Water hammer
Hydraulic shock is a pressure surge or wave caused when a fluid, usually a liquid but sometimes also a gas, in motion is forced to stop or change direction suddenly; a momentum change. This phenomenon commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe.
This pressure wave can cause major problems, from noise and vibration to pipe rupture or collapse. It is possible to reduce the effects of the water hammer pulses with accumulators, expansion tanks, surge tanks, blowoff valves, and other features. The effects can be avoided by ensuring that no valves will close too quickly with significant flow, but there are many situations that can cause the effect.
Rough calculations can be made either using the Zhukovsky equation or more accurate ones using the method of characteristics.
History
In the 1st century B.C., Marcus Vitruvius Pollio described the effect of water hammer in lead pipes and stone tubes of the Roman public water supply. Water hammer was exploited before there was even a word for it; in 1772, Englishman John Whitehurst built a hydraulic ram for a home in Cheshire, England. In 1796, French inventor Joseph Michel Montgolfier built a hydraulic ram for his paper mill in Voiron. In French and Italian, the terms for "water hammer" come from the hydraulic ram: coup de bélier and colpo d'ariete both mean "blow of the ram". As the 19th century witnessed the installation of municipal water supplies, water hammer became a concern to civil engineers. Water hammer also interested physiologists who were studying the circulatory system.Although it was prefigured in work by Thomas Young, the theory of water hammer is generally considered to have begun in 1883 with the work of German physiologist Johannes von Kries, who was investigating the pulse in blood vessels. However, his findings went unnoticed by civil engineers. Kries's findings were subsequently derived independently in 1898 by the Russian fluid dynamicist Nikolay Yegorovich Zhukovsky, in 1898 by the American civil engineer Joseph Palmer Frizell, and in 1902 by the Italian engineer Lorenzo Allievi.
Cause and effect
When a pipe is suddenly closed at the outlet, the mass of water before the closure is still moving, thereby building up high pressure and a resulting shock wave. In domestic plumbing this is experienced as a loud banging resembling a hammering noise. Water hammer can cause pipelines to break if the pressure is high enough. Air traps or stand pipes are sometimes added as to water systems to absorb the potentially damaging forces caused by the moving water.In hydroelectric generating stations, the water traveling along the tunnel or pipeline may be prevented from entering a turbine by closing a valve. For example, if there is of tunnel of diameter full of water travelling at, that represents approximately of kinetic energy that must be arrested. This arresting is frequently achieved by a surge shaft open at the top, into which the water flows. As the water rises up the shaft its kinetic energy is converted into potential energy, which causes the water in the tunnel to decelerate. At some hydroelectric power stations, such as the Saxon Falls Hydro Power Plant In Michigan, what looks like a water tower is actually one of these devices, known in these cases as a surge drum.
At home, a water hammer may occur when a dishwasher, washing machine or toilet shuts off water flow. The result may be heard as a loud bang, repetitive banging, or as some shuddering.
On the other hand, when an upstream valve in a pipe closes, water downstream of the valve attempts to continue flowing creating a vacuum that may cause the pipe to collapse or implode. This problem can be particularly acute if the pipe is on a downhill slope. To prevent this, air and vacuum relief valves or air vents are installed just downstream of the valve to allow air to enter the line to prevent this vacuum from occurring.
Other causes of water hammer are pump failure and check valve slam. To alleviate this situation, it is recommended to install non-slam check valves as they do not rely on gravity or fluid flow for their closure. For vertical pipes, other suggestions include installing new piping that can be designed to include air chambers to alleviate the possible shockwave of water due to excess water flow.
Water hammer can also occur when filling an empty pipe that has a restriction such as a partially open valve or an orifice that allows air to pass easily as the pipe rapidly fills, but once full the water suddenly encounters the restriction and the pressure spikes.
Related phenomena
Steam distribution systems may also be vulnerable to a situation similar to water hammer, known as steam hammer. In a steam system, a water hammer most often occurs when some of the steam condenses into water in a horizontal section of the piping. The rest of the steam picks up the water, forming a "slug", and hurls this at high velocity into a pipe fitting, creating a loud hammering noise and greatly stressing the pipe. This condition is usually caused by a poor condensate drainage strategy: having more condensate in the pipe makes the slug easier to form. Vacuum caused by condensation from thermal shock can also cause a steam hammer.Steam hammer can be avoided by using sloped pipes and installing steam traps. Where air-filled traps are used, these eventually become depleted of their trapped air over a long period through absorption into the water. This can be cured by shutting off the supply, opening taps at the highest and lowest locations to drain the system, and then closing the taps and re-opening the supply.
