Pressure surge

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Effect of Joukowsky shock on a liquid swimmer

A pressure surge (including water hammer , or hammer , English pressure surge ) denotes the dynamic pressure change of a fluid . The rise in pressure in a pipeline that occurs when a shut-off or control valve closes too quickly is known as the Joukowski shock .

Pressure surges are generally unavoidable in technical systems (they could only be prevented with an infinitely long closing time) because they are regulated by means of valves. However, the magnitude of a pressure surge can be reduced.

Pressure surges cause higher pressure rises in liquid- filled systems than in gas - filled systems , because liquids are less compressible than gases.

The pressure information is passed on by pressure waves . It is always about longitudinal waves .

history

Nikolai Joukowsky

The basic causes of pressure surges in liquid-filled pipelines and the associated risk of system damage / destruction have been known since ancient times. In the 1st century BC, Marcus Vitruvius Pollio described the occurrence of pressure surges in lead and stone pipes of the Roman water supply .

In 1883 Johannes von Kries published the theory of the pressure surge in a paper on blood flow in arteries . In doing so, contrary to popular belief , he set up the Joukowsky formula before Nikolai Joukowsky . In 1897 he carried out extensive experiments on drinking water pipes and published his results in 1898. The term Joukowsky shock then became the general term for pressure surge .

causes

If a fluid is to be accelerated or decelerated in a pipeline (braking as negative acceleration), a certain force is necessary for this due to the inertia of the fluid . Newton's second law says:

With

  • the power
  • the pressure
  • the cross-sectional area of the pipeline.

The necessary force results in a change in pressure. Accelerated (or decelerated) a fluid in a pipe z. B. by closing a valve or a butterfly valve (flap impact) and by starting and stopping pumps .

Most pumps have non-return valves . If two or more such pumps are operated in parallel and the pumps are switched over, the draining pump (s) can cause a backflow, which should be prevented by the non-return valve. If a conventional (relatively slowly closing) non-return valve is used, it only closes when the backflow has already partially developed; in this case a pressure surge occurs.

Effects

Excessive pressure surges can damage the affected system. In the worst case, pipelines can burst or the pipe supports can be damaged. Valves, pumps , foundations and other components of the pipe system (e.g. heat exchangers ) are also at risk. In the case of drinking water pipes, a pressure surge can lead to dirty water being sucked in from the outside.

Since damage to pipelines is not necessarily immediately apparent (e.g. when a flange is damaged ), it is necessary to deal with the pressure surge when planning a pipeline.

With the hydraulic ram, however , the effect of the pressure surge is essential for its function.

Pressure increase

A fluid is decelerated in a pipe through a valve so the valve is upstream kinetic energy released:

With

  • the liquid mass  m
  • the speed  v .

This amount of energy is converted into volume change work :

With

  • the initial volume V1
  • the final volume V2
  • the change in pressure p dV.

The fluid is thus compressed. Since, for example, water is almost incompressible due to its high compression modulus , high pressures arise when the volume change work is performed.

This relationship is analogous to the braking distance of a car: the shorter the braking distance, the higher the forces the vehicle occupants are exposed to.

Since water-carrying pipes sometimes have to be closed very quickly when operating a system (e.g. in the event of a load shedding ), the resulting pressure surges are correspondingly high.

Damage

Despite modern simulation programs and long experience with pressure surges, damage to pipelines can still be observed today.

One of the most spectacular accidents in recent years occurred in New York City in 1998 when a 48- inch water main  broke and flooded Fifth Avenue .

In Hamburg , too, there were several pressure surge damage on Saturday, July 4th, 2009. After a voltage drop in the power supply, pumps in 14 waterworks suddenly failed in the entire Hamburg city area. This caused inadmissibly high pressure surges. When the pressure rose again when the pumps started up, the previously damaged lines broke. As a result, there were a total of 16 burst water pipes between 5:20 p.m. on Saturday and 6:45 p.m. on Sunday  .

Pressure reduction

When a valve is closed, the fluid moves downstream away from the valve. The change in pressure therefore becomes negative. If the pressure falls below the vapor pressure of the fluid, a vapor bubble forms. The then prevailing negative pressure accelerates the fluid in the opposite direction and hits the closed valve. A cavitation shock occurs , which has the same effects as a pressure surge. This tearing off of the water column is also known as macrocavitation .

calculation

The Joukowsky shock

The pressure surge was recognized by Joukowsky in 1898 and theoretically derived by Allievi in ​​1905:

With

  • the change in pressure in  N / m²
  • the density in kg / m³
  • the wave propagation speed in m / s; it amounts for fluids with
  • the change in speed in m / s.

This relationship only applies to pipelines where

  • the wall friction is in areas of water transport or below,
  • the speed change is below the wave propagation speed ( ) and
  • the period of the change in speed is less than the reflection time ( ).

Magnitude

For water , a typical change in velocity produces a Joukowsky shock

.

