Surge 10000 m Pipe Rasinari

7/31/2019 Surge 10000 m Pipe Rasinari

1/25

TITULO DEL PROYECTO (PROVINCIA)TIPO DE PROYECTO

CLCULOS HIDRULICOS

ANNEX N X.

SURGE CALCULATION

Referencia Obra ANEJO N X. Pg. n 1


2/25


CLCULOS HIDRULICOS

INDEX

AX.1.- INTRODUCTION

AX.2.- CCALCULATION CRITERIA

AX.3.- INITIAL DATA

AX.4.- OVERPRESSURE FROM SURGE DETERMINATION

AX.5.- SURGE WITH DEPRESSION

A X.6.- GRAPHIC REPRESENTATION OF SURGE

A X.7.- SECURITY DEVICES

A X.8.- TRANSIENT EVENT STUDY

A X.8.1.- INSTALLATION COMPONENTS

A X.8.2.- SIMULATION MODEL

A X.8.2.2.- Matemathical modelization

A X.8.2.3.- Numerical model: Characteristic's method

A X.8.3.- REPORTS AND CHARTS

A X.8.3.1.- Evolvent Pressures

A X.8.3.3.- Maximum and minimum pressures in profile points

AX.2.1.- SHUT DOWN TIME (T)

A X.8.3.2.- Installation reports

AX.2.2.- CELERITY (a)

AX.2.3.- SURGE (DH)

AX.2.3.1.- Short surge

AX.2.3.2.- Long surge

A X.8.2.1.- Initial conditions

A X.8.3.4.- Stationary regime chart

A X.8.3.5.- Transitory regime chart



3/25


CLCULOS HIDRULICOS

A X.1.- INTRODUCTION

Surge is a phenomenon of great interest due to the important repercussions that i t can have inpressure pipes. It consists of a pressure variation provoked by changes in the normal conditions of theflow parameters.

In this annex, we have listed the criterias used for calculating surge in a pipe and determined themaximum overpressure that can be reached according to the installation charactersitics. This data isaccompanied by graphic representations.

A great number of scientists have realised studies in order to develop mathematical calculations todescribe surge, the conclusions of which have been relied upon by numerous experts to continuestudying this phenomenon.

According to the results obatined, the adequate safety measures will be adopted.



4/25


CLCULOS HIDRULICOS

A X.2.- CALCULATION CRITERIA

where:

T:

C, K:

L:

V:

g:

Hm:

C = 1

C = 0

C = 0,6

Pumping length (m)

Acceleration of gravity (m/s2)

Manometric head (m.w.c.)

The coefficient C has been required experimentally and is function of the pipe pitch (Hm/L). Theadopted values can be:

Regime velocity (m/s). The formula is valid only for velocities bigger than0,5 m/s

A X.2.1.- SHUTDOWN TIME (T)

Stop time (s)

The shutdown time T is determined according to Mendiluces` expression:

Variable dimensionless coefficients

Following the sudden cut off of a pumping group where the velocity reaches zero, the so-calledshutdown time (T) occurs, producing the hydraulic transient event.

mgH

KLVCT +=

20,0Lm

H 1.500

where:

a:

D:

e:

Km:

Km

33.3

6.6

5.4

1

0.5Steel

Polyester

Asbesto-cement

Material

Coefficient depending on the material

The Km values depending on the pipe material are shown in the table below:

Pipe thickness (mm)

PVC

Cast iron

Celerity (m/s)

A X.2.2.- CELERITY (a)

Once the shutdown time (T) is known, the value of celerity (a), defined as the propogation velocity ofthe pressure waves for the water contained in the pipe, can be determined. For this calculation Allievihas deduced the following expression:

The coefficient K mainly represents the inertial effect of the pumping group. Its experimental values

may vary with the pumping length:

Interior diameter of the pipe (mm)

e

Dm

K48,3

9.900a

+

=



6/25


CLCULOS HIDRULICOS

where: H = overpressure produced (m.w.c.)

