Abstract
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Award date  10 Mar 1994 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513844021 
Publication status  Published  1994 
MoE publication type  G5 Doctoral dissertation (article) 
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Keywords
 modelling
 models
 mathematical models
 flow models
 fluid flow
 twophase flow
 nuclear power plants
 SFAV
 PLIM
 equations
 validation
 errors
Cite this
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Characteristicsbased modelling of flow problems : Dissertation. / Saarinen, Mika.
Espoo : VTT Technical Research Centre of Finland, 1994. 102 p.Research output: Thesis › Dissertation › Collection of Articles
TY  THES
T1  Characteristicsbased modelling of flow problems
T2  Dissertation
AU  Saarinen, Mika
N1  Project code: ENE040537
PY  1994
Y1  1994
N2  The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the twophase flow equations based on the SFAV (Separation of the twophase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal twophase flow. In calculating the fluid dynamics of nuclear power plants, twophase flow has to be considered. Numerical methods that are applied to solve twophase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of twophase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive onedimensional twophase flow equations leads to nonphysical equations and to a mathematically illposed initial boundary value problem. Mathematically wellposed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in twophase flow problems have been studied, especially in the case of horizontal twophase flow, in which new results have been obtained for the flooding phenomenon.
AB  The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the twophase flow equations based on the SFAV (Separation of the twophase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal twophase flow. In calculating the fluid dynamics of nuclear power plants, twophase flow has to be considered. Numerical methods that are applied to solve twophase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of twophase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive onedimensional twophase flow equations leads to nonphysical equations and to a mathematically illposed initial boundary value problem. Mathematically wellposed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in twophase flow problems have been studied, especially in the case of horizontal twophase flow, in which new results have been obtained for the flooding phenomenon.
KW  modelling
KW  models
KW  mathematical models
KW  flow models
KW  fluid flow
KW  twophase flow
KW  nuclear power plants
KW  SFAV
KW  PLIM
KW  equations
KW  validation
KW  errors
M3  Dissertation
SN  9513844021
T3  VTT Publications
PB  VTT Technical Research Centre of Finland
CY  Espoo
ER 