Study on Mechanism and Control Methods of Water Hammer in Pump Station and Pipe Lines

A pumping system can never be operated in steady-state condition all the time, since starting up and stopping the pump alone will change the duty conditions.

Generally speaking, every change in operating conditions and every disturbance cause pressure and flow variations or, put differently, cause the flow conditions to change with time. Flow conditions of this kind are commonly referred to as unsteady or transient. Referring specifically to pressures, they are sometimes called dynamic pressure changes or pressure transients. The main causes of transient flow conditions are:

• Pump trip as a result of switching off the power supply or a power failure.
• Starting or stopping up one or more pumps whilst other pumps   are in operation.
• Closing or opening of shut-off valves in the piping system.
• Excitation of resonant vibrations by pumps with an unstable H/Q curve.
• Variations of the inlet water level.

 

 

 

 Transient flow occurs when sudden change in flow velocity happens. The pipeline design including the safety factor against upsurge and down surge pressures needs many costs. When the cavitations and column separation occurs despite the high safety factor of equipments; damage is not refutable during operation. So water hammer calculation and application of protective equipments is necessary to protect the pipeline. Surge vessel is one of useful equipment that can balance both upsurge and down surge phases. Selection of tank volume and Size of connection line/Nozzle is very important due to safe system.

 

 

KEY WORDS:  water hammer, cavitations, upsurge, down surge, transient flow, surge vessel.

 

 

INTRODUCTION

 

If power failure occurs at the motor of the pumps which supply water to long discharge line, the initial negative surge wave may cause water column separation to occur at the high points of the discharge line which are near the hydraulic gradient. When the negative surge reach to end of line change to positive type but this surge is not too large and commonly is at safe side.

Water hammer following the tripping of pumps can lead to overpressures, which may either require excessive pipe wall thickness or some form of water hammer protection. The most appropriate type of water hammer protection depends on the pipeline profile as well as the flow characteristics of the pipeline. Low head lines can be protected with surge shafts or one-way discharge tanks or even nonreturn valves if negative pressures are tolerable. However, the most effective way of preventing negative pressures and also for reducing overpressures is the use of compressed air vessels(also known as air chambers, pressurized surge tanks, pneumatic tanks, or accumulators).

Air vessels generally alleviate negative pressures more effectively

than other forms of water hammer protection, and they can

maintain a positive pressure in the line at all stages following

pump trip. it will only be on the return flow back into the air vessel that the overpressures are cushioned. The damping effect could be negligible if there were no throttling or line friction, resulting in a large

reverse flow into the vessel and subsequent overpressures.

optimization of tank volume and Size of connection should be consider during  analysis. Suitable connection in size and type despite protect system against column separation, damps the upsurge pressure.

Compressed air vessels must be designed and manufactured to rigid quality standards, as burst vessels containing air are much more dangerous than those containing only liquid. Air expands with explosive force, whereas water pressure drops as soon as there is a leak.

In this paper optimization of surge vessel of a sea water pump station project is considered with regarding elastic water column theory. 

 

  

TRANSIENT FLOW

 

A pumping system can never be operated in steady-state condition all the time, since starting up and stopping the pump alone will change the duty conditions.

Generally speaking, every change in operating conditions and every disturbance cause pressure and flow variations or, put differently, cause the flow conditions to change with time. Flow conditions of this kind are commonly referred to as unsteady or transient. Referring specifically to pressures, they are sometimes called dynamic pressure changes or pressure transients. The main causes of transient flow conditions are:

• Pump trip as a result of switching off the power supply or a power failure.
• Starting or stopping up one or more pumps whilst other pumps   are in operation.
• Closing or opening of shut-off valves in the piping system.
• Excitation of resonant vibrations by pumps with an unstable H/Q curve.
• Variations of the inlet water level.

 

 

PRESSURE VARIATION RESULT OF VELOCITY VARIATION

 

Water hammer wave quantity will be decrease when the phenomena occur in elastic area. This element is one of effective ways of protection against water hammer damages. when a liquid flows inside elastic pipe and both of liquid and pipe are in elastic form , length of fluid be comes shorter and pipe diameter will be expand and the pressure rise extends as wave shape. the velocity of wave propagation  is near to voice velocity and approximately is 1000 m/s. to clarification assume a piece pipe with dx in length and  velocity of   water in side pipe is  constant (v). (fig. 1) 

The velocity at section 2 becomes zero during dt and pressure wave causes to engenders. The pressure wave reaches to section 1 with wave speed (a) after dt  . The distance between section 1  and 2 is dx. The Nuton , s law can be use for water column

Fig.1 wave movement inside elastic pipe

 

between section 1 and 2. the effective force quantity is :

                                                                        (1)                Because the initial quantity of velocity is V that reaches to zero later the momentum of water column will be as below :                                                                         

                                 (2)

 

Finally the result is below equation:

 

                                                                          (3)

 

AIR VESSELS

 

Air vessels generally alleviate negative pressures more effectively

than other forms of water hammer protection, and they can maintain a positive pressure in the line at all stages following pump trip. This is accomplished by forcing water out of the vessel into the cavity, otherwise created following pump trip or flow stoppage at the upstream end. The compressed air forces water from the air vessel into the pipeline, allowing the water column traveling up the pipeline to maintain its momentum. Friction and other head losses tend to reduce the water velocity and therefore the subsequent oscillations. Thus, some degree of flow throttling is often used in conjunction with the cushioning effect of air vessels. In particular, throttling of the outflow from the vessel may assist in reducing the water velocities more rapidly than a pure cushioning air vessel However, it is more common to throttle the return flow back into the vessel than it is to throttle the outflow (see Fig. 2). In this manner, a continuous deceleration of the returning water column occurs rather than only at the end of the gas compression cycle. In fact, if the air (or other gas) is used primarily as a cushion, it will only be on the return flow back into the air vessel that the overpressures are cushioned. The damping effect could be egligible if there were no throttling or line friction, resulting in a large reverse flow into the vessel and subsequent overpressures.

It is generally good practice to install a nonreturn or check valve immediately downstream of the pumps (i.e., between the pumps and air vessel) to prevent flow backward through the pumps. This is the situation assumed in the analysis herein.

Air vessels are not just installed at the pump discharge end to guard against the consequences of pump trips. They can also be installed in other suitable places in a piping system. For example in long inlet pipes, an additional air vessel at the inlet end of the pump provides effective surge control. If the pump fails or trips, an upstream vessel will absorb energy, while a downstream vessel will dissipate energy.

 

Fig.2  Schematic layout of a compressor-type air vessel. To avoid

excessive pressures on return of the vessel water, the connecting pipe may have to be fitted with a swing check valve with a throttled bypass.

 

 

The operating reliability of air vessels is high. During their operation, attention has to be paid to the following:

• Monitoring of the water level in the vessel.

• For reasons of hygiene, the water volume must be continuously or regularly replaced.

• The compressed air must not contain any oil.

• To be able to take the air vessel out of service for an inspection, spare vessels should be available.

• It must be possible to lock the shut-off valves in the connecting

pipeline against unintentional closure; the open position has to be monitored.

 

CLASSICAL WATER HAMMER THEORY

 

Water hammer equations are applied for calculation of the liquid unsteady pipe flow. The assumptions in the development of the water hammer equations are:

1- Flow in the pipeline is considered to be one-dimensional with the velocity averaged and the pressure uniform at a section.

2- Unsteady friction losses are approximated as quasi-steady state losses.

3- The pipe is full and remains full during the transient.

4- There is no column separation during the transient event, i.e. the pressure is greater than the liquid vapor pressure.

5- Free gas content of the liquid is small such that the wave speed can be regarded as a constant.

6- The pipe wall and the liquid behave linearly elastically.

7- Structure-induced pressure changes are small compared to the water hammer pressure wave in the liquid.

 

Water hammer equations include the continuity equation and the equation of motion :

 

                        (4)

 

                           (5)

 

Appendix explains the symbols.

