Formulation of a weakly compressible two-fluid flow solver and the development of a compressive surface capturing scheme using the volume-of-fluid approach

[摘要] ENGLISH ABSTRACT:This study presents the development and extension of free-surface modellingtechniques for the purpose of modelling two-fluid systems accurately and efficiently.The volume-of-fluid (VOF) method is extended in two ways: Firstly, it is extendedto account for variations in the gas density through a weakly compressible formulation.Secondly, a compressive free-surface interface capturing formulation thatpreserves the integrity of the interface shape is detailed. These formulations wereimplemented and evaluated using the Elemental software.Under certain flow conditions liquid-gas systems may be subjected to largevariations in pressure, making it necessary to account for changes in gas density.Modelling this effectively has received relatively little attention in the context offree-surface modelling and remains a challenge to date. To account for the variationsin gas density a weakly compressible free-surface modelling formulation isdeveloped for low Mach number flows. The latter is formally substantiated via anon-dimensional analysis. It is proposed that the new formulation advances on existingfree-surface modelling formulations by effecting an accurate representationof the dominant physics in an efficient and effective manner.The proposed weakly compressible formulation is discretised using a vertexcentrededge-base finite volume approach, which provides a computationally efficientmethod of data structuring and memory usage. Furthermore, this implementationis applicable to unstructured spatial discretisation and parallel computing. Inthis light, the discretisation is formulated to ensure a stable, oscillatory free solution.Furthermore, the governing equations are solved in a fully coupled mannerusing a combination of dual time-stepping and a Generalised Minimum Residualsolver with Lower-Upper Symmetric Gauss-Seidel preconditioning, ensuring a fastand efficient solution.The newly developed VOF interface capturing formulation is proposed to advanceon the accuracy and efficiency with which the evolution of the free-surfaceinterface is modelled. This is achieved through a novel combination of a blendedhigher-resolution scheme, used to interpolate the volume fraction face value, andthe addition of an artificial compressive term to the VOF equation. Furthermore,the computational efficiency of the higher-resolution scheme is improved throughthe reformulation of the normalised variable approach and the implementation of anew higher-resolution blending function.For the purpose of evaluating the newly developed methods, several test casesare considered. It is demonstrated that the new surface capturing formulation offersa significant improvement over existing schemes, particularly at large CFL numbers.It is shown that the proposed method achieves a sharper, better defined interfacefor a wide range of flow conditions. With the validation of the weakly compressibleformulation, it is found that the numerical results correlate well with analyticalsolutions. Furthermore, the importance of accounting for gas compressibilityis demonstrated via an application study. The weakly compressible formulation isalso found to result in negligible additional computational cost while resulting inimproved convergence rates.

[发布机构] Stellenbosch University