Physics-constrained Random Forests for Turbulence Model Uncertainty Estimation

To achieve virtual certification for industrial design, quantifying the uncertainties in simulation-driven processes is crucial. We discuss a physics-constrained approach to account for epistemic uncertainty of turbulence models. In order to eliminate user input, we incorporate a data-driven machine learning strategy. In addition to it, our study focuses on developing an a priori estimation of prediction confidence when accurate data is scarce.Comment: Workshop on Synergy of Scientific and Machine Learning Modeling, SynS & ML ICM

Physically constrained eigenspace perturbation for turbulence model uncertainty estimation

Aerospace design is increasingly incorporating Design Under Uncertainty based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in Computational Fluid Dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier-Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the Eigenspace Perturbation Framework (EPF), involving perturbations to the modeled Reynolds Stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in depth Verification and Validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.Comment: The following article has been submitted to Physics of Fluid

Improved self-consistency of the Reynolds stress tensor eigenspace perturbation for Uncertainty Quantification

The limitations of turbulence closure models in the context of Reynolds-averaged NavierStokes (RANS) simulations play a significant part in contributing to the uncertainty of Computational Fluid Dynamics (CFD). Perturbing the spectral representation of the Reynolds stress tensor within physical limits is common practice in several commercial and open-source CFD solvers, in order to obtain estimates for the epistemic uncertainties of RANS turbulence models. Recent research revealed, that there is a need for moderating the amount of perturbed Reynolds stress tensor tensor to be considered due to upcoming stability issues of the solver. In this paper we point out that the consequent common implementation can lead to unintended states of the resulting perturbed Reynolds stress tensor. The combination of eigenvector perturbation and moderation factor may actually result in moderated eigenvalues, which are not linearly dependent on the originally unperturbed and fully perturbed eigenvalues anymore. Hence, the computational implementation is no longer in accordance with the conceptual idea of the Eigenspace Perturbation Framework. We verify the implementation of the conceptual description with respect to its self-consistency. Adequately representing the basic concept results in formulating a computational implementation to improve self-consistency of the Reynolds stress tensor perturbationComment: The following article has been submitted to AIP/Physics of Fluid

Evaluation of physics constrained data-driven methods for turbulence model uncertainty quantification

In order to achieve a virtual certification process and robust designs for turbomachinery, the uncertainty bounds for Computational Fluid Dynamics have to be known. The formulation of turbulence closure models implies a major source of the overall uncertainty of Reynolds-averaged Navier-Stokes simulations. We discuss the common practice of applying a physics constrained eigenspace perturbation of the Reynolds stress tensor in order to account for the model form uncertainty of turbulence models. Since the basic methodology often leads to overly generous uncertainty estimates, we extend a recent approach of adding a machine learning strategy. The application of a data-driven method is motivated by striving for the detection of flow regions, which are prone to suffer from a lack of turbulence model prediction accuracy. In this way any user input related to choosing the degree of uncertainty is supposed to become obsolete. This work especially investigates an approach, which tries to determine an a priori estimation of prediction confidence, when there is no accurate data available to judge the prediction. The flow around the NACA 4412 airfoil at near-stall conditions demonstrates the successful application of the data-driven eigenspace perturbation framework. Furthermore, we especially highlight the objectives and limitations of the underlying methodology

Applicability of machine learning in uncertainty quantification of turbulence models

The aim of this work is to apply and analyze machine learning methods for uncertainty quantification of turbulence models. In this work we investigate the classical and data-driven variants of the eigenspace perturbation method. This methodology is designed to estimate the uncertainties related to the shape of the modeled Reynolds stress tensor in the Navier-Stokes equations for Computational Fluid Dynamics (CFD). The underlying methodology is extended by adding a data-driven, physics-constrained machine learning approach in order to predict local perturbations of the Reynolds stress tensor. Using separated two-dimensional flows, we investigate the generalization properties of the machine learning models and shed a light on impacts of applying a data-driven extension

Applicability of machine learning in uncertainty quantification of turbulence models

The aim of this work is to apply and analyze machine learning methods for uncertainty quantification of turbulence models. In this work we investigate the classical and data-driven variants of the eigenspace perturbation method. This methodology is designed to estimate the uncertainties related to the shape of the modeled Reynolds stress tensor in the Navier-Stokes equations for Computational Fluid Dynamics (CFD). The underlying methodology is extended by adding a data-driven, physics-constrained machine learning approach in order to predict local perturbations of the Reynolds stress tensor. Using separated two-dimensional flows, we investigate the generalization properties of the machine learning models and shed a light on impacts of applying a data-driven extension

Assessment of data-driven Reynolds stress tensor perturbations for uncertainty quantification of RANS turbulence models

