RANS closure approximation by artificial neural networks

Turbulence modelling remains a challenge for the simulation of turbomachinery flows. Reynolds Averaged Navier-Stokes (RANS) equations will still be used for high-Reynolds number flows for several years and so there is interest in improving their prediction capability. Machine learning techniques offer several strategies which could be exploited for this purpose. In this work, an approach to improve the Spalart-Allmaras model is investigated. In particular, the model is used to predict the flow around the T106c low pressure gas turbine cascade. As a first step, an Artificial Neural Network (ANN) is trained on the data generated by the original model. Then, an optimisation procedure is applied in order to find the weights of the network which minimise the error between the predicted results and the available experimental data. The new model is tested at different Reynolds numbers on the T106c cascade and on a wind turbine airfoil in post-stall conditions. Significant improvements are observed in the condition chosen for the optimisation. Future work will be devoted to the generalisation of the approach by including multiple working conditions optimisations and adding new physical variables as inputs of the ANN

Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method

An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed

REYNOLDS STRESS CORRECTION BY MACHINE LEARNING METHODS WITH PHYSICAL CONSTRAINTS

For the past three decade, Reynolds Average Navier-Stokes models have been widely used in the industry to simulate complex flows. However, these models suffer from limitations. Indeed there are still large discrepancies in the Reynolds stresses between the RANS model and high-fidelity data provided by DNS or experiments. This paper presents a strategy to correct the Menter SST model using an explicit algebraic model and two different neural networks: An multilayer perceptron (MLP) and a generative adversarial network (GAN). Moreover, in order to preserve the physical properties of the Reynolds stress tensor, we introduce a penalisation term in the loss of the GAN

FIELD INVERSION AND MACHINE LEARNING STRATEGIES FOR IMPROVING RANS MODELLING IN TURBOMACHINERY

Turbulence and transition modelling are critical aspects in the prediction of the flow field in turbomachinery. Recently, several research efforts have been devoted to the use of machine learning techniques for improving Reynolds-averaged Navier-Stokes (RANS) models. In this framework, a promising technique is represented by field inversion which requires to find an optimal correction field that minimises the error between numerical predictions and experimental data. In this work, Artificial Neural Networks and Random Forests are investigated as tools to generalise the correction provided by field inversion. An approach to automatically identify the regions where the correction model should be computed is proposed: this improves the fitting and reduces the calls to the model during the predictions. Furthermore, a correction-based weighting of the database is introduced in order to improve the training performances. The potential and the issues of the methods are investigated on a high-lift gas turbine cascade at low Reynolds number

A non-linear observer for unsteady three-dimensional flows

A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on expanding the velocity field in terms of empirical basis functions. The main idea is to impose that the coefficients of the modal expansion of the velocity field give the best approximation to the available measurements and that at the same time they satisfy as close as possible the non-linear low-order model. The practical use may range from feedback flow control to monitoring of the flow in non-accessible regions. The proposed technique is applied to the flow around a confined square cylinder, both in two- and three-dimensional laminar flow regimes. Comparisons are provided. with existing linear and non-linear estimation techniques

Set of Boundary Conditions for Aerodynamic Design

Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be nonreflecting, to avoid spurious perturbations that can provocate unsteadiness or instabilities. The reflectiveness of various boundary conditions is analyzed in the context of the Godunov methods. A nonlinear, isentropic wave propagation model is used to investigate the reflection mechanism on the flowfield borders, and a parameter τ is defined to give a measure of the boundary reflectiveness. A new set of boundary conditions, in which τ =0, that is, totally nonreflecting, is then proposed. The approach has been integrated in an aerodynamic design procedure using a distributed boundary control

Low rank approximation of multidimensional data

In the last decades, numerical simulation has experienced tremendous improvements driven by massive growth of computing power. Exascale computing has been achieved this year and will allow solving ever more complex problems. But such large systems produce colossal amounts of data which leads to its own difficulties. Moreover, many engineering problems such as multiphysics or optimisation and control, require far more power that any computer architecture could achieve within the current scientific computing paradigm. In this chapter, we propose to shift the paradigm in order to break the curse of dimensionality by introducing decomposition to reduced data. We present an extended review of data reduction techniques and intends to bridge between applied mathematics community and the computational mechanics one. The chapter is organized into two parts. In the first one bivariate separation is studied, including discussions on the equivalence of proper orthogonal decomposition (POD, continuous framework) and singular value decomposition (SVD, discrete matrices). Then, in the second part, a wide review of tensor formats and their approximation is proposed. Such work has already been provided in the literature but either on separate papers or into a pure applied mathematics framework. Here, we offer to the data enthusiast scientist a description of Canonical, Tucker, Hierarchical and Tensor train formats including their approximation algorithms. When it is possible, a careful analysis of the link between continuous and discrete methods will be performed.IV Research and Transfer Plan of the University of SevillaInstitut CarnotJunta de AndalucíaIDEX program of the University of Bordeau

Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method

An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references