Linear Instability Analyses of Supersonic and Hypersonic Flows over Rotating Cones

Kurzfassung

Rotating objects in super- and hypersonic flow fields are part of many real-world applications, for example, the entry of space debris or the reentry of launch-vehicle stages in the atmosphere. Investigating the physics and especially the transition process in boundary layers of such objects could help to understand and control their motion, as turbulent behaviour is disadvantageous due to the drag increase. Therefore, in this work, the rotating cone is used as a generic configuration to examine the influence of rotation on the instabilities in the laminar boundary layer. The results of local (parallel) linear stability analysis are presented and a parameter study is performed in order to answer the following questions: How does the rotation intensity affect the boundary-layer instabilities and what influence have the half-opening angle and the oncoming flow velocity on the instabilities? Moreover, the influence of rotation terms in the stability equations are investigated as well as the influence of the metric terms to better understand the influence of the considered geometry on the boundary layer, as the flat plate and the cone in super- and hypersonic flow fields form similar instabilities. The basic flow is calculated using the flow-field solver TAU. A grid convergence analysis is performed, in order to ensure sufficient resolution of the used grids. Also, it is ensured that the simulations converge in time. The stability analysis focuses on a specific position on the cone. Four different instability types are investigated, namely the 1st-Mode, the 2nd-Mode, the CrossflowInstability and the Centrifugal-Instability. The NOLOT extension for rotational coordinate systems presented in the work of Dechamps & Hein [8] is used as the solver for the stability equation and is corrected, as scale factors have falsely been included in the Coriolis and centrifugal terms of the extension (which does not invalidate the results presented in the work of Dechamps & Hein [8]). The results of the investigation of the non-rotational setup is in accordance with previous works. Rotation has a general destabilising effect on the 1st- and 2ndMode. Further, the 1st-Mode destabilises for waves travelling with and stabilises for waves travelling against the direction of the cone’s rotation, whereas it is the other way around for the 2nd-Mode. Rotation causes a cross-flow velocity component in the basic flow, which leads to the destabilisation of the Crossflow-Instability. With inclusion of rotation terms in the stability equation, the Centrifugal-Instability destabilises. With the inclusion of both the metric and rotation terms, two additional modes have been found to destabilise and are interpreted as Crossflow-Modes, while the question is discussed, whether they represent physically valid instabilities or not. The increase of the rotation intensity destabilises each considered mode further. With the increase of the oncoming flow velocity each mode also destabilises except for the 1st-Mode, that stabilises instead. The increase of the half-opening angle leads to waves with higher circumferential wavenumbers to be unstable. The increase of the half-opening angle also has a destabilising effect on each mode but the Centrifugal-Instability and one of the newly found modes. Rotation terms destabilise and metric terms stabilise every considered mode.