Browsing by Author "Gao, Xinfeng, advisor"
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Item Open Access A fourth-order finite volume algorithm with adaptive mesh refinement in space and time for multi-fluid plasma modeling(Colorado State University. Libraries, 2022) Polak, Scott E., author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Tomasel, Fernando, committee member; Ghosh, Debojyoti, committee member; Bangerth, Wolfgang, committee memberImproving our fundamental understanding of plasma physics using numerical methods is pivotal to the advancement of science and the continual development of cutting-edge technologies such as nuclear fusion reactions for energy production or the manufacturing of microelectronic devices. An elaborate and accurate approach to modeling plasmas using computational fluid dynamics (CFD) is the multi-fluid method, where the full set of fluid mechanics equations are solved for each species in the plasma simultaneously with Maxwell's equations in a coupled fashion. Nevertheless, multi-fluid plasma modeling is inherently multiscale and multiphysics, presenting significant numerical and mathematical stiffness. This research aims to develop an efficient and accurate multi-fluid plasma model using higher-order, finite-volume, solution-adaptive numerical methods. The algorithm developed herein is verified to be fourth-order accurate for electromagnetic simulations as well as those involving fully-coupled, multi-fluid plasma physics. The solutions to common plasma test problems obtained by the algorithm are validated against exact solutions and results from literature. The algorithm is shown to be robust and stable in the presence of complex solution topology and discontinuities, such as shocks and steep gradients. The optimizations in spatial discretization provided by the fourth-order algorithm and adaptive mesh refinement are demonstrated to improve the solution time by a factor of 10 compared to lower-order methods on fixed-grid meshes. This research produces an advanced, multi-fluid plasma modeling framework which allows for studying complex, realistic plasmas involving collisions and practical geometries.Item Open Access A fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains(Colorado State University. Libraries, 2019) Owen, Landon, author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Marchese, Anthony, committee member; Estep, Donald, committee memberAccurate computational modeling of reacting flows is necessary to improve the design combustion efficiency and emission reduction in combustion devices, such as gas turbine engines. Combusting flows consists of a variety of phenomena including fluid mixing, chemical kinetics, turbulence-chemistry interacting dynamics, and heat and mass transfer. The scales associated with these range from atomic scales up to continuum scales at device level. Therefore, combusting flows are strongly nonlinear and require multiphysics and multiscale modeling. This research employs a fourth-order finite-volume method and leverages increasing gains in modern computing power to achieve high-fidelity modeling of flow characteristics and combustion dynamics. However, it is challenging to ensure that computational models are accurate, stable, and efficient due to the multiscale and multiphysics nature of combusting flows. Therefore, the goal of this research is to create a robust, high-order finite-volume algorithm on mapped domains with adaptive mesh refinement to solve compressible combustion problems in relatively complex geometries on parallel computing architecture. There are five main efforts in this research. The first effort is to extend the existing algorithm to solve the compressible Navier-Stokes equations on mapped domains by implementing the fourth-order accurate viscous discretization operators. The second effort is to incorporate the species transport equations and chemical kinetics into the solver to enable combustion modeling. The third effort is to ensure stability of the algorithm for combustion simulations over a wide range of speeds. The fourth effort is to ensure all new functionality utilizes the parallel adaptive mesh refinement infrastructure to achieve efficient computations on high-performance computers. The final goal is to utilize the algorithm to simulate a range of flow problems, including a multispecies flow with Mach reflection, multispecies mixing flow through a planar burner, and oblique detonation waves over a wedge. This research produces a verified and validated, fourth-order finite-volume algorithm for solving thermally perfect, compressible, chemically reacting flows on mapped domains that are adaptively refined and represent moderately complex geometries. In the future, the framework established in this research will be extended to model reactive flows in gas turbine combustors.Item Open Access A novel smoother-based data assimilation method for complex CFD(Colorado State University. Libraries, 2024) Hurst, Christopher L., author; Gao, Xinfeng, advisor; Guzik, Stephen, advisor; Troxell, Wade, committee member; van Leeuwen, Peter Jan, committee memberAccurate computational fluid dynamics (CFD) modeling of turbulent flows is necessary for improving