Calculation of stop water hammer and its protective measures

Abstract: This paper briefly introduces the calculation basis of stopping water hammer and uses computer software to simulate the working condition of stopping water hammer of actual project. According to a number of projects and computer simulation results, proposed pumping station and pipeline design should pay attention to the problem and stop pump water hammer protection measures.

Key words: stop pump, water hammer, calculation and protection measure

Stop water hammer is a phenomenon of water hammer, refers to the pump unit due to sudden power failure or other reasons caused by the sudden stop valve open state, in the pump and piping system, due to sudden changes in flow rate caused A series of sharp pressure alternating hydraulic lift impact. Under normal circumstances, the most serious pump stop water hammer, which has a great threat to the safety of pumping stations and pipelines, there are several domestic pumping station water pump has occurred and lead to pump house submerged or pipeline rupture of a major accident.

Pump stop water hammer size and pump room in the water pipeline and the specific circumstances. In the pump room and water pipeline design should take into account the water hammer may occur, and take appropriate precautions to prevent the occurrence of water hammer, or the impact of water hammer control within the allowable range. Based on the latest achievements in research on water hammer at home and abroad, combining with the experiences of many years of engineering practice, our hospital developed the water hammer calculation program based on the characteristic line method. This procedure can well simulate the water hammer condition of water pump and water pipe system under various working conditions and provide the design basis for high-lift long-distance water conveyance project.

1, stop pumping water hammer calculation principle

There are several ways to stop the calculation of pump water hammer: graphic method, numerical solution method and electric method. Its basic principle is to establish the equations of motion and continuous equations of water hammer process according to the theory of elastic water column. These two equations are hyperbolic partial differential equations.

The equation of motion is:

The continuous equation is:

Where: H - head of a point in the tube

V - tube flow rate

a - water hammer wave propagation speed

x - some point in the pipeline coordinates

g - acceleration of gravity

t-- time

f - pipeline friction coefficient

D - diameter

The most important basic equation for water hammer analysis is obtained by simplifying the solution:

H-H 0 = F (t-x / a) + F (t + x / a) (3)

V-V 0 = g / a × F t-x / a -g / a × F t + x / a (4)

Where F (t-x / a) - direct wave

F (t + x / a) - Reflected wave

In vibra- tion, the direct wave and the reflected wave propagate in the coordinate axis (H, V) as a ray, ie, the characteristic line. It shows the pipe at a certain point in the process of water hammer at the corresponding moment of head H and the relationship between flow velocity V. In order to facilitate the calculation of the computer, the equations above are transformed into a head balance equation and a speed change equation, ie, two boundary condition equations of the pump at the time of stopping the pump:

F 1 = PM - BQv + H n ⁢ β 2 + v 2 ⁢ A 0 + A 1 ⁢ x - ΔH 0 ⁢ v 2 / τ 2 =

F 2 = (β 2 + v 2 ) (B 0 + B 1 x) + m 0 -C 3 (β 0 -β) = 0 (6)

Where β - N / N n (actual speed / rated speed)

v - Q / Q n (actual flow / rated flow)

By the simultaneous connection of these two equations, the Newton-Raphson iterative formula can be used to find the approximate values ​​of v and β.

Transforming the pump's overall performance curve into full-scale performance curves related only to speed and flow, so that the computer takes values ​​when solving equations, that is:

WH (x) = h / (β 2 + v 2 ) (7)

WM (x) = m / (β 2 + v 2 ) (8)

Where h - H / H n (actual head / rated head)

m - M / M n (actual torque / rated torque)

The current water hammer calculation method is based on the above principle.

2, several kinds of boundary conditions under the conditions of water hammer simulation results

According to the actual situation of the water pump and water pipelines of the water intake pump room of a city in southern China, the water hammer simulation by the computer program is as follows (all calculated according to the lowest dry water level):

basic situation:

Pump units: Q n = 5 000 m 3 / h, H n = 55 m, N n = 741 r / min, N s = 132.4, GD 2 = 874.7 kg · m 2 , M n = 932.72 kg · m, Single run, long-term two run.

Water line: DN = 1 400 mm, L = 5 750 m, geometric head: 35 m (short), 45 m (forward).

Pump room and water pipeline shown in Figure 1:

2.1 Suppose there is valve pipe stop water hammer

① ordinary check valve

Ordinary check valve pipeline stop water hammer calculation results shown in Table 1.

