The prediction of aircraft aerodynamic quantities of interest remains among the most pressing challenges for computational fluid dynamics. The aircraft aerodynamics are inherently turbulent with mean-flow three-dimensionality, often accompanied by laminar-to-turbulent transition, flow separation, secondary flow motions at corners, and shock wave formation, to name a few. However, the most widespread wall models are built upon the assumption of statistically-in-equilibrium wall-bounded turbulence and do not faithfully account for the wide variety of flow conditions described above. This raises the question of how to devise models capable of accounting for such a vast and rich collection of flow physics in a feasible manner. In this work, we propose tackling the wall-modeling challenge by devising the flow as a collection of building blocks, whose information enables the prediction of the stress as the wall. The model relies on the assumption that simple canonical flows contain the essential flow physics to devise accurate models. Three types of building block units were used to train the model: turbulent channel flows, turbulent ducts and turbulent boundary layers with separation. This limited training set will be extended in future versions of the model. The approach is implemented using two interconnected artificial neural networks: a classifier, which identifies the contribution of each building block in the flow; and a predictor, which estimates the wall stress via non-linear combinations of building-block units. The output of the model is accompanied by the confidence in the prediction. The latter value aids the detection of areas where the model underperforms, such as flow regions that are not representative of the building blocks used to train the model. The model is validated in a unseen case representative of external aerodynamic applications: the NASA Juncture Flow Experiment.
A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows}, Phys. Rev. Fluids, 2017, 2(8), 084604] and derive an eddy conductivity closure for wall-modeled large-eddy simulation of high-speed flows. We show that while the semi-local scaling does not collapse high-speed direct numerical simulation (DNS) data, the resulting eddy conductivity and the wall model work fairly well. The paper attempts to answer the following…
Kinematic aspects of flow separation in external aerodynamics are investigated in the Lagrangian frame. Specifically, the initial motion of upwelling fluid material from the wall is related to the long-term attracting manifolds in the flow field. While the short-time kinematics are governed by the formation of a material spike upstream of the zero-skin-friction point and ejection of particles in direction of the asymptotic separation line, the trajectories of the fluid tracers are guided by attracting ridges in the finite-time Lyapunov exponents once they leave the vicinity of the wall. The wa…
We investigate the performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow. We characterize the errors in the prediction of mean velocity profiles and pressure coefficient for three different locations over the aircraft: the upstream region of the fuselage, the wing-body juncture, and the wing-body juncture close to the trailing-edge. The last two locations are characterized by strong mean-flow three-dimensionality and separation. The message conveyed by our error analysis is that WMLES performs as expected in regions where the flow resembles a zero-pressure-gradien…
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 sc…
A unified subgrid-scale (SGS) and wall model for large-eddy simulation (LES) is proposed by devising the flow as a collection of building blocks that enables the prediction of the eddy viscosity. The core assumption of the model is that simple canonical flows contain the essential physics to provide accurate predictions of the SGS tensor in more complex flows. The model is constructed to predict zero-pressure-gradient wall-bounded turbulence, adverse pressure gradient effects, separation and laminar flow. The approach is implemented using a Bayesian classifier, which identifies the contributio…
Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in urban areas. Unfortunately, simulating high Reynolds number flows over complex terrain is still a big challenge. Therefore, we present a simplified version of the wall modeled immersed boundary method by Chester et al. (J. Comput. Phys. 2007; 225: 427-448). By preventing the extrapolation and iteration steps in the original method, the proposed approach is …
A promising and cost-effective method for numerical simulation of high Re wall-bounded flows is wall-modeled large-eddy simulation. Most wall models are formulated from the Reynolds-averaged Navier-Stokes equations (RANS). These RANS-based wall models are calibrated using mean turbulence data and make no use of the current vast knowledge on turbulent flow structure. Moreover, RANS-based models are limited to predicting the mean velocity profile, and the mean wall shear stress. Using the knowledge of the wall-normal self-similarity of high-$Re_τ$ wall-bounded turbulent flows, we present a coupl…
We study the sensitivity of wall model input variables to the modeling choices of the outer LES. This work is motivated by sensitivities observed in dynamic slip wall models. These dynamic wall models use variables from the near-wall LES solution as inputs to predict the wall stress without relying on a priori coefficients or equilibrium assumption. Mitigating the sensitivities in the wall model inputs allows development of robust dynamic wall models. The effects of SGS model, boundary condition type, numerics, and mesh topology are assessed through a series of WMLES calculations of turbulent …
