessive effective turbulent viscosity. Interventions that limit the production of turbulence, for example the SST limiter or curvature corrections, results in vortices that grow more slowly, changing the nature of the downstream interactions resulting in increased rolling moment. The use of more complex formulations, such as Reynolds stress models, that are inherently more capable for highly strained flows, further limits the rate of growth of the vortex cores leading to rolling moment predictions that are 2-3 times greater than those obtained with the simplest models.

Predicting the flowfield around a supersonic store at a high incidence angle is challenging due to the presence of vortices and shocks that interact with each other. The complexity of the problem is further increased by the presence of wing-body and wing-tail junctions giving rise to secondary flows. Given that the flow is turbulent, linear eddy-viscosity turbulence models are unable to account for the secondary flows and are often more dissipative than their non-linear counterparts. The high incidence angle further increases the complexity. This work investigates the effect of grid refinement and turbulence modelling on three store configurations - one with wings and fins, one without fins and wings, and one with wings only. The in-house CFD solver of the University of Glasgow is used to perform simulations at different angles of incidence and roll. Grids consisting of approximately 80 × 10e6 cells or less were found to be inadequate to capture the flow features. This shows that even if a high-order spatial method is employed, a grid of sufficient density must be used to accurately capture the aerodynamic loads of the store. In addition, grid converged results were difficult to obtain for the full configuration due to the interaction of the wing vortices with the store’s fins. Improved convergence was observed for the simplified store configurations. This further showed that the difficulty in grid convergence is related to the wing vortex interactions with the store’s fins.

The flow of high-speed air in ducts may result in the occurrence of multiple shock-wave/boundary-layer interactions. Understanding the consequences of such interactions, which may include distortion of the velocity field, enhanced turbulence production, and flow separation, is of great importance in understanding the operating limits and performance of a number of systems, for example, the high-speed intake of an air-breathing missile. In this paper, the results of a computational study of multiple shock-wave/boundary-layer interactions occurring within a high-speed intake are presented. All of the results were obtained using the in-house computational fluid dynamics solver of Glasgow University, HMB3. First simulations of a Mach $$M=1.61$$ multiple shock-wave/boundary-layer interaction in a rectangular duct were performed. The $$M=1.61$$ case, for which experimental data is available, was used to establish a robust numerical approach, particularly with respect to initial and boundary conditions. A number of turbulence modelling strategies were also investigated. The results suggest that Reynolds-stress-based turbulence models are better suited than linear eddy-viscosity models. This is attributed to better handling of complex strain, in particular modelling of the corner separation. The corner separations affect the separation at the centre of the domain which in turn alters the structure of the initial shock and the subsequent interaction. Having established a robust numerical approach, the results of a parametric study investigating the effect of Mach number, Reynolds number, and confinement on the baseline solution are then presented. Performance metrics are defined to help characterize the effect of the interactions. The results suggest that reduced flow confinement is beneficial for higher-pressure recovery.

Shock wave boundary layer interactions occur in many aerospace applications, and of particular interest are the interactions occurring in high-speed intakes. The high-speed intakes aim to decelerate the flow with minimum losses using a series of oblique shocks followed by a weak normal shock. Depending on the state of the boundary layer and on the upstream Mach number, multiple shocks can form in the throat of the intake. Often, they are referred to as shock trains, or pseudo-shocks and can have a significant impact on the inake performance. The in-house CFD solver of the Unversity of Glasgow is used here, to investigate an isolated multiple shock interaction and quantify the effect of different non-linear turbulence models. The non-linear models, and their ability to account for the Reynolds stress anisotropy, resolve the corner flows and give favourable agreement with experiments. As a second step, shock train simulations in a geometry more representative of a high-speed intake are performed. Three different pitot intakes are considered and performance metrics based on the total pressure recovery and flow distortion are evaluated at different free-stream conditions. The predicted shock trains are highly asymmetric and the strong sensitivity of the total pressure recovery and flow distortion to the intake geometry is observed which reduces at higher incidence angles.

A parametric study of Multiple Shock Wave Boundary Layer Interaction is presented in this paper.All results were obtained using the in-house CFD solver of Glasgow University.Such interactions often occur in high-speed intakes which have recently seen a renewed interest.Simulations of a multiple shock wave boundary layer interaction in a rectangular duct were first performed and the results were compared to the experiments.Using the same numerical setup a parametric study investigating the effect of Mach number, Reynolds number and confinement on the baseline solution was then performed.Efficiency metrics were also defined to quantify the interactions.The results show that Reynolds-stress based turbulence models are better suited than linear models.The corner separations affect the separation at the centreline which in turn alters the structure of the initial shock and the subsequent interaction.Reduced confinement is found to be beneficial for higher pressure recovery.Finally, results for a more realistic geometry (fore-body with an intake) featuring an oblique and multiple shock wave boundary layer interactions are presented.

This paper provides a brief overview of the activities undertaken by the Missile Facet of NATO STO AVT 316 (Vortex Interaction Effects Relevant to Military Air Vehicle Performance) since its first meeting in April 2018. Rather than setting out to provide definitive technical statements, a broader, more narrative approach is taken towards summarising some of the key developments that have occurred during the early stages of the facet’s existence. To date, work has focussed on investigating a blind test case (CFD_OTC1) based on a generic missile airframe at a supersonic flight condition. Attention is focussed on the predicted total rolling moment coefficient, the polarity of which determines the airframe’s local static roll stability. While the facet is still some way from demonstrably achieving verified CFD solutions at the flight condition of primary interest, there is now little doubt that the airframe will be predicted to be locally unstable in roll.

Reynolds Averaged Navier Stokes simulation (RANS) using the in-house CFD solver of Glasgow University is utilised to investigate the flow physics and the sensitivity to modelling assumptions of a multiple shock wave turbulent boundary layer interaction in a rectangular duct (Mr=1.61, Reδr=162000). Such interactions often occur in high-speed intakes. Two-dimensional simulations were first performed to investigate the required grid resolution. Then the sensitivity of the solution to different turbulence models is considered. Based on the required grid resolution a series of three-dimensional simulations were performed to investigate the effect of spanwise confinement and turbulence models. Lastly, using the best approach based on the above investigations, results from two additional test cases were compared to their experiments, and conclusions are drawn as to the best way to simulate multiple shock wave turbulent boundary layer interactions.

This paper provides a brief overview of the activities undertaken by the Missile Facet of NATO STO AVT 316 (Vortex Interaction Effects Relevant to Military Air Vehicle Performance) since its first meeting in April 2018. Rather than setting out to provide definitive technical statements, a broader, more narrative approach is taken towards summarising some of the key developments that have occurred during the early stages of the facet’s existence. To date, work has focussed on investigating a blind test case (CFD_OTC1) based on a generic missile airframe at a supersonic flight condition. Attention is focussed on the predicted total rolling moment coefficient, the polarity of which determines the airframe’s local static roll stability. While the facet is still some way from demonstrably achieving verified CFD solutions at the flight condition of primary interest, there is now little doubt that the airframe will be predicted to be locally unstable in roll.