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Daniel Guggenheim School of Aerospace Engineering
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ItemIgnition, topology, and growth of turbulent premixed flames in supersonic flows(Georgia Institute of Technology, 2019-11-12) Ochs, Bradley AlanSupersonic combustion ramjets (scramjets) are currently the most efficient combustor technology for air breathing hypersonic flight, however, lack of fundamental understanding and numerous engineering challenges hinder regular deployment of these devices. This work addresses scramjet-relevant knowledge gaps in supersonic turbulent premixed combustion, including laser ignition, numerical modeling, and flame-compressibility interaction. One of the main contributions of this work is introduction of a new turbulent premixed flame arrangement where flame-compressibility interaction can be systematically explored: flame kernels in an expanding flow field. The scramjet flow path is replaced by a simplified channel geometry with a well characterized mean flow acceleration that mimics flow field expansion typically imposed on scramjet combustors to avoid thermal choking. Spherically expanding flames are created via laser ignition and subsequent flame growth and morphology are investigated using combined physical and numerical experiments. Pressure-density misalignment due to flame-compressibility interaction produces vorticity at the flame surface through baroclinic torque, i.e. flame-compressibility interaction acts like a turbulence source. The flame ultimately evolves into a reacting vortex ring that increases the flame speed and enhances reactant consumption. To explore the relative importance of turbulence and compressibility on flame dynamics, the Mach number (M=1.5,1.75,2), equivalence ratio (φ= 1.0,0.9,0.8,0.7), and root-mean-squared turbulent velocity (u'=3.98,4.14,4.45 m/s) are varied systematically. This work also introduces flame kernels in an expanding flow field as a canonical numerical validation test case for flame-compressibility interaction. Inaccuracies in simulation results are easily identified due to high flow velocity and simplicity of the problem. The numerical setup and models are scrutinized to minimize errors. Using the appropriately verified numerical models, simulation results show very reasonable agreement with experimental data. Validated simulations are instrumental in enhancing understanding of the underlying physics of supersonic flame kernels. Laser ignition studies in supersonic flows have historically focused on ignition of non-premixed fuels within cavity flame holders. This work introduces a far simpler and more tractable problem: laser ignition of a fully premixed supersonic gas. Ignition experiments with a range of laser settings are performed to determine supersonic breakdown and ignition probabilities, length of time the ignition event influences flame growth, and Mach number influence on the ignition process. The ignition event has a long-lasting effect on kernel growth, but the influence can be minimized by properly selecting the laser energy. Mach number has a minimal impact on the ignition process, but does affect the initial kernel shape due to flow field variations with Mach number. Kernel growth matches low speed studies closely at early times, but deviates at later times due to vortex ring topology. It is not obvious how the turbulent flame speed will scale for flows with mean compressibility. Therefore, the combined physical and numerical experiments are leveraged to explore this question. The vortex ring causes significant errors in the line of sight-measured burned volume, hence correction factors to convert from line of sight to volumetric measurements are presented. Conditions for displacement and consumption speed equivalency are shown to depend heavily on the particular diagnostic used; which progress variable isocontour is measured and where it is measured within the flame brush must be considered carefully during interpretation of experimental data. Scaling with the RMS turbulent velocity cannot collapse these flame speed data, i.e. previously established flame speed scalings are inappropriate for flames interacting with compressibility. Drawing motivation from vortex ring literature, a new flame speed scaling based on the ring propagation velocity is proposed. The proposed scaling collapses the data and produces a nearly linear scaling regime, which suggests turbulence plays a secondary role to the hydrodynamic instability created by flame-compressibility interaction. In summary, flame kernels are a new and effective canonical configuration for exploring flame-compressibility interactions in supersonic flows.
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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.
