wave maker design and preformance

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Arab Academy for Science, Technology and Maritime

Transport

College of Engineering and Technology

Marine Engineering Department

B. Sc. Final Year Project

Wave Maker Design and Performance

Presented By:

Mohamed Ahmed Yakout Zeyad Yasser AlGhazoly

Mostafa Mohamed Mostafa Mahmoud Hassan Abdelfattah

Mostafa Nagy Attia

Supervised By:

Prof Dr: Mohamed Abbas Kotb Dr: Asharf Sharara

F E B R A U R Y – 2 0 1 5


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DECLARATION

I hereby certify that this report, which I now submit for assessment on the programme of

study leading to the award of Bachelor of Science in , is all my own work and contains no Plagiarism. By submitting this report, I

agree to the following terms:

Any text, diagrams or other material copied from other sources (including, but not

limited to, books, journals, and the internet) have been clearly acknowledged and

cited followed by the reference number used; either in the text or in a

footnote/endnote. The details of the used references that are listed at the end of the

report are confirming to the referencing style dictated by the final year project

template and are, to my knowledge, accurate and complete.

I have read the sections on referencing and plagiarism in the final year project template.

I understand that plagiarism can lead to a reduced or fail grade, in serious cases, for the

Graduation Project course.

Student Name: Mohamed Ahmed Yakout

Registration Number: 9200342

Signed:

Date: 26 – 01 – 2015

Student Name: Zeyad Yasser AlGhazoly


Signed:

Date: 26 – 01 – 2015

Student Name: Mostafa Mohamed

Mostafa


Signed:

Date: 26 – 01 – 2015

Student Name: Mostafa Nagy Attia


Signed:

Date: 26 – 01 – 2015

Student Name: Mahmoud Hassan Abdel-

Fatah


Signed:

Date: 26 – 01 – 2015


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Wave Maker Design and Performance

By:

Zeyad Yasser AlGhazoly

Mohamed Ahmed Yakout

Mostafa Mohamed Mostafa

Mahmoud Hassan Abdelfattah

Mostafa Nagy Attia

Chapter Title Contributors

1 Introduction Zeyad Yasser AlGhazoly

2 Theoretical analysis Mohamed Ahmed Yakout

3 Experimental analysis Mahmoud Hassan Abdelfattah


4 Results Mostafa Nagy Attia

5 Conclusions Zeyad Yasser AlGhazoly

Mostafa Nagy Attia

Mohamed Ahmed Yakout

Mahmoud Hassan Abdelfattah



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ACKNOWLEDGMENT

This group wishes to express the deep appreciation and their gratitude to

Prof.: Mohamed Abbas Kotb

Dr.: Asharf Sharara

For proposing the problem and his continuous guidance, encouragement and patience

during the course of this work. We also, grateful to:

Prof.: Amr Ali Hassan

Head of marine engineering department for his support and help.

Thanks for Doctors and engineers our lecturers. We send all the work and filling in this

project for our parents which they were here with us in there harts and hops. All thanks

for everyone and for all the help we found.


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I

TABLE OF CONTENTS

LIST OF FIGURES .......................................................................................................................................... III

LIST OF TABLES ................................................................................................................................... IV

1. INTRODUCTION ................................................................................................................................... 2

1.1. WAVE PHENOMENA. ........................................................................................................................ 2

1.2. WAVE PROPAGATION. ...................................................................................................................... 5

1.3. WAVE BREAK. ................................................................................................................................. 7

1.3.1. Spilling breakers ................................................................................................................. 8

1.3.2. Plunging breakers .............................................................................................................. 9

1.3.3. Collapsing .............................................................. ............................................................. 9

1.3.4. Surging ............................................................................................................................... 9

1.4. WAVE POWER ................................................................................................................................ 9

1.4.1.

Physical Concept .............................................................................................................. 10

1.4.2. History ........................................................ ................................................................. ..... 11

1.5. EFFECT OF WAVES ON SHIPS ............................................................................................................ 12

1.6. WAVE MAKER START ...................................................................................................................... 14

2. THEORETICAL ANALYSIS .................................................................................................................... 17

2.1. TANK DESIGN ............................................................................................................................ 17

2.1.1. Materials ............................................................... ........................................................... 17

2.1.2. Fluids ............................................................................................................................... 18 2.1.2.1. Pressure on bottom...................................................................................................................... 18

2.1.2.2. Pressure on vertical walls............................................................................................................ 19

2.1.3. Calculations ..................................................................................................................... 20

2.2. SCOTCH YOKE MECHANISM ....................................................................................................... 22

2.2.1. Over-view .............................................................. ........................................................... 22 2.2.1.1. Principle of motion .....................................................................................................................22

2.2.1.2. Advantages .................................................................................................................................23

2.2.1.3. Disadvantages .............................................................................................................................23

2.2.1.4. Parts ............................................................................................................................................23

2.2.2. Mechanism equations ................................................................. ...................................... 24

2.2.3. Dimensions and Stroke..................................................................................................... 28

2.3. WAVE ANALYSIS ....................................................................................................................... 29

2.4. WAVE ABSORBER ...................................................................................................................... 35

2.5. PLUNGER DESIGN .......................................................................................................................... 37

3. EXPERIMENTAL .................................................................................................................................. 41

3.1 TANK ........................................................................................................................................... 41

3.2. MOTOR AND GEAR BOX .................................................................................................................. 42

3.3. Inverter ................................................................................................................................. 43

3.4. STAND FOR MECHANISM ................................................................................................................. 45

3.5. MECHANISM PREPARATION ............................................................................................................. 47

3.7. WAVE ABSORBER ........................................................................................................................... 50

3.8. WAVE MAKER .............................................................................................................................. 52

4. RESULTS ............................................................................................................................................. 55

RPM VS. WAVE PERIOD .......................................................................................................................... 56

RPM VS. WAVE LENGTH ........................................................................................................................ 57

RPM VS. WAVE SPEED ........................................................................................................................... 58

EXPERIMENTAL RESULTS ........................................................................................................................ 59

Wave probe monitor .......................................................................................................................... 59

Principle of operation........................................................................................................................ 59


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II

Calibration ........................................................................................................................................ 60

5. CONCLUSION ..................................................................................................................................... 62

6. REFERENCES. ..................................................................................................................................... 65


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III

LIST OF FIGURES

FIGURE 1-1: WAVE ANATOMY ...................................................................................................................... 3

FIGURE 1-2: TYPES OF WAVE BREAKERS ....................................................................................................... 8

FIGURE 1-3: PB150 POWER BUOY WITH PEAK -RATED POWER OUTPUT OF 150 K W .................................... 11

FIGURE 2-1: PRESSURE DISTRIBUTION ON VERTICAL WALLS [19] .................................................................. 19

FIGURE 2-2: SIMULATED TANK .................................................................................................................... 20

FIGURE 2-3: STRESS-STRAIN CURVE FOR TENSION AND COMPRESSION [20] .................................................. 22

FIGURE 2-4: SCOTCH YOKE MECHANISM .................................................................................................... 23

FIGURE 2-5: SCOTCH YOKE DISK AND PIN[23] .............................................................................................. 24

FIGURE 2-6: SCOTCH YOKE SLOT AND R ODS [23] .......................................................................................... 24

FIGURE 2-7: SCOTCH YOKE MECHANISM [23] ................................................................................................ 24

FIGURE 2-8: SCOTCH YOKE PARAMETERS [23] ............................................................................................... 25

FIGURE 2-9: DISPLACEMENT VS. A NGULAR VELOCITY WORK -SHEET [23] ..................................................... 26

FIGURE 2-10: DISPLACEMENT VS. A NGULAR VELOCITY GRAPH [23] ............................................................ 26

FIGURE 2-11: VELOCITY VS. A NGULAR VELOCITY WORK -SHEET [23] ........................................................... 26

FIGURE 2-12: VELOCITY VS. A NGULAR VELOCITY GRAPH [23] ..................................................................... 27

FIGURE 2-13: ACCELERATION VS. A NGULAR VELOCITY WORK -SHEET [23] ................................................... 27

FIGURE 2-14: ACCELERATION VS. A NGULAR VELOCITY GRAPH [23] ............................................................. 28

FIGURE 2-15: SIMULATED POSITIONS AND STROKE ..................................................................................... 29

FIGURE 2-16: WAVE PARAMETERS .............................................................................................................. 30

FIGURE 2-17: DEEP WATER WORK -SHEET ................................................................................................... 32

FIGURE 2-18: WAVE RESULTS ON DEEP WATER ........................................................................................... 32

FIGURE 2-19: HEIGHT-STROKE RATIO VS. R ELATIVE DEPTH ON DEEP WATER ............................................. 33

FIGURE 2-20: SHALLOW WATER WORK -SHEET ............................................................................................ 34

FIGURE 2-21: WAVE RESULTS ON SHALLOW WATER ................................................................................... 34

FIGURE 2-22: HEIGHT-STROKE RATIO VS. R ELATIVE DEPTH ON SHALLOW WATER ...................................... 35

FIGURE 2-23: WAVE ABSORBER ................................................................................................................... 36 FIGURE 2-24: PLUNGER MOTION[25] ............................................................................................................ 38

FIGURE 2-25: PLUNGER DESIGN RATIOS [25] ................................................................................................. 39

FIGURE 3-1: TANK AFTER MODIFICATION ................................................................................................... 41

FIGURE 3-2: TANK DIMENSION ................................................................................................................... 42

FIGURE 3-3: GEAR BOX STANDARDS .......................................................................................................... 42

FIGURE 3-4: GEAR BOX DIAGRAM .............................................................................................................. 43

FIGURE 3-5: I NVERTER PROFILES [35] ........................................................................................................... 44

FIGURE 3-6: HOLDER DESIGN ..................................................................................................................... 45

FIGURE 3-7: HOLDER .................................................................................................................................. 46

FIGURE 3-8: R AW MATERIALS .................................................................................................................... 47

FIGURE 3-9: DISC ........................................................................................................................................ 48

FIGURE 3-10: R ODS, DISC AND PIN .............................................................................................................. 48 FIGURE 3-11: PLUNGER ............................................................................................................................... 50

FIGURE 3-12: WAVE ABSORBER FRAME ...................................................................................................... 51

FIGURE 3-13: WAVE ABSORBER ................................................................................................................. 51

FIGURE 3-14: WAVE GENERATION MECHANISM .......................................................................................... 52

FIGURE 3-15: WAVE MAKER ...................................................................................................................... 53

FIGURE 4-1: EXEL SHEET ............................................................................................................................ 55

FIGURE 4-2: RPM VS. WAVE FREQUENCY .................................................................................................. 56

FIGURE 4-3: RPM VS. WAVE PERIOD .......................................................................................................... 56

FIGURE 4-4: RPM VS. WAVE LENGTH ......................................................................................................... 57

FIGURE 4-5: RPM VS. WAVE SPEED ............................................................................................................ 58

FIGURE 4-6: WAVE GAUGE ......................................................................................................................... 60


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IV

LIST OF TABLES

TABLE 1-1: TYPICAL WAVE VS. DEPTH ........................................................................................................ 5

TABLE 2-1: MATERIAL PROPERITIES ........................................................................................................... 17

TABLE 2-2: DIFFERENT MATERIALS PLACED OVER OR UNDERNEATH THE WAVE ABSORBER [24] .................. 37

TABLE 3-1: PLUNGER DESIGN ..................................................................................................................... 49

TABLE 4-1: RPM VS. WAVE FREQUENCY ................................................................................................... 55

TABLE 4-3: RPM VS. WAVE PERIOD ........................................................................................................... 56

TABLE 4-4: RPM VS. WAVE LENGTH .......................................................................................................... 57

TABLE 4-5: RPM VS. WAVE SPEED ............................................................................................................. 58


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Chapter 1

1. Introduction

Design of new ships and coastal sea facilities requires many tests to be done prior to actual

construction. Validity of construction plans is often verified by simulations on numerical

models and on scaled-size physical models.

The use of physical models in marine engineering would be severally limited if we were unable

to create waves in small scale models that exhibited many of characteristics of waves in nature.

A far more common approach is mechanical wave generation where a movable partition is

placed in the wave facility and waves are generated by oscillation of the partition.

So far most laboratory testing of floating or bottom mounted structures and studies of wave

profiles and other related phenomena have utilized wave flumes, which are usually

characterized as long, narrow enclosures with a wave-maker of some kind at one end. For all of

these tests, the type of wave-maker is very important. The wave motion that it induces can be

determined reasonably well from linear wave theory [1].

1.1.

Wave Phenomena.

When winds blow over the surface of water, they generate capillary and gravity waves that are

generally referred to as wind waves. These waves range in length and height from a few

centimeters to lengths of up to a kilometer, and heights of over 30 m. Waves that are actively

generated by the local winds are generally referred to as wind waves. When the wind subsides,

waves propagate freely over the ocean [2].

All waves can be described using three variables: wavelength, wave height, and frequency.

Waves with a long wavelength have a low frequency and a flat face. Waves with a short Wave

length have a high frequency and a steep face. As waves come into shore they begin to feel the

bottom and slow down. Slowing down, they bunch up as their wavelengths decrease. They

continue to get steeper until the tops of the waves fall over and they break. The steeper the slope

on the beach, the faster the waves bunch up and break. This affects the shape of the breakers.

Particle motion in shallow water waves is a flat, ellipse-shaped orbit. This motion can be almost

horizontal in very shallow waters (shown as line with arrows at both ends). Note that shallow


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much longer, even after the wind has died. Swells are waves that have moved away from their

area of origin and are unrelated to the local wind conditions -- in other words, seas that have

lasted long beyond the wind.

The definition of swells can be a bit confusing when you understand that waves never

actually go anywhere. The water does not travel along with the waves, only along with the

current -- two mutually exclusive elements of water animation. If two people stand at either end

of a long rope and undulate their arms up and down in an equal rhythm, waves will develop

along the length of the rope that appear to move from one end to the other. The rope fibers aren't

actually moving at all, other than up and down. This is exactly what is happening with waves.

The speed, or velocity of the wave is measured by how long it would take a wave to pass a

given point crest to crest say a line drawn on the ground beneath the rope. There is a slight

movement of the water particles within a wave, but we'll get into that in a little bit. Waves can

be further described as:

Non-Breaking

Breaking

A non-breaking wave, is a "normal" rolling wave. A breaking wave is one whose base can no

longer support its top and it collapses. Depending on the size, this can happen with considerable

force behind it -- 5 to 10 tons per square yard. Enough force to crush the hull of a ship. Whenthe ratio of steepness of a wave is too great, it must break. This happens when a wave runs into

shallow water, or when two wave systems oppose and combine forces. The steepness ratio is

expressed as the height to the length. A 1:24 is a long, shallow swell found in deep waters. A

1:14 and up is a wave that is too steep to stay together. This can also happen if the wind quickly

grows strong and actually blows the top (crest) off the base of the wave. Wave characteristics

also change in shallow water. Imagine if the rope that we talked about earlier was lowered to the

ground so that the troughs of the waves hit the floor. This gives you some idea what happens

when a wave hits shallow water, only the height and period won't change, just the length and

hence the steepness (as the length changes, so does the height to length ratio).

Once the ratio gets high enough (like fractions, the closer together the numerator and

denominator, the higher the fraction 1:1 is the highest [that would be a wave at a right angle

with the length exactly as long as the height.] the wave will break.


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Table 1-1: Typical Wave Vs. Depth

Water Depth (feet) Wave height (feet) Wave length (feet) Period (seconds) 150 + 15 360 8

75 15 270 8

30 15 (breaks) 210 8

15 15 (breaks) 153 8

1.2. Wave Propagation.

One of the most important aspects of fluids is the wide variety of waves which can be

generated and sustained in them. The theory of water waves has been an intense

scientific research subject since the days of Airy in 1843. Stokes spent a great deal of

effort studying the ocean and came up with a solution in 1847 to waves striking a

surface. Surface waves can be considered as simply an interface deviation between two

fluids (air and sea). We will begin by discussing approximate methods to understanding

of ocean wave dynamics. In actuality, real water waves propagate in a viscous ocean

over an irregular bottom. They grow from external forces and internal instabilities and

decay due to friction and diffusion. Approximate and simplified models of wave

propagation are surprisingly helpful in understanding the most fundamental features of

ocean waves.

