Session H23: Turbulent Boundary Layers VI: Compressible

Measurement in a Hypersonic Turbulent Boundary Layer Using PIV

Experiments are reported on measuring turbulence in a flat plate boundary layer at Mach 7.4 using planar PIV in order to examine Morkovin's hypothesis and scaling at Mach numbers greater than 5. PIV measurements in hypersonic flow are hampered by high dynamic range requirements and low flow density, which leads to stringent particle sizing requirements to avoid particle lag. In addition, high shear can lead to a bias in many cross-correlation algorithms. Experiments to determine the frequency response of a range of titanium dioxide particles using the response across a shock will be detailed. Additionally, the conditions for the appropriate initial conditions for boundary layer development, such as the selection of size and type of tripping device and appropriate development length for the establishment of a fully turbulent boundary layer will be examined.   

Predictive Inner-Outer Model for Turbulent Boundary Layers Applied to Supersonic DNS

A predictive wall model for subsonic turbulent boundary layers is modified for application to supersonic and hypersonic boundary layers. The original model is based on an observed modulation of the turbulence in the inner layer by the large scale motions in the logarithmic layer. Evidence that this modulating effect also exists in compressible turbulent boundary layers is presented. The appropriate scalings applied to the model to deal with compressibility effects is discussed. Spectrally resolved data sets from direct numerical simulation (DNS) of Mach 3 and Mach 7 turbulent boundary layers are used for validation of the modified model. Predicted inner layer velocity fields at the same flow conditions as the DNS data are constructed and a comparison of statistics, such as spectra and moments, of the predicted and DNS flow field parameters is presented. This work is supported by the Air Force Office of Scientific Research under grant AF/9550-10-1-0164.   

Direct Numerical Simulation of a Mach 2.25 Turbulent Boundary Layer Over A Compliant Surface

Future high-speed air vehicles will be lightweight, flexible, and reusable, and thus susceptible to dynamic coupling between the boundary layer and vehicle surface. ~Current analysis techniques of boundary layer properties based on rigid surface assumptions may be invalid in this flight regime, and experimental approaches are difficult and expensive. Analyses involving accurate numerical predictions are therefore needed to provide data in this high-speed, coupled environment.~ Results of a Mach 2.25 turbulent boundary layer evolving over a thin, compliant panel are investigated using direct numerical simulation in the fluid coupled to a geometrically non-linear, thermomechanical finite element solver for the solid. ~The coupled response of the boundary layer-panel system are presented and compared to the rigid panel case. ~Panel deformation and fluid flow modification due to the presence of the compliant panel are analyzed, with a particular interest in the influence of panel motion on turbulence statistics. ~The maximum panel deformation extends through the viscous sublayer while space-time data show that the solid supports waves that may be useful for sensing and control.   

DNS of a Mach 3 and Mach 7 Turbulent Boundary Layer: Statistical Description and Scale Decomposed Physics

We analyze the statistical properties of supersonic turbulent boundary layers via spatial direct numerical simulations (SDNS). The computational domains are very large with 60 by 10 $\delta_{inlet}$ in the streamwise and spanwise directions respectively. The inflow is provided with a rescaling technique, where the recycling station is taken near the outlet, with $Re_{\tau} \approx 650$. We vary the nominally adiabatic wall boundary condition between a treatment that enforces a null \emph{mean} heat transfer to the wall ($T_w = T_{recovery}, T^\prime = 0$) and an \emph{instantaneously} adiabatic wall with $(\partial T/\partial z)_w = 0$. The data, including spectra, are converged over $600\delta/U_\infty$ and capture the largest scales of the flow. We study broadband relations such as the strong Reynolds analogy (SRA) and Morkovin's scaling of the turbulent shear stresses in scale decomposed manner to gain insight and physical understanding for turbulence modeling.   

Mach-number-invariant mean velocity profile of compressible turbulent boundary layers

A series of Mach-number- (M) invariant scalings are derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean velocity profile (MVP) that is superior to van Driest transformation. The new scalings are derived from an analysis of turbulent kinetic energy balance equation, and their finding substantiates Morkovin's hypothesis. In particular, a boundary layer edge, $\delta_{vw}$, is defined by equaling the intensities of wall-normal and spanwise velocity fluctuations, and is shown to better represent the M-invariant structure of CTBLs. The M-invariant mixing length has a weight of $\sqrt{\bar{\rho}^{+}}\bar{\mu}^{+}$ to the Prandtl's mixing length, which leads to a viscosity weighted transformation for the MVP of CTBLs, in contrast to the density weighted van Driest transformation. The theory is validated by direct numerical simulation of spatially-developing adiabatic CTBLs with M up to 6. These results suggest new tools for validating turbulence models and improving computations in CTBLs.   

