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Experimental Analysis into the Effects of Air
Compressibility in OWC Model Testing
Damon Howe#1, Jean-Roch Nader#2, Gregor Macfarlane#3
# National Centre for Maritime Engineering & Hydrodynamics, Australian Maritime College, University of Tasmania
Locked Bag 1395, Launceston, Tasmania 7250, Australia
1damon.howe@utas.edu.au
2JeanRoch.Nader@utas.edu.au
3gregorm@amc.edu.au
It is well documented that the effect of air compressibility will
potentially influence the performance of an Oscillating Water
Column (OWC) device, with a number of previous theoretical
studies examining these effects [1-5]. The implications of air
compressibility have the most significant effect at full scale, which
can be attributed to the large air chamber volume and the increase
in associated pressure and flow rate. However, the development of
wave energy converter technology relies significantly on model
scale testing, which is often scaled using the Froude criterion. This
scaling method are not appropriate for the modelling of air
compressibility and introduces uncertainties in the prediction the
performance results at full-scale. To account for these effects,
methods have been derived to more accurately represent the effect
of air compressibility at small scale, one of which requires scaling
the air chamber volume by the scale factor squared as opposed to
the traditional scale factor cubed following the Froude criterion
methodology [1]. This paper examines a preliminary investigation
into the effect of air compressibility through hydrodynamic
experimentation of a bent duct OWC device, from which the
behaviour of the obtained results are compared with the
expression proposed analytically by Sarmento and Falcao [1].
Keywords— Oscillating Water Column, Wave Energy
Converter, Air Compressibility, Hydrodynamic Experimentation
I. INTRODUCTION
A number of reviews have been transcribed that detail the
current status of ocean renewable energy, from technological,
economical and resource availability perspectives such as in [6-
15] to present a few. Pivotal to concept development of ocean
renewable energy technologies is model scale hydrodynamic
experimentation of devices, and the relevant interpretations and
conclusion concerning the corresponding full-scale device
characteristics. Model scale testing offers an economical
platform for concept validation, and provides a pivotal step in
the procession of a technology through the Technology
Readiness Levels (TRLs) [16].
With reference to technology maturity, the Oscillating Water
Column (OWC) Wave Energy Converter (WEC) is recognised
as the most tested and developed, whilst also being one of the
most promising and simplistic technologies for ocean wave
energy extraction. The OWC WEC also offers the largest
contingent of full-scale devices, predominantly pre-
commercial in their deployment (see [17-21]). Many device
variations have been conceptualised and tested at model scale
covering both isolated and breakwater integrated devices,
exploring features from vortex generation reduction through to
device performance [22-28]. Although advancements have
been made in testing facility capabilities, along with the
development of concept testing guidelines [29], there are still a
number of issues related to the experimentation of these devices
due to the difficulty scaling the Power Take-Off (PTO) system
and the corresponding difficulty associated with air
compressibility at small scale.
One major research and development aspect identified by
Falcao et al. is the potential discrepancies associated with the
inflow and outflow processes of air through the Power Take-
Off (PTO) system [4]. The complex mixing of the de-
pressurised lower density air within the chamber with external
atmospheric air during inflow can result in thermal changes of
the air, subsequently resulting in air compressibility. This factor
can have both positive and negative impacts on the
performance of the device [30, 31], and a number of systems
have been designed to either mitigate or alleviate this
phenomena, including latching-control mechanisms as in [2]
and also pressure release valves which have recently been
investigated by Wave Swell Energy for their bottom mounted
nearshore device [26].
As gravitational and inertial forces tend to be the dominant
forces in hydrodynamics, model scale testing is typically
undertaken using the Froude criterion. One focal uncertainty
associated with air compressibility is its inability to be
effectively scaled using the Froude criterion. With wave basin
experiments being of such crucial importance in the
development of WEC technology, the absence of air
compressibility can result in misleading performance
evaluation at the model scale, hence unreliable prediction of
full-scale performance as described by Elhanafi et al in [32].
A method has been derived in an attempt to account for the
effects of air compressibility during wave basin tests of WECs,
in which Sarmento and Falcao propose that the full-scale air
chamber volume be scaled by the scale-factor (λ) squared. This
method is opposed to scaling by the scale factor cubed which is
typically associated for volumetric scaling under the Froude
criterion [1, 5].