fluid-driven engineering designs. Traditional CFD often falls short of providing truly accurate solutions due to inherent uncertainties stemming from modeling assumptions and the chaotic nature of fluid flow. To overcome these limitations, we propose the integration of data assimilation (DA) techniques into CFD simulations. DA, which incorporates observational data into numerical models, offers a promising avenue to enhance predictability by reducing uncertainties associated with initial conditions and model parameters. This research aims to advance our understanding and application of DA for CFD modeling of highly chaotic dynamical systems. This dissertation makes several novel contributions in DA and CFD: i) A novel DA algorithm, the maximum likelihood ensemble smoother (MLES), has been developed and implemented to provide better model parameter estimation and assimilate time-integrated observations while addressing nonlinearity, ii) Multigrid-in-time techniques are applied to enhance the computational efficiency of the MLES by improving the optimization processes, and iii) The MLES+CFD framework has been validated by classical test problems such as the Lorenz 96 model and the Kuramoto-Sivashinsky equation. The effectiveness of the MLES has been demonstrated through a few test problems featuring chaos, discontinuity, or high dimensionality.Item Open Access Bayesian data assimilation for CFD modeling of turbulent combustion(Colorado State University. Libraries, 2022) Wang, Yijun, author; Gao, Xinfeng, advisor; Zupanski, Milija, committee member; Guzik, Stephen, committee member; Windom, Bret, committee member; Koslovsky, Matthew, committee memberAchieving accurate CFD prediction of turbulent combustion is challenging due to the multiscale nature of the dynamical system and the need to understand the effect of the small-scale physical features. Since direct numerical simulation (DNS) is still not feasible even for today's computing power, Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES) is commonly used as the practical approach for turbulent combustion modeling. Nevertheless, physical models employed by RANS or LES for describing the interactions between the turbulence, chemical kinetics, and thermodynamic properties of the fluid are often inadequate because of the uncertainties in the dynamical system, including those in the model parameters, initial and boundary conditions, and numerical methods. Understanding and reducing these uncertainties are critical to the CFD prediction of turbulence and chemical reactions. To achieve this, this dissertation is focused on the development of a Bayesian computational framework for the uncertainty estimation of the dynamical system. In the framework, a data assimilation (DA) algorithm is integrated to obtain a more accurate solution by combining the CFD model and available data. This research details the development, verification, and validation of a multi-algorithm system (referred to as DA+CFD system) that aims to increase the predictability of CFD modeling of turbulent and combusting flows. Specifically, in this research, we develop and apply a Bayesian computational framework by integrating our high-order CFD algorithm, Chord, with the maximum likelihood ensemble filter to improve the CFD prediction of turbulent combustion in complex geometry. The verified and validated system is applied to a time-evolving, reacting shear-layer mixing problem and turbulent flows in a bluff-body combustor with and without C3H8-air combustion. Results demonstrate the powerful capability of the DA+CFD system in improving our understanding of the uncertainties in model and data and the impact of data on the model. This research makes novel contributions, including (i) the development of a new alternative approach to improve the predictability of CFD modeling of turbulent combustion by applying data assimilation, (ii) the derivation of new insights on factors, such as where, what, and when data should be assimilated and thus providing potential guidance to experimental design, and (iii) the demonstration of data assimilation as a potentially powerful approach to improve CFD modeling of turbulent combustion in engineering applications and reduce the uncertainties with data. Future work will focus on a performance study of the present DA+CFD system for turbulent combustion of high Reynolds numbers and understanding the uncertainty in model parameters for developing and assessing physical models based on available information.Item Open Access Computational analysis of aircraft pressure relief doors(Colorado State University. Libraries, 2016) Schott, Tyler, author; Gao, Xinfeng, advisor; Guzik, Stephen, advisor; Kirkpatrick, Allan, committee member; Liu, Jiangguo, committee memberModern trends in commercial aircraft design have sought to improve fuel efficiency while reducing emissions by operating at higher pressures and temperatures than ever before. Consequently, greater demands are placed on the auxiliary bleed air systems used for a multitude of aircraft operations. The increased role of bleed air systems poses significant challenges for the pressure relief system to ensure the safe and reliable operation of the aircraft. The core