1. Complex Geometries and Higher Reynolds Numbers

2. Creating obstacle files
Current LB2D_Prime naming convention:
sizexXsizey.bmp
Current format:
‘True color’ 24 bit

3. Scaling to real world Choose a Reynolds number
Choose a combination of slit width and viscosity to give maximum velocity < ≈0.1 lu ts-1; smaller is better
Maximum velocity 3/2 of average for Poiseuille flow in slit
Best to use t = 1 for simple bounceback boundaries: yields kinematic viscosity of 1/6 lu2 ts-1
Solve for the gravitational acceleration needed to drive the flow by rearranging Poiseuille equation

4. Entry Length Effects
r is the 'radius' -- the distance from the center to the point of interest
a is the half-width (d/2)
u is the velocity at the point of interest and uavg is the average velocity
Tritton DJ (1988) Physical Fluid Dynamics, 2nd Ed. Oxford University Press, Oxford New York
x /(d Re) is dimensionless distance down the pipe. When this distance is infinite, Poiseuille flow is fully developed. If Re = 1, Poiseuille flow is well-developed in a short distance down the pipe: x/d = 1 → x = d = 2a (just 2 half-widths down the pipe). As the Reynolds number increases, this distance can become quite large. If x = 1 m with Re = 103 in a 10 cm pipe, x/(d Re) = 1 m /(10-1 m 103) = 10-2 and Poiseuille flow will not be fully developed even 1 m from the inlet.

5. Entry Length Effects
Tritton DJ (1988) Physical Fluid Dynamics, 2nd Ed. Oxford University Press, Oxford New York

6. Velocity BCs Simple compressible fluid model
Identical constant velocities at each end of the domain:
mass of fluid will change with time
Flow must be accompanied by a pressure gradient and hence the pressure must be lower at the outlet
The pressure and density are related through an ideal gas law of the form P = r/3 in this model
Densities at the input and output must be different
If the velocity boundaries on each end of the domain are equal, mass will accumulate in the system because the mass flux of fluid in (vin rin) will exceed the out flux (vout rout)
Problem increases in severity as the pressure difference increases
Incompressible model of Zou and He (1997), pressure boundaries, or gravity-driven flow can be used to avoid this complication

7. Flow Past a Cylinder
The drag force FD is defined in terms of the drag coefficient CD as
Gravitational Force

8.
Tritton DJ (1988) Physical Fluid Dynamics, 2nd Ed. Oxford University Press, Oxford New York

9. Re = 0.16

10. Re = 41
Taneda S (1956)

11. von Kármán Vortex Street, Re = 105h l
Photo by S. Taneda. S. Taneda and the Society for Science on Form, Japan

12. von Kármán Vortex Street, Re = 105: LBM Simulation (vorticity)