Verification Case 8
PRODUCT: AFT Arrow
MODEL FILE: AroVerify8.ARO
REFERENCE: Robert W. Fox and Alan T. McDonald, Introduction to Fluid Mechanics, Third Edition, John Wiley & Sons, 1985, Pages 632-633, example 12.8
GAS: Air
ASSUMPTIONS: 1) Adiabatic flow, 2) Perfect gas.
RESULTS:
| Parameter | Fox & McDonald | AFT Arrow |
| L1-3 – length to choking (meters) | 4.99 | 4.99 |
| V1– Velocity at point 1 (m/s) | 65.3 | 65.2 |
| T1– Temperature at point 1 (deg. K) | 294 | 294 |
| M1– Mach number at point 1 | 0.19 | 0.19 |
| M2 – Mach number at point 2 | 0.4 | 0.4 |
| P2– Pressure at point 1 (mm Hg gage) | -18.9 | -18.9 |
| L1-2 – length to measured pressure (meters) | 4.29 | 4.29* |
* AFT Arrow does not have the ability to solve for pipe length, so the length was input. With this known length, the AFT Arrow Mach number at M2 should agree with Fox & McDonald’s, and it does. The resulting mass flow rate is then used as input for AFT Arrow pipe #2.
DISCUSSION:
The predictions agree very closely.
The two pipes in the AFT Arrow model represent the solutions to stations 2 and 3.
Note that the friction factor in Fox & McDonald is the Fanning friction factor. To obtain the Darcy-Weisbach friction factor used in AFT Arrow, multiply the Fanning friction factor by 4.
It should also be noted that, from time to time, AFT finds it is necessary to modify the Solver used by Arrow to improve application performance, or for other reasons. These modifications to the Solver may cause slight changes to the appropriate pipe lengths determined by Arrow.
