M. Pino Martin

Direct Numerical Simulation of Supersonic Turbulent Boundary Layer over a Compression Ramp

A direct numerical simulation of shock wave and turbulent boundary layer interaction for a 24 deg compression ramp configuration at Mach 2.9 and Re θ 2300 is performed. A modified weighted, essentially nonoscillatory scheme is used. The direct numerical simulation results are compared with the experiments of Bookey et al. at the same flow conditions. The upstream boundary layer, the mean wall-pressure distribution, the size of the separation bubble, and the velocity profile downstream of the interaction are predicted within the experimental uncertainty. The change of the mean and fluctuating properties throughout the interaction region is studied. The low frequency motion of the shock is inferred from the wall-pressure signal and freestream mass-flux measurement.

Analysis of shock motion in shockwave and turbulent boundary layer interaction using direct numerical simulation data

Direct numerical simulation data of a Mach 2.9, 24○ compression ramp configuration are used to analyse the shock motion. The motion can be observed from the animated DNS data available with the online version of the paper and from wall-pressure and mass-flux signals measured in the free stream. The characteristic low frequency is in the range of (0.007–0.013) U ∞/δ, as found previously. The shock motion also exhibits high-frequency, of O ( U ∞/δ), small-amplitude spanwise wrinkling, which is mainly caused by the spanwise non-uniformity of turbulent structures in the incoming boundary layer. In studying the low-frequency streamwise oscillation, conditional statistics show that there is no significant difference in the properties of the incoming boundary layer when the shock location is upstream or downstream. The spanwise-mean separation point also undergoes a low-frequency motion and is found to be highly correlated with the shock motion. A small correlation is found between the low-momentum structures in the incoming boundary layer and the separation point. Correlations among the spanwise-mean separation point, reattachment point and the shock location indicate that the low-frequency shock unsteadiness is influenced by the downstream flow. Movies are available with the online version of the paper.

Subgrid-Scale Models for Compressible Large-Eddy Simulations ?

Abstract:An a priori study of subgrid-scale (SGS) models for the unclosed terms in the energy equation is carried out using the flow field obtained from the direct simulation of homogeneous isotropic turbulence. Scale-similar models involve multiple filtering operations to identify the smallest resolved scales that have been shown to be the most active in the interaction with the unresolved SGSs. In the present study these models are found to give more accurate prediction of the SGS stresses and heat fluxes than eddy-viscosity and eddy-diffusivity models, as well as improved predictions of the SGS turbulent diffusion, SGS viscous dissipation, and SGS viscous diffusion.

Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments

A systematic procedure for initializing supersonic and hypersonic turbulent boundary layers at controlled Mach number and Reynolds number conditions is described. The initialization is done by locally transforming a true direct numerical simulation flow field, and results in a nearly realistic initial magnitude of turbulent fluctuations, turbulence structure and energy distribution. The time scales necessary to forget the initial condition are studied. The experimental conditions of previous studies are simulated. The magnitude of velocity and temperature fluctuations, as well as the turbulent shear stresses given by the direct numerical simulations are in agreement with the experimental data.

Assessment of inflow boundary conditions for compressible turbulent boundary layers

A description of different inflow methodologies for turbulent boundary layers, including validity and limitations, is presented. We show that the use of genuine periodic boundary conditions, in which no alteration of the governing equations is made, results in growing mean flow and decaying turbulence. Premises under which the usage is valid are presented and explained, and comparisons with the extended temporal approach [T. Maeder, N. A. Adams, and L. Kleiser, “Direct simulation of turbulent supersonic boundary layers by an extended temporal approach,” J. Fluid Mech. 429, 187 (2001)] are used to assess the validity. Extending the work by Lund et al. [J. Comput. Phys. 140, 233 (1998)], we propose an inflow generation method for spatial simulations of compressible turbulent boundary layers. The method generates inflow by reintroducing a rescaled downstream flow field to the inlet of a computational domain. The rescaling is based on Morkovin’s hypothesis [P. Bradshaw, “Compressible turbulent shear layers,” ...

Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3

We demonstrate that data from direct numerical simulation of turbulent boundary layers at Mach 3 exhibit the same large-scale coherent structures that are found in supersonic and subsonic experiments, namely elongated, low-speed features in the logarithmic region and hairpin vortex packets. Contour plots of the streamwise mass flux show very long low-momentum structures in the logarithmic layer. These low-momentum features carry about one-third of the turbulent kinetic energy. Using Taylors hypothesis, we find that these structures prevail and meander for very long streamwise distances. Structure lengths on the order of 100 boundary layer thicknesses are observed. Length scales obtained from correlations of the streamwise mass flux severely underpredict the extent of these structures, most likely because of their significant meandering in the spanwise direction. A hairpin-packet-finding algorithm is employed to determine the average packet properties, and we find that the Mach 3 packets are similar to those observed at subsonic conditions. A connection between the wall shear stress and hairpin packets is observed. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long low-momentum structures. This finding is consistent with the very large-scale motion model of Kim & Adrian (1999).

New Experimental Data of STBLI at DNS/LES Accessible Reynolds Numbers

An experimental investigation was conducted to study four shock/turbulent boundary layer interactions. In Mach 2.9 flow, a 24o compression corner and a 12o reflected shock interaction were studied at Reθ = 2400. In a Mach 8 flow, an 8o compression corner and a 10o sharp fin were studied at Reθ = 3500. These low Reynolds number flows were chosen to coincide with DNS accessible Reynolds numbers in order to make direct comparisons. Measurements included mean flow surveys, surface pressure distributions, surface flow visualizations and Filtered Rayleigh Scattering (FRS). FRS was used to make twodimensional images of the flow in the streamwise direction giving a qualitative picture of the nature of the interaction. Statistical data of the boundary layer characteristics was also obtained from the FRS images. The results show the incoming boundary layer at both Mach numbers to be fully turbulent. The interactions in Mach 2.9 flow produced large areas of separation. The compression ramp in the Mach 8 flow was found to remain attached throughout the interaction, while the 10o sharp fin produced a large threedimensional separated region. The preliminary results indicate good agreement between experiment and DNS computations.

EFFECT OF CHEMICAL REACTIONS ON DECAYING ISOTROPIC TURBULENCE

There have been many studies of turbulent combustion flows, however the interaction between turbulent motion and the chemical reactions that occur in hypersonic flows has not been studied. In these flows, the rate of product formation depends almost exclusively on the temperature, and small temperature fluctuations may produce large changes in the rate of product formation. To study this process, we perform direct numerical simulations of reacting isotropic turbulence decay under conditions typical of a hypersonic turbulent boundary layer flow. We find that there is a positive feedback between the turbulence and exothermic reactions. That is, positive temperature fluctuations increase the reaction rate, thereby increasing the heat released by the reaction, which further increases the temperature. Simultaneously, the pressure increases causing localized expansions and compressions that feed the turbulent kinetic energy. The Reynolds stress budget shows that the feedback occurs through the pressure-strain t...

DNS of Hypersonic Turbulent Boundary Layers

We present a direct numerical simulation database of supersonic and hypersonic turbulent boundary layers. The systematic procedure for initializing the turbulent flow fields at controlled Mach number and Reynolds number conditions is described. It is shown that simulation transients are less than 10% of the time required for gathering statistical data of the turbulent flows. The experimental conditions of Debieve and Elena are simulated. The magnitude of velocity and temperature fluctuations, as well as the turbulent shear stresses given by the direct numerical simulations are in excellent agreement with the experimental data. Using the direct numerical simulation database we perform parametric studies varying freestream Mach number in the range of 3 to 8 and wall-temperature condition for wall-to-freestream-temperature ratio of 2 to 5.5.

A parallel implicit method for the direct numerical simulation of wall-bounded compressible turbulence

A new second-order accurate implicit temporal numerical scheme for the direct numerical simulation of turbulent flows is presented. The formulation of the implicit method and the corresponding tunable parameters are introduced. The numerical simulation results are compared with the results given by explicit Runge-Kutta schemes, theoretical results, and published experimental and numerical data. An assessment of the accuracy and performance of the method to simulate turbulent flows is made for temporally decaying isotropic turbulence and subsonic and supersonic turbulent boundary layers. Whereas no significant advantage over typical explicit time integration methods are found for the incompressible flows; it is shown that the implicit scheme yields significant reduction in computer cost while assuring time-accurate solutions for compressible turbulence simulations.