Session HX: Compressible Flows II

Low-order stochastic model for the low-frequency shock motions in shock/boundary-layer interactions

The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. Starting from an exact form of the momentum integral equation and guided by large-eddy-simulation data, a stochastic ordinary differential equation for the reflected-shock foot low-frequency motions is derived. The frequency of the most energetic fluctuations is shown to be a robust feature over a wide range of input parameters in agreement with experimental observations. Under some assumptions, the coupling between the shock and the boundary layer is mathematically equivalent to a first-order low-pass filter. Therefore, it is argued that the observed low-frequency unsteadiness is not necessarily a property of the forcing, either from upstream or downstream of the shock, but simply an intrinsic property of the coupled dynamical system.   

Shock Wave--Boundary Layer Interaction in Reflecting Detonations

The interaction of a reflecting shock wave with the boundary layer induced by the incident shock wave results in a unique flow field that has been examined in shock tubes. Our recent experiments studying reflecting detonations examine an incident detonation impinging on a normal, planar wall to create a reflected shock wave. We have observed that the pressure records taken near the location of reflection show that the measured speed of the reflected shock wave is inconsistent with the measured wall pressures. We present new experimental results of high-speed video taken of the reflecting detonation and highly-resolved two-dimensional numerical simulations of compressible viscous flow. These results show that the interaction of the reflected shock wave with the boundary layer can result in a three-dimensional shock front structure with an oblique front in the boundary layer similar to that observed in non-reacting shock tubes.   

Techniques for PIV-CFD Comparison in a Shock-boundary Layer Interaction

The outputs of a PIV experiment and a simulation of the same system are fundamentally different. PIV includes spatial averaging effects, particle travel effects, sampling effects, and multiple potential biases. In addition, there are many uncertainties, some of which are poorly understood or documented. These issues make direct comparisons between the two fields inappropriate in certain cases. To address this, a hierarchy of techniques for performing meaningful comparisons between simulations and experiments is described. The simplest transformation incorporates only spatial averaging. At the highest level of fidelity, a method for creating simulated PIV data from the simulation is outlined. This technique allows direct comparisons between PIV and CFD, and can also provide uncertainty estimates for quantities such as the turbulence intensity which are traditionally difficult to quantify experimentally. High-resolution PIV results of an investigation of a Mach 2.1 shock-boundary layer are shown. The PIV effects most relevant to a PIV-CFD comparison in this system are discussed, along with the necessary steps required to transform a CFD simulation of this system into a field that can be directly compared to the PIV.   

Upstream Boundary Condition Sensitivity of the Shock-Boundary Layer Interaction

A low aspect ratio Mach 2.1 wind tunnel with a wall-mounted compression wedge is being used to validate uncertainty quantification techniques for CFD. The tunnel is operated continuously, with a mass flow rate of approximately 0.6kg/s. The incoming pressure, temperature, and mass flow rate are monitored, and the variation in these boundary conditions is documented to provide bounds for the fluctuations applied in the CFD. The compression wedge generates an oblique shock, resulting in flow separation at the base of the wedge. High-resolution PIV measurements are taken throughout the field, with a focus on the shock-boundary layer interaction at the base of the compression wedge and on the location of shock impingement on the opposite wall. The boundary layer is perturbed in a Monte Carlo type experiment using various configurations of well-defined bumps placed upstream of the compression wedge on the opposite wall. The perturbed velocity field is measured at the location where the oblique shock from the compression wedge impinges upon the opposite wall. PDFs of these velocity data are constructed and compared to the predictions of CFD simulations of varying fidelity.   

Zones of Influence and Low Frequency Shock Motion in a Shock Boundary Layer Interaction

Shock-wave / boundary layer interactions usually exhibit unsteadiness with strong low frequency content. The present work aims at analyzing the low frequency shock motion using high resolution data from long-time large-eddy simulations. Three different flow configurations are considered yielding incipient to full separation of the boundary layer in the interaction region. Filtered cross-correlation are used to identify the flow regions being able to influence the shock at low-frequency. It is demonstrated that the information paths deduced from the cross-correlations coincide with the pressure characteristic lines. A theoretical computation of the phase velocity along the shock of perturbations induced by the ``breathing'' of the interaction region is derived. For all the three flow configurations, two different velocities are found, depending on the location of the sources along the boundary of the decelerated zone. These velocities match quite accurately velocities along the shock computed from the LES data by means of cross-correlations.   

