Prediciton of Suspensions Bulk Viscosity Using Immersed Boundary Approach in the Framework of the Lattice Boltzmann Method

Farnoush, Somayeh | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47194 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Taghizadeh Manzari, Mehrdad
  7. Abstract:
  8. In this study, bulk viscosity of suspensions is predicted using numerical simulation.The elaborated numerical method consists of the lattice Boltzmann (LB) method for fluid matrix simulation and the immersed boundary (IB) method for solid boundary implementation. In order to successfully implement the IB method in the frame-work of the LB method, two important challenges, which are body force modeling in the LB method and numerical velocity slip on solid boundaries, are discussed. As a first challenge, body force modeling in the LB method is studied by using a uni-fied framework which has been devised in this study. Using this unified framework,firstly, errors of different body force modelings are compared at macroscopic level.Secondly, the roots of some seemingly contradicting statements about body force models are shown. Finally, a new body force modeling, which is the most accurate among existing models at macroscopic level, is devised for the steady state simula-tion. Moreover,asa second challenge, numerical velocity sliperrorson both straight and curved solid boundaries using different immersed boundary methods in the lat-tice Boltzmann context are compared with respect to the relaxation time parameter and virtual domain thickness. In this comparative study, it is shown that the vir-tual domain thickness has significant impact on numerical velocity slip. Using the above mentioned studies, it is deduced that among different immersed boundary-lattice Boltzmann methods both of the IB-MRT (Multi Relaxation Time version of IB-LB method) and IMB-LB methods can be used to predict bulk viscosity of suspensions. The IB-MRT method is used in this study instead of previously used IMB-LB method. First, Galilean invariance of the IB-MRT method is shown. Then,implementation of Lees-Edwards boundary condition and stress computation in the IB-MRT method are discussed. Finally, computed bulk viscosities using the IB-MRT method are compared with those obtained using IMB-LB method and those obtained from already existing semi-analytical and analytical relations in the solids volume fraction range of less than 0.25
  9. Keywords:
  10. Suspension ; Immersed Boundary Method (IBM) ; Lattice Boltzmann Method ; Bulk Viscosity ; Immersed Moving Boundary Method (IMBM)

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