On turbocharged internal combustion engines, a "gas hammer" can take place when the throttle is closed while the turbocharger is forcing air into the engine. There is no shockwave but the pressure can still rapidly increase to damaging levels or cause compressor surge. A pressure relief valve placed before the throttle prevents the air from surging against the throttle body by diverting it elsewhere, thus protecting the turbocharger from pressure damage. This valve can either recirculate the air into the turbocharger's intake, or it can blow the air into the atmosphere and produce the distinctive hiss-flutter of an aftermarket turbocharger.
Water hammer from a jet of water
If a stream of high velocity water impinges on a surface, water hammer can quickly erode and destroy it. In the 2009 Sayano-Shushenskaya power station accident, the lid to a 640 MW turbine was ejected upwards, hitting the ceiling above. During the accident, the rotor was seen flying through the air, still spinning, about 3 meters above the floor. Unrestrained, per second of water began to spray all over the generator hall. The geyser caused the structural failure of steel ceiling joists, precipitating a roof collapse around the failed turbine.Water hammer during an explosion
When an explosion happens in an enclosed space, water hammer can cause the walls of the container to deform. However, it can also impart momentum to the enclosure if it is free to move. An underwater explosion in the SL-1 nuclear reactor vessel caused the water to accelerate upwards through of air before it struck the vessel head at with a pressure of. This pressure wave caused the steel vessel to jump 9 feet 1 inch into the air before it dropped into its prior location. It is imperative to perform ongoing preventive maintenance to avoid water hammer, as the results of these powerful explosions have resulted in fatalities.Mitigating measures
Water hammer has caused accidents and fatalities, but usually damage is limited to breakage of pipes or appendages. An engineer should always assess the risk of a pipeline burst. Pipelines transporting hazardous liquids or gases warrant special care in design, construction, and operation. Hydroelectric power plants especially must be carefully designed and maintained because the water hammer can cause water pipes to fail catastrophically.The following characteristics may reduce or eliminate water hammer:
- Reduce the pressure of the water supply to the building by fitting a regulator.
- Lower fluid velocities. To keep water hammer low, pipe-sizing charts for some applications recommend flow velocity at or below
- Fit slowly closing valves. Toilet fill valves are available in a quiet fill type that closes quietly.
- Non-slam check valves do not rely on fluid flow to close and will do so before the water flow reaches significant velocity.
- High pipeline pressure rating.
- Good pipeline control.
- Water towers or surge tanks help maintain steady flow rates and trap large pressure fluctuations.
- Air vessels such as expansion tanks and some types of hydraulic accumulators work in much the same way as water towers, but are pressurized. They typically have an air cushion above the fluid level in the vessel, which may be regulated or separated by a bladder. Sizes of air vessels may be up to hundreds of cubic meters on large pipelines. They come in many shapes, sizes and configurations. Such vessels often are called accumulators or expansion tanks.
- A hydropneumatic device similar in principle to a shock absorber called a 'Water Hammer Arrestor' can be installed between the water pipe and the machine, to absorb the shock and stop the banging.
- Air valves often remediate low pressures at high points in the pipeline. Though effective, sometimes large numbers of air valves need be installed. These valves also allow air into the system, which is often unwanted. Blowoff valves may be used as a alternative.
- Shorter branch pipe lengths.
- Shorter lengths of straight pipe, i.e. add elbows, expansion loops. Water hammer is related to the speed of sound in the fluid, and elbows reduce the influences of pressure waves.
- Arranging the larger piping in loops that supply shorter smaller run-out pipe branches. With looped piping, lower velocity flows from both sides of a loop can serve a branch.
- Flywheel on a pump.
- Pumping station bypass.
The magnitude of the pulse
Water hammer can be analyzed by two different approaches—rigid column theory, which ignores compressibility of the fluid and elasticity of the walls of the pipe, or by a full analysis that includes elasticity. When the time it takes a valve to close is long compared to the propagation time for a pressure wave to travel the length of the pipe, then rigid column theory is appropriate; otherwise considering elasticity may be necessary.
Below are two approximations for the peak pressure, one that considers elasticity, but assumes the valve closes instantaneously, and a second that neglects elasticity but includes a finite time for the valve to close.