It is called short surge when:

A X.2.3.1.- Short surge

Once the shutdown time (T) values and the celerity (a) values are known, it is possible to determinethe maximum value of the overpressure produced in the pipe. Two cases are distinguished:

A X.2.3.- SURGE (H)

In this case, the Michaud expression is used for the calculation of the overpressure:

a

2LT >

gT

2LvH =D



7/25


8/25


CLCULOS HIDRULICOS

A X.3.- INITIAL DATA

Interior diameter of the pipe (mm) 204.5

Pipe thickness (mm): 22.7

Pipe material: HDPE

Pipe length (m): 10000

Maximum flow (m/h): 87.2

Fluid velocity (m/s): 0.74

Maximum geometric head (m): 218

Manometric head (m.w.c.): 247.64

A X.4.- OVERPRESSURE FROM SURGE DETERMINATION

1.00

Variable coefficient (C): 1.00

Coefficient depending on the material (Km): 33.3

Propagation velocity (a): 530.5 m/s

Stop time (T): 4 sec.

Crtical length (Lc): 1070.4 m

Overpressure produced (m.w.c.): 39.88

(LONG SURGE)

(Alievi formula)

Variable coefficient (K):



9/25


CLCULOS HIDRULICOS

Maximum overpressure in pump discharge (m.w.c.): 258

Maximum depression in pump discharge (m.w.c.): 178

With the surge value obtained we may calculate the pressures in the most unfavourable cases:

We can observe that a negative depression in the pump discharge has been obtained, therebysupposing a future danger for the pipe. In the following part, we will show the reasoning which justifiesthe "normality" of this data.

In this case, we obtained maximum values of overpressure and depression that are perfectly realisticfor the type of network designed and for the safety devices detailed below.



10/25


CLCULOS HIDRULICOS

A X.5.- SURGE WITH DEPRESSION

In most studies on the surge in pipes, it can be observed that the pressure value reached during asurge is less than the static pressure, while later, at the maximum depression moment right after theengine has shut down, the pressure in the pipe continues to be positive.

In a significant proportion of elevations (around 40%) which work perfectly in spite of the production ofdepressions, researchers have carried out experimental studies demonstrating that the excess pressure

is linked directly to geometric head, which is why the the depressions provoked by the engine shutdowncannot be very elevated.

In spite of these observations, i t is normal that contradictory results may be obtained from thecalculations carried out, as in our case, where the overpressure value is higher that the geometricalhead.

These vacuum bags separate the flow in two parts: one of them will continue in the same direction

while the possibility exists that the other will flow back downwards. As a consequence of the reflexion atthe extremity, these two flows may meet each other at inverse speeds, producing very highoverpressures.

Studies on cavitation are also important in understanding this phenomenon. Cavitation can be definedas the vaporization of a fluid that flows through a zone in which the pressure is sufficiently low, given itstemperature, as to actually produce a change in its condition from liquid to gaseous, forming vacuumbags or vapours, which disappear by condensation when they are translated to areas of higherpressure.

Nevertheless, it has been proved that water can withstand great descents below athmosphericpressure without changing its state. This implies that the pressure required for water to vaporize at thetemperatures usually encountered in the pumping system is so close to absolute vacuum that it is notpossible for cavitation to be produced with released air because the simple action of the unforeseenengine shutdown prevents it.



11/25


CLCULOS HIDRULICOS

mm Hg %

0 0

665 87

743 97.7

747 98.4

751 98.8

753 99.1

To illustrate the aforementioned, it is appropriate to make reference to some significant values

demonstrating the boiling points of water at different depressions and absolute vacuum.

50 92

17

1215

Taking this into account in the conduction that concern us, we calculate a vacuum of 631,8 mm Hg,which corresponds to 8,6 m.w.c. These values indicate a boiling point of water at this pressure taht isfar superior to the temperature actually present in the conduction.

Boiling Point Temps. ( C)

20

Absolute Pressure mm Hg Depression

100 760

In light of this information and the security mechanisms that are described later on, we can concludethat the installation is free of danger in the event that an instant shutdown is produced in the pumpinggroup.

V (cm Hg)=

10

5

9

6.2

P0.8

(m.w.c.)

The vacuum increase caused by a linear decrease in pressure must be exponential and not linear asusually considered. The expression relating negative pressures to vacuums is the following:

As we can see, the absolute pressures necessary for cavitation to occur in water at 10 to 15 degrees,temperatures that are usually encountered in pumping systems, stand at 9 to 12 mm Hg. Saidpressures correspond to depressions of 98,4 to 98,8 percent of absolute vacuum; almost no industrialmachine can reach such extreme values.