We will first ask the question: Where do waves come from? Two components lead to waves:

turbulence and Fourier series. Turbulence is due to strong winds that create disorder and in

homogeneities on the ocean surface. Waves most commonly are formed from fetch: a region

where the wind is blowing in a prominent direction for some region of space. The shapes that

form, we can Fourier transform it to see the components that build it up as shown in Figure 16.

The greater the area of wind and the stronger the wind blows, the greater the fetch and the

greater the resultant waves. Emerging from a fetch is a collection of waves known as the wave

train. For reasons that will become obvious later, waves of the longest period will extend our

first over the wave train while the waves of smaller period which travel slower will be at the

back.

The spectral density of ocean waves that exist in our ocean span over a wide range. A spectrum

would include peaks at the tidal periods of 24 and 12 hours. At the lower end there is some


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structure for different capillary waves. Beyond these extremes there is a broad hump spanning a

period between 30 seconds and 1 second with a peak at around 10 seconds.

The waves surfers are interested in are considered the long wavelength limit.

Any surfer know that a ride able wave corresponds to a "wave period" of at least 10 seconds.

Likewise, from watching waves break from above, on a cliff or a pier, it is easy to guess that

waves are spaced out by about 100 ft. as an order of magnitude guess. Thus, knowing the

characteristic frequency of an ocean wave (0.1 seconds) and a characteristic wavelength (100 m)

we are able to guess a wave velocity of about 10 ft. /sec. This corresponds to a speed of about

20 mph. [3]

The highest part of the wave is called the crest. The lowest part is called the trough. The wave

height is the overall vertical change in height between the crest and the trough and distance

between two successive crests (or troughs) is the length of the wave or wavelength.

While one normally associates an up and down motion with the passage of each wave. Actually,

a circular motion occurs. It is this orbital motion of the water (or objects on the surface of the

water) that causes an object to bob up and down, forward and backward as waves pass under it.

But even this motion is not exactly circular but is trochoidal (line form traced by a point on a

rolling wheel). While the motion in a wave over deep water move is an almost closed circular

path there is a tiny forward motion with the passage of each wave, particularly in large waves.

Also, in deep water, the motion changes as the depth increases fairly rapidly. The trochoidal

shape at the surface flattens with increasing depth as well as a decrease in the total motion. This

flattening of motion/decreasing size continues with increasing depth until all that remains is a

small back and forth movement and even that will cease to be noticed which occurs at one-half

of the wave's total length. For shallow water waves, the same flattening in the motion occurs but

there is no decrease in the forward/backward motion.

The speed at which a wave moves through the water is dependent on the wave's length and the

depth of the water. Generally, the longer the length of the wave the faster is moves through the

water. Tsunamis can have extremely long wave lengths (60 miles/100 km or more) and thus

move around 550 mph (900 k/h).


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As a deep water wave reaches shore, at the point where the depth of the water is one-half of the

wave's length, it begins to "feel" the bottom. The wave will slow down, grow taller and become

shaped like peaks. These wave peaks reach a height where they become unstable and, moving

faster than the water below, they break forward. [4]

1.3. Wave Break.

In fluid dynamics, a breaking wave is a wave whose amplitude reaches a critical level at which

some process can suddenly start to occur that causes large amounts of wave energy to be

transformed into turbulent kinetic energy. At this point, simple physical models that describe

wave dynamics often become invalid, particularly those that assume linear behavior.

The most generally familiar sort of breaking wave is the breaking of water surface waves on a

coastline. Because of the horizontal component of the fluid velocity associated with the wave

motion, wave crests steepen as the amplitude increases; wave breaking generally occurs where

the amplitude reaches the point that the crest of the wave actually overturns — though the types

of breaking water surface waves are discussed in more detail below. Certain other effects in

fluid dynamics have also been termed "breaking waves," partly by analogy with water surface

waves. In meteorology, atmospheric gravity waves are said to break when the wave produces

regions where the potential temperature decreases with height, leading to energy dissipation

through convective instability; likewise Rossby waves are said to break when the potentialvelocity gradient is overturned. Wave breaking also occurs in plasmas, when the particle

velocities exceed the wave's phase speed.

Breaking of water surface waves may occur anywhere that the amplitude is sufficient, including

in mid-ocean. However, it is particularly common on beaches because wave heights are

amplified in the region of shallower water (because the group velocity is lower there). See

also waves and shallow water.

During breaking, a deformation (usually a bulge) forms at the wave crest, either leading side of

which is known as the "toe." Parasitic capillary waves are formed, with short wavelengths.

Those above the "toe" tend to have much longer wavelengths. This theory is anything but

perfect, however, as it's linear. There have been a couple non-linear theories of motion

(regarding waves). One put forth uses a perturbation method to expand the description all the

way to the third order, and better solutions have been found since then. As for wave

deformation, methods much like the boundary integral method and the Boussinesq model have

been created.

It has been found that high-frequency detail present in a breaking wave plays a part in crest

deformation and destabilization. The same theory expands on this, stating that the valleys of the

http://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Wavehttp://en.wikipedia.org/wiki/Amplitudehttp://en.wikipedia.org/wiki/Wave_turbulencehttp://en.wikipedia.org/wiki/Kinetic_energyhttp://en.wikipedia.org/wiki/Linearhttp://en.wikipedia.org/wiki/Ocean_surface_wavehttp://en.wikipedia.org/wiki/Meteorologyhttp://en.wikipedia.org/wiki/Gravity_wavehttp://en.wikipedia.org/wiki/Potential_temperaturehttp://en.wikipedia.org/wiki/Convective_instabilityhttp://en.wikipedia.org/wiki/Rossby_waveshttp://en.wikipedia.org/wiki/Potential_vorticityhttp://en.wikipedia.org/wiki/Potential_vorticityhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Phase_speedhttp://en.wikipedia.org/wiki/Waves_and_shallow_waterhttp://en.wikipedia.org/wiki/Perturbation_analysishttp://en.wikipedia.org/wiki/Boundary_element_methodhttp://en.wikipedia.org/wiki/Boussinesq_approximation_(water_waves)http://en.wikipedia.org/wiki/Boussinesq_approximation_(water_waves)http://en.wikipedia.org/wiki/Boundary_element_methodhttp://en.wikipedia.org/wiki/Perturbation_analysishttp://en.wikipedia.org/wiki/Waves_and_shallow_waterhttp://en.wikipedia.org/wiki/Phase_speedhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Potential_vorticityhttp://en.wikipedia.org/wiki/Potential_vorticityhttp://en.wikipedia.org/wiki/Rossby_waveshttp://en.wikipedia.org/wiki/Convective_instabilityhttp://en.wikipedia.org/wiki/Potential_temperaturehttp://en.wikipedia.org/wiki/Gravity_wavehttp://en.wikipedia.org/wiki/Meteorologyhttp://en.wikipedia.org/wiki/Ocean_surface_wavehttp://en.wikipedia.org/wiki/Linearhttp://en.wikipedia.org/wiki/Kinetic_energyhttp://en.wikipedia.org/wiki/Wave_turbulencehttp://en.wikipedia.org/wiki/Amplitudehttp://en.wikipedia.org/wiki/Wavehttp://en.wikipedia.org/wiki/Fluid_dynamics


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Because of this, spilling waves break for a longer time than other waves, and create a relatively

gentle wave. Onshore wind conditions make spillers more likely. As shown in (figure: 2).

1.3.2. Plunging breakers

A plunging wave occurs when the ocean floor is steep or has sudden depth changes, such as

from a reef or sandbar. The crest of the wave becomes much steeper than a spilling wave,

becomes vertical, then curls over and drops onto the trough of the wave, releasing most of its

energy at once in a relatively violent impact. A plunging wave breaks with more energy than a

significantly larger spilling wave. The wave can trap and compress the air under the lip, which

creates the "crashing" sound associated with waves. With large waves, this crash can be felt by

beachgoers on land. Offshore wind conditions can make plungers more likely. As shown in

(figure: 2).

1.3.3. Collapsing

Collapsing waves are a cross between plunging and surging, in which the crest never fully

breaks, yet the bottom face of the wave gets steeper and collapses, resulting in foam. As shown

in (figure: 2).

1.3.4. Surging

Surging breakers originate from long period, low steepness waves and/or steep beach profiles.