compartment pressure relief door (PRD) is an essential component of the pressure relief system which functions to relieve internal pressure in the core casing of a high-bypass turbofan engine during a burst duct over-pressurization event. The successful modeling and analysis of a burst duct event are imperative to the design and development of PRD's to ensure that they will meet the increased demands placed on the pressure relief system. Leveraging high-performance computing coupled with advances in computational analysis, this thesis focuses on a comprehensive computational fluid dynamics (CFD) study to characterize turbulent flow dynamics and quantify the performance of a core compartment PRD across a range of operating conditions and geometric configurations. The CFD analysis was based on a compressible, steady-state, three-dimensional, Reynolds-averaged Navier-Stokes approach. Simulations were analyzed, and results show that variations in freestream conditions, plenum environment, and geometric configurations have a non-linear impact on the discharge, moment, thrust, and surface temperature characteristics. The CFD study revealed that the underlying physics for this behavior is explained by the interaction of vortices, jets, and shockwaves. This thesis research is innovative and provides a comprehensive and detailed analysis of existing and novel PRD geometries over a range of realistic operating conditions representative of a burst duct over-pressurization event. Further, the study provides aircraft manufacturers with valuable insight into the impact that operating conditions and geometric configurations have on PRD performance and how the information can be used to assist future research and development of PRD design.Item Open Access Development of reduced polynomial chaos-Kriging metamodel for uncertainty quantification of computational aerodynamics(Colorado State University. Libraries, 2018) Weinmeister, Justin, author; Gao, Xinfeng, advisor; Roy, Sourajeet, committee member; Guzik, Stephen, committee member; Alves, Dino, committee memberComputational fluid dynamics (CFD) simulations are a critical component of the design and development of aerodynamic bodies. However, as engineers attempt to capture more detailed physics, the computational cost of simulations increases. This limits the ability of engineers to use robust or multidisciplinary design methodologies for practical engineering applications because the computational model is too expensive to evaluate for uncertainty quantification studies and off-design performance analysis. Metamodels (surrogate models) are a closed-form mathematical solution fit to only a few simulation responses which can be used to remedy this situation by estimating off-design performance and stochastic responses of the CFD simulation for far less computational cost. The development of a reduced polynomial chaos-Kriging (RPC-K) metamodel is another step towards eliminating simulation gridlock by capturing the relevant physics of the problem in a cheap-to-evaluate metamodel using fewer CFD simulations. The RPC-K metamodel is superior to existing technologies because its model reduction methodology eliminates the design parameters which contribute little variance to the problem before fitting a high-fidelity metamodel to the remaining data. This metamodel can capture non-linear physics due to its inclusion of both the long-range trend information of a polynomial chaos expansion and local variations in the simulation data through Kriging. In this thesis, the RPC-K metamodel is developed, validated on a convection-diffusion-reaction problem, and applied to the NACA 4412 airfoil and aircraft engine nacelle problems. This research demonstrates the metamodel's effectiveness over existing polynomial chaos and Kriging metamodels for aerodynamics applications because of its ability to fit non-linear fluid flows with far fewer CFD simulations. This research will allow aerospace engineers to more effectively take advantage of detailed CFD simulations in the development of next-generation aerodynamic bodies through the use of the RPC-K metamodel to save computational cost.Item Open Access Entropy stability for a fourth-order accurate finite-volume method for Burgers' equation(Colorado State University. Libraries, 2019) Meisner, Noah, author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Liu, Jiannguo, committee memberComputational fluid dynamics (CFD) algorithms need efficiency, accuracy, and robustness to be useful to engineers. Faster computers improve the effective speed of a given method, and larger memories allow higher grid resolution, improving accuracy. However, robustness cannot be achieved through advancements in computer hardware. Improvements in this area require a fundamental understanding of the mathematical and physical aspects of the algorithm being investigated. For high-order numerical algorithms, the stability can easily be aggravated with the presence of strong gradients. Many methods in CFD incorporate some kind of numerical limiter to suppress spurious oscillations and handle nonlinear instabilities for flows with strong discontinuities. However, these limiters often lack a basis in the physics that governs the fluid