# units of straight duct flow

Hi :

``````I want to simulate water duct flow, and for the units conversion I follow the article on the forum 'Choice of units in lattice Boltzmann simulations' by Jonas Latt.
``````

My siulation domain: 1 cm width * 1 cm height * 6cm length
inlet velocity 0.4m/s
water density=1000kg/m^3
water viscosity (nu_p) =8.55*10^-7 m^2/s

characteristic length l_p=1cm (hydraulic diameter)
reference speed u_p=0.4m/s (inlet velocity)
characteristic time l_p/u_p=0.01(m)/0.4(m/s)=0.025(s)

Re=u_pl_p/nu_p=0.40.01/(8.55*10^-7)=4678.3

We want a grid consisting of 6565390 =>
the discrete grid spacing delta_x=1/65
let’s choose delta_t=2*10^-4

u_lb =(delta_t/delta_x)u_d=([i]210^-[/i]4)[b]//b*1=0.013 (here the dimensionless speed u_d=1, right?)

nu_lb=(delta_t/delta_x^2)/Re=( i/(1/65)^2[/i] )/4678.3=1.8*10^-4
or

## tau=0.5+nu_lb3=0.5+0.000183=0.50054

Could anybody help me check the processes above? I know Re=4000 would be turbulent flow, and some modifications should be involved.

I just wnat to make sure first if my units-conversion is correct or not.

Please do me a favor if not too troubled.

Regards

Peterson

This is not correct. The physical velocity is u[sub]p[/sub] = 0.4 m/s, the lattice constant dx = 0.000154 m (1cm/65) and your time step dt = 0.0002 s. The lattice velocity u[sub]l[/sub] then is u[sub]p[/sub] * dt / dx = 0.519, which is too large. The lattice velocity should not exceed 0.1. You have to rechoose your time step.
By the way, my approach usually is to first set the characteristic lattice velocity and lattice viscosity (to ensure reasonable values), and then the time step. But everybody has different preferences. Important is that in the end everything is working nicely.

Dear Timm:

Thank you very much for replying.

For the same problem

My siulation domain: 1 cm width * 1 cm height * 6cm length
inlet velocity 0.4m/s
water density=1000kg/m^3
water viscosity (nu_p) =8.55*10^-7 m^2/s

characteristic length l_p=1cm (hydraulic diameter)
reference speed u_p=0.4m/s (inlet velocity)
characteristic time l_p/u_p=0.01(m)/0.4(m/s)=0.025(s)

Re=u_pl_p/nu_p=0.40.01/(8.55*10^-7)=4678.3

We want a grid consisting of 6565390 =>
dx=0.01m/65=0.000154m

4.
I choose tau=0.5009
(I would like to use tau=0.8-0.9, but it’s quite difficult to tune so for u_p=0.4 m/s and nu_p=8.5510^-7 m2/s)
=>nu_LB=(tau-0.5)/3=0.0003
so
dt=(nu_LB/nu_p)dx^2=0.0003/(8.5510^-7m2/s)
(0.000154m)^2=8.32*10^-6 s

5.
The lattice velocity
u_LB=u_pdt/dx=0.4m/s(8.32*10^-6 s)/(0.000154 m)=0.02161<0.1

And is this u_LB the inlet velocity in the LB program coding if the Zou/He velocity BC’s is applied?

Another question here. I read the paper ‘Shear Stress in Lattice Boltzmann simulations’, equation (45)
s_ab=-3/(2taurho)summation(ciacib-delta_ab/3ci dot ci)f_neq

for D2Q9
625
301
748

s_11=summation(ci1ci1-delta_11/3ci dot ci)f_neq
=(c11c11-1/31)(f1-f1_eq)+(c21c21-1/31)(f2-f2_eq)+(c31c31-1/31)(f3-f3_eq)+(c41c41-1/31)(f4-f4_eq)
+(c51c51-1/32)(f5-f5_eq)+(c61c61-1/32)(f6-f6_eq)+(c71c71-1/32)(f7-f7_eq)+(c81c81-1/32)(f8-f8_eq)+(c01c01-1/30)(f0-f0_eq)
=(1-1/3)(f1-f1_eq)+(1-1/3)(f3-f3_eq)+(1-2/3)(f5-f5_eq)+(1-2/3)(f6-f6_eq)+(1-2/3)(f7-f7_eq)+(1-2/3)(f8-f8_eq)

s_22
=(1-1/3)(f2-f2_eq)+(1-1/3)(f4-f4_eq)+(1-2/3)(f5-f5_eq)+(1-2/3)(f6-f6_eq)+(1-2/3)(f7-f7_eq)+(1-2/3)(f8-f8_eq)

s_21=(f5-f5_eq)-(f6-f6_eq)+(f7-f7_eq)-(f8-f8_eq)

of course the term -3/(2tau*rho) should be multiplied first. May I ask if the processes above are correct?