Ship drag reduction
by air cavities
Ship drag reduction
by air cavities
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op vrijdag 28 maart 2014 om 12:30 uur
door
Oleksandr ZVERKHOVSKYI werktuigkundig ingenieur
Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. ir. T.J.C. van Terwisga
Prof. dr. ir. J. Westerweel
Samenstelling promotiecommissie:
Rector Magnificus, Technische Universiteit Delft, voorzitter
Prof. dr. ir. T.J.C. van Terwisga, Technische Universiteit Delft, promotor
Prof. dr. ir. J. Westerweel, Technische Universiteit Delft, promotor
Prof. dr. M. Atlar, Newcastle University
Prof. dr. R. Bensow, Chalmers University of Technology
Prof. dr. ir. R.H.M. Huijsmans, Technische Universiteit Delft
Dr. -Ing. C.H. Thill, Universitat Duisburg-Essen, DST
Dr. C. Sun, Universiteit Twente
Prof. dr. ir. G. Ooms, Technische Universiteit Delft, reservelid
Dr. R. Delfos heeft als begeleider in belangrijke mate aan de totstandkoming van het proefschrift bijgedragen.
This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by Ministry of Economic Affairs (project number 07781).
Copyright© 2014 by O. Zverkhovskyi
All rights reserved. ISBN 978-94-6108638-9
Contents
Summary vii
Samenvatting ix
Nomenclature xi
1 Introduction 1
1.1 Background and motivation . . . 1
1.2 Objectives and scope of the research . . . 2
1.3 Outline of the theses . . . 3
2 Literature overview and theoretical background 5 2.1 Introduction . . . 5
2.2 Laboratory and full-scale experiments . . . 9
2.3 Potential flow theory . . . 10
2.4 Air flow in the cavity . . . 11
3 Experimental facilities 17 3.1 Introduction . . . 17
3.2 The water tunnel test . . . 18
3.2.1 The water tunnel . . . 18
3.2.2 Test section . . . 20
3.2.3 Test plate . . . 21
3.2.4 Force balance . . . 22
3.2.5 PIV and high-speed imaging . . . 24
3.2.6 Pressure and gas flow rate measurement . . . 25
3.3 Ship model test . . . 26
3.3.1 Ship model . . . 26
3.3.2 Air supply system . . . 27
3.3.3 Suspension of the model and force measurement . . . 28
3.3.4 Towing tank . . . 28 iii
iv Contents
4 On the physics of an air cavity in a steady flow. Experimental results. 31
4.1 Introduction . . . 31
4.2 Characterization of incoming flow . . . 32
4.3 Cavity length . . . 33
4.4 Cavity closure and air flux . . . 41
4.5 Velocity measurements . . . 42
4.6 Cavity stability . . . 45
4.7 Conclusions . . . 46
5 Flat plate drag reduction by air cavities 49 5.1 Introduction . . . 49
5.2 Setup . . . 50
5.3 Measurement procedure and data processing . . . 50
5.3.1 Measurement procedure . . . 50 5.3.2 Data processing . . . 51 5.4 Uncertainty analysis . . . 51 5.4.1 Bias limit . . . 53 5.4.2 Precision limit . . . 56 5.4.3 Total uncertainties . . . 56
5.5 Flat plate friction measurements . . . 56
5.6 The flat plate with air cavities . . . 60
5.6.1 Single cavity case . . . 60
5.6.2 Multiple cavity case . . . 63
5.7 Discussion on the drag reduction estimation . . . 65
5.8 Conclusions . . . 68
6 Ship model experiments with air cavities 69 6.1 Introduction . . . 69
6.2 A concept of the air cavities system and experimental program. . . 70
6.3 The hydrostatic stability of the ship model. . . 71
6.4 The length and thickness of air cavities . . . 74
6.5 On the stability of the air cavity system . . . 75
6.6 Ship model drag reduction by the air cavities . . . 77
6.6.1 Ship scale model drag reduction in calm water . . . 78
6.6.2 Ship scale model drag reduction in waves . . . 81
6.7 Conclusions . . . 82
7 Conclusions & Recommendations 85 7.1 The water tunnel experiments. . . 85
7.1.1 On the physics of an air cavity in a steady flow. . . 85
7.1.2 Flat plate drag reduction by air cavities . . . 86
7.2 The ship model experiment . . . 87
Contents v
A Calibration of the force balance 89
A.1 Calibration procedure . . . 89
A.2 Relative reproducibility and repeatability errors . . . 90
A.3 Relative interpolation error . . . 90
A.4 Relative reversibility error . . . 91
A.5 Relative zero error . . . 91
A.6 Calibration results . . . 91
B Seakeeping and Manoeuvring Basin 95
Bibliography 98
Acknowledgements 103
Summary
Ship drag reduction by air cavities – Oleksandr Zverkhovskyi
Transportation over water is an important link in the logistics chain. Although it is one of the most efficient way of transporting, there are ways to improve it. Ship’s resistance reduction leads to fuel savings and/or an increased in speed. For most cargo vessels the friction of water with the hull contributes more than one half to the total ship’s resistance. One of the most promising viscous drag reduction techniques for a ship is so-called air lubrication. Despite the great potential of this technique, it has not been widely applied in the shipbuilding industry. The reason is a lack of understanding of the working principles of air lubrication, scaling effects, and stability issues.
The present study focused on drag reduction by air cavities underneath a horizontal sur-face, with the aim to implement this technology in the shipbuilding industry. The inland waterway vessels are considered to benefit most from this technology, because of the rel-atively large rate of drag caused by the friction on the bottom of this type of ships. The objectives of this work are to study the hydrodynamic properties of air cavities, and their potential for ship drag reduction. Experimental methods were chosen since these are the most reliable and accurate tools for studying complex two-phase flow. The study was di-vided into two phases using different experimental facilities.
First, we used a flat plate experiment in a high-speed water tunnel. The objective of this part was to gain insight in the general aspects of the air cavities, such as formation, devel-opment and stability of the cavities, as well as dependence on the main flow parameters (such as velocity, pressure, and air flux). The cavity was created by injecting air behind a cavitator. The results show that the cavity length is equal to approximately one half of the gravity wave length. The cavity length and thickness can somewhat be influenced by the initial flow conditions as well as by the cavity closure conditions. However, the gravity wave is dominant in defining the cavity length. Furthermore, it was found that the shallow-water effect might substantially increase the cavity length. It was also shown that the angle of attack of the plate has a strong effect on the cavity parameters, which is likely caused by a pressure gradient along the cavity. The experimental data show a correlation between the water velocity, cavity length, thickness, and pressure. A positive pressure in the cavity was measured for developed cavities, whereas for developing cavities it turned
viii Summary out it can be negative.
Two mechanisms, which govern the air discharge from the cavity, were observed. The first mechanism is governed by the presence of the re-entrant jet, that is continuously shedding bits of the air cavity in the closure region. The second mechanism is caused by waves on the free surface of the cavity water interface. The contribution of each of these mechanisms depends on the flow conditions (e.g. flow velocity and turbulence intensity) and the geom-etry of the cavity. Furthermore, stability issues of the cavity were discussed. If the wave amplitudes at the free surface are comparable to the cavity thickness, the cavity will break up. In that case, the maximum cavity length based on the gravity wave length cannot be reached.
The drag reduction efficiency of the air cavities was assessed by directly measuring the friction force on the test plate. The measurements were performed with one or two air cavities created on the lower surface of the test plate. The results showed a possibility to reduce the friction up to 60% on a plate by applying air cavities. The analysis of the results led to the conclusion that the number of cavities can be optimized for specific flow conditions in order to maximize the drag reduction.
