Matthew Ringuette

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).

Wall-Pressure Measurements in a Mach 3 Shock-Wave Turbulent Boundary Layer Interaction at a DNS Accessible Reynolds Number

Experiments are performed to investigate the uctuating wall pressure in a Mach 2.9 shock-wave turbulent boundary layer interaction with a low Reynolds number based on momentum thickness of 2400. This Reynolds number is accessible to present direct numerical simulations (DNS), so that the data can be used for DNS validation. The conguration studied is a nominally two-dimensional 24 compression corner. Compared to data at higher Reynolds numbers (of order 10 4 {10 5 ), the results show a smaller peak in the RMS of the pressure uctuations. The wall-pressure signal does not exhibit the large degree of intermittency found in the shock-foot region at higher Reynolds numbers. Spectra show that the signal energy is more distributed over the range of shock oscillation frequencies, resulting in a smaller peak energy as compared to data at high Reynolds numbers. The shock motion has a broadband frequency distribution with a peak slightly below 1 kHz, similar to that seen in higher Reynolds number o ws. The mean-wall pressure distribution, RMS pressure uctuation prole, wall-pressure signal, and shock-motion frequency agree well with a DNS performed at matching conditions.

Experimental Investigation of a Hypersonic Turbulent Boundary Layer

p pressure, Pa Reθ Reynolds number based on momentum thicknessr Reτ friction Reynolds number u fluctuating component of velocity, streamwise direction, m/s uτ friction velocity, m/s U streamwise velocity, m/s v fluctuating component of velocity, wall-normal direction, m/s x streamwise distance, mm y normal distance from the wall, mm δ boundary layer thickness, mm ν kinematic viscosity, Pa · s ρ density, kg/m

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.

The Turbulence Structure of Shockwave and Boundary Layer Interactions in a Compression Corner

Shockwave and turbulent boundary layer interactions (STBLI) result in intense localized heating rates and pressure loads, making them extremely important flow features that must be identified for engineering design. The absence of detailed and complete experimental and numerical data at the same flow and boundary conditions is one of the major stumbling blocks in the development of accurate turbulence models for the prediction of STBLI. We use a set of direct numerical simulation data (Wu & Martin, 2006) that has been validated against experiments (Bookey et al., 2005) at the same conditions to present detailed flow features of the STBLI over a compression corner at Mach 3 and low Reynolds number with Reθ=2100. Details regarding the evolution of the turbulence structure angle, characteristic streamwise length scales, and hairpin packets through the interaction are presented. The three-dimensionality of the turbulence field and main shock are illustrated and the strength of shocks and shocklets through the interaction are considered.