This paper details a preliminary investigation into effect of
air compressibility through hydrodynamic experimentation of
a bent duct type OWC device at 1:20 scale conducted in shallow
water wave basin. The behaviour of the results obtained are
analysed and compared with the analytically derived
expression proposed by Sarmento and Falcao [1]. Based on the
alternate methodology for air chamber scaling proposed by
Sarmento and Falcao (λ2), the OWC model would require an air
chamber volume around 0.5 m3. The volumetric variations
investigated here varies from no additional volume
(corresponding to previous studies using this device [22-24]),
through to an additional 1.5 m3 of volume, with 0.5 m3
increment.
A thin-walled bent duct type OWC WEC facing towards the
incoming incident wave propagation is considered for the
experimental investigation. The surface piercing device
operates in constant water depth h. The device in designed
having an inlet width WD, inlet height HD, and thickness tD,
highlighted in Fig. 1.
II. THEORY
Fig. 1 Schematic diagram of OWC device detailing front and side views. The
chamber chord length correlates to the sum of the variables s1, s2, s3 and s4.
A. Theoretical Hydrodynamic Consideration
The propagating monochromatic incident plane wave travels
towards the OWC device with amplitude η0 and frequency ω.
Linear water-wave theory is assumed, whilst considering
irrotational and inviscid flow.
As interaction between incident waves and the OWC device
occurs, a volume flux Q is generated within the chamber, which
when interacting with the PTO system, creates a dynamic
pressure Pc that oscillates around the mean atmospheric
pressure. Following Sarmento and Falcao [1], a linear
relationship between pc and q (complex forms of Pc and Q in
the frequency domain) is considered for the PTO system
damping, which is typically associated with a Wells turbine.
This relationship is written in the frequency domain as,
( )
r cc
q ip
γγ
= −
(1)
where,
0,
t
ra
KD
N
γρ
=
(2)
K is the empirical turbine coefficient based on the design,
number of and set up of the turbines, Dt is the turbine diameter,
N is the rotational speed of the turbine and ρ0,a is air density,
and
0,
20,
c
caa
V
c
ω
γρ
=
(3)
where, V0,c is the chamber volume and ca is the velocity of
sound in air.
B. Experimental Hydrodynamic Consideration
When considering the total volume flux from an
experimental standpoint, it can be express as follows,
cc
s sc
SS
Q ds v ds v S
t
η
∂
= = =
∂
∫∫ ∫∫
(4)
where vs represents the velocity of the free surface, Sc is the
cross sectional area of the chamber and v
̄s is the average
velocity under the assumption the free surface will move
uniformly.
Considering the performance of the device, the
instantaneous power at a given time t, is derived as,
( )
c
P t PQ=
(5)
where P is power in Watts. The mean hydrodynamic power
absorbed over a given wave period is equated as,
0
1
T
hc
P PQ dt
T
=∫
(6)
where Ph is the mean absorbed hydrodynamic power and T is
the wave period.
With reference to Equation (1),
irc
ei
γ
ϕ
γγ γ γ
= = −
(7)
where φγ represents the phase, found as,
c
Qp
γ
ϕϕϕ
= −
(8)
where φQ represents the phase of the volume flux, and φpc
represents the phase of the dynamic pressure. The
hydrodynamic coefficients are determined experimentally
using the amplitude of pressure and volume flux.
()
()
c
ampl Q
ampl p
γ
=
(9)
Finally, the capture width, Lpc, is defined as,
2
0
1
2
h
pc
g
P
LgC
ρη
=
(10)
where ρ is the water density, g is gravitational acceleration and
Cg is group velocity.
Fig. 2 Side and top view of the experimental configuration within the AMC Model Test Basin, all units in mm (not to scale).
III. METHODOLOGY
A. Experimental Considerations
1) Pneumatic Damping: To simulate the desired linear
damping relationship between dynamic chamber pressure and
total volume flux, a porous fabric mesh termed Enviro-Cloth
was sealed to the chamber outlet to provide a PTO
representation at model scale, as previously used in [22-24].
The previous methodology to establish the pneumatic damping
coefficient is outlined in [22], which includes the sources of
error associated with the required numerical derivations. It
should be noted that the mass-flow rate through the Enviro-
Cloth as a function of the pressure difference between internal
dynamic pressure and atmospheric pressure obeys the
approximately linear relationship as proposed in [1].
B. Model Test Basin
The experimental investigation was conducted in the
Australian Maritime College’s 35 m long × 12 m wide × 1 m
maximum depth Model Test Basin. The facility houses a multi-
element piston-type wavemaker capable of producing both
regular and irregular waveforms. The basin also incorporates a
damping beach at the opposite end of the basin to dissipate the
systems energy. A schematic of the experimental configuration
within the basin is illustrated in Fig. 2.