Direct numerical simulation of a hypersonic shock wave/turbulent boundary layer interaction

The direct numerical simulation of a hypersonic shock wave/turbulent boundary layer interaction generated by a 33-degree compression ramp is presented. The fully-turbulent inflow boundary layer is at Mach 7.2, and the Reynolds number based on momentum thickness is $Re_{\theta}=3500$. The evolution of the mean and fluctuating field through the interaction region and the properties of the low-frequency unsteadiness are investigated.   

Wall-modeled large-eddy simulations of shock/turbulent-boundary layer interaction in a duct

We present wall-modeled LES of the interaction of an oblique shock wave and a turbulent boundary layer in a low-aspect-ratio duct, following the experiment by Campo, Helmer \& Eaton, 2012. A $M=2.05$ air stream is deflected by a small compression wedge that spans the top wall of the duct at $20^{\circ}$, generating an oblique shock that reflects off the turbulent boundary layer at the bottom wall. The Reynolds number of the incoming flow based on the boundary layer momentum thickness is $Re_{\theta}=6,500$. Simulations are performed with a control-volume-based, finite-volume solver of the filtered, compressible Navier-Stokes equations, utilizing a grid-based blend of non-dissipative central and dissipative upwind fluxes, Vreman (2004) subgrid scale model and ENO shock-capturing scheme, active only near shocks. An equilibrium wall model (Kawai and Larsson, 2012) is used. Turbulence is generated at the inflow from experimental data. Simulation results are compared to PIV data on four planes normal to the spanwise coordinate. A grid-convergence study is performed. Two heights of the compression wedge are considered, resulting in an increased strength of the interaction. Simulation results are also used to study the evolution of corner flows, complementing experimental findings.   

Direct Numerical Simulations of Turbulent Boundary Layers Over A Circular Aperture

Motivated by the use of acoustic liners to reduce jet engine and aircraft noise, we use direct numerical simulation to study the interaction of a turbulent Mach 0.5 boundary layer with a circular aperture connected to a honeycomb cavity under acoustic excitation. The geometry and flow conditions correspond to experiments conducted at NASA Langley. The hole, whose diameter is on the order of the boundary layer's momentum thickness, interacts with the boundary layer in qualitatively different ways depending on the acoustic forcing amplitude. The influence of the hole on the boundary layer is quantified under a range of acoustic excitations and the details of the hole/boundary layer interaction will be presented. The acoustic impedance of the hole is determined, compared to experimentally educed values, and related to the dynamics of the hole/boundary layer interaction. These analyses will be helpful for improved understanding and low-order models of aircraft acoustic liners at realistic operating conditions.   

Large Eddy Simulation of a Film Cooling Technique with a Plenum

Factors that affect the film cooling performance have been categorized into three main groups: (i)coolant \& mainstream conditions, (ii)hole geometry \& configuration, and (iii)airfoil geometry Bogard et al.(2006). The present study focuses on the second group of factors, namely, the modeling of coolant hole and the plenum. It is required to simulate correct physics of the problem to achieve more realistic numerical results. In this regard, modeling of cooling jet hole and the plenum chamber is highly important Iourokina et al.(2006). Substitution of artificial boundary conditions instead of correct plenum design would yield unrealistic results Iourokina et al.(2006). This study attempts to model film cooling technique with a plenum using a Large Eddy Simulation.Incompressible coolant jet ejects to the surface of the plate at an angle of 30$^{\circ}$ where it meets compressible turbulent boundary layer which simulates the turbine inflow conditions. Dynamic multi-scale approach Araya (2011) is introduced to prescribe turbulent inflow conditions. Simulations are carried out for two different blowing ratios and film cooling effectiveness is calculated for both cases. Results obtained from LES will be compared with experimental results.   

Turbulence Structure and its Signature in Hypersonic Turbulent Boundary Layers

We will investigate the turbulence structure from direct numerical simulation (DNS) data of Mach 3 and Mach 7 turbulent boundary layers. In particular, we will use geometric packet identification techniques and statistical tools to track and study hairpin packets, as well as their wall signatures and their association with superstructures. In addition, we will use a spatio-temporal pattern finding process to track multiple packets evolutions concurrently.