The most important objective of the research was to assess the effectiveness of air cavities for drag reduction. This study was performed in the second phase on a ship model in a towing tank. The reached drag reduction in calm water was about 8 to 12%. The ship model with air cavities system was also tested in the regular head waves. Furthermore, the presence of short period waves appeared to have an influence on the dynamics and stabil-ity of the cavities. It was observed that the cavstabil-ity length fluctuated within approximately 10% during a wave passage, sometimes causing instability of one or more cavities. The efficiency of the drag reduction drops to 5 to 7% in short period waves, whereas at long period waves it is the same as in calm water.
Samenvatting
Schip weerstandsvermindering door luchtholtes – Oleksandr Zverkhovskyi Transport over water is een belangrijke schakel in de logistieke keten. Hoewel het een van de meest effici¨ente manieren van transport is, zijn er mogelijkheden om dit te verbeteren. Weerstandsvermindering van een schip leidt tot brandstofbesparingen en/of een verhoogde snelheid. Voor het grootste deel van de vrachtschepen bedraagt de wrijving van het water met de romp meer dan de helft van de totale weerstand van een schip. Een van de meest veelbelovende reductie technieken van de viskueze weerstand van een schip is zogenaamde luchtsmering. Ondanks het grote potentieel van deze techniek, is deze nog niet op grote schaal toegepast in de scheepsbouw. De reden daarvoor is het gebrek aan inzicht in de werkingsprincipes van luchtsmering, de scaling effecten, en de stabiliteitsproblemen. Deze studie is gericht op weerstandsvermindering door luchtholtes onder een horizontaal oppervlak, met als doel deze technologie te implementeren in de scheepsbouw. De binnen-vaartschepen worden verondersteld het meest van deze technologie te profiteren, omdat een relatief grote hoeveelheid weerstand veroorzaakt wordt door de wrijving op de bo-dem van dit type schepen. De doelstellingen van dit werk zijn de studie van de hydrody-namische eigenschappen van de luchtholtes, en hun potentieel voor weerstandsvermindering van schepen. Experimentele methoden zijn gekozen omdat dit de meest betrouwbare en nauwkeurige technieken zijn voor het bestuderen van complexe tweefasenstroming. Het onderzoek werd verdeeld in twee fasen met verschillende experimentele faciliteiten.
Allereerst is een experiment met een vlakke plaat in een watertunnel gebruikt. Het doel van dit deel was om meer te leren over de algemene aspecten van de luchtholtes, zoals de vorming, ontwikkeling en stabiliteit van de holtes, alsook de afhankelijkheid van de pa-rameters van de hoofdstroom (bijv. de snelheid, druk, luchtstroom). De holte is gecre¨erd door het injecteren van lucht achter een cavitator. De resultaten tonen aan dat de lengte van de holte gelijk aan ongeveer de helft van de lengte van de oppervlaktegolven is. De lengte en dikte van de holte kan enigszins worden be¨ınvloed door de initi¨ele condities van de stroming en de omstandigheden van de sluiting van de holte. Echter is de oppervlak-tegolf dominant voor het bepalen van de lengte van de holte. Verder is gevonden dat het ondiep water effect de lengte van de holte behoorlijk kan verhogen. Er is ook aangetoond dat de invalshoek van de plaat een sterk effect heeft op de parameters van de holte,
x Samenvatting geen mogelijk veroorzaakt wordt door een drukgradi¨ent langs de holte. De experimentele gegevens laten een correlatie zien tussen de watersnelheid, lengte en dikte van de holte, en de druk. In een ontwikkelde holte werd een positieve druk gemeten, terwijl de druk in een ontwikkelende holtes negatief kan zijn.
Twee mechanismen, die de luchtafvoer uit de holte bepalen, zijn waargenomen. Het eerste mechanisme wordt bepaald door de aanwezigheid van een jet, welke continue voortdurend afstoten bits van de luchtspouw op het afsluitende gebied. Het tweede mechanisme wordt veroorzaakt door golven op het grensvlak tussen de luchtholte en het water. De bijdrage van elk van deze mechanismen is afhankelijk van de stroming (bijv. de stroomsnelheid en turbulentie intensiteit) en de geometrie van de holte. Verder worden stabiliteitsproble-men van de holte besproken. Wanneer de amplitude van de golven op het vrije oppervlak vergelijkbaar zijn met de dikte van de holte, zal de holte opbreken. In dat geval wordt de maximale lengte van de holte, op basis van de lengte van oppervlaktegolven, niet behaald. De effici¨entie van de weerstandsreductie van de luchtholtes werd bepaald door direct de wrijvingskracht op de testplaat te meten. De metingen werden uitgevoerd met een of twee luchtholtes op het oppervlak aan de onderkant van de testplaat. De resultaten tonen een mogelijkheid aan om de wrijving op een plaat tot 60% te reduceren door het gebruik van luchtholtes te reduceren. De analyse van de resultaten leidde tot de conclusie dat het aan-tal holtes geoptimaliseerd kan worden voor specifieke stromingsomstandigheden om zo de weerstandsvermindering te maximaliseren.
Het belangrijkste doel van dit onderzoek was om de effectiviteit van luchtholtes voor ver-mindering van de weerstand te bepalen. Deze studie werd uitgevoerd in de tweede fase op een schipmodel in een sleeptank. De weerstandsvermindering die in kalm water behaald werd, was ongeveer 8 tot 12% . Het schipmodel met luchtholtes werd ook getest in de reg-uliere hoofdgolven. Verder blijkt dat de aanwezigheid van korte golven van invloed is op de dynamiek en stabiliteit van de holtes. Er is waargenomen dat tijdens een golf passage de lengte van de holte fluctueert binnen ongeveer 10%, waardoor soms instabiliteit van een of meer holtes kan optreden. De effici¨entie van de vermindering van de weerstand daalt tot 5 tot 7% in korte golven, terwijl de effici¨entie bij langere golven hetzelfde is als in kalm water.
Nomenclature
A - wave amplitude [m] a - wedge length [m] B - width [m] Cf - friction coefficient [−] D - water depth [m] F - force [N ]f - inverse square of the Froude number [−] G - center of gravity [−]
g - gravitational acceleration [m/s2] H - maximum cavity thickness [m] Hf - shape factor [m]
Ht - tunnel depth [m]
h - cavitator height [m] hc - cavity height [m]
L - length [m]
Lpp - length between perpendiculars [m]
l - half of the cavity length [m] p - free stream pressure [kg/(ms2)] pc - pressure in the cavity [kg/(ms2)]
Q - air flux [m3/s]
Q∗ - non-dimensional air flux [−] Q1 - discharge per unit area [−]
S - wetted surface area [m2]
T - draft [m]
Tw - wave period [s]
t - temperature [◦C]
U, V - free stream velocity [m/s]
U∗ - velocity on the boundary of the cavity [m/s] Uu - local gas velocity in the cavity [m/s]
u - local velocity [m/s] W - displacement [m3]
x - streamwise direction [m]
xii Nomenclature α - wedge angle [deg]
η - cavity contour coordinate [m] λ - length of the gravity wave [m] λs - model scale ratio [−]
µ - dynamic viscosity [kg/(ms)] ρ - density [kg/m3]
σ - cavitation number [−] τ - shear stress [kgm/s]
Chapter 1
Introduction
Abstract
This chapter gives the background and motivation that lead to the study presented in this thesis. The objectives of the thesis and the methods for their realization are discussed. Finally, the outline of the thesis including a short description of each Chapter are presented.
