A parallel finite element algorithm for 3D incompressible flow in velocity-vorticity form

In the last decade, developments and advancement in computer technology, especially the availability of the massively parallel machine, have escalated the numerical treatment of complex fluid flow problems to a new height. Numerical simulation of incompressible viscous fluid flow, often associated with practical industrial and environmental situations, is receiving intense scrutiny to perform in the promising distributed parallel computing environment. On the other hand, the field of computational fluid dynamics continues to explore and exploit unified and versatile formulations, in contention with the notorious divergence-free velocity field constraint, for incompressible Navier-Stokes equations that encompass fluid flow in two- and threedimensions. The velocity-vorticity formulation for the incompressible Navier-Stokes equations is chosen with the full extent to resolve these issues. In the present dissertation, a new finite element implementation for two- and three-dimensional incompressible fluid flow is developed in the velocity-vorticity form. Pressure is eliminated analytically by taking the curl of the momentum equations, and vorticity is introduced as the active variable. The formulation consists of the three derived vorticity transport equations in conjunction with three velocity Poisson equations. Satisfaction of the continuity constraint is cast onto the specific treatment of the kinematic vorticity boundary condition for the no slip wall. A divergence-free solution is guaranteed with equal order finite element interpolation functions for all state variables

Hermes-3: Multi-component plasma simulations with BOUT++

A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. This design enables the same code to be configured at run-time to solve systems of partial differential equations in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs). Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests.Comment: Submitted to Computer Physics Communication

Enhancement Of Jet Impingement Heat Transfer Using Shape Modification And Phase Change

The overall goal of the present study is to enhance heat transfer rate performance on high heat flux surfaces while maintaining a uniform and low temperature of the substrate. The specific objectives are to determine shapes which maximize heat transport from heater surfaces when using jet impingement cooling method and to model a two phase jet impingement process which incorporates phase change at the impingement substrate

A study of the turbulent flow of a high speed Coanda jet

This thesis presents an experimental investigation into a compressible turbulent wall jet issuing from a slot, and flowing over a surface with streamwise curvature, followed by a plane wall recovery region. The purpose of this data was to provide suitable test cases to aid in the design and validation of turbulence models used for curved flow situations in computational fluid dynamics. The presence of streamwise curvature provides an extra rate of strain to the flow which effects both the mean flow field and the turbulence structure. The effects of curvature are dependent on the ratio of the slot width to the radius of curvature. The effects are increased with the magnitude of this ratio. Hot film anemometry was used to measure the mean flow and Reynolds stresses under six different flow regimes. Four experiments were performed using a constant slot to radius ratio, and the supply pressure ratio was varied. Two further experiments were performed at a constant pressure ratio, but at differing slot to radius ratios. In all cases, the extra rate of strain was found to increase the jet growth and velocity decay rates beyond those of a plane wall jet. 'History effects' were apparent where there was a change from flow with streamwise wall curvature to that without. The turbulence structure was found to require a finite distance along the recovery section before it reverts to a plane wall turbulence structure. The presence of the extra rate of strain, and the history effects at sudden changes in surface curvature, make strong demands on any turbulence model. Various turbulence models have been tested, and although no one turbulence model has proved robust enough for all flow situations, a number of models have been identified to provide superior performance under certain conditions. The use of a higher order numerical scheme has also been found to reduce the effects of numerical diffusion, leading to improvements in the predictions of the flow shock cell structure and the breakaway performance of the jet

Parallel computational strategies for modelling transient Stokes fluid flow.

