Dominic von Terzi

Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3

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.

Reliable and Accurate Prediction of Three-Dimensional Separation in Asymmetric Diffusers Using Large-Eddy Simulation

Large-eddy simulations (LES) and Reynolds-averaged Navier―Stokes (RANS) calculations of the flow in two asymmetric three-dimensional diffusers were performed. The setup was chosen to match an existing experiment with separation. Both diffusers possess the same expansion ratio but differ in performance. The aim of the present study is to find the least expensive method to reliably and with reasonable accuracy account for the impact of the change in geometry. RANS calculations failed to predict both the extent and location of the separation. In contrast, LES with wall-functions delivered results within the accuracy of the experimental data.

Numerical Investigation of Transitional Supersonic Base Flows with Flow Control

Drag reduction by means of flow control is investigated for supersonic base flows at Mach number M = 2.46 using Direct Numerical Simulations (DNS) and the Flow Simulation Methodology (FSM). The objective of the present work is to understand the evolution of coherent structures in the flow and how flow control techniques modify these structures. For such investigations, simulation methods that capture the dynamics of the large turbulent structures are required. DNS are performed for transitional base flows at Re_D = 30,000. Due to the drastically increased computational cost of DNS at higher Reynolds numbers, a hybrid RANS/LES method (FSM) is applied to simulate base flows with flow control at Re_D = 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 (coherent) structures is presented.

Scrutinizing Velocity and Pressure Coupling Conditions for LES with Downstream RANS Calculations

A RANS calculation is connected to an upstream LES via explicit coupling conditions at a pre-defined interface. The role of the interface is to allow for mean flow information to propagate upstream and for fluctuations to leave the LES domain without reflections. To this end, the mean velocity is directly coupled across the domain boundaries whereas the fluctuations at the downstream end of the LES zone are treated using either the so-called enrichment strategy (Quemere & Sagaut, 2002) or a parameter-free generalization of this method based on a convective condition (von Terzi, Frohlich & Mary, 2006). For incompressible flows, both techniques require a complementary coupling condition for the pressure or an equivalent variable enforcing continuity. Two distinct techniques are investigated: (i) The instantaneous pressure is computed in a coupled fashion for the union of the LES and RANS domains and (ii) the pressure is completely decoupled and mass conservation across the interface is ensured by an adjustment of the velocities on both sides. The performance of the different methods is scrutinized for turbulent channel flow and the flow over periodic hills. It was found that the convective condition with decoupled pressure fields and an explicit mass flux correction was the most robust technique delivering results of equal or increased quality in comparison to other combinations considered.

Diffusers with Three-Dimensional Separation as Test Bed for Hybrid LES/RANS Methods

The turbulent flow in two asymmetric diffusers with complex three-dimensional separation was computed employing Large-Eddy Simulations (LES) and Reynolds-Averaged Navier–Stokes (RANS) calculations. The computational setup matches existing experiments in the literature. The objective of the present study is to obtain reference data to be used for assessing the performance of newly developed hybrid LES/RANS techniques.

Coherent Structures in Trailing-Edge Cooling and the Challenge for Turbulent Heat Transfer Modelling

In the present paper, we test the capability of a standard Reynolds-Averaged Navier-Stokes (RANS) turbulence model to predict the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable reference data. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness. In contrast, the model failed in predicting this behavior and yielded significant overpredictions. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes, which were found to cause the counter-intuitive decrease of the cooling effectiveness.Copyright

Impact of Secondary Vortices on Separation Dynamics in 3D Asymmetric Diffusers

The flow in two three-dimensional (3D) asymmetric diffusers with the same expansion but different aspect ratios was recently measured (Cherry et al., 2008). The results revealed complex 3D separation patterns with a severe sensitivity to the geometric variation. The setup served as a test case for two ERCOFTAC workshops (Jakirlic et al., 2010) that aimed at assessing the predictive capabilities of various turbulence modeling approaches. Reynolds-Averaged Navier–Stokes (RANS) models based on the eddy-viscosity assumption yielded qualitatively wrong results. These models cannot reproduce secondary vortices (SV) in the inlet duct. Methods that account for SV or even resolve these structures fared better. In particular Large-Eddy Simulation (LES) was able to compute the flow in both diffuser geometries within measurement uncertainty (Schneider et al., 2010). The hypothesis that SV have a strong impact on the separation dynamics was further corroborated by recent experiments (Grundmann et al., 2010). At the inlet of one of the diffusers, localized (steady and unsteady) perturbations were introduced. The authors conjectured that the forcing generated streamwise vortices and that these SV were responsible for the observed change in pressure recovery by up to 14%. In the present paper, the hypothesis is tested by controlled numerical experiments using LES and manipulation of (mean) SV in the inlet duct for both diffuser geometries.

The Late Nonlinear Stage of Oblique Breakdown to Turbulence in a Supersonic Boundary Layer

Oblique breakdown to turbulence was initiated by low amplitude forcing in a laminar flat-plate boundary layer at Mach three. The growth of the instability waves was investigated using spatial Direct Numerical Simulations (DNS). Excellent agreement with theory was obtained in the linear stage corroborating that the entire transition process from the linear regime to the final breakdown was captured. A fully turbulent flow was reached demonstrating that this transition scenario is a viable path to turbulence. Key events in the late nonlinear stage of breakdown are studied in detail.

Segregated LES/RANS Coupling Conditions for the Simulation of Complex Turbulent Flows

The paper presents hybrid LES/RANS computations of turbulent flows with a segregated approach. This approach employs strict steady RANS and strict LES in pre-defined regions of the computational domain coupling the solution between them by specifically designed interfaces. The latter can be obtained by enhancement of the interfaces needed for domain decomposition in any block structured code. The paper covers inflow and outflow conditions of the LES subdomain when linked to a RANS domain as well as tangential coupling. Compressible as well as incompressible simulations are reported.

The Impact of Secondary Mean Vortices on Turbulent Separation in 3D Diffusers

In rectangular ducts with fully-developed turbulent flow, mean vortices in the corners form secondary flow patterns whose energy contents is orders of magnitude lower than that of the flow in the streamwise direction. In the present numerical experiments, it is demonstrated using Large Eddy Simulations (LES) that these Mean Secondary Vortices (MSV) exert a profound influence on flow separation in three-dimensional asymmetric diffusers following such a duct. By removing, enhancing or switching the sense of rotation of the MSV in the inlet duct of two diffusers the shape, location and extent of separation zones farther downstream were drastically altered and, hence, the performance of the device. These results provide an explanation why eddy-viscosity based Reynolds-Averaged Navier–Stokes (RANS) models, that inherently cannot account for MSV, fail in predicting even the location of the separated flow in such diffusers.