 

 

For most engineering applications, the convective terms V(∂H/∂x), V(∂V/∂x),and Vsinθ, are very small compared to the other terms and may be neglected.A simplified form of Eqs (4) and (5) using the discharge Q=VA instead of

the flow velocity V is:

                                                                    (6)

 

                                               (7)

 

The applied software uses the most widely used and tested method, known as the Method of Characteristic, to solve governing equations (6) and (7) for unsteady pipe flow Using the Method of Characteristic, the two partial differential equations can be transformed to the following two pairs of equations:  

            

                                                                 C⁺                                                      (8)

                                                                            

 

i	Time (Sec)	physical   model Head (mH2O)	software model Head (mH2O)	1/n (ΣHpi-Hmi)	1/n (ΣHmi)
1	0.02	32.282	32.564	0.018	2.018
2	0.05	57.452	58.582	0.071	3.591
3	0.08	8.187	5.358	0.177	0.512
4	0.106	7.888	5.342	0.159	0.493
5	0.162	57.381	57.948	0.035	3.586
6	0.22	7.819	5.836	0.124	0.489
7	0.250	33.552	31.289	0.141	2.097
8	0.305	30.970	31.821	0.053	1.936
9	0.358	31.787	32.070	0.018	1.987
10	0.419	8.820	6.560	0.141	0.551
11	0.449	34.539	31.164	0.211	2.159
12	0.531	11.564	6.207	0.335	0.723
13	0.612	51.722	55.967	0.265	3.233
14	0.671	12.344	6.402	0.371	0.772
15	0.753	31.816	31.539	0.017	1.988
16	0.783	14.256	6.897	0.460	0.891
SUM				2.597	27.024
Rv				0.096

 

 

             

                                                                 C^-                                                       (9)

                                                                           

 

                                                                               

Equations (8) and (9) cannot be solved analytically, but they can be expressed graphically in space-time as characteristic lines (or curves), called characteristics, that represent signals propagating to the right (C⁺) and to the left (C^-) simultaneously and from each location in the system. At each interior solution point, signals arrive from the two adjacent points simultaneously. A linear combination of H and V is invariant along each characteristic if friction losses are neglected; therefore, H and V can be obtained exactly at solution points. With head losses concentrated at solution points and the assumption that friction is small, an iterative procedure is used in conjunction with Method of Characteristic to advance the solution in time.

 

NUMERICAL MODEL CALIBRATION AND VALIDATION

 

As part of its expert witness and break-investigation service e has calibrated and validated the software (hammer V8 XM). Comparison has done  between computer models and a physical model had done with Anton bergant and hiss colleagues (John vitkovsky, Arris Tijsseling, Angus simpson, Martin Lambert and Dida covas ) at 2003. They had tested effect of unteady friction  on water hammer wave forms.   

The example piping system used for investigating water hammer wave forms comprises a metal (copper) pipeline of length 37.2 m, 22 mm internal diameter and 1.6 mm wall thickness that is upward sloping (Fig. 3). The transient event is generated by a rapid closure of the downstream end valve. The initial flow velocity in case studies is V0 = 0.2 m/s, static head in the tank 2, HT = 32 m, valve closure time tc = 0.009 s, and water hammer wave speed a = 1319 m/s.

 

 

Fig. 3 Experimental apparatus with copper pipeline (pipe length L = 37.2 m; pipe diameter D = 22. mm)

 

Total head variations of water hammer wave on midpoint of pipeline Is calculated with below equation (table 1):

 

                                                                                                (10)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                Table 1.  Head variations of water hammer wave on midpoint

 

 

And then according to Eq. 10

 

 

 

 

 

 

 

Fig. 3 head variations of water hammer wave on midpoint

 

Calibration results (Fig. 3, table 1) shows that the validity of hammer soft ware I around 96% and it can be claimed that software has good accordance with physical model.

 

 

CASE STUDY

 

In order to transportation of sea water from Persian gulf to the Bandar Abbas refinery pond, it is necessary to supplied a Central Seawater Intake and pumping station with cleaned and treated seawater to Battery limits (Levels) at the requested pond conditions. Due to high seawater temperature of the surrounding Persian Gulf, during summer, the seawater is pumping from depth of -13.5m CD of the ocean. Only from this depth it can be guaranteed to supply seawater with 35°C up to the battery limits of the refinery, which is the maximum temperature accepted by the refinery.

The discharge capacity for operation flow rate is 75000 m³/h.There are totally 8 pumps at intake where 6 pumps are in duty and 2 of them are as standby. Each of 4 pumps is connected to a common header and supply sea water along a 2200 mm diameter pipeline to the pond that located at battery limits of refinery plant. Each pump discharge flow rate is 12500 m3/h at rate point. Above ground pipelines is made of carbon steel and under ground ones will be made of GRP (Reinforced Fiber Glass) type with total thickness of 23.39 mm. The pipeline to be modeled as well as its length and diameter are shown in Tables 2.

