Analiza semnalelor tranzitorii caracteristice instabilităților din instalațiile hidroelectrice Analysis of transient signals characterizing the… [308284]

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Analiza semnalelor tranzitorii caracteristice instabilităților din instalațiile hidroelectrice

Analysis of transient signals characterizing the hydraulic instabilities in hydro power equipment

Autor: [anonimizat]: Conf. Dr. Ing. Diana Maria BUCUR

Conf. Dr. Ing. Cornel Eugen IOANA

Promoția 2017

Contents

Introduction …………………………………………………………………………….4

The issue ………………………………………………………………………………..5

Chapter 1: Water hammer and wave analysis

The Principle of water hammer …………………………………………6

Formula of the water hammer …………………………………………13

[anonimizat] ……………………….14

Effect of the closing time …………………………………….………..15

Effect of the head losses ……………………………………..…………17

[anonimizat] …………………………………..19

Water hammering effect in hydro power plant …………………………21

Surge tank in hydro power plant ………………………………..22

Use of surge tanks ………………………………………………22

Function or advantages of surge tanks ………………………….22

Types of surge tanks used in hydro power plants ………………23

Signal processing……………………….…………………………..…..25

Digital signal processing (DSP)…………………………………25

Signal sampling …………………………..…………………………..26

Domains ………………………………………………………..26

Implemantation …………………………………………………26

Wave analysis ………………………………………………………….27

Fourier Analysis ………………………………………………..28

Fast Fourier transform ………………………………………….28

Chapter 2: The experimental facility

2.1. The initial state of the facility…………………………………………….30

2.2. Increasing the length of the circuit ………………………………………31

2.3. Installation of the ribbon sensor …………………………………………34

2.4. Hardware and software ……………………………………………….…35

Chapter 3: Data processing

3.1. Scenarios …………………………………………………………….…..38 3.2. Description of the signals ……………………………………..…………39

3.2.1. Pressure signals ……………………………………………….…39

3.2.2. Electrical resistance signal (ribbon sensor) …………………….41

3.3. The celerity and hydroacoustic period ……………………………………42 Chapter 4: Signal processing

4.1. Test with the constant head equals to 130 cm …..…………….………..…45

4.2. Test with the constant head equals to 120 cm …..…..……………….……48

4.3. Test with the constant head equals to 110 cm …..…..……………………50

4.4. Test with the constant head equals to 100 cm…..…..……………………..52

4.5. Matlab code ………………………………………………………………54

Chapter 5: Conclusions and perspectives

Bibliograpy ……………………………………………………………………………58

Introduction

The name of the thesis is “Analysis of the transient signals characterizing the hydraulic instabilities in hydro power equipment” and the objective is to control the level of overpressure which the forced pipes are subjected during transients.

These experiments simulate the real life conditions of a hydroelectric power plant pipes and the pressure to which they are subjected with the help of the signals received from the pressure sensor.

In a hydroelectric power plant this method can be measure by having pressure sensors placed at the foot of the pipe and sensors for the opening and closing angle of the vanne.

The processing of the signals received makes it possible to find operating malfunctions (diagnostic) and furthermore to estimate the evolution of the anomalies of the hydraulic system (surveillance and prognosis).

This method is made to help and develop an automatic monitoring tool that allows detection of faults so that the preventive maintenance operations could be done.

The thesis has 4 chapters.

The 1st one is explaining the theory that I’ve used and it has 2 main subjects: the hydro part and the signals processing part.

In the 2nd chapter is presented the facility. The way how it is working and how I managed to put it into operation.

In the 3rd chapter I described the signals and the way I record them.

In the 4th chapter I analyzed the signals and I explained the method that I used (including coding).

In the 5th charter I presented the conclusions and perspective of this thesis.

The issue

From one (or more) reservoir(s), water is fed through a gently sloping (a network of) pipeline to a location overlooking the hydroelectric generating plant. From there, the water reaches the turbines through a pipe running down on an abrupt slope: the forced pipe. A chimney is used to stabilize the load at the start of the forced pipe by damping the large-scale oscillations that can occur in the hydraulic network.

The control valve in Fig. 1 is the most important maneuvering device of a hydroelectric plant. During the operating processes this valve is likely to be operated by the turbine speed regulator. These maneuvers can generate more or less violent transients in the fluid. In order to monitorize the loads which the forced pipes undergo during operation, they have been equipped with a relative pressure sensor located at the foot of the pipe, where the loading is the most important.

Fig 1. Schematic representation of a standard installation of a hydroelectric power plant with medium or high head.

One phase of operation is the turbine shutdown. When the turbine is stopped, the complete closing of the control valve generates a water hammer in the forced pipe. We then observe a succession of periodic oscillations of decreasing amplitudes. These oscillations characterize the free response of the system (resting fluid) between the reflection on the closure valve at the bottom of the pipe and a reflection at the top of the pipe.

Their frequency depends on:

– the length of the pipe between the control valve and the high reflection point;

– the elasticity of the steel piping.

The closing time of the control valve is calculated by the turbine manufacturer in such a way that the pressure in the pipe does not exceed a maximum safety value, referred to as Maximum Guaranteed Pressure (MGP). This parameter is set when the plant is put into function and then during periodic maintenance operations.

Chapter 1: Water hammer and signal processing

The principle of water hammer

For a design, the analysis is done for the worst case scenario which correspond usually to the complete stop of the flow, subsequent to the closure of a valve or the sudden stop of pumps due to a power break (as in a normal operating procedures, valves are slowly closed before pumps are switch off if not conttolled by a soft starter).

Fig 1.1.1. Schematic of the principle of water hammer[2]

When a valve is suddenly closed in the middle of a pipe linking two tanks, as illustrated above, the inertia of the upstream water column will create an overpressure at the valve by compressing the water and expanding the pipe before the water is stopped. This change in the water condition (increase in pressure and decrease in velocity) will then be transmitted upstream segment by segment. Similarly, the inertia of the down steam water column leaving the valve, will create a depression of the water and a contraction of the pipe. This depression can easily reach the vapour pressure and then create cavitation in the pipe. These phenomena are well known as water hammer.

The situation in the pipe upstream and downstream is opposite but similar. The downstream situation will be studied, as it is what is happening in the delivery pipe of a pumping station, the case that concerns us the most.

The water hammer is a cyclical phenomenon. Each cycle can be divided into four phases as represented below:

Before the valve is closed

A pressure P0 exists in the pipe. In this example, we ignore friction losses, so the pressure is constant throughout the pipe.

Fig. 1.1.2. Before the valve is closed[2]

Phase 1 (t between 0 and L/c)

At T0 the valve is closed. Due to inertia, a downstream wave begins to propagate along the pipe at a speed c. This wave will continue until it reaches the tank. In the depression zone, water is expanded and the pipe diameter is contracted, the speed of water is nil.

Fig 1.1.3. Phase 1 (t between 0 and L/c) [2]

At t equals L/c

The pressure wave will reach the tank after a time L/c. Then, water has no more speed and is depressurized all along the pipe. As the water in the tank has a pressure higher than the one in the pipe, a reversed flow will start and thus, the wave will be reflected.