Influence of wall heating on a shock-wave / turbulent boundary layer interaction

Shock / boundary layer interactions, if strong enough, are known to result in separation of the incoming boundary layer and to exhibit strong unsteadinesses. The main purpose of this work is to study the influence of wall heating on these features by means of Large-Eddy Simulations. Six LES have been carried out for two shock angles, either with adiabatic or heated lower walls. The unsteady data thus obtained will be used to evaluate the effects of wall temperature fluxes on the interaction size, the separation state and the unsteady behavior of the separated flow at low and medium frequencies. The influence of the wall heating on the three-dimensional modulations found within the separation bubble, either intrinsic or induced by side walls, will also be analyzed. Computations taking into account side boundary layers will particularly be used to demonstrate that lower wall heating is an effective way to achieve experiments exhibiting large separation bubbles with restricted influences of the wind tunnel side walls.   

Direct Numerical Simulation of Mach 3 Compression Ramp Flow

We present the direct numerical simulation (DNS) of a shockwave and turbulent boundary layer interaction (STBLI) generated by a compression ramp. The flow conditions are Mach 2.9 and $Re_{\theta}=2900$, and the ramp angle is 24 degrees. STBLI flows are known to display low-frequency unsteadiness, typically at frequencies 1-2 orders of magnitude lower than that of the incoming undisturbed boundary layer. The presence of these low-frequency motions in the DNS data and their relationship with the upstream and downstream flow regions have been demonstrated (Priebe and Martin, AIAA paper 2010-108). The DNS data show that the low-frequency shock motion is significantly correlated with the downstream flow. A statistically significant but small correlation is also found with the upstream flow. In the present paper, we investigate the flow structure associated with the downstream flow regions and study the time-and-space resolved dynamics of the shock motion, shear layer and separated flow regions.   

A-priori and a-posteriori assessment of SGS models for shock-boundary layer interactions

A-priori and a-posteriori assessments of subgrid-scale (SGS) large-eddy simulation (LES) models are made for an incident shock wave interacting with a Mach 2 flat-plate supersonic turbulent boundary layer using direct numerical simulation (DNS) data. The governing equations for DNS and LES are solved using the seventh-order Monotonicity Preserving scheme for Euler fluxes and the sixth-order compact scheme for viscous terms. The SGS models tested included constant coefficient and dynamic eddy-viscosity and similarity models. A-priori tests confirm that the similarity- and mixed-type models are superior to those developed based purely on eddy-viscosity assumption. However, some of the eddy-viscosity models still perform adequately in a-posteriori tests. Overall, dynamic models show reasonably good agreement with the DNS data.   

DNS of shock-turbulent boundary layer interaction

A novel DNS/LES capability for high speed viscous flows on unstructured grids is being developed. Shock-turbulent boundary layer interaction results in flow separation, shock unsteadiness, and increased aerodynamic and thermal loads. This paper focuses on the DNS of a Mach 3 turbulent boundary layer flow past a 24 degree compression corner. In our simulations, the upstream turbulent boundary layer is obtained by roughness--induced transition of a laminar boundary layer, and not by rescaling methods. The simulations are performed at the conditions of experiments by Bookey et al (AIAA Paper 2005). The results will be compared to experimental data. We will present the evolution of the boundary layer flow across the shock, low frequency unsteadiness, and the upstream influence of the corner. Both numerical issues and their physical implications will be discussed.   

Similarity scaling in shock-turbulence interactions

The interaction of turbulence with a normal shock is an important problem of both fundamental and practical interest. While some trends are relatively established (e.g., turbulent kinetic energy amplification) quantitative predictions remain elusive when different flow conditions are considered. Data are typically compared with the Linear Interaction Approximation (LIA, Ribner 1953) which neglects the influence of Reynolds and turbulent Mach numbers, though data show that their effect is significant at conditions achievable in simulations and experiments. Without a suitable criterion to identify different regimes including what constitutes asymptotic states (e.g., high Reynolds number) one can come to varying conclusions from simulations and experiments. Similarity scaling is used to analyze available data of isotropic turbulence interacting with a normal shock wave. The proposed analysis suggests that incomplete similarity occurs for several parameters as opposed to complete similarity assumed in LIA. A combination of similarity parameters related to the shock thickness is found to be key even when it is small and, therefore, cannot be neglected. Within this theoretical framework, data on e.g., amplification factors and shock structure are found to present universal behavior in the proposed parameter which allows for identification of different regimes. Simple models based on these results can capture the scaling of the shock structure. Further implications of findings will be discussed.