Wave Interaction with a Double Chamber Oscillating ... - SAGE Journals

21

Wave Interaction with a Double Chamber Oscillating Water Column Device Wilbert1, R., Sundar2, V. and Sannasiraj3, S.A. 1Research Scholar, Email: [email protected] 2Professor, Email: [email protected] 3Professor Email: [email protected] Department of Ocean Engineering, Indian Institute of Technology Madras Chennai 600 036, India. ABSTRACT The principle of oscillating water column within a chamber due to the propagating oscillatory ocean waves being converted into clean energy through wave energy convertor referred to as Oscillating water column (OWC) device is a well proven concept that still remains as one of the most promising alternate sources of energy from the Ocean. The OWC has single column of water oscillation, whereas, Double Chamber Oscillating Water Column (DCOWC) has two chambers of water oscillation. DCOWC is relatively a new concept. In this paper, the performance characteristics of a DCOWC is evaluated through a well-controlled experimental investigation in a wave flume. The conceptual design aspect of DCOWC and its uniqueness compared with the present state of art in wave energy converters (WECs) are explained. The efficiency of the system is assessed by considering the variations in the geometrical dimensions of the system along with the different characteristics of incident waves. The methodology adopted for evaluating the hydrodynamic performance in terms of energy conversion efficiency, the development of additional structural stability and the wave amplification at the mouth are discussed and its significances are highlighted by presenting the results in a dimensionless form. The analysis of the results indicates the feasibility of the DCOWC concept in harnessing energy from the waves. Key words: Wave energy, air chamber, dynamic pressure, energy conversion, pneumatic power, waves, OWC.

1. INTRODUCTION In historical point of view, even before the beginning of industrial revolution, energy transport by ocean waves had occupied the scientific thinking for harnessing it to supplement the energy needs of the society which is evident from the first patent of David Ross (1981). The technological developments in electricity generation and power grid system have made it possible to transmit available mechanical energy in the form of electrical energy. Need of the hour being sustainable clean energy, there has been tremendous progress in research and development in the area of alternate sources of energy of which the one from the Oceans has been dominating. In the case of conversion of wave energy into electricity, the kinetic and potential energy available in the wave are first converted into mechanical energy by means of a wave interface device known as WEC. The mechanical energy is then made to do work through a device via electric generator. The selection of the WEC is an important aspect, since, it governs the efficiency of the system. Salter (1974) explained the basic design philosophy of a WEC through his classical device. The important aspect in

Volume 4 · Number 1 · 2013

22

Wave Interaction with a Double Chamber Oscillating Water Column Device

this design was that the WEC in operation should radiate waves to a lesser extent to absorb maximum energy. This was claimed to have achieved through the special shape given to the device. Hagermen and Heller (1988) presented an overview of the state of the art WECs. Based on the conversion principle, it was classified into three categories namely overtopping devices, wave activated bodies and OWC. Among the above concepts, OWC has a unique distinction of keeping the turbine, the only moving component, above the water surface and, thus facilitates easier operational and maintenance of the device. In its geometric configuration, OWC consists of a partly submerged caisson having an opening at the bottom of the front wall. The dynamic pressure below the wave applies the excitation force through the opening to cause oscillation inside the chamber. In phase with the water oscillation, the air inside the chamber contracts and expands to develop pneumatic power and the same can be made use of in rotating the turbine. The turbine is coupled with generator for producing electricity. This simplicity in configuration and operation has led the OWC technology to be a promising one in wave energy conversion process. There have been numerous studies both experimental and theoretical on the OWC concept for achieving maximum efficiency and economic viability in energy conversion. Ambli et al. (1982) developed the multi resonant oscillating water column concept by adding side walls in front of the OWC device. It was found that the side walls enhanced the resonant characteristics of the device. Hunter (1982) through an experimental study found that the efficiency of multi resonant OWC improves as the length of harbour wall matches an odd multiple of a quarter wavelength of the incident wave due to the formation of standing wave resonance which enhances the water column excitation. Count and Evans (1984) numerically studied the effect of projecting wall on device performance using boundary integral method. Malmo and Reitan (1986) numerically studied the wave power absorption by an OWC with a reflecting wall and established that the performance is dependent on geometry of the device, wave frequency and the direction of the wave. McIver and Evans (1988) developed a theory for the performance of wave energy devices within harbours set into a reflecting wall. The method of matched asymptotic expansion was used to solve hydrodynamic problem and the power absorption characteristics. It was found that the power absorption depends on the position of harbour mouths and the best spacing for multi-harbour system was established. Zheng (1989) conducted several experiments on the parametric optimisation of the prototype OWC device. It was observed that flared rather than the rectangular harbour could significantly increase the wave energy extraction for a wide range of wave periods. Evans and Porter (1995) theoretically studied the OWC efficiency with linear wave theory. The parameters considered are depth of submergence and the normalised chamber length with water depth. It was observed that larger values of submergence depth caused to decrease the resonance frequency of the device. Ma (1995) based on experimental results formulated an empirical relationship for resonant frequency of OWC connecting the depth of submergence of side wall and the length of stream line that runs between the internal free surface of OWC and a point between the OWC lip and sea bottom. Sundar et al. (2010) presented the conceptual designs for integrating OWC with coastal defence works. This highlights the socio-economic benefits achievable in wave energy development programmes. Boccotti (2007a) presented a modified concept in OWC working principle by incorporating an additional duct on the wave beaten side. Here the dynamic pressure available at mouth elevation causes flow oscillation inside air chamber. Using linear wave theory, analytical expressions were derived for the energy absorption capacity of the device. The theoretical calculations showed that upper bound value for energy absorption reaching 100% of incoming energy flux on wave structure interaction. To validate the above model, Boccotti et al. (2007) reported the test results carried out from a physical model with a scale ratio of 1:6. Performance observations under random waves were in consistent with the theoretical predictions. Boccotti (2007b) observed that in addition to increase in power absorption, the new concept enhances the stability of OWC system. In summary, the new concept of OWC, claimed to be an improvement in efficiency of the conventional OWC by Boccotti (2007a), is an innovative method. In geometrical configuration, it consists of two connected chambers and hence it is called Double Chamber Oscillating Water Column