Fig 1.1.4. At t equals L/c[2]

Phase 2 (t between L/c and 2L/c)

The pressure wave has been reflected by the tank and is being propagated always at a speed c, leaving behind a pressure equals to the initial pressure. As the pipe volume increases and water is recompressed; thus, to fill in this volume water has to flow from the tank into the pipe. Therefore, a flow is generated backwards from the initial flow at a same but opposite speed v.

Fig 1.1.5. Phase 2 (t between L/c and 2L/c) [2]

At t equals 2L/c

The pressure wave has reached the valve and the situation in the downstream pipe is now similar as the one in the upstream pipe before the valve closure. The pressure equals the initial pressure in the whole pipe and the speed of water is -v in the whole pipe. Thus, the wave will be reflected as an overpressure.

Fig 1.1.6. At t equals 2L/c[2]

Phase 3(t between 2L/c and 3L/c)

The overpressure is being propagated at a speed c. In the pressured zone, water is compressed and the pipe diameter is expanded, the speed of water is nil.

Fig 1.1.7. Phase 3(t between 2L/c and 3L/c) [2]

At t equals 3L/c

The pressure wave reaches again the tank after a time of 3L/c. Then, water has no more speed and is pressurized all along the pipe. As the water in the tank has a presure lower than the one in the pipe, a reserved flow will start and thus, the wave will be reflected.

Phase 4 (t between 3L/c and 4L/c)

The pressure wave leaves behind a flow at initial pressure. As the pipe is being contracted again and water decompressed, water must flow out of the pipe (towards the tank). Therefore, water will flow in its original direction and at its intial velocity.

Fig 1.1.9. Phase 4 (t between 3L/c and 4L/c) [2]

At t equals 4L/c

The wave reaches the valve and the wole pipe is under initial pressure and velocity. The pressure wave will be reflected and the whole cycle will begin with an underpressure wave travelling downstream.

Fig 1.1.10. At t equals 4L/c[2]

Thus, we can see that conditions (pressure and flow) are changing over time and along the pipe. The following charts illustrate the pressure situation over time for different point along the pipe. Those charts will help us to see if the over pressure exceed the maximum PN allowed for the pipe and if the underpressure might go below vapour pressure, breaking the water column with a cavitation pocket.

This cyclic phenomenon is mainly attenuated by the hydraulic losses, but can last for a long while if they are small.

In order to avoid that the over pressure will blow-up the pipe or that the depressure will collapse a plastic pipe, gasket or just suck dirt into the pipe through the leakages, it is important to be able to estimate the pressure through the time along the pipe.

In the following charts, head losses absorption and closure time are ignored. It will be shown afterwards which effect they have and how to take them in to consideration.

At the valve

Assuming an instantaneous closure of the valve at the time to, the pressure is instantaneously decreased by the inertia of the water column. Once the pressure wave comes back after having been reflected by the tank (after t=2L/c), the flow is reversed in the pipe. Thus, the valve has to "stop" the flow and is subject to an overpressure due to the inertia of the water column. The cycle will then start again after the pressure waves come back for the second time (t=4L/c).

Fig 1.1.11. At the valve[2]

At a third of the pipe

The pressure wave takes t=L/3c to reach this point, during this time the flow and pressure keep their initial values. Then the water will be stopped and the pressure will drop. The condition will be constant until the pressure wave comes back from the tank after t=4L/3c. It will then regain its initial pressure and have its flow reversed but of the same velocity as the initial flow. The pressure wave will then be reflected by the valve and come back after t=2L/3c stopping the flow. Therefore, the pressure will rise until the wave comes back from the tank where it will re-establish the initial conditions.

Fig 1.1.12. At a third of the pipe[2]

At two third of the pipe

If the situation is monitored at a point situated at two third of the pipe (between the valve and the tank), the phenomenon will be similar but the pressure peak periods shorter and the time with water velocity longer. Thus the first wave will come after two third of L/C, have the wave back after the same time and then have a reverse flow for two time two third of L/C, for the wave to reach the valve and come back.

Fig 1.1.13. At two third of the pipe[2]

In the tank

The pressure is constant, although the level will increase and decrease according to its diameter but this can be neglected. The velocity of the water at the entrance of the tank will be constant till the surge arrive after L/c, then it will be reversed for two time L/c before it find its original value.

Fig 1.1.14. In the tank[2]

An useful way to represent what is happening in the pipe through th time is shown in the attached chart.

In horizontal, the pipe length is given and in vertical, it shows the evolution through the time.

The arrows are showing the flow direction in the pipe.

The light spotted areas are the zone of the pipe with depression and heavy spotted area

with over pressure.

By following the dotted line at 1/3 or 2/3 of the pipe length, the pressure and the flow velocity of the previous charts can be figured out.

Fig 1.1.15. Phases in the pipe[2]

Formula of the water hammer

Joukowsky has shown in 1898 that the pressure surge in the water hammer is directly proportional to the initial water speed, the velocity of the pressure wave and the density of the water. This formula is only if there is no cavitation and not too much gas (air) in the water.

It should be noticed that the pressure surge is not dependent of the length of the pipe.

ΔP: pressure surge [Pa]

p: density of water [kg/m3]

Δv: variation of water velocity [m/s]

c: velocity of pressure wave [m/s]

Δh: head surge [m]

g: earth gravity

This equation is also valid for variation of water speed. It means that if the velocity will change of 10% the pressure surge will be of 10% of what it would be in the worst case.

The velocity of pressure wave depends on the Young's modulus of the pipe, the bulk modulus of water, the wall thickness and diameter of the pipe:

velocity of the pressure wave

Kwater: bulk modulus of water

Kpipe: Young's modulus of pipe

internal diameter of the pipe

wall thickness of the pipe

ρ: density of water -1000 kg/m3

Velocity of the pressure wave is close to the sound speed in the water (1450 at 10 °C) in "hard" pipes and can decrease quickly according to materials and thickness. The following table shows range of expected values for typical materials.

Tabel 1.2.1. Range of values of typical materials

The time taken by the wave to go to the tank and come back is given by the following equation:

Tr: return time of the wave

L: length of pipe

c: speed of pressure wave

Graphical methodology of Schnyder-Bergeron

Based on simplification of the water hammer equations, the Schnyder-Bergeron or characteristics methodology allows a rough graphical estimation of pressure surges and facilitates the understanding of the phenomenon in different situations. It can be used in quite complicate system and it was the methodology most used before the computer age.

Its principle is to follow an observer travelling through the system at the velocity of the pressure wave, as indicated by the red lines in the time / pipe length attached chart. If the observer crosses a pressure surge, its new condition (velocity / head) will be found by at the intersection of the characteristics (line with a slope c/g) and the known parameter.

For instance for a pipe connected to a tank with a given head (h0) facing a sudden closure of a valve with an initial velocity (v0) and with losses neglected.

In this basic case our observer will start from the tank at t=0 (C0), meet the surge at t=L/c/2 (B½) and reach the valve at t=L/c (A1). Then he will go back, crossing the surge at B1½ and reaching the tank at C2 and so on as represented by the red line.

