Stephan Priebe

DNS of a Large-Domain, Mach 3 Turbulent Boundary Layer: Turbulence Structure

We introduce a Mach 2.9, Re? = 640, spatially developing direct numerical simulation on a very large domain which is about 60 incoming boundary layer thicknesses long in the streamwise direction. Using the rescaling technique of Xu & Martin, 1 with the rescaling plane taken near the exit, at about 57 incoming boundary layer thicknesses (just under 0.4 meters downstream of the inlet), we obtain a clean inflow with a good sampling of even the largest scales. We show that the simulation can be run for long times ‚ 450‐/U1 without the forcing of artificial acoustic modes in the free stream. We proceed to examine the turbulence structure through spectral analysis and filtered instantaneous flow fields. Special attention is paid to the largest structures, with turbulence modeling, especially aspects unique to compressible boundary layers, in mind.

Analysis of Low-Frequency Unsteadiness in the Direct Numerical Simulation of a Shockwave and Turbulent Boundary Layer Interaction

The direct numerical simulation (DNS) of a compression ramp shockwave and turbulent boundary layer interaction (STBLI) is presented. The incoming flow conditions are Mach 2.9 and Reθ 2900. The ramp angle is 24 . The dominant time scales in the flow are inferred from a spectral analysis of pressure signals along the wall, and pressure and massflux signals in the flow. The low-frequency shock motion in the DNS is broadband with a dominant frequency of approximately 900Hz, which is two orders of magnitude lower than the characteristic frequency of the turbulence in the incoming boundary layer. The present DNS is significantly longer in time than a previous DNS and covers close to ten periods of the low-frequency unsteadiness (based on the dominant frequency). We also determine the statistical link between the shock motion and the fluctuations in the downstream, separated flow.

Direct Numerical Simulation of a Hypersonic Turbulent Boundary Layer on a Large Domain

The direct numerical simulation (DNS) of a spatially-developing hypersonic turbulent boundary layer is presented. The freestream Mach number is M∞ = 7.2. The simulation is performed on a large computational domain resulting in a variation of Reynolds number based on momentum thickness from a value of Reθ = 1650 at the inlet of the domain to Reθ = 3300 at the outlet. A large rescaling length is used in the prescription of the inflow boundary condition to minimize spurious numerical correlation between the inflow and recycling plane. The evolution of boundary layer parameters and basic statistics with streamwise distance through the computational box is investigated. An effect of the wall temperature condition in the DNS (cold wall) on the behavior of the boundary layer is observed.

LES Study of Shock Wave and Turbulent Boundary Layer Interaction

nx The large eddy simulation (LES) of a compression ramp shock wave and turbulent boundary layer interaction (STBLI) is presented. The ramp angle is 24 and the incoming boundary layer ow conditions are Mach 2.9 and Re 2900. The LES data are in good agreement with existing direct numerical simulation (DNS) data with the same incoming ow parameters. The accuracy and reduced resolution requirements of the LES as compared to the DNS enables the ability to resolve the aperiodic cycle of the low-frequency unsteadiness characteristic of these ows.

Direct Numerical Simulation of Shockwave and Turbulent Boundary Layer Interactions

Past and current work on direct numerical simulations of shockwave and turbulent boundary layer interactions at the CRoCCo Laboratory at Princeton University is presented. Direct numerical simulations of compression ramp and reflected shock configurations are discussed, with particular emphasis on the validation of the simulations against experiments at matching flow conditions. The low-frequency motion of the shock system is analyzed. A ‘long-time’ DNS of a Mach 3 boundary layer, which will serve as an inflow boundary condition for future STBLI simulations, is presented. In an effort to extend the simulations to higher, hypersonic Mach numbers, the DNS of a Mach 8 boundary layer is also briefly presented.

Upstream and downstream influence on the unsteadiness of STBLI using DNS data in two configurations

Statistical analysis of the upstream and downstream flow influence on shock unsteadiness in shock and turbulent boundary layer interactions are performed using DNS data of a compression corner Wu & Martin and a reflected shock case interaction. For both cases, the scaling proposed by Dussauge et al. for the characteristic low frequency applies. The statistical analysis for the compression corner shows that the unsteadiness of the shock is dominated by the downstream flow. The same analysis applied to the reflected shock case also indicates downstream influence. Additional studies are required to fully characterize the reflected shock case DNS data.

Effect of Wall Temperature and Mach Number on the Turbulence Structure of Hypersonic Boundary Layers

The characterization of the turbulence structure using statistical analysis 1 and a geometric packet-finding algorithm 2 is explored. We follow structures which have been identified by the geometric packet-finding algorithm, using automated object segmentation and feature tracking software, 3,4 and observe how these structures and their associated wall signatures evolve in time. Using a direct numerical simulation database, we begin to assess the turbulence structure given by each method and the evolution of this structure.

Analysis of the Large Eddy Simulation of a Shock Wave and Turbulent Boundary Layer Interaction

The large eddy simulation (LES) of a compression ramp shock wave and turbulent boundary layer interaction (STBLI) is presented. The ramp angle is 24◦ and the incoming boundary layer flow conditions are Mach 2.9 and Reθ 2900. The LES data cover approximately 1300 Lsep/U∞ to statistically resolve the aperiodic cycle of the low-frequency unsteadiness that is characteristic of these types of flows. The dynamics of the flow downstream of the shock are characterized using this new numerical data set.

Low-Frequency Unsteadiness in DSN of Shock Wave/Turbulent Boundary Layer Interaction

The direct numerical simulation (DNS) of a compression ramp shock wave/ turbulent boundary layer interaction (STBLI) is presented. The ramp angle is 24◦, and the inflow boundary layer conditions are Mach 2.9 and Reθ = 2900. For the discretization of the inviscid fluxes, a modified weighted essentially nonoscillatory (WENO) scheme is used. The numerical code has previously been validated in the context of a compression ramp DNS against experiments at matching flow conditions. The low-frequency dynamics of the unsteadiness are investigated using low-pass filtered flow fields. It is observed that the nature of the shear layer changes depending on the phase of the shock motion, and it is conjectured that these changes are the manifestation of a shear layer instability.

SDNS of large domain supersonic boundary layers over weakly and strongly adiabatic walls

We present spatially developing direct numerical simulations (DNS) of turbulent boundary layers at Mach 3 and Mach 7 with Reτ ≈ 600. In this work we make an explicit distinction in the wall thermal boundary condition, which, to our knowledge, has not been addressed in the literature. Namely, we deem “weakly adiabatic” walls as those whose temperature is fixed at the recovery temperature, and “strongly adiabatic” walls as those that enforce null heat transfer in the local and instantaneous sense. These two boundary conditions are bracketing cases for real materials that have finite, non-zero thermal diffusivities. Using scaling arguments, we propose a dimensionless quantity, the “fluctuation Nusselt number,” as the relevant similarity parameter describing the thermal damping at the wall. Furthermore, we demonstrate that this parameter can vary by many orders of magnitude due to different thermal diffusivities of relevant wall materials and different edge Mach numbers. By design, the “weakly adiabatic” boundary condition damps near wall temperature fluctuations, which helps to enforce the assumption of weak total temperature fluctuations built into much of the theory for compressible boundary layers. Adopting a “strongly adiabatic” wall will place greater strain on these assumptions. Here we present data at Mach 3 and Mach 7 for both boundary conditions. The simulations are spatially developing and have large domains to prevent unphysical forcing due to the inflow and spanwise boundary conditions, as discussed in Beekman, Priebe, Kan & Martin. For all four data sets we present basic turbulence statistics and quantities relating the velocity field to the temperature field.