Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Applications in CFD-DEM

In this work, a coarse-graining method previously proposed by the authors in a companion paper based on solving diffusion equations is applied to CFD-DEM simulations, where coarse graining is used to obtain solid volume fraction, particle phase velocity, and fluid-particle interaction forces. By examining the conservation requirements, the variables to solve diffusion equations for in CFD-DEM simulations are identified. The algorithm is then implemented into a CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a general-purpose, three-dimensional CFD solver based on unstructured meshes. Numerical simulations are performed for a fluidized bed by using the CFD-DEM solver with the diffusion-based coarse-graining algorithm. Converged results are obtained on successively refined meshes, even for meshes with cell sizes comparable to or smaller than the particle diameter. This is a critical advantage of the proposed method over many existing coarse-graining methods, and would be particularly valuable when small cells are required in part of the CFD mesh to resolve certain flow features such as boundary layers in wall bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that the overhead computational costs incurred by the proposed coarse-graining procedure are a small portion of the total costs in typical CFD-DEM simulations as long as the number of particles per cell is reasonably large, although admittedly the computational overhead of the coarse graining often exceeds that of the CFD solver. Other advantages of the present algorithm include more robust and physically realistic results, flexibility and easy implementation in almost any CFD solvers, and clear physical interpretation of the computational parameter needed in the algorithm. In summary, the diffusion-based method is a theoretically elegant and practically viable option for CFD-DEM simulations

Applied Filtered Density Function

An overview is presented of recent advances in the filtered density function (FDF) modeling and simulation of turbulent combustion. The review is focused on the developments that have facilitated the FDF to be broadly applied in large eddy simulation (LES) of practical flows. These are primarily the development of a new Lagrangian Monte Carlo solver for the FDF, and the implementation of this solver on Eulerian domains portrayed by unstructured grids. With these developments, it is now much easier to apply FDF for predictions of reacting flows in complex geometrical configurations

Application of FDS and firefoam in large eddy simulations of a turbulent buoyant helium plume

Large eddy simulations are conducted in the near-field region of a large turbulent buoyant helium plume. Such plumes are of relevance for fire safety research due to the similar flow features as in the buoyant (smoke) plumes above the fire source. The transient and mean flow dynamics are discussed with and without the use of a Smagorinsky-type subgrid scale (SGS) model. For this purpose, two different computational fluid dynamics (CFD) packages are used. Small-scale structures, formed at the edge of the plume inlet due to a baroclinic and gravitational mechanism and subject to flow instabilities, interact with large-scale features of the flow, resulting in a puffing cycle. This puffing cycle is recovered in the simulations. In general, the LES calculations reproduce the main features of the turbulent plume. Mean velocity results compare well with the experimental data. The mass fractions are overpredicted on the centerline though, and higher on the domain

High-Fidelity Simulation of Compressible Flows for Hypersonic Propulsion Applications

In the first part of this dissertation, the scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. The SFMDF is a subgrid scale closure and is simulated via a Lagrangian Monte Carlo solver. US3D is an Eulerian finite volume code and has proven very effective for compressible flow simulations. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) of compressible turbulent flows on unstructured meshes. Simulations are conducted of subsonic and supersonic flows. The consistency and accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology. In the second part of this dissertation, a new methodology is developed for accurate capturing of discontinuities in multi-block finite difference simulations of hyperbolic partial differential equations. The fourth-order energy-stable weighted essentially non-oscillatory (ESWENO) scheme on closed domains is combined with simultaneous approximation term (SAT) weak interface and boundary conditions. The capability of the methodology is demonstrated for accurate simulations in the presence of significant and abrupt changes in grid resolution between neighboring subdomains. Results are presented for the solutions of linear scalar hyperbolic wave equations and the Euler equations in one and two dimensions. Strong discontinuities are passed across subdomain interfaces without significant distortions. It is demonstrated that the methodology provides stable and accurate solutions even when large differences in the grid-spacing exist, whereas strong imposition of the interface conditions causes noticeable oscillations

