me 5708 pressure surges in liquid & gas flow systems · low flow velocity – mainly a problem...

ME 5708

Pressure Surges in Liquid & Gas Flow

Systems

Report on Pressure Surge Analysis

April 13, 2015

National University of Singapore

Aravind Baskar – A0136344

ME 5708 – Pressure Surges in Liquid & Gas flow Systems

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Contents

Introduction .............................................................................................................................................. 3

LITERATURE STUDY ................................................................................................................................ 9

Surge Relief Valves ............................................................................................................................. 9

Advantages ..................................................................................................................................... 10

Disadvantages ............................................................................................................................... 10

Surge Suppressors............................................................................................................................ 10

Advantages ..................................................................................................................................... 11

Disadvantages ............................................................................................................................... 11

Rupture Discs ..................................................................................................................................... 11

Advantages ..................................................................................................................................... 12

Disadvantages ............................................................................................................................... 12

PRESSURE SURGE ANALYSIS ............................................................................................................. 14

Introduction ........................................................................................................................................ 14

Scope of Analysis .............................................................................................................................. 14

List of Assumptions .......................................................................................................................... 14

Parameters used ............................................................................................................................... 15

Basic Equations & Theory .............................................................................................................. 16

(a) Water Hammer Effect ................................................................................................... 16

(b) Column separation ......................................................................................................... 16

Governing Equations ....................................................................................................................... 17

MOC Method ..................................................................................................................................... 18

Finite Difference equations ........................................................................................................... 19

Pump characteristic equations..................................................................................................... 20


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Plots of Pressure Surge Analysis ................................................................................................. 21

Data used for simulations ......................................................................................................... 21

Discussion & Recommendations ................................................................................................ 26

References ........................................................................................................................................... 27


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Introduction

Pressure surges in liquid and gas flow systems has been widely studied and is still being researched

to reduce the effects of the phenomenon. During the operations of complex fluid systems, such as

pumping installation, oil-gas pipeline system, and nuclear power plant, unsteady and transient flow

conditions will be inevitably encountered. Pressure transients in pipeline systems are caused by fluid

flow interruption from operational changes such as starting/stopping of pumps, changes to valve

setting, changes in power demand, etc. Consequently, there are unexpectedly high pressure surges

occurring in the pipeline, these pressure surges may cause the damage/collapse of the pipeline and

hydraulic components, devices in the system. One typical case of the fluid transient accident is the

burst pipe of the Oigawa power station in 1950 in Japan (Bonin, 1960) in which three workers died.

The plant was designed in the early 20th century. A fast valve-closure due to the draining of an oil

control system during maintenance caused an extremely high-pressure water hammer wave that

split the penstock open. The resultant release of water generated a low-pressure wave resulting in

substantial column separation that caused crushing (pipe collapse) of a significant portion of the

upstream pipeline. Careful considerations are thus required in the system design stages to make

sure that the unsteady fluid system operations do not give rise to unacceptable flow and/or excessive

pressure transient conditions. Suitable methods for system control must be designed to avoid such

severe flow situation.

The principal use of transient analysis, both historically and present day, is the prediction of peak

positive and negative pressures in pipe systems to aid in the selection of appropriate strength pipe

materials and appurtenances, and to design effective transient pressure control systems. Therefore,

computational and modelling fluid transient in complex systems has been attracted research efforts

in recent years

Fluid transient analysis is commonly based on the assumption that there is no air in the liquid. In

fact, air entrainment, trapped air pockets, free gas, and dissolved gases frequently present in the

pipeline. Air bubbles will be evolved from the liquid during the passage of low-pressure transients.

When the liquid is subject to high transient pressure, the free gas will be compressed and some may

be dissolved into the liquid. The process is highly time- and pressure- dependent. The effects of


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entrapped or entrained air on pressure transient in pipeline systems can be either beneficial or

detrimental; the outcome highly depends on the characteristics of the pipeline concerned and the

nature and cause of the transient. The previous studies show that reasonable predictions of initial

pressure surges are obtained by including gas release. However, the existence of entrained air

bubbles within the fluid, together with the presence of pockets of air complicates the analysis of the

transient pressures and makes it increasingly difficult to predict the true effects on surge pressures.