The present work is centred on two main research areas; the development of finite element techniques for the modelling of transient Stokes flow and implementation of an effective parallel system on distributed memory platforms for solving realistic large-scale Lagrangian flow problems. The first part of the dissertation presents the space-time Galerkin / least-square finite element implicit formulation for solving incompressible or slightly compressible transient Stokes flow with moving boundaries. The formulation involves a time discontinuous Galerkin method and includes least-square terms in the variational formulation. Since the additional terms involve the residual of the Euler- Lagrangian equations evaluated over element interiors, it prevents numerical oscillation on the pressure field when equal lower order interpolation functions for velocity and pressure fields are used, without violating the Babuska-Brezzi stability condition. The space-time Galerkin / least-square formulation has been successfully extended into the finite element explicit analysis, in which the penalty based discrete element contact algorithm is adopted to simulate fiuid-structure or fluid-fluid particle contact. The second part of the dissertation focuses on the development of an effective parallel processing technique, using the natural algorithm concurrency of finite element formulations. A hybrid iterative direct parallel solver is implemented into the ELFEN/implicit commercial code. The solver is based on a non-overlapping domain decomposition and sub-structure approach. The modified Cholesky factorisation is used to eliminate the unknown variables of the internal nodes at each subdomain and the resulting interfacial equations are solved by a Krylov subspace iterative method. The parallelization of explicit fluid dynamics is based on overlapping domain decomposition and a Schwarz alternating procedure. Due to the dual nature of the overlapping domain decomposition a buffer zone between any two adjacent subdomains is introduced for handling the inter-processor communication. Both solvers are tested on a PC based interconnected network system and its performances are judged by the parallel speed-up and efficiency

Magnetoconvection in sunspot umbrae :steady and oscillatory localised states

PhD ThesisAstrophysical observations of the solar photosphere uncover a wealth of detailed structures that arise from the interaction of vigorously convecting plasma and the internally generated magnetic elds. The most prominent features are sunspots, which exhibit sub-structures on a range of scales. Speci cally within the umbra is an intensity pattern consisting of individual small bright points, referred to as umbral dots. These states are thought to indicate the presence of localised magnetoconvective motions. This thesis discusses the applications of magnetoconvection to the umbra, with the aim of investigating the occurrence of steady and oscillatory localised states known as convectons. Convectons are isolated convective plumes from which magnetic ux is at least partially expelled. In two-dimensional Boussinesq magnetoconvection we examine both a simpli ed model, in which the vertical structure has been reduced, and a fully-resolved model. In performing parametric surveys of the steady modes we attempt to understand how localised states di er between the two models. Examining the oscillatory localised cells we locate, for the rst time, these states in the fully-resolved system. Both of these models are horizontally periodic. We nd that by altering these horizontal boundaries so that they are impermeable to uid motions does not impede the existence of these states but leads to the additional existence of a new set of solutions that are localised at the boundaries. To examine the bifurcation structure of these states we develop a numerical continuation model. However, due to the limitations of the continuation program, AUTO-07p, this model has restricted symmetries and impermeable horizontal boundaries. Despite these simpli cations the symmetries of the model ensure that convectons can still be found and in addition allows the examination of the wall states. The remainder of this thesis focuses on compressible magnetoconvection. In studying oscillatory convectons in two-dimensions we nd a new type of oscillation not found in the Boussinesq models. This state no longer retains Boussinesq point symmetry but has more gentle extended up ows characteristic of a three-dimensional cylindrical plume. In three dimensions a new type of steady convecton is found with a broken symmetry such that the cross-section corresponds to a single overturning roll

Enhancement of engine simulation using LES turbulence modeling and advanced numerical schemes

The goal of this study is to develop advanced numerical models and algorithms to improve the accuracy of engine spray combustion simulation. This study developed a large eddy simulation (LES) turbulence model and adaptive mesh refinement (AMR) algorithms to enhance the accuracy and computational efficiency of engine simulation. The LES approach for turbulence modeling is advantageous over the traditional Reynolds Averaged Navier Stokes (RANS) approach due to its capability to obtain more detailed flow information by resolving large-scale structures which are strongly geometry dependent. The current LES approach used a one-equation, non-viscosity, dynamic structure model for the sub-grid stress tensor and also used a gradient method for the sub-grid scalar fluxes. The LES implementation was validated by comparing the predicted spray penetrations and structures in a non-evaporating diesel spray. The present LES model, when coupled with spray breakup and detailed chemistry models, were able to predict the overall cylinder pressure history, heat release rate data, and the trends of NOx and soot emissions with respect to different injection timings and EGR levels in a heavy-duty diesel engine. Results also indicated that the LES model could predict the unsteadiness of in-cylinder flows and have the potential to provide more detailed flow structures compared to the RANS model. AMR algorithms were also developed to improve transient engine spray simulation. It is known that inadequate spatial resolution can cause inaccuracy in spray simulation using the stochastic Lagrangian particle approach due to the over-estimated diffusion and inappropriate liquid-gas phase coupling. Dynamic local mesh refinement, adaptive to fuel spray and vapor gradients, was developed to increase the grid resolution in the spray region. AMR was parallelized using the MPI library and various strategies were also adopted in order to improve the computational efficiency, including timestep control, reduction in search of the neighboring cells on the processor boundaries, and re-initialization of data at each adaptation. The AMR implementation was validated by comparing the predicted spray penetrations and structures. It was found that a coarse mesh using AMR could produce the same results as those using a uniformly fine mesh with substantially reduced computer time. The parallel performance using AMR varied depending on the geometry and simulation conditions. In general, the computations without valve motion or using a fine mesh could obtain better parallel performance than those with valve motion or using a coarse mesh

