Hydraulic calculation of single-phase flow of liquids and gases
A hydraulic analysis of a branch is performed for individual components. A component is a straight pipe or a minor component (valve, fitting, etc.).
Gas density and flow velocity for a hydraulic analysis of a straight pipe are determined based on pressure and temperature. If the fluid density at pipe ends differs significantly then the piping component is separated into shorter pipes. Head loss analysis is performed using the pipe average values for fluid density and flow velocity. Pressure change due to pipeline elevation and lowering is considered. Major head loss is determined based on flow pattern, pipe wall roughness and consideration of welds [1]. The analysis of the Darcy–Weisbach friction factor under turbulent flow uses equations approximating G.A. Murin’s experimental [7], as well as G.K. Filonenko’s formulas [9] in zone of smooth friction. In areas of laminar flow, Hagen-Poiseuille formula [1] is used. The effect of welds was accounted for using recommended methodology [1] with corrections using P.A. Shevelev’s experimental data [8]. This algorithm allows the analysis of the friction factor with an error of no greater than 3%.
The analysis of minor resistance coefficient is performed using formulas and equations approximating experimental data based on I.E. Idelchik’s references [1-2]. The analysis of the minor resistance coefficients of tees is adjusted based on modern experimental data [3-6]. The properties of local resistance can be set in the input or accepted as standard. Standard properties are considered to be: entrance is flush with equipment wall; bends with a radius of 1.5*DN (DN – nominal pipe size) and turn angle of 90° (with a radius of 1.0*DN when DN > 500); fully opened valves; orifice with the opening diameter of 0.5xDin; tees with a turn angle of 90°; etc. For valves, the flow coefficient, Kv, can be entered in input data.
Pump analysis is performed using the input pump head and NPSHR curves. When fluid viscosity is higher than 4 cSt, the program automatically performs a recalculation of pump curves based on viscosity according to methodology in [10].
The program automatically checks the input value of valve opening, as well as butterfly valve closing angle. Given a relative opening lower than 0.2 or closuring angle of 90°, the valve is considered to be closed and the program automatically “closes” the branch with this valve.
References
1. I.E. Idelchik. Handbook of Hydraulic Resistance. 4th Edition Revised and Augmented. Begell House, 2008. 861 pp
2. Handbook of Hydraulic and Ventilation Systems (in Russian). S.-Petersburg, «Mir i Semya», 2002
3. Gardel A. 1957. Les Pertres de Charge dans les Écoulements au Travers de Branchements en Té. Bull. Tech. De la Suisse Romande 83:123-130, 144-148.
4. Ito H., Imai K. Energy Losses at 90° Pipe Junctions. Proceedings of ASCE. Journal of Hydraulic Division. Vol. 99, No HY 9, 1973, pp.1353-1368.
5. Kenji Oka, Takahito Nozaki, Hidesato Ito. Energy Losses Due to Combination of Flow at Tees. JSME International Journal Series B. Vol. 39, No 3, 1996, pp. 489-498.
6. Kenji Oka, Hidesato Ito. Energy Losses at Tees with Large Area Rations. Transactions of ASME. Journal of Fluid Engineering. Vol. 127, No 1, 2005, pp.110-116.
7. Murin G.A. The hydraulic resistance of steel pipes. Izv. VTI, N10(162), 1948. (in Russian)
8. F.A. Shevelev. Investigations of Basic Hydraulic Patterns of Turbulent Movements in Pipes (in Russian). Mossow, Stroyizdat, 1953.
9. Filonenko G.K. On Friction Factor for a Smooth Tube. Izv, VTI, N10 (162), 1948. (in Russian)
10. Effect of Liquid Viscosity on Rotodynamic (Centrifugal and Vertical) Pump Performance. ANSI/HI 9.6.7-2004. Americal National Standards Institute, Inc.