Fluid transient is unsteady flow in pipe which is followed by the change in the flow rate condition.

Unsteady or transient flows may be initiated by the system operator, be imposed by an external

event, be caused by a badly selected component or develop insidiously as a result of poor

maintenance. The causes of unsteady and transient flows in fluid systems can be summarized as

follow:

Uncontrolled pump trip, often resulting from a power failure. The magnitude of transient

pressure caused by a sudden pump stop can be significant for low-pressure pipelines whose

initial section goes uphill for a certain extent.

Check valve slam.

Rapidly closure of pump delivery valves.

Valves and similar flow control devices anywhere in the system can initiate unwelcome

fluctuations in pressure and flow.

The most serious pump-start problem is in system in which borehole and submerged deep well

pumps with check valves mounted at ground level.

Pipeline supports are a matter of compromise.

The potential for resonance to occur should also be considered.

Changing elevation of reservoir.

Waves on a “reservoir” or surge tank.

Vibration of impellers or guide vanes in pumps.

Suction instability due to vortex formation.

Unstable pump characteristics.


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If fluid transient happens in complex systems, unacceptable conditions or failure can be created.

Some of these fluid transient events can be predicted and controlled by designer and plant operator,

but other events, such as power failure or self-excited resonance can be unplanned and possibly

unexpected. Even though, designer should still assess the risks for any unacceptable conditions that

may arise. Some of unacceptable conditions may be listed below:

Pressure too high – leading to permanent deformation or rupture of the pipeline and

components; damage to joints, seals and anchor blocks; leakage out of the pipeline, causing

wastage, environment contamination and fire hazard.

Pressures too low – may cause collapse of the pipeline; leakage into the line at joints and seals

under sub-atmospheric conditions; contamination of the fluid being pumped; fire hazard with

some fluids if air is sucked in.

Reverse flow – causing damage to pump seals and brush gear on motors; draining of storage

tanks and reservoirs.

Pipeline movement and vibration; overstressing and failure of supports. Leading to failure of

the pipe; mechanical damage to adjacent equipment and structures.

Low flow velocity – mainly a problem in slurry lines, causing settlement of entrained solids and

line blockage.

Surge pressure is defined as the rapid change in pressure as consequence of fluid transient in a

pipeline. The surge pressure can be dangerously high if the change of flow rate is too rapid. The

excessive pressure surges may cause the collapse of the pipeline or the damage of the hydraulic

equipment in the system. Therefore, in order to protect complex systems from severe accidents, the

transient or unsteady behaviour of the systems needs to be analysed, and suitable surge protection

devices and operation process need to be proposed to control the fluid transient conditions at the

design stage. In short, there are three very important reasons to carry out an analysis of the fluid

transient in complex systems:

To protect the pipe network against abnormal or faulty conditions that can provoke too high

or too low pressures which can eventual cause pipe ruptures with fluid leakage or

contamination and indirect hazards.


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To verify the hydraulic behaviour of both the overall network and of its each component for

different conditions, including the transient regimes (e.g. pump start-up or trip-off and valve

or gate manoeuvres) due to operational needs.

To implement advanced operational control techniques for the pipe network, both off-line and

on-line, in order to minimize energy and fluid losses or to improve the system capacity and the

system water quality.

There is a wealth of literature available addressing the study of fluid transients or ‘water hammer’,

the most notable work is of Wylie and Streeter (1978). Many hydraulics textbooks provide a useful

elementary overview of the background theory (e.g. Nalluri and Featherstone, 2001) for non-

specialist civil engineers. The works of Thorley (2004) provide, in case of the former, guidelines for

computational formulations, and in the latter, a broader descriptive background with practical case

studies.