International Journal of Ocean and Climate Systems

Wilbert, R., Sundar, V. and Sannasiraj, S.A.

23

(DCOWC) device. A detailed literature review has revealed that a number of researchers have carried out studies on the performance characteristics of OWC, while, the literature on DCOWC is rather limited. This prompted to carry out well controlled physical model tests on the hydrodynamic performance characteristics of DCOWC exposed to the action of regular waves in the present study. 2. EXPERIMENTAL SET-UP The experiments were carried out in the wave flume of 72.5m long, 2m wide and 2.7m deep at the Department of Ocean Engineering, IIT Madras, India. Three smaller units of DCOWC each of 0.30m x 0.60m x 1.45m and one bigger unit, 1.0m x 0.60m x 1.45m were fabricated for simultaneous testing since the number of parameters dictating the model and the measuring parameters were more. In order to test the above stated four models simultaneously without the interference effect between the adjacent units, plywood partitioning was provided for a length of 11m in between the units. The plan and cross section of the DCOWC model adopted for the present study are shown in Fig. 1. The model parameters of interest are the bottom opening depth (O) of the oscillation chamber and the mouth clearance (h) at the entrance. The width of the front duct (b) was kept at 0.30m. The water depth (d) was maintained at 1m throughout the study. Herein, the depth of water inside the DCOWC model, di is same as d. To simulate the damping being exerted by the turbine in prototype structure, a circular air hole having a cross sectional area equal to 0.65% of plan area of the air chamber is provided. Wang et al. (2002) have reported OWC experimental works carried out with similar provisions for damping. Thiruvenkatasamy and Neelamani (1997) observed that as air hole area increased beyond 0.85% of the water plane area, efficiency was found to be decreasing. Rapaka (2007) through extensive model studies concluded that the energy conversion processes is optimum for the air hole area within the range of 0.45% to 0.68% of water plane area. Four wave heights (H’s) of 0.045m, 0.055m, 0.065m and 0.095m were chosen and the wave periods (T’s) varying between 1.2s to 2.4s were employed at an interval of 0.1s. Wave gauges of conductivity type were used for measuring the time histories of wave surface elevation and pressure sensors having maximum range of 0.2bar and 0.5bar were used for measuring air and water pressures respectively. The locations of these measurements are indicated in the above figure. All the signals from the pressure transducers are amplified and then sent to the A/D converter in a computer. The digital signals are then stored in a computer for later viewing and analysis. The error estimate of various measurements has been made: 0.0386% for wave probe; 0.629% for the pressure transducer at the device mouth; and, 0.0281% for the pressure transducer inside the air chamber. The layout of the flume showing the positions of the wave maker, absorber, model units, partitioning of the flume are projected in Fig.2, a closer view of the test section with the wider unit mounted with a pressure sensor are depicted in Fig.3. For exploring the DCOWC working principle, three test cases were considered by varying the relative depth of mouth, h/di of 0.15, 0.30 and 0.45. In each of the condition, the relative depth of bottom opening, O/di for the bigger unit was maintained as 0.3, while it was varied as 0.15, 0.30 and 0.45 for the smaller units. The above test set-ups facilitated simultaneous testing with specified wave characteristics that resulted in a total of 156 runs for various regular wave incidence test cases.


