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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-modelled 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 $\\pm 10\\,\\%$ at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, the 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.

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.

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 sectional pressure forces will be used to corroborate the accuracy of the integrated quantities. Good agreement with experimental$C_L$data is obtained across the lift curve with the coefficient of lift at maximum lift,$C_{L,max}$, consistently being predicted to within five lift counts of the experimental value. The grid point requirements to achieve this level of accuracy are reduced compared with recent estimates (even for wall modelled LES), with the solutions showing systematic improvement upon grid refinement, with the exception of the solution at the lowest angles of attack, which will be discussed later in the text. Simulations that include the wind tunnel walls and aircraft body mounting system are able to replicate important features of the flow field noted in the experiment that are absent from free air calculations of the same geometry, namely, the onset of inboard flow separation in the post-stall regime. Turnaround times of the order of a day are made possible in part by algorithmic advances made to leverage graphical processing units. The results presented herein suggest that this combined approach (meshing, numerical algorithms, modelling, efficient computer implementation) is on the threshold of readiness for industrial use in aeronautical design.

Thwaites ( Aeronaut. Q. , vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971 ). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

In this work, a non-equilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity (u_tau) and the viscous-pressure gradient velocity (up). In regions where the pressure gradient velocity is comparable to the friction velocity (up \\sim u_tau, the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA-Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model can capture the onset of boundary layer separation observed in experiments or DNS calculations at resolutions where the equilibrium wall model fails to separate.

The governing equations for large-eddy simulation (LES) are derived from the application of a low-pass filter to the Navier-Stokes equations. LES has shown to be a tractable method for the computation of high Reynolds number turbulent flows, primarily because the filtration of the Navier-Stokes equations removes the small scales of motion that would otherwise impose prohibitive resolution requirements. The effect of the scales of motion that are smaller than the filter width on the large, resolved scales are then modeled. In practice, the filter used to derive the LES governing equation is not formally defined and instead, it is assumed that the discretization of LES equation will implicitly act as a low-pass filter. This study investigates an alternative derivation of the LES governing equations that requires the formal definition of the filtration operator, known as explicitly filtered LES. It is shown that decoupling the filtering operation from the underlying grid allows for the isolation of subgrid-scale (SGS) modeling errors from numerical discretization errors. In this grid-independent context, it is demonstrated that standard eddy viscosity models are inaccurate at coarse resolutions. By leveraging the definition of the filtering operator, an SGS model is subsequently derived from a low order perturbation of the explicitly filtered governing equations. LES of canonical wall bounded flows (e.g., channels and ducts) at coarse resolutions validate the improved accuracy of the proposed SGS model. Simulations of practical engineering configurations require the ability to handle complex geometries. Previous explicitly filtered LES calculations have been limited to structured grid discretizations because of the difficulty in constructing a low-pass filter on unstructured grids. The explicitly filtered framework and the proposed SGS model are extended for use in unstructured grid environments through the use of differential filters. Unstructured grids also provide the ability to locally increase resolution in regions of the flow where the SGS model is unable to accurately model the stress provided by the unresolved scales of motion. A novel adaptation technique is suggested where the mesh (and/or filter) is refined in regions of the flow where estimates of the SGS fluctuations are largest. An LES of a three-dimensional stalled diffuser is performed to demonstrate the efficacy of the SGS model based mesh refinement criteria and the capabilities of the differential filters on unstructured grids. Lastly, a dynamic wall boundary condition is derived from the differential filter for wall-modeled large-eddy simulation where the near wall turbulence is not resolved. This differential filter based wall model successfully predicts mean dynamics of both wall-bounded flows (channels) and separating flows in complex geometries (airfoil at near-stall conditions) without the prescription of any ad hoc coefficients or RANS/LES hybridization.

