Session J12: Boundary Layers: Wall Modeling

Predictive modeling of boundary-layer flows with pressure gradients

This study has two objectives. Firstly, we investigate how well existing RANS models predict the skin friction coefficient and incipient flow separation for a boundary layer subjected to pressure gradients. Secondly, we develop a new physics-based model by leveraging a recently established universal mean velocity transformation. Four existing models are considered: the local equilibrium wall model with and without Kay’s correction, the one-equation transport Spalart-Allmaras model, and the two-equation transport Wilcox k-omega model, and data in previous studies by Volino, Marusic, Vinuesa, Yang and coauthors are used. While the existing models prove to be quite accurate under mild and moderate pressure gradients, they fall short when facing strong pressure gradients. In contrast, the new model performs reasonably well across all conditions investigated. In addition to presenting the results, we will also attempt to provide a physical explanation for observed behaviors. In particular, the local models predict instant response of the Reynolds stresses to pressure gradients, and the wall treatments in the two transport models are based on the equilibrium law of the wall, both of which are not physical.   

Assessment of wall models in large eddy simulation of turbulent separation bubble with and without sweep

Wall-modeled LES of turbulent separation bubble over a flat plate is conducted using three wall models: ODE equilibrium, integral nonequilibrium, and PDE nonequilibrium wall model. The flow configuration is based on the two DNS studies of Coleman et al. (J. Fluid Mech. (2018), vol. 847, 28-70, and J. Fluid Mech. (2019), vol. 880, 684–706), where suction and blowing from the top results in a pressure-gradient-induced separation bubble at the bottom wall. The incoming freestream velocity vector is unswept in the former case, and swept at 35° to the pressure-gradient vector in the latter. These two cases allow us to assess the performance of wall models in 2D- and 3D-turbulent-boundary-layers undergoing separation, the latter being more representative of practical flows. Mean velocity, boundary layer integral quantities, wall shear stress predictions, and skewness of profiles from WMLES will be analyzed to explore how the differing physics in the two cases affect different wall-models.   

Resolvent modes as the foundation for LES wall models

In Wall-Modelled Large-Eddy Simulations (WMLES) the flow away from a solid surface is resolved while the wall-layer is modelled. Typically, the interface between inner and outer layers does not coincide with the first grid point, and a buffer region is used to allow eddies to be created and develop into physically realistic structures. The present research aims to use Resolvent Analysis to synthesize near-wall eddies that are neglected in WMLES, thereby resulting in a more accurate representation of the momentum exchange between the bypassed near-wall layer and the outer flow. As a first step we calculate the force due to selected resolvent modes, and add it to the Navier-Stokes equations, that are subsequently solved in a Wall-Resolved LES configuration. The use of a wall-resolving grid allows us to minimize or remove errors due to grid resolution, errors in the sub-filter scale model or in the wall model. We can then isolate the effect of the resolvent-mode forcing on the flow field, prior to their use in an actual WMLES. The resolvent modes are characterized by their wavelengths in streamwise and spanwise directions, by their frequency and, very importantly, by the extent of their support in the wall-normal direction. We find that (1) by changing the wavelengths of the resolvent modes we can affect independently various Reynolds stresses; (2) the resolved stresses adjust to the forcing, both in terms of their magnitude, and spectral distribution of the eddies responsible for the generation of shear stress〈u'v'〉; (3) that resolvent modes that span the inner/outer layer interface are more effective than those that lie entirely below this interface. Future work will concentrate on deploying optimal combinations of resolvent modes to generate eddy content in the buffer region in actual WMLES, for increasing Reynolds numbers and in increasingly complex flow configurations.   

Wall Modelled LES of Heterogeneous Rough Surfaces

Surface roughness is present in many applications in engineering and natural sciences. Its effect is not only that of increasing drag, but also of modifying the turbulence-generation cycle. Furthermore, heterogeneous roughness has an even more significant impact on the flow-field by inducing non-equilibrium effects. Resolved numerical simulations can provide useful insights on the flow state over rough walls, but are limited to low Reynolds-numbers. Wall-modelled large-eddy simulations (WMLES), on the other hand, allow us to reach high Reynolds numbers. In this work, WMLES were performed to simulate the flow over roughness strips placed normal to the mean flow. We compared the standard log-law based equilibrium wall-model with the generalized Moody-diagram model of Meneveau [J. Turbulence, 21(11):650–673, 2020] and with the Lagrangian Relaxation-Towards-Equilibrium (LaRTE) wall model [Fowler et al., J. Fluid Mech., 934(A44):1–37, 2022]. This model allows the inclusion of non-equilibrium effects in the response of the wall shear-stress to perturbations. A new formulation of the LaRTE model to rough walls is also proposed that allows the model to switch seamlessly between smooth-wall behaviour and transitionally or fully rough flow conditions. Applications of the extended LaRTE wall model are presented in the homogeneous rough-walls channel configuration and the in the normal-strips case.   