C. Physical Model
The OWC model utilised for the experimental investigation
is a 1:20 scale device having rectangular cross-sectional
geometry, which has previously been employed for various
hydrodynamic experimentation as in [22-24]. Alterations to the
design of the device were conducted to incorporate a separate
but directly linked receptacle to increase the OWC air chamber
volume.
The variable air chamber volume model was devised to
incorporate three identical compartments, which could be
incrementally combined to increase the air volume
methodically throughout the experimental investigation. The
connection of the additional air compartments and the OWC
device was achieved through a specifically designed adapter
plate, which allowed an airtight seal to be maintained between
the device and the additional compartments. Each compartment
was designed to have a specific volume corresponding to 0.5
cubic metres, subsequently the air chamber volume variations
tested were 0.5, 1 and 1.5 cubic metres of additional volume.
The additional compartments were constructed of 12 mm
plywood, and sealed with an epoxy coating to create an
impermeable layer. Each compartment had a 70 mm top and
bottom flange utilised in the connection of the modular units,
which were clamped together to compress an 8 mm × 13 mm
rubber gasket to maintain airtightness.
The compartments had a 0.23 m × 0.3 m opening at the top
and bottom symmetrical about the longitudinal and transverse
midpoint. These openings corresponded to the dimensions of
the device outlet cross-section, and were utilised for the
purpose of connection and as an outlet to which the PTO
damping simulant could be applied as shown in Fig. 3.
Fig. 3 Model scale OWC device fitted with additional 1.5 m3 air chamber (left), 1 m3 air chamber (middle) and PTO simulant secured using sealing plate (right)
D. Instrumentation and Calibration
To measure the performance of the OWC device, along with
the accuracy of the desired incident wave train, a series of
resistance-type wave probes, and a Honeywell Controls
TruStability board mount pressure sensor were utilised
throughout the experimental investigation. The pressure sensor
was configured with the OWC device through a small pressure
tap located on the side of the device and was connected to an
Ocean Controls KTA-284 instrumentation amplifier to increase
the data quality.
The three wave probes were configured as an incident, phase
and internal OWC probe respectively, having locations within
the wave basin corresponding to those presented in Fig. 2.
All probes were calibrated daily to reduce the uncertainties
associated with daily changes to the facility environment.
Calibration and sensitivity data can be found in Table I.
TABLE I
SENSOR PROPERTIES
Sensor
Range
Sensitivity
Output
Wave - Incident
± 40 mm
0.25 VDC/mm
±10 VDC
Wave - Phase
± 40 mm
0.25 VDC/mm
±10 VDC
Wave - OWC
± 60 mm
0.167 VDC/mm
±10 VDC
Pressure - OWC
± 400 Pa
25 mVDC/Pa
±10 VDC
E. Experimental Test Regime
The experimental test regime investigated four separate air
chamber volume variations. Each volumetric variation of the
device was subjected to 20 mm height across a frequency
bandwidth of 0.4 Hz - 1.2 Hz, with the results obtained
processed using phase averaging, a technique previously
employed in analysing model scale hydrodynamic
experimental data [22-24, 33, 34]. The frequency increment
resolution was increased around resonance to provide better
detail of the device performance at resonance.
F. Data Processing
As with previous experimental investigations associated
with bent duct type model scale OWC devices, the phase
averaging data post processing technique was employed to
accurately evaluate the performance of the OWC conditional
variations [22-24, 33-36]. Orphin et al. conducted a suite of
experiments investigating the uncertainty associated with
model scale hydrodynamic experimental testing of an OWC
device where they concluded that that results obtained via
phase averaging are within ± 2% of the results obtained from
10 identical repeat runs [24]. The methodology followed is the
same as that outlined in [22], from which the processed data
was then utilised to derive the measurements of interest
pertaining to the volumetric and damping variations.
IV. RESULTS AND DISCUSSION
A. Pneumatic Damping Coefficient, δ
As previously addressed, a linear damping relationship for
the model scale PTO substitute was desired for the
hydrodynamic testing. Previous evaluations of Enviro-Cloth
fabric mesh as a PTO simulant yielded results that indicated its
ability to provide linear damping characteristics at model scale
[22-24]. With these characteristics in mind, the fabric mesh was
applied identically across the four volumetric variations of the
OWC air chamber to establish how additional air chamber
volume influences the linearity of the damping, and the
relationship between pressure and volume flux within the
chamber.
