Water hammer

A pressure surge ( water hammer also, Eng. Pressure surge ) denotes the dynamic pressure change of a fluid. Colloquially, the term is Joukowskistoß for the pressure rise in a pipe used, which occurs when too rapid closing of a shut-off valve (or adjusting the valve). Pressure surges are generally unavoidable in industrial plants (which would be possible only with an infinitely long closing time), because these are regulated by means of valves. The extent of a pressure surge can reduce, however. Cause pressure surges in liquid systems the pressure increases than in gas systems because liquids are less compressible than gases. The pressure information is passed from pressure waves. It is always about longitudinal waves.

History

Since ancient times are known, the fundamental causes of pressure surges in liquid-filled pipes and the associated risk of plant damage / destruction. Marcus Vitruvius Pollio describes in the 1st century BC, the occurrence of pressure surges in lead and stone pipes of the Roman water supply. 1883 published Johannes von Kries theory of pressure surge in a publication of the blood flow in arteries. Contrary to popular belief, he has established the Joukowsky formula before Nikolai Egorovich Joukowsky ( 1847-1921 ). This led in 1897 detailed experiments on drinking water lines through and published his results in 1898. As a general designation of the pressure pulse, the term Joukowsky shock prevailed.

Causes

A fluid to be accelerated in a pipeline, but a certain amount of force is required. Newton's second law states:

With

The necessary force results in a change of pressure. Is accelerated a fluid in a pipe, for example, by closing a valve or a butterfly valve (butterfly stroke ) as well as the startup and shutdown of pumps. Most pumps are fitted with non-return valves. If two or more such pumps are operated in parallel and there is a switching of the pump instead, may by the outgoing (s) pump (s) back flow occur which should be avoided by the non-return valve as possible. If a conventional ( relatively slow closing ) Check Valve used includes this when the return flow has already partially formed, a pressure surge occurs.

Effects

Due to high pressure pulses cause damage at the plant concerned. Pipes can burst at worst or holders of the pipes may be damaged. In addition, valves, pumps, foundations and other components of the conduction system (eg heat exchangers ) are at risk. With drinking water pipelines, a pressure surge cause dirty water is sucked from the outside. Since damage to pipelines are not necessarily immediately apparent (eg damage to a flange ), it is necessary to deal with the planning of a pipe with the pressure surge. When hydraulic ram but the effect of the pressure pulse is desired.

Pressure surge phenomena

The Joukowsky shock

The increase in pressure was detected by Joukowsky in 1898 and derived theoretically from Allievi in 1905:

Where:

The relationship is only valid for pipes, in which the wall friction lower than in areas of the water transport or the change in speed is in any case of the wave propagation velocity, and the period of the speed change as compared to the reflection time is in any case short. The thus calculated pressure pulse using the wave propagation speed of the flow medium is ideal maximum physically possible pressure increase in an infinitely rigid pipe dar. To achieve more realistic values ​​, the reduction of the wave propagation velocity is taken into account by observing the elasticity of the tube wall for the calculation.

Calculation of water hammer in pipes

Must also be noted that the wave propagation speed c [m / s] is reduced by numerous factors. For c applies:

Where:

Special case of thin-walled tube

The thin-walled tube, the equation of wave propagation speed C [ m / s] simplifies to:

Where the variables definition applies from before.

Special case of rock tunnels

When carved into rock tunnel, the wall thickness is indeterminate extremely large and thus are not preceded formulas applicable, therefore applies to these applications following equation of wave propagation speed c [m / s]:

Where:

Generally

The thus calculated pressure surge, the technically maximum possible pressure increase dar. Taking the closing time of the lever or pump overrun time, however, lower values ​​are obtained:

Pressure surge in pipelines in accordance with the closing time

However, since this estimate in most cases is too conservative, the following calculation method can be used:

Where:

With the reflection time [s]:

Where:

The reflection time is the time that is necessary to ensure that the information " pressure change " of the valve is to the end of the line and passed back to the valve. In this estimation of the pressure pulse wave propagation velocity is no longer of weight. For a more precise estimation of valve characteristics can be included. In detail, one can then apply the recursion formula after Allievi (without pipe friction ) in order to calculate the pressure increase due to the valve-closing operation.

Line -packing

However, since friction losses in the piping must be added to the surge, the resulting real pressure surge can still reach higher pressures (eg in oil pipelines ). When a stoppage of the flow due to a valve closing process no more friction is present and the now missing pressure reduction results by the frictional pressure drop in an additional increase in pressure, the " draufgepackt " on the Joukowsky shock is. It must be noted that the Joukowsky equation, inter alia, therefore represents only an imprecise approximation and therefore pressure surges may need to be simulated numerically.

Pressure increase

, A fluid braking in a pipe through a valve, kinetic energy is released in the direction upstream of the valve. In this economy:

This amount of energy is converted into volume change work. For the change in volume of work is:

With

The fluid is thus compressed. For example, since water is almost incompressible due to its high bulk modulus, high pressures arise in the performance of the volume change work. This relationship is analogous to the braking distance of a car. The shorter the braking distance, the higher forces are exposed to the vehicle occupants. Since water pipes in the operation of an installation must be partially closed very quickly (eg, during load shedding ), the resulting pressure surges are accordingly high.

Pressure reduction

When closing a valve located downstream of the fluid moves away from the valve. The pressure change is therefore negative. The pressure drops below the vapor pressure of the fluid, a vapor bubble forms (see cavitation). Then by the prevailing negative pressure, the fluid is accelerated in the opposite direction and impinges upon the closed valve. The result is a so-called Kavitationsschlag which has the same effect as a pressure surge. This tearing of the water column, also referred to as Makrokavitation.

Druckstoßreduzierende measures and factors

• An increase in the valve closing timing results in a reduction of the pressure surge.
• The use of hydraulically assisted flaps increases their closing time.
• Quick -closing check valves prevent pressure surge when switching from pump.
• Flywheels cause long start-up and shutdown of pumps.
• Cause water locks that the fluid can swing freely.
• Vacuum Breaker reduce the Kavitationsschlag.

Numerical Methods

For piping systems pressure surge calculations are performed numerically way. There are special, powerful computer programs. The basis of these programs serve water hammer equations which result from the laws of conservation of mass and conservation of momentum. Compared to analytical methods, these are not only suitable for compressible, but also for incompressible media. In addition, provide numerical simulations, because boundary conditions such as pressures, mass flows, friction losses, speeds of pumps and positions of fittings are calculated time-dependent. The pipe is divided into a number of individual segments, and calculates the pressure pulse in the small time intervals. Be issued in the results, for example, as time functions of the pressures, the densities, the mass flows, the control variables of the valves or the pump data. It can also be calculated dynamic loads which are of a structural analysis of the pipe system. However, fast computer systems are required for numerical solution methods. It must also be operated to calculate a number of staff required. Since so immense costs can be caused a pressure surge should only be calculated numerically if it is absolutely necessary.

Damage

Despite modern simulation programs and experience with pressure surges damage to pipelines are always observed even today. One of the most spectacular accidents in recent years occurred in 1998 broke in New York City when a water main with 48 inch diameter and the famous Fifth Avenue flooded. In Hamburg it was on Saturday, July 4, 2009, to several surge damage. After a voltage drop in the power supply fell in the entire city of Hamburg in 14 pumps water from plants. As a result, there were between 17.20 on Saturday and 18.45 clock clock on Sunday to a total of 16 water pipe ruptures. The voltage drop caused an abrupt stop of pumps and so impermissibly high pressure surges. When the pressure when starting the pump rose again, came the break of the previously damaged lines.