Browsing by Author "Malan, Arnaud G"

Now showing 1 - 13 of 13
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    Open Access
    A Higher-Order VOF Interface Reconstruction Scheme for Non-Orthogonal Structured Grids - with Application to Surface Tension Modelling
    (2021) Ilangakoon, Niran A; Malan, Arnaud G
    The volume-of-fluid (VOF) method [24] is widely used to track the interface for the purpose of simulating liquid-gas interfacial flows numerically. The key strength of VOF is its mass conserving property. However, interface reconstruction is required when geometric properties such as curvature need to be accurately computed. For surface tension modelling in particular, computing the interface curvature accurately is crucial to avoiding so-called spurious or parasitic currents. Of the existing VOF-based schemes, the height-function (HF) method [10, 16, 18, 42, 46, 53] allows accurate interface representation on Cartesian grids. No work has hitherto been done to extend the HF philosophy to non-orthogonal structured grids. To this end, this work proposes a higher-order accurate VOF interface reconstruction method for non-orthogonal structured grids. Higher-order in the context of this work denotes up to 4 th-order. The scheme generalises the interface reconstruction component of the HF method. Columns of control volumes that straddle the interface are identified, and piecewise-linear interface constructions (PLIC) are computed in a volume-conservative manner in each column. To ensure efficiency, this procedure is executed by a novel sweep-plane algorithm based on the convex decomposition of the control volumes in each column. The PLIC representation of the interface is then smoothed by iteratively refining the PLIC facet normals. Rapid convergence of the latter is achieved via a novel spring-based acceleration procedure. The interface is then reconstructed by fitting higher-order polynomial curves/surfaces to local stencils of PLIC facets in a least squares manner [29]. Volume conservation is optimised for at the central column. The accuracy of the interface reconstruction procedure is evaluated via grid convergence studies in terms of volume conservation and curvature errors. The scheme is shown to achieve arbitrary-order accuracy on Cartesian grids and up to fourth-order accuracy on non-orthogonal structured grids. The curvature computation scheme is finally applied in a balanced-force continuum-surface-force (CSF) [4] surface tension scheme for variable-density flows on nonorthogonal structured grids in 2D. Up to fourth-order accuracy is demonstrated for the Laplace pressure jump in the simulation of a 2D stationary bubble with a high liquid-gas density ratio. A significant reduction in parasitic currents is demonstrated. Lastly, second-order accuracy is achieved when computing the frequency of a 2D inviscid oscillating droplet in zero gravity. The above tools were implemented and evaluated using the Elemental®multi-physics code and using a vertex-centred finite volume framework. For the purpose of VOF advection the algebraic CICSAM scheme (available in Elemental®) was employed.
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    An Algebraic Volume of Fluid Method for Strongly Coupled Spacecraft Fuel Slosh Modelling
    (2020) Jones, Bevan W S; Malan, Arnaud G
    The increase in the number of commercial space missions has resulted in the increased need for efficient and effective spacecraft designs. A key contributor to the accuracy of space vehicle simulation is the prediction of fuel slosh loads during in-orbit manoeuvres, particularly due to the large fuel-to-solid mass ratios involved. To this end, this thesis details a high resolution mathematical model capable of predicting the dynamic interaction between fuel slosh and the rigid structure of a spacecraft. The Volume of Fluid (VoF) method provides a framework in which Computational Fluid Dynamics (CFD) can be used to model the fluid dynamics of two phase fuel slosh in a mass conservative manner. To be applicable to industrial geometries, an unstructured finite volume median dual cell methodology is employed for spatial discretisation. This gives rise to the first novel contribution of this work, namely the development of a new volume conservative VoF initialisation method for arbitrary interfaces on unstructured meshes. The scheme, called the Arbitrary Grid Initialiser (AGI), is rigorously validated and proven conservative to machine precision [1]. An algebraic, as opposed to geometric, VoF advection method is used due to being similarly well suited to unstructured grids. Improvements to the algebraic VoF method is therefore the next contribution of this thesis; where the CICSAM [2] and HiRAC [3] VoF methods are improved, and the first conservative HiRAC method presented. The improved CICSAM and HiRAC methods are shown to be competitive with their geometric counterparts on unstructured grids while being mass conservative. Both CICSAM and HiRAC are then coupled (HiRAC for the first time) to a well balanced Continuum Surface Force (CSF) surface tension discretisation. The surface tension implementation, for which standard height functions are used, is shown to be well-balanced with an accuracy that compares favourably to existing methods. In the final part of the thesis, the complete spacecraft model is constructed. A numerical rigid body code is developed for this purpose, which can additionally track its orientation. The rigid body and fluid schemes are finally coupled together in a strong, stable, and partitioned manner using the Aitken's ∆2 method [4]. The model is demonstrated to be numerically stable for large liquid-to-solid ratios via a benchmark test case.
