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 channels. Probability density functions are computed from planes of the WMLES solutions at a wall-normal sampling height and are used as a metric for sensitivity. Sensitivity to SGS model is alleviated when the fraction of total wall stress carried by the SGS model is held constant. Use of hexagonal close-packed grids mitigated numerical sensitivities.
In the turbulence modeling community, significant efforts have been made to quantify the uncertainties in the Reynolds-Averaged Navier--Stokes (RANS) models and to improve their predictive capabilities. Of crucial importance in these efforts is the understanding of the discrepancies in the RANS modeled Reynolds stresses. However, to what extent these discrepancies can be predicted or whether they are completely random remains a fundamental open question. In this work we used a machine learning algorithm based on random forest regression to predict the discrepancies. The success of the regressi…
In the present work, an attempt is made to map the sensitivity of the existing zero pressure gradient (ZPG) turbulent boundary layer (TBL) wall-pressure spectrum models with different TBL parameters, and eventually, with different Reynolds Averaged Navier Stokes (RANS) turbulence models, simulated in OpenFOAM and ANSYS Fluent solvers. This study will help future researchers to choose a particular RANS turbulence model vis-à-vis a particular wall-spectrum model in order to obtain a reasonably accurate wind tunnel result predicting capability. First, the best-predicting pressure spectrum models …
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…
A hybrid RANS/LES framework is developed based on a recently proposed Improved Delayed Detached Eddy Simulation (IDDES) model combined with a variant of recycling and rescaling method of generating inflow turbulence. This framework was applied to investigate spatially developing flat plate turbulent boundary layer up to momentum thickness Reynolds number, $R_θ = 31000$ and the results are compared with the available experimental data. Good agreement was obtained for the global quantities such as mean velocity and skin friction at all momentum thickness Reynolds numbers considered. The trends o…
This paper aims at extending the code verification methodology to high-order accurate scheme implementations on curved wall-bounded domains as well as for realistic turbulent flows such as the flat plate boundary layer modelled by the Reynolds-averaged Navier-Stokes (RANS) equations. Two new manufactured solutions (MSs) are introduced with demonstrated ability to verify the treatment of slip and no-slip boundary conditions in high-order frameworks on curved domains. These MSs serve as well to discuss the impact of the method of computation of boundary normals on the order of accuracy (OOA) of …
Density-based topology optimization for turbulent fluid flow using the standard k-epsilon RANS model with wall-functions imposed through an implicit wall penalty formulation
A new slow growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow growth modeling concepts to complex boundary layer flows. As in previous slow growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the …
Predictive simulation of many complex flows requires moving beyond Reynolds-averaged Navier-Stokes (RANS) based models to representations resolving at least some scales of turbulence in at least some regions of the flow. To resolve turbulence where necessary while avoiding the cost of performing large eddy simulation (LES) everywhere, a broad range of hybrid RANS/LES methods have been developed. While successful in some situations, existing methods exhibit a number of deficiencies which limit their predictive capability in many cases of interest, for instance in many flows involving smooth wal…
This work determines the inaccuracy of using Reynolds averaged Navier Stokes (RANS) turbulence models in transition to turbulent flow regimes by predicting the model-based discrepancies between RANS and large eddy simulation (LES) models and then incorporates the capabilities of machine learning algorithms to characterize the discrepancies which are defined as a function of mean flow properties of RANS simulations. First, three-dimensional CFD simulations using k-omega Shear Stress Transport (SST) and dynamic one-equation subgrid-scale models are conducted in a wall-bounded channel containing …
University of Notre Dame（圣母大学）；Missouri University of Science and Technology（密苏里科技大学）；Virginia Tech（弗吉尼亚理工大学）
Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonical incompressible flows. However, its performance on high-Mach-number flows is still not clear. In this work we use the PIML approach to predict the discrepancies in RANS modeled Reynolds stresses in high-Mach-number flat-plate turbulent boundary lay…
A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by artificial neural network (ANN) based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model for the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than 18%. In an a posteriori analysis, detailed compari…
Reliably predictive simulation of complex flows requires a level of model sophistication and robustness exceeding the capabilities of current Reynolds-averaged Navier-Stokes (RANS) models. The necessary capability can often be provided by well-resolved large eddy simulation (LES), but, for many flows of interest, such simulations are too computationally intensive to be performed routinely. In principle, hybrid RANS/LES (HRL) models capable of transitioning through arbitrary levels of modeled and resolved turbulence would ameliorate both RANS deficiencies and LES expense. However, these HRL app…
The goal of this dissertation is to investigate the PANS model capabilities in providing significant improvement over RANS predictions at slightly higher computational expense and producing LES quality results at significantly lower computational cost. The objectives of this study are: (i) investigate the model fidelity at a fixed level of scale resolution (Generation1-PANS/G1-PANS) for smooth surface separation, (ii) Derive the PANS closure model in regions of resolution variation (Generation2-PANS/G2-PANS), and (iii) Validate G2-PANS model for attached and separated flows. The separated flow…
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…
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…
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…
The main objective of this work is to develop a unified framework that can be used as a lens to quantitatively assess and augment a wide range of coarse-grained models of turbulence, viz. large eddy simulations (LES), hybrid Reynolds-averaged/LES methods and wall-modeled (WM)LES. Taking a turbulent channel flow as an example, optimality is assessed in the wall-resolved limit, the hybrid RANS/LES limit and the WMLES limit, via projections at different resolutions suitable for these approaches. These optimal a priori estimates are shown to have similar characteristics to existing a posteriori so…
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.…
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…
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…
Modelling flow and acoustics in a constricted duct at low Mach numbers is important for investigating many physiological phenomena such as phonation, generation of arterial murmurs, and pulmonary conditions involving airway obstruction. The objective of this study is to validate computational fluid dynamics (CFD) and computational aero-acoustics (CAA) simulations in a constricted tube at low Mach numbers. Different turbulence models were employed to simulate the flow field. Models included Reynolds Average Navier-Stokes (RANS), Detached eddy simulation (DES) and Large eddy simulation (LES). Th…
A method for inverse design of horizontal axis wind turbines (HAWTs) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds Averaged Navier Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM); this approach is referred to as RANS/ADM. The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; …
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…
A fully discrete formalism is introduced to perform stability analysis of a turbulent compressible flow whom dynamics is modeled with the Reynolds-Averaged Navier-Stokes (RANS) equations. The discrete equations are linearized using finite differences and the Jacobian is computed using repeated evaluation of the residuals. Stability of the flow is assessed solving an eigenvalue problem. The sensitivity gradients which indicate regions of the flow where a passive control device could stabilize the unstable eigenvalues are defined within this fully discrete framework. Second order finite differen…
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 …
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…
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 …
