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ItemDirect and Large-Eddy Simulations of Spatially Evolving Supercritical Turbulent Shear Layers(Georgia Institute of Technology, 2024-04-27) Purushotham, DhruvA given pure component supercritical fluid at a thermodynamic state in the vicinity of its critical point exhibits significant susceptibility to perturbations in the state. The variation of the thermodynamic and transport properties at these loci are strongly nonlinear as a result of non-negligible intermolecular forces in the fluid. These nonlinearities stress the formulations of existing LES subfilter closures, which are derived based on assumptions that break down at these states. The performance of certain subfilter closures under these conditions is largely unclear and the extension of this argument to multi-component settings adds further uncertainty. The research in this dissertation aims to address a judiciously selected subset of these concerns through a multi-faceted approach based on the joint application of the DNS and LES techniques. Specific outcomes of the research are as follows. First, the DNS data set produced for this work shows that Lagrangian enstrophy is amplified by baroclinicity in an instantaneous sense, and is likely associated with highly-strained local vortical structures. At certain times, the baroclinic contribution can be as much as roughly half the dominant vortex stretching contribution. However, the importance of baroclinicity in the mean diminishes. Enstrophy generation through elemental dilatation is also instantaneously significant, but diminishes in the mean. A detailed analysis of turbulence anisotropy shows that some select points within the shear layer are subject to statistically two, or even one-component turbulence, implying attenuation likely stemming from regions of high density gradient magnitude which are known to appear in systems at these conditions. This is a particular manifestation of the thermo-fluid coupling present in such flows. Comparisons between three LES calculations indicate that coarser grids result in higher shear layer growth rates relative to that predicted by the reference DNS data. An evaluation of turbulent kinetic energy spectra and transport property ratios indicates that this could be a result of over-active subfilter models. Mean molecular transport properties are found to rival their corresponding turbulent analogs, and this is likely a unique behavior due to the thermodynamic setting. The rough equivalence of the molecular transport properties to their turbulent counterparts essentially doubles the action of the diffusive operator in the filtered system of equations, thus imparting additional diffusion to the field. This helps correct for amplified field anisotropies which likely arise not only naturally from the lack of grid resolution at the coarse limit, but also from the presence of regions of high density gradient magnitude which attenuate turbulent fluctuations and inhibit mixing. In this light, the extra diffusion imparted by the models serves as a corrective mechanism, however, it appears that in this thermodynamic setting in the coarse grid limit, the specific models employed ought to be attenuated to some level, given the mismatch in shear layer growth rates. Finally, to isolate and analyze subfilter model performance in a rigorous fashion, an a priori analysis of three classes of subfilter closures is performed. The results indicate that, as expected, the dynamic mixed class of closure performs best. However, quantitative data from this analysis indicates that performing LES using the mixed dynamic closures at grid resolutions 4-5x coarser in each coordinate direction than the required DNS resolution at a given Reynolds number yields acceptable performance. At these resolutions, modeled subfilter stresses remain well correlated with the true subfilter stresses, however, the coarsening represents significant computational savings which can aid engineering design in practical settings. The specific resolution guideline here in particular represents a novel outcome of this research in the area of subfilter modeling for LES.
