Data-Driven Adaptive Reynolds-Averaged Navier-Stokes \u3cem\u3ek - ω\u3c/em\u3e Models for Turbulent Flow-Field Simulations

The data-driven adaptive algorithms are explored as a means of increasing the accuracy of Reynolds-averaged turbulence models. This dissertation presents two new data-driven adaptive computational models for simulating turbulent flow, where partial-but-incomplete measurement data is available. These models automatically adjust (i.e., adapts) the closure coefficients of the Reynolds-averaged Navier-Stokes (RANS) k-ω turbulence equations to improve agreement between the simulated flow and a set of prescribed measurement data. The first approach is the data-driven adaptive RANS k-ω (D-DARK) model. It is validated with three canonical flow geometries: pipe flow, the backward-facing step, and flow around an airfoil. For all 3 test cases, the D-DARK model improves agreement with experimental data in comparison to the results from a non-adaptive RANS k-ω model that uses standard values of the closure coefficients. The second approach is the Retrospective Cost Adaptation (RCA) k-ω model. The key enabling technology is that of retrospective cost adaptation, which was developed for real-time adaptive control technology, but is used in this work for data-driven model adaptation. The algorithm conducts an optimization, which seeks to minimize the surrogate performance, and by extension the real flow-field error. The advantage of the RCA approach over the D-DARK approach is that it is capable of adapting to unsteady measurements. The RCA-RANS k-ω model is verified with a statistically steady test case (pipe flow) as well as two unsteady test cases: vortex shedding from a surface-mounted cube and flow around a square cylinder. The RCA-RANS k-ω model effectively adapts to both averaged steady and unsteady measurement data

RANS Turbulence Model Development using CFD-Driven Machine Learning

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method (Weatheritt and Sandberg, 2016), but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.Comment: Accepted by Journal of Computational Physic

ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature regimes. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties. The self-similar radial profile and the development of large-scale structures are reproduced, including the rate of entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. Coarse particles partially decouple from the gas within eddies, modifying the turbulent structure, and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the gravity. By these mechanisms, gas-particle non-equilibrium is able to influence the large-scale behavior of volcanic plumes.Comment: 29 pages, 22 figure

Sub-grid modelling for two-dimensional turbulence using neural networks

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the sub-grid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a-priori and a-posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability density function based validation of sub-grid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for sub-grid quantity inference. In addition, it is also observed that some measure of a-posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data

The quasi-periodic doubling cascade in the transition to weak turbulence

The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier-Stokes flow on a three-periodic domain. Special symmetries are imposed on the flow field in order to reduce the computational effort. Thus we can apply tools from dynamical systems theory such as continuation of periodic orbits and computation of Lyapunov exponents. We propose a model ODE for the quasi-period doubling cascade which, in a limit of a perturbation parameter to zero, avoids resonance related problems. The cascade we observe in the simulations is then compared to the perturbed case, in which resonances complicate the bifurcation scenario. In particular, we compare the frequency spectrum and the Lyapunov exponents. The perturbed model ODE is shown to be in good agreement with the simulations of weak turbulence. The scaling of the observed cascade is shown to resemble the unperturbed case, which is directly related to the well known doubling cascade of periodic orbits

Fast spectral solutions of the double-gyre problem in a turbulent flow regime

Several semi-analytical models are considered for a double-gyre problem in a turbulent flow regime for which a reference fully numerical eddy-resolving solution is obtained. The semi-analytical models correspond to solving the depth-averaged Navier–Stokes equations using the spectral Galerkin approach. The robustness of the linear and Smagorinsky eddy-viscosity models for turbulent diffusion approximation is investigated. To capture essential properties of the double-gyre configuration, such as the integral kinetic energy, the integral angular momentum, and the jet mean-flow distribution, an improved semi-analytical model is suggested that is inspired by the idea of scale decomposition between the jet and the surrounding flow