Stefan Wernz

Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer

The transition process in a supersonic flat-plate boundary layer at Mach 2 is investigated numerically using linear stability theory (LST) and direct numerical simulations (DNS). The experimental investigations by Kosinov and his co-workers serve as a reference and provide the physical conditions for the numerical set-up. In these experiments, the weakly nonlinear regime of transition was studied. This led to the discovery of asymmetric subharmonic resonance triads, which appear to be relevant for transition in a Mach 2 boundary layer. These triads were composed of one primary oblique wave of frequency 20 kHz and two oblique subharmonic waves of frequency 10 kHz. While the experimentalists have focused on this new breakdown mechanism, we have found that the experimental data also indicate the presence of another mechanism related to oblique breakdown. This might be the first experimental evidence of the oblique breakdown mechanism in a supersonic boundary layer. With the simulations presented here, the possible presence of oblique breakdown mechanisms in the experiments is explored by deliberately suppressing subharmonic resonances in the DNS and by comparing the numerical results with the experimental data. The DNS results show excellent agreement with the experimental measurements for both linear and nonlinear transition stages. Most importantly, the results clearly show the characteristic features of oblique breakdown. In addition, we also investigated the subharmonic transition route using LST and DNS. When forcing both the subharmonic and the fundamental frequencies in the DNS, a subharmonic resonance mechanism similar to that in the experiments can be observed.

Numerical investigation of transition mechanisms influencing the development of turbulent wall jets

The transitional region downstream of the nozzle exit in wall jets over plane and curved surfaces at high Reynolds numbers (Rej=10,000) is investigated using three-dimensional Navier{Stokes simulations. The transition process is crucial for the development of the turbulent wall jet since it leaves a strong signature farther downstream. During transition, energetic vortical structures (spanwise, streamwise) develop from hydrodynamic instabilities and propagate into the turbulent o w, while strongly inuencing the meano w characteristics, e.g., the spreading rate, the skin-friction, and ultimately the separation location. Smaller-sized Navier{Stokes simulations are employed for investigating the inuence of various o w parameters, such as the shape of the jet prole at the nozzle exit, the disturbance level, and also the eect of wall curvature on the overall development of the vortical structures and the mean o w. For some o w congurations, the transition mechanisms are investigated in greater detail using Direct Numerical Simulations with a grid-resolution that is ne enough for capturing the transition mechanisms during the later stages of the breakdown. The simulations show that the development of spanwise vortices during wall-jet transition leads to the formation of braid vortices that loop around the spanwise vortices and appear as streamwise vortices in the time-averaged o w. In the presence of wall curvature (Coanda wall jet), the strength of the spanwise vortices is

Numerical Investigation of Localized Separation Induced by a Three-Dimensional Pressure Gradient

Steady and unsteady separation on a flat-plate generated by a localized three-dimensional pressure gradient has been studied with Direct Numerical Simulations for a range of flow parameters. The fundamental characteristics of this type of flow have been analyzed and three distinctly different topologies were found. Fundamental features described for threedimensional separated flows in general as well as for the flow over a hemisphere-cylinder in particular could be reproduced. The closed separation topologies are all very similar near the line of separation. One pattern in particular displays features that closely resemble the flow over a cylinder with a hemispheric cap. In addition to the closed separation patterns, we also found an open separation topology that may not have been documented before.

Nonlinear resonances in a laminar wall jet: ejection of dipolar vortices

Nonlinear mechanisms leading to the ejection of dipolar vortices from a laminar wall jet are being investigated using highly accurate Navier-Stokes simulations. With a set of well-defined numerical experiments for a forced Glauert wall jet, the nonlinear resonant interaction between the large-amplitude harmonic disturbance and a small-amplitude wave packet is systematically explored using two-dimensional simulations. Generated by a small-amplitude pulse, the wave packet experiences rapid resonant growth in the subharmonic part of its spectrum resulting in vortex mergings and, ultimately, the ejection of a pair of counter-rotating vortices from the wall jet. This two-dimensional subharmonic instability, if not mitigated by competing three-dimensional instabilities, can lead to the detachment of the entire wall jet from the surface. As shown using three-dimensional direct numerical simulations, vortex ejection still occurs in a forced transitional wall jet if the two-dimensional wave packet can reach a large amplitude level upstream of the region of three-dimensional turbulent breakdown. Movies are available with the online version of the paper.

Linearized navier-stokes calculations of the spatial stability of a hypersonic boundary layer on a 5°sharp cone with high temperature effects

Recent transition experiments by Jewell et al. in the high enthalpy T5 tunnel at GALCIT have shown turbulent spots on a 5 degree cone. In contrast to earlier experiments, such as for example at Purdue, the freestream was hot compared to the wall temperature. Because of the short duration of the experiments, the wall remained essentially at ambient temperature and thus was cold compared to the freestream. To date, no Direct Numerical Simulations are available for comparison with the experimental data. In this paper basic flow calculations for the T5 experiment Test Shot 2718 are provided, and also results from Direct Numerical Simulations are presented. Moreover, a Linearized Compressible NavierStokes code was developed that is employed for investigating the linear spatial stability. The stability investigations provide insight into the effects of the wall temperature on the linear stability behavior.

Numerical Investigation of Resonance Phenomena in Wall Jet Transition

The competition between 2-D and 3-D resonances in wall jet transition is analyzed using DNS. In 2-D DNS strong growth of subharmonic disturbances is observed which leads to a subharmonic resonance cascade. When the forced flow is also perturbed by a small pulse, massive vortex ejections occur. With 3-D DNS it is shown that additional 3-D forcing can prevent vortex mergings and vortex ejections by reducing the spanwise coherence of the vortices, particularly close to the wall.

Numerical Investigation of Vortex Onset in Supersonic Taylor-Couette Flow

The compressible flow between concentric cylinders, in the case where the inner cylinder rotates and the outer one is at rest, has been computed using a pseudospectral/finite difference method. The onset of turbulence in rarefied supersonic gap flows for flywheel applications, and particularly the impact of surface roughness on the development of Taylor vortices, has been explored. An immersed boundary method using an external force field was employed to model the surface roughness. The Navier‐Stokes code was validated against results from the literature for a supersonic wide-gap flow. To validate the immersed boundary method, the rotor wall was replaced by a smooth offset wall modeled with an external force field. Very good agreement with the analytical solution for steady Couette flow was achieved. The growth of Taylor vortices in a narrow gap with smooth walls was studied first. Then, the external force field was used to create a riblet on the rotor to investigate the influence of the roughness of the rotor on the flow and, more particularly, on the onset of the instability. The most interesting feature is the early appearance of vortices for Taylor numbers where the flow with smooth walls is in the subcritical regime.