# LBM unit and physical properties.

Hi, all I tried to simulate to 2D MCMP model using LBM and I got the result which is similar with original result. However, I wonder whether it is exact one or not because I do not know real values of property. According to some paper and information, I should find the lattice unit and calculate the values using the lattice unit and physical properties. I mean….when I want to check the simulation of water droplet using LBM, I could not use real density of water, air which are 1000Kg/m^3 and 1Kg/m^s respectively. Density value in LBM is needed and calculated using lattice unit instead of real physical value. Okay, my question is…

Lx=300 lattices
Ly=40 lattices
Density1=0.97
Density2=0.03
Tau=1.0
Viscosity=1./3.*(tau-1./2.)=1./6.
Time iteration number=10000

1. How could I calculate gravitational accelerator (body force per mass)?
2. Lattice unit = 1/300. And time unit=1/10000, these values are exact one?
3. If I want to adapt water density, in this simulation, how could I calculate the density of water in LBM unit system.
4. When I change the domain from 300x40 lattices to 100x100 lattices, the lattice unit and other parame-ters will be changed?

I am looking forward to receiving response and I really need your help. Thanks.

i am also facing the similar problem. did u get any information yet can we exchange information … i am trying to find some easy way to convert units from LBM to real world. i got this paper

Physical and computational scaling issues in lattice Boltzmann simulations of binary fluid mixtures
BYM. E. CATES,J.-C. DESPLAT,P.STANSELL,A.J.WAGNER,K. STRATFORD,R.ADHIKARI AND I. PAGONABARRAGA

Phil. Trans. R. Soc. A(2005)363, 1917–1935
doi:10.1098/rsta.2005.1619

I am translating units betweem real world and lb over dimensionless ones.

Real units <-> dimension less units <-> LB units

so you need to define some reference value for lenght and for time or velocity.

I did modifiy one class in palabos to help me do those translation, I can post it here on monday if you want

yes it is the right way … but every one have taken their own scale system… some people have calculated using Reynolds number (dimensionless parameter) Re=Lo Uo/V
Lo= Charectric Length … we can take it as the dimension of our computation if i am making the length like 100x100x30 which length i should take
for flow Problem we can take the. it look to have some logic, that if we take the length in the direction of flow (for flow problem)
but what length it should be if we are dealing the problems like droplet impect on the surface?
Uo = Charectric velocity …fare the case of flow problem, we can use the flow velocity of the Liquid in the physical system to calculate
which paper i am using as reference have used (Lo g)^1/2 as Uo g is the gravitational acceleration
how much u have taken the gravitational acceleration ?

PHYSICAL REVIEW E87, 013301 (2013)
Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method

V = viscosity (Kinematic viscosity)

if u can send me ur one i will b thankfull to u… how u r calculating the Gravitational acceleration in the lattice units to use in the LBM models

umar_farooq_17

I am also trying to understand this mechanism and I could understand what vetor told. However, I confirm one of the important things which are key point for understanding was missed. I do not know yet.

Okay, as you mentioned, some people use the dimensionless parameters, such as Reynolds number, Bond number, and Capillary number, for calculation of other variables. I also found some parameters, especially gravitational effect.
This mechanism is really simple. We could think just matching system. If you want to find the velocity in LB unit, you could use the Reynolds number as dimensionless parameter. Like this… (It is just example and it does not use for simulation. Please, check only mechanism.)

=============Re=100(fixed value)==============

Real units (Re=100)

U=0.1ms^-1
R=1.mm=1.*10^-3m
Kinematic viscousity(nu) =1.*10^-6m^2s^-1

Lattice units (Re=100)
(tau=1.0)
U_lb=?
R_lb=6
Kinematic vis-cousity(nu)_lb=1/6

Solution) U_lb=2.78

============================================
DON’T FORGET! Lattice units do not have any units. For example, U has unit, (m/s) but U_lb(lattice ve-locity) does not have any unit.

As you can see here, this mechanism is really similar with Buckingham’s pi theory which is one of the methods when we find the dimensionless parameter in Fluid mechanics (Mechanical engineering).
Okay! That is everything that I know about Lattice Units.

Vetor

Thanks for your response. I also understood what you mean. If your conditions are okay, please post it.

Hi gamsrl,
Your scaling of the LBM units seems ok. (I presume that you assumed dx = dt = 1, and nu = (2tau-1)/6 * dx^2/dt )
However, if you try to use the LBM velocity you computed (U_lb=2.78) in your simulation it will most likely not be stable.
This is because in the LBM, the velocity U allows needs to be small compared to the lattice speed dx/dt. ( U << dx/dt , i.e. low Mach number flows)
I advise that you choose a LBM velocity first, for instance U_lb = 0.1, and then compute the kinematic viscosity (and thus the relaxation time) you need to achieve the Reynolds number you want.
Good luck.

Nick

Thanks, Nick Your information could be really helpful.

umar_farooq_17, I forgot to tell about the gravitational acceleration. Bond number is used for finding gravitational acceleration because I already know the exact Bond value. Bond numbers are changed according to different gravitational acceleration vise versa.

Hello gamsrl,
About your method, I have a question. In your transformation process, you have not mentioned the Sound velocity. But according to Succi’s book, the real sound velocity and the lattice sound velocity are used in the process. Could you give me some idea about what value can the real sound velocity be after your transformation? Thank you.

Hi

I think there is a fundamental concept of error/misunderstanding in what it has been trying to achieve with such questions.
In paper here

Chemical Engineering Science
Volume 69, Issue 1, 13 February 2012, Pages 628–643

which also available
here

it is read: “The standard pre-calculation in LB starts with a certain amount of dimensionless numbers…”. I suggest you to read that paper.

Good luck
Mecobio

Dear gamsrl
I am also working on droplet simulation. please let me know how you have convereted the physical porbloem of water droplet motion inot lattice units. I am not able to understand how to decide dx, dt, g, force conversion

Pitambar

## gamsrl Wrote:

Hi, all I tried to simulate to 2D MCMP model using
LBM
and I got the result which is similar with
original result. However, I wonder whether it is
exact one or not because I do not know real values
of property. According to some paper and
information, I should find the lattice unit and
calculate the values using the lattice unit and
physical properties. I mean….when I want to
check the simulation of water droplet using LBM, I
could not use real density of water, air which are
1000Kg/m^3 and 1Kg/m^s respectively. Density value
in LBM is needed and calculated using lattice unit
instead of real physical value. Okay, my question
is…

Lx=300 lattices
Ly=40 lattices
Density1=0.97
Density2=0.03
Tau=1.0
Viscosity=1./3.*(tau-1./2.)=1./6.
Time iteration number=10000

1. How could I calculate gravitational accelerator
(body force per mass)?
2. Lattice unit = 1/300. And time unit=1/10000,
these values are exact one?
3. If I want to adapt water density, in this
simulation, how could I calculate the density of
water in LBM unit system.
4. When I change the domain from 300x40 lattices
to 100x100 lattices, the lattice unit and other
parame-ters will be changed?

I am looking forward to receiving response and I