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ItemInvestigation of Explicit Residual Filtering for LES of the Compressible Navier-Stokes Equations(Georgia Institute of Technology, 2023-12-06) Theuerkauf, Scott WilliamLarge Eddy Simulation (LES) is a useful tool for modeling turbulent, non-statistically-stationary flow without resolving the entire range of turbulent scales. While it is frequently calculated using the implicit filter applied by the numerical discretization used to solve the equations of flow, another form of LES uses an explicitly-defined filter to control the range of scales present in the flow. This method seeks to decouple the LES solution from the grid and numerical method in order to effectively eliminate competition between the required subfilter-scale models and the numerical discretization errors. Several methods for Explicitly Filtered LES (EFLES) have been attempted in the past with this goal and others in mind. This work uses a familiar method, grounded in novel derivation from the Navier-Stokes equations governing compressible, reacting flows. By applying a discrete, sufficiently commuting, low-pass filter that is sufficiently sharp and wide relative to the filtering effects of the underlying numerical scheme to the numerical residual of each equation, the effects of the implicit filter can be minimized, overriding them with those of the explicitly-defined filter. Additionally, by applying the filter once to each equation, the cost of successive filter operations is minimized, reducing the cost of EFLES. Finally, the structure of this method allows existing Implicitly Filtered LES (IFLES) numerical methods to be adapted to EFLES in a straightforward and computationally efficient manner. The following work validates this EFLES method on a Taylor-Green Vortex for both incompressible and compressible cases. A stability analysis examines the requirement to apply a residual filter as part of the EFLES method to each conservation equation and explores the stabilizing effect of residual filtering. Identifying the computational costs of this approach in context with its advantages provides the advanced knowledge necessary to achieve grid- and scheme-independent results using EFLES for more advanced flows.
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ItemA Kinetic Energy Preserving and Entropy Conserving Scheme for Stable Simulation of Fluid Flow(Georgia Institute of Technology, 2023-10-31) Schau, Kyle ArthurThis work contributes to the non-linear stability of fluid flow simulation by indirectly enforcing entropy evolution through the numerical internal energy flux. Existing numerical methods are improved and extended to a fully discrete numerical method for solving the Euler equations. The presented scheme preserves the accurate evolution of kinetic energy and is entropy conservative. The developed scheme demonstrates improved stability and accuracy over existing methods by formulating the numerical internal energy flux as a temperature weighted average. The presented scheme is extended to multicomponent simulations and demonstrates improved entropy properties over existing methods; however, numerical mixing rules prevent desired entropy conservation. Finally, a shock capturing extension of the presented scheme is designed from kinetic energy preserving and entropy stability principles. The scheme demonstrates the ability to resolve shocks and provides a novel method for prescribing entropy dissipation through the internal energy dissipation.
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ItemSubgrid scale modeling for large eddy simulation of supercritical mixing and combustion(Georgia Institute of Technology, 2021-11-11) Unnikrishnan, UmeshLarge eddy simulation (LES) is a widely used modeling and simulation technique in turbulent flow research. While the LES methodology and accompanying subgrid scale (SGS) modeling have been developed and applied over decades, primarily in the context of ideal gas conditions, their extension to complex multi-physics flows encountered in aerospace propulsion requires further refinement. In particular, the application of LES to turbulent flows at supercritical conditions presents several new modeling challenges and uncertainties. The scope of this dissertation is to investigate the theoretical LES formalism and SGS modeling framework for multi-species turbulent mixing and combustion at supercritical pressures. The goal is to identify the deficiencies with the current methodology and to establish a refined and consistent framework that accurately accounts for all the necessary physics. In this dissertation, a consistent theoretical formulation of the filtered governing equations for LES is derived. Direct numerical simulations (DNS) are performed for spatially evolving non-reacting and reacting mixing layers at supercritical pressures. The complete set of terms in the filtered equations are quantified and analyzed using the DNS datasets. Based on the analyses, two new groups of subgrid terms are identified as important quantities to account in the LES framework. Parametric analyses are performed as a function of the filter resolution to derive resolution considerations for practical LES applications. The performance and accuracies of two state-of-the-art subgrid modeling approaches for the traditional subgrid fluxes are assessed. The study demonstrates the better performance of scale-similarity based models over the eddy-viscosity based approaches. The study also reveals the deficiencies of conventional subgrid modeling approaches for LES of supercritical combustion. To address the additional modeling requirement for the filtered equation of state, novel subgrid modeling approaches are proposed. The performance of these models are tested and good improvements are demonstrated.