 

 

 

 

NO	System	Length	Diameter
1	Discharge pipe between pump Discharge and header.	4 × 10,5 (m)	1200/1400 (mm)
2	Pump discharge header	12.4 (m)	2800 (mm)
3	Header to pond	5550 (m)	2200 (mm)

Table 2.  Pipeline Lengths, Diameters

 

Due to transient water hammer analysis it is sufficient to model one pipe line with 4 pumps because both groups are similar to each other.

Primary analysis shows that Due to protect the system from water hammer shocks, use of surge vessel is necessary.

 Examinations are done on various size of vessel and connection as below: 

1. Surge vessel volume 60 m³ , connection 1000 mm.
2. 2- Surge vessel volume 60 m3 , connection 900 mm.
3. 1- Surge vessel volume 65 m3 , connection 1000 mm.
4. 1- Surge vessel volume 65 m3 , connection 900 mm.
5. 1- Surge vessel volume 70 m3 , connection 1000 mm.
6. 1- Surge vessel volume 70 m3 , connection 900 mm.
7. 1- Surge vessel volume 75 m3 , connection 1000 mm.
8. 1- Surge vessel volume 75 m3 , connection 900 mm.

 

Fig. 4   H-t graph, with out protection device

 

Fig. 5   H-t graph, 60 m^3 V, 900, 1000 mm Connection

 

 

 

 

 

 

 

Fig. 6   H-t graph, 65 m^3 V, 900, 1000 mm Connection

 

 

Fig. 7   H-t graph, 70 m^3 V, 900, 1000 mm Connection

 

Fig. 8   H-t graph, 75 m^3 V, 900, 1000 mm Connection

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 9   H-t graph, 900 mm Connection

 

Fig. 10   H-t graph, 1000 mm Connection

 

CONCLUSION

 

Fig 4 shows that the dominant wave in pipe line is down surge. as mentioned above, connection size is important to balance the upsurge pressure therefore we can predict that effect  of connection or orifice size in pressure balance  is small. So use of surge vessel with bypass orifice (Fig 2) is not necessary in this system. Fig 5 to 8 shows that connection size is not effective.

However the comparison of figures indicates that vessels with 75 and 70 m³ are suitable for this pipeline. Economic selection offers selection of 70 m³ and 900 mm connection of vessel because furthermore this case guaranties our system against water hammer.

This case shows that the pump stations with low level variation, dominate state is down surge and system protection against cavitations and low pressure is important. 

 

 

 

 

 

 

 

 

REFERENCES

Streeter, V.L and Benjamin. 1960, “Hydraulic Transient” McGraw-Hill company, New York.

Parmakian, john, 1955 “water hammering analysis” Dover publications, INC, New York.

stephanson,D (1989).”pipline desigen for water engineering”3rd ED., Elsevier,Amesterdam.

Stephanson ; D(2002).”Simple Guide for Design of Air Vessels for water hammer Protection of Pumping Lines" Journal OF Hydraulic Engineering. ASME, PP.0733-4929.

Antonio Roasario Di santo;Umberto Fratino;Vito lacobellis; Alberto Ferruccio Piccinni; (2002)”Effect of Outflow in Rising Mains with Air chamber” Journal OF Hydraulic Engineering .ASME,PP.999-1001

Chaudrhry,M.H,”Applied Hydraulic Transients”,1987,Van Nostrand Reinhold Cmpany,New York

Jaeger,C.”Areview of Surge Tank Stabilioty Criteria”1960,J.of Basic Engineerig,ASME,PP.765-783

Bergant,A & Tijsseling.A; 2001 ” Parameters Affecting Water Hammer Wave Attenuation, Shape and Timing”,IAHR 10th , Trondheim, Norway.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDIX

A = pipe area

a = water hammer (pressure) wave speed

D = pipe diameter

e = pipe wall thickness

V = flow velocity

g = gravitational acceleration

L = pipe length

p = pressure

mp = midpoint

R = inner pipe radius

t = time

tc = valve closure time

x = distance along pipe

z = pipeline elevation

Dt = time step

Dx = reach length

q = pipe slope

D s = jump in axial stress

n = kinematic viscos., Poisson ratio

r = mass density

s = axial stress

T = tank (reservoir)

u = unsteady part

v = vapour

ve = valve

MOC = method of characteristics