1.1
Background and motivation
Fluid flow has always been strongly related with human activities. Since its origin humans are fascinated and studied flows that occur in 3 out of 4 basic elements of the ancient world: earth, water, air and fire. Nowadays, we have to deal with flows in our daily life as well as in many industrial processes. In order to be able to manage the flow we need to understand its features. The knowledge about fluid flows is described by fluid dynamics. One of the most important features of internal and external flows is the frictional drag that a solid body experiences in contact with a fluid when moving relative to the fluid. This is a result of the fact that a fluid has molecular viscosity. In many applications the friction is an undesirable phenomenon causing significant energy losses. The viscous friction between water and a ship’s hull contributes the most to the total resistance of a ship (Larsen and Raven, 2010). This fraction can be up to 70% depending on the type of vessel and flow regimes.
The reduction of friction resistance is therefore one of the most significant challenges in hydrodynamics. A number of techniques to reduce the viscous drag are known. The most familiar ones are adding polymers to the flow, the application of structured surfaces (for example, riblets) and certain coatings. However, most of them can not be applied effi-ciently on ships because of various practical limitations, including costs.
One of the most promising viscous drag reduction techniques for a ship is so-called air 1
2 Chapter 1. Introduction lubrication. From previous studies it is known that injecting air underneath a ship can significantly reduce its drag. Especially when air forms a stable layer that prevents water contact with the hull (e.g. Butuzov,1965; Titov, 1975; Sverchkov, 2007; Gorbachev and Amromin, 2012).
This study was performed within a project called ”Ship drag reduction by air lubrication”. This project was funded by the Dutch Technology Foundation STW. The main objectives of the project are to develop an understanding of the drag reduction mechanism(s) of air bubble and cavities induced drag reduction. Two more PhD studies were performed within this project focusing on bubble induced drag reduction (Harleman, 2012; van Gils, 2011).
1.2
Objectives and scope of the research
Analyzing the literature (e.g. Butuzov,1965; Savchenko, 2008; Ceccio, 2010; Sverchkov, 2007), the drag reduction by air cavities was acknowledged as a prospective technology for ships. However, this technology is not widely used in practice yet. The present study has focuses on the drag reduction by air cavities under a horizontal surface aiming to approach this technology for implementation in the shipbuilding industry. The inland waterway ves-sels are considered to benefit the most from this technology because of the relatively large rate of drag caused by the friction on the bottom of this type of ships. The objectives of this work are to study further the hydrodynamic properties of air cavities, and their poten-tial for the ship drag reduction. Experimental methods were chosen to meet the objectives as the most reliable and accurate tools in exploring the complex two-phase flow.
Because of the complexity of the problem the study was split in two phases using different experimental facilities. First, a flat plate experiments in a high-speed water tunnel were carried out. The objective of this part was to learn more about the general aspects of the air cavities, such as formation, development and stability of the cavities, as well as dependence on the main flow parameters (velocity, pressure, air flux etc.). The drag reduction efficiency of the air cavities was assessed by direct measurement of the friction force on the test plate.
The most important objective of this study is to assess the effectiveness of air cavities for drag reduction on a ship model in a towing tank that was performed in the second phase. The influence of the flow around the ship model and waves on the cavities were also studied. The dynamics and stability of the system of cavities on the ship model was explored in these tests as well.
1.3. Outline of the theses 3
1.3
Outline of the theses
This thesis represents the results of a systematic, extensive research done on the friction drag reduction by air cavities. A reader going through the thesis will be familiarized, first with the background in the ship drag reduction by air lubrication, then with the experi-mental facility used in the current research and results from a flat plate and ship model experiment.
In Chapter 2 of this thesis an introduction to the topic of the drag reduction in general is given. Then, more specifically, to the drag reduction by air lubrication and air cavities. The current state of the art on drag reduction by air lubrication is summarized.
In Chapter 3 the main details of the experimental facilities used during this research are presented. The first part of this Chapter contains the description of the flat plate test facility. Namely the description of the water tunnel, test section, flat plate, force balance, and the other instrumentation used. In the second part explains the details of the ship model experiment. The details of the towing tank and the ship model are presented. The details of the system that generates the air cavities are introduced as well.
Chapter 4 aims to give an insight into the physics of an air cavity flow. A relation between the flow characteristics and the cavity properties is investigated. The effect of the shallow water is explored as well as the flow velocity, pressure and air flux.
In Chapter 5 the potential of the drag reduction by air cavities on a flat plate is investi-gated. A force balance to measure the integral friction force on the flat plate is used. By comparing the drag measurements on the plate with and without the cavities the efficiency of this technology can defined.
Using the knowledge obtained from the flat plate test, air cavities were applied to a ship model. The results from the ship model test are presented in Chapter 6.
Chapter 2
Literature overview and theoretical
background
Abstract
In this Chapter the basics of the drag reduction by air lubrication are introduced. The spe-cific application of this technology to ships is explained. The potential of the drag reduction is discussed. The relevant studies that have been done by different research groups on the subject of the drag reduction by air lubrication are presented.
2.1
Introduction
A significant frictional drag reduction in water is possible by gas injection in a space be-tween water and a body moving in it. This is made possible because the values of viscosity and density for gases are much smaller than for water. There are basically two regimes of gas distribution in water: the stratified regime and the dispersed regime. The stratified regime is characterized by a sustainable gas layer between the body surface and water. In the case of the dispersed flow a liquid is saturated by gas bubbles. Taking into account the fact that viscosity and density of the mixture are higher than for gas the most attractive method of frictional drag reduction is the first one.
From existing literature one may conclude that gas lubrication can be used for the purpose of drag reduction on objects moving completely submerged in water and on the water sur-face; see Figure 2.1.
Supercavitation can be used as a gas lubrication for fully submerged objects. Depending on the nature of a gas it can be natural, when the supercavity is filled with water vapour, or an artificial one, filled with any other gas. Application of supercavities can be on objects moving at high Froude number, thus not significantly influenced by the gravity and can have an axisymmetrical shape. It is known to be a very efficient drag reduction
6 Chapter 2. Literature overview and theoretical background
Gas lubrication in water
Submerged objects
Surface vehicle
Hi-speed
vessels
Low-speed
displacement vessels
-0high0Froude0number 0(Applications:0propellers,0hydrofoils, 00projectiles0and0torpedos) -0low0Froude0number -0bottom0cavities -0Froude0number0>0.5 -0single0bottom0cavity -0redans -0Froude0number0<0.25 -0multi-wave0or0series 000of0bottm0cavitiesFigure 2.1: Classification of gas lubrication technique for drag reduction in water.
ogy, which makes it possible to move under water with velocities above a hundred meters per second and even reaching the speed of sound in water (∼1500 m/s) (Savchenko and Zverkhovskyi, 2009).
For vehicles moving on the water surface, like ships, air lubrication can usually be applied to the bottom of the ship. As shown in Figure 2.2, there are several options to create a sustainable gas layer under a horizontal surface. Although different authors use different names for each of the approaches, throughout this work we use the most frequently used classification: air layer (a), air cavity (b) and air chamber (c). These approaches are dis-cussed in more detail in the following.
An air layer can be formed under a horizontal surface by injecting a sufficient amount of air. Elbing et al., (2008) describe the transition of a bubbly flow to an air layer flow at certain air flux rates injected under a test plate in a water tunnel. An advantage of this technology is that a bottom does not have a special shape. The drawbacks are the high air flux required to form the air layer, the low stability of this air layer flow, and the sensitivity to misalignment of the surface from the horizontal position. Fukuda (2000) reports the use of a super-water-repellent surface that helps to create the air layer underneath a horizontal surface.