In the characteristics graph, the point C0 represent the initial condition, this position will be kept till the surge is met then the new position will be the intersection of the characteristic line with the known velocity (V=0) thus allowing to find the depressure value (cv/g) for the position A1. This condition will be kept until the wave back is met (B1½), then the new position (C2) will be the intersection of the characteristic line but with a negative slope and the known head (the tank level as losses are neglected). The same is done to find A3 and C4 bring the observe back to the initial position.

Fig. 1.3.1. Characteristic graphs for a sudden closure without head losses[2]

Effect of the closing time

The closure time (Tc) is the time during which the flow varies. For example, in the case of a power cut, the pump will not stop instantaneously but will gradually reduce its flow depending on its inertia and water pressure.

Similarly, valves need some time to be closed. The way the flow is reduced is usually not linear, for instance, gate valves have their flow reduced mainly during the last 20% of the closure run. The attached chart is showing the actual flow reduction according to the closure run for a gate valve, a butterfly valve and a linear globe valve.

Fig. 1.4.1. Closing characteristics of vannes[2]

Thus, the wave front of the pressure surge will depend on the closure characteristic and speed. Without this information the over and under pressure along the pipe cannot the properly defined as it will be illustrated in the section about envelopes for pumping stations.

Fig. 1.4.2. [2]

Front wave of linear Front wave of gate

globe valve closure valve closure

The charts below show the pressure and velocity over time at the valve and in the middle of the pipe for a instantaneous closure (Tc = 0) in blue, a quick closure (Tc = Tr/6) in green and a slower closure (Tc = 4Tr/6) in red.

At the pipe

The pressure surge is attenuated in the quick and slower closure case but in the maximum pressure is not changed. The velocity, once the valve is closed, remains zero.

Fig. 1.4.3. At the pipe[2]

At the middle of the pipe

As at the valve level, the quick closure has not much effect on the pressure surge, but with the slower closure the pressure surge is reduced.

Fig. 1.4.4. At the middle of the pipe[2]

Effect of the head losses

Influences of head losses in the water hammer phenomena are complex and difficult to calculate, but their consequences might be quite important and not very intuitive. In this section, the effect of the phenomena will be roughly explained and a simplified way to calculate the attenuated pressure surge will be explain.

In the following explanation, it is assumed that the valve is instantaneously closed so that the front wave of the surge is strait.

Fig. 1.5.1. Visualisation of the head losses[2]

These illustrations show the difference of a system where the head losses were neglected (in dark blue/red) and a system where they were taken into consideration (in light blue/pink).

At the initial time (t0) at the valve, the difference between the heads values (illustrated by the dark blue and light blue lines) are the losses. Right after the closure, both will drop of the same value – h. In the case with losses neglected, the pressure will stay constant until the return of the surge and will be constant along the pipe, from the valve until the tank.

In the second case, the pressure will be constant throughout the zone under depressure but will decrease slowly over time (as illustrated by the blue colour becoming darker in the pipe distance chart) till it reaches the same depressure as with losses neglected just before the return time (2L/c). This reduction of pressure is due to the fact that the head surge, getting closer to the tank, will be more important, inducing in the pipe a small flow that will keep a the pressure constant throughout the depressure zone at a given time. This flow is constant at a given place during the depressure time but is increasing along the pipe, passing from zero at the valve to its maximum (vrt1) just before the tank. This phenomenon is not at intuitive and clearly not respecting the Bernoulli's law specifying that the flow along a pipe is constant. Thus, when the surge is reflected at the tank, as the velocity is not nil there, the reflection velocity will be reduced of twice this remaining velocity (as illustrated in the velocity / time chart.

It is important to notice that the first negative surge was not attenuated by the head losses.

In the reversed flow zone, the flow is this time following the Bernoulli's law, as it is the same through out the pipe, increasing slowly over the time, until the surge arrives for the second time from the valve. Thus, a new gradient of pressure is created in the pipe due to the headlosses (as illustrated with the white to light blue colour in the reverse flow zone).

In the overpressure zone, the situation will be similar as the one described for the under pressure, but as the maximum velocity of the reverse flow is smaller than the initial velocity, the maximum over pressure (at t=4L/C) will be these time smaller then in the system where head losses were neglected.

Fig. 1.5.2. Representation of the head losses[2]

Thus we can see that the first depressure is not attenuated at the valve but is gradually attenuated along the pipe till a value of hlosse/2 at the tank. Then the over pressure is much more attenuated from the valve till the tank. The graphical methodology gives us rather good approximations for the attenuations of the first circle of depressure (illustrated in the previous page chart), if the head losses are not too important, slightly over estimating them.

hv-att: attenuation of head surge at the valve [m]

velocity of pressure wave [m/s]

kLP: friction coefficient [-]

vin: initial velocity [m/s]

earth gravity [m/s2]

vrt1: remaining velocity at the tank [m/s]

ht-att: attenuation of head surge at the tank [m]

Speed of pressure waves in non-rigid pipes

In practice the pressure rise may be sufficient to deform the pipe, increasing its cross-section. The pipe itself absorbs strain energy and reduces the speed of the pressure wave.

To include the area-change effects in the continuity equation we need to relate the change in cross-sectional area to the pressure rise. Formally, the internal pressure is balanced by an increased circumferential (”hoop”) stress, which is related to the change in diameter and thence the change in area by the elastic propierties of the pipes.

Fig. 1.6.1. Forces in a non-elastic pipe[1]

From the diagram, an increase in pressure Δp induces a hoop of stress σ. If D is the internal diameter of the pipe and t is the wall thickness then, equating forces pe unit length:

(6)

But, stress = Young’s modulus * strain

So that (7)

This is the fractional change in diameter. We requaired the fractional change in area. From the geometry:

=> =>

Hence,

(8)

Fig.1.6.2. Representation of the equations in the pipe[2]

The pressure change across the shock is still given by Δp=ρcu (consider the acceleration of fluid on the centreline) but continuity must account for the change of cross-sectional area:

(9)

Dividing by :

(10)

Hence, using (from momentum), (from compressibility) and (from elasticity):

(11)

whence:

(12)

For convenience, and by comparison with the rigid-pipe limit, we write this as

(13)

in term of an effective bulk modulus K’.

Pressure wave speed in non-rigid pipes:

(14)

Where the effective bulk modulus K’ is given by:

(15)

We will use the formula given by Korteweg in 1878:

(16)

Where CR – celerity of the thermodinamic sound

C – celerity of the real sound

ρ – volumic mass of the fluid

E – Young’s module

D – interior diameter

e – thickness

Water hammering effect in hydro power plant

When the load on the generator is reduced suddenly (load throw-off), governor closes the turbine gates and thus create an increase in  pressure on the penstock. This may result in water " hammering effect" and may require pipe of extra ordinary strength this pressure, otherwise the penstock may burst. To avoid this positive water hammering pressure some means is provided to take the rejected flow of water. This can be achieved by providing small storage reservoir or tank to accommodate this rejected flow. This small storage reservoir is surge tank and located close to the power station. When the turbine gates suddenly opens due to requirement of more water due to increase in the load demand on the generator, water has to rush through the pipe (penstock) and there is a tendency to cause a vacuum in the pipe supplying the water.
The pipe supplying the water must withstand the high pressures caused by the sudden closing of the turbine gates (known as positive water hammer) and there should not be any vacuum in the pipe line when the gate suddenly opens.
The water hammering is defined as the change in the pressure rapidly above or below normal pressure caused by sudden changes in the rate of water flow through the pipe according to the demad of the prime-mover. The water hammer occurs at all the points in the penstock between the forebay or surge tank and the turbine because of the sudden changes in the demand of the water during the load fluctuations.