Instant valve closure; compressible fluid
The pressure profile of the water hammer pulse can be calculated from the Joukowsky equationSo for a valve closing instantaneously, the maximal magnitude of the water hammer pulse is
where ΔP is the magnitude of the pressure wave, ρ is the density of the fluid, a0 is the speed of sound in the fluid, and Δv is the change in the fluid's velocity. The pulse comes about due to Newton's laws of motion and the continuity equation applied to the deceleration of a fluid element.
Equation for wave speed
As the speed of sound in a fluid is, the peak pressure depends on the fluid compressibility if the valve is closed abruptly.where
Slow valve closure; incompressible fluid
When the valve is closed slowly compared to the transit time for a pressure wave to travel the length of the pipe, the elasticity can be neglected, and the phenomenon can be described in terms of inertance or rigid column theory:Assuming constant deceleration of the water column, this gives
where:
The above formula becomes, for water and with imperial unit,
For practical application, a safety factor of about 5 is recommended:
where P1 is the inlet pressure in psi, V is the flow velocity in ft/s, t is the valve closing time in seconds, and L is the upstream pipe length in feet.
Hence, we can say that the magnitude of the water hammer largely depends upon the time of closure, elastic components of pipe & fluid properties.
Expression for the excess pressure due to water hammer
When a valve with a volumetric flow rate Q is closed, an excess pressure ΔP is created upstream of the valve, whose value is given by the Joukowsky equation:In this expression:
The hydraulic impedance Z of the pipeline determines the magnitude of the water hammer pulse. It is itself defined by
where
The latter follows from a series of hydraulic concepts:
- compressibility of the liquid, defined by its adiabatic compressibility modulus Bl, resulting from the equation of state of the liquid generally available from thermodynamic tables;
- the elasticity of the walls of the pipe, which defines an equivalent bulk modulus of compressibility for the solid Bs. In the case of a pipe of circular cross-section whose thickness t is small compared to the diameter D, the equivalent modulus of compressibility is given by the formula, in which E is the Young's modulus of the material of the pipe;
- possibly compressibility Bg of gas dissolved in the liquid, defined by
- : γ being the specific heat ratio of the gas,
- : α the rate of ventilation,
- : and P the pressure.
As a result, we see that we can reduce the water hammer by:
- increasing the pipe diameter at constant flow, which reduces the flow velocity and hence the deceleration of the liquid column;
- employing the solid material as tight as possible with respect to the internal fluid bulk ;
- introducing a device that increases the flexibility of the entire hydraulic system, such as a hydraulic accumulator;
- where possible, increasing the fraction of undissolved gases in the liquid.
Dynamic equations
where V is the fluid velocity inside pipe, is the fluid density, B is the equivalent bulk modulus, and f is the Darcy–Weisbach friction factor.
Column separation
Column separation is a phenomenon that can occur during a water-hammer event. If the pressure in a pipeline drops below the vapor pressure of the liquid, cavitation will occur. This is most likely to occur at specific locations such as closed ends, high points or knees. When subcooled liquid flows into the space previously occupied by vapor the area of contact between the vapor and the liquid increases. This causes the vapor to condense into the liquid reducing the pressure in the vapor space. The liquid on either side of the vapor space is then accelerated into this space by the pressure difference. The collision of the two columns of liquid causes a large and nearly instantaneous rise in pressure. This pressure rise can damage hydraulic machinery, individual pipes and supporting structures. Many repetitions of cavity formation and collapse may occur in a single water-hammer event.Simulation software
Most water hammer software packages use the method of characteristics to solve the differential equations involved. This method works well if the wave speed does not vary in time due to either air or gas entrainment in a pipeline. The wave method is also used in various software packages. WM lets operators analyze large networks efficiently. Many commercial and non-commercial packages are available.Software packages vary in complexity, dependent on the processes modeled. The more sophisticated packages may have any of the following features:
- Multiphase flow capabilities.
- An algorithm for cavitation growth and collapse.
- Unsteady friction: the pressure waves dampens as turbulence is generated and due to variations in the flow velocity distribution.
- Varying bulk modulus for higher pressures.
- Fluid structure interaction: the pipeline reacts on the varying pressures and causes pressure waves itself.
Applications
- The water hammer principle can be used to create a simple water pump called a hydraulic ram.
- Leaks can sometimes be detected using water hammer.
- Enclosed air pockets can be detected in pipelines.