Ellis,J. Pressure transients in water engineering, A guide to analysis and interpretation of behaviour

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The distinction between surge or slow transients and waterhammer

or fast transients arose partly from the different methods of analysis

which have been employed in the past. For instance, the analysis of a

long-period surge or mass oscillation in a low-pressure conduit would

usually be analysed using relatively large time steps to reduce the

effort required and the faster waterhammer phenomenon necessarily

studied with much smaller time steps.

In common with many other branches of engineering, hydraulic tran-

sient or pressure surge analysis has been transformed over the past 20

years or so by the increasing availability and power of digital computers.

This has led to a considerable blurring of distinction between slower and

faster transients as the same computer program can be used to investi-

gate pressure transient behaviour throughout a system. The title

Pressure Surge has been used for the long series of international confer-

ences organised by the British Hydromechanics Research Association

(BHRA) which includes both long-period and fast transients. In this

book the terms pressure surge and hydraulic transient are considered to

be interchangeable and applied to all aspects of behaviour.

Concurrent with hardware developments, increasingly sophisticated

computer modelling programs have been introduced which allow a wide

range of pipeline network conﬁgurations to be represented. Whereas in

the past a substantial factor of safety would be applied to any design,

research has improved understanding of transient behaviour allowing

reduction in the factor of safety. Better understanding both helps to

prevent damage and also permits cost savings through a reduction in

the factor of safety. Continued pressure to reduce costs makes use

of the properties of pipes and ﬁttings to a greater extent and also

drives the computational ability to analyse systems in increasing

detail. In the past, limits on ability to analyse systems may have led

to the adoption of simpler pipeline arrangements whereas today compu-

tational ability and understanding of behaviour allows pressure surge

events to be studied in even very complicated networks.

User-friendly graphical interfaces have been included in many of

these programs which permit the user to select system components

from a range of elements. Thus the transient analysis of quite compli-

cated pressure pipeline systems has increasingly moved from being an

activity undertaken by a fairly limited number of specialist organisations

towards becoming a capability within design ofﬁces generally.

Within specialist consultancies a wealth of knowledge will have been

accumulated which is at the client’s disposal but in order that the client

should be able to appreciate detailed aspects of system behaviour it is

Pressure transients in water engineering

desirable that he should have on his team someone familiar with aspects

of transient behaviour. The better informed the client’s representative

the less scope for misunderstanding.

However, until now this type of analysis remains an activity which is

not encountered on a very regular basis within consultancy organisa-

tions generally and a considerable time may elapse between one

analysis and the next. Coupled with turnover of staff, this can make

the process of gaining experience somewhat protracted. The new

graduate or novice engineer may be provided with a quite sophisticated

modelling tool but still be unsure of what design cases should be consid-

ered and for how long a computer simulation is required to be continued

to ensure that all transient activity of signiﬁcance has been predicted.

Being new to surge analysis, the novice may be uncertain whether or

not the predictions which he has obtained from the modelling

exercise are realistic, or possibly contain the consequences of some

mistake in the information provided to the computer or even the

result of using the program inappropriately. These concerns are not

unique to pressure transient analysis and have also arisen in connection

with the use of computer software in other areas of engineering such as

structural analysis where similar concerns have been raised.

However, the frequency with which transient investigations are

undertaken may increase generally if a novel approach to mains con-

dition assessment using controlled surges becomes widespread. As

described by Misiunas et al. (2007), this technique is in the early

stages of development but offers hope of a low-cost means of mains

assessment.

In a recent article, Gordon (2004) described how a computer

program written by a mathematician without adequate understanding

of engineering had resulted in expensive repairs and several months

delay in commissioning of a scheme. This article highlighted the

dangers of subcontracting the hydraulic transient study based on

lowest cost, without determining whether the program was adequate

for the task and had a proven track record on other projects. The

client had not worked on a project of this kind for a few years and

experienced personnel were no longer available. In another instance,

Gordon (2006a) described how a high head turbine runner was fabri-

cated with an even number of blades with the corresponding number

of wicket gates also being even. The basic principle laid down back in

1941, that an even number of wicket gates should be accompanied

by an odd number of runner blades, had been lost. The result was

that a large number of blades were cracked after a couple of months

Introduction

in service, leading to an expensive repair job. The failure to appreciate

this long-established principle was attributed to the retirement of nine

engineers of long experience, and design being then left exclusively

in the hands of younger personnel all under the age of 30. Gordon

challenged industry to come up with a handbook containing recent

examples of projects and equipment.