Table 1 ordinary check valve pipeline stop water hammer calculation results

Operating conditions	Pump outlet maximum pressure value (kPa)	When increasing the pump unit moment of inertia multiples of the maximum pressure at the pump outlet (kPa)
Two pumps run in parallel	1536 (156.7 m)	830 (84.68 m)
A pump is running	892 (91.05 m)	617 (63.0 m)

The data presented in Table 1 is the value of the water hammer pressure generated by the immediate closure of the valve assuming the flow rate at the outlet of the pump is zero. Actual conditions, the valve closed for some time, so the actual water hammer value will be different from the data listed in the table. According to the computer simulation results, if under this condition, increase the moment of inertia of the pump unit can reduce the water hammer pressure significantly.

② Slow closing check valve

Slow closing check valve pipeline stop water hammer calculation results shown in Table 2.

Table 2 slow closing check valve pipeline stop water hammer calculation results

Operating conditions	The best valve closing conditions at the pump outlet maximum pressure value (kPa)	Pump reverse speed ratio (β / β n )	Pump maximum reverse flow ratio (Q / Q n )	The best valve closing combination conditions (Closing time and valve closing degree)
Two pumps run in parallel	867 (88.5 m)	0.06	-0.23	Fast off: 3 s, 80% Slow down: 24 s, 20%
A pump is running	655 (66.8 m)	0.03	-0.15	Fast off: 3 s, 80% Slower: 21 s, 20%

After computer simulation, when the valve closing time and speed combination with the best simulation conditions are different, the maximum pressure before the pump will increase. Therefore, a two-stage shut-off valve with the water delivery system, the valve operation should be calculated and determined, and should be adjusted during commissioning. Such equipment orders should be made to the manufacturer of the specific technical requirements (fast, slow closing time and adjustability).

③ pipeline stop flow stop water hammer (that is, to close the water hammer)

This pump house outlet pipe hump at the embankment (40m from the pump outlet) formed, calculated that here will close the water hammer. The actual observation and computer simulation results are similar, the computer simulation results shown in Table 3.

Table 3 ordinary check valve pipeline to close the water hammer calculation results to run

Operating conditions	Dry water when the pump outlet maximum pressure value (kPa)	Pump outlet maximum pressure at flood level (kPa)	Dry water hump at the hump pressure value (kPa)	Flood water hump pressure at the hump (kPa)
Two pumps run in parallel	1 705 (173.95 m)	1 312 (133.85 m)	1 695 (172.97 m)	1 302 (132.85 m)
A pump is running	1 171 (119.5 m)	644 (65.7 m)	1 068 (110.93 m)	605 (61.7 m)

It can be seen from Table 3 that when the stop-flow water hammer (that is, close the water hammer) is cut off in the pipeline, the water hammer value is large and reaches more than 4 times of the geometric lift, which must be paid great attention.

2.2 Concluding observations

The size of the stop water hammer is mainly related to the geometric lift of the pump house. When the geometric lift is more than or equal to 30 m, the ratio of the maximum water hammer pressure (Hmax) to the geometric lift (Ho) under various working conditions, the maximum reverse rotation speed The ratio of βmax to the rated speed βn is given in Table 4, respectively.

Table 4 several pipeline conditions to stop the pump water hammer calculation results table water hammer boundary

Water hammer boundary conditions	No check valve line	Normal check valve	Slow closing check valve	Common check valve pipeline has to bridge the water hammer occurred
H max / H o	0.9 ~ 1.44	1.9	1.25	3.0 ~ 5.0
β max / β n	-1.25		-0.2

In order to avoid the danger of stopping the water hammer, the following measures can be taken:

① no check valve for the pipeline system

This stop pump water hammer situation is not serious, the maximum water hammer value of about 1.40 times the geometric head, should be noted that the pump unit reversal and water loss caused by a large number of back and damage. Under normal circumstances, no check valve line should be avoided in the main pump unit overturned for a long time to prevent loosening of pump shaft and unit resonance. Through the simulation program has the following rules: water distance in the range of 1.2 ~ 5.0 km, the longer the pipeline, stop the pump water hammer the greater the more serious pump unit reversal. If the length of the pipeline exceeds 5.0 km, the continuous increase of the length will have little effect on the water hammer value. The geometric head lift increased , the maximum water hammer value and the pump set reverse value increased. When the geometric lift> 50 m, the pump set reverse value will continuously exceed the rated positive speed (β max / β n ≤ -1.0), exceeding the allowable standard range. In this case, contact the pump manufacturer and take appropriate technical measures to ensure that the pump is safe during reverse operation. For the non-check valve line selection torque (M n ) is smaller, larger moment of inertia (GD 2 ) of the pump unit will help to stop the water pump to stop the pump and pipeline conditions, postpone the pump reverse , Reduce the reverse value.