Taking into account the closing time

Principle of wave reflection

If the closing time of the shut-off device (or the after-running time of the pump) is observed, the values ​​are less conservative than the above. technically maximum possible pressure increase:

With

With

  • the reflection time in s:
    • the length of the pipeline in m
  • the closing time of the valve in s.

The reflection time describes the time that is necessary for the information "pressure change" to be passed on from the valve to the end of the line and back to the valve. With this estimation of the pressure surge, the wave propagation speed is no longer relevant. Valve characteristics can be included for a more precise estimate . The Allievi recursion formula (without pipe friction) can then be used in detail to calculate the pressure increase due to the valve closing process.

Pressure surges in lines

General

The Joukowsky pressure surge calculated above using the wave propagation speed of the flow medium represents the ideal , physically maximum possible pressure increase in an infinitely stiff pipe. In order to achieve more real values, the elasticity of the pipe wall is taken into account in the calculation, which is the wave propagation speed and thus the pressure increase reduced.

For c in m / s the following applies:

With

  • = Compression modulus of the fluid in N / m²
  • = Inner diameter of the pipe in m
  • = Poisson's ratio of the pipe material
  • = Modulus of elasticity of the pipe wall in N / m²
  • = Pipe wall thickness in m.

Special case of thin-walled pipe

In the case of a thin-walled tube, the equation for the wave propagation speed is simplified to

Special case of rock tunnels

In the case of tunnels carved in rock , the wall thickness is indefinitely extremely large, so the following applies to this application:

With

  • = Modulus of elasticity of the rock in N / m².

Line packing

In a flowing pipeline flow, pressure losses due to friction (wall friction and dissipation ) lead to a pressure reduction. If the flow comes to a standstill as a result of a valve closing process, this suddenly ceases, which leads to an additional pressure increase that has to be added to the Joukowsky shock.

The Joukowsky equation provides u. a. therefore only an imprecise approximation , the pressure surge that actually occurs can reach even higher pressures (e.g. in pipelines ). Therefore, pressure surges may have to be simulated numerically .

Reducing measures and factors

  • An increase in the valve closing time reduces the pressure surge. This can be done e.g. B. can be achieved by hydraulically assisted flaps.
  • Quick-closing non-return valves avoid a pressure surge when switching pumps.
  • Flywheels result in longer start-up and shutdown times for pumps.
  • Water locks ensure that the fluid can swing freely.
  • Vacuum breakers reduce the cavitation impact.
  • Pressure surge boilers, cylindrical pressure vessels connected to the pipeline near the pumps, which are filled with air and dampen the shock

Numerical calculation methods

For pipeline systems, pressure surge calculations are carried out numerically . There are special, powerful computer programs for this.

These programs are based on pressure surge 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. The pipeline is divided into numerous individual segments and the pressure surge is calculated in small time segments. The results are output e.g. B. as time functions of the pressures, the densities, the mass flows, the manipulated variables of the valves or the pump data. It is also dynamic loads are calculated, which serve a structural analysis of the pipeline system.

However, fast computer systems are required for numerical solution methods. In addition, the calculation of personnel costs must be used. Since such immense costs can be caused, a pressure surge should only be calculated numerically if it is absolutely necessary.

See also

Individual evidence

  1. A. Ismaier: Investigation of the fluid dynamic interaction between pressure surges and system components in centrifugal pump systems. Dissertation . 2010, ISBN 978-3-8322-9779-4 .
  2. AS Tijsseling, A. Anderson: A precursor in water hammer analysis - Rediscovering Johannes von Kries. Pp. 1-15. (pdf)
  3. ^ NE Joukowsky: About the hydraulic shock in water pipes. In: Mémoires de I'Académie Impériale des Sciences de St.-Pétersbourg, Ser. 8, 9, 1900, pp. 1-72.
  4. a b c H.-J. Lüdecke , B. Kothe: The pressure surge (=  KSB know-how . Volume 1 ). KSB AG, Halle 2013, p. 5, 11, 14 ( ksb.com [PDF; 1000 kB ; accessed on June 25, 2016]).
  5. E. Doering, H. Schedwill, M. Dehli: Fundamentals of technical thermodynamics: textbook for students of engineering. Volume 6, 2008, ISBN 978-3-519-46503-4 , p. 13.
  6. ^ Water Main Break. ( February 10, 2008 memento on the Internet Archive ) on the New York Department of Environmental Protection website
  7. ↑ A voltage drop in the Hamburg power grid leads to numerous water pipe bursts. ( Memento of April 30, 2016 in the Internet Archive ) on: Hamburg Wasser , accessed on January 2, 2011.
  8. Theodor Strobl, Franz Zunic: Engineering, Current basics - new developments. Springer Verlag, Berlin / Heidelberg 2006, p. 321.
  9. G. Wossog: Manual pipeline construction. Volume 2: Calculation. Vulkan-Verlag, Essen 1998, ISBN 3-8027-2716-9 , p. 279.
  10. Ernesto Ruiz Rodriguez: Young's modulus. ( Memento from April 7, 2014 in the Internet Archive ) Part of a study project at the Wiesbaden University of Applied Sciences. (MS Excel; 85 kB)