PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,

The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasised. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.Comment: 23 pages, 10 figure

A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation, modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (e.g. the mean pressure) and to track particles. All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean model is adopted. An adaptive algorithm that computes the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows

HPC-enabling technologies for high-fidelity combustion simulations

With the increase in computational power in the last decade and the forthcoming Exascale supercomputers, a new horizon in computational modelling and simulation is envisioned in combustion science. Considering the multiscale and multiphysics characteristics of turbulent reacting flows, combustion simulations are considered as one of the most computationally demanding applications running on cutting-edge supercomputers. Exascale computing opens new frontiers for the simulation of combustion systems as more realistic conditions can be achieved with high-fidelity methods. However, an efficient use of these computing architectures requires methodologies that can exploit all levels of parallelism. The efficient utilization of the next generation of supercomputers needs to be considered from a global perspective, that is, involving physical modelling and numerical methods with methodologies based on High-Performance Computing (HPC) and hardware architectures. This review introduces recent developments in numerical methods for large-eddy simulations (LES) and direct-numerical simulations (DNS) to simulate combustion systems, with focus on the computational performance and algorithmic capabilities. Due to the broad scope, a first section is devoted to describe the fundamentals of turbulent combustion, which is followed by a general description of state-of-the-art computational strategies for solving these problems. These applications require advanced HPC approaches to exploit modern supercomputers, which is addressed in the third section. The increasing complexity of new computing architectures, with tightly coupled CPUs and GPUs, as well as high levels of parallelism, requires new parallel models and algorithms exposing the required level of concurrency. Advances in terms of dynamic load balancing, vectorization, GPU acceleration and mesh adaptation have permitted to achieve highly-efficient combustion simulations with data-driven methods in HPC environments. Therefore, dedicated sections covering the use of high-order methods for reacting flows, integration of detailed chemistry and two-phase flows are addressed. Final remarks and directions of future work are given at the end. }The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the CoEC project, grant agreement No. 952181 and the CoE RAISE project grant agreement no. 951733.Peer ReviewedPostprint (published version

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor

Adaptive and convergent methods for large eddy simulation of turbulent combustion

textIn the recent past, LES methodology has emerged as a viable tool for modeling turbulent combustion. LES computes the large scale mixing process accurately, thereby providing a better starting point for small-scale models that describe the combustion process. Significant effort has been made over past decades to improve accuracy and applicability of the LES approach to a wide range of flows, though the current conventions often lack consistency to the problems at hand. To this end, the two main objectives of this dissertation are to develop a dynamic transport equation-based combustion model for large- eddy simulation (LES) of turbulent spray combustion and to investigate grid- independent LES modeling for scalar mixing. Long-standing combustion modeling approaches have shown to be suc- cessful for a wide range of gas-phase flames, however, the assumptions required to derive these formulations are invalidated in the presence of liquid fuels and non-negligible evaporation rates. In the first part of this work, a novel ap- proach is developed to account for these evaporation effects and the resulting multi-regime combustion process. First, the mathematical formulation is de- rived and the numerical implementation in a low-Mach number computational solver is verified against one-dimensional and lab scale, both non-reacting and reacting spray-laden flows. In order to clarify the modeling requirements in LES for spray combustion applications, results from a suite of fully-resolved direct numerical simulations (DNS) of a spray laden planar jet flame are fil- tered at a range of length scales. LES results are then validated against two sets of experimental jet flames, one having a pilot and allowing for reduced chemistry modeling and the second requiring the use of detail chemistry with in situ tabulation to reduce the computational cost of the direct integration of a chemical mechanism. The conventional LES governing equations are derived from a low-pass filtering of the Navier-Stokes equations. In practice, the filter used to derive the LES governing equations is not formally defined and instead, it is assumed that the discretization of LES equations will implicitly act as a low-pass filter. The second part of this study investigates an alternative derivation of the LES governing equations that requires the formal definition of the filtering operator, known as explicitly filtered LES. It has been shown that decoupling the filter- ing operation from the underlying grid allows for the isolation of subfilter-scale modeling errors from numerical discretization errors. Specific to combustion modeling are the aggregate errors associated with modeling sub-filter distribu- tions of scalars that are transported by numerical impacted turbulent fields. Quantities of interest to commonly-used combustion models, including sub- filter scalar variance and filtered scalar dissipation rate, are investigated for both homogeneous and shear-driven turbulent mixing.Aerospace Engineerin

