Parviz Moin

Accurate prediction of laminar-turbulent transition in boundary layers remains challenging for wall-modeled large-eddy simulations (WMLESs), particularly on coarse computational grids. The thin laminar region preceding transition requires significantly higher grid resolution than turbulent regions, making high-fidelity simulations computationally expensive (Slotnick et al., 2014). This study presents a novel hybrid approach combining nonlinear parabolized stability equations (NLPSE) with WMLES to efficiently simulate transitional flows.We use the Falkner-Skan wall model (FSWM) to economically generate accurate base flow states for NLPSE analysis, which predicts transition onset and provides spatially and temporally varying inflow conditions for downstream WMLES. This methodology is demonstrated on flat-plate transition scenarios, including H-type, K-type, and oblique modes, achieving comparable accuracy to direct numerical simulations and wall-resolved LES while using 95% fewer grid points.We further introduce the PSE-Sponge method, which directly couples PSE solutions with LES through sponge-layer forcing, eliminating the need for separate inflow generation. This approach simplifies transitional flow modeling over complex geometries. The method is validated on flat plate cases and successfully applied to transition simulation on an NLF(01)-0416 natural laminar flow airfoil. Sensitivity analysis reveals robust performance across key parameters, including sponge strength and number of PSE modes.

Turbulence–chemistry interaction in a Mach-7 hypersonic boundary layer with significant production of radical species is characterised using direct numerical simulation. Overriding a non-catalytic surface maintained as isothermal at 3000 K, the boundary layer is subject to finite-rate chemical effects, comprising both dissociation/recombination processes as well as the production of nitric oxide as mediated by the Zel’dovich mechanism. With kinetic-energy dissipation giving rise to temperatures exceeding 5300 K, molecular oxygen is almost entirely depleted within the aerodynamic heating layer, producing significant densities of atomic oxygen and nitric oxide. Owing to the coupling between turbulence-induced thermodynamic fluctuations and the chemical-kinetic processes, the Reynolds-averaged production rates ultimately depart significantly from their mean-field approximations. To better characterise this turbulence–chemistry interaction, which arises primarily from the exchange reactions in the Zel’dovich mechanism, a decomposition for the mean distortion of finite-rate chemical processes with respect to thermodynamic fluctuations is presented. Both thermal and partial-density fluctuations, as well as the impact of their statistical co-moments, are shown to contribute significantly to the net chemical production rate of each species. Dissociation/recombination processes are confirmed to be primarily affected by temperature fluctuations alone, which yield an augmentation of the molecular dissociation rates and reduction of the recombination layer’s off-wall extent. While the effect of pressure perturbations proves largely negligible for the mean chemical production rates, fluctuations in the species mass fractions are shown to be the primary source of turbulence–chemistry interaction for the second Zel’dovich reaction, significantly modulating the production of all major species apart from molecular nitrogen.

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.

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.

In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two decades, through appropriate localization of the artificial bulk viscosity for capturing shocks. However, for capturing contact discontinuities, either a density or internal energy variable is used as a detector. An issue with this sensor is that it not only detects contact discontinuities but also falsely detects the regions of shocks and vortical motions. Using this detector to add artificial mass/thermal diffusivity for capturing contact discontinuities is hence unnecessarily dissipative. To overcome this issue, we propose a sensor similar to the Ducros sensor (for shocks) to detect contact discontinuities and further localize artificial mass/thermal diffusivity for capturing contact discontinuities. The proposed method contains coefficients that are less sensitive to the choice of the flow problem. This is achieved by improved localization of the artificial diffusivity in the present method. A discretely consistent dissipative flux formulation is presented and is coupled with a robust low-dissipative scheme, which eliminates the need for filtering the solution variables. The proposed method also does not require filtering for the discontinuity detector/sensor functions, which is typically done to smear out the artificial fluid properties and obtain stable solutions. Hence, the challenges associated with extending the filtering procedure for unstructured grids are eliminated, thereby making the proposed method easily applicable for unstructured grids. Finally, a straightforward extension of the proposed method to two-phase flows is also presented.

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0060.

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 have shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [J. Bardina, J. Ferziger, and W. Reynolds, Improved subgrid-scale models for large-eddy simulation, in Proceedings of the 13th Fluid and Plasmadynamics Conference, AIAA (1980); C. Meneveau and K. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32, 1 (2000)]. 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., Proceedings of the 13th Fluid and Plasmadynamics Conference (1980); R. A. Clark, J. Ferziger, and W.C. Reynolds. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech. 91, 1 (1979); S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699 (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 large-eddy simulation (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, and wall-modeled turbulent channel flow at high Reynolds numbers. The results show favorable agreement with DNS data. It has been shown that DTCSM offers similar predictive capabilities as the dynamic Smagorinsky model for canonical flows. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump (Boeing speed 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 existing static coefficient (Vreman) and dynamic Smagorinsky model. The computational cost of performing LES with this model is up to 15% higher than the dynamic Smagorinsky model.