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ItemA generalized Maccormack scheme for low Mach number, chemically-reacting large-eddy simulations(Georgia Institute of Technology, 2017-06-16) Gallagher, Timothy PatrickChemically reacting flows contain a wide range of regimes with many velocity and time scales. The increasing access to computational resources enables higher-fidelity simulations of these flows. In order to take advantage of these capabilities, numerical schemes must be robust, efficient and accurate in all of the regimes present in the flow. Pressure-based schemes are suitable for many low Mach number flows, but are limited to low velocities and relatively small temperature variations. Density-based schemes struggle to converge in low-speed flows due to the time-step restrictions imposed by the acoustic velocity, which may be orders of magnitude larger than the convective velocity. Furthermore, such codes may exhibit excessive numerical dissipation due improper scaling of the dissipative properties of the scheme. Chemical reactions introduce another set of temporal scales associated with the kinetics mechanism used to model the system. These scales are often much smaller than the convective or acoustic scales and impose additional restrictions on the time-step. This disparity requires numerical schemes designed to handle the challenges that occur in low Mach number, chemically reacting flows. Analysis of density-based schemes at the low Mach number limit suggests that the development of improved, robust preconditioning with suitable operator splitting techniques leads to improved solution fidelity. In this work, a dual-time framework with low-Mach preconditioning is developed for complex, chemically reacting large-eddy simulations. A new version of the well-known MacCormack scheme is proposed and the resulting scheme improves the solution quality significantly at low Mach numbers. An established ordinary differential equation solver for stiff systems treats the stiffness associated with the chemical source terms. Methods to couple the PDE and ODE solvers in both pseudo-time and in physical time are proposed and analyzed. Validation of the non-reacting scheme and the coupled reacting scheme using canonical test cases demonstrates the improved solution fidelity and simulations of representative industrial applications demonstrate the combined scheme.
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ItemAn embedded boundary approach for simulation of reacting flow problems in complex geometries with moving and stationary boundaries(Georgia Institute of Technology, 2017-05-16) Muralidharan, BalajiMany useful engineering devices involve moving boundaries interacting with a reacting compressible flow. Examples of such applications include propulsion systems with moving components such as Internal Combustion (IC) engines, hypersonic propulsive devices such as Oblique Detonation Wave (ODW) engines and solid rocket motors involving regressing propellant surfaces. Computational Fluid Dynamics (CFD) can be effectively employed to study these systems. However, conventional numerical methods face several difficulties related to grid generation, treatment of moving boundaries, lack of adequate grid resolution at an affordable computational cost, and shortcomings in closure models required for Large Eddy Simulation (LES). This thesis demonstrates new accurate numerical models and subgrid closures for LES of problems in non-trivial geometries with moving boundaries. A new high-order adaptive cut-cell based embedded boundary method is developed for viscous flows, which can provide a smooth and accurate reconstruction to predict the near-wall shear stress and pressure distribution. The method can achieve a high order of accuracy even under adverse geometrical constraints such as narrow gaps and sharp corners due to a novel and robust cell clustering algorithm. This algorithm also enforces the stability of the numerical scheme in the presence of arbitrary low volume cells formed in the cell cutting process. Additionally, an extended cell clustering approach, which can achieve exact conservation of mass, momentum, and energy is proposed for moving boundaries. The embedded boundary method is built on a massively parallel framework that performs block structured Adaptive Mesh Refinement (AMR) by interfacing with the BoxLib open source library. This modeling framework is then applied to study fundamental physics in high-speed propulsion systems, for example, shock-turbulence interactions, flame-turbulence interaction, and flame/detonation stabilization in a reacting system. LES using the multilevel subgrid closure for flow and chemistry is used to study flame anchoring in a transverse reacting jet in cross flow. Important mechanisms that stabilize the flame are identified and shown to be consistent with past observations from experiments and using direct numerical simulations (DNS) but obtained here using much coarser grid LES. Finally, to demonstrate the ability of the methodology to simulate moving bodies in a reactive system, DNS of a hypersonic projectile fired into a reacting flow is performed to reveal key effects of pressure on the stabilization of detonation ahead of the projectile.
