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this method, a number of commercial CFD software packages are now
available.
CFD is based on the analysis of fl uid fl ow in a large number of points
(elements/volumes) in the system, which are further connected in a
numerical grid/mesh. The system of differential equations describing the
fl uid fl ow is converted, using appropriate methods, to a system of
algebraic equations at discrete points. The obtained system of algebraic
equations, which can be linear or nonlinear, is large and requires the use
of computers to be solved. With the increase in speed and available
computer memory, more complex problems can be solved relatively
quickly using the CFD method. Finally, the solution presents fl ow
quantities at the grid points (Sayma, 2009).
CFD software packages are based on highly complex nonlinear
mathematical expressions derived from fundamental equations of fl uid
fl ow, heat, and mass transfer, and can be solved by complex algorithms
built into the program. Fluid fl ow in a given system can be simulated for
defi ned inlet and outlet conditions (also called boundary conditions).
Modeling outputs are usually presented numerically or graphically.
7.2.1 Mathematical description of the fl uid fl ow
The kind of equations describing fl uid fl ow are differential equations,
which represent the relationship between fl ow variables and their
evolution in time and space. Basic equations of fl uid fl ow include Euler's
equations for inviscid fl ow and Navier-Stokes equations for laminar fl ow
of viscous fl uid. With appropriate modifi cations, the Navier-Stokes
equations can also be used for turbulent fl ow. Namely, the variation in
time for turbulent fl ow is random, and detailed information on its
variation is of little relevance. The average quantity is more useful for
practical application. The mean value of fl ow quantity is determined in a
time interval that is suffi ciently large to neglect small variations, but
suffi ciently small to take into account large, signifi cant variations. The
Reynolds-averaged Navier-Stokes equations are based on this principle,
and represent the primary means for describing turbulent fl ows. Different
approaches are further applied to obtain a closed system of equations,
that is, to obtain an appropriate number of equations for a given number
of variables, which is called turbulence modeling (Blazek, 2005; Sayma,
2009). More detailed information on fl ow governing equations and
turbulent modeling methods can be found in numerous fl uid mechanics
textbooks.
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