12/25


CLCULOS HIDRULICOS

A X.6.- GRAPHIC REPRESENTATION OF THE OVERPRESSURE SHUTDOWN

0

50

100

150

200

250

300

0 2000 4000 6000 8000 10000 12000

m

m

SURGE

Field line

Static head line

Maximum head in shutdown

Minimum head in shutdownManometric head line



13/25


CLCULOS HIDRULICOS

A X.7.- SECURITY MECHANISMS

-

-

-

Once the overpressure that the unforeseen shutdown of the pumping group could produce in theinstallation is calculated and represented, we can study the use of devices that are able to reduce andcontrol it.

Installation of a balance chimney, whose mission is to facilitate the oscillation in massof the water, eliminating the overpressure of shutdown.

It is possible to utilize numerous systems to achieve this objective; in this case, the following devices

are determined based on the elevation characteristics.

Due to the crucial influence of the shutdown time in the value of the surge, a flywheel isincorporated in the rotary part of the elevation group, the inertia of which will delayengine revolution loss and, as a consequence, increase the shutdown time of the water.

In many cases, the pipes have sufficient safety margins to withstand foreseen overpressure;nevertheless, sudden pressure alterations with wide oscillat ions causing quick material tensionvariations are not advisable for the good conservation of the pipes - for this reason, it is advisable touse some type of protection to lessen these maximum pressure oscillations.

This device achieves two objectives: the potential energy of the compressed air favourswater moving in an upwards direction inmediately after shutdown when it combines withthe cinetic energy of the water, meanwhile, in the backward phase it acts as a brake,absorbing most of the gravity energy. The result is that it favours mass oscillation, widelyobtained in chimneys, minimizing importance to the wave movement which can be verydangerous.

Fitting of an air container to the elevation pipe, consisting of a hermetical camera filled

partially with air which is compressed to the manometric pressure at the fitting point.



14/25


CLCULOS HIDRULICOS

-

-

-

-

-

-

Incorporation ofoptimizer pumping valves, which are automatic retention valves thatwork in combination with the start-up or shutdown of the pumps as well as in the case ofan eventual abrupt shutdown such as during an energy supply failure.

As an additional safety measure, check valves will be installed that prevent flow frommoving in a reverse direction to that established, thereby preventing the passage ofoverpressure waves originating at the end of the installat ion. In addit ion, in the lowersegment, they serve to unload the static pressure of the upper section.

Check valves with diferential by-pass that are made up of a main body that, inessence, is similar to those of ordinary retention.

Incorporation ofrelease valves or discharge valves which automatically and suddenlyallow the release of the necessary quantity of water so that the pipeline pressure doesnot exceed the limit.

One type of air container is the air bladder bumperof compressed air. It has the

advantage that since the air is enclosed inside a bladder, it cannot be be dissolved orescaped, provided that a good valve is used.

Placement ofair valves at the high points of the profile that open once the pressurereached is equal to the atmospheric one, accepting air inside the pipe to avoid theformation of vacuums.



15/25


CLCULOS HIDRULICOS

A X.8.- TRANSIENT EVENT STUDY

The evolution of the pressure transitories created in a conduction by disturbances that survive in aprogrammed or unexpected manner in one or several of its points can produce undesired effects thatcould ultimately have catastrophic proportions. For this reason, it is important to foresee these events inorder to prevent their effects.

As its name indicates, the package allows for the analysis of the transient event (surge) which occurs ina simple pipe (pumped and/or gravity) when one or more disturbance(s) divert the system away from itsstationary regime. The option of using the data bases incorporated in the package, the ability to easily

vary the type, location and / or characterist ics of various protection devices and the opportunity toreanalize the problem, allows us to develop a design work that yields one or more strategies from whicha choice based on non-technical criteria can be made.

For this simulation, we have used the computer package DYAGATS (Diseo Y Anlisis del Golpede Ariete en Tubera Simple - Design and Analysis of Surge in a Simple Pipe) developed in theMechanic Docent Teaching of Fluids of the Hydraulic Engineering and Environmental Department of thePolitechnic of Valencia (Spain), whose objective is precisely the aforementioned.

