arXiv subjects

Heng Xiao

Publications and source records attributed to Heng Xiao.

At least 55 records · Page 3Linked to original sources

arXiv2019

RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned

Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linear eddy viscosity models are intrinsically unable to handle flows with non-equilibrium turbulence. Reynolds stress models, on the other hand, are plagued by their lack of robustness. Recent studies in plane channel flows found that even substituting Reynolds stresses with errors below 0.5% from direct numerical simulation (DNS) databases into RANS equations leads to velocities with large errors (up to 35%). While such an observation may have only marginal relevance to traditional Reynolds stress models, it is disturbing for the recently emerging data-driven models that treat the Reynolds stress as an explicit source term in the RANS equations, as it suggests that the RANS equations with such models can be ill-conditioned. So far, a rigorous analysis of the condition of such models is still lacking. As such, in this work we propose a metric based on local condition number function for a priori evaluation of the conditioning of the RANS equations. We further show that the ill-conditioning cannot be explained by the global matrix condition number of the discretized RANS equations. Comprehensive numerical tests are performed on turbulent channel flows at various Reynolds numbers and additionally on two complex flows, i.e., flow over periodic hills and flow in a square duct. Results suggest that the proposed metric can adequately explain observations in previous studies, i.e., deteriorated model conditioning with increasing Reynolds number and better conditioning of the implicit treatment of Reynolds stress compared to the explicit treatment. This metric can play critical roles in the future development of data-driven turbulence models by enforcing the conditioning as a requirement on these models.

physics.flu-dyn↗

arXiv2018

A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling

Although an increased availability of computational resources has enabled high-fidelity simulations of turbulent flows, the RANS models are still the dominant tools for industrial applications. However, the predictive capabilities of RANS models are limited by potential inaccuracy driven by hypotheses in the Reynolds stress closure. Recently, a Physics-Informed Machine Learning (PIML) approach has been proposed to learn the functional form of Reynolds stress discrepancy in RANS simulations based on available data. It has been demonstrated that the learned discrepancy function can be used to improve Reynolds stresses in different flows where data are not available. However, owing to a number of challenges, the improvements have been demonstrated only in the Reynolds stress prediction but not in the corresponding propagated quantities of interest. In this work, we introduce the procedures toward a complete PIML framework for predictive turbulence modeling, including learning Reynolds stress discrepancy function, predicting Reynolds stresses in different flows, and propagating to mean flow fields. The process of Reynolds stress propagation and predictive accuracy of the propagated velocity field are investigated. To improve the learning-prediction performance, the input features are enriched based on an integrity basis of invariants. The fully developed turbulent flow in a square duct is used as the test case. The discrepancy model is trained on flow fields obtained from several Reynolds numbers and evaluated on a duct flow at a Reynolds number higher than any of the training cases. The predicted Reynolds stresses are propagated to velocity field through RANS equations. Numerical results show excellent predictive performances in both Reynolds stresses and their propagated velocities, demonstrating the merits of the PIML approach in predictive turbulence modeling.

physics.flu-dyn↗

arXiv2018

Turbulence Modeling in the Age of Data

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier--Stokes (RANS) equations. In the past few years, with the availability of large and diverse datasets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. Key principles, achievements and challenges are discussed. A central perspective advocated in this review is that by exploiting foundational knowledge in turbulence modeling and physical constraints, data-driven approaches can yield useful predictive models.

physics.flu-dyn↗

arXiv2018

Quantification of Model Uncertainty in RANS Simulations: A Review

In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier--Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.

physics.flu-dyn↗

arXiv2018

Seeing Permeability From Images: Fast Prediction with Convolutional Neural Networks

Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples, (2) computation of permeability via fluid dynamics simulations, (3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny-Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN, however improvements vary with implemented heterogeneity.

physics.comp-ph↗

arXiv2018

Prediction of Reynolds Stresses in High-Mach-Number Turbulent Boundary Layers using Physics-Informed Machine Learning

