Negative pressures often do not get the focus they deserve when evaluating a piping system. It is more natural to be concerned with the maximum pressure ratings of a pipe. In fact, when determining the root cause of a system failure, it is all too common to seek out and settle upon what circumstance could have caused such catastrophic high pressures. In reality, however, negative pressures are just as likely to occur in nearly every system, and quite often they are the unknown root cause of piping failures. With the right tools, engineers and operators can not only uncover such root causes, they can also design effective mitigation solutions adding years of life to a pipeline.
Using examples of computer modeling, part 1 of this article will reveal how common system events such as valve closures induce low pressure transient waves that have potential to be just as destructive as more intuitive high pressure waves.
By Amy Marroquin, Senior Hydraulic Engineer – BLACOH, and Scott Lang, Engineering Software Developer – Applied Flow Technology
Background
A transient pressure wave is essentially a slice of fluid where the pressure on one side is different than the pressure on the other side.1 This ‘slice’ is communicated through a pipeline as a wave and moves with a speed near the speed of sound. Its behavior is much like a sound wave. Another contributor to wavespeed is gas or air dispersed within the fluid. While typically unfavorable, air entrainment can greatly reduce the wavespeed. Wavespeed is critical in surge calculations for two reasons. It is one of two primary factors in determining a wave’s communication time, and it is also one of the most important factors when quantifying the magnitude of pressure rise or fall.2,3 communicated through air. The cause of these pressure waves is quite simple. They are induced by a change in fluid velocity. While it is quite intuitive that a change in velocity would cause a change in pressure, the magnitude and behavior of a transient pressure wave as it moves through a system is not nearly as intuitive.
How quickly a transient pressure wave moves through a pipeline is largely a function of a fluid and pipe system’s elasticity. In general, the wavespeed will be higher for more rigid systems. In fact, in a steel piping system, the wavespeed will quite commonly exceed 4,000 ft/sec. The following factors increase wavespeeds:
• Higher Young’s Modulus (lower pipe elasticity),
• Higher Bulk Modulus (lower fluid elasticity),
• Thicker pipe walls,
• Stronger or additional pipe restraints,
• Lower fluid density (at the same bulk modulus).
Another contributor to wavespeed is gas or air dispersed within the fluid. While typically unfavorable, air entrainment can greatly reduce the wavespeed. Wavespeed is critical in surge calculations for two reasons. It is one of two primary factors in determining a wave’s communication time, and it is also one of the most important factors when quantifying the magnitude of pressure rise or fall.2,3
Note; the immediate change in pressure as calculated with the Joukowsky equation, will not always be the most extreme change in pressure. The Joukowsky equation offers a common ‘Rule of Thumb’ approach to pressure surge. This equation accounts for the immediate pressure rise or fall associated with an instant change in velocity at a specific location. However, it does not capture complexities like frictional dissipation, line pack, cavitation, or fluid structure interaction. This can easily lead to a mistaken judgement on maximum or minimum pressures.6
Period & Propagation Phases
A transient pressure wave’s period, also known as communication time, is the time it takes for the pressure wave to travel the length of the pipe and back. The time can be quantified by the following equation,
Where,τ = wave period, L = pipe length and c = wavespeed.
The faster the velocity changes, the greater the pressure increase or decrease. If the velocity change happens abruptly – faster than the pressure wave’s period – the theoretical total pressure change will be near a maximum. This is because the pressure change can only be relieved by reflection from a system boundary. If the velocity change is completed before a reflection has occurred, no opportunity for relief has been presented. For instance, a negative wave will be reflected with a change in fluid velocity direction, bringing some relief to the initial pressure drop. This action will repeat itself before eventually being dampened out by friction.3,4
Quantifying Transient Pressures
When a moving mass is suddenly stopped, its kinetic energy shifts to potential energy. Stopping a moving fluid is no different. When an incoming flow is halted by a closing valve (reference Figure 1) – the fluid’s kinetic energy (velocity) is converted into potential energy (pressure).
This immediate increase in pressure can be dramatic but is not difficult to quantify thanks to the building work of scholars dating all the way back to Newton. The most common method for quantifying the immediate change in pressure is through the Joukowsky equation:
Where, ΔH = change in pressure (ft/m), c = wavespeed, ΔV = change in velocity and g = acceleration of gravity.1,2,3,5
Whether or not the change in pressure is positive or negative depends on the location of measurement relative to the inducer. If the upstream side of the valve experiences a sudden increase in pressure, what happens on the downstream side? The fluid still comes to a rest but the pressure decreases, creating a low pressure transient wave. Why? The fluid on the upstream side coming to rest is in some ways like compressing a spring – energy is stored and the spring pushes back against the applied force. On the downstream side it is like stretching the spring – energy is still stored but in this case the spring pulls away from the applied force. The fluid has inertia but cannot continue flowing and the pressure falls to compensate.