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    A ball-vertex approach to r-refinement for accuracy enhancements in CFD Calculations
    (2015) Jones, Bevan W S; Malan, Arnaud G; van Rooyen, Jacobus A
    Presented in this paper is an accuracy enhancing r-refinement scheme based on the ballvertex method [1, 2]. Due the success of the method in mesh movement, this work seeks to extend its use to error minimization for computational fluid dynamics calculations. To this end, element edges are loaded via error driven monitor functions. The latter are estimated from both field gradients and curvature. Boundary nodal movement is facilitated via the use of automated B`ezier surface reconstruction. The application study involves both analytical as well as industrial test-cases. The latter involves 2D and 3D transonic flow calculations. When compared with the mesh independence solution, an error reduction in the computed coefficient of lift and moment of 60% was achieved even on relatively coarse meshes and close to an order of magnitude on finer meshes. Finally, a mesh deformation, moving boundary, problem was completed to demonstrate duality as both a mesh optimisation and deformation tool.
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    Open Access
    Computational fluid dynamic based optimisation of an industrial axial fan for rapid prototyping
    (2017) Van Rooyen, Jacobus A; Malan, Arnaud G
    Axial air flow fans are widely used for air movement. In an increasingly international and competitive market, smaller fan companies find themselves in need of rapid preliminary design. This need is addressed in this study through the development of a first-revision, Computational Fluid Dynamics (CFD) based, optimisation tool which allows for rapid prototyping of a ducted axial fan. The result is an ElementalTM-based multi-disciplinary software tool, comprising 2D CFD, mesh movement, and constrained geometric optimisation. The analytical equation employed to represent the aerofoil significantly reduces the cost of the optimisation. A pseudo-3D fan model is generated by superimposing 2D CFD results. This is done without the general assumption of the free-vortex method, which is not a necessity for fan design and other velocity distributions may be used. For this purpose, an enhanced finite volume discretisation method was developed. A penalty function minimisation, by means of an unconstrained optimisation algorithm, is implemented thereafter. The primary objective is to deliver a specific fan static pressure rise, while optimising for fan static efficiency by means of altering the rotor blade geometry. The spherical quadratic steepest descent method is employed, which does not rely on any explicit line searches, as required by traditional steepest descent techniques. The rapid prototyping tool is finally applied to an under-performing base fan (Fan-D) which cannot meet a specified duty point. The resulting optimised fan (Fan-Optim) is manufactured and experimentally tested, in accordance with the ISO 5801 standard. The pseudo-3D model is proven to predict fan performance accurately at the target duty point, while capturing fan behaviour over a range of volumetric flow rates. The former is to within 13% of the fan static pressure rise and within 2.3% of fan static efficiency. While Fan-Optim meets the desired duty point within 2%, it offers a considerable improvement in fan static efficiency over Fan-D. Furthermore, an approximate 38% reduction in blade material is achieved as a secondary effect.