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AH

PA3 WOODEN PARTITION

WAVE MAKER

H PR3

h

1.45m

0.6m 0.85m

PF3

b

di

d

O

SECTION AT X-X AH - AIR HOLE P*- PRESSURE TRANSDUCER

b

AH

0.24m

B

0.24m

WOODEN PARTITIONS

W

PF4 PR4

0.14m

0.14m

0.14m PR3

PA4 x

PA3

AH

PF3

0.11m

0.14m PR2

PA2 AH AH

PR1

0.16m

PF2

0.11m PA1

0.11m

0.30m

0.30m

0.30m

x

PF1

PLAN

Figure 1. Plan and section of the model


Volume 4 · Number 1 · 2013 WP4 WP3 WP2 WP1

WP8 WP7 WP6 WP5

Figure 2. Plan view of the model placed within the flume

DCOWC model

wave energy absorbing beach plywood partitions

wave maker

WP0

WP

WAVE PROBE

wave energy absorber

Wilbert, R., Sundar, V. and Sannasiraj, S.A. 25

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Figure 3. A view of the model

3. HYRODYNAMIC PERFORMANCE The wave power conversion capacity of the device is expressed by the term energy conversion efficiency in percentage. The energy conversion efficiency across the width (W) of the device is the ratio of average pneumatic power developed inside the chamber to the incoming wave energy flux over the width. The energy flux (Ein) associated with a wave height (H) and period (T) over water depth (d) across the width (W) is given by the rate of change of total energy in the system. Following linear wave theory the energy flux is,

Ein =

 ρgH 2 C  2 kd + 1W .   8 2  sinh 2 kd

(1)

where, k=2π/L and C=L/T and L=wave length. The pneumatic power developed inside the air chamber is calculated following Evans (1978). Here, the water surface inside the pneumatic chamber is assumed to be a weightless piston moving with a velocity of oscillation. The pneumatic energy flux (Eout) is calculated as follows,

Eout =

1 T

t +T

∫

pAvdt

(2)

t

where p is the pneumatic pressure, v is the velocity of free surface movement and A is the horizontal surface area of the pneumatic chamber.



v=

27

ηi+1 − ηi ∆t

(3)

where, ηi and ηi+1 are the water surface elevations at ith and i+1th instants and ∆t is time increment. Energy conversion efficiency (λ) is then estimated by,

λ=

Eout × 100 Ein

(4)

In DCOWC the trajectory of flow induces additional vertical load which can be computed by Reynold’s transport theorem. Considering the control volume between its bottom and mouth elevation (Clement, 2009),

 d ∂  mv ) =  ∫∫∫ ( ρv)dV  + ∫∫ ( ρv)v.dA ( dt ∂t  CV  CS

(5)

where m = mass of flow, CV = control volume and CS =control surface. Considering no variation for mass within the control volume, the additional vertical force is,

d ( mv ) = dt

∫∫ ( ρv )v.dA

(6)

CS

This increase of vertical load is represented by the term load factor (Ω) defined as,

Ω=

Additional vertical load × 100 Ab ρ gd

(7)

where, Ab is the bottom area of DCOWC device. The phase difference, φd between the excitation pressure at mouth and the pneumatic pressure within the DCOWC is computed as,

φ d = 360 ×

T* T

(8)

where, T* is the lag of the absolute maximum of cross-correlation between wave pressure (Pin) at the mouth and the pneumatic pressure (p ) inside the air chamber.

( )

(

Ψ T ∗ = Pin ( t ) p t + T ∗

)

(9)

The wave height growth at the mouth is represented by the amplification factor (β) defined by,

β=

Hm H in

where, Hm is the wave height at mouth and Hin is the incident wave height.