A considerable body of literature exists on the topic of pressure tran-

sient analysis including texts which derive the basic equations of motion

and show how these equations can be used to develop practical

methods of computation for implementation on the digital computer.

The manner in which various system components, such as valves,

pumps and turbines for example, can be incorporated into the model-

ling process has also been described.

Many engineers new to the area of hydraulic transient prediction will

nonetheless have been exposed, at least in part, to the theory and

concepts underlying the models which they will be required to use in

conducting analyses of pipeline and tunnel systems. In this volume it

is not the intention to duplicate the material contained within these

existing texts to any appreciable extent but rather to describe and

examine a range of circumstances encountered during many years of

practice in this ﬁeld. This book should therefore be considered as

complementary to these other texts which introduced the basic

concepts and theories. Where equations are derived or introduced,

this has been done with the intention of adding to the description of

different aspects of pressure transient behaviour. Some programs have

the capacity to permit additional ‘modules’ to be added to facilitate

modelling of features which are not available in the original program.

One or two examples are given of less common features together

with relevant equations which may be used to develop extra modules

for inclusion in programs.

On occasion, hydraulic transient analysis of a pipeline system has

been left until the design and even construction process is well

advanced. Many factors such as pipeline route, pipe material and

diameter, and types of equipment such as valves may all have been

chosen on the basis of steady ﬂow analyses and prior to any considera-

tion of transient analysis and cannot readily be altered without ﬁnancial

penalty. Yet a transient investigation which demonstrates the need for

surge protection of a network can also be used to examine a variety of

different options which may include alternative pipeline routes, pipe

materials and diameter for instance, which may possibly show that

adoption of a particular pipeline conﬁguration may reduce or even

Pressure transients in water engineering

remove the requirement for surge protection. If understanding of

hydraulic transient behaviour generally were improved then an initial

transient analysis undertaken in parallel with study of steady ﬂow

behaviour, may yield savings in overall costs or some improvement in

network behaviour through selection of more suitable equipment.

Where preliminary investigations of a pipeline system have demon-

strated that unacceptable pressure surge behaviour is likely to

develop, differing philosophies may exist regarding how to control

these surges. The philosophy which is adopted may depend upon

whether one was brought up in what may be termed the American or

European school (McCrone, undated). Once a surge has developed

in a pipeline, American practice relies upon extensive use of special

surge control valves to limit or minimise the effect of these transient

pressure conditions. In contrast, the European approach is more

orientated towards prevention rather than cure, with emphasis on

avoiding the spread of unacceptable surging in the ﬁrst instance.

With the emergence of very large global engineering ﬁrms, perhaps

with employees from both traditions, it may be important to have

some understanding of these alternative approaches. Some considera-

tion has been given to application of surge control measures from

both sources.

This book is intended for engineers who are relatively new to the

topic of pressure surge analysis and has been written in the hope that

it will be helpful in avoiding some of the pitfalls that await. After consid-

ering the requirement for transient analysis and possible objectives of

such studies, consideration is then given to derivation of pertinent

equations. Two methods of analysis of hydraulic transient behaviour

are discussed. Equations derived from ‘elastic theory’ have been used

for purposes of illustration of transient phenomena throughout the

book and it has not been the intention to review other techniques of

analysis such as the impedance method or graphical approaches.

These alternative methods have been amply covered in existing texts.

The exception has been use of the ‘rigid column’ analogy which has

particular uses with regard to estimating preliminary dimensions for

pressure vessels and surge tanks.

Implementation of the ‘elastic equations’ is then considered with

discussion of alternative methods of numerical implementation on

the digital computer. ‘Boundary conditions’ are introduced covering

some of the more common features of pipeline systems.

Application of the ‘elastic’ approach to a simple pipeline, neglecting

the inﬂuence of pipeline resistance and gradient, is discussed. This is

Introduction

followed by a study of actual simple pipelines to highlight some of the

differences in behaviour which can occur.

A series of chapters is included in which the relative merits of alter-

native forms of surge protection are discussed together with case studies

of their application. Included are chapters on the behaviour of air and

gas in pipelines and the attendant dangers if even modest pockets of gas

are allowed to develop.

Problems associated with the selection of an inappropriate check

valve are considered and some guidance is given on choosing a valve

to suit a particular situation.

The volume concludes with consideration of some aspects of systems

which can produce departures of predicted conditions from observation.