flow. For this reason, the present research employs a limiting method that is based on the second law of thermodynamics to achieve numerical robustness for a higher order code in solving flows with strong discontinuities. The aim of this work is to address the question of robustness for a high-order finite-volume method (FVM) by extending the entropy stability strategy developed by Marshal L. Merriam for a second-order FVM. Unlike generic limiters or artificial viscosity, the approach explored in this thesis provides a physical, quantitative explanation for artificial viscosity or limiters in the form of entropy. The mathematical derivation of the entropy stability method is presented in detail, shortcomings of the method by Merriam are explored, and a more robust approach to deriving an entropy stable limiting method was carried out for the low-order methods. As a first step, this study focuses on the application to Burgers' equation for both a first- and second-order accurate solution to a problem with the onset of shocks. Then, a cell entropy fix for the fourth-order discretization scheme is derived and applied to Burgers' equations. Although the oscillations near the discontinuities can be mitigated, the logical conditions associated with ensuring the entropy constraints become impractical to implement for high-order discretization schemes. Through this research, it is deemed that the entropy stability method proposed by Merriam may not be a viable solution to effectively suppress oscillations near strong discontinuities of problems governed by systems of nonlinear equations, particularly, for high-order schemes.Item Open Access Geometry considerations for high-order finite-volume methods on structured grids with adaptive mesh refinement(Colorado State University. Libraries, 2022) Overton-Katz, Nathaniel D., author; Guzik, Stephen, advisor; Gao, Xinfeng, advisor; Weinberger, Chris, committee member; Bangerth, Wolfgang, committee memberComputational fluid dynamics (CFD) is an invaluable tool for engineering design. Meshing complex geometries with accuracy and efficiency is vital to a CFD simulation. In particular, using structured grids with adaptive mesh refinement (AMR) will be invaluable to engineering optimization where automation is critical. For high-order (fourth-order and above) finite volume methods (FVMs), discrete representation of complex geometries adds extra challenges. High-order methods are not trivially extended to complex geometries of engineering interest. To accommodate geometric complexity with structured AMR in the context of high-order FVMs, this work aims to develop three new methods. First, a robust method is developed for bounding high-order interpolations between grid levels when using AMR. High-order interpolation is prone to numerical oscillations which can result in unphysical solutions. To overcome this, localized interpolation bounds are enforced while maintaining solution conservation. This method provides great flexibility in how refinement may be used in engineering applications. Second, a mapped multi-block technique is developed, capable of representing moderately complex geometries with structured grids. This method works with high-order FVMs while still enabling AMR and retaining strict solution conservation. This method interfaces with well-established engineering work flows for grid generation and interpolates generalized curvilinear coordinate transformations for each block. Solutions between blocks are then communicated by a generalized interpolation strategy while maintaining a single-valued flux. Finally, an embedded-boundary technique is developed for high-order FVMs. This method is particularly attractive since it automates mesh generation of any complex geometry. However, the algorithms on the resulting meshes require extra attention to achieve both stable and accurate results near boundaries. This is achieved by performing solution reconstructions using a weighted form of high-order interpolation that accounts for boundary geometry. These methods are verified, validated, and tested by complex configurations such as reacting flows in a bluff-body combustor and Stokes flows with complicated geometries. Results demonstrate the new algorithms are effective for solving complex geometries at high-order accuracy with AMR. This study contributes to advance the geometric capability in CFD for efficient and effective engineering applications.Item Open Access Influence of anatomic valve conditions and coronary flow on aortic sinus hemodynamics(Colorado State University. Libraries, 2015) Moore, Brandon L., author; Dasi, Lakshmi Prasad, advisor; Gao, Xinfeng, advisor; Kirkpatrick, Allan, committee member; Orton, Christopher, committee memberHeart disease is the leading cause of death in the US, and aortic valve stenosis represents a significant portion of this disease. While the specific causes of stenosis are not entirely clear, its development has been strongly linked to mechanical factors such as localized solid and fluid stresses and strains, especially on the aortic side of the valve leaflets. These mechanical cues can be tied to valvular hemodynamics, however the factors regulating these hemodynamics are relatively