When there is a velocity increase, like the opening of a valve, the physics is the same, except this time the ‘spring’ is compressed on the downstream side and stretched on the upstream side, see Figure 2. For instance, if the inducer (valve, pump etc.) creates a velocity increase, a negative transient wave is emitted backwards on the upstream side of the inducer and a positive transient wave is emitted outward on the downstream side of the inducer.
Unmitigated Risks
While aged pipes are certainly a foundational factor, age alone is not the only reason a pipe will break. Some event must still break the pipe, and extreme pressure fluctuations – especially low pressure transients – exacerbate the possibility when left unmitigated.
Contaminants
Aside from failures, contamination is a real concern for piping systems experiencing low pressure transients. Negative pressures can draw in contaminants through poor joints, cracks, or other faults. This is a particular concern for potable water systems where pipe leaks and breaks are a daily challenge as discussed above. There are different forms of contamination and regulations to comply with. A simple yet alarming instance of contamination is the presence of particular organisms in potable water systems such as Naegleria fowleri ameba, also known as brain eating ameba.
The current approach toward maintaining aging water systems is one of repair and replace. It is only when a greater focus is placed on detecting and mitigating transient pressures that significant ground will be gained towards increasing the quality of piping systems and better preventing contamination.
Cavitation
During a low pressure transient or even in a secondary phase of a high pressure transient, vapor pockets will form where the pressure has dropped to the fluid’s vapor pressure. It is beneficial to apply a simple valve closure example, this time with the help of computer simulation.
Example 1: Figure 3 depicts a system operating under a normal flow of 9,000 gpm and 50 psig pressure at the valve discharge. A quick valve closure, faster than the wave period, will initiate a substantial pressure change on both sides of the valve.
Looking first at the downstream side of the closed valve in Figure 4, the fluid very suddenly decreases in velocity when the valve is closed. The pressure immediately drops to vapor pressure and a vapor pocket begins forming. Fluid continues flowing at a slower rate away from the vapor pocket as it grows. At 18 seconds into the simulation, the flow begins to reverse and the vapor pocket is compressed until it collapses completely causing a dramatic 500+psi pressure spike. The process repeats itself, decreasing in magnitude each time due to friction.
In Figure 5, it is seen that the upstream side of the valve will also see a low pressure surge at some time. When the valve closes, a high pressure wave travels upstream from the valve to a reservoir, where it is reflected back towards the valve. However, an important change occurs – initially, the flow was towards the valve, building pressure. After the reflection, the flow direction reverses, lowering pressure. When the reflected high pressure wave reaches the valve, the fluid wants to move away from the valve. This causes the pressure to fall below the steady state pressure, and a low pressure surge is propagated through the upstream pipe.
Collapsed Pipe
A large diameter pipe under low pressure service may be specified with a small wall thickness and protected from high pressure surges with typical means such as pressure safety valves or rupture disks. A simple event like closing an upstream valve can cause unexpectedly low downstream pressures, which can collapse such a pipe with relative ease. This is significantly more likely for buried or submerged pipes under external loading, and can be very dangerous.10
Mitigation Tools
Due to the complexities of interconnected piping networks, computer simulation and high frequency transient monitoring are the only practical means of unveiling and numerically quantifying critical risks within a liquid piping system. Transient pressure monitoring enables engineers and operators the ability to see pressure transients typical pressure recording devices cannot capture. Further, computer models help identify the most effective mitigation strategies, minimizing complexity and cost. With the advancement of technology and modeling software, it is becoming more common for both resources to be used, especially for sophisticated and/or critical systems.
Modeling and Uncertainty in Simulations
Computer simulations are effective tools in the low pressure surge mitigation process – they are capable of handling very complex mathematical details with ease and therefore fewer simplifications are needed compared to a solution by hand. In general, this makes them more accurate, but they are still only models, and every mathematical model carries with it some uncertainty.
How uncertain a model is, and what situations it can accurately capture, becomes a primary concern. The behavior of transient waves in liquids is well understood and a substantial technical body of research exists on the topic. Models often utilize key assumptions for simplicity, such as: one dimensional flow, constant fluid properties, constant wavespeed, and rigid piping. Each of these assumptions neglects physical effects that occur in real systems. Verification of the models against field and lab tests has demonstrated that these differences are acceptable for most engineering purposes. Often, the primary driver of inaccuracy in the model is uncertainty in the wavespeed – as the pressure response is directly related to wavespeed, any inaccuracies here directly affect the calculated surge. Typical models allow for variability on wavespeed of around 15%.
