A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer at Mach 3. Its downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using linear-stability theory, parabolized stability equations and direct numerical simulations (DNS). In the present paper, the linear regime is studied first in great detail. The focus of the second part is the early and late nonlinear regimes. It is shown how the disturbance wave spectrum is filled up by nonlinear interactions and which flow structures arise and how these structures locally break down to small scales. Finally, the study answers the question whether a fully developed turbulent boundary layer can be reached by oblique breakdown. It is shown that the skin friction develops such as is typical of transitional and turbulent boundary layers. Initially, the skin friction coefficient increases in the streamwise direction in the transitional region and finally decays when the early turbulent state is reached. Downstream of the maximum in the skin friction, the flow loses its periodicity in time and possesses characteristic mean-flow and spectral properties of a turbulent boundary layer. The DNS data clearly demonstrate that oblique breakdown can lead to a fully developed turbulent boundary layer and therefore it is a relevant mechanism for transition in two-dimensional supersonic boundary layers.

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The possibility of a subharmonic-resonance triad in the transition process for a flat-plate boundary layer at Mach three was demonstrated using Direct Numerical Simulations (DNS). The parameters controlling such a resonance triad were investigated in detail. Finally, the interaction of this triad with the so-called 'oblique breakdown' scenario was studied. To this end, the mechanisms were invoked separately and in combination. By itself the oblique breakdown leads to a faster growth of instability waves than the subharmonic resonance. However, in a combination with a subharmonic-resonance triad, the dominant modes of the oblique breakdown experience a slower growth, whereas those of the subharmonic resonance are more amplified. Overall, the interaction promotes transition and the rise in skin friction and the drop in shape factor are moved upstream when compared to the oblique breakdown.

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The final stage of transition to turbulence in a supersonic flat-plate boundary layer at Mach 3 is investigated using Direct Numerical Simulations (DNS). A set of six simulations was performed to study the development of a pair of oblique waves from their initiation at low amplitudes to final breakdown to turbulence. In a previous paper (part I of this study), the linear and early nonlinear regimes of this so-called "oblique breakdown scenario" were discussed. The focus of the present paper (part II) is on the early turbulent regime, i.e. the region of the flow downstream of the maximum of skin friction. In this region, the flow is shown to have lost periodicity in time and to exhibit the typical mean flow and spectral properties of a turbulent boundary layer as known from the literature and theory. The DNS data clearly demonstrate that oblique breakdown can lead to a fully developed turbulent boundary layer and therefore may be a relevant mechanism for practical applications. authors.@en

Direct numerical simulation data of supersonic axisymmetric wakes are analysed for the existence of large coherent structures. Wakes at Ma = 2.46 are considered with results being presented for cases at Reynolds numbers ReD = 30, 000 and 100,000. Criteria for identification of coherent structures in free-shear flows found in the literature are compiled and discussed, and the role of compressibility is addressed. In particular, the ability and reliability of visualisation techniques intended for incompressible shear-flows to educe meaningful structures in supersonic wakes is scrutinised. It is shown that some of these methods retain their usefulness for identification of vortical structures as long as the swirling rate is larger than the local compression and expansion rates in the flow field. As a measure for the validity of this condition in a given flow the 'vortex compressibility parameter' is proposed which is derived here. Best 'visibility' of coherent structures is achieved by employing visualisation techniques and proper orthogonal decomposition in combination with the introduction of artificial perturbations (forcing of the wake). The existence of both helical and longitudinal structures in the shear layer and of hairpin-like structures in the developing wake is demonstrated. In addition, elongated tubes of streamwise vorticity are observed to emanate from the region of recirculating flow.@en

A pair of oblique waves at low amplitudes is introduced in a supersonic at-plate boundary layer. Its downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using Direct Numerical Simulations (DNS). In the present paper, first the linear regime is studied in great detail. Comparisons to linear stability theory clearly determine that the so-called "oblique breakdown" mechanism is initiated. The focus of the second part is the nonlinear regime. It is shown how the spectrum is filled up by nonlinear interactions, what flow structures arise and how these structures locally break down to small scales. Finally, a logarithmic region of the mean streamwise velocity profile is formed indicating the beginning of a fully turbulent flow region. The simulations demonstrate that oblique breakdown is a viable path to turbulence.