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data has shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [Bardina et al., AIAA 1980; Meneveau and Liu, Ann. Rev. Fluid Mech. 2002]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g.: Bardina et al., AIAA 1980; Clark et al. J. Fluid Mech., 1979; Stolz and Adams, Phys. of Fluids, 1999]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for LES, vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence (HIT), and wall-modeled turbulent channel flow at high Reynolds numbers; the results show favorable agreement with DNS data. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to the existing static coefficient (Vreman) and dynamic Smagorinsky model.

This article utilizes the Large-Eddy Simulation (LES) paradigm with a physics-based turbulence modeling approach, including a dynamic subgrid-scale model and an equilibrium wall model, to examine the flow over the NASA transonic Common Research Model (CRM), a flow configuration that has been the focus of several AIAA Drag PredictionWorkshops (DPWs). The current work explores sensitivities to laminar-to-turbulent transition, wind tunnel mounting system, grid resolution, and grid topology and suggests current best practices in the context of large-eddy simulations of transonic aircraft flows. It is found that promoting the flow transition to turbulence via an array of cylindrical trip dots, including the sting mounting system in the simulations, and leveraging stranded boundary layer grids all tend to improve the quality of the LES solutions. Non-monotonic grid convergence in the LES calculations is observed to be strongly sensitive to grid topology, and stranded meshes rectify this issue relative to their hexagonal close-packed (HCP) counterparts. The details of the boundary layer profiles both at the leading edge of the wing and within the shock-induced separation bubble are studied, with thicknesses and integral measures reported, providing details about the boundary layer characteristics to turbulence modelers not typically available from complex aircraft flows. Finally, an assessment of the initial buffet prediction capabilities of LES is made in the context of a simpler NACA 0012 flow, with computational predictions showing reasonable agreement with available experimental data for the angle of attack at initial buffet onset and shock oscillation frequency associated with sustained buffet.

Accurate modeling of ice accretion is important for safe and efficient design of aircraft and wind turbine systems. Heat transfer predictions obtained from fluid flow solvers are used as input in ice accretion codes. In glaze ice conditions, freezing rates and resulting ice shapes are highly sensitive to input values of the heat transfer coefficient. Hence, accurate prediction of heat transfer on iced airfoils is crucial for correctly predicting the ice accretion process. In this study, we perform conjugate heat transfer (CHT) simulations using wall-modeled large-eddy simulation (WMLES) over surfaces characterized by ice roughness. The results show that WMLES with CHT accurately captures surface temperature distributions and heat fluxes across a range of roughness geometries. For cases considered, large roughness-to-boundary-layer thickness ratios disrupt outer-layer similarity, leading to substantial errors in estimating equivalent sandgrain roughness when applying traditional empirical models based on surface statistics. The simulations further show that local heat fluxes vary significantly across roughness elements due to low thermal conductivity of the solid; in particular, roughness crests exhibit reduced fluxes in contrast to slopes and valleys. Notably, as roughness height increases, wall heat flux at the crest diminishes, even leading to heat flux reversal in some cases, where thermal energy is transferred from fluid to solid. These effects are not captured in isothermal wall simulations, which overestimate the Stanton number, especially at roughness peaks. By enabling calculation of Stanton number using heat flux distributions, not directly available in experiments, the present simulations augment experimental results and highlight the importance of including solid conduction effects for accurately modeling heat transfer over rough, low-conductivity surfaces such as ice.

Thwaites (1949) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of a flow parameter, \\(m = \\theta^2/\\nu \\frac{dU_e}{ds}\\), thus reducing the von Karman momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. However, for turbulent flows, a similar approximation for turbulent boundary layers subjected to pressure gradients does not yet exist. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed. It is shown that the method provides good estimates of the momentum thickness, when compared to available high-fidelity simulation data, for multiple boundary layers including both favorable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model which is shown to be in agreement with prior empirical observations (Alber, \\textit{\\(9^{th}\\) Aerospace Sciences Meeting, 1971}). The sensitivity of the separation location with respect to upstream perturbations is also analyzed through this model for the NASA/Boeing speed bump and the transonic Bachalo-Johnson bump