(10)

28


4. RESULTS AND DISCUSSION Based on conceptual model, DCOWC operates like a forced vibration system. Due to the existence of a phase shift between the pressure excitation at the mouth and the corresponding discharge, the total power absorbed at the mouth is the apparent power having both active and reactive components. The active component determines the magnitude of kinetic energy of the system, while, the reactive component controls the variation in potential energy. In the energy conversion process, the difference between active and reactive component determines the efficiency of the system. The fundamental significance of the present work as the earlier works of Boccotti (2007a & b, 2012) and Boccotti et al, (2007) is to investigate the influence of this complex physical process in energy conversion capacity of the device and the wave amplification near the structure. 0.08

(a)

0.04 0 -0.04 -0.08 0 800

10

20

30

40

10

20

30

40

10

20

30

40

20

30

40

(b)

p (Pa)

400 0 -400 -800 0 800 (c)

p (Pa)

400 0 -400 -800 0 800

(d)

p (Pa)

400 0 -400 -800 0

10

t (s)

Figure 4. Time history of (a) incident wave surface elevation, (b) front wall pressure, (c) rear wall pressure and (d) air pressure Typical time histories of incident wave surface elevation, pressures on the front wall, rear wall and within the air chamber for the given incident wave parameters (d/L =0.1919 and H/L=0.0182) and the DCOWC system parameters O/di=0.30 and h/di of 0.30 are shown in Fig.4. The measurements were carried out such that at least three steady state cycles in the pneumatic pressure variation could be



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captured during a particular test. The pneumatic power developed has been calculated as the average of the three steady cycles. The experiments were carried out with two longitudinal lengths (W/B=5/3 and 1/2, where, W is the length of one chamber parallel to the wave crest and B is the width of the oscillating chamber) of DCOWC to evaluate the effect of water plane area on pneumatic damping. The closeness in efficiency of both systems indicated that the variation in the length of the unit parallel to the wave crest is having insignificant influence on pneumatic damping and hence, the results obtained were reported collectively for considering the variation of other system parameters. 4.1 ENERGY CONVERSION EFFICIENCY 4.1.1 Effect of h/di and O/di The efficiency (λ) of the DCOWC system was derived following Eq. [4]. The variation of λ with d/L for h/di=0.15, 0.30 and 0.45 is depicted in Figs. 5a, 5b and 5c, respectively. The results cover of wave steepness, H/L ranging between 0.0426 and 0.0143. Three different bottom openings were considered for each system (O/di=0.15, 0.30 and 0.45). The efficiency, λ decreases with an increase of d/L and the rate of decrease is found to be rapid for d/L up to about 0.30. The trend in the variations is found to be similar for all the three h/di tested. The maximum efficiency has been achieved under long wave incidence and is of the order of 60% to 80%. It is noted that larger bottom opening absorbs more energy. It can be clearly seen that the h/di of 0.30 exhibit higher efficiency. The foregoing discussion demonstrate the relative significance of wave frequency (d/L) and system characteristics (O/di and h/di) in energy conversion capacity of the device. The basic design principle of DCOWC device is to make use of the hyperbolic variation of dynamic pressure beneath the water surface. The device should aim for a configuration that can experience high excitation pressure near the mouth of the front wall and at the same time minimise the phase difference between the excitation pressure and air pressure in the chamber. For decrease in h/di, the dynamic pressure excitation over the front duct will be more and the corresponding performance expected is more. But the experimental measurements show that the relation between energy conversion efficiency and the decrement fall in h/di are not in direct proportion. It necessitates evaluating a critical value of h/di for optimum conversion efficiency, which in turn depend on the incident wave characteristics. Boccotti (2007a) based on theoretical analysis suggested a similar concept regarding the mouth clearance at front duct. For h/di=0.15, as the wave crosses the vertical plate, it becomes steeper to decompose into higher harmonic components, thereby changing its dynamic pressure intensity. This is evident from the trend in the variation of λ with d/L. The other dominant mechanism for the low level performance is the phase difference between the pressure excitation and the air pressure. This phase difference depends on the eigen period of the device which depends on the length of stream line that the fluid particle has to traverse within the device. Thus for a constant relative duct opening O/di the decrease in h/di causes an increase in the eigen period of the device. However, it is understood that the flow of energy into the device increases with h/di. The optimum depth of device opening (h/di) has been found to be 0.30 to obtain maximum efficiency. For O/di=0.15, the water within the oscillating chamber behaves like a solid body with lower oscillation at different h/di values. It is attributed to the effect of changes in both eigen period and discharge excitation. Herein the loss due to friction on the walls is not considered. The increase in eigen period and the energy loss associated with longer flow stream line length are the factors behind for lower efficiency at a relatively lower h/di. Both of the above factors balance each other for the entire frequency range. As the O/di increases it positively influence the energy conversion capacity of the device. This is mainly due to the decrease in stream line length and corresponding decrease in eigen period and energy loss in the flow oscillation. Thus, these results indicate the system has to be tuned for maximum efficiency by considering O/di and h/di for the prevailing wave characteristics, for which the present results could serve as a basic guideline. The influence of relative water depth shows that the efficiency is predominantly dependent on the wave frequency. For the relative water depth beyond 0.35, the energy conversion capacity falls below 20% and this range is susceptible for developing the pneumatic power for rotating the turbine in the