Fig. 1.7. Hydro Power plant sketch

Surge tank in hydro power plant:

Surge tank is an open tank which is often used with the pressure conduit of considerable length. The main purpose of providing surge tank is to reduce the distance between the free water surface and turbine thereby reducing the water hammer effect on the penstock and also and also protecting upstream tunnel from high pressure rises. Surge tank also serves as a supply tank to the turbine when the water in the pipe is accelerating during increased load conditions and as storage tank when the water is decelerating during the reduced load conditions. Surge tanks are generally built high enough so that the water cannot overflow with a full load on the turbine.

Use of surge tank:

When load demand on the generator decreases, it leads to rise in the water level in the surge tank. This produces a retarding head and reduces water velocity in the penstock. The reduction in the velocity to the desired levels, makes the water in the tank to rise and fall until oscillations are damped out.

When load demand on the generator increases, governor opens the turbine gates in order to allow more water flow through the penstock to supply the increased load demand thereby creating a negative pressure or vacuum in the penstock. This negative pressure in the penstock creates necessary acceleration force and is objectionable for very long conduits due to difficult turbine regulation. Under this condition additional water flows from the surge tank. As a result the water level in the surge tank falls, an acceleration head is created and flow of water in the penstock increases.

Thus surge tank helps in stabilizing the velocity and pressure in the penstock and protects penstock from water hammering and negative pressure or vacuum.

Function or advantages of surge tanks

The functions of the surge tank are listed below:

It reduces the distance between the free water level of the reservoir  and turbine and also reduces the intensity of the water hammering in the surge chamber to such an extent above the water hammering effect can be neglected in the design of the tunnel. Only relatively short length of the conduit (penstock) below the surge tank must be designed to withstand the water hammering effect

Other function of surge tank is that it acts as relief valve when the load on the turbine is reduced and the pressure in the pipe suddenly increased by diverting the main conduit flow partly into this tank. The water level in the tank rises until it exceeds the level in the main reservoir thus retarding the main conduit flow and absorbing the surplus kinetic energy

The tank acts as a temporary reservoir during increased load demand on the turbine. It provides sufficient water to enable the turbine to pickup the new load quickly and safely and to keep it running at the increased load until the water level in the surge tank falls below its original level. Sufficient head is created thereby to accelerate the flow in the penstock until it is sufficient to meet the new load demand

Types of surge tanks used in hydro power plants

The main and the general types of surge tanks are:

Simple surge tank

Simple surge tank is a simple vertical pipe which is connected to penstock which supplies the water to the turbine generator. The surge tanks are built in high enough so that the water cannot overflow even under full load condition on the prime mover. Some cases the surge tanks can be over flowed to reduce the high pressure but this is not economical to use. Under some circumstances where there is no suitable space to construct high tank, the high of the tank should be increases with some support to obtain the required pressure at the inlet of the turbine.

Fig. 1.7.4.1 Simple Surge Tank

Inclined surge tank

When the tank is inclined to the horizontal its effective water surface increases and therefore lesser height surge tank is required of the same diameter. If the high tank is used the diameter can be reduced for the same purpose. So the occupied space is less when inclined surge tank is used. But this type of tank is more costly than the normal surge tank. It is rarely used tank, mostly used when the topological conditions are in favor.

Fig. 1.7.4.2. Inclined surge tank

Gallery type (Expansion Chamber type) surge tank

This type of surge tank has an expansion tank at top and expansion gallery at the bottom which reduces the extreme pressure surges at the inlet of the turbine. In erecting this type of tank the care should be taken to the upper expansion chamber up above the dam level and lower gallery tank below the dam level.

Fig 1.7.4.3. Expansion chamber type

Restricted orifice surge tank

This is also called as throttled surge tank. This tank contains a throttle or orifice before the surge tank. The main objective of this orifice is to provide a friction loss when the water is flowing to or from the tank. When the load demand on the turbine is reduced, the water enters through the surge tank orifice which provides a friction to the water and hence the pressure surge of the water reduces. The size of the orifice can be designed according to the retarding head that it has to build in conduit. Normally the size is calculated by the amount of rise of the water in the surge tank when the gate valve is closed.

Fig. 1.7.4.4. Restricted orifice surge tank

Differential surge tank

A differential surge tank has a riser with a small hole at its lower end through which the water enters when the surge rises. In this way the surge pressure can be minimised at the prime mover inlet.

Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements. For example, signal processing techniques are used to improve signal transmission fidelity, storage efficiency, and subjective quality, and to emphasize or detect components of interest in a measured signal.

Digital signal processing (DSP)

Digital signal processing (DSP) is the use of digital processing, such as by computers, to perform a wide variety of signal processing operations. The signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency.

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech signal processing, sonar, radar and other sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control of systems, biomedical engineering, seismic data processing, among others.

Digital signal processing can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, and spatio-temporal domains.

The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression. DSP is applicable to both streaming data and static (stored) data.

Signal sampling

The increasing use of computers has resulted in the increased use of, and need for, digital signal processing. To digitally analyse and manipulate an analog signal, it must be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization and quantization. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding real numbers to integers is an example.

The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal. In practice, the sampling frequency is often significantly higher than twice that required by the signal's limited bandwidth.

Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an analog-to-digital converter (ADC). The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a digital-to-analog converter (DAC).

Domains

In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wave domains. They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is, the frequency spectrum.

Implemantation

DSP algorithms have long been run on general-purpose computers and digital signal processors. DSP algorithms are also implemented on purpose-built hardware such as application-specific integrated circuit (ASICs). Additional technologies for digital signal processing include more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors.[3]

Depending on the requirements of the application, digital signal processing tasks can be implemented on general purpose computers.

Often when the processing requirement is not real-time, processing is economically done with an existing general-purpose computer and the signal data (either input or output) exists in data files. This is essentially no different from any other data processing, except DSP mathematical techniques (such as the FFT) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. For example: processing digital photographs with software such as Photoshop.

However, when the application requirement is real-time, DSP is often implemented using specialized microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixed-point arithmetic, though some more powerful versions use floating point. For faster applications FPGAs might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate.

Wave analysis

Historically, wave analysis is a new method, even if its mathematical foundations are based on the work of Joseph Fourier in the 19th century. J. Fourier laid the foundations in his theory of frequency analysis, which is one of the most important and influential methods of signal processing.

The first mention of the term "wave" was made by Alfred Haar in his thesis in 1909. It was introduced in the mathematical language by Jean Morlet in the early 1980s.

A wave is a waveform of fixed duration of zero average. Compared to the sinusoids, predictable waves of infinite duration, which form the basis of the Fourier analysis, the waves are irregular and asymmetric.

Fig. 1.9.1. Comparasion between sine wave and wave[3]

Fourier analysis decomposes a signal into components of sinusoidal shapes at different frequencies. In the same way, wave analysis decomposes a signal in different delayed and changed scale versions of a wave called wave-mother.