In order to achieve a more simulation-based design and certification process of jet engines in the aviation industry, the uncertainty bounds for computational fluid dynamics have to be known. This work shows the application of machine learning to support the quantification of epistemic uncertainties of turbulence models. The underlying method in order to estimate the uncertainty bounds is based on eigenspace perturbations of the Reynolds stress tensor in combination with random forests

A comparison of methods for introducing synthetic turbulence

Scale resolving simulations are indispensable to provide in-depth knowledge of turbulence in order to improve turbulence modelling approaches for turbomachinery design processes. However, the in flow conditions of spatially evolving turbulent flow simulations are of utmost significance for the accurate reproduction of physics especially for Large Eddy Simulations. The present paper compares two approaches to introduce synthetically generated velocity fluctuations for Large Eddy Simulations: an in flow boundary condition and a source term formulation. In case of the boundary condition the velocity fluctuations are added to the mean velocity components at the inlet panel of the computational domain. The source term formulation uses an additional volume term in the momentum equation to add the fluctuating velocity field at an arbitrary location. The functionality of these methods in combination with the synthetic generation of fluctuations is validated in the generic test case of spatially decaying homogeneous isotropic turbulence. Furthermore, the spatial variation and anisotropy of turbulent statistics in a turbulent boundary layer as well as the development length of the different combinations, needed to reach a fully developed flow, are analysed for a turbulent channel flow

Improved Impingement Cooling Using Flow Enhancing Structural Elements

This investigation is part of a study seeking to improve impingement cooling in internal combustion turbomachinery using flow modifying elements within the cooling channel. A simplified geometry of a jet impingement cooling configuration is chosen for well-defined numerical simulations and complementary experiments. The generic cooling channel setup features of a square cross-section that is closed on one end and is supplied by 9 inline jets that are directed toward a heated plate. Using RANS, the presence of an arc-conic placed immediately downstream of each jet nozzle was found to increase the heat transfer and prompted the present experimental study to elucidate the fluid mechanical mechanisms leading to the improved performance. Central to the study is an extensive data base of time-resolved 2d-2c PIV data for both channel configurations, with and without installed arc-conics, on a field of view that simultaneously captures up to 3 jets. Using two-point correlations, an interaction or modal coupling between the jets is not observed, suggesting that each jet may be treated individually. The arc-conics tend to stabilize the jets by capturing and redirecting the bulk cross-flow, thereby increasing the self-similarity of the jet impingement pattern, in particular toward the channel exit. Modal analysis using both snap-shot POD and spectral POD (SPOD) capture the dynamics of the flow, ideally to achieve a dimensionality reduction for reduced order modeling. However, the fully turbulent flow with highly stochastic dynamics exhibits only weak spatial or temporal signatures, with the energy content spread across a large number of modes. Among the dominant modes are pulsations of the jet onto the surface along with spanwise sweeping motions. The stabilization of the jet by the arc-conic results in a more defined impingement flow with the signature of the jet's shear layer visible in the higher modes of the energy spectrum and is considered the main mechanism of improved heat transfer

Experimental and Numerical Investigation of a Multi-Jet Impingement Cooling Configuration

In order to protect turbine blades from thermal damage or thermally induced aging, internal impingement cooling has found common use throughout engine design, both in stationary gas turbines as well as aircraft engines, but also finds applications in other areas requiring cooling. The present investigation is focused on a generic impingement cooling configuration that can be easily modelled with computational fluid dynamics (CFD) and at the same time can be studied in detail experimentally. The acquired experimental data can be directly used for the validation of the CFD simulations, ultimately allowing their application in more complex, realistic configurations where experimental investigations become prohibitively expensive or otherwise impossible. The investigated configuration consists of 9 evenly spaced jets of Reynolds number Re D = 10000 issuing into a square channel that is sealed at one end. The jets directly impinge on a uniformly heated target plate. With previous work on similar configurations well described in literature, the focus of the present contribution is to further exploit the potentials offered by snap-shot based and time-resolved measurements. The flow field within the channel is characterized with both conventional, snap-shot particle image velocimetry (PIV) as well as with high-speed, time-resolved PIV (TR-PIV) to, respectively, capture overview data as well as detailed information on temporally evolving flow structures. In addition, measurements of the unsteady surface temperature distribution on the heated channel wall are performed by means of a newly developed unsteady temperature sensitive paint (iTSP) measurement technique. The interaction of the turbulent jets with the wall and with its neighbors is studied in detail using correlation and spectral analysis as well as modal decomposition. Where possible, this is supplemented with corresponding data obtained from numerical modelling. None of the applied postprocessing methods reveal a significant interaction between jets suggesting that the jet-driven dynamics of heat transfer at the wall are restricted to their immediate vicinity which may simplify the requirements on numerical models of similar cooling configurations