A more stable flow can be formed by application of an air cavity. The air cavity as shown in Figure 2.2(b) can be created by injecting air behind a cavitator. The cavitator is an obstruction in the span-wise direction that creates a suction pressure immediately down-stream of it. The cavity should be restricted on the sides by skegs/keels. The cavity can
2.1. Introduction 7
Flow
Air
Air
Air
a) b) c)Figure 2.2: Alternative ways of the stratified flow generation. a) - air layer, b) - air cavity, and c) - air chamber.
be generated only for non-zero flow velocity and has a limited length, which is equal to half the gravity wavelength.
The air chamber concept, Figure 2.2(c), is based on injecting air into a recess formed in the bottom. The free surface is not limited in length and can form a multi-wave cavity profile without water attaching the bottom, at sufficient depth of the recess.
The air cavity and air chamber concepts have been proven to be efficient for the drag reduc-tion on low-speed ships (Gorbachev and Amromin, 2012). They can be applied to a ship as shown in Figure 2.3. Several cavities are required to cover the bottom of a low-speed ship because of the limited cavity length, whereas the air chamber comprising the multi-wave cavity can spread along the whole bottom as well as can be separated in compartments. In both cases, with cavities or chambers, if a ship operates without air it provides additional resistance and draft compared to the initial hull. These are important drawbacks of the technology. However some foldable designs were suggested for that case.
The drag reduction by the air cavities/chambers is achieved by the reduction of the wetted surface on the bottom of the vessel. The efficiency of the drag reduction depends on the fraction of the frictional drag in the total drag of a ship, the fraction of the wetted area on the bottom in the total wetted area, and the efficiency of the drag reduction system on the bottom (Figure 2.4). The ideal system would reduce the frictional drag on the bottom to zero and add no additional drag by its elements. For example, for a ship with 70% of the frictional drag and 50% of the wetted surface located on the bottom, the ideal drag reduction system would reduce the total drag by 35%. However, the efficiency of a realistic
8 Chapter 2. Literature overview and theoretical background
without air
with air
air cavities air chamber
Figure 2.3: A ship with air cavities and air chambers with and without air.
system can be estimated from the efficiency of a flat plate and appears to be of the order of 50%. This results in a realistic drag reduction value for the given ship in order of 18%. As one of the objectives of this thesis it will explained the drag reduction potential of air cavities and possible ways to improve it.
residuals
friction
on the bottom
added drag
net DR
friction reduction
Figure 2.4: Effectiveness of drag reduction depending on the fraction of friction drag on the total drag of the vessel, the fraction of the bottom surface with respect to the total surface, and the added drag by the elements of the system.
2.2. Laboratory and full-scale experiments 9
2.2
Laboratory and full-scale experiments
Most of the published work on air cavities and chambers was done in the USSR/Russia, the USA, the Netherlands and Sweden. The most popular configuration that was tested is the air chamber, either on a flat plate in a water tunnel or on a ship model in a towing tank. In case of ship model tests the configurations vary by the number of cavities in longitudinal and transverse directions.
Gorbachev and Amromin (2012) give an overview of work on air cavity ships that has been done in the USSR/Russia, staring from 1966 till 2012. Significant input in exploring the air cavities for ship drag reduction was done by A.A. Butusov. In 1960 he developed a theoretical model, performed water tunnel and ship model tests on a single and a series of air cavities formed behind a wedge-type cavitator. The model test results were confirmed by full-scale tests on different inland waterway vessels. It was confirmed that the air cav-ities can reduce the overall drag of a ship by 12-20 %. In order to increase the efficiency even further and improve the negative effect of the increased draft of a ship due to the cavities, a new configuration was suggested with a multi-wave cavity profile formed in the bottom recess. Some of the results of the model and full scale tests available in literature are presented in Tables 2.1 and 2.2.
Table 2.1: Model-scale tests.
Author Scale L (m) B (m) T (m) W (m3) DR (%) Butuzov, (1965) 1:10 90 13 2.8 2740 10 Titov, (1975) 1:10 84.6 14 3.2 3270 12 Sverchkov, (2002) 1:15 81.92 11.4 2.5 1807 20 Sverchkov, (2007) 1:20 128.2 16.5 2.8 4960 22 Amromin, (2011) 4.55 1.1 up to 25
Table 2.2: Full-scale tests (taken from Sverchkov 2007, Gorbachev 2012). Q is the air flux.
Vessel L (m) B (m) T (m) W (m3) Cavities Q (l/s) DR (%)
Barge 84.6 14 3.2 3270 7 137 20
Volga-Don 135 16.5 3.2 6140 7 240 16
Two unit train 96+97.2 14 3.5 8550 8+8 130+130 12
Extensive experimental work on a ventilated partial cavity flow has been done at University of Michigan, the US (Makiharju et al., 2010 a,b). The experiments were performed at the U.S. Navy’s W. B. Morgan Large Cavitation Tunnel, which is a unique facility in terms of its size. This device allows studying the flows also with a free surface at high Reynolds numbers. A test plate of 12.9 m long and 3.05 m wide was installed horizontally in the
10 Chapter 2. Literature overview and theoretical background middle of the test section. The cavity was formed by injecting air underneath the test plate after 0.18 m tall backward-facing step. At the design condition the cavity should close on a beach near the trailing edge of the plate. The cavity was tested at a Froude number based on the cavity length of more than 0.55, at non-multi-wave regimes. The results of the experiments give information about the gas flux needed to establish and maintain the cavity. It was suggested that the required air flux in steady flow is a function of Fr, Re and closure geometry. They also showed that the cavity can be maintained even under perturbed flow conditions, generated by a wave making mechanism above the plate that simulates presence of the waves.
A similar experiment but with the multi-wave cavity, at lower flow velocities, is described by Shiri et al. (2012). The cavity of 6 m long and 1 m wide was tested in the cavitation tunnel at SSPA, Sweden. The cavity profile and stability were investigated at different velocities, air pressure and cavity closure geometry. The results of the measurements are compared with 2-D and 3-D CFD computations. The authors used the commercial package Fluent for a computational study. The Volume of Fluid method was used to simulate the unsteady water-air interface inside the cavity. From a comparison of the computational results with the experiments it was shown that the amplitude of the waves in the cavity is similar but that the phase of the waves differs. The authors concluded that refinement of the mesh is important to capture the detail of the re-attachment process of the cavity, which is needed for the air flow and drag force determination at the cavity closure.
Foeth (2008) briefly describes results of a model test with air cavities. By using potential flow codes and experimental results, an optimal configuration was found for the air cavity system that resulted in up to 10 % of the overall drag reduction. However, it was noted that the tested system is very sensitive to the local dynamics of the flow around a hull, and he recommended that a detailed computational or experimental analysis should be done to ensure the effectiveness of the system.
2.3
Potential flow theory
Free surface profile prediction is one of the most important problems for air cavity flows. For design purposes of an air cavity ship it is essential to know the geometrical characteris-tics of the free surface for any kind of air cavity configuration that has been described above. In general, potential flow theory can be used to analyze the flow with a free surface. A mathematical model of the cavity flow created behind a slender edge on the horizontal wall was developed by Butuzov (1966). To this end, a so-called the Riabouchinsky scheme was used (Figure 2.5). According to this scheme, the closure of the cavity is on a fictitious wedge of the same geometry as the one that generates the cavity. The liquid is assumed to have mass and to be inviscid, isotropic and incompressible. The pressure in the cavity
2.4. Air flow in the cavity 11 and on its contour is considered to be constant.
-l
-a
l
a
V
0α
y
g
Figure 2.5: Riabushinskyi scheme.
