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Tobi December 4, 2012 20:24

Hi all,

i want to simulate an liquid cooler for a CPU. For that I had a look into the solvers and thought that the solver


for turbulent incompressible fluids are good.
For that I have to change the transportProperties file from air into water (25C)


transportModel Newtonian;

// Laminar viscosity
nu              nu [0 2 -1 0 0 0 0] 0.89e-06;     

// Thermal expansion coefficient
beta            beta [0 0 0 -1 0 0 0] 0.0018;

// Reference temperature
TRef            TRef [0 0 0 1 0 0 0] 298;

// Laminar Prandtl number
Pr              Pr [0 0 0 0 0 0 0] 6.1;

// Turbulent Prandtl number
Prt            Prt [0 0 0 0 0 0 0] 0.38;

Are this settings correct? How can I estimate the turbulent prandtl number in that problem?
In my case I calculated the turbulent prandtl with that equation:


Prt = 0.7 * a / nu_t
With the turbulence calculator on that website I calculated k and omega from U, I and length scale.
After that I calculated mu/mu_t and then nu_t = mu_t/rho.

Is that correct?

Thanks in advance

Bernhard December 5, 2012 04:55

The turbulent Prandtl number is not really a property of the liquid. You obtain it from the Boussinesq (or gradient diffusion) hypothesis (not to be confused with the Boussinesq approximation) from the turbulent heat flux,

-\overline{\theta'u'_j}=\alpha_t\frac{\partial\overline{T}}{\partial x_j}
and then it is assumed that \alpha_t scales wit \nu_t or \alpha_t=\frac{\nu_t}{Pr_t}, but this is by no means a way to estimate the turbulent Prandtl number. It is a property of the turbulence more than a property of the liquid. I think in general, Pr_t is somewhere in the range 0.7 to 0.9. But please read a bit more on this in books or papers to be absolutely sure.

Ahmed Khattab December 30, 2012 04:30

Dear Tobi,

a good start could be from a neighbor case multiRegionLiquidHeater .it contains a file for water properties.


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