Machine-learning wall-model large-eddy simulation accounting for roughness

Wall-modeled large-eddy simulation (WMLES) has emerged as a computationally effective framework for modeling the impact of roughness on outer flow without the need to resolve the small-scale flow and roughness geometry near the wall. Our objective here is to develop a robust rough-wall model for WMLES using machine learning (ML) techniques, capable of accurately handling a wide range of flow conditions, including both attached and separated flows, as well as various rough surfaces spanning the transitionally and fully rough regimes. To this end, we compiled an extensive DNS roughness database that encompasses irregular rough surfaces with different distributions of probability density functions and power spectra at various Reynolds numbers. The database serves as the foundation for training our ML-based wall models. The choice of non-dimensional input features for the wall model including both flow variables and roughness parameters is optimized to enhance model performance. The performance of the model is evaluated a-posteriori in WMLES of turbulent channel flows with rough walls. The results demonstrate that our wall model is able to accurately predict drag for both unseen fully and transitionally rough cases. The predictive capabilities of the wall model are also evaluated in a real flow scenario involving a geometrically complex high-pressure turbine blade with roughness.   

Evaluation of an optimal slip wall model for large-eddy simulation

The slip wall model for large-eddy simulation of wall-bounded turbulent flows is derived from application of a specific filtration to the Navier-Stokes equations (Bose & Moin 2014; Bae et al. 2019). This is in contrast to traditional equilibrium wall models, which are based on phenomenological approximations of the near-wall Reynolds-averaged equations. Recent work has shown that the structure of the near-wall velocity field and the grid convergence behavior in separated flow regimes are better captured by slip wall models than by traditional equilibrium wall models.

However, modeling the slip length has proven difficult in cases of coarsely resolved high-Reynolds-number flows. To probe this issue, a global optimization procedure is applied to find ideal slip lengths through a posteriori simulations. Results are analyzed for a range of Reynolds numbers, subgrid-scale models, and mesh resolutions in a turbulent channel flow, and a slip length scaling law is identified. Flow over the Boeing speed bump is studied to ascertain the impact of pressure gradients on the slip length scaling. Lastly, these scaling laws are applied to the flow over a realistic airframe (NASA CRM-HL) to test their validity against experimental measurements.   

Large eddy simulation of a separated turbulent boundary layer using the multi-timescale wall model

The multi-timescale (MTS) wall model for large eddy simulation (WMLES) has been shown to make accurate wall-stress predictions over a wide range of non-equilibrium conditions (Fowler et al. JFM 2022, 2023). So far, MTS applications have been limited to non-stationary flows with streamwise homogeneity such as steady channel flow with a suddenly applied spanwise pressure gradient, linearly accelerating channel flow, and pulsating channel flow. Here, the MTS wall model is tested for flows with streamwise heterogeneity such as a zero-pressure-gradient flat-plate developing boundary layer over a wide range of Reynolds numbers and a separated boundary layer induced by suction and blowing on the top surface of the domain. A hybrid pseudo-spectral finite difference LES code has been modified to handle developing boundary layers through the use of a modified rescaling-recycling inflow generation method and streamwise periodicity is achieved with the use a fringe region at the end of the domain. Wall-modeled LES results with the MTS model show good agreement with the DNS results of Coleman et al. JFM 2018 and detailed comparisons are made to the standard equilibrium wall model (which also performs well), with particular attention to pressure gradient effects in the separation region.   

Simulating an H-type transitional boundary layer in a coupled NLPSE and WMLES framework with a Falkner-Skan wall model

Numerical simulation of wall-bounded flows poses significant challenges, especially when considering flows that include a combination of laminar, transitional, and turbulent regimes. Failure to resolve the laminar and transitional regions properly can result in substantial errors when predicting mean quantities of interest, such as lift and drag. For wall-modeled large-eddy simulations (WMLES) in particular, it has been observed that the laminar and transitional regions may necessitate 10-100 times more grid points than the turbulent region (Slotnick et al., 2014) to adequately capture the amplification of disturbances that lead to transition. In this work, we will demonstrate that a nonlinear parabolized stability equation solver can be coupled with a WMLES solver to reduce the computational cost of accurately simulating an H-type transitional flat-plate boundary layer, relative to direct numerical simulation. Additionally, we show that the necessary mesh resolution in the laminar portion of the boundary layer can be reduced with the implementation of a Falkner-Skan wall model (Gonzalez et al., 2020).   

Application of multi-timescale wall model to LES of flow over periodic hills (Re = 10,595)

The elevated cost of wall-resolved LES can be relaxed by modeling the near-wall flow in wall-modeled LES (WMLES). The most widely used method is the equilibrium wall model that assumes that the wall stress is in instantaneous equilibrium with the flow in the outer region. This assumption is violated in many instances due to non-equilibrium effects. Recently, a new wall modeling approach was developed, the multi-timescale (MTS) wall model (Fowler et al. JFM 934, 2022) to include different effects of the various timescales affecting the inner region of boundary layers.  In the present study, the MTS and classical equilibrium wall models are applied to the flow over periodic hills, at a bulk Reynolds number Re= 10,595. The flow experiences the influence of separation, reattachment, wall curvature, and a small separation bubble on the windward side of the hill. Particular attention is placed on the effects of pressure gradient that enters in the generalized Moody formula used in the quasi-equilibrium portion of the wall model. The value of the pressure-gradient parameter at the matching location for WMLES is found to be on the order of 1,000 at which point it can have an impact. The performance of the equilibrium and MTS wall models for this flow are assessed by comparison to experimental, DNS, and WRLES results.