The outcome is the rapid movement of the base of the wave up the swash slope and the

disappearance of the wave crest. The front face and crest of the wave remain relatively smooth

with little foam or bubbles, resulting in a very narrow surf zone, or no breaking waves at all.

The short, sharp burst of wave energy means that the swash/backwash cycle completes before

the arrival of the next wave, leading to a low value of Kemp's phase difference (< 0.5). Surging

waves are typical of reflective beach states. On steeper beaches, the energy of the wave can be

reflected by the bottom back into the ocean, causing standing waves. As shown in (figure: 2).

1.4. Wave Power

Wave power is the transport of energy by ocean surface waves, and the capture of that

energy to do useful work – for example, electricity generation, water desalination, or

the pumping of water (into reservoirs). A machine able to exploit wave power is

generally known as a wave energy converter (WEC).

Wave power is distinct from the diurnal flux of tidal power and the steady gyre of ocean

currents. Wave-power generation is not currently a widely employed commercial

http://en.wikipedia.org/wiki/Surf_zonehttp://en.wikipedia.org/wiki/Standing_wavehttp://en.wikipedia.org/wiki/Ocean_surface_wavehttp://en.wikipedia.org/wiki/Mechanical_workhttp://en.wikipedia.org/wiki/Electricity_generationhttp://en.wikipedia.org/wiki/Water_desalinationhttp://en.wikipedia.org/wiki/Pumphttp://en.wikipedia.org/wiki/Tidal_powerhttp://en.wikipedia.org/wiki/Ocean_currentshttp://en.wikipedia.org/wiki/Ocean_currentshttp://en.wikipedia.org/wiki/Ocean_currentshttp://en.wikipedia.org/wiki/Ocean_currentshttp://en.wikipedia.org/wiki/Tidal_powerhttp://en.wikipedia.org/wiki/Pumphttp://en.wikipedia.org/wiki/Water_desalinationhttp://en.wikipedia.org/wiki/Electricity_generationhttp://en.wikipedia.org/wiki/Mechanical_workhttp://en.wikipedia.org/wiki/Ocean_surface_wavehttp://en.wikipedia.org/wiki/Standing_wavehttp://en.wikipedia.org/wiki/Surf_zone


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Figure 1-3: PB150 Power Buoy with peak-rated power output of 150 kW

1.4.2.

History

The first known patent to use energy from ocean waves dates back to 1799, and was

filed in Paris by Girard and his son.[10] An early application of wave power was a device

constructed around 1910 by Bochaux-Praceique to light and power his house at Royan,

near Bordeaux in France.[11] It appears that this was the first oscillating water-column

type of wave-energy device.[12] From 1855 to 1973 there were already 340 patents filed

in the UK alone.[10]

Modern scientific pursuit of wave energy was pioneered by Yoshio Masuda's

experiments in the 1940s.[13] He has tested various concepts of wave-energy devices at

sea, with several hundred units used to power navigation lights. Among these was the

concept of extracting power from the angular motion at the joints of an articulated raft,

which was proposed in the 1950s by Masuda.[14]

A renewed interest in wave energy was motivated by the oil crisis in 1973. A number of

university researchers re-examined the potential to generate energy from ocean waves,

among whom notably were Stephen Salter from the University of Edinburgh, Kjell

Budal and Johannes Falnes from Norwegian Institute of Technology(now merged

into Norwegian University of Science and Technology), Michael E.

http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Royanhttp://en.wikipedia.org/wiki/Bordeauxhttp://en.wikipedia.org/wiki/Wave_power#cite_note-17http://en.wikipedia.org/wiki/Wave_power#cite_note-17http://en.wikipedia.org/wiki/Wave_power#cite_note-17http://en.wikipedia.org/wiki/Wave_power#cite_note-morris2007-18http://en.wikipedia.org/wiki/Wave_power#cite_note-morris2007-18http://en.wikipedia.org/wiki/Wave_power#cite_note-morris2007-18http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Yoshio_Masudahttp://en.wikipedia.org/wiki/Wave_power#cite_note-19http://en.wikipedia.org/wiki/Wave_power#cite_note-19http://en.wikipedia.org/wiki/Wave_power#cite_note-19http://en.wikipedia.org/wiki/Wave_power#cite_note-ey2006-20http://en.wikipedia.org/wiki/Wave_power#cite_note-ey2006-20http://en.wikipedia.org/wiki/Wave_power#cite_note-ey2006-20http://en.wikipedia.org/wiki/1973_oil_crisishttp://en.wikipedia.org/wiki/Stephen_Salterhttp://en.wikipedia.org/wiki/University_of_Edinburghhttp://en.wikipedia.org/w/index.php?title=Kjell_Budal&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Kjell_Budal&action=edit&redlink=1http://en.wikipedia.org/wiki/Johannes_Falneshttp://en.wikipedia.org/wiki/Norwegian_Institute_of_Technologyhttp://en.wikipedia.org/wiki/Norwegian_University_of_Science_and_Technologyhttp://en.wikipedia.org/wiki/Michael_E._McCormickhttp://en.wikipedia.org/wiki/Michael_E._McCormickhttp://en.wikipedia.org/wiki/Norwegian_University_of_Science_and_Technologyhttp://en.wikipedia.org/wiki/Norwegian_Institute_of_Technologyhttp://en.wikipedia.org/wiki/Johannes_Falneshttp://en.wikipedia.org/w/index.php?title=Kjell_Budal&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Kjell_Budal&action=edit&redlink=1http://en.wikipedia.org/wiki/University_of_Edinburghhttp://en.wikipedia.org/wiki/Stephen_Salterhttp://en.wikipedia.org/wiki/1973_oil_crisishttp://en.wikipedia.org/wiki/Wave_power#cite_note-ey2006-20http://en.wikipedia.org/wiki/Wave_power#cite_note-19http://en.wikipedia.org/wiki/Yoshio_Masudahttp://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16http://en.wikipedia.org/wiki/Wave_power#cite_note-morris2007-18http://en.wikipedia.org/wiki/Wave_power#cite_note-17http://en.wikipedia.org/wiki/Bordeauxhttp://en.wikipedia.org/wiki/Royanhttp://en.wikipedia.org/wiki/Wave_power#cite_note-cle2002-16


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McCormick from U.S. Naval Academy, David Evans from Bristol University, Michael

French from University of Lancaster, Nick Newman and C. C. Mei from MIT.

Stephen Salter's 1974 invention became known as Salter's duck or nodding duck,

although it was officially referred to as the Edinburgh Duck. In small scale controlled

tests, the Duck's curved cam-like body can stop 90% of wave motion and can convert

90% of that to electricity giving 81% efficiency.[15]

In the 1980s, as the oil price went down, wave-energy funding was drastically reduced.

Nevertheless, a few first-generation prototypes were tested at sea. More recently,

following the issue of climate change, there is again a growing interest worldwide for

renewable energy, including wave energy.[16]

The world's first marine energy test facility was established in 2003 to kick start the

development of a wave and tidal energy industry in the UK. Based in Orkney, Scotland,

the European Marine Energy Centre (EMEC) has supported the deployment of more

wave and tidal energy devices than at any other single site in the world. EMEC provides

a variety of test sites in real sea conditions. Its grid connected wave test site is situated

at Billie Croo, on the western edge of the Orkney mainland, and is subject to the full

force of the Atlantic Ocean with seas as high as 19 meters recorded at the site. Wave

energy developers currently testing at the center include Aquamarine Power, Plames

Wave Power, Scottish Power Renewables and Well.[17]

1.5. Effect of Waves on ships

Ship stability, as it pertains to naval architecture, has existed for hundreds of years.

Historically, ship stability calculations for ships relied on rule of thumb calculations,

often tied to a specific system of measurement. Some of these very old equations

continue to be used in naval architecture books today. However, the advent of the ship

model basin allows much more complex analysis.

