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

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

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

An optimization based multi-block-structured grid generation method

Summary A new optimization based meshing technique for block-structured meshes is presented. Given a topological block partition, block sizes, and distance constraints, meshes are generated automatically. The optimization effort is limited by using a BSpline based intermediate layer with reduced degrees of freedom, making it suitable for high resolution meshes. The optimization itself minimizes approximated grid criteria defined in the intermediate layer domain. Sampling the intermediate layer results in a mesh, which is projected in order to preserve geometric constraints. The capability of the new method is shown for 2D and 3D geometries

Assessment of Source Term and Turbulence Model Combinations for Film Cooling in Turbines

Modern gas turbines require an active cooling system with fluid taken from the compres- sor to withstand the high turbine inlet temperature. CFD is a useful tool to estimate the effects of different cooling configurations on the blade aerodynamics and the thermal loads. However, this usually requires resolving every cooling hole with a high number of grid cells. To reduce the computational cost of such simulations, a reduced order model using source terms was implemented in TRACE. Different variants are tested on a cylin- drical and a laid back fan shaped cooling hole to address issues with accuracy and grid dependency known from the literature. Additionally, two different turbulence and heat flux model combinations are compared to each other. Overall, a differential Reynolds Stress Model with an algebraic heat flux model combined with the simplest approach to modeling film cooling holes, introducing a constant source term at the wall, provided the best results for the considered geometries and blowing ratios. The different strategies to improve the predictions were only able to provide a benefit for some of the cases, while usually having a detrimental effect in other cases

Characterization of the flow field inside a Ranque-Hilsch vortex tube using filtered Rayleigh scattering, Laser-2-Focus velocimetry and numerical methods

The design process of aero engines as well as stationary gas turbines is largely dominated by the cost and time efficient methods of Computational Fluid Dynamics (CFD). Over the past decade the CFD solver TRACE for Favre-averaged compressible Navier-Stokes equations has been developed at the Institute of Propulsion Technology and has been adopted for research as well as industrial applications. In the context of turbomachinery design, reliable modeling of the turbulent flow phenomena involved is a crucial aspect and one of the major subjects of numerical research in fluid dynamics. Novel approaches accounting for the anisotropy of the Reynolds stress tensor promise an improved accuracy in the simulation of industrially relevant configurations. One key aspect in the development strategy of turbulence models is the direct comparison of computational results with validation data produced from appropriate experimental setups with well-defined geometries and boundary conditions. The Ranque-Hilsch vortex tube (RHVT) was chosen in this respect due to its simple geometry with no moving parts on the one hand and its nevertheless complex 3D flow features on the other hand. To provide suitable experimental data the filtered Rayleigh scattering technique extended by the method of frequency scanning (FSM-FRS) was chosen to characterize the RHVT's averaged flow field, since it is capable of simultaneously providing planar information on temperature, pressure and flow field velocity (through the Doppler shift). As the reconstruction of a three component velocity field from FSM-FRS data would require the measurement plane to be observed from three independent directions, the point-wise Laser-2-Focus (L2F) technique is applied to provide 2C velocity profiles at discrete positions downstream from the cold exit

Transitional Delayed Detached-Eddy Simulation for a Compressor Cascade:A Critical Assessment

The accurate prediction of transitional flows is crucial for the industrial turbomachinery design process. While a Reynolds-averaged Navier–Stokes approach inherently brings conceptual weaknesses, large-eddy simulation will still be too expensive in the near future to affordably analyze complex turbomachinery configurations. We introduce a transitional delayed detached-eddy simulation (DDES) model, namely, DDES-γ, and analyze the numerical results of the compressor cascade V103. A comparison with the fullyturbulent DDES approach emphasizes the benefit of coupling DDES with a transition model. Issues with undesired decay of modeled turbulent kinetic energy in the freestream are improved when running DDES-γin combination with the synthetic turbulence generator method. The best results for DDES-γ are obtained when changing the inviscid flux solver blending from dynamic to constant mode. We show that DDES-γ is capable ofpredicting the transitional flow through a linear compressor cascade, but we also critically discuss the general concept and results

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