Verification Case 9
PRODUCT: AFT Arrow
MODEL FILE: AroVerify9.ARO
REFERENCE: Michael R. Lindeburg, P.E., Mechanical Engineering Review Manual, Seventh Edition, Professional Publications, Belmont, CA, 1984, Pages 8-11, 8-12, example 8.12
GAS: Unspecified except that the k value (i.e., γ) is 1.4
ASSUMPTIONS: 1) Adiabatic flow, 2) Perfect gas, 3) The gas is air, but for purposes of the example it only matters that the gas has k = 1.4, 4) No temperature was specified, so assume 70 deg. F
RESULTS:
| Parameter | Lindeburg | AFT Arrow |
| M2 – Mach number at exit | 0.35 | 0.36 |
| P2– Pressure at exit (psia) | 10.26 | 10.09 |
DISCUSSION:
As specified, inlet conditions are known and outlet conditions need to be determined. 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 Mach number is 0.3, P1 = 12 psia, T1 = 70 F (assumed). From the ideal gas law, density, sonic speed and mass flow rate are:
With this flow rate at the exit, the predictions agree very closely.
Note that the friction factor in Lindeburg is the Fanning friction factor. To obtain the Darcy-Weisbach friction factor used in AFT Arrow, multiply the Fanning friction factor by 4.
