Session E14: Boundary Layers: General I

Scaling of turbulence near isothermal and adiabatic walls

Compressibility affects near-wall turbulence in wall-bounded flows. We have recently shown that the asymptotic behavior of turbulent fluxes at the wall differs from incompressible scaling laws with systematic trends in Mach number, M. This, however, is found to depend on the specific wall thermal conditions. To study a range of thermal conditions, we carry out very-well resolved simulations of adiabatic channels ranging from incompressible to supersonic speeds and study the asymptotic behavior of turbulent fluxes in the near-wall region. Emphasis is placed on comparisons between isothermal and adiabatic wall conditions which provide different constraints on the behavior of temperature fluctuations at the wall. At very low M, fluxes follow Taylor series as in incompressible flows but deviate significantly from incompressible or non-solenoidal Taylor-series scaling laws as M increases, especially for fluxes containing temperature or wall-normal velocity fluctuations. This is due, in part, to the increased level of dilatation at the wall as M increases which also depends on the thermal boundary condition. Adiabatic walls lead to smaller dilatational content as compared to isothermal walls for the same M. Reynolds stress budgets and implications for models are briefly discussed.   

The origin of skin-friction increase in laminar-to-turbulence transition: a stochastic Lagrangian analysis

A general feature of transition in wall-bounded flows is the significant increase in skin friction, whose origin has been speculated but never rigorously demonstrated. In this work, the skin friction is expressed in terms of wall vorticity and can thus be calculated as the expectation of a stochastic Cauchy invariant in backward time. Contributions arise from (i) wall vorticity flux (Lighthill source) and (ii) pre-existing interior vorticity evolved by nonlinear advection, viscous diffusion, vortex stretching and tilting. These contributions are quantified along backward stochastic Lagrangian trajectories, which are determined by the exact Navier-Stokes solutions. Our analysis is performed using the transitional boundary layer dataset of the Johns Hopkins Turbulence Databases (Z. Wu, J. Lee, C. Meneveau and T. Zaki, 2019, Phys. Rev. Fluids, 4(2), 023902), and examines an ensemble of wall-stress maxima in the transitional region. The analysis demonstrates that the dominant source of skin-friction increase in transition is spanwise stretching of pre-existing near-wall spanwise vorticity. Our formulation may assist more generally in understanding physical phenomena in transitional and turbulent wall-bounded flows, such as drag reduction, flow separation and extreme stress events.   

Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

We propose a transformation that maps mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2000.   

Decomposition of the forcing to the compressible resolvent operator for laminar and turbulent boundary layers

Recent work by Bae et al. (J. Fluid Mech., vol. 883, 2020, pp. 336–382, pp. A29) used the resolvent analysis framework of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to show that, within the regime of compressible turbulent boundary layer flows, the linearized Navier-Stokes equations capture two distinct sets of modes: the relatively subsonic modes that have an equivalent in the incompressible flow regime, and the relatively supersonic modes. In the current work we aim to analyze if the forcing to this compressible resolvent operator for boundary layers can be appropriately decomposed so as to isolate these relatively subsonic and relatively supersonic modes. We verify this decomposition of the forcing in laminar and turbulent boundary layers, with and without wall cooling. Implications for low-order modeling and connections with the incompressible resolvent operator will be briefly described.   

Perturbation evolution in high-speed flat plate boundary layers: Non-equilibrium flow-thermodynamic interaction effects

In low-speed incompressible fluid flows, pressure acts as a Lagrange multiplier to ensure the solenoidal nature of the velocity field. On the other hand, in high-speed flows the fundamental nature of pressure changes, triggering significant flow thermodynamic interactions. In this work, we use direct numerical simulation (DNS) data to examine the effect of velocity and pressure initial conditions on the development of perturbations on a flat plate boundary layer at high speeds. DNS of temporally evolving boundary layers are performed in the Mach number (M) range of 0.12-6 for various low intensity initial perturbations. The dependence of the linear transient non-equilibrium behaviour on initial conditions is examined. The underlying flow-thermodynamic interactions in the transient regime are analysed for both first and second mode. Additionally, the velocity field is decomposed into a solenoidal and dilatational component using Helmholtz decomposition. The evolution of the solenoidal and dilatational fields is monitored and the physics underpinning the observed behaviour is explored.   