The transient flow in a pipeline can be divided into three phases: water hammer, cavitation and

column separation. In the water hammer phase the release of dissolved gas is small and the wave

speed depends on the void fraction, which in turn depends on the local pressure. In the cavitation

phase, gas bubbles are dispersed throughout the liquid owing to the reduction of the local transient

pressures to the vapour pressure of the liquid. The liquid boils at that pressure and the local pressure

will not drop further. The liquid in this phase behaves like a gas-liquid mixture. Depending upon the

pipeline geometry and velocity gradient, the gas bubbles may become as large as to fill the entire

cross-section of the pipe. This is the column separation phase. Fluid transient analysis is commonly

based on the assumption of no air in the water. However, air entrainment, trapped air pockets, free

gas, and dissolved gases frequently present in the pipeline. Air in pressurized system comes from

three primary sources. The first source of air is trapped air pockets at the top of the pipe cross-

section at high points along the pipe profile. Prior to start-up, pipeline is full of air. As the line fills,

much of this air will be removed through hydrants, faucets, etc. However, a large amount of air will

still be trapped at high points since air is lighter than water. This air will continuously be added due

to the progressive upward migration of pockets of air as the system operation continues. The second

source of air is free gas, dissolved gases in the flow. For example, water contains approximately 2%


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dissolved air by volume (Fox, 1977). During system operation, the entrained air can be evolved from

the liquid or compressed, dissolved into the liquid due to the pressure transient. The third source of

air is that which enters through mechanical equipment. This air may be forced into the system as a

result of: falling jets of fluid from the inlet into the sump; attached vortex formation; and the adverse

flow path towards the operating pump. Air may also be admitted through packing, valves, air vessel,

etc. under vacuum conditions. In short, air always presents in a pressurized pipeline. The pockets of

air accumulating at a high point can result in a line restriction which increases head loss, extends

pumping cycles and increases energy consumption. As the air pockets grow, the fluid velocity will

be increased and one of the following two phenomena will occur. The first possibility is a total flow

stoppage. As the flow decreases in a pipeline due to the present of air-entrainment, the pumps are

forced to work harder and are less efficient; this could result in a total system blockage. The second

possibility is that all or part of the pocket would suddenly dislodge and be pushed downstream. The

sudden and rapid change in fluid velocity when the pocket dislodges and is then stopped by another

high point, can lead to a high pressure surge. Under low pressures, the phenomenon of gas release,

or cavitation, creates vapour cavities which, when swept with the flow to locations of higher pressure

or subject to the high pressures of a transient pressure wave, can be collapsed suddenly and creating

further ‘impact’ pressure rise, thus potentially causing severe damage to the pipeline. In normal

pipeline design, cavitation risk is to be avoided as far as is possible or practicable. The work of

Burrows and Qui (1995) highlighted that the presence of air pockets can be further detrimental to

pipelines subject to unsuppressed pressure transients and localized cavitation, such that substantial

underestimation of the peak pressures might result. Generally, fluid transient with air entrainment

are considerably different from those computed according to models with no air. Numerous practical

and numerical experiments show several distinct characteristic differences of fluid transients with

and without air entrainment. In general, the first pressure peak with entrained air is found to be

higher than that predicted by models with no air. The pressure periods are longer when air

entrainment is considered. The pressure surges are asymmetric with respect to the static head, while

the pressure surges are symmetric with respect to the static head for models with no air presented

in the flow. The pressure transient damping with air entrainment is faster than the damping with no

air entrainment. Computational and modelling of fluid transient with air entrainment has been


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carried out by many researchers together with practical experiments and field measurements. Most

fluid transient studies based on single fluid models use the method of characteristics to solve the

resulting finite difference equations which are derived from the continuity equation and momentum

equation of one dimension fluid flow. The governing equations of motion (continuity and

momentum) are expressed in terms of changes over finite intervals in space along the pipeline (∆x)

and time (∆t). The resulting finite difference equations can then be solved by the method of

characteristics (MOC), derivations being widely available (Wiley and Streeter, 1978; Thorley, 2004).

