LBM to Physical Temperature Conversion

Lattice Boltzmann Method LBM: Theory
#1

How can we convert Physical temperatures to LB? ( for example I want to insert my physical boundary condition temperatures into my LB code)
For velocity, in a lid driven cavity problem for instance, we use (u/Ucavity)_physical=(u/Ucavity)_LB. Where Ucavity_LB is obtained by Re and nu_LB independent from its physical value. But no such ability is available for temperature to be computed.
I have not found an answer despite so many unit conversion discussions, except natural convection case in which we can use Ra number that has deltaT term in it.

#2

Hi Omish,

the general way to convert units in LBM to the physical units is using a dimensionless number like Re, Gr, Ra and etc.

the calculation you mentioned doesn’t convert units “(u/Ucavity)_physical=(u/Ucavity)_LB)”, it normalizes the velocity in both units.

for the temperature, you can use a dimensionless number like Ra or Gr. but if you know the high and the low value of temperature in the physical unit follow the below calculation:

T_phy = T_LBM * Diff_T_phy + T_low_phy.

for example:

T_low_phy = 20
T_high_phy = 100
Diff_T_phy = 100 - 20 = 80

T_low_LBM = 0
T_high_LBM = 1

T_LBM = 0.5

T_phy = 0.5 * 80 + 20 = 60

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#3

Yes maybe as you say the calculations are not called “conversion”, but by it I meant that I can find physical velocities from LBM code results by using 0 to 1 scale.
The method you mentioned had come to my mind since it’s also the same 0 to 1 scaling for temperature; However I thought it is mandatory to use a dimensionless number to get a LB temperature independently first (just like finding Ucavity_LB independent from its physical values), and then use this variable change (frequently called theta) as a scale; I couldn’t find such a dimosionless number that contains T or delta T for a general case, so in fact that was the problem.
Thanks for your answer

#4

Hi Arman, I am developing a code for melting of phase change material. In that case, the code is running, but after some time it becomes unstable . I think the problem is in unit conversion. Will you help me, how to convert units?