30


primary energy conversion process. For the best configuration efficiency reaches an asymptote for d/L lower than 0.20, for which reactive component of the device is diminishing. In dynamic systems at lower reactance, the total energy absorbed in the system alternates between kinetic energy and potential energy. This is one of the desirable aspects to be considered since it can prevent the high wave amplification near structure.

0.1

0.15

0.2

0.25

0.3

100

(a)

O/di

80

0.15 0.30 0.45

60

40

20

1000

(b)

SCOWC

80

(%)

60

40

20

1000

(c) 80

(%)

60

40

20

0 0.1

0.2

0.3

d/L

0.4

0.5

Figure 5. Effect of relative mouth clearance on efficiency at (a) h/di=0.15, (b) h/di=0.30 and (c) h/di=0.45.



31

To show the degree of variation in energy conversion between single chamber and double chamber the λ values of Single Chamber Oscillating Water column(SCOWC) for a bottom opening of O/di=0.45 is superimposed with figure 5b. The trend shows the degree of control double chamber produces in its functioning for a specified bottom opening. 4.1.2 Effect of wave steepness (H/L) The effect of wave steepness on λ as a function d/L for the most favourable configuration (h/di=0.30 and O/di=0.45) is brought out in Fig.6. In general, the order of difference is 10%. The maximum difference is observed to be about 12% for the high frequency waves. The lack of coherence in the efficiency with wave steepness over the intermediate frequency values suggests that wave steepness is not having any predominant influence in energy conversion process. It may be due to the effect of radiated discharge because of the pressure fluctuations within the air chamber and the subsequent nonlinearities in the flow regime.

B/L 0.1

0.15

0.2

0.25

0.3

100

H/L

80

0.0068-0.0100 0.0103-0.0200 0.0202-0.0430

60

40

20

0 0.1

0.2

0.3

d/L

0.4

0.5

Figure 6. Effect of wave steepness on efficiency at h/di=0.30, O/di=0.45 4.2 Stability enhancement After having analysed for the efficiency of the system for the chosen test conditions, the next step was to determine the manifestation of vertical load which if enhances is expected to contribute to the vertical stability. This is one extra entity which makes DCOWC different from the conventional OWC. The provision of front duct is expected to regulate the flow so that the flow trajectory induces additional vertical force. Another advantage that could be derived out of the front duct is that weight of water column within the duct act as the integral part of the device adding to its dead weight. The vertical load factor, Ω was determined following Eqn. [7]. The variation of Ω as a function d/L for O/di =0.45 are presented for h/di=0.15, 0.30 and 0.45 in Fig. 7. The measurements were grouped in three ranges of wave steepness. The magnitude of free surface oscillation inside the chamber increases with increase in excitation pressure causing higher velocity. For d/L less than 0.25, Ω varies between 0.1 and 0.3, whereas, for d/L greater than 0.25, the Ω is less than 0.05. The load factor quantitatively does not indicate any significance but the qualitative analysis of the effects being developed by virtue of the front duct is significant. The primary concern in any engineering structure over coastal area is its survivability in severe environmental conditions. In a conventional OWC, since, the inlet is at the lower


32


end, under severe wave conditions the vertical wall portion at the surface level is subjected to severe horizontal loading resulting in a high risk factor in sliding failure. This can also cause development of high overturning moment leading to excessive stresses in structural components. In DCOWC, the front duct wall is at lower level so the environmental loading will be less severe and the waves on the upper portion past the front duct wall experiences a damping effect since the water inside the device behaves like a spring. Boccotti (2007b) through field experiments reported that the additional vertical load due to wave interaction is of the order of 6.5% of its weight.