unknown. Therefore, the overarching hypothesis of this research is that aortic valve sinus hemodynamics are regulated by anatomic valve conditions and presence of coronary flow. This hypothesis is explored through three specific aims: 1) to develop methodologies for quantifying hemodynamics within the aortic sinuses, 2) to characterize the differences in native valve flow patterns that occur due to patient and sinus variability, and 3) to evaluate the hemodynamic impacts of different prosthetic aortic valve implantations. In this work, experimental methods have been developed to study a broad range of aortic valve conditions, and computational models were also employed to validate and enhance experimental findings. An in vitro setup is presented using a surgical bioprosthesis as a native aortic valve model, while additional valve implantations were also tested. Physiological pressures and flow rates were imposed across these valves via an in-house pumping loop, which included a novel coronary flow branch. Two-dimensional time-resolved particle image velocimetry (PIV) protocols were developed and employed to analyze sinus vorticity dynamics. Computationally, both 2D and 3D simulations were run in ANSYS Fluent to enhance experimental findings. Results from this research demonstrate that aortic sinus hemodynamics are indeed regulated by anatomic valve conditions and coronary flow. From a clinical perspective, average valve geometric parameters tend to produce hemodynamics that are least likely to initiate disease than those near the upper or lower anatomical limits. Coronary flow was likewise found to increase sinus velocities and shear stresses near the leaflets, which is also beneficial for valve health. The prosthetic valves tested – transcatheter and sutureless – both severely limited sinus perfusion, which could help explain an increased risk of thrombus formation in the transcatheter case and suggests similar risk for sutureless valves. These findings could help educate clinicians on proper courses of treatment based on patient-specific valve parameters, and could also provide useful information for engineers when designing new valve prostheses.Item Open Access Large-eddy simulation of compressible flows using the stretched-vortex model and a fourth-order finite volume scheme on adaptive grids(Colorado State University. Libraries, 2022) Walters, Sean, author; Guzik, Stephen, advisor; Gao, Xinfeng, advisor; Randall, David, committee member; Yalin, Azer, committee memberState-of-the-art engineering workflows are becoming increasingly dependent on accurate large-eddy simulations (LES) of compressible, turbulent flows for off-design conditions. Traditional CFD algorithms for compressible flows rely on numerical stabilization to handle unresolved physics and/or steep gradient flow features such as shockwaves. To reach higher levels of physical-fidelity than previously attainable, more accurate turbulence models must be properly incorporated into existing, high-order CFD codes in a manner that preserves the stability of the underlying algorithm while fully realizing the benefits of the turbulence model. As it stands, casually combining turbulence models and numerical stabilization degrades LES solutions below the level achievable by using numerical stabilization alone. To effectively use high-quality turbulence models and numerical stabilization simultaneously in a fourth-order-accurate finite volume LES algorithm, a new method based on scale separation is developed using adaptive grid technology for the stretched-vortex subgrid-scale (SGS) LES model. This method successfully demonstrates scheme-independent and grid-independent LES results at very-high-Reynolds numbers for the inviscid Taylor-Green vortex, the temporally-evolving double-shear-flow, and decaying, homogeneous turbulence. Furthermore, the method clearly demonstrates quantifiable advantages of high-order accurate numerical methods. Additionally, the stretched-vortex LES wall-model is extended to curvilinear mapped meshes for compressible flow simulations using adaptive mesh refinement. The capabilities of the wall-model combined with the stretched-vortex SGS LES model are demonstrated using the canonical zero-pressure-gradient flat-plate turbulent boundary layer. Finally, the complete algorithm is applied to simulate flow-separation and reattachment over a smooth-ramp, showing high-quality solutions on extremely coarse meshes.Item Open Access Time integration for complex fluid dynamics(Colorado State University. Libraries, 2021) Christopher, Joshua C., author; Gao, Xinfeng, advisor; Guzik, Stephen M., committee member; Marchese, Anthony J., committee member; Bangerth, Wolfgang, committee memberEfficient and accurate simulation of turbulent combusting flows in complex geometry remains a challenging and computationally expensive proposition. A significant source of computational expense is in the integration of the temporal domain, where small time steps are required for the accurate resolution of chemical reactions and long solution times are needed for many practical applications. To address the small step sizes, a fourth-order implicit-explicit additive Runge-Kutta (ARK4) method is developed to integrate the