Computer simulation of the behaviour of such devices is an irreplaceable tool to elaborate the mostadecuate surge protection diagram.

Adequate protection elements and their location and behaviour must be carefully studied in order tokeep the installation safe at all times.



16/25


CLCULOS HIDRULICOS

A X.8.2.- SIMULATION MODEL

A hydraul ic transitory is analyzed by the combined solution of the equations that describe themanagement of the pressure waves inside the pipel ines and the equations that express the limitcondit ions or behavior of the devices that start and / or modify the disturbances. Specif ically, it is aquestion of solving the system described by the continuity and movement equations within the limitconditions of the system.

A pressurised pipe is composed of the following elements: the transported fluid, the pipelines thattransport it and the devices mounted in certain points of the installation that speed up or slow down therate of transportation by introducing or capturing energy from the system,. DYAGATS's aim is tosimulate the combined behavior of the fluid, pipelines (conductors) and devices in a simple pipeline.

A X.8.1.- INSTALLATION COMPONENTS

This simulation is obtained from the superimposition of the behaviour of each one of the elementspresent. The behaviour of each element comes described in physical-mathematics models that allow forthe numeric cuantification of the variables that characterise the behaviours.

The aim is to obtain a quanti tative description of the transitory by understanding the unkownfunctions, generally Piezometric Head H, Speed V or Flow Q, in the points of interest of the system(which is probably all of them) at the time in which the transitory turns out to be relevant.



17/25


CLCULOS HIDRULICOS

The calculation of the permanent regime or the initial stationary state is direct and can be preciselyobtained provided that the friction and pipeline losses are suitably represented. A program that perfomssimulations of transitories must include a calculation method for the initial condition, since it is thestarting point of the transitory.

Since this condition is, in general, a stationary condition, it can be described given the heights of thesystem nodes and the flow or speed in the lines. From the mathematical point of view, these valuesconstitute the initial condition for the integration process that is used to solve the system of differentialequations in partial derivatives that constitute the continuity and movement equations.

A X.8.2.1.- The Initial Condition

The transitory modifies a previous state of equilibrium (generally the permanent regime) and drives thesystem to another state of final "equilibrium". The initial equilibrium condition can be described in termsof various pressure values, piezometric heads, and speeds and flows which are necessary to know andwhich constitue the commencement point of the surge.



18/25


CLCULOS HIDRULICOS

H(x,0), Q(x,0) para 0


19/25


CLCULOS HIDRULICOS

These differential equations are easily integrated according to the curve characteristics, transforminginto a means of propagation for the information (disturbancies) from one moment to the next.

Therefore, the only alternative for the rigourous solution of the complete system is numeric analysis.Important numeric analysis techniques have only been efficient since the development of computers.

,characteristic curves , the partial derivative ecuation system turns into a total derivative ecuationsystem.

Amongst the numeric techniques employed to solve the problem that concerns us, - some of whichhave been developed very recently -, the most popular and widespread form is the classic method ofthe characteristics (CM).

Such curves, - that exist if the system is a hyperboloidal type - for the particular case of surge where V


20/25


CLCULOS HIDRULICOS

A X.8.3.3.- Minimum and Maximum Pressures in Profile Points

A X.8.3.4.- Stationary Regime Graphic

A X.8.3.2.- Installation Reports

A X.8.3.- REPORTS & GRAPHICS

A X.8.3.5.- Transitory Regime Graphic

In order to il lustrate everything referred to above and to show the results obtained, a series of graphics and reports provided by the I.T packet DYAGATS are included below:

A X.8.3.1.- Envolvent Pressures



21/25


CLCULOS HIDRULICOS

A X.8.3.1.- Envolvent Pressures



22/25


CLCULOS HIDRULICOS

A X.8.3.2.- Installation Reports



23/25


CLCULOS HIDRULICOS

A X.8.3.3.- Minimum and Maximum Pressures in Profile Points



24/25


CLCULOS HIDRULICOS

A X.8.3.4.- Stationary Regime Chart



25/25


CLCULOS HIDRULICOS

A X.8.3.5.- Transitory Regime Chart

Surge 10000 m Pipe Rasinari

Documents

Transcript of Surge 10000 m Pipe Rasinari