② For ordinary piping with check valve system

This stop pump water hammer situation is more serious, the largest water hammer value of about 1.90 times the geometric head. Water distance in the range of 1.2 ~ 5.0 km, the longer the pipeline, stop pumping water hammer greater. If the length of the pipeline exceeds 5.0 km, the continuous increase of the length will have little impact on the above parameters. Geometric head lift, stop pumping water hammer value is also greater. For the water pumping station, if the conditions permit (short water pipeline, the pump allows a short time reversal), cancel the ordinary check valve. If ordinary check valves are used, the maximum water hammer pressure value should be taken into account in the pressure rating and the stability of the pump units, piping fittings and piping systems.

③ with slow closing check valve piping system

Slow closing check valve for reducing the water pump to stop the pump has a significant effect. The use of slow-closing check valve should be combined with the specific circumstances, the speed of two stages of the valve duration should be based on the pumping station pump performance and water pipeline boundary conditions for computer simulation to arrive at the best combination of theoretical time and test run In order to obtain the best valve closure duration and speed of the two phases of the distribution of valve lasted duration. If the valve closing time is longer or shorter than the best valve closing time or speed of the two stages of the valve lasted improperly used, will result in a large water hammer pressure value. Computer simulation results show that adjusting the ideal slow-closing check valve line can control the pump head water hammer value about 1.45 times of the geometric lift head, but not the ideal condition of slow closing check valve line of the maximum stop pump The value of up to 2.5 ~ 2.8 times the geometric head. In addition, the two stages of the delay valve selection is also very particular about the duration, the general requirements within 5 s after stopping the pump should be closed more than 80% of the valve. If the entire valve closing process is uniform, will lead to a larger water hammer pressure, the simulation results in Table 5.

Table 5 slow closing check valve simulation results closed valve lasted

Turn off valve time and speed distribution of time	Simulate the best valve closing time and time and speed distribution	Other closed valve duration and time distribution of the situation
		1	2	3	4
Valve closing time (s)	18	18	twenty four	9	18
Quick off time (80% off, s)	3	Close evenly	3	3	6
Slow off time (turn off remaining 20%, s)	15		twenty one	6	12
The maximum stop water hammer value (kPa)	900 (91.8 m)	1 315 (134.2 m)	1 726 (176.1 m)	1 324 (135.1 m)	1 063 (108.5 m)
Basic parameters: geometric head 62 m, three pumps work in parallel, the water pipeline 1.3 km, diameter of 1.0 m.

④ common check valve pipeline to bridge the water hammer occurred

In the water pipeline routing should try to avoid sudden changes in the longitudinal slope, in particular, to prevent the emergence of "hump or knee," or it may lead to bridging the water hammer, and to close the water hammer maximum pressure value for the geometric head of 3 to 5 times , Which will have a great harm to the pump room and water pipe system. Under normal circumstances, the hump appears where the elevation of the geometric head of 30% to 80% of the most unfavorable (water hammer maximum). According to the simulation, the maximum water hammer value will exceed 980 kPa (100 m water column) when the geometry head is over 25 m and there is a "hump or knee" at a certain elevation in the pipeline. To bridge the inevitable situation of water hammer (humps have been built in the water delivery system), you should take engineering and technical measures for water hammer protection.

3, stop pump water hammer protection measures

It is necessary to take corresponding measures according to the actual situation, as stopping the water hammer may cause serious accidents in the pump station and the water delivery system (such as pump house submerged due to the broken equipment or pipes in the pump house and the water pipe rupture) To stop the pump to stop water hammer or reduce water hammer pressure.

① reduce the flow rate of water pipelines, water hammer pressure can be reduced to some extent, but will increase the diameter of the water pipe to increase project investment .

② water pipeline layout should be considered as far as possible to avoid the hump or sharp gradient.