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 layers by using an existing DNS database. Specifically, the discrepancy function is first constructed using a DNS training flow and then used to correct RANS-predicted Reynolds stresses under flow conditions different from the DNS. The machine-learning technique is shown to significantly improve RANS-modeled turbulent normal stresses, the turbulent kinetic energy, and the Reynolds-stress anisotropy. Improvements are consistently observed when different training datasets are used. Moreover, a high-dimensional visualization technique and distance metrics are used to provide a priori assessment of prediction confidence based only on RANS simulations. This study demonstrates that the PIML approach is a computationally affordable technique for improving the accuracy of RANS-modeled Reynolds stresses for high-Mach-number turbulent flows when there is a lack of experiments and high-fidelity simulations.

physics.flu-dyn↗

arXiv2018

Particle dynamics in self-generated dunes over a range of hydraulic and sediment transport conditions using LES--DEM

Direct measurement of vertical and longitudinal sediment fluxes on migrating sandy bedforms are extremely difficult to perform in both the field and laboratory. In this study we use the LES--DEM (large eddy simulation--discrete element method) solver SediFoam to examine the individual particle motions and resulting fluxes in a domain of self-generated dunes. In SediFoam, the motions of, and collisions among, the sediment grains as well as their interactions with surrounding turbulent flows are resolved. The numerical simulations are performed over a range of transport settings, spanning bedform inception through washout conditions, to examine the individual particle dynamics. The space-time evolution of dune surfaces is demonstrated. The self-generated dunes are stable at relatively low Reynolds numbers, but then become increasingly unstable at higher Reynolds numbers; eventually washing out as the number of bypass grains and particles in suspension increase. Data from the simulation are used to examine the vertical entrainment rate of particles and the fractionation of total sediment load into bed and suspended fractions as a function of transport conditions. The study also compares the sediment transport rate obtained using the bedform geometry and celerity to the true transport rate at different transport stages.

physics.geo-ph↗

arXiv2018

Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields

Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the vicinity of the feature. Particularly, they rely on definition of suitable criteria (i.e. point-based or neighborhood-based derived properties) and proper selection of thresholds. For instance, among other techniques, vortex identification can be done through computing the Q-criterion or by considering the center of looping streamlines. However, these methods rely on creative visualization of physical idiosyncrasies of specific features and flow regimes, making them non-universal and requiring significant effort to develop. Here we present a physics-based, data-driven method capable of identifying any flow feature it is trained to. We use convolutional neural networks, a machine learning approach developed for image recognition, and adapt it to the problem of identifying flow features. The method was tested using mean flow fields from numerical simulations, where the recirculation region and boundary layer were identified in a two-dimensional flow through a convergent-divergent channel, and the horseshoe vortex was identified in three-dimensional flow over a wing-body junction. The novelty of the method is its ability to identify any type of feature, even distinguish between similar ones, without the need to explicitly define the physics (i.e. through development of suitable criterion and tunning of threshold). This provides a general method and removes the large burden placed on identifying new features. We expect this method can supplement existing techniques and allow for more automatic and discerning feature detection. The method can be easily extended to time-dependent flows, where it could be particularly impactful.

physics.flu-dyn↗

arXiv2017

Are Discrepancies in RANS Modeled Reynolds Stresses Random?

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 regression--prediction procedure indicates that, to a large extent, the discrepancies in the modeled Reynolds stresses can be explained by the mean flow feature, and thus they are universal quantities that can be extrapolated from one flow to another, at least among different flows sharing the same characteristics such as separation. This finding has profound implications to the future development of RANS models, opening up new possibilities for data-driven predictive turbulence modeling.

physics.flu-dyn↗

arXiv2017

Representation of Reynolds Stress Perturbations with Application in Machine-Learning-Assisted Turbulence Modeling