For the single fluid problem, this approach is normally acceptable for predictive design.


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LITERATURE STUDY

Surge pressures result from a sudden change in fluid velocity and, without surge relief, these surge

pressures can damage pipes, other piping components, equipment and personnel. These pressure

surges can be generated by anything that causes the liquid velocity in a line to change quickly (e.g.,

valve closure, pump trip, Emergency Shut down (ESD) closure occurs) and subsequently packing

pressure. Total surge pressure may be significantly above the maximum allowable pressure of the

system, leading to serious damage to your valuable assets.

Surge Relief Valves

FIG.1 TYPICAL SURGE RELIEF SYSTEM & PERFORMANCE

Surge relief valves are widely being used to counter the effects of pressure surges. The valves prevent

instantaneous pressure rise and also ensure the closure of valve without slamming. Various types of

surge relief valves are available and selection is based on the requirements. A simple example is

discussed below.

DANFLO Surge Relief Valves are engineered to track unabated surge-wave pressure transients-open

quickly, then closes without slamming shut. The “speed of response” in surge valves is defined as

the ability of the valve/valves to relieve peak wave surge flow in the time stated in a hydraulic

transient surge analysis. Although this time varies with each application, timed responses of 100

milliseconds or less are not unusual.

DANFLO surge valve operation is simple. The cavity behind the valve plug is filled with nitrogen gas

to affect proper relief set pressure of the valve. This cavity loading force seats the valve and opposes

the force generated by line pressure in front of the valve. The valve remains closed until surge wave


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pressure exceeds the force behind the plug (set pressure). The DANFLO surge valve then opens

quickly to track the unabated surge wave. The closing cycle responds directly to pressure decay in

the upstream piping in front of the DANFLO surge valve.

A M&J Valve DANFLO surge relief system consists of the appropriate quantity of specific sizes of

gas-loaded valves to handle requested flow conditions. High flow coefficients of DANFLO surge

valves usually mean fewer and/or smaller size valves to meet user requirements. Operation at

recommended settings provides flow reserve for protection against surges larger than expected.

Advantages

1) Fast speed of response with soft closure to prevent generating a second surge event.

2) Can be used on high viscosity products such as crude oil.

3) Good flow characteristics (Cv)

4) No blowdown, reseats at the set point.

Disadvantages

1) Only as repeatable as the system controlling the nitrogen pressure.

2) Performance is greatly impacted by any restrictions in the gas line between the relief valve and

the plenum tank.

3) Many manufacturers recommend burring the plenum for temperature stability.

Surge Suppressors

Surge suppressors perform surge relief by acting as a pulsation dampener. Most suppressors have a

metal tank with an internal elastic bladder in it. Within the tank they pressurize the top of the bladder

with a compressed gas while the product comes in the bottom of the pressure vessel. The gas in the

bladder is supplying the system with its set point. During normal operation, as the process conditions

begins to build pressure; the internal bladder contracts from the pressure gain allowing liquid to

move into the surge suppressor pressure vessel adding volume to the location. This increase in

physical volume prevents the pressure from rising to dangerous levels.


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FIG.2 SURGE SUPPRESSORS

Advantages

1) Very fast speed of response.

2) Zero loss of product from the pipeline from a surge event.

3) Can be used as both a surge suppressor and for surge relief.

Disadvantages

1) Limited capacity of volume for surge relief.

2) The surge suppressor must be as physically close as possible to the area where the surge is

generated. Surge Suppressors can become very large depending on line size.

3) Has a limited maximum working pressure.

Rupture Discs

A rupture disc, also known as a burst disc, bursting disc, or burst diaphragm, is a onetime use, non-

reclosing pressure relief device that, in most uses, protects a pressure vessel, equipment or system

from over pressurization or potentially damaging vacuum conditions. A rupture disc is a sacrificial

part because it has a one-time-use membrane that fails at a predetermined differential pressure,

either positive or vacuum. The membrane is usually made out of metal, but nearly any material can

be used to suit a particular application.