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    Direct numerical simulation of free-surface and interfacial flow using the VOF method: cavitating bubble clouds and phase change
    (2018) Malan, Leon; Zaleski, Stéphane; Malan, Arnaud G; Rousseau, Pieter G
    Direct Numerical Simulation of two-phase ow is used extensively for engineering research and fundamental fluid physics studies. This study is based on the Volume-Of-Fluid (VOF) method, originally created by Hirt and Nicols. This method has gained increased popularity, especially when geometric advection techniques are used coupled with a planar reconstruction of the interface. The focus of the first part of this work is to investigate the hydrodynamics of isothermal cavitation in large bubble clouds, which originated from a larger study of micro-spalling, conducted by the French CEA. A method to deal with volume-changing vapour cavities, or pores, was formulated and implemented in an existing code, PARIS. The ow is idealized by assuming an inviscid liquid, negligible thermal effects and vanishing vapour pressure. A novel investigation of bubble cloud interaction in an expanding liquid using Direct or Detailed Numerical Simulation is presented. The simulation results reveal a pore competition, which is characterised by the Weber number in the ow. In the second part of the study the governing equations are extended to describe incompressible ow with phase change. The description of the work commences with the derivation of the governing equations. Following this, a novel, geometric based, VOF solution method is proposed. In this method a novel way of advecting the VOF function is invented, which treats both mass and energy conservation in conservative form. New techniques include the advection of the interface in a discontinuous velocity field. The proposed algorithms are consistent and elegant, requiring minimal modifications to the existing code. Numerical experiments demonstrate accuracy, robustness and generality. This is viewed as a significant fundamental development in the use of VOF methods to model phase change.
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    Effect of Pulsatility on the Transport of Thrombin in an Idealized Cerebral Aneurysm Geometry
    (2022-01-11) Hume, Struan; Tshimanga, Jean-Marc Ilunga; Geoghegan, Patrick; Malan, Arnaud G; Ho, Wei Hua; Ngoepe, Malebogo N
    Computational models of cerebral aneurysm thrombosis are designed for use in research and clinical applications. A steady flow assumption is applied in many of these models. To explore the accuracy of this assumption a pulsatile-flow thrombin-transport computational fluid dynamics (CFD) model, which uses a symmetrical idealized aneurysm geometry, was developed. First, a steady-flow computational model was developed and validated using data from an in vitro experiment, based on particle image velocimetry (PIV). The experimental data revealed an asymmetric flow pattern in the aneurysm. The validated computational model was subsequently altered to incorporate pulsatility, by applying a data-derived flow function at the inlet boundary. For both the steady and pulsatile computational models, a scalar function simulating thrombin generation was applied at the aneurysm wall. To determine the influence of pulsatility on thrombin transport, the outputs of the steady model were compared to the outputs of the pulsatile model. The comparison revealed that in the pulsatile case, an average of 10.2% less thrombin accumulates within the aneurysm than the steady case for any given time, due to periodic losses of a significant amount of thrombin-concentrated blood from the aneurysm into the parent vessel’s bloodstream. These findings demonstrate that pulsatility may change clotting outcomes in cerebral aneurysms.
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    A finite volume discretization method for flow on structured and unstructured anisotropic meshes
    (2015) Merrick, Dane Glen; Malan, Arnaud G
    This project is concerned with advection discretization technology within the field of Computational Fluid Dynamics (CFD). To this end, two novel methods are proposed which are dubbed the Enhanced Taylor (ET) Schemes. The model equation for this work is the advection-diffusion equation with the industrial application being incompressible ow. The objective of the proposed schemes is to achieve increased accuracy on structured and unstructured anisotropic meshes. One of the schemes focuses on improving advection accuracy, and the other on improving total advection-diffusion accuracy. Fundamental to the design of the ET schemes is the primary focus on face accuracy, with the additional incorporation of the up and downwind mesh stretching factors and ow gradients. Additionally, non-linear blending with the existing NVSF scheme was effected in the interest of robustness and stability, particularly on equispaced meshes. The developed schemes, along with prominent linear ĸ-Upwind schemes were critically assessed and compared. Current methods were shown to be at best 3rd and 1st-order accurate at non-equispaced faces and nodes respectively. In contrast, the developed schemes were shown to be up to 4th and 2nd-order accurate. Numerical experiments followed. This involved applying the prominent and developed schemes to solve the 1D advection-diffusion equation on stretched meshes. The 2D case involved incompressible ow in a lid-driven cavity. Anisotropic structured and unstructured meshes were employed. Significant improvements in accuracy were found with the ET schemes, with average reductions in error measuring up to a 50%. In comparison to existing methods, it is proposed that state-of-the-art technology has been developed.
