Parallel finite element modeling of the hydrodynamics in agitated tanks

Agitated tanks operating in the transition flow regime are often encountered in industrial processes. Knowledge of the flow generated within the mixing tanks is useful to determine optimal operating conditions or to propose design guidelines. Computational fluid dynamics (CFD) models are able to give such insight. The main problem of the CFD models is the high computational cost required to accurately predict the transition flow regime in stirred tanks. In order to circumvent this limitation, the general scope of the thesis is to develop a numerical strategy to model the transition flow regime of agitated tanks employing parallel computing.;The second step involves the design of a parallel sliding mesh technique in view of the necessity to take into account the unsteady motions of the agitators. Lagrange multipliers are used at the sliding interlaces to enforce the continuity between the fixed and moving subdomains. To handle the convective term, both the Newton-Raphson scheme and the semi-implicit linearization are utilized. The method is validated for concentric cylinders and stirred tank flows. Running on 16 processors, the obtained speed-up is close to 8.;Finally, to show the utility of the constructed parallel algorithms the last part of this thesis consists in the characterization of the hydrodynamics of a coaxial mixer in the transition regime. The coaxial mixer is composed of a large paddle (Maxblend) impeller and a double helical ribbon agitator mounted on two independent coaxial shafts rotating at different speeds. The used tetrahedral grids consisted on 1.4 to 3.8M of nodes producing 4.4 and 13.5M equations to solve. The simulations are based on the resolution of the Navier-Stokes equations with help of the developed parallel three-dimensional finite element solver. To model the rotation of agitators, which rotates at different speeds, a hybrid approach based on the novel finite element sliding mesh and the fictitious domain method is used. The power consumption and mixing times obtained from the simulations show good agreement with the ones acquired from a laboratory pilot rig. The simulations allow observing the flow as it evolves from deep laminar to transition regime.;To accomplish the main objective, the first stage of the project focuses on the development of a parallel finite element algorithm capable to predict the hydrodynamics of three-dimensional incompressible fluid flow problems on unstructured grids. The parallelization is based on non-overlapping domain decomposition methods. Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled resolution of the velocity-pressure-Lagrange multiplier system of the discrete Navier-Stokes equations by a distributed memory parallel ILU preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the locking of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is shown that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5 to 13 is obtained with 16 processors.