Fig. 4 Damping relationship between pressure and volume flux for increasing chamber volumes: a) No additional volume b) 0.5 m3 additional volume c) 1.0 m3
additional volume d) 1.5 m3 additional volume.
Fig. 4 illustrates the pneumatic damping characteristics of
the OWC PTO simulant as the air chamber volume increases.
Fig. 4a displays the typical damping relationship previously
established for the unaltered OWC device in isolation, where it
is illustrated that for all experimental incident wave frequencies
(characterized by contrasting coloured lines) that an
approximate linear relationship can be assumed, defined by the
dashed line. Further investigating Fig. 4a, it can be recognised
that the effects of air compressibility are not conclusive due to
the lack of observable phase shift between the pressure and
volume flux data. This is most easily observed at the local
maxima and minima for pressure, where the corresponding
maxima and minima for volume flux are also observable. For
this case, which also represents a large portion of experimental
testing of OWC devices, the air-compressibility is usually
overlooked. It should be however noted that the apparent
hysteresis visible in Fig. 4a is associated with a pressure leak at
the outlet of the chamber. Subsequently the results obtained for
γr, γc and L̃pc. for the no added volume are considered erroneous
and are not presented in the following.
As the volume of the OWC air chamber incrementally
increases (0.5 m3, 1 m3 and 1.5 m3 in Fig. 4b, 4c and 4d
respectively), the effects of air compressibility become
apparent, as a phase shift is clearly discernible between the
internal pressure and volume flux as the corresponding maxima
and minima are unaligned. The linear regression to obtain the
pneumatic damping coefficient cannot be applied for these
cases. It should also be noted that the relationship between Pc
and Q seems to change with frequency.
In order to further investigate the air compressibility effect,
γr and γc were derived using Equation (7-9).
B. Compressibility Coefficient, γc
Analysis of the hydrodynamic components of the pneumatic
damping is presented in which detail the compressibility
against frequency and against different air chamber volumes,
V0,c, and turbine coefficients respectively.
First investigating the compressibility coefficient, γc, in Fig.
5, the coefficient is plotted for the different air chamber
volumes, V0,c, on the x-axis and different frequencies
represented by the colour markers. In Fig. 6, the coefficient is
plotted for the different frequencies on the x-axis and the air
chamber volumes, V0,c, are represented by the colours markers.
Analysing the result, the value of the compressibility
a)
b)
c)
d)
coefficient is seen to increase with respect to both V0,c, and f
the incident wave frequency. A linear trend seem to appear in
the data in both Fig. 5 and Fig. 6, which corresponds correctly
with the expected outcomes governed by Equation (3).
Fig. 5 Compressibility coefficient, γc, with respect to volumetric and incident
wave frequency increases
Fig. 6 Compressibility coefficient, γc, with variations of incident wave
frequency for varying volume cases.
Rewriting Equation (3) in the form of
( )
0,cc
CV k
γω
= +
(11)
the values of C and k where derived using the experimental data
and presented in Table II for the different V0,c and compare with
its theoretical value.
TABLE II
C AND K VALUE FOR VOLUMETRIC VARIATIONS
Previous hydrodynamic experimentation from the authors
was able to establish that for small values of V0,c the value of γc
will be very close to zero, subsequently resulting in no
discernible phase shift between the volume flux and dynamic
pressure [22]. In the same way, as the incident wave frequency
tends toward zero, indicating still water conditions, the value
for γc will also be zero. This correlates correctly to the
theoretical expression derived by Sarmento and Falcao [1]
which tends toward zero as both volume and frequency tend
towards zero.
The results illustrated in Fig. 5, Fig. 6 and Table II indicate
a disparity from the theoretical expression. It was established
that as V0,c and ω tend away from zero, the data followed a
relationship defined by the newly derived expression presented
in Equation (11). The value for C remains relatively constant
throughout the volumetric air chamber variations tested, but is
different from the theoretical value proposed, as found in Table
II. Similarly, the newly derived expression presents the
coefficient k, which appears to be a function of volume, as such
can be considered dependent upon the value of V0,c.
As illustrated in Fig. 5 and Fig. 6, a key finding from the
experimental investigation was the linearity of the relationship
between γc and both V0,c and ω respectively. This provides
evidence indicating the trend adheres to the linearity of the
theoretical expression, which provides a promising foundation
for future development. The variation in the magnitude of the
slope, and subsequent introduction of the coefficient k indicates
that revision of the theoretical model should be investigated at
full scale and verified through experimental measures to
provide greater understanding of the influence of air
compressibility in large scale devices.
