Andreas C. Laible

Numerical Investigation of Supersonic Transition for a Circular Cone at Mach 3.5

The Direct Numerical Simulation (DNS) of the transition process in a supersonic boundary layer from the laminar to the turbulent state signican tly challenges existing numerical codes. High{order accurate methods are commonly used to improve the accuracy of simulations and thus reduce the number of required grid points. In this paper the development of a high{order code which is tailored towards stability and nonlinear transition simulations over a circular cone is discussed. A thoroughly conducted validation is presented. In particular, small amplitude disturbances are introduced to study the linear wave amplication (eigenbehavior). The results are compared to Linear Stability Theory (LST). Moreover, a three{dimensional stability diagram { in the downstream{frequency{azimuthal mode domain (Rx F k) { is extracted from these calculations and analyzed. Finally, the possible occurrence of oblique breakdown is highlighted by performing simulations with continuously forced nite{amplitude disturbances.

Numerical Investigation of Hypersonic Transition for a Flared and a Straight Cone at Mach 6

Hypersonic boundary layer stability and transition for two dieren t cone geometries at Mach 6 are studied using direct numerical simulation (DNS). The two geometries are (i) the ared cone investigated in the NASA Langley Test Chamber Facility 1 and (ii) its straight (non{ared) counterpart. We present a detailed comparison between these geometries with respect to the base o w, i.e. the undisturbed laminar o w, and the linear stability regime. Furthermore, a parameter study regarding secondary fundamental instability was performed for each geometry. Then a wave which experienced a high secondary growth rate was used to initialize numerical simulations deep into the transitional regime. The resulting nonlinear process, which can be considered to be a ‘classical’ fundamental (Ktype) breakdown, is analyzed in detail. By comparing the results for the two dieren t geometries, qualitative and quantitative insight into the hypersonic transition process for ared cones is obtained. In particular the question how strong the nonlinear transition process is altered by the cone are is discussed.

Numerical Simulations of Controlled Transition for a Sharp Circular Cone at Mach 8

The linear and nonlinear development of disturbance waves in an axisymmetric boundary layer on a sharp circular cone at Mach 8 are investigated by numerical solution of the full 3D, time dependent, compressible Navier-Stokes equations. Disturbances are introduced by wall-normal blowing and suction near the upstream boundary of the computational domain. Small amplitude disturbances are introduced to study their linear stability behavior and the results are compared with Linear Stability Theory (LST) for validation. These results are also used to guide parameter selection for simulations of nonlinear transition phenomena. In particular, for simulations with large amplitude 2D disturbances, fundamental resonance can be observed. This resonance leads to nonlinear amplification of 3D modes and the classical aligned ⁄-vortex pattern as the boundary layer begins to transition to turbulence. Simulations of oblique breakdown are also performed and the two transition mechanisms are compared.

Numerical investigation of transition initiated by a wave packet on a cone at Mach 3.5

Transition initiated by a wave packet in a cone boundary layer at Mach 3.5 has been investigated using LST and DNS. Disturbances have been introduced into the boundary layer by pulsing the wall-normal velocity through a hole on the cone surface. The computational setup is very close to experiments by Corke et al. and Matlis. The present study can be divided into three parts. In the first part, the linear development of a wave packet is studied in detail. Disturbance spectra in the frequency–azimuthal mode number plane based on wall-pressure amplitudes and time envelopes of the disturbance signal are discussed. The second part of the present study focuses on the identification of possible, asymmetric resonance triads for the most dominant oblique instability waves of the wave packet. New triads have been found that have not yet been reported for a supersonic boundary layer. These triads might explain some major findings in the third and final part of the present work, which focuses on the weakly nonlinear development of a wave packet that was generated by a large amplitude pulse. The initial disturbance development of this wave packet remains still linear, while farther downstream nonlinear wave interactions alter the shape and the disturbance spectrum of the packet. The disturbance spectrum from this study and the results of other investigations performed in parallel (Laible et al.) suggest that oblique breakdown might be the strongest nonlinear transition mechanism for a supersonic boundary layer.