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ItemSimulations of vitiated bluff body stabilized flames(Georgia Institute of Technology, 2016-05-17) Smith, Andrew GerardBluff bodies have a wide range of applications where low-cost, light weight methods are needed to stabilize flames in high-speed flow. The principles of bluff body flame stabilization are straightforward, but many details are not understood; this is especially true in vitiated environments where measurements are difficult to obtain. Most work has focused on premixed flames but changing application requirements are now driving studies on non-premixed gaseous and spray flames. This thesis aims to improve the understanding of vitiated, bluff body stabilized flames, specifically on non-premixed, spray flames, through the use of Large Eddy Simulation (LES). The single flameholder facility at Georgia Tech was chosen as the basis for the simulations in this thesis. The flameholder was a rectangular bluff body with an aerodynamic leading edge with discrete liquid fuel injectors embedded just upstream of the trailing edge in a configuration described as “close-coupled.” The liquid phase was modeled using a Lagrangian particle approach where discrete fuel droplets were injected into the domain. Experimental data was used to tune model parameters as well as the stripped droplet velocities and sizes. The discharge coefficient needed to be taken into account to achieve the correct fuel jet penetration. The experiments were conducted over a range of global equivalence ratios; lean equivalence ratios, φ global ≈ 0.5, exhibited symmetric flame shedding and conversely large scale sinusoidal B ́ernard/von-K ́arm ́an shedding was observed when the equiva- lence ratio was near unity. Reacting flow LES were computed at these two fuel flow rates to improve understanding of the different flame dynamics. LES were first com- pleted using a quasi-laminar subgrid turbulence-chemistry interaction model. Span- wise averaging of instantaneous and time-averaged LES results were compared with experimental high- and low-speed imaging and showed the LES was in qualitative agreement at both fuel flow rates. At phi_global ≈ 0.5, the fuel jet did not penetrate as far into the crossflow compared to phi_global ≈ 0.95 and thus more fuel was delivered to the shear layers of the bluff body resulting in higher heat release in the shear layers for the low fuel flow rate. The heat release damped the large sinusoidal structures via gas expansion and baroclinic torque generation. Higher fuel jet penetration in the phi_global ≈ 0.95 case meant less fuel was delivered to the shear layers and so less heat release occurred directly behind the bluff body so the large scale sinusoidal shedding was not damped. The impact of the subgrid turbulence-chemistry interaction model on the flame dynamics was tested by comparing the quasi-laminar LES with LES using the subgrid linear eddy model (LEMLES). The flame structure predicted with LEMLES matched that of the quasi-laminar LES, at both fuel flow rates in the near- field behind the bluff body but deviated farther downstream. A flame edge analysis showed little sensitivity to the choice of subgrid model in the region x < 4D. A high-order hybrid finite-difference solver with consisting of a WENO upwind method and compact central scheme was implemented to assess the effects of the numerical method. A series of test cases was used to verify, validate and compare several of the available spatial and temporal methods before the high fuel flow rate bluff body case was run. For the simple test cases the higher-order methods were clearly more efficient but for more complex cases the differences between the second- order and high-order methods are smaller. To test the hypothesis that the fuel jet penetration was the main factor in the flame dynamics another configuration with a modified fuel injector diameter was simulated. The injector size was chosen to match the spray penetration of phi_global ≈ 0.5 case while maintaining the fuel flow rate of the phi_global ≈ 0.95 case. The results confirmed the hypothesis as the flame dynamics of this configuration match the original low fuel flow rate case.
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ItemHybrid RANS-LES closure for separated flows in the transitional regime(Georgia Institute of Technology, 2016-04-04) Hodara, JoachimThe aerodynamics of modern rotorcraft is highly complex and has proven to be an arduous challenge for computational fluid dynamics (CFD). Flow features such as massively separated boundary layers or transition to turbulence are common in engineering applications and need to be accurately captured in order to predict the vehicle performance. The recent advances in numerical methods and turbulence modeling have resolved each of these issues independent of the other. First, state-of-the-art hybrid RANS-LES turbulence closures have shown great promise in capturing the unsteady flow details and integrated performance quantities for stalled flows. Similarly, the correlation-based transition model of Langtry and Menter has been successfully applied to a wide range of applications involving attached or mildly separated flows. However, there still lacks a unified approach that can tackle massively separated flows in the transitional flow region. In this effort, the two approaches have been combined and expended to yield a methodology capable of accurately predicting the features in these highly complex unsteady turbulent flows at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, circular cylinder in crossflow and NACA 63-415 wing. Cost and accuracy correlations with URANS and prior hybrid URANS-LES approaches with and without transition modeling indicate that this new method can capture both separation and transition more accurately and cost effectively. This new turbulence approach has been applied to the study of wings in the reverse flow regime. The flight envelope of modern helicopters has increased significantly over the last few decades, with design concepts now reaching advance ratios up to μ = 1. In these extreme conditions, the freestream velocity exceeds the rotational speed of the blades, and a large region of the retreating side of the rotor disk experiences reverse flow. For a conventional airfoil with a sharp trailing edge, the reverse flow regime is generally characterized by massive boundary layer separation and bluff body vortex shedding. This complex aerodynamic environment has been utilized to evaluate the new hybrid transitional approach. The assessment has proven the efficiency of the new hybrid model, and it has provided a transformative advancement to the modeling of dynamic stall.
