Matthias Niethammer

M. Sc. Matthias Niethammer

+49 6151 16-21464
+49 6151 16-21472

Alarich-Weiss-Straße 10
64287 Darmstadt

Office: L2|06 408

Viscoelasic Fluid Flows

Research

Our research deals with rheological complex fluid flow problems. Particular expertise includes:

- mathematical modelling of viscoelastic single- and two-phase fluid flow problems

- development of robust and efficient numerical methods and algorithms

- numerical stabilization of high Weissenberg number viscoelastic fluid flows

- transient and steady-state simulations of viscoelastic fluid flows in complex 3D geometrys (such as porous media, injection molding, macro- and microchannels, etc.)

We have developed a generic numerical framework that provides full combinatorial flexibility between a wide range of rheological models for viscoelastic polymer melts and solutions on the one hand, and cutting-edge stabilization methods on the other hand. The framework has been implemented into a new comprehensive and flexible C++ library which is build on top of the open source library OpenFOAM.

Project

The “High Weissenberg Number Problem’’ (HWNP) has been a major challenge in computational rheology for the past three decades. It refers to the loss of convergence of all numerical methods beyond some limiting value of the fluid elasticity, quantified by a critical Weissenberg number. The critical value varies with the problem, in particular with regard to the flow geometry and the fluid constitutive model. Although a complete solution is not known until today, several effective numerical stabilization methods have been developed to cope with the HWNP [1, 2]. However, there is a multitude of constitutive models describing viscoelastic material behavior, with which the stabilization approaches are to be combined. For the first time, this combination has been realized in a general way by deriving model-independent forms of the stabilized equations. We have developed a generic numerical framework that provides full combinatorial flexibility between a wide range of rheological models for viscoelastic polymer melts and solutions on the one hand, and cutting-edge stabilization methods on the other hand. The framework has been implemented into a new comprehensive and flexible C++ library which is build on top of the open source library OpenFOAM. Our methods have been validated in several computational benchmark problems over a large range of Weissenberg numbers [3].

Flow pattern and flow-type parameter of an Oldroyd-B fluid in a planar 4:1 contraction. Image: M.Sc. Matthias Niethammer
Flow pattern and flow-type parameter of an Oldroyd-B fluid in a planar 4:1 contraction. Image: M.Sc. Matthias Niethammer

Acknowledgements

The authors would like to acknowledge BASF SE for the financial support of this work, as well as Christian Kunkelmann, Erik Wassner and Sebastian Weisse for their cooperation, assistance, and enlightening discussions.

References

[1] R. Fattal and R. Kupferman: Constitutive laws for the matrix-logarithm of the conformation tensor, Journal of Non-Newtonian Fluid Mechanics, Vol. 123, pp. 281–285 (2004)

[2] N. Balci, B. Thomases, M. Renardy, C.R. Doering: Symmetric factorization of the conformation tensor in viscoelastic fluid models, Journal of Non-Newtonian Fluid Mechanics, Vol. 166, pp. 546–553 (2011)

[3] M. Niethammer, H. Marschall, C. Kunkelmann, D. Bothe: A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes. In preparation. (2015)

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