Verification Case 2
PRODUCT: AFT Arrow
MODEL FILE: AroVerify2.ARO
REFERENCE: Michel A. Saad, Compressible Fluid Flow, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1993, Page 215, example 5.3
GAS: Methane
ASSUMPTIONS: 1) Adiabatic, 2) Perfect gas
RESULTS:
| Parameter | Saad | AFT Arrow |
| Maximum pipe length (m) | 4,024 | 4,031 |
| P2– Static pressure at exit (kPa) | 48.2 | 48.11 |
| V2– Velocity at exit (m/s) | 433.17 | 433.11 |
| T2– Static temperature at exit (deg. K) | 278.43 | 277.88 |
DISCUSSION:
As specified, inlet conditions are known and the outlet conditions are sonic. The pipe length that yields sonic flow is the objective. With the known inlet conditions, an implied mass flow rate exists. To pose the problem in AFT Arrow terms, a few simple calculations are needed to obtain the mass flow rate. Once obtained, it is applied as a flow demand at the exit.
The problem states that the inlet velocity V1 is 30 m/s, P1 = 0.8 MPa, T1 = 320 K. From the ideal gas law, density, sonic speed and mass flow rate are:
AFT Arrow does not solve for pipe length. To obtain the maximum pipe length, different lengths must be guessed with lengths that exceed sonic flow discarded. Alternatively, the GSC Module can be used.
Note that the friction factor in Saad 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.
