Session Q08: Boundary Layers: Modeling

Advances in subgrid-scale and wall modeling for simulations of complex, separated turbulent flows

Recent studies (Agrawal et al., Phys. Rev. Fluids 2022; Goc et al., Ann. Res. Briefs, CTR 2020) have shown that traditional eddy viscosity models when used with the equilibrium wall model exhibit a non-monotonic convergence (on grid refinement) in the prediction of separation bubble sizes in certain mild adverse pressure gradient regimes such as those observed in the Boeing speed bump (Williams et al., AIAA Scitech 2020).

In this work, we focus on the impact of modeling closures in the vicinity and inside the separation bubble. We have developed a class of novel dynamic SGS models such as the dynamic tensor coefficient Smagorinsky model (DTCSM) and a variant of the mixed Clark model (DTCCM). In the simulations of flow over the Boeing speed bump, both DTCSM and DTCCM recover monotonic convergence of the quantities of interest (QoI) such as skin friction and pressure drag. DTCCM accurately predicts the QoI and the mean velocity profiles on relatively coarse grids w.r.t. the DNS (Uzun and Malik, AIAA J. 2022). Results from these simulations and other flows will be presented and compared against reference data.   

Stochastic modeling of rough wall turbulent boundary layers: a wind tunnel and atmospheric scale study

The statistical properties of uniform momentum zones (UMZ) in rough wall turbulent boundary layers are investigated at the laboratory and field scales to identify potential similarities in their probability distribution functions in the logarithmic region. In particular, we focus on the thickness H_m and the modal velocity U_m , as a function of the wall distance. These are critical to reproduce the attached eddy scaling laws and the mean velocity profile, while providing a significant contribution to the observed variability of the streamwise velocity component. We will show that building and inverting the H_m, U_m cumulative density functions, allow us to generate synthetic velocity profiles, from the ground up, that mimic the vertical distribution of UMZs while retaining some of the statistical properties of turbulent boundary layers, such as the mean velocity and the variance profiles. Spatio-temporally resolved PIV velocity fields, acquired as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA) collaboration and covering a field of view of 8 x 9 m 2 in the atmospheric surface layer, allow us to derive and test our semi-stochastic algorithm at high Reynolds numbers. Preliminary results show the generalizability of our framework and the potential to develop a computationally affordable, low dimensional, dynamic near wall model.   

A new LES wall model for quasi-equilibrium to non-equilibrium conditions and its applications

The Lagrangian relaxation towards equilibrium (LaRTE) wall model for large eddy simulation (LES) developed in Fowler et al. (2022) is tested over a wide range of unsteady conditions from quasi-equilibrium to non-equilibrium. This includes linearly accelerating and pulsatile channel flow for several acceleration rates and forcing frequencies, respectively. The LaRTE model’s ability to extract quasi-equilibrium dynamics from LES inputs allows for separate modeling of non-equilibrium dynamics such as the laminar non-equilibrium model in Fowler et al. (2022) which captures the wall stress response to fast changes in the pressure gradient and a newly developed turbulent non-equilibrium model based on LES velocity fluctuations’ deviations from the LaRTE quasi-equilibrium profile. This type of an approach allows us to uncover dynamics previously masked in existing wall models, such as the equilibrium wall model, which attempt to model all dynamics at once. Test results including the LaRTE quasi-equilibrium plus laminar and turbulent non-equilibrium wall models show good agreement with direct numerical simulation data over a vast range of conditions. A “corrected equilibrium wall model” (supplemented with the laminar non-equilibrium model) is also introduced as a simpler alternative.   

Falkner-Skan wall model for laminar boundary layers

Modeling of the laminar and transitional regions of flow remains one of the key challenges in the numerical simulation of wall-bounded flows. As described in NASA’s CFD Vision 2030 Study (Slotnick et al. 2014), this issue is of particular concern for wall-modeled large-eddy simulations, in which it has been shown that the laminar region can require 10-100 times more grid points than the turbulent region to properly capture the amplification of disturbances leading to transition. Under-resolving the laminar region can lead to large errors in the prediction of mean quantities of interest such as lift and drag. A wall model based on the Falkner-Skan similarity solution of laminar wedge flows has been developed for use in the laminar portion of transitional wall-bounded flows, particularly for use near the leading edge of airfoils (Gonzalez, et al., 2020) at coarse resolutions. This wall model has previously been tested on stagnation flow and pressure gradient boundary layer flows where it has been shown to provide an improvement in the prediction of wall-stress compared to other existing models. In this study, we present further results from the model when applied to a NACA0012 airfoil.   