Looking at the signals in Fig. 1.5.1, it can be seen that signals with sharp transitions can be better analyzed with waves than with sinusoids.

To better understand the wave analysis, a signal processing with the existing methods will be made in the following chapter.

Fourier Analysis

As has been seen previously, the Fourrier analysis decomposes a signal into sinusoidal components of different frequencies. This method can also be seen as a mathematical technique that transforms the temporal representation of a signal into a frequency representation. The Fourier transform is written mathematically in the following way:

(17)

A temporal and frequency representation of a signal is given in Fig 1.5.2.

Fig. 1.9.1. Fourier Transform[3]

For signal processing, Fourier analysis is essential because the frequency content of most signals is of great importance. However, the Fourier analysis has the great drawback that with the transformation in the frequency domain we lose the information in the temporal domain. More precisely, if one looks at the frequency representation of a signal, one can not determine when a local phenomenon or discontinuity has taken place.

If the signal does not change too much in time, that is to say if the signal is stationary, this drawback is not very important. However, most real signals, interesting, contain non-stationary and transient parts whose presence reflects the manifestation of phenomena and information. However, these very important non-stationary parts can not be detected by using Fourier analysis.

Fast Fourier transform

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N2 to 2NlgN, where lg is the base-2 logarithm.

FFTs were first discussed by Cooley and Tukey (1965), although Gauss had actually described the critical factorization step as early as 1805 (Bergland 1969, Strang 1993). A discrete Fourier transform can be computed using an FFT by means of the Danielson-Lanczos lemma if the number of points  is a power of two. If the number of points  is not a power of two, a transform can be performed on sets of points corresponding to the prime factors of N which is slightly degraded in speed. An efficient real Fourier transform algorithm or a fast Hartley transform (Bracewell 1999) gives a further increase in speed by approximately a factor of two. Base-4 and base-8 fast Fourier transforms use optimized code, and can be 20-30% faster than base-2 fast Fourier transforms. prime factorization is slow when the factors are large, but discrete Fourier transforms can be made fast for N=2, 3, 4, 5, 7, 8, 11, 13, and 16 using the Winograd transform algorithm.

Fast Fourier transform algorithms generally fall into two classes: decimation in time, and decimation in frequency. The Cooley-Tukey FFT algorithm first rearranges the input elements in bit-reversed order, then builds the output transform (decimation in time). The basic idea is to break up a transform of length N into two transforms of length N/2 using the identity:

The DFT, like the more familiar continuous version of the Fourier transform, has a forward and inverse form which are defined as follows:

Forward Discrete Fourier Transform (DFT):

Inverse Discrete Fourier Tranfsorm (IDFT):

The transformation from xn→Xk is a translation from configuration space to frequency space, and can be very useful in both exploring the power spectrum of a signal, and also for transforming certain problems for more efficient computation.

Chapter 2: The experimental facility

2.1. The initial status of the facility:

Fig 2.1.1. The initial status of the facility

The facility was composed of a reservoir, a tank, a pipe to connect them with two pressure sensors, two valves, a recorder to receive the signals and a PC.

The reservoir was upper than the tank because the water was flowing under the influence of the gravity force. Also, the pressure sensors and the valves were at the same level on the pipe.

The way of operation was simple, the reservoir was filled and all the valves were closed at the beginning an the were open. The pressure was checked to see if all the facility can reproduce the same situation as the ones in the real life. After that, the valves near the sensors were open and closed, each, to see how the wave propagation can be seened on the PC.

The facility was working good, there was no technical problems encountered during the tests.

After analysing the singnals received, and calculus made (see chapter 3), we found that the lenght of the pipe was too short to analyse the hydroacoustic period. The pipe that was used was aproximately 2 metres and because of that, the time for the wave propagation was too short (approximately 0.099 sec with a frequency of 10 Hz).

So, after that, we decided to increased the length of the pipe by adding a rubber pipe. The new pipe that we add was around 10 meters and was placed near the reservoir, in order to keep the dimension off the whole facility.

The pressure sensors:

The pressure sensors of the PS series operate with piezo-resistive ceramic measuring cells. The ceramic diaphragm is unbalanced in proportion to the pressure applied. Depending on the sensor type, the voltage produced is made available either as switching or analog output signals. Non-rotatable and rotatable sensors, numerous thread types, front-flush od dead-zone free diaphragms and an accuracy of 0.5% of full scale guarantee highest flexibility and safe process interfacing.

The pressure sensor have a reading of adjusted values without tool, recessed pushbutton and keylock for secure programming and permanent indication of pressure. By having this, I could check is the received data is valid or not.

2.2. Increasing the length of the circuit

The facility was composed of:

1 cylindric tank made of plexiglas (reservoir) (h = 150 cm; Di = 38 cm; t = 1 cm)

1 rectangular tank made of plexiglas (L = 200 cm; h = 100 cm; l = 100 cm)

1 rubber pipe (Di = 80 mm; L = 10 m; t = 5 mm)

1 plexiglas pipe

1 ball valve (pump)

1 ball valve (pipe)

1 butterfly valve

1 pump (KSB, φ = 128mm; v = 1m/s2; n =1472min-1; H = 5m)

2 pressure sensors (Turk)

4

Fig. 2.2.1 The facility after adding the 10m pipe

In the Fig. 2.1.2.1. we can see that the facility was quite big, in total ocupies almost 5×5 meters, like the size of a room. For this reasons, the adding of the pipe was made around the reservoir to save some space. The material we choosed was rubber reinforced with metal circles.

Also, the sealings at the ends was a problem, because the pipe was not rigid, neither elastic, so we had to order connection that could made tightness possible.

Before, the water was flowing from the reservoir (1) directly through the plexiglass pipe (4) into the big tank (2). After, we add the green pipe (3) that is connecting the reservoir and the plexiglass pipe, where is placed the second pressure sensor (9.2) between the two vannes, but more closer to the ball vanne (6).

The first pressure sensor (9.1) was positioned near the discharge of the reservoir and before the connection with the rubber pipe (3). At the bottom of the tank there is an output for the pump (8) that is situated under the left side of the reservoir. The pump is reintroducing the water back in the system near the connection of the rubber and plexiglass pipes, by having a vanne (5) which facilitates the flowing. On the plexiglass pipe there is another vanne (7) used to control the flow.

An aditional small pump was used to refill the resevoir easily. The pump was immersed in water and could filled the reseservoir with a hose through which was connected.

The circuit of the water is simple: starting from the reservoir, flowing through the green pipe and through the transparent pipe after ending into the tank. The recirculation was done by the pump.

Fig. 2.2.2. Sketch of the facility

Furthermore, more add-ons were made. The reservoir needed to be scale in order to measure the head of the water. The distance between labels is 10 cm with a mark between them at 5 cm.

Fig. 2.2.3. Scaled tank

The reservoir was big, considering the dimensions of it (height = 150 cm; interior diameter = 38 cm; thickness = 1 cm). The volume is:

What was important is the shape of the reservoir. The fact that is tall and thin helped me to take measurements at different heights.

The reservoir is suspended on a metal frame having the discharge at the same level with the discharge of the pipe. This required that the level of the reservoir should be above and near the rectangular tank.