Included is damping of pressure waves in ﬂexible pipes and also

ampliﬁcation of surge pressures either as a consequence of the system

conﬁguration or through development of a resonant condition. Case

studies based upon actual systems have been included to illustrate

some of these aspects of hydraulic transient behaviour. Some aspects

of hydraulic transient analysis have not been included in this volume

but are amply covered elsewhere. A case in point is modelling of

condensers of power plants, detailed discussion of which may be

found in the recent IAHR Synthesis Report (2000) which is the

result of two decades of study into the phenomenon of hydraulic tran-

sients.

Actual design ﬂows have been used in the majority of examples

throughout the book but where it was considered that a particular

phenomenon could be more clearly demonstrated, discharge conditions

have been allowed to vary to some extent from actual parameters.

Pressure transients in water engineering

Motivation for hydraulic

transient analysis

In times past when methods of analysis and materials were perhaps less

clearly understood than now or quality control was less exacting, a

relatively large factor of safety would be applied to any design. With

increasingly sophisticated computer modelling capabilities available

and with new materials available and a better understanding of these,

there has been a movement towards more detailed analysis and better

use of materials. Strengths of pipes and pipeline ﬁttings are of para-

mount importance in determining whether a design is safe and so this

chapter examines some aspects of pipe materials and allowable internal

pressures before proceeding to consider analysis of pressure transients in

pipeline systems. Also included is some mention of pipe linings as these

can have a bearing upon allowable pressures. Other aspects such as

trench conditions and ﬂexibility which can inﬂuence allowable pres-

sures will be considered at a later stage.

1.1 Primary purpose of analysis

Pipelines have been described as one of the arteries of modern civiliza-

tion and so protection of these is of great importance. The primary

concern underlying the majority of studies into unsteady ﬂow behaviour

in pipelines is to establish a safe operating environment. This usually

involves analyses designed to predict extremes of pressure, both

maximum and minimum, which may potentially develop within the

system during its operating lifetime and the probability of occurrence

of each extreme event. These extremes may be the consequence of

planned or accidental changes in ﬂow. A transient event can produce

pressures which exceed those maxima developed during steady ﬂow

and also pressures below the anticipated minimum steady ﬂow

pressures. Steady ﬂow is also taken to include static or no-ﬂow

conditions.

1.2 Secondary objectives

Additional information which may be required of a hydraulic transient

investigation can include operating times for equipment such as pumps,

turbines and valves, rates of ﬁlling or emptying of tanks and vessels and/

or necessary volumes of these tanks. Other pertinent information

relates to the timescale of the transient event, such as the time taken

for a steady ﬂow to become established following a pump start or the

time for quiescent conditions to develop after some change in ﬂow,

say after an alteration of valve setting. The analysis will also yield

parameters for the selection of suitable equipment such as self-acting

valves, for instance air valves and check valves, in order to avoid

unnecessary or unacceptable transient behaviour.

1.3 Permitted pressures

When considering maximum and minimum pressures, these must be

compared with deﬁned maximum pressures. These allowable pressures

are determined by the strength of the pipeline, by the nature of the

liquid being conveyed and possibly by the nature and characteristics of

any pipe lining. For example, a relatively brittle lining such as cement

mortar may crack if pipe deformation is too great. Any crack in the

lining will potentially allow pipe contents to attack the pipe wall itself.

1.4 Maximum pressures

Regarding allowable peak pressures these are usually deﬁned by the

supplier in accordance with codes of practice. For instance, with

respect to pipes the allowable maximum sustained pressure or long-

term pressure can be found in manufacturers’ literature. Likewise for

ﬁttings the permissible pressure is readily obtainable from suppliers.

1.5 Pipe materials

Pipes come in a range of materials each having particular strengths and

weaknesses, from cast iron, which has been in use for well in excess of a

century, to medium density polyethylene (MDPE) introduced little

more than 20 years ago. Analysis often has to be undertaken on pipeline

Pressure transients in water engineering

systems comprising a mix of old and new pipes and the properties of

both types are important as well as any deterioration in these over

time. Since pipeline systems will usually be in service for many years

and be subject to extension and upgrading, to suit changes in

demand for instance, an understanding of properties of older or even

historic materials must still be retained as some reanalysis is often

necessary to accommodate changes to a network.

1.6 Rigid pipes

1.6.1 Grey cast iron

One of the earliest materials was grey cast iron (CI), with the ﬁrst

recorded use being in 1455. Some of the cast iron pipes installed at

the Palace of Versailles in 1664 were removed relatively recently and

found to be in reasonable condition. Other pipes at Versailles are still

in service. Cast iron contains 3.5% carbon in the form of graphite

ﬂakes and the pipe is designed as a rigid structure under combined

loadings from earth pressure, trafﬁc, impact and transient pressures.