The accuracy and computational cost of a large eddy simulation are highly dependent on the computational grid. Building optimal grids manually from a priori knowledge is not feasible in most practical use cases; instead, solution-adaptive strategies can provide a robust and cost-efficient method to generate a grid with the desired accuracy. We adapt the grid-adaptation algorithm developed by Toosi and Larsson to a Discontinuous Galerkin Spectral Elements Method (DGSEM) and show its potential on fully unstructured grids. The core of the method is the computation of the estimated modeling residu…
Motivated by the needs of wall modeled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier-Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness eff…
High-fidelity wall-resolved large-eddy simulations (LES) are utilized to investigate the flow-physics of small-amplitude pitch oscillations of an airfoil at Re = 100,000. The investigation of the unsteady phenomenon is done in the context of natural laminar flow airfoils, which can display sensitive dependence of the aerodynamic forces on the angle of attack in certain "off-design" conditions. The dynamic range of the pitch oscillations is chosen to be in this sensitive region. Large variations of the transition point on the suction-side of the airfoil are observed throughout the pitch cycle r…
We conducted WMLES to examine the performance of a simple and widely used ODE-based equilibrium wall model in a spatially-developing 3D TBL inside a bent square duct (Schwarz and Bradshaw 1994) and 3D separated flows behind a skewed bump (Ching et al. 2018a,b; Ching and Eaton 2019). From the square duct simulation, the mean velocity profiles and crossflow angles in the outer region were predicted with high accuracy for all the considered mesh resolutions. Some disagreement was observed in the crossflow angles in the bend region where the non-equilibrium effect is most significant. Also, the si…
Harvard University（哈佛大学）；California Institute of Technology（加州理工学院）；ETH Zurich（苏黎世联邦理工学院）
The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulation…
The predictive accuracy of wall-modeled large eddy simulation is studied by systematic simulation campaigns of turbulent channel flow. The effect of wall model, grid resolution and anisotropy, numerical convective scheme and subgrid-scale modeling is investigated. All of these factors affect the resulting accuracy, and their action is to a large extent intertwined. The wall model is of the wall-stress type, and its sensitivity to location of velocity sampling, as well as law of the wall's parameters is assessed. For efficient exploration of the model parameter space (anisotropic grid resolutio…
DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Prediction
Massachusetts Institute of Technology（麻省理工学院）；Technical University of Munich（慕尼黑技术大学）；Department of Mechanical Engineering（机械工程系）；Department of Computer Science（计算机科学系）
We investigate the role of the bulk eddy-viscosity variation on the well-known log-layer mismatch problem. An analysis of the mean momentum-balance shows that the modeled stress term close to the wall can dominate because of the bulk eddy-viscosity. Consequently, the momentum-balance equation lacks a degree-of-freedom and the mean velocity conforms to an incorrect profile to satisfy the momentum-balance. We show that zonal enforcement of the target mass flow-rate can be an effective strategy to introduce an additional degree of freedom to the mean momentum-balance, which led to a significant r…
One of the greatest challenges to using large-eddy simulations (LES) in engineering applications is the large number of grid points required near walls. To mitigate this issue, researchers often couple LES with a simplified model of the flow close to the wall, known as the wall model. One feature common to most wall models is that the first few (about 3) grid points must be located below the inviscid log-layer, and the grid must have near-isotropic resolution near the wall. Hence, wall-modeled LES may still require a large number of grid points in both the wall-normal and span-wise directions.…
This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations (DNS) are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW …
We present applications of modal analysis techniques to study, model, and control canonical aerodynamic flows. To illustrate how modal analysis techniques can provide physical insights in a complementary manner, we selected four fundamental examples of cylinder wakes, wall-bounded flows, airfoil wakes, and cavity flows. We also offer brief discussions on the outlook for modal analysis techniques, in light of rapid developments in data science.
The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number Re=2000 for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls (Case A), motion of a wall in its plane along its diagonal (Case B1), motion of two perpendicular walls outward the common edge (Case B2), and the parallel cavity walls in motion either in parallel directions (Case B3) or in opposite direc…
A stochastic modeling framework to generate 2-D rough-wall high-Reynolds-number turbulent boundary layers
Saint Anthony Falls Laboratory, University of Minnesota（明尼苏达大学圣安东尼瀑布实验室）；Department of Civil, Environmental, and Geo-Engineering, University of Minnesota（明尼苏达大学土木、环境与地球工程系）
We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning (MARL). The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall along the computational grid points. The model utilizes a wall eddy-viscosity formulation as the boundary condition, which is shown to provide better predictions of the mean velocity field, rather than the typical wall-shear stress formulation. Each agent receives states based on local instantaneous flow quantities at an off-wa…