Master shipbuilders of the past used a system of adaptive and variant design. Ships were

often copied from one generation to the next with only minor changes being made, and

by doing this, serious problems were not often encountered. Ships today still use the

process of adaptation and variation that has been used for hundreds of years;

http://en.wikipedia.org/wiki/Michael_E._McCormickhttp://en.wikipedia.org/wiki/U.S._Naval_Academyhttp://en.wikipedia.org/wiki/David_Evans_(mathematician)http://en.wikipedia.org/wiki/Bristol_Universityhttp://en.wikipedia.org/wiki/University_of_Lancasterhttp://en.wikipedia.org/wiki/John_Nicholas_Newmanhttp://en.wikipedia.org/wiki/C._C._Meihttp://en.wikipedia.org/wiki/MIThttp://en.wikipedia.org/wiki/1974_in_sciencehttp://en.wikipedia.org/wiki/Salter%27s_duckhttp://en.wikipedia.org/wiki/Wave_power#cite_note-21http://en.wikipedia.org/wiki/Wave_power#cite_note-21http://en.wikipedia.org/wiki/Wave_power#cite_note-21http://en.wikipedia.org/wiki/Wave_power#cite_note-falnes2007-22http://en.wikipedia.org/wiki/Wave_power#cite_note-falnes2007-22http://en.wikipedia.org/wiki/Wave_power#cite_note-falnes2007-22http://www.emec.org.uk/http://www.aquamarinepower.com/http://www.pelamiswave.com/http://www.pelamiswave.com/http://www.emec.org.uk/about-us/wave-clients/scottishpower-renewables/http://www.wello.eu/http://en.wikipedia.org/wiki/Wave_power#cite_note-23http://en.wikipedia.org/wiki/Wave_power#cite_note-23http://en.wikipedia.org/wiki/Rule_of_thumbhttp://en.wikipedia.org/wiki/Ship_model_basinhttp://en.wikipedia.org/wiki/Ship_model_basinhttp://en.wikipedia.org/wiki/Ship_model_basinhttp://en.wikipedia.org/wiki/Ship_model_basinhttp://en.wikipedia.org/wiki/Rule_of_thumbhttp://en.wikipedia.org/wiki/Wave_power#cite_note-23http://www.wello.eu/http://www.emec.org.uk/about-us/wave-clients/scottishpower-renewables/http://www.pelamiswave.com/http://www.pelamiswave.com/http://www.aquamarinepower.com/http://www.emec.org.uk/http://en.wikipedia.org/wiki/Wave_power#cite_note-falnes2007-22http://en.wikipedia.org/wiki/Wave_power#cite_note-21http://en.wikipedia.org/wiki/Salter%27s_duckhttp://en.wikipedia.org/wiki/1974_in_sciencehttp://en.wikipedia.org/wiki/MIThttp://en.wikipedia.org/wiki/C._C._Meihttp://en.wikipedia.org/wiki/John_Nicholas_Newmanhttp://en.wikipedia.org/wiki/University_of_Lancasterhttp://en.wikipedia.org/wiki/Bristol_Universityhttp://en.wikipedia.org/wiki/David_Evans_(mathematician)http://en.wikipedia.org/wiki/U.S._Naval_Academyhttp://en.wikipedia.org/wiki/Michael_E._McCormick


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however computational fluid dynamics, ship model testing and a better overall

understanding of fluid and ship motions has allowed much more in-depth analysis.

Transverse and longitudinal waterproof bulkheads were introduced in ironclad designs

between 1860 and the 1880s, anti-collision bulkheads having been made compulsory in

British steam merchant ships prior to 1860.[1] Prior to this, a hull breach in any part of a

vessel could flood the entire length of the ship. Transverse bulkheads, while expensive,

increase the likelihood of ship survival in the event of damage to the hull by limiting

flooding to breached compartments separated by bulkheads from undamaged ones.

Longitudinal bulkheads have a similar purpose, but damaged stability effects must be

taken into account to eliminate excessive heeling. Today, most ships have means to

equalize the water in sections port and starboard (cross flooding), which helps to limitthe stresses experienced by the structure and also to alter the heel and/or trim of the

ship.

Controllability encompasses all aspects of regulating a ship’s trajectory, speed and orientation at

sea, as well as in restricted waters where positioning and station keeping are of particular

concern. Controllability includes starting, steering a steady course, and turning, slowing,

stopping and backing. In the case of submarines, diving has to be added to these controllabilitytasks too.

The study of the complex subject of controllability is usually divided into three distinct areas of

functions:

Course keeping (or steering)

This aspect yields the maintenance of a steady mean course or heading. Interest centers on the

ease with which the ship can be held to the course.

Maneuvering

This aspect yields the controlled change in direction of motion; turning or course changing.

Interest centers on the ease with which change can be accomplished and the radius and distance

required to accomplish the change.

Speed changing

This aspect yields the controlled change in speed including stopping and backing. Interest

centers on the ease, rapidity and distance covered in accomplishing changes.

http://en.wikipedia.org/wiki/Computational_fluid_dynamicshttp://en.wikipedia.org/wiki/Ship_motion_testhttp://en.wikipedia.org/wiki/Bulkhead_(partition)http://en.wikipedia.org/wiki/Ironclad_warshiphttp://en.wikipedia.org/wiki/Merchant_vesselhttp://en.wikipedia.org/wiki/Ship_stability#cite_note-1http://en.wikipedia.org/wiki/Ship_stability#cite_note-1http://en.wikipedia.org/wiki/Ship_stability#cite_note-1http://en.wikipedia.org/wiki/Sailing#Heelinghttp://en.wikipedia.org/wiki/Sailing#Heelinghttp://en.wikipedia.org/wiki/Ship_stability#cite_note-1http://en.wikipedia.org/wiki/Merchant_vesselhttp://en.wikipedia.org/wiki/Ironclad_warshiphttp://en.wikipedia.org/wiki/Bulkhead_(partition)http://en.wikipedia.org/wiki/Ship_motion_testhttp://en.wikipedia.org/wiki/Computational_fluid_dynamics


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Performance varies with water depth, channel restrictions and hydrodynamic interference from

nearby vessels and obstacles. Course keeping and maneuvering characteristics are particularly

sensitive to the ship’s trim. For conventional ships, the two qualities of course keeping and

maneuvering may tend to work against each other; an easy turning ship may be difficult to keep

on course whereas a ship which maintains course well may be hard to turn. Fortunately, a

practical compromise is nearly always possible.

Since controllability is so important, it is an essential consideration in the design of any floating

structure. Controllability is, however, but one of many considerations facing of naval architects

and involves compromises with other important characteristics. Some solutions are obtained

through comparison with the characteristics of earlier successful designs. In other cases,

experimental techniques, theoretical analyses, and rational design practices must all come into

play to assure adequacy.

Three tasks are generally involved in producing a ship with good controllability:

Establishing realistic specifications and criteria for course keeping, maneuvering

and speed changing.

Designing the hull, control surfaces, appendages, steering gear and control

systems to meet these requirements and predicting the resultant performance.

Conducting full-scale trials to measure performance for comparison with

required criteria and predictions.[18]

1.6. Wave maker start

The hydraulic design of coastal structures is a complex task. In the past decades physical scale

models often were the only possibility to verify the design. Nowadays computer models are

very powerful but some physical processes still cannot be calculated accurately. Therefore

physical scale models are still intensively used as design tools in almost all major coastal

engineering projects.

Since the 80’s of the previous century Flanders Hydraulics Research has invested in 3 wave

facilities: 2 wave flumes for two-dimensional scale models and 1 wave basin for three

dimensional scale models. The dimensions (L x W x D) of the small wave flume are 41m x


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0.7m x 0.86m, the large wave flume 70m x 4m x 1.4m and the wave basin 17.5m x 12.2m x

0.45m.

This poster gives a limited overview of some scale models dealing with research on coastal

structures of Flanders Hydraulics Research.


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Chapter 2

2. Theoretical analysis

Wave flume is a high important facility used to test the effect of waves on ships and

offshore structure, but to design a wave flume we should go through several steps such

as tank design, mechanism used, required motor power, analysis of wave and plunger

design. So in this chapter we are going to discuss how to prepare a perfect design for a

wave flume through the mentioned procedures.

2.1.

Tank design

In order to design a tank, we should take in consideration many parameters such as

Material used, fluid included, calculations of design and proper dimension to satisfy the

need of designing a tank.

