scholarly journals Some mathematical properties of a barotropic multiphase flow model

2020 ◽  
Vol 69 ◽  
pp. 70-78
Author(s):  
Khaled Saleh ◽  
Nicolas Seguin
Keyword(s):  
Multiphase Flow ◽  
Multiphase Flows ◽  
Flow Model ◽  
Strict Convexity ◽  
Symmetric Form ◽  
Mathematical Properties ◽  
Weak Hyperbolicity

We study a model for compressible multiphase flows involving N non miscible barotopic phases where N is arbitrary. This model boils down to the barotropic Baer-Nunziato model when N = 2. We prove the weak hyperbolicity property, the non-strict convexity of the natural mathematical entropy, and the existence of a symmetric form.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

Numerical Modelling of Multiphase Flow With Application to Industrial Processes

2021 ◽  
Author(s):  
◽  
Ashutosh Bhokare
Keyword(s):  
Numerical Modelling ◽  
Multiphase Flow ◽  
Multiphase Flows ◽  
Oil And Gas ◽  
Fresh Concrete ◽  
Industrial Applications ◽  
Fluidised Bed ◽  
Bingham Model ◽  
Drag Models ◽  
Concrete Flow

Multiphase flows are witnessed often in nature and the industry. Simulating the behaviour of multiphase flows is of importance to scientists and engineers for better prediction of phenomena and design of products. This thesis aims to develop a multiphase flow framework which can be applied to industrial applications such as placement of concrete in construction and proppant transport in oil and gas. Techniques available in literature to model multiphase flows are systematically introduced and each of their merits and demerits are analysed. Their suitability for different applications and scenarios are established. The challenges surrounding the placement of fresh concrete in formwork is investigated. Construction defects, the physics behind these defects and existing tests used to monitor fresh concrete quality are evaluated. Methods used to simulate fresh concrete flow as an alternative to experiments are critically analysed. The potential benefits of using numerical modelling and the shortcoming of the existing approaches are established. It is found that the homogeneous Bingham model is currently the most widely used technique to model fresh concrete flow. Determining the Bingham parameters for a given concrete mix remains a challenge and a novel method to obtain values for them is demonstrated in this work. The Bingham model is also applied to a full-scale tremie concrete placement procedure in a pile. Knowledge on the flow pattern followed by concrete being placed using a tremie is extracted. This is used to answer questions which the industry currently demands. The need for a more sophisticated model is emphasised in order to obtain an even greater understanding of fresh concrete flow behaviour. A CFD-DEM framework in which the multiphase nature of concrete is captured is developed. To validate this framework a new benchmark test is proposed in conjunction with the fluidised bed experiment. A comparative study of the drag models used in CFD-DEM approaches is performed to systematically assess each of their performances. CFD-DEM modelling is then applied to model fresh concrete flow and its potential to model defect causing phenomena is demonstrated. A model to capture more complex behaviours of concrete such as thixotropy is introduced and demonstrated.

Sign in / Sign up

Export Citation Format

Share Document