In his work Butuzov derives an equation that describes the relation between the main parameters of the cavity flow behind a slender edge. The resulting equation is presented in terms of a function of the cavity contour η :
f η(x) + 1 π Z l −l η0(ξ)dξ ξ − x + σ 2 = α πln (1 + a)2− x2 1 − x2 , (2.1)
where f is the inverse square of the Froude number based on a half the cavity length:
f = gL
2U2; (2.2)
and σ is the cavitation number:
σ = p − p1 c
2ρU2
. (2.3)
The calculations show that there is a maximum possible cavity length. The limiting cavity length in terms of the Froude number Fr∗ based on the cavity length L was found to be in
the range of 0.42-0.44.
Further work on the limiting parameters of air cavities including the influence by propul-sion and lift-enhancing devices was followed up by Matveev (2003). However, this has a limited interest within the scope of this thesis, where we concentrate on the drag reduction for low-speed cargo vessels. But also a simplified three-dimensional model based on the linearized potential flow theory for a multi-wave air cavity was investigated by Matveev (2007).
2.4
Air flow in the cavity
A sufficient air injection rate is one of the factors that determine the stability of the air cavity. The cavity is stable when the air flow rate injected into the cavity is equal or higher
12 Chapter 2. Literature overview and theoretical background than the flux of air carried by the flow from the cavity. The air entrainment rate depends mostly on closure conditions of the cavity. The air velocity distribution in the cavity has hardly any effect on the drag reduction and is determined by the relative velocity of the free surface and the air flux.
The definition of the air entrainment from the cavity is a challenging task that is also difficult to model by an experiment or by numerical simulations. A full-scale experiment is expected to be the most trusted method to determine it. It is known that there is a differ-ence between the air flux required for creation and maintenance of the cavity (Makiharju et al., 2010 a,b). The air flow rate to maintain the air cavity is an important parameter for the estimation of the net power reduction on an air lubricated ship. The existing ex-perimental data can be used to estimate an order of magnitude of the air flux for an air cavity ship with a given ship beam B at a certain velocity. We use the non-dimensional air flux Q* according to Equation 2.4 to present the data shown in Figure 2.6.
Q∗ = Q U B ∗ [1m], (2.4) 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.5 1 1.5 2 2.5 3 3.5 4x 10 −3 Q* V [m/s] Jang & Kim (1999) Titov (1975) Shiri et al. (2012)
Gorbachev & Amromin (2012) Lay et al. (2010)
Figure 2.6: Dimensionless air flux Q∗defined in (2.4) versus the velocity from different model, tunnel and full-scale experiments described in the literature. The data points from Shiri et al. (2012) and Lay at al.(2010) are for the air chamber configuration, the rest points are for air cavities.
The power needed to compress air for the air lubrication can be estimated as suggested by Makiharju et al. 2012. For an inland waterway vessel it is typically 1.5-3 % of the total
2.4. Air flow in the cavity 13 power on a vessel (Titov, 1979).
The air velocity profile inside of the ventilated cavity was measured experimentally by Rogdestvensky & Khlyupin (1969). In this experiment the cavity was formed under a horizontal flat plate behind a wedge-shaped cavitator. The experiments were done in a cavitation tunnel, used as a water tunnel. The measurements were done at a given gas discharge and different Froude numbers.
The gas velocity profiles were measured in three cross-sections along the cavity by mea-suring the dynamic pressure of the flow. At the location of the measurements Pitot tubes were installed on vertical traverses. To measure the gas dynamic pressure, micro-gauges of the balanced drop type were employed. The working principle of this type of pressure gauges is also explained in Rogdestvensky & Khlyupin (1969).
The results of the measurements were compared with a Couette flow with a pressure gra-dient.
For the cavity free surface bounding streamline the Bernoulli’s equation reads: p + ρU
2
2 = pc+ ρ U∗2
2 − ρghc, (2.5)
where p - free stream pressure, pc- cavity pressure, U∗ - flow velocity on the cavity
bound-ary. The velocity on the boundary of the cavity can be defined as follows:
U∗ = U r
1 + σ +2ghc
U2 , (2.6)
The velocity profile for the Couette flow for various values of pressure gradient is found to be: Uu = U∗η − h2c 2µη(1 − η) dp dx, (2.7)
where Uu is a local gas flow velocity at given coordinate, η = hyc - non-dimensional vertical
coordinate, hc - cavity height at the given cross-section.
To obtain the expression for the pressure gradient dxdp for (2.7) the cavity contour is required to be a streamline. Q1 = Z hc 0 Uudy = Z 1 0 Uuhcdη = U∗hc 2 − h3c 12µ · dp dx, (2.8)
14 Chapter 2. Literature overview and theoretical background dp dx = 6µ U∗ h2 c − 12µg Q1 h3 c . (2.9)
Substituting (2.9) into (2.7) we obtain: Uu = 3U∗− 6Q1 hc η2+ −2U∗+ 6Q1 hc η , (2.10) or U∗ = (3 − 6Q∗)η2+ (−2 + 6Q∗)η , (2.11) where U∗ = Uu U∗- is a non-dimensional velocity.
The velocity profiles for Couette flow with various pressure gradients are show in Figure 2.7. Due to the no-slip condition the gas velocity at the wall is equal to zero and on the water surface equals the local water velocity. The profile in between depends on the pressure gradient.
dP/dx=0
dP/dx<0
dP/dx>0
Figure 2.7: Velocity profiles for the Couette flow for various values of the pressure gradient.
An adverse pressure gradient, i.e. dp/dx>0, can be representative for the case when the air entrainment is zero. In this situation air circulates inside the cavity. It is interesting to notice that for this flow the drag force on a wall is negative. Whereas for the first two cases there should be some air entrainment from the cavity.
The results of the measurements and calculated profiles by (2.11) are plotted in Figure 2.8. As can be seen, the velocity profile inside the cavity can be modeled with sufficient accu-racy by the Couette flow equation with a pressure gradient.
2.4. Air flow in the cavity 15
(a)
(b)
Figure 2.8: Velocity profile of the air flow in the cavity: measurements vs. theory. The results are presented for two different Froude numbers at three cross-sections along the cavity. Taken from Rogdestvensky and Khlyupin (1969).
Chapter 3
Experimental facilities
Abstract
This chapter describes the experimental facilities and measurement techniques that are used to obtain the results presented in the thesis. First, the water tunnel facility for the flat plate test is described. Measurement techniques used, such as a force balance and PIV are presented. Second, the test set up of a scaled ship model in a towing tank is described. The information about the ship model, the design of the air cavities system, the towing tank and the instrumentation used in the experiment are given.
3.1
Introduction
The viscous drag reduction in liquids and gases has been a subject of interest for many decades. In many applications the friction drag is responsible for a great part of the energy losses associated with the transport in/of liquids or gases. There are a number of viscous drag reduction techniques suggested for different applications. Experimental facilities are required in order to study the physical aspects of drag reduction and efficiency.
There are different facilities used for drag reduction studies for both internal and external flows on laboratory scales. For internal flows typically pipe or channel flow facilities are used, whereas for external flows water/wind tunnels and towing tanks are used.
The shear force measurement, which is needed for the assessment of the drag reduction effi-ciency, can be performed locally or globally. Local shear stress sensors of different working principles can be used for internal as well as external flows. Recent development of optical measurement techniques allow for an indirect measurement of the drag force (Harleman, 2012). The measurement of pressure drop is used as an indication for the global wall-shear stress for the internal flows. The global drag tests for external flows are typically done in water/wind tunnels or towing tanks.
