Page 351 - Computational Fluid Dynamics for Engineers

11.5 Model Problem: Sudden Expansion Laminar Duct Flow 341

Table 11.2. Effect of (3 on attachment location x r/H for Rh = 50.

0 X r/H rh x=o — rh x=L

1 2.9250 -0.0547
50 3.3750 -0.0125
100 3.3750 -0.0090

Table 11.3. Effect of grid on the reattachment location and conservation of mass, (3 = 100.

Grid Xr/H rh x=o —
50 x 25 3.00000 -0.0053
80 x 40 3.18750 -0.0082
100 x 50 3.30000 -0.0086
150 x 75 3.40000 -0.0089
200 x 100 3.3750 -0.0090

Table 11.4. Effect of grid on the reattachment location and conservation of mass, (3 = 1.
Grid X r/H ra x=o -

50 x 25 2.7000 -0.0433
80 x 40 2.8125 -0.0522
100 x 50 2.8500 -0.0537
150 x 75 2.9000 -0.0552
200 x 100 2.9250 -0.0547

Table 11.5. Comparison of Calculated Results [12,13,14,15].

Investigator x r/(hRh) Rh
Present Method 0.135 50
Allen [9] 0.138 50
Kwon et al. [10] 0.138 50
Hung [11] 0.132 46.6
Agarwal [12] 0.136 46.6

and (3 = 100. Table 11.4 shows similar results for (3 = 1. These results show
that, as expected, the reattachment location x r/H becomes constant with a
value equal to 3.3750 as the mesh is refined (grid convergence).
The results shown in Table 11.5 indicate that the reattachment length
x r/(hRh) is in good agreement with the boundary-layer solutions of Allen [12]
and Kwon et al. [13] and the Navier-Stokes solutions of Hung [14] and Agarwal
[15].