A Hybrid Discontinuous Galerkin-Monte Carlo Simulator for Filtered Density Function

A new computational scheme is developed for large eddy simulation (LES) of compressible turbulent reacting flows via the filtered density function (FDF) subgrid scale closure. This is a hybrid scheme, combining the discontinuous Galerkin (DG) Eulerian solver with a Lagrangian Monte Carlo FDF simulator. The methodology is shown to be suitable for LES, as a larger portion of the resolved energy is captured as the order of spectral approximation increases. Simulations are conducted of both incompressible and compressible flows. The consistency and the overall performance of the DG-MC solver, and the realizability of the simulated results are demonstrated via LES of a temporally developing mixing layer under both non reacting and reacting conditions. It is also shown that the scheme is capable of accurate simulation of shock dominated flows

Modelling of Multiphase Fluid flow in Heterogeneous Reservoirs

Computational modeling of multiphase fluid flow in highly heterogenous problems with complicated geometries is a challenging problem for reservoir engineers, with a rich research in establishing best methods and approaches. The novelty in this work is centered around the implementation and comparison of simulation results from two software - the open source ICFESRT and the commercial software ECLIPSE - for a two-phase multiphase problem (oilwater) in both simple and complex geometries. The work involves: (a) implementation and comparison of simulation results from the two software on three different, hypothetical but typical geometries; (b) consideration of a real field case and the associated data analysis, rock characterization, and geostatistics of a real field representative of a highly heterogeneous reservoir; and (c) implementation of both software on the real field case for predictions of oil production at the site, and comparison of the simulation results from the two software. The initial comparison of simulation results for was carried out using three hypothetical (but common) geometries, these being: (a) a quarter five spot with one geological layer; (b) the same geometry as in (a) but with a vertical heterogeneity i.e. 5 different geological layers; (c) and lastly a full 5 spot with 5 different geological layers was implemented. Three different mesh resolutions were applied in both software and comparisons were carried out for mesh-independency. The results showed that in all these three scenarios, good agreement was observed between IC-FERST (coarse mesh) and ECLIPSE (fine mesh) with an average percentage difference at the production well ranging between 2.5% and 10.5% for the oil production and 12% and 26% for the water production. Both the ICFERST and ECLIPSE were subsequently implemented on a real, heterogeneous field – which consisted of 25 producing wells and 8 injections wells. Prior to the software implementation, a data analysis and rock characterization was carried out –Using data from the 33 wells. The logging and core data (a total of 30,000 log readings and 1150 core samples) were utilized and a novel rock characterization technique -Balaha Rock Characterization Code- was implemented to allow for the optimal clustering of rock types within the reservoir, The rock characterization resulted in identifying 7 rock types with their unique porosity-hydraulic permeability relationships. Subsequently, geostatistical methods were implemented – which enabled populating the computational cells of the two software with the corresponding reservoir properties (porosity, hydraulic permeability). To achieve the property population into the unstructured computational domain of the ICFERST software, a newly-developed script was written in Matlab and Python. The rock properties data populated on IC-FERST consist of porosity, permeability, relative permeability, capillary pressure and connate water saturation. A further comparison between the IC-FERST simulation results with the corresponding ECLIPSE simulations was carried out – were all simulations were carried out for a period of 40 years. The percentage differences between the two software simulations were estimated for : (i) ten individual production wells and (ii) the total of all production wells. The results showed that a good agreement exists between the IC-FERST and ECLIPSE simulations, with an average percentage difference for the total oil production of 10.5%, the total water production of 26% and the total water injection of 14%. The results for the ten individual wells showed an average percentage difference of 15.5% ranging from 3 to 29% for the oil production in the late time period. Slightly higher differences were observed when the overall period was considered, due to the large difference at the early time period of the simulation. The results indicated that IC-FERST, when incorporating the necessary rock characterization information – which highlight the heterogeneity of the reservoir – can produce results that can compete with the industry standard ECLIPSE. Additional aspects need to be considered within the current real field IC-FERST simulation, the inclusion of possible fractures and faults, as these were incorporated in the computational domain of ECLIPSE. Additional capabilities also still need to be embedded into IC-FERST, such as the incorporation of the fluid density and viscosity variations with pressure and the consideration of the volume factors, in order to enhance its competitiveness with existing commercial reservoirs simulators such as ECLIPSE