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ItemA study of magnetoplasmadynamic effects in turbulent supersonic flows with application to detonation and explosion(Georgia Institute of Technology, 2015-07-28) Schulz, Joseph C.Explosions are a common phenomena in the Universe. Beginning with the Big Bang, one could say the history of the Universe is narrated by a series of explosions. Yet no matter how large, small, or complex, all explosions occur through a series of similar physical processes beginning with their initiation to their dynamical interaction with the environment. Of particular interest to this study is how these processes are modified in a magnetized medium. The role of the magnetic field is investigated in two scenarios. The first scenario addresses how a magnetic field alters the propagation of a gaseous detonation where the application of interest is the modification of a condensed-phase explosion. The second scenario is focused on the aftermath of the explosion event and addresses how fluid mixing changes in a magnetized medium. A primary focus of this thesis is the development of a numerical tool capable of simulating explosive phenomenon in a magnetized medium. While the magnetohydrodynamic (MHD) equations share many of the mathematical characteristics of the hydrodynamic equations, numerical methods developed for the conservation equations of a magnetized plasma are complicated by the requirement that the magnetic field must be divergent free. The advantages and disadvantages of the proposed method are discussed in relation to explosion applications.
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ItemA study of dispersion and combustion of particle clouds in post-detonation flows(Georgia Institute of Technology, 2015-07-24) Gottiparthi, Kalyana ChakravarthiAugmentation of the impact of an explosive is routinely achieved by packing metal particles in the explosive charge. When detonated, the particles in the charge are ejected and dispersed. The ejecta influences the post-detonation combustion processes that bolster the blast wave and determines the total impact of the explosive. Thus, it is vital to understand the dispersal and the combustion of the particles in the post-detonation flow, and numerical simulations have been indispensable in developing important insights. Because of the accuracy of Eulerian-Lagrangian (EL) methods in capturing the particle interaction with the post-detonation mixing zone, EL methods have been preferred over Eulerian-Eulerian (EE) methods. However, in most cases, the number of particles in the flow renders simulations using an EL method unfeasible. To overcome this problem, a combined EE-EL approach is developed by coupling a massively parallel EL approach with an EE approach for granular flows. The overall simulation strategy is employed to simulate the interaction of ambient particle clouds with homogenous explosions and the dispersal of particles after detonation of heterogeneous explosives. Explosives packed with aluminum particles are also considered and the aluminum particle combustion in the post-detonation flow is simulated. The effect of particles, both reactive and inert, on the combustion processes is analyzed. The challenging task of solving for clouds of micron and sub-micron particles in complex post-detonation flows is successfully addressed in this thesis.
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ItemTowards multi-scale reacting fluid-structure interaction: micro-scale structural modeling(Georgia Institute of Technology, 2015-04-15) Gallagher, TimothyThe fluid-structure interaction of reacting materials requires computational models capable of resolving the wide range of scales present in both the condensed phase energetic materials and the turbulent reacting gas phase. This effort is focused on the development of a micro-scale structural model designed to simulate heterogeneous energetic materials used for solid propellants and explosives. These two applications require a model that can track moving surfaces as the material burns, handle spontaneous formation of discontinuities such as cracks, model viscoelastic and viscoplastic materials, include finite-rate kinetics, and resolve both micro-scale features and macro-scale trends. Although a large set of computational models is applied to energetic materials, none meet all of these criteria. The Micro-Scale Dynamical Model serves as the basis for this work. The model is extended to add the capabilities required for energetic materials. Heterogeneous solid propellant burning simulations match experimental burn rate data and descriptions of material surface. Simulations of realistic heterogeneous plastic-bound explosives undergoing impact predict the formation of regions of localized heating called hotspots which may lead to detonation in the material. The location and intensity of these hotspots is found to vary with the material properties of the energetic crystal and binder and with the impact velocity. A statistical model of the hotspot peak temperatures for two frequently used energetic crystals indicates a linear relationship between the hotspot intensity and the impact velocity. This statistical model may be used to generate hotspot fields in macro-scale simulations incapable of resolving the micro-scale heating that occurs in heterogeneous explosives.