Fortunately, the onset of cavitation can very accurately be predicted, as it is a function primarily of vapor pressure and local pressure. In the vast majority of systems, the goal is to prevent cavitation entirely, rather than determine the results of severe cavitation. To this end, computer simulation is still recommended as by far the most effective approach to mitigation design, despite modeling uncertainties.1,2,3,4
REFERENCES
1. Thorley, A.R.D., 2004, Fluid Transients in Pipeline Systems, 2nd Ed., Professional Engineering Publishing Limited, London, UK.
2. Wood, D.J., Lingireddy, S, and Boulos, P.F., 2005, Pressure Wave Analysis of Transient Flow in Pipe Distribution Systems, MWH Soft, Pasadena, CA.
3. Wylie, E.B. and Streeter, V.L., 1982, Fluid Transients, Thomson-Shore, Dexter, MI
4. Chaudhry, M.H., 2014, Applied Hydraulic Transients, 3rd Ed., Springer, New York.
5. Wylie. E.B. and Liou, J.C.P., “Water Hammer in Transmission and Distribution Systems”, ASCE Continuing Education 2019.
6. Walters, T.W., and Leishear, R.A., 2019, “When the Joukowsky Equation Does Not Predict Maximum Water Hammer Pressures”, ASME J. Pressure Vessel Technology, 141, p. 060801.
7. Gold, M. and Zaveri, M., “Subway Service Disrupted After Water Main Break on Upper West Side”, January 13, 2020, https://nyti.ms/3868ahT.
8. Offenhartz, J., “Here’s What A Massive Water Main Break Does To The NYC Subway System”, January 13, 2020, https://gothamist.com/news/mta-subway-water-main-commuting-hell.
9. Yoder, J.S., Straif-Bourgeois, S., Roy, S.L., Moore,
T. A., Visvesvara, G.S., Ratard, R.C., Hill, V.R., Wilson, J.D., Linscott, A.J., Crager, R., Kozak, N.A., Sriram, R., Narayanan, J., Mull, B., Kahler, A.M., Schneeberger, C., Silva, A.J., Poudel, M., Baumgarten, K.L., Xiao, L., and Beach, M.J., “Primary Amebic Meningoencephalitis Deaths Associated With Sinus Irrigation Using Contaminated Tap Water”, 2012, Oxford University Press, DOI: 10.1093/cid/cis626.
10. “National Primary Drinking Water Regulations”, EPA 816-F-09-004, May 2009, https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations.
11. Bergant, A., Simpson, A.R. and Tijsseling, A.S.,
“Water Hammer With Column Separation: A Review of Research In The Twentieth Century”, 2006, Journal of fluids and structures.
12. Vigdor, N. and Wilson, M., “Cooking Grease Down a Drain Eyed in Sewage Flood of at Least 80 Homes”, November 30, 2019, https://nyti.ms/2Dvq4gv.
13. Hicks, N., “Pipe Collapse – Not Grease Clog – Caused Queens Sewage Flood: Report”, December 19, 2019, https://nypost.com/2019/12/19/pipe-collapse-not-grease-clog-caused-queens-sewage-flood-report/.
14. Stewart, M., Walters, T.W., Wunderlich, G. and Onat, E.A., 2018, “A Proposed Guideline For Applying Waterhammer Predictions Under Transient Cavitation Conditions”, ASME PVP Conference, July 15-20, 2018, Prague, Czech Republic, ASME PVP2018-84338
15. Walters, T., Marroquin, A., and Smith, F., 2019,
“Understanding Waterhammer in Pumping Systems and Surge Suppression Options,” Proceedings of the 48th Turbomachinery & 35th International Pump Users Symposia, Houston, TX, September 10-12, 2019, TPS Paper No. TPS148 Rev 5, 6/3/19
16. Walters, T., “Gas-Flow Calculations: Don’t Choke”, January 2000, Chemical Engineering www.che.com.
Look for Part 2 of this article in the August Issue of Valve World Americas to learn about the types of valves that can be used to mitigate the risk of pipe failures.
ABOUT THE AUTHORS
Amy Marroquin is an Engineering Project Manager for BLACOH Surge Control. She is highly experienced in the field of modeling and analysis with almost 20 years of engineering and management experience specifically in piping systems, pressure vessels and packaged equipment. Designs have encompassed numerous land and offshore applications including water, sewer, chemical, natural gas and sour gas fluid media.
Scott Lang, PE, is a Sr Engineering Software Developer at Applied Flow Technology where he helps lead the software development efforts to research, improve, and create models for fluid analysis within AFT products. Scott holds a Bachelor of Science in Mechanical and Electrical Engineering from Colorado School of Mines.