Page 376 - Computational Fluid Dynamics for Engineers

Appendix 12 A 367

Table 12.2. Comparison of reattachment locations according to four methods.

Method x r/(hR h)
Finite Volume 0.126
B-W 0.132
MacCormack 0.128
INS 0.138

Table 12.3. Effect of dissipation parameters on the reattachment locations.
£i X r/(hR h)

1/16 0.132
1/8 0.138

12.6.3 Solution Procedure and Sample Calculations

The solution procedure and sample calculations are now discussed separately
for the three methods discussed in Sections 12.3 to 12.5 and comparisons are
made with those obtained from the INS method of Section 11.5. The computer
program for each method is given in Appendix B.
Table 12.2 shows a comparison between the predictions of the four methods
for the reattachment locations. Except for the INS method, all calculations are
for MQO = 0.15, a value low enough for the flow to be considered incompressible.
Table 12.3 shows the effect of dissipation parameters on the reattachment
locations according to the B-W method.
Figures 12.3 and 12.4 show the effect of the Reynolds number on the reat-
tachment locations and velocity profiles according to the B-W method.

Appendix 12A
Jacobian Matrices of Convection and Diffusion Terms
E, F, E v and F v

To derive the Jacobian matrices of the convective flux terms E and F, we first
express E and F by the components of Q:

qi
Q ~ ]
QU Q2
QV
E t _94J