Numerical Simulation of Turbulent Flames based on Reaction-Diffusion Manifolds (REDIM) Reduced Chemistry

Die Simulation reagierender Strömungen beinhaltet komplexe Wechselwirkungen zwischen Thermodynamik, chemischen Reaktionen, molekularem Transport und Fluiddynamik. Für die meisten technischen Anwendungsbereiche liegen turbulente reagierende Strömungen vor, und ein Verständnis aller zugrundeliegenden Prozesse spielt eine wichtige Rolle für die Beschreibung der zugrundeliegenden Phänomene. Direkte Numerische Simulationen (DNS, engl. „direct numerical simulations“) lösen die Erhaltungsgleichungen für reagierende Strömungen in Raum und Zeit ohne Modellierung der Turbulenz vollständig auf, was höchste Anforderungen an die zur Verfügung stehende Rechenleistung stellt. Zusätzlich erfordert die Modellierung von Verbrennungs¬prozessen chemische Reaktionsmechanismen mit mehr als tausend Elementarreaktionen und chemischen Spezies. Turbulenz erhöht die Komplexität und die Dimension des Systems, so dass sich anwendungsnahe reagierende Strömungen (z. B. turbulente Verbrennungsprozesse) auch heute nicht unter Verwendung detaillierter Kinetik und direkten numerischen Simulationen simulieren lassen. Vor diesem Hintergrund erfolgt in der Dissertation die Modellierung turbulenter reagierender Strömungen durch eine statistische Beschreibung der Turbulenz mit Wahrscheinlichkeitsdichtefunktionen (engl. Probability Density Function, PDF) und eine Vereinfachung der chemischen Reaktionen auf Basis von Reaktions-Diffusions-Mannigfaltigkeiten (engl. Reacition-Diffusion Manifolds, REDIM). In der PDF-Methode müssen die Diffusionsprozesse durch ein Mischungsmodell modelliert werden. Obwohl Mischungsmodelle und Methoden für die Modellreduktion für die Chemie bereits untersucht und unabhängig voneinander entwickelt wurden, wurde deren Kopplung bisher nicht umfassend untersucht. Die Koppelung zwischen Mischungsmodellen und reduzierter Chemie spielt jedoch eine zentrale Rolle für die Genauigkeit der Modellierung. Eine nicht optimale Kopplung zwischen beiden Prozessen kann zu erheblichen qualitativen und quantitativen Fehlern führen. Der Hauptbeitrag der vorliegenden Arbeit ist die Untersuchung der Kopplung zwischen Mischungsmodellen und reduzierter Chemie für turbulente reagierende Strömungen. In der Arbeit wird ein Modell basierend auf einer Projektion der Mischungsmodelle auf die reduzierte Kinetik für die Kopplung vorgeschlagen. Unterschiedliche Projektionsstrategien auf Basis von physikalischen Betrachtungen werden motiviert, mathematisch formuliert und untersucht. Die vorgeschlagenen Kopplungsstrategien werden anhand der Modellierung von nicht-vorgemischten pilot-stabilisierten turbulenten Flammen („Sandia Flame D, E und F“) validiert. Der Vergleich der Simulationsergebnisse mit experimentellen Ergebnissen aus der Literatur belegt die Qualität der entwickelten Modelle. Die vorgestellten und validierten Konzepte lassen sich zur Modellierung technisch relevanter Verbrennungsprozesse (Verbrennung in Motoren, Gasturbinen) - aber auch für andere technisch relevante turbulente reagierende Strömungen (chemische Energiespeicherung) verwenden