Abstract
In this thesis, the applicability of the homogeneous
mixture model of FINFLO for the free surface problem is
studied. The free surface problem is fundamental in
marine hydrodynamics, and a special case in twophase
flows. The work explores the basis of this type of
modelling from mathematical and numerical viewpoints, and
verifies the mixture model for the problem.
The mathematical background of the problem is presented,
together with the nature of it from the perspective of
marine hydrodynamics. The bulk flow equations are usually
averaged conditionally such that the governing equations
of the multiphase model are formally the same as in the
case of singlephase flow. It can be shown that one
additional equation suffices for the description of the
segregated phases. Here, the convection equation of the
void fraction is utilized. The void fraction equation is
derived in conservative form based on the
incompressibility constraint of the individual phases.
The convection of the void fraction corresponds to the
socalled Riemann problem. This is studied thoroughly by
developing a twodimensional solver for the comparison of
some wellknown schemes for the spatial discretization of
the convective quantity. This solver is applied to the
convection of a discontinuous distribution of the void
fraction. In addition, the socalled SUPERBEE limiter is
implemented to the FINFLO code for the extrapolation of
the convective void fraction.
The numerical solution of the NavierStokes equations for
simulations of twophase flows is covered
comprehensively. The code YAFFA, developed at the Aalto
University, has a modern VOF model implemented, and for
this reason, it is here used as a reference code. The
solution algorithms, the computation of the convective
quantities, the pressure correction stages as well as the
treatment of the segregated phases in both of the codes
are discussed in detail. The twophase flow over a
submerged ground elevation is computed using the codes
FINFLO and YAFFA, and the forming free surface wave is
compared to the corresponding results found from the
literature.
The aim of this thesis is to get acquainted with the
nature of the problem in conjunction with the specific
methodology used to solve such flows. This is done in
order to understand the requirements and possible
modifications needed for the model when we wish to
accurately predict ship flow phenomena that are not
solvable using the traditional free surface tracking
strategies. This way, the verification of the mixture
model of FINFLO is achieved.
Original language  English 

Qualification  Master Degree 
Awarding Institution 

Award date  15 Jan 2015 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9789513883157 
Electronic ISBNs  9789513883164 
Publication status  Published  2015 
MoE publication type  G2 Master's thesis, polytechnic Master's thesis 
Keywords
 VOF
 CFD
 twophase flow
 hydrodynamics
 free surface
 FINFLO
 YAFFA
 numerical modelling
 convection
 interface capturing
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Cite this
Viitanen, V. (2015). Verification of a homogeneous micture model for the free surface problem: Master's thesis. VTT Technical Research Centre of Finland. http://www.vtt.fi/inf/pdf/science/2015/S98.pdf