Numerical simulations based on Reynolds-Averaged Navier--Stokes (RANS) equations are widely used in engineering design and analysis involving turbulent flows. However, RANS simulations are known to be unreliable in many flows of engineering relevance, which is largely caused by model-form uncertainties associated with the Reynolds stresses. Recently, a machine-learning approach has been proposed to assist RANS modeling by building a functional mapping from mean flow features to discrepancies in RANS modeled Reynolds stresses as compared to high-fidelity data. However, it remains a challenge to represent discrepancies in the Reynolds stress eigenvectors in machine learning due to the requirements of spatial smoothness, frame-independence, and realizability. In this work, we propose three schemes for representing perturbations to the eigenvectors of RANS modeled Reynolds stresses: (1) discrepancy-based Euler angles, (2) direct-rotation-based Euler angles, and (3) unit quaternions. We compare these metrics by performing a priori and a posteriori tests on two canonical flows: fully developed turbulent flows in a square duct and massively separated flows over periodic hills. The results demonstrate that the direct-rotation-based Euler angles representation lacks spatial smoothness while the discrepancy-based Euler angles representation lacks frame-independence, making them unsuitable for being used in machine-learning-assisted turbulence modeling. In contrast, the representation based on unit quaternion satisfies all the requirements stated above, and thus it is an ideal choice in representing the perturbations associated with the eigenvectors of Reynolds stress tensors. This finding has clear importance for uncertainty quantification and machine learning in turbulence modeling and for data-driven computational mechanics in general.

physics.flu-dyn↗

arXiv2017

Investigating the Settling Dynamics of Cohesive Silt Particles With Particle-Resolving Simulations

The settling of cohesive sediment is ubiquitous in aquatic environments. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. While it is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond number, particle size distribution), little is known about the exact influence of these characteristics on the cohesive behaviors. In the present work, three-dimensional settling process is investigated numerically by using CFD--DEM (Computational Fluid Dynamics--Discrete Element Method). The inter-particle collision force, the van der Waals force, and the fluid--particle interaction forces are considered. The numerical model is used to simulate the hindered settling process of silt based on the experimental setup in the literature. The results obtained in the simulations, including the structural densities of the beds, the characteristic lines, and the particle terminal velocity, are in good agreement with the experimental observations in the literature. To the authors' knowledge, this is the first time that the influences of non-dimensional Bond number and particle polydispersity on the structural densities of silt beds have been investigated separately. The results demonstrate that the cohesive behavior of silt in the settling process is attributed to both the cohesion among silt particles themselves and the particle polydispersity. To guide to the macro-scale modeling of cohesive silt sedimentation, the collision frequency functions obtained in the numerical simulations are also presented based on the micromechanics of particles. The results obtained by using CFD--DEM indicate that the binary collision theory over-estimated the particle collision frequency in the flocculation process at high solid volume fraction.

cond-mat.soft↗

arXiv2017

Propagation of Input Uncertainty in Presence of Model-Form Uncertainty: A Multi-fidelity Approach for CFD Applications

Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for CFD applications. A particular obstacle for uncertainty quantifications in CFD problems is the large model discrepancies associated with the CFD models used for uncertainty propagation. Neglecting or improperly representing the model discrepancies leads to inaccurate and distorted uncertainty distribution for the Quantities of Interest. High-fidelity models, being accurate yet expensive, can accommodate only a small ensemble of simulations and thus lead to large interpolation errors and/or sampling errors; low-fidelity models can propagate a large ensemble, but can introduce large modeling errors. In this work, we propose a multi-model strategy to account for the influences of model discrepancies in uncertainty propagation and to reduce their impact on the predictions. Specifically, we take advantage of CFD models of multiple fidelities to estimate the model discrepancies associated with the lower-fidelity model in the parameter space. A Gaussian process is adopted to construct the model discrepancy function, and a Bayesian approach is used to infer the discrepancies and corresponding uncertainties in the regions of the parameter space where the high-fidelity simulations are not performed. The proposed multi-model strategy combines information from models with different fidelities and computational costs, and is of particular relevance for CFD applications, where a hierarchy of models with a wide range of complexities exists. Several examples of relevance to CFD applications are performed to demonstrate the merits of the proposed strategy. Simulation results suggest that, by combining low- and high-fidelity models, the proposed approach produces better results than what either model can achieve individually.