0.1

0.15

B/L

0.2

0.25

0.3

0.3

(a)

H/L 0.0430-0.0202 0.0200-0.0103 0.0100-0.0068

Ω (%)

0.2

0.1

0.3

(b)

Ω (%)

0.2

0.1

0.3

(c)

Ω (%)

0.2

0.1

0 0.1

0.2

0.3

0.4

0.5

Figure 7. Effect of wave steepness on load factor at (a) h/di=0.15, (b) h/di=0.30 and (c) h/di=0.45



33

4.3 Phase difference The phase difference, φd between pressure at mouth and the air pressure within the air chamber was evaluated following Eqn.[8]. The variation of φd with d/L for h/di = 0.15, 0.30 and 0.45 are shown in Figs. 8a, 8b and 8c, respectively. Three different bottom opening (O/di) were considered. The phase difference increases with d/L for all O/di and h/di tested and it tends to reach an asymptotic value of about 70o. The phase varies due to the difference in the speed of a particle that requires to traverse the flow length within the device. Although the φd for h/di =0.45 is found to be less than that for h/di =0.30, the efficiency for the latter is found to be higher. The logical proposition sufficient for explaining the

0.1

0.15

B/L

0.2

0.25

0.3

(a)

80

φd

60

40

O/di

20

0.15 0.30 0.45

0

-20

(b)

80

φd

60

40

20

0

-20

(c)

80

φd

60

40

20

0

-20 0.1

0.2

0.3

d/L

0.4

0.5

Figure 8. Effect of relative mouth clearance on phase difference for (a) h/di=0.15, (b) h/di=0.30 and (c) h/di=0.45.


34


performance of the device can be derived from the linear circuit theory of electrical engineering. The energy conversion capacity is directly proportional to the power factor, which is cosine function of phase angle. When the power factor is one all the energy coming into the system is expected to be converted in to pneumatic energy and as the power factor becomes zero, all the energy coming to the device will be reflected without being converted in to pneumatic energy. The trend observed in this experimental program agrees with the above mentioned concept. Hence in DCOWC, it is possible to bring in a tuning effect in to the system by suitably fixing h/di and O/di in accordance with the wave characteristics. For the trend occurred over the phase difference, an empirical relationship has been proposed for natural period determination of DCOWC (Eqn.[11]). Based on the fundamental principle of natural frequency determination for the oscillation inside the vertical tube, here stream line length of flow is expressed in terms of system parameters. This equation has been validated with the phase difference obtained for the test condition at O/di=0.45 and h/di=0.45. The natural period (Tn) thus calculated for various d/L are presented in Table 1. The limiting conditions for maximum energy conversion in terms of h/di and O/di are represented in Eqs. [12] and [13].

  2 d − h  d − 2 O  d + 2b   i  d  i  d  i  , for B/b =2  i  i Tn = 2π g 1.5 ≤

O ≤ 1.8 h

(11)

(12)

O h  0.80 ≤  +  ≤ 0.90  di di 

(13)

4.4. Wave amplification The wave height amplification near the mouth of the device, represented in terms of amplification factor, β (Eqn.[10]) is presented in Figs.9a-c. There is progressive increase in wave amplification with the increase of relative water depth. But for the lowest energy level there is drawdown in the curve. This indicates that the front wall modulates the high frequency wave. For design of device in coastal environment, the wave amplification is an important criterion in deciding the free board for the structure. In this figure irrespective of h/di, the wave amplification assumes lowest values around 1.2 Table 1. Natural period (Tn) of DCOWC considered in the study.

h/di 0.15 0.15 0.15 0.3 0.3 0.3 0.45 0.45 0.45

O/di 0.15 0.3 0.45 0.15 0.3 0.45 0.15 0.3 0.45

Tn(s) 2.9400 2.7272 2.4963 2.8356 2.6143 2.3724 2.7272 2.4963 2.2417

d/L 0.1178 0.1288 0.1435 0.1229 0.1356 0.1529 0.1288 0.1435 0.1645



35

for the low frequency wave. The phase difference between the wave excitation and air pressure as well as the damping effect wave energy experiences by virtue of the device configuration are the reasons that can be attributed for the behaviour observed over the wave height amplification. For greater phase differences, there is a dynamic wave set up near the mouth of the device. With the phase difference getting reduced, there will be progressive increase in the free surface oscillation inside the chamber. It is due to the more flow of water into the air chamber and thus, less energy available near the mouth of the device. The reduction in wave amplification for d/L less than 0.3 has shown an increase of the free surface oscillation inside the chamber.

