Meshfree One-Fluid Modelling of Liquid-Vapor Phase Transitions

Suchde, Pratik; Kraus, Heinrich; Bock-Marbach, Benjamin; Kuhnert, Jörg

doi:10.48550/arxiv.2203.10383

Cited by 3 publications

(3 citation statements)

References 46 publications

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“…Such diffusion operators appear in both momentum and energy conservation equations, where 𝜂 can be the viscosity, the heat conductivity, or density [1,2]. Our goal is to find a discrete diffusion operator using a meshfree method.…”

Section: Motivationmentioning

confidence: 99%

Elliptic operators with discontinuous coefficients in meshfree GFDM

Kraus,

Kuhnert,

Meister

et al. 2023

Proc Appl Math and Mech

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In phase change simulations, material properties such as density, viscosity, or thermal conductivity may exhibit jump discontinuities, possibly of several orders of magnitude. These jump discontinuities represent interfaces between the phases, and they emerge naturally during the simulation; thus, their exact location is generally unknown a priori. Our goal is to simulate phase change processes with a meshfree generalized finite difference method in a monolithic model without distinguishing between the different phases. There, the material properties mentioned above appear as coefficients inside elliptic operators in divergence form and the jumps must be treated adequately by the numerical method. We present a numerical method for discretizing elliptic operators with discontinuous coefficients without the need for a domain decomposition or tracking of interfaces. Our method facilitates the construction of diagonally dominant diffusion operators that lead to M‐matrices for the discrete Poisson's equation, and thus, satisfy the discrete maximum principle. We demonstrate the applicability of the new method for the case of smooth diffusivity and discontinuous diffusivity. We show that the method is first‐order accurate for discontinuous diffusion problems and provides second‐order and fourth‐order convergence for continuous diffusion coefficients.

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Section: Motivationmentioning

confidence: 99%

Elliptic operators with discontinuous coefficients in meshfree GFDM

Kraus,

Kuhnert,

Meister

et al. 2023

Proc Appl Math and Mech

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“…Hence, the numerical solution of a large variety of simulations regarding flow and solid mechanic problems is feasible [12][13][14] [15]. A more detailed description of the FPM and the modelling of vapor as a monolithic phase can be seen in [16].…”

Section: Simulation Setupmentioning

confidence: 99%

Heat Transfer Study for Oil-in-Water Emulsion Jets Impinging onto hot Metal Surface

Nabbout¹,

Pasternak²,

Sommerfeld³

et al. 2022

World Congress on Mechanical, Chemical, and Material Engineering

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The purpose of this work is to analyse numerically as well as experimentally liquid jets impinging at different angles (30°, 60° and 90°) and different velocities (4.7 m/s, 7.0 m/s and 9.7 m/s) onto a hot circular plate made of Inconel 718. Liquids used in the experiments are water and oil-in-water emulsion with 8% concentration of the mineral oil Adrana AY 401 from Houghton Deutschland GmbH. An infrared camera is used to measure the black-coated rear face of the plate during the jet cooling process. The temperature field obtained is then used as input to estimate the heat transfer coefficient. The heat transfer coefficient is estimated by solving an Inverse Heat Transfer Problem (IHTP). In addition, the transient growth of the wetting area is also shown for both liquids. The heat transfer coefficient obtained from the experiments are utilised as input in numerical simulations with the Finite-Pointset-Method (FPM).Comparison between experiments and simulations is done to validate the recently implemented evaporation modelling in the MESHFREE software.

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“…The eventual goal is to describe a multiphase flow in a monolithic approach without explicitly distinguishing between the different phases or tracking the interfaces. This approach leads to jumps in material coefficients, such as thermal conductivity, density and viscosity [4]. All of these material properties appear in diffusion operators of the form ∇ • (η∇u) with discontinuities in η.…”

Section: Introductionmentioning

confidence: 99%

Meshfree Collocation for Elliptic Problems with Discontinuous Coefficients

Kraus,

Kuhnert,

Meister

et al. 2022

Preprint

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We present a meshfree generalized finite difference method (GFDM) for solving Poisson's equation with coefficients containing jump discontinuities up to several orders of magnitude. To discretize the diffusion operator, we formulate a strong form method that uses a smearing of the discontinuity, and a conservative formulation based on locally computed Voronoi cells. Additionally, we propose a novel conservative formulation of enforcing Neumann boundary conditions that is compatible with the conservative formulation of the diffusion operator. Finally, we introduce a way to switch between the strong form and the conservative formulation to obtain a locally conservative and positivity preserving scheme. The presented numerical methods are benchmarked against four test cases with varying complexity and different jump magnitudes on point clouds that are not aligned to the discontinuity. Our results show that the new hybrid method that switches between the two formulations produces better results than the standard GFDM approach for high jumps in the diffusivity parameter.

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Meshfree One-Fluid Modelling of Liquid-Vapor Phase Transitions

Cited by 3 publications

References 46 publications

Elliptic operators with discontinuous coefficients in meshfree GFDM

Elliptic operators with discontinuous coefficients in meshfree GFDM

Heat Transfer Study for Oil-in-Water Emulsion Jets Impinging onto hot Metal Surface

Meshfree Collocation for Elliptic Problems with Discontinuous Coefficients

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