18 Chapter 3. Experimental facilities Because of the different research objectives of the project and complexity of the studied phenomena of the air cavity flow and the drag reduction efficiency, this study was performed in two different experimental facilities. First, for the flat plate experiment a water tunnel facility was used. The objective for this experiment was to study the air cavity flow under a horizontal surface and efficiency of the drag reduction on a flat plate. Next, a ship scale model was used in a towing tank experiment. The objectives of these tests were to estimate the drag reduction by air cavities and interaction of the flow around a model and the effect of surface waves on the motion of the ship and stability of the air cavities. In this Chapter it is describe in detail both facilities and instrumentation that were used to obtain the results presented in this thesis.
3.2
The water tunnel test
3.2.1
The water tunnel
The cavitation tunnel at the Ship Hydromechanics group of the Delft University of Tech-nology was used as a laboratory facility for the flat plate experiments. This tunnel was originally constructed to study cavitation on propellers and hydrofoils. It is a closed loop tunnel made of stainless steel. The velocity in the tunnel is set by a frequency controlled asynchronous motor that drives an impeller. The maximum velocity in the test section with a cross section of 300×300 mm2 is 8 m/s. More information about the initial
config-uration of the cavitation tunnel can be found in the PhD thesis of Foeth (2008a).
For the purpose of friction drag studies by air lubrication, the cavitation tunnel was refur-bished in order to house a new test section that allows for tests with air cavities and the dedicated study of the boundary layer flow. The old test section and the diffuser were re-designed and replaced for this purpose. A schematic representation of the tunnel is shown in Figure 3.1. The new test section (4) is significantly longer than the old one, which could be achieved by shortening the diffuser. Two guiding vanes were installed in the new diffuser. The other components of the tunnel remain unchanged. The overall performance of the tunnel did not change due to this modification.
The cavitation tunnel operated as a water tunnel under atmospheric pressure in the test section. The maximum water velocity in the test section is 7 m/s. However, the maximum velocity with air injection is limited to 3 - 3.5 m/s. At higher velocity air injected in the test section recirculates in the tunnel. At lower velocities air can be removed from the flow as a result of buoyancy in the de-aeration tower (1) that is located after the diffuser (5). The velocity in the test section is determined by measuring the pressure drop over the contraction part (3) by a differential pressure sensor.
3.2. The water tunnel test 19 1 2 1 5 4 3 6 7 diffuser top view
Figure 3.1: Schematic representation of the cavitation tunnel at the Ship Hydromechanics group of the Delft University of Technology. The cavitation tunnel used as a water tunnel with an opened test section. The main components of the tunnel are de-aeration chambers (1), honeycomb (2), contraction part (3), test section (4), diffuser (5), electrical motor (6) and the impeller position (7).
20 Chapter 3. Experimental facilities
3.2.2
Test section
The new test section of the cavitation tunnel was designed and built for the purpose of this project (see Figure 3.2). The main requirements for the test section were to make it longer compared to the old one, to improve the optical access, and to allow for the use a force balance for the friction drag measurement on a flat plate.
The new test section has a rectangular cross-section. The length of the test section is 2130 mm. The frame of the test section is made of stainless steel. Two parallel side walls and the bottom are made of Plexiglass plates of 35 mm thickness, which ensure optical access along the whole test section. The cross-section at the entrance is 300×300 mm2. The bottom of the test section is inclined in such a way that the cross-section at the end is 300×315 mm2. This increase in depth of the measuring section is to partially compensate
for the boundary layer growth and to maintain a nearly constant center-line velocity (at least for the single phase (water) flow case).
The top wall of the channel consists of a horizontal test plate. It can either be firmly mounted to the frame of the test section or suspended on the force balance. The test plate can easily be removed from the test section, which allows for a convenient change of the configuration of an experiment.
test plate
3.2. The water tunnel test 21
3.2.3
Test plate
The test plate is a 10 mm thick Plexiglass plate with an area of 2000×298 mm2. This
plate allows for an optical access also from the top. It is mounted to a frame of aluminum profiles (see Figure 3.2) and can easily be replaced. The frame can either be firmly fixed to the test section or suspended by means of leaf-springs for the shear force measurement. The plate is mounted flush with the top walls of the contraction part and diffuser in the tunnel. There is a gap of 1 mm between the tunnel side walls and the plate, which is essential for the force measurement.
In the experiments we used two different configurations of the test plates. The first one is a conventional flat plate that was used for a reference flat plate friction measurement, described in Chapter 5. The second test plate is equipped with a system for generating of air cavities.
The principle of generating of the air cavity on the test plate is shown in Figure 3.3. The air cavity is formed by injecting air via an air distribution channel behind a vertical obstruc-tion with a sharp edge, called a cavitator, protruding out of the test plate with a height h. As can be seen from Figure 3.3, the cavitator is fixed to the test plate. The height of the cavitator can be selected from a set of cavitators, each with a different height in the range of 0.5-2 mm. The test plate is equipped with four positions for the cavitators. The first is located 50 mm from the leading edge of the test plate. The others are spaced with a longitudinal distance of 500 mm from each other. Most of the results that are presented for the flat plate experiments were conducted with the cavity formed at position P1 (see Figure 4.1). Those positions that are not used can be closed by an insert, which makes the test plate smooth. The plate is fitted with two vertical skegs of 30 mm height and 2 mm thickness along the two sides to prevent air escaping from the cavity through the side gaps (see Figure 3.4).
As already explained, a gap between the plate and the tunnel is needed in order to ensure free movement of the plate for the drag force measurement. However, the presence of the gaps might result in a disturbance of the flow at the front and the rear edge of the plate, as well as the flow above the plate through the side gaps. All these effects might influence the friction force measurement on the lower surface of the test plate. In order to avoid or reduce these effects, the gaps around the plate are sealed. The edges at the front and rear are overlapped with a thin brass plate and plastic foil respectively, as shown in Figure 3.4. The brass foil at the front of the plate is fixed to the top wall of the test section. It closes the gap and overlaps with the plate over a distance of 2-3 mm. The rear plastic foil is fixed to the test plate and overlaps with the top wall part of the test section. Contact of the foils with the overlapping surfaces is assumed to be small and does not affect the measured friction force on the lower surface of the plate. As an argument in support our assumption we refer to the calibration results presented in Appendix A.
22 Chapter 3. Experimental facilities
air supply
air distribution
channel
cavitator
air cavity
test plate
h
Figure 3.3: Schematic of the test plate (see text).
3.2.4
Force balance
A custom-made force balance was designed and build to assess the drag reduction efficiency by the air cavities on the test plate. In our case, we are interested in the total friction force on the lower surface of the test plate with an area of 2000×298 mm2. The expected shear force on the test plate is less than 50 N. The accuracy and calibration procedure for the force balance are given in Chapter 5 ans Appendix A.
The force balance design is shown schematically in Figure 3.5. The test plate is fixed to the moving frame (shown in light green). The moving frame is connected to the test section frame by means of the leaf springs. The test plate can be aligned by an adjustable connection between the test section and the fixed frame. This configuration allows for a free movement of the test plate with the moving frame in the flow direction but not in other directions. Further, the moving frame is also connected to the load cell, which measures the longitudinal displacement. It this way, the load cell measures the test plate displacement induced by the drag force. The displacement can be related to a force by calibration with a known force, which is a part of the force balance. From the other side, the load cell is connected to a construction that is not connected to the tunnel. This helps to avoid additional error in the force measurement that can be caused by vibrations of the tunnel.
