# Modelling and Simulation of High-viscosity, Non Iso-thermal Fluids with a Free Surface

### Dimitri Harder, Edmond Skeli, Dirk Weidemann

#### Abstract

With the aim of using efficient control and/or diagnostic methods, more and more companies in the process engineering industry are using mathematical models to describe the underlying physical processes in sufficient detail. Against this background, the modeling and simulation of the behaviour of a non-isothermal, highly viscous fluid flow is examined in this paper. The behaviour of the fluid is decribed by a system of partial differential equations, which includes the incompressible Navier-Stokes equations as well as the thermal energy equation. With regard to the numerical calculation of the process variables, a combination of the Marker and Cell (MAC) method and a temperature calculation on a curvilinear grid is presented. The MAC method is used to identify the free surface by inserting particles without masses over the initialized fluid area and moving them with the calculated velocities. A characteristic feature of the typical use of the MAC method is that the defining partial differential equations are discretized spatially on a rectangular grid. However, this leads to the problem that a large part of the grid nodes lies within the obstacles which are surrounded by the fluid. In the present model, on the other hand, a curvilinear grid is used. The main advantage of this is that the outer grid nodes lie directly on the surrounding obstacles, resulting in a reduced system of differential-algebraic equations.

Download#### Paper Citation

#### in Harvard Style

Harder D., Skeli E. and Weidemann D. (2018). **Modelling and Simulation of High-viscosity, Non Iso-thermal Fluids with a Free Surface**.In *Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 978-989-758-321-6, pages 557-563. DOI: 10.5220/0006857405570563

#### in Bibtex Style

@conference{icinco18,

author={Dimitri Harder and Edmond Skeli and Dirk Weidemann},

title={Modelling and Simulation of High-viscosity, Non Iso-thermal Fluids with a Free Surface},

booktitle={Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2018},

pages={557-563},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006857405570563},

isbn={978-989-758-321-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - Modelling and Simulation of High-viscosity, Non Iso-thermal Fluids with a Free Surface

SN - 978-989-758-321-6

AU - Harder D.

AU - Skeli E.

AU - Weidemann D.

PY - 2018

SP - 557

EP - 563

DO - 10.5220/0006857405570563