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ItemNumerical simulations of real-gas flows with phase-equilibrium thermodynamics(Georgia Institute of Technology, 2020-07-20) Tudisco, PrincipioMotivated by the complex physics of multi-component mixtures in strongly non-ideal, real-gas (RG) conditions reported in the field of chemical engineering, this work aims to address the behavior of multi-phase thermodynamics from a broader point of view. The focus is to evaluate the differences, as well as the possible sources of errors that would arise in a computational fluid-dynamics (CFD) simulation when conventional single-phase and multi-phase equilibrium RG thermodynamics are employed: an area of research that despite the active interest in many communities (especially CFD), has not been completely understood. Knowledge of the effects that multi-phase RG thermodynamics with the assumption of vapor-liquid equilibrium (VLE) can have on a flow dynamics is important because it establishes the relevance of the fully coupled CFD-VLE solver. In fact, this relevance may go beyond the stand-alone calculation of a multi-phase state, providing important insights about the physics that may not be captured if the single-phase assumption is invoked. This work provides an extensive study of RG mixtures from a physical and numerical point of view. The difficulties associated with their modeling are discussed in detail and solutions are provided accordingly. Emphasis is given to the occurrence and suppression of numerical noise in form of pressure oscillations that can pollute the simulation to the point that it cannot be performed. Extension of existing models to eliminate such problem is achieved by incorporating the effects of VLE thermodynamics in a consistent manner, ultimately forming a new and robust tool to investigate the physics further. The resulting model is applied to non-reacting and reacting flows in canonical setups where emphasis is devoted to the discussion of the differences and sources of errors that would occur if this multi-phase behavior is not taken into account. Results show that the different thermodynamic states reached by this advanced model can have an impact on the flow physics, especially in a non-reacting (or more in general cold) regime. In particular, the strong non-linear coupling between the VLE thermodynamics and the transport properties is identified as a key element of difference with respect to the single-phase model counterpart. These differences manifest into the occurrence of localized changes in the fluid properties (such as density) that affect the flow-field in their vicinity, causing visible discrepancies even when time-averaging is performed. Concurrently, results obtained on the reacting side and carried out (for the first time) with finite-rate kinetics suggest that any VLE formation between the products and the reactants may be considered of minor importance. The latter conclusion is supported by the analysis conducted on the multi-phase field which appears to be largely composed of the vapor solution, as expected, hence limiting the analogous effect observed the non-reacting system where a broader range of phase-separation appears instead.
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ItemInvestigation of ODE-based non-equilibrium wall shear stress models for large eddy simulation(Georgia Institute of Technology, 2019-07-30) Dzanic, TarikFor high Reynolds number flows, wall modeling is essential for performing large eddy simulation at a reasonable computational cost. In this work, a novel low-cost ODE-based non-equilibrium wall model is introduced for wall shear stress modeling in LES. Using polynomial approximations of the pressure gradient and convective terms obtained from interpolation of the LES solution, as opposed to direct evaluation of these gradients within the wall model, the governing wall model equations reduce from coupled PDEs to uncoupled ODEs that do not require an embedded wall model grid within the LES grid. Additionally, the steady form of the wall model equations was utilized, feasible due to the spatial decoupling of the wall model equations, and the effects of the temporal evolution on the wall shear stress were modeled. The effects of polynomial degree on the accuracy of the wall shear stress predictions were explored, and an empirical lag model was built to model the unsteady effects without requiring the solution of a time-stepping problem. Wall resolved large eddy simulations of separated flow around the NASA wall mounted hump and an iced NACA 63A213 airfoil were performed and used as a reference for the comparison of the non-equilibrium wall model to a commonly used equilibrium wall model. The proposed non-equilibrium wall model was able to predict separated flow and laminar flow regions in much better agreement with the wall resolved results than the equilibrium wall model. Underpredictions in the skin friction coefficient in non-equilibrium flow regimes were reduced from 20-50% to less than 10% between the equilibrium and the non-equilibrium wall modeled approaches. Minor improvements in the pressure coefficient predictions were observed with the non-equilibrium model in the separated flow region of the iced airfoil. The results suggest that the proposed wall model can offer better predictions of separated and/or laminar flows compared to equilibrium wall models with negligible computational cost increase.