Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed

Large-Eddy Simulations of Flow and Heat Transfer in Complex Three-Dimensional Multilouvered Fins

The paper describes the computational procedure and results from large-eddy simulations in a complex three-dimensional louver geometry. The three-dimensionality in the louver geometry occurs along the height of the fin, where the angled louver transitions to the flat landing and joins with the tube surface. The transition region is characterized by a swept leading edge and decreasing flow area between louvers. Preliminary results show a high energy compact vortex jet forming in this region. The jet forms in the vicinity of the louver junction with the flat landing and is drawn under the louver in the transition region. Its interaction with the surface of the louver produces vorticity of the opposite sign, which aids in augmenting heat transfer on the louver surface. The top surface of the louver in the transition region experiences large velocities in the vicinity of the surface and exhibits higher heat transfer coefficients than the bottom surface.Air Conditioning and Refrigeration Project 9

Fluid and thermal behaviour of multi-phase flow through curved ducts

Fluid flow through curved ducts is influenced by the centrifugal action arising from duct curvature and has behaviour uniquely different to fluid flow through straight ducts. In such flows, centrifugal forces induce secondary flow vortices and produce spiralling fluid motion within curved ducts. Secondary flow promotes fluid mixing with intrinsic potential for thermal enhancement and, exhibits possibility of fluid instability and additional secondary vortices under certain flow conditions. Reviewing published numerical and experimental work, this thesis discusses the current knowledge-base on secondary flow in curved ducts and, identifies the deficiencies in analyses and fundamental understanding. It then presents an extensive research study capturing advanced aspects of secondary flow behaviour in single and two-phase fluid flow through curved channels of several practical geometries and the associated wall heat transfer processes.As a key contribution to the field and overcoming current limitations, this research study develops a new three-dimensional numerical model for single-phase fluid flow in curved ducts incorporating vortex structure (helicity) approach and a curvilinear mesh system. The model is validated against the published data to ascertain modelling accuracy. Considering rectangular, elliptical and circular ducts, the flow patterns and thermal characteristics are obtained for a range of duct aspect ratios, flow rates and wall heat fluxes. Results are analysed for parametric influences and construed for clearer physical understanding of the flow mechanics involved. The study formulates two analytical techniques whereby secondary vortex detection is integrated into the computational process with unprecedented accuracy and reliability. The vortex inception at flow instability is carefully examined with respect to the duct aspect ratio, duct geometry and flow rate. An entropy-based thermal optimisation technique is developed for fluid flow through curved ducts.Extending the single-phase model, novel simulations are developed to investigate the multiphase flow in heated curved ducts. The variants of these models are separately formulated to examine the immiscible fluid mixture flow and the two-phase flow boiling situations in heated curved ducts. These advanced curved duct flow simulation models are validated against the available data. Along with physical interpretations, the predicted results are used to appraise the parametric influences on phase and void fraction distribution, unique flow features and thermal characteristics. A channel flow optimisation method based on thermal and viscous fluid irreversibilities is proposed and tested with a view to develop a practical design tool

Computational fluid dynamics of coupled free/porous regimes: a specialised case of pleated cartridge filter

The multidisciplinary project AEROFIL has been defined and coordinated with the idea of developing novel filter designs to be employed in aeronautic hydraulic systems. The cartridge filters would be constructed using eco-friendly filtration media supported by unconventional disposable or reusable solid components. My main contribution to this project is the development of a robust and cost-effective design and analysis tool for simulating the hydrodynamics in these pleated cartridge filters. The coupled free and porous flow regimes are generally observed in filtration processes. These processes have been the subject of intense investigation for researchers over the decades who are striving hard to resolve some of the critical issues related to the free/porous interfacial constraints and their mathematical representations concerning its industrial applications. [Continues.

High fidelity simulations of electrokinetic phenomena in microfluidic devices

Electroosmotic flow with electrokinetic effects is the primary method of fluid handling in micro-total analysis systems. Under external applied electric fields, electrokinetic micro-devices allow for innovative functionality in a wide range of microfluidic applications including sample injection, separation, rapid micromixing, and miniaturized chemical and biochemical analysis and detection. This dissertation focuses on simulations of two electrokinetic phenomena, isotachophoresis (ITP) and electrokinetic instability (EKI). A set of coupled governing equations including the incompressible Naiver-Stokes equations, Nernst-Planck transport equations and a charge conservation equation are solved in the simulation. A multiblock in-house solver based on high-order finite difference schemes is developed to solve the system of equations and thus to numerically capture essential physics of ITP and EKI in microfluidic devices. Validation of the solver is provided for one-dimensional ITP problems in which sharp gradients present in species concentration and electric fields. It is demonstrated that the current solver can offer an accurate non-oscillatory solution with reduced numerical diffusion compared to several existing numerical schemes on a given uniform grid. Two-dimensional ITP and EKI problems are then simulated to acquire a good understanding of the basic mechanism and behavior of the two electrokinetic phenomena under certain conditions. Finally, a series of three-dimensional simulations are carried out to predict EKI phenomena in a realistic cross-shaped microchannel. It is shown that the current solver has the capability to capture the threshold value of applied electric field for the onset of instabilities and it offers a better prediction for the critical features of EKI phenomena in the considered cross-shaped microchannel compared to the numerical and experimental results presented in the literature. Moreover, in the general parametric study the present solver also explores several useful guidelines showing the effect of different parameters, including the electric field strength, the conductivity ratio, the channel depth as well as the electric field ratio on EKI in a cross-shaped microchannel

On computations of the integrated space shuttle flowfield using overset grids

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our contributions to the state-of-the-art are twofold: Firstly, we present a high-performance discontinuous Galerkin solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures. The performance results presented in this work focus on the node-level performance and our results suggest that there is great potential for further performance improvements for current state-of-the-art discontinuous Galerkin implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows