title: Characterisation of the stability of compression corner geometries under supersonic flow conditions
Creators: name: Cerulus, Nicolas
Publisher: name: University of Liverpool Repository
Year: 2022

description: Identifying the mechanism by which flow transitions to turbulence is of particular interest for the design and control of atmospheric flight vehicles. Compression corners are present on many key components of aerospace vehicles whose performance is essential for safe operation. Therefore, it is crucial to understand the transition mechanisms to avoid excessive thermal loading of the vehicle which is caused by separated flow and shock boundary layer interaction. The transition mechanisms involved in many high-speed separated boundary layer scenarios, are not fully understood. Linear stability theory, developed in the last century, describes the decomposition of a flow into a basic state and a small amplitude disturbance. The behaviour of these disturbances can be described as damped or growing. When growing disturbances are uncovered, these will begin to grow exponentially, leading to transition. This behaviour is known as modal. When a flow is subject to high external disturbance levels, it may cause a bypass of the modal amplification scenario, leading to the non-modal stability becoming a path to transition. In order to truly represent flows for the purposes of stability analysis, highly accurate base states are required. Several methods for this are described; Direct Numerical Simulation (DNS) using second and high order methods, Direct Simulation Monte-Carlo (DSMC) used for rarefied gases, and triple deck theory used as a validation tool and method for characterising stability. The necessity for high order base-states is justified by the presence of unsteadiness in second order methods, in the form of small amplitude oscillations propagating throughout the domain even at low Reynolds numbers. These unsteady artefacts disappear when using high order methods, as well as the far greater decay and convergence of residuals achieved using these methods. These high order base-states show excellent agreement in the vicinity of separation with triple deck theory which provides confidence in the accuracy of these base-states. Once appropriate base-states are calculated, modal and non-modal stability analysis can be undertaken. Throughout the planar and axisymmetric compression corners studied, an intimate link exists between the separation region and associated shocks through the modal mechanism. At high Reynolds numbers, a stationary unstable mode is identified, taking the form of the well documented separated boundary layer mode. This mode is studied over a wide range of Reynolds numbers characterising the neutral loop of this flow. An analogous mode is found using DSMC that is stable and on the hollow cylinder-flare that becomes unstable at high enough corner angles and Reynolds numbers. Further travelling modes are identified that are modally damped but show the potential to grow downstream out of the domain, which is corroborated using local spatial analysis. These structures are also compared with those of experimental work, showing a similar shape of periodic perturbations triggered in the separation region. Non-modal analysis is performed on unstable planar ramp cases and describes significant short term growth which has the potential to bypass the modal mechanism, even when this modal behaviour is unstable. The large time required for the modal growth to achieve the same non-modal maximum gain suggests this modal behaviour will be bypassed in the transition mechanism. On the stable modal scenarios shown using high angle DSMC base-states, large energy gain is shown at short time suggesting that, in this case even a modally stable case may transition to turbulence.