0.1

0.15

0.2

0.25

0.3

2.5

(a) 2

1.5

O/di 0.15 0.30 0.45

1

(b)

2

1.5

1

(c)

2

1.5

1 0.1

0.2

0.3

d/L

0.4

0.5

Figure 9. Effect of relative mouth clearance on wave amplification before DCOWC for (a) h/di=0.15, (b) h/di=0.30 and (c) h/di=0.45


36


4.5 Wave power absorption capacity The interaction effect of monochromatic wave with the DCOWC device gives rise to the development of power at the mouth. Boccotti (2007a) measured this power as the percentage of energy flux for evaluating the hydrodynamic performance of the device and expressed as absorption coefficient (CA). In the present study, it is computed by means of Eqs.[14-15].

CA = Emouth =

Emouth × 100 Ein 1 T

(14)

t +T

∫

pmouthQdt

(15)

t

where, Q is the discharge at the mouth and is equal to the discharge inside the air chamber. Ein is computed as per Eq.[1]. The variation in CA over a range of wave steepness varying within in the limits of 0.0430 and 0.0068 as the function of d/L is expressed in Fig. 10 for the best configuration identified in the testing process (O/di=0.45 and h/di=0.30). Paradoxically, CA assumes higher values compared with its counterpart λ discussed earlier and this explicitly indicates the predominance of reactive component over its performance. The maximum value of CA reaching nearly 100% agrees with the findings of Boccotti et al. (2007). The possible explanation for this can be developed from the theory of oscillating systems under dynamic loading. The predominant factor which influences the output is the frequency of excitation and there will be progressive increase in performance until it reaches the resonance period. In the present experiment for the frequencies away from resonance, there will be dynamic wave set up to satisfy the conservation of mass over the flow entering the duct. This creates additional potential head being developed near the mouth causing the pressure measured more and this apparent increase in pressure increases the computed power at mouth. The variation of nearly 30% is seen over CA for d/L around 0.45 and the same reduces to nearly 15% for d/L around 0.15. The progressive widening in the variation of CA for varying wave steepness with the increase in d/L shows that dynamic wave set up contribute significantly to CA for lower period waves.

H/L 0.0068-0.0100 0.0103-0.0200 0.0202-0.0430 B/L

0.1

0.15

0.2

0.25

0.3

120

CA (%)

100 80 60 40 20 0 0.1

0.2

0.3

d/L

0.4

0.5

Figure 10. Effect of wave steepness on wave power absorption



37

H/L 0.0068-0.0100 0.0103-0.0200 0.0202-0.0430

B/L 0.1

0.15

0.2

0.25

0.3

0.8

(pmax/ρgH)

(a) 0.6 0.4 0.2 0

(pmax/ρgH)

0.8

(b)

0.6 0.4 0.2 0

(p ma x/ρgH)

0.8 (c)

0.6 0.4 0.2 0 0.1

0.2

0.3

0.4

0.5

Figure 11. Effect of wave steepness on pressure at (a) PF3, (b) PR3 and (c) PA3.

4.6 Characteristics of maximum pressure To bring forth clarity on understanding of the hydrodynamic aspect of DCOWC, the measured maximum pressures at locations PF3, PR3 and PA3 for the optimised system parameters O/di=0.45 and h/di=0.30 are plotted in figures 11a-c having normalised with respective wave heights. Figure11a presents the effect of wave steepness on the dynamic pressure excitation at the mouth of the device for varying frequency parameter d/L. The trend seen over the higher values of d/L suggests that the wave steepness decreases with the increase in the pressure. This is an indication that at a particular wave