stiff chemical reactions implicitly while advancing the convective and diffusive physics explicitly in time. Applications involving complex geometry, stiff reaction mechanisms, and high-order spatial discretizations are challenged by stability issues in the numerical solution of the nonlinear problem that arises from the implicit treatment of the stiff term. Techniques for maintaining a physical thermodynamic state during the numerical solution of the nonlinear problem, such as placing constraints on the nonlinear solver and the use of a nonlinear optimizer to find valid thermodynamic states, are proposed and tested. Verification and validation are performed for the new adaptive ARK4 method using lean premixed flames burning hydrogen, showing preservation of 4th-order error convergence and recovery of literature results. ARK4 is then applied to solve lean, premixed C3H8-air combustion in a bluff-body combustor geometry. In the two-dimensional case, ARK4 provides a 70× speedup over the standard explicit four-stage Runge-Kutta method and, for the three-dimensional case, three-orders-of-magnitude-larger time step sizes are achieved. To further increase the computational scaling of the algorithms, parallel-in-time (PinT) techniques are explored. PinT has the dual benefit of providing parallelization to long temporal domains as well as taking advantage of hardware trends towards more concurrency in modern high-performance computing platforms. Specifically, the multigrid reduction-in-time (MGRIT) method is adapted and enhanced by adding adaptive mesh refinement (AMR) in time. This creates a space-time algorithm with efficient solution-adaptive grids. The new MGRIT+AMR algorithm is first verified and validated using problems dominated by diffusion or characterized by time periodicity, such as Couette flow and Stokes second problem. The adaptive space-time parallel algorithm demonstrates up to a 13.7× speedup over a time-sequential algorithm for the same solution accuracy. However, MGRIT has difficulties when applied to solve practical fluid flows, such as turbulence, governed by strong hyperbolic partial differential equations. To overcome this challenge, the multigrid operations are modified and applied in a novel way by exploiting the space-time localization of fine turbulence scales. With these new operators, the coarse-scale errors are advected out of the temporal domain while the fine-scale dynamics iterate to equilibrium. This leads to rapid convergence of the bulk flow, which is important for computing macroscopic properties useful for engineering purposes. The novel multigrid operations are applied to the compressible inviscid Taylor-Green vortex flow and the convergence of the low-frequency modes is achieved within a few iterations. Future work will be focused on a performance study for practical highly turbulent flows.Item Open Access Unsteady Reynolds-averaged Navier-Stokes simulations of inlet flow distortion in the fan system of a gas-turbine aero-engine(Colorado State University. Libraries, 2015) Spotts, Nathan, author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Sakurai, Hiroshi, committee member; Alves, Goldino, committee member; Liu, Jiangguo, committee memberAs modern trends in commercial aircraft design move toward high-bypass-ratio fan systems of increasing diameter with shorter, nonaxisymmetric nacelle geometries, inlet distortion is becoming common in all operating regimes. The distortion may induce aerodynamic instabilities within the fan system, leading to catastrophic damage to fan blades, should the surge margin be exceeded. Even in the absence of system instability, the heterogeneity of the flow affects aerodynamic performance significantly. Therefore, an understanding of fan-distortion interaction is critical to aircraft engine system design. This thesis research elucidates the complex fluid dynamics and fan-distortion interaction by means of computational fluid dynamics (CFD) modeling of a complete engine fan system; including rotor, stator, spinner, nacelle and nozzle; under conditions typical of those encountered by commercial aircraft. The CFD simulations, based on a Reynolds-averaged Navier-Stokes (RANS) approach, were unsteady, three-dimensional, and of a full-annulus geometry. A thorough, systematic validation has been performed for configurations from a single passage of a rotor to a full-annulus system by comparing the predicted flow characteristics and aerodynamic performance to those found in literature. The original contributions of this research include the integration of a complete engine fan system, based on the NASA rotor 67 transonic stage and representative of the propulsion systems in commercial aircraft, and a benchmark case for unsteady RANS simulations of distorted flow in such a geometry under realistic operating conditions. This study is unique in that the complex flow dynamics, resulting from fan-distortion interaction, were illustrated in a practical geometry under realistic operating conditions. For example, the compressive stage is shown to influence upstream static pressure distributions and thus suppress separation of flow on the nacelle. Knowledge of such flow physics is valuable for engine system design.