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

Prediction of combustion instability limit cycle oscillations by combining flame describing function simulations with a thermoacoustic network model

Accurate prediction of limit cycle oscillations resulting from combustion instability has been a long-standing challenge. The present work uses a coupled approach to predict the limit cycle characteristics of a combustor, developed at Cambridge University, for which experimental data are available (Balachandran, Ph.D. thesis, 2005). The combustor flame is bluff-body stabilised, turbulent and partially-premixed. The coupled approach combines Large Eddy Simulation (LES) in order to characterise the weakly non-linear response of the flame to acoustic perturbations (the Flame Describing Function (FDF)), with a low order thermoacoustic network model for capturing the acoustic wave behaviour. The LES utilises the open source Computational Fluid Dynamics (CFD) toolbox, OpenFOAM, with a low Mach number approximation for the flow-field and combustion modelled using the PaSR (Partially Stirred Reactor) model with a global one-step chemical reaction mechanism for ethylene/air. LES has not previously been applied to this partially-premixed flame, to our knowledge. Code validation against experimental data for unreacting and partially-premixed reacting flows without and with inlet velocity perturbations confirmed that both the qualitative flame dynamics and the quantitative response of the heat release rate were captured with very reasonable accuracy. The LES was then used to obtain the full FDF at conditions corresponding to combustion instability, using harmonic velocity forcing across six frequencies and four forcing amplitudes. The low order thermoacoustic network modelling tool used was the open source OSCILOS (http://www.oscilos.com). Validation of its use for limit cycle prediction was performed for a well-documented experimental configuration, for which both experimental FDF data and limit cycle data were available. The FDF data from the LES for the present test case was then imported into the OSCILOS geometry network and limit cycle oscillations of frequency 342 Hz and normalised velocity amplitude of 0.26 were predicted. These were in good agreement with the experimental values of 348 Hz and 0.21 respectively. This work thus confirms that a coupled numerical prediction of limit cycle behaviour is possible using an entirely open source numerical framework

[Research activities in applied mathematics, fluid mechanics, and computer science]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995

The mitral valve computational anatomy and geometry analysis

We present a novel methodology to characterize and quantify the Mitral Valve (MV) geometry and physical attributes in a multi-resolution framework. A multi-scale decomposition was implemented to model the MV geometry by using superquadric shape primitives and spectral reconstruction of the finer-scale geometric details. Superquadrics provide a basis to normalize the size and approximate a basic model of the MV geometry. The point-wise difference between the original geometry and the superquadric model denotes the finer-scale geometric details, which can be modeled as a scalar attribute for the MV model development. The additive decomposition of the basic MV geometry from geometric details (attributes) allows recovering the actual geometry by superposition of the superquadric approximation and the finer-details model. We implemented a lasso optimization algorithm to perform spectral analysis and develop the Fourier reconstruction of the geometric details. The spectral modeling enabled us to resample the geometric details or use spectral filters in order to adjust the spatial resolution in the model reconstruction. It also provides the basis to control the level of detail in the final model reconstruction by applying low-pass filters in the frequency domain. The higher-order attributes such as internal fiber architecture can be integrated with the geometric models using the same framework. We applied our pipeline to create models of three ovine MVs based on computed-tomography 3D images with micrometer resolution. We were able to quantify the MV leaflet geometry, reconstruct models with custom level of geometric details, and develop medial representation of the MV leaflet structure. The results show that our methodology for geometry analysis provides a basis for assessing patient-specific geometries and facilitates developing population-averaged models. Ultimately, this approach allows building personalized image-based computational models for medical device design and surgical treatment simulations.Mechanical Engineerin