Hypersonic flows over a compression ramp with different leading-edge radii are numerically investigated. Flow separation occurs on the cold-wall compression ramp with a free-stream Mach number of 7.7 and a unit Reynolds number of $4.2 \times 10^6$ m$^{-1}$. By performing direct numerical simulations (DNS), it is shown that the separation bubble enlarges when the leading-edge radius is increased from zero up to a critical value. Beyond the critical radius, the separation bubble conversely shrinks as the radius is further increased. Global stability analysis (GSA) is employed to investigate the three-dimensional instability of the two-dimensional base flows. It is found that the inherent instability in the flow field also exhibits a reversal trend, that is, the flow system firstly becomes more unstable and then tends to be more stable with increasing leading-edge radius. The growth rate and spanwise wavelength of the unstable modes identified by GSA are verified by DNS. Accompanying the occurrence of three-dimensionality, streamwise heat-flux streaks are formed on the ramp surface downstream of reattachment. The present study demonstrates that a proper blunting of the leading edge can suppress flow separation, reduce aerodynamic heating and stabilise the flow system for a hypersonic compression-ramp flow.

In this paper, the incident shock–separation shock interactions on a surface plate near the leading edge are studied theoretically and experimentally, and the transition from regular reflection (RR) to Mach reflection (MR) is the main focus. The theoretical method employs free interaction theory (FIT) and the minimum entropy production (MEP) principle to analyse the separation shock strength of flow separated from the boundary layer and separated from the leading edge, respectively, the criterion based on the MEP principle is employed to predict the RR-to-MR transition near the leading edge. The experiments were performed on a rotatable wedge situated over a sharp leading-edge plate such that the wedge could continuously change the flow deflection angle from $0^{\circ }$ to $40^{\circ }$ by means of a high-precision control device. Fast-response transducers and a high-speed camera were used to measure dynamic pressures and to take schlieren images, respectively. The influences of wedge positions, Reynolds numbers and Mach numbers on shock reflections are investigated by careful tests. The theoretical and experimental results for Mach numbers 5, 6, 7 and 8 show good agreement, indicating that the theoretical method is applicable.

We present experimental and theoretical results for the adjustment of a fluid (homogeneous or linearly stratified), which is initially rotating as a solid body with angular frequency ${\it\Omega}-{\rm\Delta}{\it\Omega}$, to a nonlinear increase ${\rm\Delta}{\it\Omega}$ in the angular frequency of all bounding surfaces. The fluid is contained in a cylinder of square cross-section which is aligned centrally along the rotation axis, and we focus on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, where $\mathit{Ro}={\rm\Delta}{\it\Omega}/{\it\Omega}$ is the Rossby number. The flow development is shown to be dominated by unsteady separation of a viscous sidewall layer, leading to an eruption of vorticity that becomes trapped in the four vertical corners of the container. The longer-time evolution on the standard ‘spin-up’ time scale, $E^{-1/2}{\it\Omega}^{-1}$ (where $E$ is the associated Ekman number), has been described in detail for this geometry by Foster & Munro (J. Fluid Mech., vol. 712, 2012, pp. 7–40), but only for small changes in the container’s rotation rate (i.e. $\mathit{Ro}\ll 1$). In the linear case, for $\mathit{Ro}\ll E^{1/2}\ll 1$, there is no sidewall separation. In the present investigation we focus on the fully nonlinear problem, $\mathit{Ro}=O(1)$, for which the sidewall viscous layers are Prandtl boundary layers and (somewhat unusually) periodic around the container’s circumference. Some care is required in the corners of the container, but we show that the sidewall boundary layer breaks down (separates) shortly after an impulsive change in rotation rate. These theoretical boundary-layer results are compared with two-dimensional Navier–Stokes results which capture the eruption of vorticity, and these are in turn compared to laboratory observations and data. The experiments show that when the Burger number, $S=(N/{\it\Omega})^{2}$ (where $N$ is the buoyancy frequency), is relatively large – corresponding to a strongly stratified fluid – the flow remains (horizontally) two-dimensional on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, and good quantitative predictions can be made by a two-dimensional theory. As $S$ was reduced in the experiments, three-dimensional effects were observed to become important in the core of each corner vortex, on this time scale, but only after the breakdown of the sidewall layers.

Large-scale longitudinal vortices in high-speed turbulent separated flows caused by relatively small irregularities at the model leading edges or at the model surfaces are investigated in this paper. Oil-flow visualization and infrared thermography techniques were applied in the wind tunnel tests at Mach numbers 3 and 5 to investigate the nominally 2-D ramp flow at deflection angles of 20°, 25° and 30°. The surface contour anomalies have been artificially simulated by very thin strips (vortex generators) of different shapes and thicknesses attached to the model surface. It is shown that the introduced streamwise vortical disturbances survive over very large downstream distances of the order of 104 vortex-generator heights in turbulent supersonic flows without pressure gradients. It is demonstrated that each vortex pair induced in the reattachment region of the ramp is definitely a child of a vortex pair, which was generated originally, for instance, by the small roughness element near the leading edge. The dependence of the spacing and intensity of the observed longitudinal vortices on the introduced disturbances (thickness and spanwise size of vortex generators) and on the flow parameters (Reynolds numbers, boundary-layer thickness, compression corner angles, etc.) has been shown experimentally.