FIG.3 RUPTURE DISCS

http://en.wikipedia.org/wiki/Rupture_disc


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Rupture discs provide instant response (within milliseconds) to an increase or decrease in system

pressure, but once the disc has ruptured it will not reseal. Due to the one time usage of this disc it

requires someone to replace the plate once it has ruptured. One time usage devices are initially cost

effective, but can become time consuming and labour-intensive to repeatedly change out.

Advantages

1) Isolates equipment from the process conditions, protecting the equipment until it is needed

for a surge relief event.

2) Cost effective installation.

3) Very fast response time.

Disadvantages

1) One time use.

2) Requires down time to replace.

3) A rupture disk has only one set point.

Attached below are the 2 literatures that have been critically reviewed for the project.

“Sizing the Protection Devices to Control Water Hammer Damage” has been analysed by I.

Abuiziah, A. Oulhaj, K. Sebari and D. Ouazar.

Abstract : The primary objectives of transient analysis are to determine the values of transient

pressures that can result from flow control operations and to establish the design criteria for system

equipment and devices (such as control devices and pipe wall thickness) so as to provide an

acceptable level of protection against system failure due to pipe collapse or bursting. Because of the

complexity of the equations needed to describe transients, numerical computer models are used to

analyse transient flow hydraulics. An effective numerical model allows the hydraulic engineer to

analyse potential transient events and to identify and evaluate alternative solutions for controlling

hydraulic transients, thereby protecting the integrity of the hydraulic system. This paper presents the

influence of using the protection devices to control the adverse effects due to excessive and low

pressure occurs in the transient.


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“Modelling and controlling flow transient in pipeline systems: Applied for reservoir and pump

systems combined with simple surge tank” has been studied by I. Abuiziah, A. Oulhaj, K. Sebari,

D. Ouazar and N. Shakameh.

Abstract: When transient conditions (water hammer) exist, the life expectancy of the system can be

adversely impacted, resulting in pump and valve failures and catastrophic pipe rupture. Hence,

transient control has become an essential requirement for ensuring safe operation of water pipeline

systems. To protect the pipeline systems from transient effects, an accurate analysis and suitable

protection devices should be used. This paper presents the problem of modelling and simulation of

transient phenomena in hydraulic systems based on the characteristics method. Also, it provides the

influence of using the protection devices to control the adverse effects due to excessive and low

pressure occurring in the transient. We applied this model for two main pipeline systems: Valve and

pump combined with a simple surge tank connected to reservoir. The results obtained by using this

model indicate that the model is an efficient tool for water hammer analysis. Moreover, using a

simple surge tank reduces the unfavourable effects of transients by reducing pressure fluctuations.


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PRESSURE SURGE ANALYSIS

Introduction

Pressure surge analysis is done by incorporating the boundary and necessary governing equations

of the given system into a mathematical model and solving using numerical methods such as finite

difference schemes, etc. Initially the test setup is tested without any pressure protection devices and

the maximum level of pressure surge is computed and compared with the requirements. The next

step was finding the pressure surge with the recommended pressure protection devices such as

surge tanks, air vessels, etc. The simulation of pump failure is also analysed to find the optimal

protection system. The results are then analysed to predict the optimal pressure protection setup for

the system.

Scope of Analysis

The scope of analysis was to develop a mathematical model for the given system and also to

compute the numerical solution of the model. The given system has been carefully analysed and

governing equations such as continuity, momentum, etc. have been used for computing the

mathematical model. Finite difference scheme has been employed to solve the model. Matlab has

been chosen for programming the model. Failure of all 3 pumps operating on the main was

simulated as it possesses the greatest risk to the given setup.