The ball vanne

The vanne is “The practical one” ball vanne, type 375 from GF company. The range of uses starts from simple water applications to basic applications in water treatment. The 375 ball valve has been designed for easy maintenance and a long service life. And because it is so compact, we choose it because it was easy to install and remove from the piping system.

For the vanne there is need low maintenance with tool integrated in lever.

Fig 2.2.4. Flow diagram

2.3. Installation of the ribbon sensor

In order to measure the closing angle of the vanne it was needed a potentiometer to be installed. Considering the positioning of the vanne and it’s shape, the only reliable solution was to have a ribbon sensor because of the small dimensions and the flexibility of it that allowed me to wrap it to the main body of the vanne as it can be seend in the following figure:

Ribbon sensor

Rubber hose

Fig. 2.3.1. Position of the ribbon sensor and rubber hose

The Handyscope HS4 can measure different signals. This gave me the possibility to install a potentiometer that helped me to find the closing angle of the vanne.

The ribbon sensor:

The ribbon sensor was placed under the lever, on the frame of the vanne. A cursor was made attached to the lever of the vanne, so, the movement of it could be translated to the sensor.

The ribbon sensor is basically a nominal 10K resistance across the two outer leads. The middle pin resistance with respect to either of the outer pins changes depending on where on the strip one presses. When no pressure is applied, the middle pin floats, so we use some sort of weak pullup, such as 100 kΩ.

Fig 2.3.2. Ribbon sensor

The rubber hose:

The rubber hose is connecting the pipe and the pressure sensor that is near the vanne.

When the vanne is closed, a mechanical shock its produced and the pressure sensor might be influenced by that. To minimize this shock, I installed a hose made of rubber, to have some elasticity that can reduce the errors.

2.4. Hardware and software

2.4.1. The hardware

The hardware part was components by three essential:

Handyscope HS4

U-I Converter

PC and laboratory workstation

U-I Converter

PC Handyscope HS4

Fig. 2.4.1.1. Hardware and software

The Handyscope HS4 is a powerful computer controlled USB oscilloscope that features four imput channels. The Handyscope HS4 oscilloscope features a user selectable 12 bit, 14 bit or 16 bit resolution (14 bit effective, SNR 95 dB), 200 mV to 80 V full scale input range and 128 Ksamples record length per channel. Four Handyscope HS4 oscilloscope models are available, with a maximum sampling rate of respectively 5 MHz, 10 MHz, 25 MHz or 50 MHz on all four channels simultaneously.

The converter transform the signal received U-I so that can be translated to oscilloscope. The connection diagram of the converter is shown below:

Fig. 2.4.1.2. Diagram of the U-I converter

The connection:

Every pressure sensor was connected to the U-I converter and from there to the Handyscope HS4. For the first pressure sensor I used the channel no. 1 and for the second pressure sensor I used the channel no. 2. The connection to the PC was possible with a USB wire.

In this moment was needed the closing angle of the valve. A solution was to buy a valve with the indication of the closing angle or to install a potentiometer to measure it. I chose the second option because was easier and cheaper.

The software:

The software used to view the signals on the PC was LibTiePie and it is under the license of TiePie engineering. The program is easy to use and has a friendly interface.

It’s offering the possibility to combine and synchronizing multiple instruments with many input signal.

With the help of the spectrum analyzer it can be graphically displayed the signal amplitude against frequency, in the frequency domain. It’s showing which frequency components are present in the signal and how strong can be.

The software gave me the possibility to see fully configurable graphs, with multiple displaying of the measurements that I’ve take and to process each of them.

Also, there are a large variety of mathematical operations like adding, multiplying, dividing, etc. Combining these mathematical processing blocks gives a lot of opportunities in constructing complex mathematical operations to analyze the measurements and obtain all the information from the data.

To be converted and to apply signal processing I used a code in Matlab 2016 (see chapter 4).

Fig. 2.4.1.3. Interface of the TiePie software

To analyze all three signals I used 3 different channels to display the graphs. In Fig 2.4.1.3. can be seen the three lines with different colours.

The green line belongs to channel one that its connected to the first pressure sensor (9.1 in the fig. 2.2.1) that is situated near the vanne. The blue line belongs the channel two and its connected to the other pressure sensor (9.2 in the fig. 2.2.1) that is situated at the discharge of the reservoir.

The yellow line belongs to channel three and its connected to a different sensor then the others two, more precisly to the ribbon sensor but can be displayed on the same screen with the others signals.

The software allows me to set the numbers of samples and the frequency, in this way I can see the period that I want to analyze:

(17)

T = time [sec]

n = sample [S]

f = frequency [Hz]

Ussualy, the time for the trials were around 20 seconds, so the number of samples that I used was 5 kS and the frequency was 256 Hz.

Chapter 3: Data processing

Scenarios

For a better understanding of the phenomena, different scenarios was applied regarding the closing time of the vanne or the head level of the water from the reservoir.

Three speed of closing the ball vanne:

Slow (<0,75V);

Medium (0,75V – 1,75V);

Fast (>1,5V).

Remark: This is a hypothesis, furthermore we will see that the speed of closure will be determined by calculus

Two ways of taking signals regarding the head level:

Different level;

Same level.

Fig. 3.1. The facility and the aditional pump for keeping the head level constant

Description of the signals

Pressure signals

The pressure signals were taken by the two pressure sensors. The first one that is placed near the openning vanne and the second one that is placed near the discharge from the reservoir.

Fig. 3.2.1.1. Exemple of a signal

In fig. 3.2.1. is an exemple of a signal recorded at the head level of 120 cm with a drop of 5 cm. The speed of closure of the vanne was slow.

Remark: This is a signal after applying the Matlab code and is not directly taken from the TiePie software, but they are showing the same wave.

On the horizontal axis is the time axis measured in seconds [s]. On the vertical is the voltage axis measured in volts [V] but this is only for exemplification, furthermore, the analisys will be done in kilopascals [kPa] as we will see in this chapter.

Pstat: the hydrostatic pressure – is the pressure when nothing is happening; the vanne and the pump are closed and the water is not flowing through the circuit.

This pressure can be easily calculated with the formula:

(18)

On the signal it can be seen as the straight line with small fluctuations from the beginning. Here, there is no transient and the pressure is constant.

Pmin : the minimum pressure – is the pressure when the vanne is partially or fully opened and the water is starting to flow untill the vanne is closed (the minimum peak)

When the vanne is opened, the pressure begins to decrease, due to head losses into the pipe system. Then, a miminum is reached, because the pressure will start rising when the vanne will be closed.

Pmax: the maximum pressure – is the highest pressure that the system can reach (the maximum peak)

The value is reached due to the propagation of the waves (water hammer)

Pmin and Pmax are very important because we can determine the time of rising:

Trising: time of rising – the closing time of the vanne.

The time between the mimimum an the maximimum peak.

The bigger the difference is between the mimimum and the maximum peak, the dangerous it is. Having a small time of rising its means that the vanne was closed quickly and very distant peaks.

Fig 3.2.1.2. Comparasion between a slow and a fast closing time of the vanne.

As we can see in fig 3.2.1.2., in the left graphic is a vanne that is slowly beeing closed. We can observe that by looking at the voltage scale and the difference between peaks that is aproximately 1 volt.

