Page 350 - Computational Fluid Dynamics for Engineers

340 11. Incompressible Navier-Stokes Equations

1.0
0.9 1 1.0
0.9 1
0.7 1 0.7 1
0.8 0.8
y/H ^^'
^ ^ 0.6
y/H"
0.5 0.5 T ^ ^
0.4 /y"' 0.4
beta = 100.0 beta* 100.0
0J 03
beta = 50.0 — beta =50.0
/
0.2 T / beta = 1.00 0.2 beta = 1.00
0.1 0.1
T «
0.0 i i — * 1 1— 0.0 J— i 1 1 —• -* 1 1
u/u 0 U/Un
(a) (b)

u/u© u/uo
(c) (d)
Fig. 11.3. Effect of (3 on the velocity profiles for RH — 25, h/H 0.5, L/H = 15 at x/H
(a) 0.9, (b) 1.8, (c) 9 and (d) 15.

Analysis of the flow solutions indicate that steady state convergence within
the specified tolerance is reached at about t = 500 for j3 = 100 and that the
reattachment location is essentially independent of /? as shown in Table 11.2.
However, the error on the conservation of mass defined by

m x=o - m x=L
where
m — I udy
Jo
becomes smaller as (3 increases. Here, m x=o is the mass flow rate at x = 0 and
rn x=L at x = L.
Table 11.3 shows the effect of the grid size on the reattachment location,
x r/H, and on the error of conservation of mass (rh x=o - rn x=h) f° r Rh = 50