physics.comp-ph↗

arXiv2017

A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. Recently, a data-driven turbulence modeling approach via machine learning has been proposed to predict the Reynolds stress anisotropy of a given flow based on high fidelity data from closely related flows. In this work, the closeness of different flows is investigated to assess the prediction confidence a priori. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. The flow over periodic hills at Re=10595 is used as the test set and seven flows with different configurations are individually used as training set. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of the data source and to assess the prediction confidence for data-driven turbulence modeling.

physics.comp-ph↗

arXiv2017

A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been proposed as a promising alternative to the traditional approaches of turbulence model development. In this work we propose a data-driven, physics-informed machine learning approach for predicting discrepancies in RANS modeled Reynolds stresses. The discrepancies are formulated as functions of the mean flow features. By using a modern machine learning technique based on random forests, the discrepancy functions are first trained with benchmark flow data and then used to predict Reynolds stresses discrepancies in new flows. The method is used to predict the Reynolds stresses in the flow over periodic hills by using two training flow scenarios of increasing difficulties: (1) the flow in the same periodic hills geometry yet at a lower Reynolds number, and (2) the flow in a different hill geometry with a similar recirculation zone. Excellent predictive performances were observed in both scenarios, demonstrating the merits of the proposed method. Improvement of RANS modeled Reynolds stresses enabled by the proposed method is an important step towards predictive turbulence modeling, where the ultimate goal is to predict the quantities of interest (e.g., velocity field, drag, lift) more accurately by solving RANS equations with the Reynolds stresses obtained therefrom.

physics.flu-dyn↗

arXiv2016

Realistic Representation of Grain Shapes in CFD--DEM Simulations of Sediment Transport: A Bonded-Sphere Approach

Development of algorithms and growth of computational resources in the past decades have enabled simulations of sediment transport processes with unprecedented fidelities. The Computational Fluid Dynamics--Discrete Element Method (CFD--DEM) is one of the high-fidelity approaches, where the motions of and collisions among the sediment grains as well as their interactions with surrounding fluids are resolved. In most DEM solvers the particles are modeled as soft spheres due to computational efficiency and implementation complexity considerations, although natural sediments are usually mixture of non-spherical particles. Previous attempts to extend sphere-based DEM to treat irregular particles neglected fluid-induced torques on particles, and the method lacked flexibility to handle sediments with an arbitrary mixture of particle shapes. In this contribution we proposed a simple, efficient approach to represent common sediment grain shapes with bonded spheres, where the fluid forces are computed and applied on each sphere. The proposed approach overcomes the aforementioned limitations of existing methods and has improved efficiency and flexibility over existing approaches. We use numerical simulations to demonstrate the merits and capability of the proposed method in predicting the falling characteristics, terminal velocity, threshold of incipient motion, and transport rate of natural sediments. The simulations show that the proposed method is a promising approach for faithful representation of natural sediment, which leads to accurate simulations of their transport dynamics. The proposed method also opens the possibility for first-principle-based simulations of the flocculation and sedimentation dynamics of cohesive sediments. Elucidation of these physical mechanisms can provide much needed improvement on the prediction capability and physical understanding of muddy coast dynamics.

physics.comp-ph↗

arXiv2016

Sediment Micromechanics in Sheet Flows Induced by Asymmetric Waves: A CFD-DEM Study