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    First Order Assessment of Heat Transfer due to the Loss of Inventory in a Spent Fuel Pool
    (2018) Fillis, Vernon W; Malan, Arnaud G; Malgas, Isaac
    The Fukushima Daiichi Nuclear Power Plant accident created renewed international interest in the behaviour of spent fuel subsequent to a complete loss of water inventory in a spent fuel pool (SFP). The study conducted in this dissertation serves as a starting point in gaining an understanding of the thermal hydraulics and associated heat transfer processes involved when spent fuel assemblies (SFAs) become uncovered in air. The complete loss of cooling in a SFP is a complex 3-D problem, hence several simplifications were necessary in this research to narrow the scope. Further, due to the complexity of this topic, the results obtained serves purely as a first order approximation. Accordingly, the Flownex systems CFD code (version 8.6.1.2630) was used to simulate the thermal response of the uncovered SFAs in the SFP of a typical Pressurised Water Reactor (PWR) during a severe accident scenario. Two network models were developed. The first was to identify the dominant heat transfer mechanisms with-in the spent fuel pool and it therefore accounted for a range of physics. This included convective heat transfer through the composite SFA channel walls, conduction along the vertical axial direction of the SFAs and through the inner and outer rack wall as well as through the fuel building (FB) roof and side walls. The model also took into account the radiative heat transfer from the cladding surface of the composite SFAs to the FB roof and side walls. This network model informed that the heat transfer with-in the SFA during the considered extreme accident scenario is dominated by radiative heat transfer. This informed the development of an improved 2-D network model using conduction elements which were specially calibrated in this work to account for radiative heat loss. An effective conduction for the fuel volume which is dependent on temperature was determined and was used to assess the severe accident. Transient results showed that the spent fuel may reach cladding oxidation temperature within circa 10.5 hrs after a complete loss of inventory.
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    Mesh adaptation through r-refinement using a truss network analogy
    (2015) Jones, Bevan W S; Malan, Arnaud G
    This project investigates the use of a truss network, a structural mechanics model, as a metaphor for adapting a computational fluid dynamics (CFD) mesh. The objective of such adaptation is to increase computational effi- ciency by reducing the numerical error. To drive the adaptation, or to give the scheme an understanding of accuracy, computational errors are translated into forces at mesh vertices via a so-called monitor function. The ball-vertex truss network method is employed as it offers robustness and is applicable to problems in both two and three dimensions. In support of establishing a state-of-the-art adaptive meshing tool, boundary vertices are allowed to slide along geometric boundaries in an automated manner. This is achieved via feature identification followed by the construction of 3rd order bezier surface patches over boundary faces. To investigate the ability of the scheme, three numerical test cases were investigated. The first comprised an analytical case, with the aim of qualitatively assessing the ability to cluster vertices according to gradient. The developed scheme proved successful in doing this. Next, compressible transonic flow cases were considered in 2D and 3D. In both cases, the computed coefficient of lift and moment were investigated on the unrefined and refined meshes and then compared for error reduction. Improvements in accuracy of at least 60% were guaranteed, even on coarse meshes. This is viewed as a marked achievement in the sphere of robust and industrially viable r-refinement schemes.
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    Numerical investigation of the convective heat transfer coefficient of the human body using a representative cylindrical model
    (2017) Eferemo, Daniel; Bello-Ochende, Tunde; Malan, Arnaud G
    The principal objective of this study is to investigate, develop and verify a framework for determining the convective heat transfer co-efficient from a cylindrical model that can easily be adaptable to more complex geometry - more specifically the human body geometry. Analysis of the model under forced convection airflow conditions between the transition velocity of about 1m/s - calculated using the Reynolds number - up until 12m/s were carried out. The boundary condition, however, also included differences in turbulence intensities and cylinder orientation with respect to wind flow (seen as wind direction in some texts). A total of 90 Computational Fluid Dynamic (CFD) calculations from these variations were analysed for the model under forced convective flow. Similar analysis were carried out for the model under natural convection with air flow velocity of 0.1m/s. Here, the temperature difference between the model and its surrounding environments and the cylinder orientation with respect to wind flow were varied to allow for a total of 15 CFD analysis. From these analysis, for forced convection, strong dependence of the convective heat transfer coefficient on air velocity, cylinder orientation and turbulence intensity was confirmed. For natural convection, a dependence on the cylinder orientation and temperature difference between the model and its environment was confirmed. The results from the CFD simulations were then compared with those found in texts from literature. Formulas for the convective heat transfer coefficient for both forced and natural convection considering the respective dependent variables are also proposed. The resulting formulas and the step by step CFD process described in this thesis provides a framework for the computation of the convective heat transfer coefficient of the human body via computer aided simulations. This framework can easily be adaptable to the convective heat transfer coefficient calculations of the human body with some geometric modelling adjustments, thus resulting in similar representative equations for a human geometric model.