Various types of pipe joints have been provided including spigot and

socket, ﬂanged, rubber gasket and joints with locking devices to resist

longitudinal thrust. Unlined pipes are subject to tuberculation with

nodular granules frequently developed in corrosive waters. Continued

exposure results in a gradual reduction in carrying capacity. Cast iron

has been produced in several classes. Some details of ratings and test

pressures are given in Tables 1.1 and 1.2.

Table 1.1. Ratings and test pressures for various classes of cast iron

Nominal

internal

diameter

(mm)

Description Maximum working

pressure rating

including surge

Recommended

maximum site test

pressure

bar g mWG bar g mWG

80—500 Spigot and socket

centrifugally cast iron pipe

class 1

10 100 16 160

80—500 Spigot and socket

centrifugally cast iron pipe

class 3

16 160 25 250

80—200 Standard ﬁttings 12.5 125 20 200

mWG ¼metres water gauge

Motivation for hydraulic transient analysis

Cast iron fails catastrophically.

1.6.2 Asbestos cement

Asbestos cement (AC) as a pipe material was invented around 1930.

Pipes are usually manufactured in diameters up to 900 mm. Several

layers of asbestos ﬁbres are soaked in cement. Being entirely non-

conducting it was thought impervious to electrolytic corrosion although

being cement-based AC is susceptible to attack by acidic, soft or

sulphate-bearing waters and soils. Asbestos cement is a brittle material

which can fail catastrophically. Pressure may be deﬁned by pressure

classes B, C and D for pressure head ranges 61—122 mWG or alterna-

tively as shown in Table 1.3.

1.6.3 Concrete pipes

Concrete pressure pipes can be classed as rigid or semi-rigid depending

on design. Pipe design pressures will commonly be from 14.1 kgf/cm

This includes a 7.6 kgf/cm

transient pressure allowance. Large-

diameter prestressed pipes are produced by a few manufacturers and

are available in larger diameters of 700—1200 mm and for heads up to

180 mWG. These become relatively more expensive at pressures

>17.6 kg/cm

. These pipes tend to be heavy and may come in shorter

Table 1.2. Test pressures for various classes of cast iron

Nominal internal

diameter (mm)

Description Works proof test pressure

bar g mWG

80—500 Spigot and socket centrifugally cast

iron pipe classes 1 and 3

35 350

80—200 Standard ﬁttings 20 200

Table 1.3. Pressure classes for asbestos cement

Description Class

15 20 25

Test pressure (bar g) 15 (153 mWG) 20 (204 mWG) 25 (255 mWG)

Maximum working

pressure (bar g)

7.5 10.0 12.5

Pressure transients in water engineering

lengths thus requiring to have a larger number of joints. Unlike other

pipe types, concrete pipes cannot be cut to length. Compression-type

rubber gaskets are a fairly standard form of joint.

1.7 Flexible pipes

1.7.1 Ductile iron

Ductile iron (DI) is designed as a ﬂexible pipe and has largely replaced cast

iron. It contains 3.5% carbon in the form of spheroids or nodules and has

similar corrosion characteristics as cast iron. It is a ductile material with

strength characteristics more like those of steel. Large-diameter pipes

are designed to withstand external loads as well as internal pressures.

Minimum wall thickness assumes a factor of safety against collapse

under vacuum pressures and provides working pressure ratings of at

least 14.1 kgf/cm

þ 7kgf/cm

transient pressure allowance. Pipes may

be provided in diameters ranging to 1600 mm or more. Typically allowable

pressure falls with increasing diameter as illustrated by Table 1.4.

For cement-lined pipes allowable deﬂection is largely governed by the

need to avoid cracking of this lining. Suppliers will be able to provide

data on permitted deﬂections. In the case of Stanton Integral DI

pipes for example, the ratio of allowable vertical deﬂection  to

diameter D is expressed as a function of pipe size in Table 1.5.

Deﬂection can be obtained from the modiﬁed Spangler formula.

1.7.2 Steel pipe

Steel pipe is produced in various grades. Yield points are typically in the

range 1760—2950 kgf/cm

with still higher strengths available. Pipe

design for normal waterworks operations may use a working tensile

stress 50% of yield point stress. Typical diameters may range from

Table 1.4. Allowable pressures for various pipe diameters

Nominal internal diameter (DN)

80—300 350—600 700—1200 1400—1600

Test pressure

(bar g)

50 40 32 25

Maximum working

pressure (bar g)

40 25 25 25

Motivation for hydraulic transient analysis