List of Assumptions

The assumptions made during the analysis are as follows:

1. Flow is assumed to be an incompressible fluid flow.

2. Valve closure is instantaneous.

3. Wave speed is assumed to be constant throughout the pipeline.

4. Check valve closes automatically on reversal of flow.

5. Reduction in speed of pump due to failure is gradual.


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Parameters used

Symbol Description Units

a Wave Speed ms-1

A1,A2,A3 Pump Speed Constants

B1,B2,B3 Pump Torque Constants

g Gravitational force ms-2

h Pressure Head m

v Velocity of flow ms-1

Angle of inclination - pipe degrees

t Time s

dx Node distance m

p Pressure of system m

z Datum Height m

A Area of pipeline m2

𝜂 Efficiency %

𝜌 Density kgm-3

f Friction factor -

D Diameter m


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Basic Equations & Theory

FIG.4 TYPICAL CONFIGURATION OF A PUMPING STATION WITH TRANSIENT PROTECTION DEVICES

A typical configuration of a pumping station with various protection devices is shown above. In order

to develop a pressure protection system it is essential to understand the problems associated with

it.

(a) Water Hammer Effect

Water hammer effect or pressure transient is commonly caused due to improper valve closure

process or failure of hydraulic units and non – availability of adequate pressure protection devices.

FIG.5 PRESSURE TRANSIENTS

(b) Column separation

Column separation is a phenomenon that can occur during a water-hammer event. If the pressure

in a pipeline drops rapidly to the vapour pressure of the liquid, the liquid vaporises and a "bubble"

of vapour forms in the pipeline. This is most likely to occur at specific locations such as closed ends,


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high points or knees (changes in pipe slope). When the pressure later increases above the vapour

pressure of the liquid, the vapour in the bubble returns to a liquid state, which leaves a vacuum in

the space formerly occupied by the vapour. The liquid either side of the vacuum is then accelerated

into this space by the pressure difference. The collision of the two columns of liquid, (or of one liquid

column if at a closed end,) results in cavitation and 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.

FIG.6 COLUMN SEPARATION & EFFECTS

Having studied the problems it is necessary to devise a mathematical model by incorporating the

various physical relationships for solving by numerical methods.

Governing Equations

FIG.7 FLOW THROUGH CONDUIT


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The net mass inflow per unit time into the selected space must be equal to time rate of increase of

the mass within the space and we get,

𝜌𝐴𝑉 − [𝜌𝐴𝑉 + (𝜌𝐴𝑉)𝑥𝛿𝑠] = (𝜌𝐴𝛿𝑠)𝑡 … (1)

Eq.(1) divided by mass and after rearranging we get,

𝜌𝑥 (𝑉

𝜌) +

𝜌𝑡𝜌

+ 𝐴𝑥 (𝑉

𝐴) +

𝐴𝑡𝐴

+ [(𝛿𝑠)𝑡

𝛿𝑠+ (𝑉)𝑥] = 0 … (2)

𝑃′

𝜌𝐴2 + (𝑉)𝑥 = 0 … (3)

𝑃′

𝜌𝐴2 + (𝑉)𝑥 =𝐷𝑃

𝐷𝑡+

𝑉𝜕𝑃

𝜕𝑥… (4)

𝑃 = 𝜌𝑔(𝐻 − 𝑧) … (4)

𝜕𝑃

𝜕𝑥= 𝜌𝑔 (𝐻𝑥 −

𝜕𝑧

𝜕𝑥) = 𝜌𝑔(𝐻𝑥 + 𝑠𝑖𝑛𝛼)

∴𝑎2

𝑔𝑉𝑥 + 𝑉(𝐻𝑥 + 𝑠𝑖𝑛𝛼) + 𝐻𝑡 = 0 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑖𝑡𝑦 … (5)

∴ 𝑔𝐻𝑥 + 𝑉𝑡 + 𝑉𝑉𝑥 +𝑓

2𝐷𝑉|𝑉| = 0 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 … (6)

MOC Method

For the method of characteristics method, from the equation of continuity and motion the

characteristic equations are derived and they are as follows:

C+ equation:

𝑔

𝑎

𝑑𝐻

𝑑𝑡+

𝑑𝑉

𝑑𝑡+

𝑔

𝑎𝑉𝑠𝑖𝑛𝛼 +

𝑓𝑉|𝑉|

2𝐷= 0;

𝑑𝑥

𝑑𝑡= 𝑉 + 𝑎

C- equation:

−𝑔

𝑎

𝑑𝐻

𝑑𝑡+

𝑑𝑉

𝑑𝑡−

𝑔

𝑎𝑉𝑠𝑖𝑛𝛼 +

𝑓𝑉|𝑉|

2𝐷= 0;

𝑑𝑥

𝑑𝑡= 𝑉 − 𝑎


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Finite Difference equations

FIG.8 CHARACTERISTIC GRID

The finite difference grid is as shown above and is used for numerical calculations. For the analysis a

detailed grid is shown as below:

FIG.9 FINITE DIFFERENCE SCHEME

The finite difference equations are as follows:

C+ equation:

𝑔

𝑎

𝐻(𝑖)𝑛+1 − 𝐻(𝑖 − 1)𝑛

∆𝑡+

𝑉(𝑖)𝑛+1 − 𝑉(𝑖 − 1)𝑛

∆𝑡+

𝑔

𝑎𝑉(𝑖)𝑛𝑠𝑖𝑛𝛼 +

𝑓𝑉(𝑖 − 1)𝑛|𝑉(𝑖 − 1)𝑛|

2𝐷= 0

𝑑𝑥

𝑑𝑡= 𝑉(𝑖 − 1)𝑛 + 𝑎


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C- equation:

−𝑔

𝑎

𝐻(𝑖)𝑛+1 − 𝐻(𝑖 + 1)𝑛

∆𝑡+

𝑉(𝑖)𝑛+1 − 𝑉(𝑖 + 1)𝑛

∆𝑡−

𝑔

𝑎𝑉(𝑖)𝑛𝑠𝑖𝑛𝛼 +

𝑓𝑉(𝑖 + 1)𝑛|𝑉(𝑖 + 1)𝑛|

2𝐷= 0

𝑑𝑥

𝑑𝑡= 𝑉(𝑖 + 1)𝑛 − 𝑎

At the boundary only one of the characteristic equations can be applied and the HQ equation

provides the 2nd equation for solving the 2 unknown’s, i.e. pressure head and velocity of flow. At all

the interior points we have 2 equations with 2 unknowns and can be solved simultaneously to obtain

the solution. Change in x, ∆𝑥 is basically the length divided by the number of nodes, whereas change

in time step is based on the following CFL criteria,

∆𝑥

∆𝑡= 𝑉 ± 𝑎

Pump characteristic equations

Centrifugal pump characteristic curves are drawn based on the relationship between head, discharge

and speed.

FIG.10 PUMP CURVES


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Pump Head, Hk = A1Nk2+A2NkQk+A3Qk

2

Pump Torque, Tk = B1Nk2+B2NkQk+B3Qk

2 = −𝐼𝑑𝜔

𝑑𝑡, 𝜔 =

2𝜋𝑁

60

Pump Efficiency, 𝜂k = C1Nk2+C2NkQk+C3Qk

2

Plots of Pressure Surge Analysis

The simulation was carried out using Matlab and the results of the pressure surge analysis are as

follows:

Data used for simulations

TABLE 1. SIMULATION DATA

Modulus of Elasticity 2.20E+11 N/m2 Nos 3 units Modulus of Elasticity 2.15E+09 N/m2

Poisson Ratio 0.287 Diameter of Impeller 655 mm Density 1000 kg/m3

Friction factor 0.0022 0.0015 Inertia 33.4 kg.m2 c1 0.91763

Wall thickness 12.5 mm Speed 730 rpm Dynamic Viscosity 9.00E-04 Ns/m2

Lining Thickness 20 mm NPSH 5.8 m Re 2.12E+06

Mean diameter 1025 mm Flow Rate 1.6 m3/s g 9.81 m/s2

ID 985 mm Flow Velocity 1.94 m/s

Pipe thickness 20 mm Max. Pressure Surge Head 201.136 without friction

Area 0.824741 m2 Max. Pressure Surge 1973142

Surge Wave Speed 1017.082 m/s

Pipeline Materials Pump Fluid


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FIG.11 PUMPING STATION PROFILE