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Drag reduction by means of flow control is investigated for supersonic base flows at M = 2.46 using direct numerical simulations and the flow simulation methodology. The objective of the present work is to understand the evolution of coherent structures in the flow and how flow control techniques can modify these structures. For such investigations, simulation methods that capture the dynamics of the large turbulent structures are required. Direct numerical simulations are performed for transitional base flows at ReD = 30,000. Because of the drastically increased computational cost of direct numerical simulations at higher Reynolds numbers, a hybrid methodology (flow simulation methodology) is applied to simulate base flows with flow control at ReD = 100,000. Active and passive flow control techniques that alter the near wake by introducing axisymmetric and longitudinal perturbations are investigated. A detailed analysis of the dynamics of the resulting turbulent structures is presented.@en

A flow simulation Methodology (FSM) is presented for computing the time-dependent behavior of complex compressible turbulent flows. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The objective of FSM is to provide the proper amount of turbulence modeling for the unresolved scales while directly computing the largest scales. The strategy is implemented by using state-of-theart turbulence models (as developed for Reynolds averaged Navier-Stokes (RANS)) and scaling of the model terms with a "contribution function." The contribution function is dependent on the local and instantaneous "physical" resolution in the computation. This physical resolution is determined during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that it approaches direct numerical simulations (DNS) in the fine-grid limit and such that it provides modeling of all scales in the coarse-grid limit and thus approaches a RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in large eddy simulation (LES). However, FSM is distinctly different from LES in that it allows for a consistent transition between RANS, LES, and DNS within the same simulation depending on the local flow behavior and "physical" resolution. As a consequence, FSM should require considerably fewer grid points for a given calculation than would be necessary for a LES. This conjecture is substantiated by employing FSM to calculate the flow over a backward-facing step and a plane wake behind a bluff body, both at low Mach number, and supersonic axisymmetric wakes. These examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating (physically) complex flows, and, on the other hand, demonstrate the potential of the FSM approach for simulations of turbulent compressible flows for complex geometries.@en

Supersonic axisymmetric base flows are prototypical for flows behind projectiles and missiles, For these flows, drag reduction can be achieved by means of passive control of the near wake. Thereby, large (turbulent) coherent structures play a dominant role. The objective of the present investigation is to elucidate if and how successful passive flow control techniques modify these structures. To this end, first Direct Numerical Simulations (DNS) for a Reynolds number of ReD = 100,000 and Mach number of Ma =2.46 were performed using a high-order accurate and highly parallelized research code which was developed at the University of Arizona. Thereby, roughly 52 million grid points were employed. The DNS data serve to visualize typical structures of the unsteady flow field and to verify that the use of less computational costly RANS/LES methods is applicable for this flow. Two of these methods, the Flow Simulation Methodology (FSM) and Detached Eddy Simulations (DES), were then employed to investigate the supersonic base flow at ReD =3.3 × 106 and Ma = 2.46 using between 460,000 and seven million grid points. For the DES, the commercial CFD-code Cobalt was employed. This unstructured grid solver allowed then to perform simulations with boat-tailing. The obtained mean flow data are compared to available experimental results.@en

For the flow simulation methodology (FSM) of Speziale and Fasel, turbulent stresses and heat fluxes are computed using a state-of-the-art RANS turbulence model, but where the model contribution is scaled according to a contribution function which depends on the physical resolution of the computation. In flow regions (and instants of time) with high physical resolution only the smallest (unresolved) scales of motion are modelled while the larger structures are computed directly (similar to LES), whereas in regions of very coarse resolution an unsteady RANS simulation is recovered. The methodology thus may be classified as a RANS-LES hybrid or better, a unified approach to RANS and LES. In order to evaluate the potential of this methodology, it is applied to the unsteady flow over a backward-facing step at ReH = 3000 and Ma = 0.25, with laminar separation and turbulent reattachment. The results are compared to DNS, LES, and unsteady RANS.@en