Application of the multiblock method in computational aerodynamics

The main challenge in computational aerodynamics is to provide practical, credible, cost and schedule effective methods for routine design application and for full integration of these methods into the design cycle. Although advances in physical modelling and solution algorithms are continuing requirements of the aerospace industry, other more practical difficulties also impede the full realisation of the potential of existing methods. The contribution of this thesis is to examine and tackle several of these issues and to evaluate computational aerodynamics as a tool for engineering design and scientific enquiry. An advanced computational aerodynamics method is evaluated as an engineering tool for axisymmetric forebody and base flow problems. First the adaption of an existing two-dimensional flow solver to axisymmetric flow is described, then specific test cases are considered. The motivation for creating an axisymmetric flow solver is the considerable performance improvements compared to a fully three-dimensional method. The accuracy and robustness of the method are very good for forebody problems. For base flow problems accuracy and robustness are less satisfactory, although the performance of other prediction methods is also poorer for this more demanding problem. For both problem types the speed of the flow solver, the required computing resource and the time and effort necessary for pre- and post-processing are all satisfactory for routine calculation in an engineering environment. Shock reflection hysteresis and plume structure in a low density, axisymmetric highly underexpanded air jet is examined using a Navier-Stokes flow solver. This type of jet is found in a number of applications e.g. rocket exhausts and fuel injectors. The plume structure is complex, involving the interaction of several flow features, making this a demanding problem. Two types of shock reflection appear to occur in the plume, regular and Mach, depending on the jet pressure ratio. The existence of a dual solution domain where either type may occur has been predicted, in agreement with experiment where the same phenomenon has been observed for a nitrogen jet. There is a hysteresis in the shock reflection type; the reflection type observed in the dual solution domain depends on the time history of the plume development. A quasi-steady approach is employed in order to calculate the entire hysteresis loop. The results of the computational study are used to examine the structure of the plume, and are compared with experimental data where possible. Some flow features not initially recognised from experiment have been identified, notably curvature of the Mach disc, recirculation behind the Mach disc and the 'regular' reflection having Mach reflection characteristics. Included in the study is a review of the two dimensional shock reflection hysteresis problem to establish a theoretical background. The value of CFD as a tool for scientific investigation is clearly demonstrated by this study. The need for automation of the multiblock grid generation process is discussed. A new approach to automatically process a multiblock topology in order to prepare it for the grid generation process is described. The method is based on a cost function which attempts to model the objectives of the skilled grid generation software user who at present performs the task of block positioning and shaping in an interactive manner. A number of test cases are examined. It is also suggested that an existing unstructured mesh generation method could be adopted as an initial topology generation tool. Further work towards creating a fully automatic grid generation tool and extension into three dimensions are discussed. The parallel execution of an aerodynamic simulation code on a non-dedicated, heterogeneous cluster of workstations is examined. This type of facility is commonly available to CFD developers and users in academia, industry and government laboratories and is attractive in terms of cost for CFD simulations. However, practical considerations appear at present to discourage widespread adoption of this technology. The main obstacles to achieving an efficient, robust parallel CFD capability in a demanding multi-user environment are investigated. A static load-balancing method is described which takes account of varying processor speeds. A dynamic re-allocation method to account for varying processor loads has been developed. Use of proprietary software has facilitated the implementation of the method