FIG. 12 HYDRAULIC GRADIENT LINE AT STEADY STATE

92.8m

107.5m

112.5 m

1000 2000 3000 4000 5000 0

115

110

105

95

100

90

Chainage (In meters)

Pip

e I

nvert

Level

(In

mete

rs)


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Following are the results simulated via AFT Impulse Software Release 4.0

FIG. 13 HYDRAULIC GRADIENT LINE - TRANSIENT




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FIG. 16 PRESSURE TRANSIENT




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From the analysis it is found that the pressure transient is reduced by the surge tank setup

and has reduced the pressure variant to its allowable limits. The location of the surge tank at

various locations was tried and found that the location has little effect on overall pressure

transient.


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Discussion & Recommendations

Pressure transient is induced by a number of factors such as slamming of valves, pump failure, non-

availability of surge devices such as surge tanks, air vessels, etc. to reduce/prevent the slamming

effect of valves it is necessary to install surge relief valves or surge suppressors to accumulate the

effect of sudden and erratic valve closure. To overcome pressure surges, surge tanks needs to be

positioned at almost the peak location of the pipeline system. The major part of pressure surge

suppression lies in carefully selecting the appropriate sixe of devices and it has been already studied

by and I. Abuiziah, A. Oulhaj, K. Sebari and D. Ouazar and it shows that carefully modifying the surge

devices is essential for proper surge protection and also for minimizing the cost of the system.

FIG. 21 SURGE PROTECTION DEVICES

Bladder type surge tanks are currently being employed as it has a very good efficiency of

operations and also the in-operation maintenance capabilities. Surge relief valves can function as a

second protection system in case of failure of primary protection devices.


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References

1. Applied Hydraulic Transients by M. Hanif Chaudhry, College of Engineering and

Computing, University of South Carolina, Columbia, SC, USA, ISBN 978-1-4614-8538-4

(eBook)

2. Fluid transients in complex systems with air entrainment by NGUYEN DINH TAM

3. Tullis, J.P., 1989 , Hydraulics of Pipelines – Pumps, Valves, Cavitation, Transients, John

Wiley & Sons, New York

4. “Sizing the Protection Devices to Control Water Hammer Damage” has been analysed by

I. Abuiziah, A. Oulhaj, K. Sebari and D. Ouazar.

5. “Modelling and controlling flow transient in pipeline systems: Applied for reservoir and

pump systems combined with simple surge tank” has been studied by I. Abuiziah, A. Oulhaj,

K. Sebari, D. Ouazar and N. Shakameh.

6. http://www.pumpfundamentals.com

7. http://www.aft.com/impulse

8. DANFLO Liquid Surge Relief Valve Case papers.

9. Ramalingam, Dhandayudhapani, "DESIGN AIDS FOR AIR VESSELS FOR TRANSIENT

PROTECTION OF LARGE PIPE NETWORKS - A FRAMEWORK BASED ON

PARAMETERIZATION OF KNOWLEDGE-BASE DERIVED FROM OPTIMIZED NETWORK

MODELS" (2007). University of Kentucky Doctoral Dissertations. Paper 489 -

http://uknowledge.uky.edu/gradschool_diss/489

10. Surge Control in Pumping Systems – A case study by VAL-MATIC VALVE AND

MANUFACTURING CORP - www.valmatic.com.

http://www.pumpfundamentals.com/

http://www.aft.com/impulse

http://uknowledge.uky.edu/gradschool_diss/489

http://www.valmatic.com/

me 5708 pressure surges in liquid & gas flow systems · low flow velocity – mainly a problem...

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