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Uniform Fixed Valu $ \omega$

The widely used boundary condition for 2 8 simple fixed valued everywhere at the inlet patch.

omega:

 boundaryField
 {
".*_inlet"
    {
        type            fixedValue;
        value           uniform 1000;
    }
 }

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Next: Model setting without an Up: Alternative formulation Previous: Alternative formulation   Contents   Index

Running Simulation - Convergence Monitoring - Residuals

When simulation is running there is easy way how to watch residual convergence process. gnuplot software is convenient for analyzing log file during the computation. Initial residuals can be plotted following way. Simple gnuplot script file:

 

set grid
set xlabel "iterations"
set ylabel "initial residuum"
set logscale y
set key box above

plot "< grep 'Solving for Ux' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "u 4", \
     "< grep 'Solving for Ux' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "u 3", \
     "< grep 'Solving for Ux' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "u 2", \
     "< grep 'Solving for Ux' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "u 1", \
     "< grep 'Solving for Uy' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "v 4", \
     "< grep 'Solving for Uy' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "v 3", \
     "< grep 'Solving for Uy' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "v 2", \
     "< grep 'Solving for Uy' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "v 1", \
     "< grep 'Solving for Uz' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "w 4", \
     "< grep 'Solving for Uz' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "w 3", \
     "< grep 'Solving for Uz' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "w 2", \
     "< grep 'Solving for Uz' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "w 1", \
     "< grep 'Solving for p' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "p 4", \
     "< grep 'Solving for p' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "p 3", \
     "< grep 'Solving for p' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "p 2", \
     "< grep 'Solving for p' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "p 1", \
     "< grep 'Solving for k' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "k 4", \
     "< grep 'Solving for k' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "k 3", \
     "< grep 'Solving for k' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "k 2", \
     "< grep 'Solving for k' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "k 1", \
     "< grep 'Solving for epsilon' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "epsilon 4", \
     "< grep 'Solving for epsilon' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "epsilon 3", \
     "< grep 'Solving for epsilon' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "epsilon 2", \
     "< grep 'Solving for epsilon' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "epsilon 1", \
     "< grep 'Solving for omega' log | sed -n '4~4p' | cut -f 9 -d ' '" with lines title "omega 4", \
     "< grep 'Solving for omega' log | sed -n '3~4p' | cut -f 9 -d ' '" with lines title "omega 3", \
     "< grep 'Solving for omega' log | sed -n '2~4p' | cut -f 9 -d ' '" with lines title "omega 2", \
     "< grep 'Solving for omega' log | sed -n '1~4p' | cut -f 9 -d ' '" with lines title "omega 1"


pause 10

#reread
#pause mouse

    

The residuum.gp script can be found in:

$WM_PROJECT_INST_DIR/waterTurbines-CFD-XX.XX/tutorials/kaplanTutorial/
and/or
$WM_PROJECT_INST_DIR/waterTurbines-CFD-XX.XX/tutorials/francisTutorial/

Run the gnuplot script:

# gnuplot residuum.gp

openfoam example residuum water turbine

Figure: Water turbine CFD, convergence monitoring plot example.

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Center of mass of a surface

Consider a two dimensional surface $ \mathfrak{S}$, choose a system of coordinates and define a position vector $ \vec{r}_{\mathfrak{S}}$ of its center of mass as followingimg209 where $ \vec{r}$ is a position vector of an element $ \mathrm{d} S$.

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