0/epsilon

Epsilon is the dissipation factor. Initial epsilon and input epsilon: Set initial epsilon as high to help stability. Calculate epsilon from {http://www.openfoam.org/docs/user/cavity.php#x5-290002.1.7} and http://en.wikipedia.org/wiki/Turbulence_kinetic_energy as,

# turbulent ke
k = lambda ux, uy, uz, ti: 0.5*((ti * ux)**2 + (ti*uy)**2 + (ti*uz)**2) 

# turbulence damping based on mixing length.
epsilon = lambda l, k, Cmu:  Cmu ** 0.75 * k ** 1.5 / l;  

# mu_t http://www.cfd-online.com/Wiki/Standard_k-epsilon_model
turbViscosity = lambda rho, Cmu, k, epsilon: rho * Cmu * k**2 / epsilon 

-------------Calculations-------------------------------

k(10, 0, 0, 0.05) # input turbulent kinetic energy at 5% ti, 10m/s
# 0.125
k(10, 0, 0, 0.01) # input turbulent kinetic energy at 1% ti, 10m/s
# 0.005

Cmu = 0.09 # a constant.
l = 0.07* 0.4; # turbulent mixing length, say 0.07 of the width of the tunnel from the link above.
epsilon(l, k(10, 0, 0, 0.05), Cmu)  # epsilon in noisy tunnel (5% ti)
# 0.26
epsilon(l, k(10, 0, 0, 0.01), Cmu)  # epsilon in quiet tunnel (1% ti)
# 0.0021
l=0.07*0.05 # cylinder diameter.
epsilon(l, k(10, 0, 0, 0.01), Cmu)  # epsilon in quiet free-space using cylinder diameter (1% ti)
# 0.017

So the 1% quiet tunnel has 25 times lower k but 124 times lower epsilon
than the 5% noisy one.  Using the cylinder diameter instead of the
tunnel diameter resulted in epsilon increasing by factor 8.

-----------Examples----------------------------------------------

dimensions [0 2 -3 0 0 0 0];
internalField uniform 1;
boundaryField { 
   in { type fixedValue; value uniform 1; }
   in { type turbulentMixingLengthDissipationRateInlet; value uniform 0.1;}
   out { type fixedValue; value uniform 1; }
   sym { type symmetryPlane; }
   wall { type compressible::epsilonWallFunction; value uniform 1; }
   }

The following converged ok with circularCylinder case 22.

FoamFile{version 2.0; format ascii; class volScalarField; object epsilon;}

boundaryField {
   in{type freestream; freestreamValue uniform 0.05;}
   out{type freestream; freestreamValue uniform 0.05;}
   top{type symmetryPlane;}
   wall{type zeroGradient;} // zeroGradient? calculated?  fixedValue; value uniform 0? 1E-10?
   sym{type symmetryPlane;}
   emptyf{type empty;}
   emptyb{type empty;}
}
internalField uniform 1;
dimensions [0 2 -3 0 0 0 0];