Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis
Abstract
:1. Introduction
2. Mathematical Model
2.1. Assumptions
- The filling water column is modeled using a rigid column model.
- The air–water interface is considered perpendicular to the main direction of a single pipeline.
- The friction factor is constant over the transient event.
- A polytropic model describes the air phase.
2.2. Formulations
- This equation represents the water movement adequately since in transient flows with trapped air, the compressibility of the air is much higher compared to the water and pipe system:
- A piston flow model is considered to represent the interface position, which is applicable in inclined piping installations:
- The polytropic model of the air phase [30]:This formulation shows the evolution of the air pocket pressure over time by relating the compression of an air pocket ) to the quantity of the expelled air by an air valve ():
- The air mass equation [28]:Here the air pocket density () inside of a pipe system is identical to the air density expelled by an air valve and considering , thus:Based on the variables and parameters shown in Figure 2, then:And deriving the Formulation (6), then:Plugging Formulations (6) and (7) into (5), then:
- The air valve characterization:Subsonic conditions are required to perform an adequate filling process according to recommendations given by the American Water Works Association (AWWA) [32], thus:
2.3. System Equations and Resolution
2.4. Initial and Boundary Conditions
3. Numerical Validation
3.1. Experimental Facility and Instrumentation
3.2. Experimental Test
3.3. Model Verification
3.4. Comparisons Without Air Valve
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
Cross-sectional area of pipe (m2) | |
Cross-sectional area of outlet orifice in an air valve (m2) | |
Outflow discharge coefficient an air valve (−) | |
Internal pipe diameter (m) | |
Friction factor (−) | |
Polytropic coefficient (−) | |
Gravity acceleration (m/s2) | |
Length of the filling column (m) | |
Total length of pipe (m) | |
Air mass (kg) | |
Atmospheric pressure (Pa) | |
Absolute pressure supplied by an energy source (Pa) | |
Air pocket pressure (Pa) | |
Gas constant (287 J/kg/ K) | |
Resistance coefficient of the regulating valve (m s2/m6) | |
Air temperature ( K) | |
Time (s) | |
Peak time (s) | |
Air volume (m3) | |
Air velocity (m/s) | |
Water velocity (m/s) | |
Air pocket size (m) | |
Difference elevation (m) | |
Air density (kg/m3) | |
Water density (kg/m3) | |
BV | Electro-pneumatic ball valve |
HT | Hydro-pneumatic tank |
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Test No. | (bar) | 1 (Pa) | |
---|---|---|---|
1 | 0.20 | 120060 | 0.96 |
2 | 0.20 | 120060 | 1.36 |
3 | 0.50 | 150075 | 0.96 |
4 | 0.50 | 150075 | 1.36 |
5 | 0.75 | 175087 | 0.96 |
6 | 0.75 | 175087 | 1.36 |
7 | 1.25 | 225112 | 0.96 |
8 | 1.25 | 225112 | 1.36 |
Test No. | Maximum Value of Air Pocket Pressure Head (m) | tpeak (s) | |
---|---|---|---|
1 | 15.0 | 0.96 | 0.55 |
2 | 15.0 | 1.36 | 0.58 |
3 | 21.4 | 0.96 | 0.50 |
4 | 21.4 | 1.36 | 0.52 |
5 | 29.3 | 0.96 | 0.46 |
6 | 29.1 | 1.36 | 0.49 |
7 | 46.9 | 0.96 | 0.40 |
8 | 44.9 | 1.36 | 0.44 |
Test No. | Air Pocket Pressure Head (M) | Peak Reduction Percentage (%) | |
---|---|---|---|
Without Air Vale | Using the Air Valve S050 | ||
1 | 15.9 | 15.0 | 5 |
2 | 16.0 | 15.0 | 6 |
3 | 23.6 | 21.4 | 9 |
4 | 23.1 | 21.4 | 7 |
5 | 32.2 | 29.3 | 9 |
6 | 31.4 | 29.1 | 7 |
7 | 51.1 | 46.9 | 8 |
8 | 47.4 | 44.9 | 5 |
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Coronado-Hernández, Ó.E.; Besharat, M.; Fuertes-Miquel, V.S.; Ramos, H.M. Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis. Water 2019, 11, 1814. https://doi.org/10.3390/w11091814
Coronado-Hernández ÓE, Besharat M, Fuertes-Miquel VS, Ramos HM. Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis. Water. 2019; 11(9):1814. https://doi.org/10.3390/w11091814
Chicago/Turabian StyleCoronado-Hernández, Óscar E., Mohsen Besharat, Vicente S. Fuertes-Miquel, and Helena M. Ramos. 2019. "Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis" Water 11, no. 9: 1814. https://doi.org/10.3390/w11091814