On the other hand, in the right graphic is shown a vanne that is quickly closed. The difference between peaks is more than 4 volts.

Also, the time of rising is different and the slope is sharper when a vanne is closed quickly.

Thydro – period of oscillation

After closing the vanne, the pressure drops and rises untill it becomes constant. These are the transient waves. In the circuit, the water goes back and forth due to pressure fluctuation.

The damping time consists of several Thydro (periods of oscillation) untill it becomes constant.

Electrical resistance signal (ribbon sensor)

This signal is recorded by the ribbon sensor placed on the ball vanne. The principle is simple, an electrical resistence is attached to the main body of the vanne and a cursor is stick to the level that is rotating. When the lever is moved, the cursor is also moving and it’s pressing on the eletrical resistence.

Legend:

Flow

Ribbon

Fig 3.2.2. Exemple of the electrical resistence signal

The electrical resistence (ribbon sensor) is the yellow signal. The other lines are the flow, the envelope and the magenta and turquoise are the limis of the peaks (minimum and maximum).

The scale for the ribbon is on the right side of the graphic and the unit measure is volt [V] because the signal received from the electrical resistence is converted from ohm [Ω].

The scale for pressure is on the left side and its showing the relative pressure [kPa].

In order to see when the vanne is closed or opened, I have done some tests to measure what is the voltage. Following these tests:

2.31 [V] for 0° (when the vanne is totally closed)

1.95 [V] for 90° (when the vanne is totally opened)

The beginning of the signal is constant and has the value almost 2.31 [V], meaning that the vanne is closed. The dropping of the signals means that the vanne was opened, and the value of it’s representing the closing angle.

For this exemple, if we interpolate the values, the closing angle will be 22.5° (how much the vanne remains closed), meaning that the opening angle will be 67.5°.

The celerity and hydroacoustic period

To be able to calculate the period of oscillation, it was necessary to calculate the celerity. As we saw in chapter 2, the lenght of the circuit has been changed because of the damping time was shorter than the rising time.

In order to apply relationship (16), the following values were considered:

sound celerity in water (C): 1500 m/s;

density of the liquid (ρ): 1000 kg/m3;

And the values we already have:

tickness of the pipe (e): 0.005 m;

interior diameter of the pipe (Di): 0.127 m.

Tabel 3.3. Values of hydroacoustic period with different lengths

E – Young module [Pa]

a – celerity of sound in the system [m/s]

L – length [m]

Fig. 3.3.1. Influence of length

In fig 3.3.1. it can be seen that the longer pipe, the longer hydroacoustic period will be.

The calculus was made with the estimation of the Young module for the rubber pipe equals to 109 Pa. For 10 meters length we can say that the Young module it will be:

106 Pa < E < 108 Pa. Furthermore, different values of the module for the same length will be calculated.

Tabel 3.3.2. Hydroacoustic period for different Young module and same length

The length of the system is 11 because the rubber pipe had approximately 10 m and the distance from the connection with the plexiglass pipe untill the pressure sensos is almost 1 m.

For this length (11 meters) we can see that hydroacoustic period (4L/a) decreases with the increasing of the Young module. The interval that we are looking for is 0.7 s < 4L/a < 7 s.

Fig. 3.3.2. Hydroacoustic period and Young module

Chapter 4: Signal processing

The signals were recorded at four different contants heads: 130 cm, 120 cm, 110 cm and 100 cm. For every head, I’ve done several tests with different closing angles.

For a better visualisation, an envelope and a filter was applied. Also, different colours was used for every line, as we can see in the following legend:

Legend:

Flow

Ribbon

Starting point of rising (Pmax)

Ending point of rising (Pmin)

The signals were recorded from the second pressure sensor and analyzed with Matlab. A zoomed was made for a better visualisation of the transients.

Test with the constant head equals to 130 centimeters

Test no. 1

Entire signal

This is the entire signal of a test with 130 cm head. We observe that the vanne was opened for more than a second and then is closed. After that (two seconds) the transient waves can be seen. The damping time and the rising time will be calculated with Matlab.

Zoomed signal

On the zoomed signal we can observe the start of the rising time and the end of it marked by the turquoise and magenta lines.

Time of rising (temps montée): 0.0606 sec

Time of damping (temps amortissement): 6.666 sec

Closing angle (angle du fermeture): 68.5°

Test no. 2

Entire signal

Zoomed signal

This is the second test for the head = 130 cm. Even without proccesing the signal we can observe that the closing angle of the vanne is different. This signal was recorded for a longer period that the other one to check if there is any singularities have occurred.

Zoomed signal

The opening is in a second, it’s starting with an overpressure and then with the decreasing of it. Also, there are more singularities in this signal that in the first one.

Time of rising (temps montée): 0.1918 sec

Time of damping (temps amortissement): 4.9931 sec

Closing angle (angle du fermeture): 12.5°

The first signal has the time of damping longer than the second one even if we can see that there are fewer singularities. This might be due to errors in the system (bad connections, pipe movements etc.). Even with this the time is between 0.7s and 7s.

Test with the constant head equals to 120 centimeters

Test no. 1

Entire signal

The first test with the head = 120 cm. The signal is similar with the second test at 130 cm.

Zoomed Signal

The opening is starting with an overpressure and it’s lasting for one second. After filtering, the following values were resulting:

Time of rising (temps montée): 0.2510 sec

Time of damping (temps amortissement): 4.8796 sec

Closing angle (angle du fermeture): 22.5°

Test no. 2

Entire signal

In this graphic there is an error on the ribbon signal, the dropping value of it. So, the minimum of it is at the base of the round signal and not at the sharp edge.

Zoomed signal

Time of rising (temps montée): 0.1658 sec

Time of damping (temps amortissement): 5.2428 sec

Closing angle (angle du fermeture): 20°

The time of rising is very fast; this means that the pressure can reach high values rapidly.

The closing angle is 20° so the vanne was not totally opened.

Test with the constant head equals to 110 centimeters

Test no. 1

Entire signal

Another error occurred on the ribbon sensor but it can be neglected. It doesn’t influence the signal, as we can see, the dropping (error) is before the opening and closing of the vanne.

Zoomed signal

Time of rising (temps montée): 0.1936 sec

Time of damping (temps amortissement): 5.4545 sec

Closing angle (angle du fermeture): 5°

The closing angle is 5° meaning that the vanne was almost totally opened.

The time of damping is around 5 seconds, similar with the others signal.

Test no. 2

Entire signal

This is a signal without filtering. After the vanne was closed we can barely figure it if there are any transient. Nevertheless, the time of rising and the time of damping can be calculated.

Zoomed signal

Time of rising (temps montée): 0.2482 sec

Time of damping (temps amortissement): 5.6981 sec

Closing angle (angle du fermeture): 52.5°

The vanne was almost half closed, still the time of damping remains around the same value of 5 seconds.

Test with the constant head equals to 100 centimeters

Test no. 1

Entire signal

The last set of measurements and the signal is similar to the others. Looking at the peaks, the transients had high values in the beginning but after, due to the length of the circuit the signal is constant.

