# FLOW: Methods for Lagrangian particles in complex geometries

Fluid flows comprise a wide variety of complex phenomena which, among others, depend on the geometrical configuration of the problem flow phases, as well as on the Reynolds number of the flow (Re). The flow of water in pipe systems with diluted small sand particles or that of blood in veins with pollutants are typical examples of everyday situations which incorporates both complex geometries and multi-phase flows. One way to model particle dispersion is the advection of a large number of small particles included explicitly in the flow: Each particle (there could be millions in number) is tracked individually, and its interaction with the flow is computed. Of course, various levels of approximation are possible, e.g. fluid force on particles and vice versa, collisions between particles, and accumulation of particles at solid surfaces. From a computational point of view, this so-called Lagrangian particle tracking is a very interesting problem in terms of efficient parallel implementation on thousands of processors.

Poster about this project: pdf

Slide about this project: pdf

Due to rapid advancement in computers, large-scale simulations of turbulent flows in complex geometries with particles are realizable. Nevertheless, this necessitates the use of highly parallel algorithms (MPI/OpenMP) and large computer systems. It is the aim of the present research project to devise, implement and validate algorithms and models for particle tracking in complex turbulent flows using the massively parallel spectral-element code Nek5000 [1]. This code allows the efficient computation of flows in moderately complex geometries such as curved pipes, stenotic flow, diffusers etc. The main focus of the project is to extend our experience in large-scale computations, including parallel algorithms and novel computer architectures along with proper investigation in the physical aspect of turbulent flow in complex geometries.

As a first step is chosen to build up high quality tools to study a fully developed turbulent flow in such geometries e.g. stenotic flow and curved pipes. A steady stenotic flow at two different Reynolds numbers, 500 and 1000, for axisymmetric and eccentric stenotic pipes has been performed using inflow/outflow boundary conditions along with a fringe at the outflow position. A similar technique for generating the grid of stenotic pipe, so called morphing, has been employed to generate curved pipe grid. Validation of the results for mean and fluctuations variables has been performed against the DNS data by Hüttl et al. [2]. In the next step, we investigate the effect of the curvature at friction Reynolds numbers 180 and 550 with full statistical analysis of the turbulent flow field and a comparison to straight pipes [3]. We also aim at exploring the influence of the curvature on the intermittent re-laminarisation in these Reynolds numbers which is an effect particularly important for accurate modelling. It is exactly such flow cases with serve later as the prime examples to study Lagrangian particles.

[1] See http://nek5000.mcs.anl.gov/

[2] T. J. Hüttl & R. Friedrich. Influence of curvature and torsion on turbulent flow in helically coiled pipes. Int. J. Heat Fluid Flow. 2000.

[3] A. Noorani, G. K. El Khoury & P. Schlatter. Evolution of turbulence characteristics from straight to curved pipes. In preparation.