Session E07: Boundary Layers: Compressible and Thermal (3:10pm - 3:55pm CST)

Optimal weighting of scarce measurements for accurate prediction of chaotic transition dynamics

Transition dynamics in chaotic systems are extremely sensitive to uncertainties in control parameters such as initial conditions. This uncertainty compromises predictions of models and simulations. To enhance the fidelity of simulations, we infuse them with available observations and minimize a Bayes-based cost function. The accuracy of our estimated state depends on the observations, and naively infusing all observations, equally, may be ill-suited for gradient-based optimization. Observations with chaotic dynamics create an oscillatory cost-function landscape, which is tortuous to navigate and contains multiple high-curvature optima. To smooth the landscape, we developed a sensor weighting that optimizes invariants of the Hessian matrix of the cost function. Weights are selected to reduce the most extreme curvature which we ascribe to observations that are highly sensitive to uncertainty in the control parameters. Relative to equal sensor weights, the proposed weighting accelerates convergence to the optimal estimate of the flow and improves prediction accuracy. Thermal convection and high-speed boundary-layer transition are examined in this context.   

Optimal sensor placement in high-speed transitional boundary layers

Predictions of the mechanism and location of boundary-layer transition from limited wall observations are an important challenge in high-speed flow experiments and flight tests. We have developed a framework whereby we infuse available observations in our simulations, to determine the precise flow conditions, transition mechanism and its location. However, the quality of the estimated flow field depends on the available number of sensors and their placement, which in turn may be restricted by practical considerations such as the leading-edge geometry. For a transitional boundary layer at Mach 4.5, we seek the optimal arrangement of a limited number of wall pressure probes. An ensemble of planar and oblique second-mode instabilities is used to represent environmental uncertainty. Direct numerical simulation of each inflow is used to acquire wall-pressure data, which form an observation matrix. The optimal sensor placement is then identified by a gradient-based optimization of matrix invariants. Using the predicted sensor configuration, we then perform observation-infused simulations whereby we attempt to reconstruct an independent flow state from wall observations. The accuracy of our predictions is contrasted to a traditional sensor placement.   

Perturbation evolution in high-speed flat plate boundary layers: Non-equilibrium pressure-velocity interaction effects

In fluid flows, velocity-pressure interactions undergo a marked change with increasing Mach number. In incompressible flows, pressure and velocity fields are always in equilibrium as the former is completely determined in terms of the latter via the Poisson equation. In high speed flows, pressure evolves independently as a thermodynamic variable. As a result, at high Mach numbers, out-of-equilibrium velocity-pressure interactions can significantly affect various flow phenomena. In this work, we use linear stability theory (LST) and direct numerical simulations (DNS) to establish the non-equilibrium effects on perturbation growth in high-speed flat plate boundary layers. DNS of temporally evolving flat plate boundary layers subjected to various initial perturbations are examined in the range Ma$=$ 0.12 - 6. It is demonstrated that non-equilibrium velocity-pressure interactions significantly modify the behaviour from the baseline equilibrium case. The underlying physics is explored and the observed behaviour is explained. The effect of the observed linear behaviour on the subsequent non-linear evolution and the ultimate breakdown to turbulence is discussed.   

Effect of isothermal wall condition on the inter-scale kinetic energy transfer in hypersonic boundary layer.

Effect of isothermal wall condition on the inter-scale transfer of kinetic energy in hypersonic boundary layer is studied by direct numerical simulation (DNS) using both hot wall and cold wall conditions with the high freestream Mach number $M_{\infty } =8$. The streamwise-spanwise average of the large-scale spatial convection and viscous dissipation are prominent in the near wall region and decrease rapidly away from wall, while the crest location of SGS flux is in the buffer layer. The cold wall condition enhances the local reverse transfer of kinetic energy in expansion regions and the wall inhibits the efficiency of inter-scale kinetic energy transfer. Helmholtz decomposition is introduced to analyze the compressibility effect on the solenoidal and compressible components of SGS kinetic energy flux. Strong fluctuating solenoidal kinetic energy transfer appears in the buffer layer, while intense fluctuating compressible kinetic energy transfer exists in the near wall region. The cold wall condition significantly increases the compressibility effect in the near wall region.   

Effect of wall cooling or heating on streaks and streamwise vortices developing in compressible boundary layers

Streamwise oriented vortices and streaks develop in boundary layers over flat or concave surfaces as a result of various freestream disturbances or small nonuniformities at the wall. Following the transient growth phase, these streamwise vortices become susceptible to inviscid secondary instabilities, which can lead to early transition to turbulence via bursting processes. We look at the effect of cooling and heating on streamwise vortices and streaks developing in high-speed boundary layers, using the compressible nonlinear boundary region equations. This set of equations represents the high Reynolds number asymptotic form of the Navier-Stokes equations, under the assumption that the streamwise wavenumber of the disturbances is much smaller than the wavenumbers associated with the crossflow directions. The parabolic character of these equations allows a robust and less expensive approach to study boundary layer streaks, by finding the numerical solution via marching in the streamwise direction. With different level of cooling and heating being imposed at the wall, we show that in some conditions it is possible to reduce the skin friction, which can contribute to an overall reduction of the frictional drag.   

Wall Asymptotics in Compressible Turbulent Channels

The asymptotic behavior of Reynolds stresses close to walls is important from fundamental as well as modeling perspectives. While scaling laws are well known in incompressible flows, the transition from incompressible to compressible scaling and the limiting behavior for the latter are largely unknown. Using a large well-resolved DNS database of turbulent channel flow, we investigate the effects of compressibility on the near-wall, asymptotic region of turbulent stresses. In particular, we vary the Mach number $(M)$ at a constant Reynolds number to assess compressibility effects. We observe that the near-wall behavior for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are considered and semi-local scalings are used. For flow near the incompressible regimes, the near-wall asymptotic behavior follows theoretical behavior. When $M$ increases, the wall normal stress components show a gradual decrease in the slope due to increased dilatation effects. Our database reaches high enough $M$ to exhibit an asymptotic behavior that can also be explained theoretically. We also observe that the slope of Reynolds stresses undergoes a transition with respect to the wall-normal direction which is studied in detail.