The linearity of the established relationships in culmination
with further development of the theoretical model provides a
platform that can be developed further into a methodology for
better simulating the PTO system and air compressibility
effects at model scale.
It should be noted that the highly dynamic environment
within the OWC chamber associated with the natural resonant
frequency of the device did not have any apparent effect on the
results presented in Fig. 5 and Fig. 6 where the natural
resonance frequency of the device was found around 0.55 Hz.
C. Turbine Coefficient, γr
The second of the hydrodynamic coefficients related to the
pneumatic damping imposed on the system by the PTO
simulant is the turbine coefficient, γc. Fig. 7 illustrates the
results obtained from experimental testing against the
frequencies on the x-axis and the air chamber volumes, V0,c, are
represented by the colours markers.
Volume
(m
3
)
Experimental
C (10
-4
)
Theoretical
C (10
-4
)
Experimental
k (10
-4
)
0.5
0.0926
0.0694
0.1724
1.0
0.0928
0.2004
1.5
0.0953
0.2758
γr is found to stay relatively constant over the frequencies,
well within the uncertainties related to the measurements. One
key outcome, however, is the dependence of γr with the air
chamber volumes, V0,c. Although the damping on the orifice
simulated by the layers of enviro-cloth were the same, γr
increases with V0,c which does not follow the expected outcome
from Equation (2). In practice, γr can nevertheless be altered by
changing the number of Enviro-Cloth layers utilised for the
PTO simulant.
Fig. 7 Turbine coefficient, γr, for variations in incident wave frequency across
tested volumetric variations.
The results displayed in this section can have significant
application in the scaling and testing of OWC devices in order
to include the effect of air-compressibility inside the chamber.
Linear damping is here considered but the used of added
chamber volume could also be applied for the more usual
orifice type PTO simulant.
D. Hydrodynamic Performance
In order to evaluate the effect of volumetric changes of the
OWC air chamber on the hydrodynamic performance of the
model scale OWC device, the non-dimensional capture width
was derived for all test cases to form the plot displayed in Fig.
8. Analysing Fig. 8, we can observe the performance response
curve typically associated with an isolated bent duct type OWC
device, where the peak performance output occurs at the
resonance frequency of the device [24-26], which is
approximately 0.65 Hz for this particular test configuration. As
the incident wave frequency moves away either side of the
resonance frequency, there is an observable decline in the
performance of the device.
The difference in performance for the different additional air
chamber volumes is here not conclusive. The node present
around f = 0.95Hz, as discussed in [22] for the isolated device,
has a restraining influence on the effect of air-compressibility
on the performance for this case. Further testing for different
devices would be necessary.
Fig. 8 Non-dimensional capture width of the OWC device for varying incident
wave frequencies and volumetric air chamber variations.
V. CONCLUSIONS
The purpose of this document was to present a preliminary
investigation of the effect of air compressibility on a model
scale experiment of an OWC device by scaling the chamber
volume by the scale-factor (λ) squared instead of the typical (λ)
cubed. Three different added chamber volumes were
considered and their impacts on the pneumatic coefficients and
hydrodynamic performance studied.
A recognisable phase shift between volume flux and
pressure associated with air compressibility was identified as
the air chamber volume was increased. The air compressibility
coefficient, γc, was found to follow the theoretical trend as
proposed in [1]. The γc factor values obtained experimentally
for the variations in V0,c remained relatively consistent across
the test cases, yet varied in magnitude relative to the theoretical
expression. Similarly, the newly derived expression was found
to have a volume dependant factor k, which requires further
investigation in future studies. The PTO coefficient , γr, was
also found to be relatively constant over the frequencies as
proposed in [1] but was however found to be dependent on the
added volume.
The effects of air compressibility on the hydrodynamic
performance here was not conclusive due to the natural
behaviour of the device and will certainly require further testing.
This research presents a method with the potential for
significant changes in the model scale investigation of OWC
devices. The linear relationship established for the air
compressibility coefficient provides a foundation that can be
further developed toward more accurate assessments of full-
scale OWC devices’ hydrodynamic, pneumatic and energetic
properties in experimental set-up.
ACKNOWLEDGMENT
The authors acknowledge Mr. Daniel Male, Mr. Tim
Lilienthal and Mr. Darren Young for their assistance regarding
the design and construction of the experimental configuration.
Without their expertise and guidance, this experimental
investigation would not have been possible.
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