Lumped Adiabatic Method - Detailed Discussion
When this AFT Arrow Steady Solution Method is used, all heat transfer data entered for individual pipes is neglected. The other pipe data is left as entered by the user in case the user switches back to one of the marching methods.
Elevation data is also ignored by the Solver. The output will still show the elevation as entered by the user. Since elevation effects are usually not very important in gas systems, neglecting elevation changes is frequently an acceptable approximation.
An analytical solution to Equations 1, 2, and 5 for adiabatic flow neglecting elevation changes is given by the following (e.g., see Saad, 1993, page 209):
|
|
(42) |
This equation is valid for real gases as long as the following approximation is accepted:
using a suitably averaged value of cp. Integrating from 0 to L obtains:
|
|
(43) |
Equation 43 is then solved for each pipe, using an average value of friction factor and g for each pipe. The solution of Equation 43 typically is iterative where the unknown is M2.
Note: In Saad 1993 on page 209 equation 5.27 (Equation 43 above) the square brackets are not included. They have been added above to clarify that the natural log applies to all of the encapsulated terms. Furthermore, the left-hand side in Saad contains a multiplier of 4 since the Fanning friction factor was used, whereas Equation 43 above used in AFT software uses the Darcy friction factor.