Understanding the sediment transport in oscillatory flows is essential to the investigation of the overall sediment budget for coastal regions. This overall budget is crucial for the prediction of the morphological change of coastline in engineering applications. Since the sediment transport in oscillatory flows is dense particle-laden flow, appropriate modeling of the particle interaction is critical. Although traditional two-fluid approaches have been applied to the study of sediment transport in oscillatory flows, the approaches do not resolve the interaction of the particles. Particle-resolved modeling of sediment transport in oscillatory flows and the study of micromechanics of sediment particles are still lacking. In this work, a parallel CFD-DEM solver that can resolve the inter-particle collision is applied to study the granular micromechanics of sediment particles in oscillatory flows. The results obtained from the CFD-DEM solver are validated by using the experimental data of coarse and medium sands. The comparison with experimental results suggests that the flow velocity, the sediment flux and the net sediment transport rate predicted by are satisfactory. Moreover, the micromechanic quantities of the sediment bed are presented in detail, including Voronoi concentration, coordination number, and particle interaction force. It is demonstrated that variation of these micromechanic quantities at different phases in the oscillatory cycle is significant, which is due to different responses of the sediment bed. To investigate the structural properties of the sediment bed, the correlation of the Voronoi volume fraction and coordination number are compared to the results from the fluidized bed simulations. The consistency in the comparison indicates the structural micromechanics of sediment transport and fluidized bed are similar despite the differences in flow patterns.

physics.comp-ph↗

arXiv2016

Quantifying Model Form Uncertainty in RANS Simulation of Wing-Body Junction Flow

Wing-body junction flows occur when a boundary layer encounters an airfoil mounted on the surface. The corner flow near the trailing edge is challenging for the linear eddy viscosity Reynolds Averaged Navier-Stokes (RANS) models, due to the interaction of two perpendicular boundary layers which leads to highly anisotropic Reynolds stress at the near wall region. Recently, Xiao et al. proposed a physics-informed Bayesian framework to quantify and reduce the model-form uncertainties in RANS simulations by utilizing sparse observation data. In this work, we extend this framework to incorporate the use of wall function in RANS simulations, and apply the extended framework to the RANS simulation of wing-body junction flow. Standard RANS simulations are performed on a 3:2 elliptic nose and NACA0020 tail cylinder joined at their maximum thickness location. Current results show that both the posterior mean velocity and the Reynolds stress anisotropy show better agreement with the experimental data at the corner region near the trailing edge. On the other hand, the prior velocity profiles at the leading edge indicate the restriction of uncertainty space and the performance of the framework at this region is less effective. By perturbing the orientation of Reynolds stress, the uncertainty range of prior velocity profiles at the leading edge covers the experimental data. It indicates that the uncertainty of RANS predicted velocity field is more related to the uncertainty in the orientation of Reynolds stress at the region with rapid change of mean strain rate. The present work not only demonstrates the capability of Bayesian framework in improving the RANS simulation of wing-body junction flow, but also reveals the major source of model-form uncertainty for this flow, which can be useful in assisting RANS modeling.

physics.flu-dyn↗

arXiv2016

CFD-DEM Simulations of Current-Induced Dune Formation and Morphological Evolution

Understanding the fundamental mechanisms of sediment transport, particularly those during the formation and evolution of bedforms, is of critical scientific importance and has engineering relevance. Traditional approaches of sediment transport simulations heavily rely on empirical models, which are not able to capture the physics-rich, regime-dependent behaviors of the process. With the increase of available computational resources in the past decade, CFD-DEM (computational fluid dynamics-discrete element method) has emerged as a viable high-fidelity method for the study of sediment transport. However, a comprehensive, quantitative study of the generation and migration of different sediment bed patterns using CFD-DEM is still lacking. In this work, current-induced sediment transport problems in a wide range of regimes are simulated, including 'flat bed in motion', `small dune', `vortex dune' and suspended transport. Simulations are performed by using SediFoam, an open-source, massively parallel CFD-DEM solver developed by the authors. This is a general-purpose solver for particle-laden flows tailed for particle transport problems. Validation tests are performed to demonstrate the capability of CFD-DEM in the full range of sediment transport regimes. Comparison of simulation results with experimental and numerical benchmark data demonstrates the merits of CFD-DEM approach. In addition, the improvements of the present simulations over existing studies using CFD-DEM are presented. The present solver gives more accurate prediction of sediment transport rate by properly accounting for the influence of particle volume fraction on the fluid flow. In summary, this work demonstrates that CFD-DEM is a promising particle-resolving approach for probing the physics of current-induced sediment transport.

physics.flu-dyn↗