Zoomed signal

Time of rising (temps montée): 0.2174 sec

Time of damping (temps amortissement): 4.8496 sec

Closing angle (angle du fermeture): 18°

The time of damping is less then 5 seconds, also the vanne is almost closed.

After 8 seconds there is a small constant part due to inertia but only for few miliseconds, then the signal resumes its course with another part of rising and droping singularities.

Test no. 2

Entire signal

The opening and closing of the vanne it can be clearly seen starting with second 7,5. The amplitude is starting to drop due to the decrease of head.

Zoomed signal

Time of rising (temps montée): 0.2238 sec

Time of damping (temps amortissement): 4.9931 sec

Closing angle (angle du fermeture): 0°

The vanne was fully opened for this test. The values are similar with the other ones. There are small differences between time of rising and time of damping of each test meaning that that the conditions were not changed.

Various simulations were made by having different closing angles for each head to see system behaviors.

As we can see, the difference between the head tests is 10 cm. This can be notice in the pressure of each measurement by dropping with almost 1 kPa for every each 10 cm.

The time of damping is around 5 seconds for any head but with different angles of closure.

The rising time is between 0.1 sec and 0.3 sec and in influenced by how fast I open and close the vanne. There is no automatically system to be triggered.

The pressure difference between the minimum and the maximum peak is no more than 18 kPa for the highest head level and 10 kPa for the lowest head analyzed.

When the vanne is opened and closed, the amplitude of the pressure is high in the beginning. As well, the first singularities have the value more than double than the next singularities, meaning that the most dangerous aspect of this phenomenon is impact of closure and opening of the vanne.

Tabel 4. Summary table of the tests

Matlab code

The signal was received with the help of the U-I converter and the Handyscope HS4 and the software TiePie, was the tool that made possible to see the signals in real time on the PC. After that, I had to analyze those signals and process them.

In order to calculate all the values needed like time of damping and time of rising, I had to create a code in Matlab. In the code I used different methods to find the mentioned times as follows:

clc

clear

close all

load('h=100cm_test3constbun.mat')

x = double(msrc1.Data);

fe = msrc1.SampleFrequency;

c1 = x(:,2);

l = length(x);

t = 0:1/fe:(l-1)/fe;

figure, plot(c1)

hold on

The beginning of the code, with the starting syntax. The ’x’ value its concerns us and the one to be analyzed. As we can see, the signal at 100 cm head was chose for this exemple.

The data received uses requency but to measure the damping time I converted the frequency into time.

NFFT = (length(x));

fr = fe/2*linspace(0, 1, NFFT/2);

f = fft(c1, NFFT);

[m,i] = max(f(2:end/2));

po = sin(2*pi*fr(i+1)*t);

t_amort = fr(i+1);

ifr = i;

ap = (c1-mean(c1)).*po(:);

The ‘NFFT’ in the documentation for the fft function is that it is the length of the signal to calculate the Fourier transform of. (It zero-pads the time-domain vector before calculating the transform.) Because of the nature of the fft algorithm, this is usually 2^n, where ‘n’ is any integer, because it makes the algorithm more efficient. It also increases the frequency resolution of the resulting fft, generally considered to be preferable.

Using the ‘NFFT’ argument is helping me to compare the fft of different signals of slightly different lengths and want all of them to have the same frequency resolution. Setting ‘NFFT’ to be the same for all the signals allows to compare them directly at each frequency.

[b, a] = butter(2, 2*([1 35])/fe); %%

env = (filtfilt(b, a, c1-mean(c1))); %%

ex = env;

env = env/max(abs(env)); env = env*max(c1);

c1 = filtfilt (b,a,c1)

‘Filfilt’ performs zero-phase digital filtering by processing the input data, x, in both the forward and reverse directions. ‘filtfilt’ operates along the first nonsingleton dimension of x. The vector b provides the numerator coefficients of the filter and the vector a provides the denominator coefficients. If you use an all-pole filter, enter 1 for b. If you use an all-zero filter (FIR), enter 1 for a. After filtering the data in the forward direction, filtfilt reverses the filtered sequence and runs it back through the filter. The result has the following characteristics:

Zero-phase distortion

A filter transfer function, which equals the squared magnitude of the original filter transfer function

A filter order that is double the order of the filter specified by b and a

filtfilt minimizes start-up and ending transients by matching initial conditions, and you can use it for both real and complex inputs. Do not use filtfilt with differentiator and Hilbert FIR filters, because the operation of these filters depends heavily on their phase response.

[m, ix] = max(c1);

ex = ex/max(ex);

[m,i] = max(env)

plot(circshift(env,ix-i))

t_ferm = i/fe;

si = env(i-2000:i);

[mm ,im ] = min(si);

t_mont = (2000 – im)/fe

t_amort = 4*1/t_amort

The damping time was calculate in seconds and also the rising time. Also, an envelope was needed to be created for a better visualisation of the signal.

figure, plotyy(t, [c1 mean(c1) + 0.5*(max(c1) – min(c1))*circshift(ex, ix-i)], t, smooth(smooth(x(:,3),25),25))

hold on

stem(t(ix), m, 'm', 'linewidth',1)

stem(t(i-2000 + im),m, 'c', 'linewidth',1)

title('Capteur 2 filtre [kPA] – Ouverture')

set(findobj('type','axes'),'fontsize',16)

grid on;

xlabel ({'Time [ s ]', 'Voltage [ V ]'}, 'FontSize', 20)

In the ending of the code the signal was ploted and ready to be analyzed. Also, the values of the damping and rising time was displayed.

Chapter 5: Conclusions and perspectives

The issue of surveillance is complex and timely. Moreover, at the present time, there is no automatic tool and methods to deal with and anticipate dysfunction in hydraulic installations.

The facility were the signals were recorded its called MOTRHYS and it is an abbreviation from ’Monitoring of transients for hydro safety’ and its specially built for analisysing the transients.

The time of damping and the time of rising are very important because the system can be characterized by only having these two periods of time. Also, the pressure its important and this method allows to measure the maximum and minimum values of the peaks.

The water hammer effect is very dangerous for the hydro power plants. The phenomena can be observe in in basic water applications, like closing and openning the water tap to industrial utilities.

The objective of the thesis was to develop an automatic monitoring tool that can anticipate operational drifts in hydro power plants.

In the synthesis developed above, an explanation of the physical phenomena as well as a proposal of the methods of detection of the signatures of dysfunction in the hydraulic installations have been made.

In addition, a method for analyzing the transients was presented, which made it possible to extract a lot of information from the pressure signal.

These methods allowed to extract scalars characterizing the single-channel signals. It should be noted that these scalars are not the only ones that allow to characterize the malfunctions and that a future study can be made to develop others. Even if some scalars are not directly related to physical phenomena they always provide information and their long-term monitoring can constitute a method of detecting the malfunction of the hydraulic system analyzed.

Because the actual malfunctions are rather rare, a simple model of the hydraulic system must be designed, model that will use as input to be simulated in Matlab.

In conclusion, the proposed methods are not innovative methods, innovation being the field of use.

In perspective, the scalars determined with the methods presented, can be used by a computer tool of classification and detection.

Bibliography

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Texas tech university courses – Open channel flow – Water hammer, 2014

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KSB know-how, volume 1, Water hammer

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