# MPflow

## High-fidelity simulations for multi-fluid flows

Our flagship product MPflow focuses on three main sectors of interest manufacturing, energy, and healthcare. The aim of this code is to create the next generation of models for multiphase flow systems – systems that deal with flow of gas, liquid, and, potentially, solids flowing simultaneously in pipes, channels, and reactors – to enhance productivity and efficiency across these sectors.

In many industries – including automotive, aerospace, marine and others – numerical simulation meets the growing need for an increasingly predictive, early and agile design process.

MPflow uses some state-of-the-art numerical methods for dealing with multi-fluid systems.

## Innovative approach for interphase capturing

After years of intense research and development within academic and industrial groups, out team has developed novel numerical tools for modelling the evolution of the interface between the two phases such as liquid/liquid, liquid/gas flows.

MPflow solver offers new opportunities for efficiently simulating complex flows problems that is impossible to address with other software.

## Features

Volume-of-Fluid (VOF) method

This method captures the interface through solving the transport of the marker function in the computational domain. The marker function typically used in commercial software is the volume fraction of the liquid phase. The volume fraction represents the volume occupied by the liquid phase in space within the computational cell. In two dimensions the marker function is the surface area. In its simplest form, VOF assumes that the volume occupied inside a computational cell of arbitrary shape can be occupied by liquid or gas. Each computational cell is assigned a value for liquid volume fraction between 0 and 1. The method has the advantage that is mass-conservative for each phase, and the change of topology is implicit which means that no special operations are necessary for interface reconnection or break-up. After advecting the volume fraction, the surface can be locally reconstructed. Various methods can be used for reconstructing the interface in the Volume-of-Fluid method.

Level-Set (LS) method

The Level-Set formulation is utilised transporting a continuous function like in Volume-of-Fluid method. LS has been developed at Osher and Sethian (1988) as an alternative to the Volume-of-Fluid method. The method gives an accurate representation of the liquid-gas interface and the interfacial normal and curvature. One common characteristic of this method and VOF is that the user does not interfere in the method no matter the complexity of the geometry since both VOF and LS adjust naturally to any topological changes. One of the main differences of those two is the transition from the liquid to gas which in Level-Set method occurs gradually instead of the Volume-of-Fluid where the interface exists in a one-cell layer in between the two phases. The marker function in Level-Set is a function χ(x,t) which represents the interface between the liquid and the gas. Level-set is significantly efficient in calculating the interface, although the method has the shortcoming that mass conservation is not guaranteed. This barrier can be overcome with coupling the method with the Volume-of-Fluid approach which is conservative, and the Level-Set which is highly accurate. At the moment, a novel coupling of the method is being developed to couple the two above mentioned methods.

The $\Sigma$-model

The ELSA model is used to model the atomisation process and has been extensively tested for spray injection in the automotive industry. It is used here to predict the characteristics of the liquid structures in the dense and dilute parts of the spray. The innovative idea that is introduced in ELSA, is the mean liquid/gas interface density $\Sigma$ for describing the spray. This definition is not limited to the assumption of spherical droplets which is a standard in many Lagrangian methods in commercial and open-source software. The interface density can be considered as the amount of spatial surface of liquid per unit volume at a given position, hence $\Sigma$ has units of inverse length, $m ^{-1}$. The ELSA model has been originally developed and validated in RANS and is proven to accurately model the turbulent mixing. It has been modified since its first appearance. cryoFoam uses a modified formulation for ELSA, suitable for pressurised cryogenic releases under thermodynamic non-equilibrium.