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    Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations
    (2020) Nchupang, Mojalefa Prince; Malan, Arnaud G; Nordstrom, Jan
    Numerical simulations of incompressible flows are unequivocally important due to their numerous industrial applications. These applications ranges from the large-scale fluid's flow modelling such as aerodynamics [1], atmospheric-ocean modelling [2] to a simple pipe flows in the petroleum industry [3]. This study is devoted to develop a provably stable and high order approximation for the incompressible laminar boundary layer equations. A new set of energystable boundary conditions are derived using the energy method. It is shown that both the weak and strong implementation of these boundary conditions yields an energy estimate. The semidiscrete problem is formulated by discretizing the continuous spatial derivatives using high order finite difference approximations on summation-by-parts form. The boundary conditions are implemented weakly using the simultaneous approximation terms methods. The discrete energy estimate is derived by mimicking the continuous analysis and hence, the numerical approximation is proved to be stable. The accuracy and linear stability of the developed scheme is also validated by solving the celebrated laminar flat plate flow problem. This is done by injecting the Blasius solution into the coefficient matrix as well as weak boundary conditions
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    Toward a full aircraft model platform for fuel slosh-structure interaction simulations
    (2015) Farao, Javon; Malan, Arnaud G; Gambioli, Francesco
    The purpose of this study was to initiate the development of a full aircraft model (FAM) for the purpose of non-linear loads calculation of an aircraft. The FAM is employed during the design process of an aircraft and comprises of various reduced-order models (ROMs). These are mainly structural, slosh and aerodynamic loads. This study focused on the structural and slosh aspects using Ele- mental(TM) software as the base. First, a structural ROM was developed such that it is compatible with Airbus data and processes. The developed code reads in MSC Nastran data, from which Hermitian finite element discretisation is performed followed by transient calculations. To this end, the structure was represented by Timoshenko beam theory. The structural ROM was validated and verified against the widely used MSC Nastran commercial software. Simulated dynamic responses were within 5% while eigenvalue predictions were within 2% of each other. Secondly, a strongly-coupled partitioned fluid-structure interaction (FSI) scheme was deployed to incorporate the high-fidelity sloshing fluid onto the structure. Lastly, the developed FSI technology was verified and validated against challenging analytical as well as real-world benchmark test cases. It was demonstrated to be accurate and robust in all cases.
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    Towards a hybrid CFD platform for investigating aircraft trailing vortices
    (2017) Changfoot, Donovan M; Malan, Arnaud G; Nordström, J
    This dissertation outlines the development of a parallel 3D hybrid finite-volume- finite-difference solver. As motivation for such a scheme, the specific application area under consideration is modeling the trailing vortices shed from the wings of aircraft under transonic flight conditions. For this purpose, the Elemental® finite volume code is employed in the vicinity of the aircraft, while the Essense finite difference software is employed to accurately resolve the trailing vortices. The former method is spatially formally 2nd order and the latter set to 6th order accurate. The coupling of the two methods is achieved in a stable manner through the use of Summation-by-Parts operators and weak imposition of boundary conditions through Simultaneous-Approximation-Terms (SBP-SAT). Accordingly, a special parallel SBP-SAT interface library is developed in Elemental®. In addition, the code is extended to impose boundary conditions in a weak manner via the SBP-SAT framework; as well as interface volume definitions changed to allow coupling with the 6th order code. The developed hybrid solver is successfully validated against analytical test-cases. This is followed by demonstrating its ability to model the flow field, including trailing vortex structures, around the NASA Common-Research-Model (CRM) under transonic flow conditions. Inviscid flow was assumed and the trailing vortices from both wing and horizontal stabiliser accurately resolved to 3 and 1 reference chords downstream of the lifting surface respectively. The robustness of the interface treatment is demonstrated by the smoothness of the flow solution across an interface boundary in the presence of high flow gradients and rapidly changing mesh topology. In addition, high vortex axial flow gradients were predicted while the vortex core speed is 6 % slower than free-stream.