(3) Through the simulation calculation, the pump unit with larger inertia GD2 or the flywheel with enough inertia can be selected to reduce the water hammer value to a certain extent.

④ set water hammer elimination device

a, two-way pressure regulating tower: built near the pump station or in the proper location of the pipeline, the water level of the bidirectional pressure regulating tower should be higher than the water level of the receiving basin at the end of the water pipeline and consider the head loss along the pipeline. The pressure regulating tower will make up the pipeline with the pressure change in the pipeline or drain the excessive pressure in the pipeline, so as to effectively avoid or reduce the water hammer pressure. Safe and reliable work in this way, but its application by the pumping station pressure and the surrounding topography restrictions.

b, one-way pressure regulating tower: near the pumping station or pipeline construction in place, one-way pressure regulating tower height below the pipeline pressure. When the pressure inside the pipeline is lower than the water level in the tower, the pressure regulating tower will supply water to the pipeline to prevent the water column from breaking off and avoid filling the water hammer. But its water pump outside the pump to stop the water hammer, such as valve water hammer off the role of decompression is limited. In addition, the performance of one-way valve used in the one-way pressure regulating tower should be absolutely reliable. If the valve fails, it may lead to larger water hammer.

c, pressure tank: little domestic experience in the foreign (UK) use more widely. It uses a specific law of gas volume and pressure to work. As pressure changes in the tubing, the pressure tank replenishes the tubing or absorbs excessive pressure in the tubing, acting similarly to the bi-directional pressure regulator.

d, water hammer eliminator: widely used before the 1980s. It is installed near the non-return valve and the water hammer pressure in the pipe is released through the open water hammer eliminator. Some water hammer eliminator without automatic reset function, prone to water hammer caused by misuse.

e, slow closing check valve: There are two types of heavy hammer and energy storage. This valve can be adjusted within a certain range of valve closing time as needed. Normally, the valve is closed 70% ~ 80% within 3 ~ 7 s after power outage, and the closing time of the remaining 20% ​​~ 30% is adjusted according to the condition of the pump and the pipeline, generally in the range of 10-30 s. You can use the computer simulation of the best time, and commissioning to determine the scene. It is noteworthy that, when the existence of hump in the pipeline to bridge the water hammer, slow closing check valve role is very limited.

Operating conditions Maximum pressure at the pump outlet (kPa) Maximum pressure at the pump outlet (kPa) when increasing the appropriate moment of inertia of the pump unit 1536 (156.7 m) 830 (84.68 m) Parallel operation of a pump Operating 892 (91.05 m) 617 (63.0 m)

Operating conditions

The best valve closing conditions at the pump outlet maximum pressure value (kPa)

Pump reverse speed ratio
(β / β n )

Pump maximum reverse flow ratio
(Q / Q n )

The best valve closing combination conditions
(Closing time and valve closing degree)

Two pumps run in parallel 867 (88.5 m) 0.06-0.23 Fast off: 3 s, 80%
Slow shut: 24 s, 20% A pump runs 655 (66.8 m) 0.03-0.15

Fast off: 3 s, 80%
Slower: 21 s, 20%

Operating conditions

Dry water when the pump outlet maximum pressure value (kPa)

Pump outlet maximum pressure at flood level (kPa)

Dry water hump at the hump pressure value (kPa)

Flood water hump pressure at the hump (kPa)

Two pumps run in parallel

1 705
(173.95 m)

1 312
(133.85 m)

1 695
(172.97 m)

1 302
(132.85 m)

A pump is running

1 171
(119.5 m)

644
(65.7 m)

1 068
(110.93 m)

605
(61.7 m)

No water hammer boundary line check valve ordinary slow closing check valve check valve with a common line check valve bridge water hammer occurs H max / H o 0.9 ~ 1.441.91.253.0 ~ 5.0β max / β n -1.25-0.2 closing valve time and speed distribution

Simulate the best valve closing time and time and speed distribution

Other valve closing time and the distribution of time and speed 1234 valve closing time (s) Close time
(80% closed, s) 3 Uniform close 336 Slow down time (20% closed, s) 1521612 Maximum stop water hammer value (kPa)

900
(91.8 m)

1 315
(134.2 m)

1 726
(176.1 m)

1 324
(135.1 m)

1 063
(108.5 m)

Basic parameters: geometric head 62 m, three pumps work in parallel, the water pipeline 1.3 km, diameter of 1.0 m.