In order to perform a friction test of a specific configuration of a test plate, as it is also described in Chapter 5, the following actions have to take place:
The test plate has to be mounted to the force balance.
3.2. The water tunnel test 23
cross section
longitudinal section
test platebrass foil of 0.5mm plastic film of 0.2mm sealing bar 1-2 m m 1 mm frame skeg
Figure 3.4: Sealing of the test plate.
the water tunnel and aligned. It is important to ensure a free movement of the plate once it is installed. The slot between the test plate and the test section should be kept small to avoid any flow above the plate.
The balance has to be calibrated in situ. After a single extensive calibration procedure has been completed, a simplified calibration has to be made after each time the balance is removed from the test section. This limited calibration procedure consists of checking a calibration coefficient by first applying the maximum calibration force and then returning to zero force. Also, the absence of the influence of a vertical force on the measurement should be checked when performing measurements with cavities. The calibration procedure is described in more detail in Appendix A.
24 Chapter 3. Experimental facilities
moving frame
fixed frame
Figure 3.5: Schematic of the force balance as explained in the text.
3.2.5
PIV and high-speed imaging
Particle Image Velocimetry (PIV) is used to measure the local velocity in the test section, in particular for the characterization of the boundary layer profile over the test plate. More specifically, we need to know a velocity profile at the location where the cavity is formed. But also the modification of the boundary layer by the presence of the cavity needs to be studied.
Planar PIV is used to measure the velocity profile in the vertical middle plane of the chan-nel, which is aligned parallel to the mean flow direction. A picture of the measurement system is shown in Figure 3.6 with a schematic illustration of the laser path. The measure-ment system consists of a camera, a laser and optics mounted on a traversing frame. The optics consist of a mirror and two cylindrical lenses forming a laser sheet from the laser beam with a thickness of approximately 1 mm. A calibration grid is used to determine the magnification of the optical system. The traversing frame allows for moving the PIV set-up along the channel parallel to the side windows. This makes it possible to measure the boundary layer at any position along the test plate. By shifting a position of a vertical bar that carries the optics it is also possible to change the plane of the measurement if needed. This requires refocusing and recalibration of the optical system.
For the global velocity profile in the test section we used a 50 mm objective with a field of view of 150×110 mm2. For the boundary layer measurement an objective with a 105
3.2. The water tunnel test 25 mm focal length was used, giving a field of view approximately 40×30 mm2. The flow was
seeded with hollow glass spheres with a diameter of 10 µm that act as tracer particles for the PIV measurement. The image evaluation procedure was done with a commercial code (Davis 7.2, LaVision).
laser head laser path rail optics camera
Figure 3.6: The PIV set-up as explained in the text.
A Photron FastCAM SA1 high-speed camera was used for the visualization of the air cavity flow. The maximum frame rate is 5000 full frames per second (1K×1K pixel format).
3.2.6
Pressure and gas flow rate measurement
One of the governing non-dimensional parameters for cavitating flows is the cavitation number. In order to define it, the pressure difference between the mean pressure in the cavity and the hydrostatic pressure at plate level inside the tunnel should be measured. A schematic of the measurement principle is shown in Figure 3.7. A U-tube is filled with water and connected to the test section from one side. The other side is filled with air and connected to the cavity. If the pressure in the cavity is the same as the hydrostatic
26 Chapter 3. Experimental facilities pressure on the plate level, then the free surface on the right side of the tube is at zero level. Any other pressure differences are expressed in mm H2O and can be optically read
from the scale.
Figure 3.7: Schematic of the cavity pressure measurement (see text for explanation).
Air from a central air supply is injected in the cavity by means of gas mass flow controllers (Bronkhorst F-201CV and F-202A) providing air flow rates up to 1 l/s.
3.3
Ship model test
3.3.1
Ship model
A scale model (scale factor 13.6 ) of the DAMEN River Liner is used for the ship model tests. This ship is regarded as a representative model for inland waterway vessel. The main parameters of the ship are given in Table 3.1.
Table 3.1: Main parameters of the vessel
Definition Symbol Value Unit
model scale ratio λs 13.6
-length between perpendiculars Lpp 110 m
breadth moulded B 11.4 m
draught moulded T 2.6 m
wetted surface area bare hull S 1646.6 m2
velocity V 23 km/h
The ship model was equipped with a system to create air cavities. This system consists of 11 cavitators, two skegs, and an air supply system. The cavitators with 1.5 and 2.5 mm height and 765 mm width have a similar design as was used for the flat plate test. The longitudinal distance between the cavitators is 500 mm. Two skegs are used to restrict the
3.3. Ship model test 27 cavities from the sides. The skegs are 22 mm in height, 3 mm thick and have a length of 5.5 m. A picture of the bottom of the ship model with the cavitators and skegs is shown in Figure 3.8. A grid pattern was applied to the bottom of the model to determine the cavity length from video recordings. The philosophy for this design is given in Chapter 6.2.
skeg
skeg
cavitator
air outlet
500 mm
766 mm
cavitator
Figure 3.8: Photo of the bottom of the ship model equipped with the cavitators and skegs.
3.3.2
Air supply system
Nitrogen (being a representative substitute for air) was injected from high-pressure cylin-ders to fill the cavities with gas. Similar as in the flat plate test, gas was injected behind the cavitators. A pneumatic schematic of the model is shown in Figure 3.9. Each of the 11 cavitators has an air supply. Three gas mass flow controllers connected to the air cylinders via a pressure reduction valve are used to supply air to the cavities at constant mass flow rate. The controllers indicated in Figure 3.9 by 1, 2 and 3 have a capacity of 300, 60 and 600 l/min respectively. The first controller is directly connected to the first cavity in order to ensure a high flow rate. The other cavities are connected to the controllers via buffer tanks. The buffer tanks are connected with the cavities by hoses with the same length. This ensures an equal air supply to each cavity connected to a single buffer tank.
28 Chapter 3. Experimental facilities Every even cavity is connected to controller number 2 and every odd one is connected to controller number 3. This design allows to generate different combinations air injection.
1 2
3
Figure 3.9: Schematic of air supply system of the ship model. The numbers refer to the mass flow controllers which regulate the gas flow rate, as explained in text.
3.3.3
Suspension of the model and force measurement
The initial plan was to have the model self-propelled by two propellers and measure the change in drag from the thrust measurement on the propellers. But, because of the low hydrostatic stability of the model running with air at the given loading conditions, it was fixed in roll motion by a so called pantograph. A pantograph is a mechanical connection that allows for the movement only in one plane, in our case in the vertical plane parallel to the flow direction. The free sailing mode was not possible anymore with the pantograph. That is why the model was towed by a luchtpoot with a load cell and a hinge as shown in Figure 3.10. That leaves two degrees of freedom: vertical and pitch direction. The propellers were run at a lower RPM to compensate for their drag. The total drag of the model was defined as the sum of the forces from the luchtpoot and the thrust from the propellers.
A picture of the running ship model in the towing tank is shown in Figure 3.11. Two underwater cameras are used for visualisation of the cavities on the bottom.
3.3.4
Towing tank
The ship model tests were carried out in the Seakeeping and Manoeuvring Basin (SMB) at MARIN. Description of the basin is given in Appendix C.
3.3. Ship model test 29
T1, T2
Fxt Fx= Fxt+T1+T2
Pantograph "Luchtpoot"
Figure 3.10: Schematic of the set-up of the model test in the towing tank as explained in the text.
pantograph luchtpoot
Chapter 4
On the physics of an air cavity in a
steady flow. Experimental results.
