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

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. 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 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Dynamic slip wall model for large-eddy simulation.

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, AIAA J., vol. 38 (4), 2000, pp. 605-612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.

Transitional-turbulent spots and turbulent-turbulent spots in boundary layers.

Two observations drawn from a thoroughly validated direct numerical simulation of the canonical spatially developing, zero-pressure gradient, smooth, flat-plate boundary layer are presented here. The first is that, for bypass transition in the narrow sense defined herein, we found that the transitional-turbulent spot inception mechanism is analogous to the secondary instability of boundary-layer natural transition, namely a spanwise vortex filament becomes a [Formula: see text] vortex and then, a hairpin packet. Long streak meandering does occur but usually when a streak is infected by a nearby existing transitional-turbulent spot. Streak waviness and breakdown are, therefore, not the mechanisms for the inception of transitional-turbulent spots found here. Rather, they only facilitate the growth and spreading of existing transitional-turbulent spots. The second observation is the discovery, in the inner layer of the developed turbulent boundary layer, of what we call turbulent-turbulent spots. These turbulent-turbulent spots are dense concentrations of small-scale vortices with high swirling strength originating from hairpin packets. Although structurally quite similar to the transitional-turbulent spots, these turbulent-turbulent spots are generated locally in the fully turbulent environment, and they are persistent with a systematic variation of detection threshold level. They exert indentation, segmentation, and termination on the viscous sublayer streaks, and they coincide with local concentrations of high levels of Reynolds shear stress, enstrophy, and temperature fluctuations. The sublayer streaks seem to be passive and are often simply the rims of the indentation pockets arising from the turbulent-turbulent spots.

Large-Eddy Simulation of Thermally Stratified Atmospheric Boundary-Layer Flow Using a Minimum Dissipation Model.

A generalized form of a recently developed minimum dissipation model for subfilter turbulent fluxes is proposed and implemented in the simulation of thermally stratified atmospheric boundary-layer flows. Compared with the original model, the generalized model includes the contribution of buoyant forces, in addition to shear, to the production or suppression of turbulence, with a number of desirable practical and theoretical properties. Specifically, the model has a low computational complexity, appropriately switches off in laminar and transitional flows, does not require any ad hoc shear and stability corrections, and is consistent with theoretical subfilter turbulent fluxes. The simulation results show remarkable agreement with well-established empirical correlations, theoretical predictions, and field observations in the atmosphere. In addition, the results show very little sensitivity to the grid resolution, demonstrating the robustness of the model in the simulation of the atmospheric boundary layer, even with relatively coarse resolutions.

Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations.

Log-layer mismatch refers to a chronic problem found in wall-modeled large-eddy simulation (WMLES) or detached-eddy simulation, where the modeled wall-shear stress deviates from the true one by approximately 15%. Many efforts have been made to resolve this mismatch. The often-usedfixes, which are generally ad hoc, include modifying subgridscale stress models, adding a stochastic forcing, and moving the LES-wall-model matching location away from the wall. An analysis motivated by the integral wall-model formalism suggests that log-layer mismatch is resolved by the built-in physics-based temporal filtering. In this work we investigate in detail the effects of local filtering on log-layer mismatch. We show that both local temporal filtering and local wall-parallel filtering resolve log-layer mismatch without moving the LES-wall-model matching location away from the wall. Additionally, we look into the momentum balance in the near-wall region to provide an alternative explanation of how LLM occurs, which does not necessarily rely on the numerical-error argument. While filtering resolves log-layer mismatch, the quality of the wall-shear stress fluctuations predicted by WMLES does not improve with our remedy. The wall-shear stress fluctuations are highly underpredicted due to the implied use of LES filtering. However, good agreement can be found when the WMLES data are compared to the direct numerical simulation data filtered at the corresponding WMLES resolutions.

Space-time characteristics of wall-pressure and wall shear-stress fluctuations in wall-modeled large eddy simulation.

We report the space-time characteristics of the wall-pressure fluctuations and wall shear-stress fluctuations from wall-modeled large eddy simulation (WMLES) of a turbulent channel flow at Re τ = 2000. Two standard zonal wall models (equilibrium stress model and nonequilibrium model based on unsteady RANS) are employed, and it is shown that they yield similar results in predicting these quantities. The wall-pressure and wall shear-stress fields from WMLES are analyzed in terms of their r.m.s. fluctuations, spectra, two-point correlations, and convection velocities. It is demonstrated that the resolution requirement for predicting the wall-pressure fluctuations is more stringent than that for predicting the velocity. At least δ/Δx > 20 and δ/Δz > 30 are required to marginally resolve the integral length scales of the pressure-producing eddies near the wall. Otherwise, the pressure field is potentially aliased. Spurious high wave number modes dominate in the streamwise direction, and they contaminate the pressure spectra leading to significant overprediction of the second-order pressure statistics. When these conditions are met, the pressure statistics and spectra at low wave number or low frequency agree well with the DNS and experimental data. On the contrary, the wall shear-stress fluctuations, modeled entirely through the RANS-based wall models, are largely underpredicted and relatively insensitive to the grid resolution. The short-time, small-scale near-wall eddies, which are neither resolved nor modeled adequately in the wall models, seem to be important for accurate prediction of the wall shear-stress fluctuations.

Osborne Reynolds pipe flow: Direct simulation from laminar through gradual transition to fully developed turbulence.

The precise dynamics of breakdown in pipe transition is a century-old unresolved problem in fluid mechanics. We demonstrate that the abruptness and mysteriousness attributed to the Osborne Reynolds pipe transition can be partially resolved with a spatially developing direct simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Our results with this approach show during transition the energy norms of such inlet perturbations grow exponentially rather than algebraically with axial distance. When inlet disturbance is located in the core region, helical vortex filaments evolve into large-scale reverse hairpin vortices. The interaction of these reverse hairpins among themselves or with the near-wall flow when they descend to the surface from the core produces small-scale hairpin packets, which leads to breakdown. When inlet disturbance is near the wall, certain quasi-spanwise structure is stretched into a Lambda vortex, and develops into a large-scale hairpin vortex. Small-scale hairpin packets emerge near the tip region of the large-scale hairpin vortex, and subsequently grow into a turbulent spot, which is itself a local concentration of small-scale hairpin vortices. This vortex dynamics is broadly analogous to that in the boundary layer bypass transition and in the secondary instability and breakdown stage of natural transition, suggesting the possibility of a partial unification. Under parabolic base flow the friction factor overshoots Moody's correlation. Plug base flow requires stronger inlet disturbance for transition. Accuracy of the results is demonstrated by comparing with analytical solutions before breakdown, and with fully developed turbulence measurements after the completion of transition.

Statistical description of the free-space propagation of highly aberrated optical beams.

The free-space propagation of initially aberrated optical beams is considered with an emphasis on aero-optical applications. An exact statistical solution of the paraxial wave equation is derived that can be used to obtain statistics of the beam such as beam center, spread, and higher-order statistics as algebraic functions of propagation distance, wavelength, and statistics of the initial wavefront. Correlations between the proposed description and intensity-based statistics, such as the Strehl ratio, are investigated. It is found that the root-mean-square (rms) of the gradient of the wavefront plays an important role in causing coherence degradation and that the rms of the wavefront error is not always an appropriate measure of the degradation. To illustrate the use of this statistical tool, index of refraction data from a numerical simulation of compressible flow over a cylinder are employed to perform an aero-optical analysis.