2.1.1. Materials

Various materials are used for making a tank such as plastics (polyethylene, polypropylene), glass, fiber glass, concrete, stainless steel, and steel.[19]

Table 2-1: Material properities

MaterialDensity

(Kg/m3)

Compressive

strength (MPa)

Tensile strength

(MPa)

Polyethylene 960 32 70-100

Polypropylene 946 40 19.7-80

Glass 2400-2800 80-100 33

Fiber glass 2250 140 55

Stainless steel 7850 170 515

Steel 7580 758 758

Concrete 2400 250-500 2-5


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To choose the right material we should consider some parameters:

a- The purpose for which I need a tank. Does it used for storage of fluids or

chemical manufacturing or experimental uses?

b- Location of the tank. Is it above ground or underground or elevated?

c- The fluid which the tank contains. Is it liquid or gas? And which type of

liquid or gas.

d- Dimensions of tank.

To know the optimum material can be used, we have to answer these questions.

First of all we will use it for an experimental issue so that we need a transparent

material in order to obverse the experiment parameters and changes. Second it will be

located above ground so that we need a material with relatively high compressive

strength as the pressure is not as great as pressure on underground. Also we do not need

material with very low weight as the weight is not important parameter as it is in

elevated tanks. Third the fluid used is water so that we need a non-corrosive material to

resist corrosion.

So glass and fiber glass are the best material to be used in designing a tank. Both of

materials are transparent, light weight, but fiber glass has compressive strength more

than glass has. So it depends here on the dimension of the tank which directly affects

the volume of fluid inside the tank and also the weight.

2.1.2. Fluids

The fluid, which the tank contains, plays very important role in designing the tank. As

every fluid has its own density (ρ) and therefore this will affect the pressure falling on

the tank's walls which divided into two parts:

2.1.2.1. Pressure on bottom

According to the Pascal law:

P = ρ ∗ g ∗ h

Where: ρ = density. g = gravity. h = fluid level.

We find out that as long as the density of fluid increases, this will increase the pressure

on the tank bottom wall leading to increase the wall thickness in order to withstand the

increase in pressure as: σ =


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Where σ = compressive strength

F = force due to pressure.

A = area = length ∗ width

So before designing the tank we should tank in consideration type of fluid used, in order

to determine the suitable thickness to withstand the pressure resulting of fluid.

2.1.2.2. Pressure on vertical walls

On vertical walls, the pressure distribution takes a triangle shape so the whole fluid

height does not affect the wall but we take an average pressure.

Figure 2-1: Pressure distribution on vertical walls [19]

average pressure = ρ ∗ g ∗ [19]

And resultant force Fr = average pressure ∗ A

Where A is area = wall height ∗ width

σ =Fr

A

Where A = height ∗ length ----- for side A

And A = width ∗ height ----- for side B


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Figure 2-2: simulated tank

This means that the fluid density and thickness of walls are directly proportional, if the fluid

height is assumed constant for all fluids.

2.1.3.

Calculations

Actually the main goal of calculations is to determine the proper thickness of walls can be used,

as length, width, height of tank is according to the desired requirement. Calculations should be

done in proper sequence to achieve desired goal.

These steps are:

- Step 1: Define parameters used

Tank length Tank width

ℎ Fluid height Fluid density

Pressure o Atmospheric pressure

Compressive stress for material used

All. Allowable stress Area

Modulus of elasticity Volume of fluid

Weight of fluid Mass

Gravity Area moment of inertia

- Step 2: calculate Maximum Pressure (max) on walls

Bottom = ( ∗ ∗ ℎ) + o

Walls = ( ∗ ∗ ℎ 2 ) + o


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Clearly, the pressure at bottom is higher than Pressure on walls

therefore max = bottom

- Step 3: calculate Maximum Force (max)

Max = max /

Where = ∗

- Step 4: calculate allowable stress (all.)

All. = ..

Where . . = 1.2 ∶ 1.5

- Step 5: calculate allowable Strain (all.)

= ∗

Therefore, all = all. /

- Step 6: calculate Max Deflection (max.)

The load on the bottom wall is a uniform load because fluid weight is distributed on the bottom

wall.

= ∗ ∗ ℎ

= ∗

= ∗

Therefore, max. =∗

34∗∗

-

Step 7: calculate minimum thickness ()

= ∗

Therefore, = max / all.

So it is the minimum thickness can withstand the pressure and deflection may be occurred to

walls, in order to safe and efficient performance of the tank.


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Figure 2-4: Scotch yoke Mechanism

The red pin, sits in the slot in the yoke. The pin is as close to the width of the slot as

possible. As the wheel turns the yoke is forced back and forth with in its two bushes

(black). The speed of motion follows that of a sine wave with the speed reaching a

maximum at the middle of the travel and momentarily coming to a complete stop at

each end of the travel. [21]

2.2.1.2. Advantages

High torque output with a small cylinder size.

Fewer moving parts.

Smoother operation.

Higher percentage of the time spent at top dead center (dwell)

improving engine efficiency. [22]

2.2.1.3.

Disadvantages

- Rapid wear of the slot in the yoke caused by sliding friction and

high contact pressures.

-

Lesser percentage of the time spent at bottom dead center

reducing blow down time for two stroke engines.[22]

2.2.1.4. Parts

- Disc.


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- Pin.

Figure 2-5: scotch yoke Disk and Pin[23]

-

Slot.

- 2 rods.

Figure 2-6: scotch yoke Slot and Rods [23]

- 2 bushes (guides).

Figure 2-7: scotch yoke mechanism [23]

2.2.2. Mechanism equations

The three main parameters in any mechanism are:

-

Displacement.- Velocity.


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- Acceleration.

Figure 2-8: scotch yoke parameters [23]

The displacement is function on time and angular velocity; also it can be function on

angle (θ).

=

So = =

So if the angle θ= 90, the Displacement will equal the radius and this is the maximum

displacement.

To get the velocity, we get the first differentiation of displacement with respect to time.

() = () = − ∗

To get acceleration, we get the second differentiation of displacement with respect to

time.

() = ( ) 2 = −2∗ ∗

The motion shape is a sine wave with a time period().

= 2

In order to demonstrate the relationship between displacement, velocity, acceleration

and angular velocity, we do a MATLAB sheet to plot the equations.

- Displacement vs. Angular velocity


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Figure 2-9: Displacement vs. Angular velocity work-sheet [23]

Figure 2-10: Displacement vs. Angular Velocity graph [23]

- Velocity vs. Angular velocity

Figure 2-11: Velocity vs. Angular velocity work-sheet [23]


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Figure 2-14: Acceleration vs. Angular velocity graph

[23]

2.2.3. Dimensions and Stroke

Dimensions and stroke are very important aspects while creating a mechanism.

The most two asked questions while making a mechanism are:

- What is the desirable stroke?

-

What are the suitable dimensions to achieve desirable stroke?

Stroke, in scotch yoke mechanism, is the distance that the slot moves inward and

backward. And this distance equals twice the displacement.

Therefore,

= 2 ∗ = 2 ∗

For = , and θ = 90

Therefore,

= 2 ∗ , as 90 = 1

Where =

ℎ . Assume the pin is tangent to the circle from inside, therefore,

= (2 ∗ ) +

Or = +


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Figure 2-15: simulated positions and stroke

2.3. Wave analysis

The main purpose of wave maker is to generate a wave with known characteristics, sowe should dig deep through the main parameters of wave, wave equations and

relationship between these parameters.

2.3.1. Wave parameters

- Wave Height: is the vertical distance between wave crest and

next wave trough.

- Wave length: is the horizontal distance between two respective

crests or troughs.

-

Wave period: is the time needed to complete a full wave. It can

be measured by picking stationary point and counting the

seconds it takes for two consecutive crests or troughs pass it.

-

Wave frequency: is number of waves per second.

- Wave number: number of waves occurs in 2.


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Figure 2-16: wave parameters

2.3.2.

Theoretical approach

To generate small amplitude, sinusoidal wave with a desired period and wave height,

the required stroke of the wave maker is given by:

= ℎ 2ℎ + 2ℎ2(ℎ 2ℎ − 1 )

(1)

Where is the wave height, is the wave number, and ℎ is the water depth. Equation

(1) is derived from linear wave maker theory as presented.

According to Wiegel (1964), solitary waves may be generated in laboratory using

several methods, including:

- Impulsively loaded piston.

- Rapid addition of specific volume of additional water.

- Dropping a body into the water.

All of these methods normally produce a dispersive tail which follows the desired

solitary wave. Goring and Raichlen (1980) describe method for minimizing this tail by

matching the wave maker plate velocity to the solitary wave water particle velocity. [24]

2.3.3.