A numerical solution to the onset of boundary layer separation in the flow around a circular cylinder independent of the size of the flow domain

The onset of boundary layer separation in the flow around a circular cylinder is studied as a numerical experiment using Galerkin finite elements. The flow domain is carefully chosen  to ensure undisturbed flow conditions deep inside  both in the streamwise and transverse direction. Since there has never been a numerical experiment that ensures undisturbed flow conditions deep inside a domain, a criterion is introduced that allows the implementation of such an analysis. Using a constant entrance distance from the forward stagnation point, we vary the blockage ratio in such a way to reveal an exponential behavior in the change of the Reynolds number where boundary layer separation occurs. In addition, we are able to measure the angle as well as the length of separtion and check if these magnitudes exhibit a limit that is reached in an exponential fashion as well. Indeed, we are going to show that the Reynolds number, the separation angle and the length of separation of the eddy reach a limit as the flow domain grows. We show that this kind of analysis is possible only if the size of the domain in the transverse direction is of the order of 80 millions dimensionless units and five times greater in the streamwise direction, which justifies the use of supercomputing facilitites to enable this kind of research. It is further discussed how this work complements the previous research in the field by verifing research of other workers and pointing out shortcomings, as this is the first time that such an analysis has been performed with a flow domain of such dimensions.       

A new solution for oscillatory flows over permeable beds

Water waves propagating though the ocean induce boundary layers flows near the seabed due to viscous effects. These boundary layer flows are important because they can drive different physical processes, such as sediment transport, wave damping, and mass transport. In this work, we considered the propagation of oscillatory waves over permeable beds. Using perturbation theory, the fluid velocity in the boundary layer was decomposed into an irrotational and rotational component, while the velocity inside the permeable bed followed Darcy's law. To treat the influence of the permeable bed on the boundary layer flows, three different boundary conditions were considered at the upper edge of the permeable bed: Darcy's law, Beavers and Joseph (1967), and Le Bars & Worster (2006). We also developed a set of analytical solutions that exhibit this behavior and show an agreement with the numerical solutions for different boundary conditions. Our results show that velocities and mass transport velocity modify their structure close to the boundary by increasing their magnitudes as the dimensionless hydraulic conductivity increases, while bed shear stresses behave in an opposite manner decreasing their magnitudes.   

Decoding wall-pressure sensor data in hypersonic boundary-layer transition on a cone

Hypersonic boundary-layer transition is extremely sensitive to uncertain environmental disturbances, which may mask the underlying transition mechanism. Direct measurements can reduce this uncertainty. However, observations at high speeds are often scarce, e.g., limited to discrete wall-pressure probes. To discover the true flow, we optimize the simulations to reproduce the experimental observations using an ensemble-variational (EnVar) data assimilation approach (Buchta & Zaki, J. Fluid Mech. 2021). We demonstrate our framework on sensor data acquired in the AFRL Mach-6 Ludwieg Tube for boundary-layer transition over a 7-degree cone. Without knowing the freestream condition and using only PCB measurements, we determine the inflow spectra for two types of measurements: (i) the time-history of a migrating wavepacket and (ii) the wall-pressure power spectra recorded by the sensors.  The reconstructed wavepacket is compared with quantitative Schlieren that was synchronized with the PCBs. We also evaluate the entire flow field, beyond the original limited wall sensors, and examine the transition mechanisms in detail.   

Not Participating

The study of the pressure fluctuations beneath a turbulent boundary layer passing over a transpiration region is considered. For constant wall blowing, the power spectral density of the  turbulence-induced pressure fluctuations at the wall can be characterized by low-order analytical models such as the Liepmann model. We show that the pressure fluctuations at the wall modulate the flow through the porous media and the fluctuating porous media flow is influenced by the porosity, permeability and other geometric characteristics of the porous structure. The effect of the pressure-velocity coupling at the interface of the transpiration wall and turbulent boundary layer flow is presented and the effects on the turbulence statistics are quantified.   

Large-Eddy Simulations of the flow on an airfoil with leading-edge imperfections

Results of large-eddy simulations of the flow over an airfoil with leading-edge obstacles, mimicking idealized icing geometries, at Re = 200,000 will be presented. A grid convergence study was conducted and the model was validated with experimental data in the literature. Significant variations in structure generation are observed for different roughness geometries. The three-dimensionality of the roughness is found to have a strong impact on the flow: it creates alternating regions of high-momentum and low-momentum fluid, a phenomenon termed "channelling", on both sides of the airfoil. The streamwise coherence of these regions, however, is quite sensitive to the pressure-gradient distribution. Furthermore, the width of these channels is of a similar order as the roughness size, which suggests implications on RANS modelling.