Numerical treatment of inter-phase coupling and phasic pressures in multi-fluid modelling: Dissertation

Hannu Karema

Research output: ThesisDissertationCollection of Articles


This thesis work concentrates on the area of dispersed multi-phase flows and, especially, to the problems encountered while solving their governing equations numerically with a collocated Control Volume Method (CVM). To allow flexible description of geometry all treatment is expressed in a form suitable for local Body Fitted Coordinates (BFC) in a multi-block structure. All work is related to conditions found in a simplified fluidized bed reactor. The problems covered are the treatment and efficiency of inter-phase coupling terms in sequential solution, the exceeding of the bounds of validity of the shared pressure concept in cases of high dispersed phase pressure and the conservation of mass in momentum interpolation for rapidly changing source terms. The efficiency of different inter-phase coupling algorithms is studied in typical fluidized bed conditions, where the coupling of momentum equations is moderate in most sections of the bed and where several alternatives of different complexity exist. The interphase coupling algorithms studied are the partially implicit treatment, the Partial Elimination Algorithm (PEA) and the SImultaneous solution of Non-linearly Coupled Equations (SINCE). In addition to these special treatments of linearized coupling terms, the fundamental ideas of the SINCE are applied also to the SIMPLE(C) type pressure correction equation in the framework of the Inter- Phase Slip Algorithm (IPSA). The resulting solution algorithm referred to as the InterPhase Slip Algorithm - Coupled (IPSA-C) then incorporates interface couplings also into the mass balancing shared pressure correction step of the solution. It is shown that these advanced methods to treat interphase coupling terms result in a faster convergence of momentum equations despite of the increased number of computational operations required by the algorithms. When solving the entire equation set, however, this improved solution efficiency is mostly lost due to the poorly performing pressure correction step in which volume fractions are assumed constant and the global mass balancing is based on shared pressure. Improved pressure correction algorithms utilizing separate fluid and dispersed phase pressures, the Fluid Pressure in Source term (FPS) and the Equivalent Approximation of Pressures (EAP), are then introduced. Further, an expanded Rhie-Chow momentum interpolation scheme is derived which allows equal treatment for all pressures. All the computations are carried out in the context of a collocated multi-block control volume solver CFDS-FLOW3D.
Original languageEnglish
QualificationDoctor Degree
Awarding Institution
  • Tampere University of Technology (TUT)
  • Karvinen, Reijo, Supervisor, External person
Award date1 Mar 2002
Place of PublicationEspoo
Print ISBNs951-38-5969-X
Electronic ISBNs951-38-5970-3
Publication statusPublished - 2002
MoE publication typeG5 Doctoral dissertation (article)


  • multi-phase flow
  • multi-fluid modelling
  • inter-phase coupling
  • phasic pressures
  • numerical methods
  • Control Volume Method
  • Body Fitted Coordinates
  • fluidized beds
  • chemical reactors


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