Performance Analysis:

Our purpose is to produce several linear waves with different wave height, but we

cannot change the strong as it is fixed, so that we should get a relationship between

wave Height and stroke.

From equation (1):

=2 (ℎ 2ℎ − 1)ℎ 2ℎ + 2ℎ

Where

is the wave height,

is the wave number,

ℎ is the water depth,

and is the stroke.


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As stroke and water depth are constants, we find out that wave height depends on the

wave number.

=2

Where, is the wave length, which differs from shallow water and deep water.

- Wave length in shallow water

Shallow = √ ℎ

- Wave length in deep water

Deep = 2 / 2

Where is the wave period, and = 1

Where is the wave frequency, and =

2 Where is angular velocity, and = 2

is no of revolution per minute and it is desirable.

By using MATLAB we can perform the previous equations and get different wave

heights with respect to the change in RPM.

2.3.4. MATLAB work sheet

First of all, we determine the desirable RPM, assume it starts at 0 RPM and ends to 180

RPM with 10 RPM intervals. Second the stroke equals 6 cm (0.06 m) and water depthequals 20 cm (0.2 m).

So, = [0:10:180], = 0.06 , ℎ = 0.2

- For deep water

ℎ ⁄ > 0.5


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Figure 2-17: Deep water work-sheet

Where, HS is the ratio between wave height and stroke.

Figure 2-18: Wave results on deep water

This means that we are working in deep water from [120:180] RPM and the maximum

wave height equals 12cm. as long as RPM increases the wave height increases and the


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probability to stay in deep water area increase. While from 160 to 180 RPM, the wave

height becomes steady which is shown in the next graph which describes the relation-

ship between the Height-Stroke ratio and relative depth.

Figure 2-19: Height-Stroke ratio vs. Relative depth on deep water

For shallow water

ℎ

< 0.05

Assumed RPM= [0:10:180]


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Figure 2-20: Shallow water work-sheet

Figure 2-21: Wave results on shallow water


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The performance starts on shallow water from 0 to 20 RPM. The maximum wave height

is 1.79 cm at 20 RPM. As long as RPM increases the wave height increases and the

probability to stay in shallow water area decreases.

Figure 2-22: Height-stroke ratio vs. Relative depth on shallow water

In brief, from 0 to approximately 30 RPM, the working zone is shallow water. From 30

to approximately 120 RPM, the working zone is intermediate water. Above 120 RPM,

the working zone is deep water.

2.4. Wave absorber

After the wave generator, wave absorber is the most important part in a wave flume or

basin. A great variety of designs and materials have been used throughout the world for

the construction of wave absorbers. Wave absorbers could be classified into two main

categories: active and passive absorbers. However the use of active absorbers owning to

its high cost is still very limited, except in a few cases where the wave board itself is

programmed to absorb the reflected wave. For passive absorbers, the beach of constant

slop reaching the bottom using sand, gravel or stones seems to be the most popular

arrangement, but the use of other materials such as transversal bars; horsehair and wire

screen is also popular.


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Figure 2-23: wave absorber

The slope of these absorbers has to be mild so as to obtain a good dissipation of wave

energy. This usually means a long wave absorber, thus using up valuable tank space

(Dalrymple et al. 2002). In order to reduce the length of the absorber, different

arrangements, including the addition of roughness on the surface and the use of porous

materials, have been tried.

From 43 laboratories which investigated in this study only four laboratories use active

absorbers. Most other laboratories use passive absorbers. Passive absorbers are mainly

made up of beaches of constant or varying slopes. The material which constitutes the

slop could be permeable. The beaches are often covered by many kinds of rough

materials. Some laboratories are using cages filled with different porous materials. One

of the important criteria to be satisfied is that the variation of the water depth over a

wavelength is small, because abrupt changes of the bottom profile lead to reflection.

From 43 laboratories which use passive absorbers, 27 of them use a beach of constant

slope reaching the bottom as wave absorber, 7 of them use a variation of this type of

wave absorber as a mean of absorbing wave energy, 4 of them use a parabola beach

reaching the tank bottom, and 3 of them use a parabola not reaching the bottom. The last

two laboratories use a combination of different mechanisms to absorber wave energy. It

is clear that most wave flumes tend to use simpler types of absorber shapes.[24]


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Table 2-2: Different materials placed over or underneath the wave absorber [24]

Material Percentage of laboratories

using

1 Wire screen 15%

2 Transversal bars 18%

3 Horse hair 14%

4 Sand, Gravel and stones 22%

5 Ripples 5%

6 Wooden laths 5%

7 Perforated plywood 5%

8 Cages filled with porous

materials

10%

9 Group of stainless pieces 3%

10 Plastics impregnated cocos

fiber

1.5%

11 concrete 1.5%

Among the materials used to roughen surface or to increase porosity (Table 2), there is a

wide variety, the majority being sand/gravel/stones (22%), transversal bars (18%), wire

screens (15%), and horsehair (14%). About a third of laboratories use some kind of

permeable structures. One of the main parameters to be considered is the ratio of the

absorbers length to the water depth.

slope = water depth absorber length

Usually the absorber slope is lower than 1:5

2.5. Plunger Design

In laboratory test tanks, water surface waves are created by causing a forced oscillation

of the water particles at one end of the tank. In most cases, this is done mechanically

with different kinds of wave boards and plungers. One major principle in wave maker

design is to try to get the forced oscillation to match the natural water particle

oscillation in a wave as well as possible. Usually wave makers work satisfactorily at a

limited, specific frequency range. At frequencies outside this range, horizontal


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accelerations at the wave maker surface at various depths are inadequate, causing

distortion of the wave shape.

Figure 2-24: Plunger Motion[25]

The majority of wave maker theories concern piston- or flap-type wave makers.

Especially studies on vertically oscillating plungers seem rare. Besides there may be

lesser need for theories of this kind one reason has been the difficulty to present a theory

that would in some manner cover the variety of plunger shapes in use. Actually it has

proved difficult even to find an analytical solution of the generated wave for a body of

any shape. Ursell, however, has analyzed waves generated by an oscillating circular

cylinder and found that the generated wave height only depends on a dimensionless

parameter kr, k being the wave number and r the radius. Wang used a similar reasoning

when extending the theory to plungers of more or less triangular shape, using Lewi's

conformal transformation. In Wang's study a two parameter transformation was used

that does not yield exactly the triangular shapes intended.

Wang, too, found that the wave height only depended on the dimensionless parameter

kd, where d is the breadth of the plunger at the water surface. The plunger geometry,

Wang described it by two parameters; the sectional area coefficient and the breadth at

the water surface. For prismatic plunger Galvin found an approximate solution for the

wave generators in shallow water. He stated that the height of waves generated by

displacement type wave generators equals approximately to 2nSIL times an appropriate

dimension of the wave generator. The terms S and L are the stroke of the wave

generator and the wave length, respectively. [25]


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Figure 2-25: plunger design ratios [25]

Where,d is the immersed depth of plunger, b is width at water level, and

So sin ωt is the stroke.

From the previous figure,

db ≅ 0.65. For known stroke and water level, we can figure out the

optimum dimension for the plunger.

d = h − Stroke + tolerance

Tolerance is a safety factor in order not to reach the bottom of the flume and cause

damage.


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Chapter 3

3. Experimental

3.1 Tank

The tank used already exists and we made some modification to it. The tank was constructed for

flow hydraulic test and we modify it to meet our needs. A cap with 3.5 cm diameter is used to

plug the system. We remove the two towers in order to provide a place for the mechanism and

wave absorber. The tank dimensions are 218 cm length, 15.2 cm moulded width, 15.6 cm

external width and 28 cm depth. The tank is 92 cm above the floor. It uses a closed watersystem where the water exists in the blue part.

Figure 3-1: Tank after modification


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Figure 3-2: Tank Dimension

3.2.

Motor and Gear box

A motor with 0.5 hp and 1400 rpm was selected for the experiment to satisfy the mechanism

load. To reduce rpm a gear box with 1/15 ratio is used to meet the required rpm. All of this was

selected after a market survey in order to minimize cost and effective performance.

- Gear box:

is an element of a mechanical system of gears and shafts used to reduce the rotational speed of

the input shaft to a slower rotational speed on the output shaft. This reduction in output speed

helps increase torque.

