TY - BOOK

T1 - Numerical simulations and mathematical models of flows in complex geometries

T2 - From laminar to turbulent regimes

AU - Hernandez Garcia, Anier

PY - 2016

Y1 - 2016

N2 - The research work of the present thesis was mainly aimed at exploiting one of thestrengths of the Lattice Boltzmann methods, namely, the ability to handle complicatedgeometries to accurately simulate flows in complex geometries. In this thesis, we performa very detailed theoretical analysis of the finite volume unstructured lattice Boltzmannmethod (ULBM) in three dimensions, considering the Bhatnagar-Gross-Krook (BGK)relaxation time approximation for the collision operator, one of the more commonly usedby the community. Regarding this scheme, two time integration methods are consideredand through the Chapman-Enskog multi-scale expansion technique the dependence of thekinetic viscosity on each scheme is investigated. Seeking for optimal numerical schemesto eciently simulate a wide range of complex flows a variant of the finite element,off-lattice Boltzmann method [5], which uses the characteristic based integration is alsoimplemented. Using the latter scheme, numerical simulations are conducted in flows ofdifferent complexities: flow in a (real) porous network and turbulent flows in ducts withwall irregularities.From the simulations of flows in porous media driven by pressure gradients, anomaloustransport features of Lagrangian trajectories are investigated. Several statisticalproperties of both Lagrangian and Eulerian velocities are also examined. Based on thesemeasurements, an eective model is considered to assess the role of the pressure gradienton the transport of Lagrangian tracers. In the calculations simple statistical argumentsare used, based on the approach developed by [12, 64]. Such formalisms contain asa fundamental tool the theory of Levy stable distributions[23, 14]. It is found thatthe pressure gradient induces a superdiusive behavior along the mean motion while asubdiusive scaling is observed in the orthogonal directions.Numerical simulations of turbulent flows in ducts with irregular walls are also implemented,as mentioned above. Preliminary results regarding the characterization ofthe turbulent energy landscape motivated the development of a phenomenological modelto describe the spatial probability density function of the turbulent kinetic energy uctuations.Closely following the ideas recently devoloped in [68], the proposed modelcombines recent ndings on the spatial proliferation mechanisms of turbulent spots [7],with Townsend attached eddy hypothesis [63], [68]. Preliminary results obtained fromthe numerical experiments are compared with predictions of the model. Also, some statisticalfeatures of the turbulent kinetic energy production term are illustrated. Someconcluding remarks are given in the last part of the thesis in which main ndings of thisPhD thesis are discussed.

AB - The research work of the present thesis was mainly aimed at exploiting one of thestrengths of the Lattice Boltzmann methods, namely, the ability to handle complicatedgeometries to accurately simulate flows in complex geometries. In this thesis, we performa very detailed theoretical analysis of the finite volume unstructured lattice Boltzmannmethod (ULBM) in three dimensions, considering the Bhatnagar-Gross-Krook (BGK)relaxation time approximation for the collision operator, one of the more commonly usedby the community. Regarding this scheme, two time integration methods are consideredand through the Chapman-Enskog multi-scale expansion technique the dependence of thekinetic viscosity on each scheme is investigated. Seeking for optimal numerical schemesto eciently simulate a wide range of complex flows a variant of the finite element,off-lattice Boltzmann method [5], which uses the characteristic based integration is alsoimplemented. Using the latter scheme, numerical simulations are conducted in flows ofdifferent complexities: flow in a (real) porous network and turbulent flows in ducts withwall irregularities.From the simulations of flows in porous media driven by pressure gradients, anomaloustransport features of Lagrangian trajectories are investigated. Several statisticalproperties of both Lagrangian and Eulerian velocities are also examined. Based on thesemeasurements, an eective model is considered to assess the role of the pressure gradienton the transport of Lagrangian tracers. In the calculations simple statistical argumentsare used, based on the approach developed by [12, 64]. Such formalisms contain asa fundamental tool the theory of Levy stable distributions[23, 14]. It is found thatthe pressure gradient induces a superdiusive behavior along the mean motion while asubdiusive scaling is observed in the orthogonal directions.Numerical simulations of turbulent flows in ducts with irregular walls are also implemented,as mentioned above. Preliminary results regarding the characterization ofthe turbulent energy landscape motivated the development of a phenomenological modelto describe the spatial probability density function of the turbulent kinetic energy uctuations.Closely following the ideas recently devoloped in [68], the proposed modelcombines recent ndings on the spatial proliferation mechanisms of turbulent spots [7],with Townsend attached eddy hypothesis [63], [68]. Preliminary results obtained fromthe numerical experiments are compared with predictions of the model. Also, some statisticalfeatures of the turbulent kinetic energy production term are illustrated. Someconcluding remarks are given in the last part of the thesis in which main ndings of thisPhD thesis are discussed.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122096917805763

M3 - Ph.D. thesis

BT - Numerical simulations and mathematical models of flows in complex geometries

PB - The Niels Bohr Institute, Faculty of Science, University of Copenhagen

ER -