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ItemLarge-eddy simulations of high-pressure shear coaxial flows relevant for H2/O2 rocket engines(Georgia Institute of Technology, 2013-01-11) Masquelet, Matthieu MarcThe understanding and prediction of transient phenomena inside Liquid Rocket Engines (LREs) have been very difficult because of the many challenges posed by the conditions inside the combustion chamber. This is especially true for injectors involving liquid oxygen LOX and gaseous hydrogen GH₂. A wide range of length scales needs to be captured from high-pressure flame thicknesses of a few microns to the length of the chamber of the order of a meter. A wide range of time scales needs to be captured, again from the very small timescales involved in hydrogen chemistry to low-frequency longitudinal acoustics in the chamber. A wide range of densities needs to be captured, from the cryogenic liquid oxygen to the very hot and light combustion products. A wide range of flow speeds needs to be captured, from the incompressible liquid oxygen jet to the supersonic nozzle. Whether one desires to study these issues numerically or experimentally, they combine to make simulations and measurements very difficult whereas reliable and accurate data are required to understand the complex physics at stake. This thesis focuses on the numerical simulations of flows relevant to LRE applications using Large Eddy Simulations (LES). It identifies the required features to tackle such complex flows, implements and develops state-of-the-art solutions and apply them to a variety of increasingly difficult problems. More precisely, a multi-species real gas framework is developed inside a conservative, compressible solver that uses a state-of-the-art hybrid scheme to capture at the same time the large density gradients and the turbulent structures that can be found in a high-pressure liquid rocket engine. Particular care is applied to the implementation of the real gas framework with detailed derivations of thermodynamic properties, a modular implementation of select equations of state in the solver. and a new efficient iterative method. Several verification cases are performed to evaluate this implementation and the conservative properties of the solver. It is then validated against laboratory-scaled flows relevant to rocket engines, from a gas-gas reacting injector to a liquid-gas injector under non-reacting and reacting conditions. All the injectors considered contain a single shear coaxial element and the reacting cases only deal with H₂-O₂ systems. A gaseous oyxgen-gaseous hydrogen (GOX-GH₂) shear coaxial injector, typical of a staged combustion engine, is first investigated. Available experimental data is limited to the wall heat flux but extensive comparisons are conducted between three-dimensional and axisymmetric solutions generated by this solver as well as by other state-of-the-art solvers through a NASA validation campaign. It is found that the unsteady and three-dimensional character of LES is critical in capturing physical flow features, even on a relatively coarse grid and using a 7-step mechanism instead of a 21-step mechanism. The predictions of the wall heat flux, the only available data, are not very good and highlight the importance of grid resolution and near-wall models for LES. To perform more quantitative comparisons, a new experimental setup is investigated under both non-reacting and reacting conditions. The main difference with the previous setup, and in fact with most of the other laboratory rigs from the literature, is the presence of a strong co-flow to mimic the surrounding flow of other injecting elements. For the non-reacting case, agreement with the experimental high-speed visualization is very good, both qualitatively and quantitatively but for the reacting case, only poor agreement is obtained, with the numerical flame significantly shorter than the observed one. In both cases, the role of the co-flow and inlet conditions are investigated and highlighted. A validated LES solver should be able to go beyond some experimental constraints and help define the next direction of investigation. For the non-reacting case, a new scaling law is suggested after a review of the existing literature and a new numerical experiment agrees with the prediction of this scaling law. A slightly modified version of this non-reacting setup is also used to investigate and validate the Linear-Eddy Model (LEM), an advanced sub-grid closure model, in real gas flows for the first time. Finally, the structure of the trans-critical flame observed in the reacting case hints at the need for such more advanced turbulent combustion model for this class of flow.