Figure 3-3: Gear Box Standards


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Figure 3-4: Gear Box Diagram

The reduction gear will help to reduce from 1400 rpm to 100 rpm, but to use a variation of

velocities we have to use an inverter.

3.3. Inverter

Inverter is an electronic device or circuitry that changes direct current (DC)

to alternating current (AC). The input voltage, output voltage and frequency, andoverall power handling depend on the design of the specific device or circuitry. The

inverter does not produce any power; the power is provided by the DC source.

Throughout the market survey, an ABB inverter was our best option to have variable velocities.

Specifications:

ABB Drives ACS 150 AC Variable Frequency Inverter Drive Controller for

0.75kW (1.0HP) or 0.55kW (0.75HP) 230V 3 Phase motor in VxF control to

4.7A. Converts fixed frequency Single Phase 230V input to variable frequency

Three Phase 230V output to control the speed of a standard AC Induction motor.

R1 Size - 70mm Wide x 144mm deep x 201mm high (plus cable clamp plate at

38mm) IP20 case.

Overload - 150% x 60seconds.

Speed Control Range - 0/500Hz.

Braking - To 40 Ohm Minimum, 200 Ohm Maximum external resistor (not

http://en.wikipedia.org/wiki/Direct_currenthttp://en.wikipedia.org/wiki/Alternating_currenthttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Electrical_powerhttp://en.wikipedia.org/wiki/Electrical_powerhttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Alternating_currenthttp://en.wikipedia.org/wiki/Direct_current


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supplied) - See the Resistor options linked below or use the 'Which Resistor'

button on this page.

Features - Front Mounted Potentiometer, 1 x Analogue Input, 5 Digital Inputs, 1

Relay Contact set.

Can be programmed from a pc via 'Flash drop'.

EMC Filters to EN61800-3 to the 2nd Environment C3 (Industrial). See linked

products below for external 1st Environment (Domestic) EMC Filter.

Can be used with supplies protected by RCD Type A.

Input Current - 11.4A.

Input Voltage - 200/240V single phase +-10% at 50/60Hz.

Wall mount in clean environment or cubicle mount.

Rated at 40C Ambient.

Ventilation space above and below - 75mm.

Ventilation space at sides - 0mm.

Heat Loss at max output - 62W.

Mounting onto symmetrical DIN rail or use the screw fixings for side or rear

mounting.

Full part number is - ACS150-01E-04A7-2 (68581966).[34]

Figure 3-5: Inverter profiles [35]


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3.4. Stand for Mechanism

we bought an Iron staple U-shaped long 6m and thickness 5mm , then we cut it by Iron Cutting

Machine into four legs; each leg long 1.5m.

Figure 3-6: Holder Design

Then we bought a flat plate 50*50cm and thickness 5mm , then we use Shielded Manual MetalArc in welding this plate with the legs at height 117.5cm and checked the balance using Water

Balance on the three dimensions axial , vertical and horizontal.

We also welded two single plates for the bearing which act as guide for the rod , first plate

welded at 110cm height and second plate welded at 150cm.

Then we cleaned this stand from slag by wire brush then painted the primer then the color paint.


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Figure 3-7: Holder


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3.5. Mechanism preparation

To design scotch yoke mechanism we bought a flat sheet of artellyon and 2 rods with 32 mm

diameter and 2 bearing (as guide) with 30 mm inner diameter.

Figure 3-8: Raw Materials

A group of machining processes have to be done to design our disc with diameter of 20 mm and

to reduce the rode diameter into 29.5 mm diameter to meet with bearing diameter. Also we

made a slot and pin with approximately 29 mm diameter, then 2 forks were made at both ends

of the rods in order to be fixed with the slot.


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Figure 3-9: Disc

Figure 3-10: Rods, disc and pin


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3.6. Plunger

To design the plunger we bought a stainless steel sheet with 2mm thickness and cut it to create

the five faces of plunger.

Table 3-1: Plunger Design

No. of faces required Dimensions

1

2

1


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1

Figure 3-11: Plunger

3.7. Wave absorber

We bought a staple of wood 5m long, width 2cm and thickness 2cm. We cut it into two pieces

123cm , two pieces 120cm , two pieces 25cm and two pieces 15cm, and we fix them by nails


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and surround this frame by wire baklava and fell it by gravels to absorb the wave and act as

shore to prevent the reflected waves.

Figure 3-12: Wave absorber Frame

Figure 3-13: Wave Absorber


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3.8. Wave Maker

Figure 3-14: Wave generation mechanism


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Chapter 4

4. Results

We will discuss the effect of change the RPM, only parameter can be controlled, on the

entire wave parameters (wave frequency, wave period, wave length, wave speed); in

order to find out the change on each parameter and analysis the results and compare it

with the experimental results.

The following sheet describes the change in parameters with respect to change of RPM.

Figure 4-1: Exel sheet

From the previous figure, we can notice how much the change of RPM affects the wave

characteristics, so that we will discuss it with more details to find out and predict the

wave expected to be created.

RPM vs. Wave Frequency:

Table 4-1: RPM vs. Wave Frequency

RPM Wave Frequency

0 0

10 0.17


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Clearly, wave frequency is direct proportional

with RPM, so that as long as the RPM increase

the number of waves can be seen is increased

which is good in case of small wave flumes in

order to have a full observation on waves.

-

The maximum number of waves per second is 3 waves at 180 rpm which is

considered acceptable to the flume size.

RPM vs. Wave period

Table 4-2: RPM vs. Wave period

20 0.33

30 0.5

40 0.67

50 0.83

60 1

70 1.17

80 1.33

90 1.5

100 1.67

110 1.83

120 2

130 2.17

140 2.33

150 2.5

160 2.67

170 2.83

180 3

RPM Wave period

0 NAN

10 6

20 3

30 2

40 1.5

50 1.2

60 1

70 0.86

Figure 4-2: RPM vs. Wave Frequency

Figure 4-3: RPM vs. Wave period


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From the previous graph, a sudden increasing

happens in the wave period then it starts to

decrease as long as RPM increase.

The maximum wave period is 6 seconds at 10

rpm which is too slow to perform at it with

respect to the flume length.

RPM vs. Wave length

Table 4-3: RPM vs. Wave Length

From the data and with respect to the flume

length, if RPM is between 10 to 40 rpm, the

wave length is taller than the flume length and a

complete wave will never be constructed. But

from 50 to 110 rpm, it can be constructed easily

80 0.75

90 0.67

100 0.6

110 0.55

120 0.5

130 0.46

140 0.43

150 0.4

160 0.38

170 0.35

180 0.33

RPM Wave length

0 NAN

10 8.4

20 4.2

30 5.31

40 2.99

50 1.91

60 1.33

70 0.98

80 0.75

90 0.59

100 0.48

110 0.4

120 3.85

130 3.28

Figure 4-4: RPM vs. Wave length


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- Comparing it with experimental results.

Experimental results

In order to get experimental results a wave probe monitor is used to collect the change

in wave characteristics and convert it into data and graphs.

Wave probe monitor

The wave probe monitor is a simple and reliable device for measuring rapidly changing

water levels. It operates by measuring the current that flows between two stainless steel

wires that are immersed in water. This current is converted to an output voltage that is

directly proportional to the immersed depth.

The wave probe monitors are supplied in cases that can accommodate either four or

eight monitors. These cases include the power supply for the modules, the input

connections for the wave probes and the output connections for a computer.

The cases can be supplied with a plug-n-play USB output so that they can be connected

directly to either a desktop or laptop computer without the need for any additional

analogue input cards.

The four-channel cases can also be supplied with four additional input sockets to enable

other instruments with voltage outputs to be connected directly to the computer.

Principle of operation

Each wave probe monitor contains the energizing and sensing circuits for the operation

of one wave probe. In addition to this, each monitor contains the circuits required to

compensate for the resistance of the cable that is connected to the probe. Without this,

the output of the wave probe monitor would be non-linear.

In order to avoid polarization effects at the probe surface, a high frequency square wave

voltage is used to energize the probe. The oscillator that produces this square wave may

be set to one of six different frequencies. This allows probes to be used close together

without causing any interference.

The current in each probe is detected by measuring the voltage drop across two

resistors. Because the measured voltage is alternating,

wave maker design and preformance

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