FLOWLAB SOLUTION
8.129 Conduct a parametric study for fully developed pipe flow by making use of the
pipe_fd FlowLab template. Set the pipe geometry with a radius of R = 0.05m and a
length of l = 1.0 m and use air at standard conditions. Run CFD simulations for
Reynolds numbers of Re = 500, 2000, 4000, and 10,000. What effect does increasing the
Reynolds number have on the total friction force on the pipe wall? By examining the
calculated friction factors, f, explain the trend of how the friction factor varies as the
Reynolds number is increased. Compare your calculated friction factors with the known
values and comment on any differences.
Problem Setup
The Reynolds number was varied through the boundary condition for mass flow rate
(kg/s). Depending on the Reynolds number the Viscous Condition was set to either
Laminar or Turbulent, as shown below.
When solving a turbulent flow, FlowLab gives you the option of specifying a wall
roughness, as shown in the Boundary Condition box. For these simulations, the wall
roughness was set to zero.
For all simulations, the fine grid option was selected for the mesh density as shown
below. If the flow is turbulent, the wall function used is also displayed in the Mesh box
(see FlowLab Template Descriptions for more information on wall function).
The convergence limit was set to either 1x10-5 or 1x10-6 for the various Reynolds number
cases, which is shown in the Solve box below. For example, at Re = 2000, laminar flow,
and fine grid, the simulation took approximately 4800 iterations for the tighter limit and
1950 iterations for the relaxed limit. If the student is working on a slow machine, then the
grid could be reduced to medium and/or make use of the relaxed convergence limit. The
results for these changes are discussed in the next section.
Answer
The convergence history is shown below for Re = 500. For the turbulent pipe flow cases,
additional variables are included in the convergence plot (see following plot).
A typical velocity profile is shown in the following plot for fully developed flow.
To examine the effect of Reynolds number on the total pipe wall friction force,
simulations were performed for Re = 500, 2000, 4000, and 10,000. One of the summary
items reported by FlowLab in the Reports section is the Total Friction Force on the wall,
as shown in the snapshot below.
The results of the total friction force study are summarized in the table below. With
increasing Reynolds number, the total friction force also increases on the pipe wall.
Re
500
2000
4000
10,000
Total friction force (N)
2.75973e-005
0.000110362
0.000595487
0.00299871
The student is also asked to discuss the trend on the variation of the friction factor with
Reynolds number. The figure below shows the computed friction factors as a function of
Reynolds number. The plot shows the same trends as the Moody chart in Fig. 8.20 of the
text.
0.14
0.12
Friction Factor
0.1
0.08
0.06
0.04
0.02
0
0
2000
4000
6000
8000
Reynolds Number
10000
12000
A comparison can be made between the calculated values and the known values. The
following table summarizes the calculated friction factor values from the CFD analysis
along with analytic comparison values.
Reynolds
number
500
2000
4000
10,000
f - CFD
0.1278
0.0319
0.0430
0.0347
f - laminar
(Eqn. 8.19)
0.128
0.032
n/a
n/a
f (Moody
chart)
n/a
n/a
~ 0.039
~ 0.03
f (Blasius eqn.)
n/a
n/a
0.0397
0.0316
For the first two Reynolds numbers, where the flow is laminar, the CFD simulations
compare well to the laminar equation for friction factor (Eqn. 8.19). For the two
turbulent flow cases, the computed results are compared to values from the Moody chart
(Fig. 8.20) and values calculated from the Blasius equation (see Example 8.5 of the text).
The computed f values are within 8-10% of the Blasius equation.
Some experimentation was conducted on the sensitivity to convergence limit and grid
resolution. For the Re = 2000 case, the fine grid and medium grid produced friction factor
values of 0.03194 and 0.0320, respectively. For a convergence limit of 1x10-5, the fine
grid took 1950 iterations, while the medium grid took 570. Note that this grid resolution
issue was not checked at the highest Reynolds number. These results might not hold for
fully turbulent pipe flow. The convergence limit was reduced to 1x10-6 for Re = 2000 and
4000 with no significant changes in the results.