Abstract
This chapter describes an experimental study on the air cavity tested in a water tunnel. The cavity was created under a horizontal flat plate in the turbulent boundary layer behind a cavitator. Several aspects of the flow with the cavity were investigated. The results show that the cavity length is equal to approximately a half gravity wave length. It can be influenced by the initial flow conditions as well as by the cavity closure conditions. The shallow-water effect due to the finite channel depth might substantially increase the cavity length. It was also shown that the angle of attack of the plate has a strong effect on the cavity parameters, possibly because of a pressure gradient that occurs along the cavity. It was found that thin cavities become unstable due to relatively strong distortions of the free surface of the cavity. As a result, the maximum cavity length based on a gravity wave length criterion could not be reached.
4.1
Introduction
The frictional resistance makes up to some 70% of the total resistance of a cargo ship (Larsen and Raven, 2010). This motivates the development of a technology for frictional drag reduction applicable to ships. It is known that the creation of artificially developed air cavities on the bottom of a ship can significantly reduce its drag (Butuzov, 1965; Sver-chkov, 2007). This is achieved by reducing the wetted surface on a horizontal part of the ship. One of the ways to create an air cavity under a horizontal surface is to inject air behind a cavitator. A cavitator is an obstruction mounted to the plate (or ship bottom) in span-wise direction that creates a suction pressure immediately downstream of it (as for example shown in Figure 4.1).
Numerous theoretical and experimental studies were carried out on drag reduction by air cavities (Gorbachev and Amromin, 2012). One of the first successful applications of this
32 Chapter 4. On the physics of an air cavity in a steady flow. Experimental results. technology was reported from the Krylov Shipbuilding Research Institute in Russia in 1960. Theoretical investigations of an artificial cavitation flow behind a wedge under a horizontal plate were supported by experiments (Butuzov, 1966). Nowadays, potential flow models to predict the behaviour of the free surface are available (Matveev, 2003). However, there are still many questions open that need an answer before a wide practical application of this technology is achieved. Actual flow conditions, such as the presence of turbulence, require a deeper understanding of the free surface problem. The influence of the turbulent boundary layer on the hydrodynamic characteristics of thin air cavities is one of the open issues. Related problems like the influence of the shallow-water effect, air discharge from the cavity, stability issues are investigated experimentally and reported in this Chapter. A parameter study was performed in order to define the main characteristics of the cavity such as dimensions, pressure and air consumption. During these experiments the following parameters were varied: cavitator height h (0.5, 1, 1.5 and 2 mm), flow velocity V (between 1 and 3 m/s) and air flow rate Q (between 0.24 and 12 l/min). The cavity length L, the maximum cavity thickness H, and the relative pressure in the cavity were measured.
Air
Lc
Plate Air cavity Cavitator
Plate Air Water
Skeg
P4 P3 P2 P1
Figure 4.1: Schematic of the test plate with the cavity. The setup allows to install the cavitator at four location on the plate: P1, P2, P3, and P4.
4.2
Characterization of incoming flow
The velocity profile at the leading edge of the test plate was measured by the PIV technique, and is shown in Figure 4.2(a). The stream-wise velocity for this measurement was 2.68 m/s. As can be seen from the graph there are two distinct velocity regions. The boundary layer region is determined to extend over 7.4 mm from the wall. The further outward velocity profile is uniform. A more detailed view of the BL is shown in Figure 4.2(b). The distance from the wall (vertical axis) is normalized by the BL thickness. The velocity is normalized by the stream-wise velocity. The shape factor Hf, which is the ration of displacement to
4.3. Cavity length 33 1.3 for a turbulent BL (White, 2006). The profile of the BL is also in a good agreement with the 1/7thpower velocity profile in the BL (Figure 4.2(b)). For all three measured velocities (0.92, 1.82 and 2.68 m/s) the BL at the beginning of the test plate was approximately 7 mm.
(a) (b)
Figure 4.2: (a) - global velocity profile at the beginning of the test plate. (b) - dimensionless boundary layer profile.
4.3
Cavity length
One of the most important parameters of the cavity is its length, since this determines the de-wetted area that achieves the drag reduction. For design purposes it is necessary to be able to accurately predict the cavity length. From previous studies (Butuzov, 1966; Matveev, 2003) it is known that the maximum and stable cavity length is equal to one half of the gravity wavelength λ. In this subsection, we investigate in more detail the influence of the following factors on the cavity length:
Effect of water velocity; The shallow water effect;
Angle of attack of the plate and the pressure gradient (static as well as dynamic); Velocity profile of the inflow.
The test section of the tunnel has a relatively small depth of 300 mm. A flow with a free surface can be influenced by the limited depth. As a result, the finite channel depth affects the cavity length. We refer to this as the shallow-water effect.
34 Chapter 4. On the physics of an air cavity in a steady flow. Experimental results. The cavity length was measured for all cavitator heights at velocities ranging from 0.5 to 3 m/s. It was observed that the maximum stable cavity length occurs at approximately a half gravity wave length, where the phase velocity of this gravity wave is corrected for the shallow water effect (Figure 4.3). The figure shows that the cavity length does not depend on the cavitator height, when the cavity is stable. Due to the limited length and depth of the test section the maximum ”wave length”- limited cavity length could only be achieved at velocities under 1.7 m/s. The relation between the wave phase velocity and the length of the gravity wave for given water depth D is given by the following relation:
V = s gλ 2πtanh 2πD λ . (4.1)
For the deep water approximation the term tanh 2πDλ approaches unity.
0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 L [m] Vp [m/s] λ/2, deep water λ/2, shallow water h=0.5 mm h=1 mm h=1.5 mm h=2 mm Fr=1 Fr=0.61
Figure 4.3: A half gravity wave length λ/2 for deep and shallow (D=0.3 m) water versus the phase velocity. Next to it a measured cavity length for different cavitators height h vs the velocity.
The influence of the shallow water effect can be estimated by the Froude number (Fr=V /√gD) based on the depth D under the plate/bottom. For Fr<0.61 the influence is negligible. For
4.3. Cavity length 35 Fr=0.77 the cavity length is expected to be 10% longer compared to the deep water case. And finally, for Fr≥ 1 the flow is supercritical, which is when the theoretical cavity length approaches infinity.
As can be seen from Figure 4.3, the cavity is slightly longer than predicted at the velocity range from 0.75 to 1.5 m/s. This phenomenon is likely related to the fact that the cavity was created close to the contraction part of the tunnel. However, similar phenomena can also be present at real conditions when the cavity is formed close to the bow of a ship, when the bow also affects the pressure distribution in the BL.
At velocities less than 0.75 m/s, when the cavity is very short, the surface tension seems to shorten the cavity. However, at realistic conditions the surface tension is not expected to have a noticeable effect, because Weber number would be much higher at full scale.
1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 V [m/s] H [ m] L=inf L = L deep+10% L = L deep+1% Fr= 0.61 Fr= 1 no influence supercritical flow Fr= 0.77 D
Figure 4.4: This figure shows whether the cavity under a ship is influenced by the shallow-water effect for different depths and velocities. For Fr < 0.61 - no influence; Fr=0.77-10% Fr≥ 11 - supercritical flow
In order to give an idea about the probability of the influence of the shallow-water effect on a full scale ship we can make an operation zones diagram. In Figure 4.4 it can be seen a plot of the water depth D on the vertical axis and the ship velocity on the horizontal axis. Three curves in the Figure represent a combination of the water depth and water velocity for the given Froude numbers 0.61, 0.77 and 1. In this way we can see whether the cavity