38


period, there is an apparent increase in pressure head near the mouth. This agrees with dynamic wave set up concept discussed in the foregoing sections. For the lowest frequency considered, the closeness over the data points indicates that the system attains highest efficiency in energy conversion. This happens due to the minimum phase variation between excitation pressure and air pressure. In oscillating systems it occurs near the resonance frequency of the system. The measured maximum rear wall pressure (figure 11b) shows that the DCOWC behaves like a linear system where the behaviour is mainly dependent on frequency of excitation. The spread over the pressure at lower frequencies indicates the effect of turbulence and corresponding energy dissipation occurring with the increase in wave steepness. The characteristic air pressure variation represented in figure11c strongly attests that water oscillation inside the air chamber follows the nature of dynamic system under periodic force excitation. The closeness across the pressure data points over the varying frequency parameter implies that the pneumatic damping being introduced inside the air chamber is only dependent on frequency of excitation. 5. CONCLUSIONS The study focussed on the influence of the inter-relationship between the bottom opening and mouth elevation of DCOWC device for its efficiency in energy conversion capacity. To understand the added effect of the front duct, tests have been conducted without front duct to simulate SCOWC. For a relative bottom opening, O/di of 0.45, the energy conversion capacity of DCOWC is nearly 10% higher than that for a SCOWC. The maximum energy conversion capacity reaching nearly 78% in the present study establishes the possibility of DCOWC also being a technological solution in wave energy conversion programmes. The energy conversion efficiency significantly depends on h/di, and the maximum performance has been observed for h/di=0.30. The effect of O/di in combination with h/di has been found to have significant influence on the energy conversion capacity of the device. The performance of the system with an O/di of 0.45 and h/di of 0.30 if found to be better. The phase variation between the excitation pressure and the air pressure for varying O/di and h/di shows that by suitably selecting the depth of water di within the device the tuning effect can be brought forth. The wave amplification in front of DCOWC reaches about 1.2 and it indicates the potential stability of the device to absorb the severe wave impact in critical environmental conditions. REFERENCES Ambli N., Bonke K. and Malmo O. and Reitan H.(1982) “The Kvaerner multiresonant OWC”, Proceedings of the 2nd International Symposium on wave Energy Utilisation, Trondheim, Norway, Tapir, pp 275-295. Boccotti P.(2007a) “Caisson breakwaters embodying an OWC with a small opening –Part I: Theory”, Ocean Engineering: 34, pp 806-819. Boccotti P., Filianoti P., Fiamma V. and Arena F.(2007 ) “Caisson breakwaters embodying an OWC with a small opening-Part II: A small -scale field experiment”, Ocean Engineering: 34, pp 820841. Boccotti P.(2007b) “Comparison between a U-OWC and a conventional OWC”, Ocean engineering 34, pp 799-805. Boccotti P.(2012) “Design of breakwater for conversion of wave energy in to electrical energy”, Ocean engineering 51, pp 106-118. Clement Kleinstreuer. (2009) “Modern Fluid Dynamics”, Springer Count B.M. and Evans D.V.(1984) “The influence of projecting side walls on the hydrodynamic performance of wave energy devices”, Journal of Fluid Mechanics: 1984, 145, pp 361-376. David Ross. (1981) “ Energy from the waves’, 2nd ed, Pergamon. Evans D, V. (1978) “The oscillating water column wave energy device”, J. Inst. Maths Applics, 22, pp 423-33.



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Evans D.V. and Porter R. (1995) “Hydrodynamic characteristics of an oscillating water column device”, Applied Ocean Research, Vol.18, pp 155-164. Hagerman G.M. and Heller T.(1988) “Wave energy: a survey of twelve near-term technologies”, Proceedings of the International Renewable Energy Conference. Honolulu.Hawaii, 18-24 September 1988, pp 98-110. Hunter R.S.(1982) “Future possibilities for the NEL Oscillating water column wave energy converter – Experimental measurements and theoretical predictions of the phase control in regular waves”, Report Pr39: WAVE/0R0 for Department of Energy, National Engineering Laboratory, East Kilbride, Glasgow Ma Q.W.(1995) “Nonlinear analysis of hydrodynamic performance of oscillating water column wave energy device with a lateral opening”, Offshore Mechanics and Arctic Engineering Conference Copenhagen, Denmark. Malmo O. and Reitan A. (1986) “Wave power absorption by an oscillating water column in a reflecting wall”, Applied Ocean Research: 8(1), pp 42-48. McIver P. and Evans D.V. (1988) “An approximate theory for the performance of a number of wave energy devices set into a reflecting wall”. Applied Ocean Research:10(2) , pp 58-65. Rapaka E.V.(2007) “Experimental investigation on a moored oscillating water column (MOWC) wave energy device”, Ph.D. thesis, Ocean Engineering Department, Indian Institute of Technology Madras, Chennai, India. Salter S. H. (1974) “Wave power. Nature”, 249, pp 720-724. Sundar V., Torgeir M. and Jorgen H.(2010) “Conceptual Designs on Integration of Oscillating Water column Devices in Breakwaters”, Proc of the ASME 2010 29th Intl Conf on Ocean, Offshore and Arctic Eng OMAE2010, pp 479-489 Thiruvenkatasamy K. and Neelamani S.(1997) “On the efficiency of wave energy caisson in array”. J. Appl Ocean Res., Vol.19, pp 61-72. Wang D. J., Katory M. and Li Y.S.(2002) “Analytical and experimental investigation on the hydrodynamic performance of onshore wave-power devices”, Ocean Engineering 29, pp 871885. Zheng W. (1989) “Experimental Research and parameters optimization of a prototype OWC wave power device”, Proceedings of the International Conference on Ocean Energy Recovery ‘89, pp 43-50.
