Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical ... more Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressurestrain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.
This study addresses the dynamics of kinetic-energy backscatter in the context of large-eddy simu... more This study addresses the dynamics of kinetic-energy backscatter in the context of large-eddy simulations (LES) of turbulent chemically-reacting compressible flows. As a case study, a-priori analyses of direct numerical simulations (DNS) of reacting and inert supersonic, time-developing, hydrogen-air turbulent mixing layers with complex chemistry and multi-component diffusion are conducted herein to examine the effects of compressibility and combustion on subgrid-scale (SGS) backscatter of kinetic energy. General formulations of SGS backscatter with dilatation are provided, including an LESbased energy-transfer diagram that illustrates the conversion dynamics. Lastly, influences of SGS backscatter on the Boussinesq eddy viscosity are analyzed.
Theoretical and Computational Fluid Dynamics, Aug 25, 2021
Accurate prediction of aerothermal surface loading is of paramount importance for the design of h... more Accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shockwave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers (Re L ≈ 11.6 × 10 6 based on freestream conditions) and the presence of cold walls (T w /T • ≈ 0.26) leading to large near-wall temperature gradients necessitate the use of wall-modeled large-eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using a standard LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three dimensionality in the mean, shock-boundary layer interactions, and flow separation. We demonstrate that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.
Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall ... more 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 (nonzero 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 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 nonzero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models . Secondly, 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 zeropressure-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.
While the computation of the boundary-layer thickness is straightforward for canonical equilibriu... more While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a method is developed based on a local reconstruction of the "inviscid" velocity profile UI [y] resulting from the application of the Bernoulli equation in the wall-normal direction. The boundarylayer thickness δ99 is then defined as the location where U/UI = 0.99, which is consistent with its classical definition for the zero-pressure-gradient boundary layers (ZPGBLs). The proposed localreconstruction method is parameter free and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the local-reconstruction method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the local-reconstruction method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar bounda... more The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation, and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within ±10% at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.
Accurate prediction of aerothermal surface loading is of paramount importance for the design of h... more Accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shockwave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers (Re L ≈ 11.6 × 10 6 based on freestream conditions) and the presence of cold walls (T w /T • ≈ 0.26) leading to large near-wall temperature gradients necessitate the use of wall-modeled large-eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using a standard LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three dimensionality in the mean, shock-boundary layer interactions, and flow separation. We demonstrate that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.
Fully developed turbulent channel flow has been simulated americally at . Reynolds number 19800, ... more Fully developed turbulent channel flow has been simulated americally at . Reynolds number 19800, based on centerline velocity and channel half width. The large-scale flow field has been obtained by directly integrating the filtered, three-dimensional, tine-dependent, Davies-Stokes equations. The smallscale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time-dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall. I. Introduction Large-eddy simulation (LBS) is a relatively new approach to the calculation of turbulent flows. The basic idea stems from two experimental observations. First, the large-scale structure of turbulent flows varies greatly from flow to flow (e.g., jets vs. boundary layers) and consequently is difficult, if not impossible, to model in a general way. Second, the small-scale turbulence structures are nearly isotropic, very universal in character (Chapman, 1979) and hence such sore amenable to general modeling. In LBS, one actually calculates the large-scale notions in a time-dependent, three-*Portions of this work were carried out while the authors held NRC Research Associateships at Ames Research Center. a locally isotropic: part and an iahomc.-Qeneous part, he employed a separate partial differential equation for SGS turbulent kinetic energy. However, the added differential equation did not improve the results over the calculations in which only an eddy viscosity model was used ( Schumann, 1975). Gr8tzbach and Schumann ( 1977) extended their channel flow calculations to account for temperature fluctuations and heat transfer. Later extensions by GrBtzbach include calculations of secondary flows in partly roughened chanr nels, inclusion of buoyancy effects, and liquid metal flows in plane channels and annuli. A recent -4view of this group's work in LES was given by Schumann et al. (1979). In all of the above computations, the dynamics of the inner region of the boundary layer (viscous sublayer and butter layer) was essentially ignored. It is in this region that virtually all of the production of turbulence kinetic energy takes place (Townsend, 1956;. Artificial boundary conditions in the logarithmic region were used to simulate the inner layers. Aside from the fact that these boundary conditions are designed to be consistent iu the mean with the law of thx wall, there is little justification or experimental evidence to warrant their use for the detailed flow field. however, the computations of and especially those of the Karlsruhe group have produced successful comparisons with experimental data in the regions away from the walls. With a relatively modest number of grid points, they have been able to extract considerable information of practical interest from their computations. The first numerical simulation of turbulent channel flow that computed ^rather than modeled the flow in the immediate neighborhood of the wall was that of . In this calculation only 16 uniformly spaced grid points were used in each of the streamwise, x, and spanwise, z, directions
We investigate the error scaling and computational cost of wall-modeled large-eddy simulation (WM... more We investigate the error scaling and computational cost of wall-modeled large-eddy simulation (WMLES) for external aerodynamic applications. The NASA Juncture Flow is used as representative of an aircraft with trailing-edge smooth-body separation. Two gridding strategies are examined: i) constant-size grid, in which the near-wall grid size has a constant value and ii) boundary-layer-conforming grid (BL-conforming grid), in which the grid size varies to accommodate the growth of the boundary-layer thickness. Our results are accompanied by a theoretical analysis of the cost and expected error scaling for the mean pressure coefficient (𝐶 𝑝 ) and mean velocity profiles. The prediction of 𝐶 𝑝 is within less than 5% error for all the grids studied, even when the boundary layers are marginally resolved. The high accuracy in the prediction of 𝐶 𝑝 is attributed to the outer-layer nature of the mean pressure in attached flows. The errors in the predicted mean velocity profiles exhibit a large variability depending on the location considered, namely, fuselage, wing-body juncture, or separated trailing-edge. WMLES performs as expected in regions where the flow resembles a zero-pressure-gradient turbulent boundary layer such as the fuselage (< 5% error). However, there is a decline in accuracy of WMLES predictions of mean velocities in the vicinity of wing-body junctions and, more acutely, in separated zones. The impact of the propagation of errors from the underresolved wing leading-edge is also investigated. It is shown that BL-conforming grids enable a higher accuracy in wing-body junctions and separated regions due to the more effective distribution of grid points, which in turn diminishes the streamwise propagation of errors.
While there have been numerous applications of large eddy simulations (LES) to complex flows, the... more While there have been numerous applications of large eddy simulations (LES) to complex flows, their application to practical engineering configurations, such as full aircraft models, have been limited to date. Recently, however, advances in rapid, high quality mesh generation, low-dissipation numerical schemes and physics-based subgrid-scale and wall models have led to, for the first time, accurate simulations of a realistic aircraft in landing configuration (the Japanese Aerospace Exploration Agency Standard Model) in less than a day of turnaround time with modest resource requirements. In this paper, a systematic study of the predictive capability of LES across a range of angles of attack (including maximum lift and post-stall regimes), the robustness of the predictions to grid resolution and the incorporation of wind tunnel effects is carried out. Integrated engineering quantities of interest, such as lift, drag and pitching moment will be compared with experimental data, while s...
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