Comparative study of wall models for LES in pressure-gradient and separated turbulent boundary layers

As wall models enable the paradigm shift from RANS modeling to LES in the simulation of high Reynolds number turbulent boundary layers (TBLs) of practical importance, it is an opportune time to systematically compare the capabilities of various wall models in incorporating nonequilibrium effects characteristic of realistic flows. In this study, we assess the predictive capabilities of three common wall models with increasing model complexity and fidelity, namely, an ODE equilibrium model, an integral nonequilibrium model, and a PDE nonequilibrium model. Two nonequilibrium flows at moderately high Re_θ (~2000-10000) are considered: (i) pressure gradient TBL experiments of Volino (J. Fluid Mech. (2020), vol. 897, A2) with acceleration parameter K=(ν/U_∞²)(dU_∞/dx) ranging from 0.25×10^-6 to 2×10^-6; (ii) DNS of separated TBL by Coleman et al. (J. Fluid Mech. (2018), vol. 847, pp. 28-70). The former case will reveal the sensitivity of wall-model predictions to the varying strength of pressure gradient, whereas the latter will assess their capability to predict separation bubble characteristics reliably. We will discuss the mechanisms for differences in different wall-models’ results, and the differing wall-model requirements among the three wall models and in different zones of the flow.   

Modeling the Reynolds Stress Spectra in Turbulent Channel Flow

The Reynolds stress spectra in turbulent channel flow are studied by numerical simulations combined with spectral analyses of the Orr Sommerfeld/Squire (OS/SQ) system of equations. The simulations vary in Re_τ from 180 to 5200. The OS/SQ equations are assumed to have stochastically-forced  source terms representing the nonlinear terms in the full dynamical equations for ?² and ω_y. Their solutions are written in terms of eigenfunction expansions leading to expressions for the v and ω_y spectra. These expressions contain the known eigenfunctions, the corresponding eigenvalues, and the yet unknown statistics of the forcing term for each mode with possible cross correlations between modes. The modeling proceeds by attempting to represent the known simulation results for the spectra by an optimal choice of the covariance matrix of the eigenmode forcing amplitudes. The modes chosen for the expansion are ranked in importance by the real part of the eigenvalues so that those with smaller real parts (slower decaying modes) are ranked higher. Once the v and ω_y   spectra and their crossspectrum are determined the remaining Reynolds stresses may be computed. We investigate in particular the contributions to the stresses associated with highly elongated streamwise structures.      

Near-wall turbulence generation in wall-modeled LES

This talk discusses how near-wall turbulence is generated in wall-modeled LES (WMLES). Although WMLES has been widely used as an efficient methodology to predict high Reynolds number turbulent flows, the mechanisms of near-wall turbulence generation in WMLES have not been fully understood. Generally, the coherent structures exist in the near-wall region of the turbulent boundary layer and play a crutial role in turbulence production. However, the near-wall turbulence structures simulated by WMLES are not obvious because the typical inner-layer streaks are not resolved in the WMLES. The statistics and mechanisms of the near-wall turbulence structures in WMLES are elucidated by using a conditional-averaging technique, and the turbulence generation mechanisms in WMLES are discussed.   

Wall-modeled large-eddy simulations of the flow over a Gaussian-shaped bump with a relaminarization sensor

Wall-modelled large-eddy simulations are conducted with a relaminarization sensor to investigate a turbulent boundary layer flow with a freestream Mach number M=0.2 over a Gaussian-shaped bump geometry at two different Reynolds numbers, Re_L=10⁶ and 2x10⁶, based on the bump length. 

The flow exhibits favorable and adverse pressure gradients driven by the bump curvature, leading to a region of relaminarization around the apex, for the Re_L=10⁶, and flow separation downstream of the bump apex, for both Reynolds numbers. This flow configuration serves as a challenging test case for wall-modeling approaches that typically assume the boundary layer to be fully turbulent, overestimating the friction and momentum losses in quasi-laminar regions.

A relaminarization sensor is developed to control the local application of the wall model and no-slip boundary conditions, adjusted by a blending function derived from flow quantities. We assess the performance of the proposed relaminarization sensor by comparing spanwise periodic simulation results with Direct Numerical Simulations by Uzun & Malik (2020, 2022) at both Reynolds numbers. The a posteriori analysis suggests that the sensor correctly distinguishes the relaminarization region in the low Re_L case and improves flow predictions.   

Development of a Data-Driven Wall Model for Large-Eddy Simulation of Gas Turbine Film Cooling Flows

A data-driven wall modeling framework is developed for large-eddy simulation (LES) of gas turbine film cooling systems. High-fidelity near-wall turbulent flow datasets are extracted from wall-resolved LES of a canonical gas turbine film cooling configuration, comprised of a flat plate with a single row of 7-7-7 shaped cooling holes, performed using a high-order spectral element CFD solver Nek5000. Wall-normal distance, near-wall fluid velocity, velocity/pressure gradients, and fluid density are used as input features and wall shear stress is predicted as the output. Two machine learning (ML) models are explored for predicting wall shear stress: Light Gradient Boosting Machine (LGBM) and artificial neural network (ANN). ML training is performed for blowing ratio (BR) of 1, whereas datasets for BRs 0.5, 1.5, and 2 are employed as the test set. It is observed that ANN tends to generalize slightly better than LGBM. Moreover, adding velocity gradient information and incorporating flow feature information from multiple streamwise/normal/spanwise neighbors improves the accuracy and generalizability of the data-driven wall model.