Minwei Wu

A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence

Two new formulations of a symmetric WENO method for the direct numerical simulation of compressible turbulence are presented. The schemes are designed to maximize order of accuracy and bandwidth, while minimizing dissipation. The formulations and the corresponding coefficients are introduced. Numerical solutions to canonical flow problems are used to determine the dissipation and bandwidth properties of the numerical schemes. In addition, the suitability and accuracy of the bandwidth-optimized schemes for direct numerical simulations of turbulent flows is assessed in decaying isotropic turbulence and supersonic turbulent boundary layers.

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.

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).

Low Reynolds Number Effects in a Mach 3 Shock/Turbulent-Boundary-Layer Interaction

Cf = skin-friction coefficient Lsep = separation length M = freestream Mach number Re = Reynolds number based on T = temperature u = velocity in the streamwise direction v = velocity in the spanwise direction w = velocity in the wall-normal direction = 99% thickness of the incoming boundary layer = displacement thickness of the incoming boundary layer = ratio of to the wall unit = momentum thickness of the incoming boundary layer = density

Analysis of Shockwave/Turbulent Boundary Layer Interaction Using DNS and Experimental Data

Shockwave/turbulent boundary layer interactions are studied by comparing direct numerical simulation and experimental data. Two canonical configurations, a 24-degree compression ramp and shock impinging a wall with reflection, are studied. The Mach number for the incoming boundary layer is 2.9. Reθ in the numerical simulation is 2400. Two experimental data sets are used, namely those of Bookey et al at the same flow conditions as the DNS and those of Selig at Reθ of about 70,000. Mean velocity profiles, wall pressure distribution, mass flux turbulence intensity, 2D density correlation and locations of the flow separation and reattachment are compared. In addition, an analysis of the turbulence structure characteristics for the DNS data is given.

Coherent Structures in DNS of Turbulent Boundary Layers at Mach 3

We demonstrate that the data from DNS of turbulent boundary layers at Mach 3 exhibit the same local flow features found in both supersonic and incompressible experiments, such as long, low-speed structures in the log region and hairpin vortex packets. Instantaneous plots of the streamwise mass-flux show very long low-momentum structures in the log layer. We use Taylor’s hypothesis to generate a velocity map in the log region with a streamwise length of about 230δ, where δ is the boundary layer thickness. The map indicates that the low-speed structures attain streamwise lengths of order 100δ. Length scales obtained from correlations of the streamwise mass flux severely under predict the extent of these structures, most likely due to 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 streamwise length of the Mach 3 packets is less than one-third of that observed at subsonic conditions. Adopting the technique of Brown & Thomas, we observe a connection between elevated levels of wall shear stress and hairpin packets. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long, low-momentum structures, consistent with the very large-scale motion model of Kim & Adrian.

Characterization of the Turbulence Structure in Supersonic Boundary Layers Using DNS Data

A direct numerical simulation database is used to characterize the structure of supersonic turbulent boundary layers at Mach numbers from 3 to 5. We develop tools to calculate the average properties of the coherent structures, namely, angle, convection velocity, and length scale, and show good agreement with the available experimental data. We find that the structure angle and convection velocity increase with Mach number, while the streamwise integral length scale decreases. The structures become taller with Mach number, which is consistent with the larger structure angle. The distribution of the streaky-structure spacing at the wall is computed, and observed to be slightly narrower and more uniform with increasing Mach number. We find that the low-speed streaks carry about one-third of the total turbulent kinetic energy. Similar to the incompressible case, we observe hairpin vortices clustered into streamwise packets at all Mach numbers, and develop an algorithm to identify and characterize these hairpin packets. The average packet convection velocity, length, and number of hairpins increase with higher Mach number, while the packet height and angle decrease.

Assessment of STBLI DNS Data and Comparison against Experiments

The direct numerical simulation data of a Mach 2.9 turbulent boundary layer flowing over a 24-degree compression ramp are assessed. A summary of the flow features and the comparison of the simulation data against experiments are given. Of main interest are discrepancies found in the wall-pressure distribution. The flow characteristics of the separation shock foot are studied to better understand the wall-pressure prediction, and the effect of the numerical shock capturing technique on the data is considered.

Assessment of Numerical Methods for DNS of Shockwave/Turbulent Boundary Layer Interaction

Various candidate sources of error for the discrepancy between previous direct numerical simulation (DNS) results of Wu et al. and experimental data of Bookey et al. are investigated. Deficiencies of current numerical methods for DNS of shockwave/turbulent boundary layer interactions (STBLI) are found. The weighted-essentially-non-oscillatory (WENO) method is improved by adding limiters in the smoothness measurement. In turn, the numerical dissipation is significantly reduced. For the compression ramp case, using the limiter results in increased size of the separation bubble and improved mean wallpressure distribution. In addition, a fourth-order low-dissipation Runge-Kutta method is found to give less dissipation than the typically used third-order low-storage Runge-Kutta method. Combining the limiter with the low-dissipation Runge-Kutta method gives better results. Good agreement is found for the size of the separation bubble and the wall-pressure distribution when comparing against the experimental data at the same conditions.