Verification Case 13
PRODUCT: AFT Arrow
MODEL FILE: AroVerify13.ARO
REFERENCE: Michel A. Saad, Compressible Fluid Flow, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1993, Page 270, example 6.5
GAS: Natural Gas
ASSUMPTIONS: 1) Isothermal, 2) Perfect gas, 3) Natural gas can be represented with methane
RESULTS:
| Parameter | Saad | AFT Arrow |
| P2– Static back pressure at exit (kPa) | 263.16 | 262.0 |
| M2 – Mach number at exit | 0.38 | 0.38 |
| L1-2 – length to reach 500 kPa (m) | 544.79 | 558.6 |
| LT – length to reach sonic choke point (m) | 710.0 | 709.8 |
| PT– Static pressure choke point (kPa) | 114.46 | 115.7 |
| MT – Mach number at isothermal choke point | 0.874 | 0.865 |
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 0.1, P1 = 1 MPa, T1 = 293 K. From the ideal gas law, density, sonic speed and mass flow rate are:
The first pipe represents the pipe from point 1 to 2. The second pipe represents the pipe from point 1 to the choking point. 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.
The results for part b) were obtained by interpolating the Internal Pipe Results for the first pipe.
All results agree closely. The AFT Arrow static pressure below which choking occurs is the pipe exit static pressure.
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.
