NUMERICAL MODELS TO SIMULATE UNDERWATER TURBINE NOISE
LEVELS
by
Renee Lippert
A Thesis Submitted to the Faculty of
The College of Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Science.
Florida Atlantic University
Boca Raton, Florida
August 2012
ABSTRACT
Author: Renee’ Lippert
Title: Numerical Models to Simulate Underwater Turbine Noise Levels
Institution: Florida Atlantic University
Thesis Advisor: Dr. Stewart Glegg
Degree: Master of Science
Year: 2012
This work incorporates previous work done by Guerra and the application of computational fluid dynamics. The structure attached to the turbine will cause unsteady fluctuations in the flow, and ultimately affect the acoustic pressure. The work of Guerra is based on a lot of assumptions and simplifications to the geometry of the turbine and structure. This work takes the geometry of the actual turbine, and uses computational fluid dynamic software to numerically model the flow around the turbine structure.
Varying the angle of the attack altered the results, and as the angle increased the noise levels along with the sound pulse, and unsteady loading increased. Increasing the number of blades and reducing the chord length both reduced the unsteady loading.
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NUMERICAL MODELS TO SIMULATE UNDERWATER TURBINE NOISE LEVELS
List of Tables ...... vii
List of Figures ...... viii
Chapter 1: Introduction ...... 1
Chapter 2: Literature Review ...... 4
2.1. Acoustic Impacts on Marine Life ...... 4
2.2. Wind Turbine Noise ...... 6
2.3. Marine Propeller Noise ...... 6
2.4. Ocean Current Turbine Testbed ...... 7
2.5. Previous Work ...... 8
2.5.1. Simplified Turbine ...... 9
2.5.2. Radiated Sound ...... 9
2.5.3. Unsteady Lift Noise ...... 12
2.5.4. Velocity Deficits and Upwash Velocity ...... 14
2.5.5. Noise Level Calculation ...... 15
2.5.5 Discussion ...... 17
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Chapter 3: Revised Analysis ...... 19
3.1.1 Simplified Turbine vs. Actual Geometry ...... 19
3.1.2 Small-Deficit Wake Theory ...... 20
3.1.3 Angle of Attack ...... 21
Chapter 4: Computational Fluid Dynamics Method and Validation ...... 22
4.1 Introduction ...... 22
4.2 Computational Fluid Dynamics ...... 23
4.3 Simplified Cases ...... 25
4.3.1 Two Dimensional Axis-Symmetric Study ...... 25
4.3.2 Thee-Dimensional Simplified Geometry Study...... 28
4.4 Validation Process ...... 30
4.5 Actual Turbine ...... 31
4.5.1 Design Considerations ...... 32
4.5.2. CFD Method ...... 32
4.5.3 Data Integration ...... 35
4.5.4 Comparison to Guerra’s Code ...... 37
Chapter 5: Acoustic Noise Estimates and Unsteady Loading ...... 38
5.1 Unsteady Loading Results ...... 38
5.2 Acoustic Results...... 39 v
Chapter 6: Turbine Modifications ...... 42
6.1 Varying the Angle of Attack ...... 42
6.2 Chord Reduction ...... 43
6.3 Number of Blades ...... 44
Chapter 7: Conclusions ...... 45
Appendix ...... 50
References ...... 109
vi
LIST OF TABLES
Table 1: Table of Constants and Variables ...... 50
Table 2: List of Mesh number with nodes and convergence criteria ...... 65
Table 3: Boundary Conditions for the Turbine Model ...... 68
Table 4: Mesh 1 Grid Information ...... 70
Table 5: Mesh 2 Grid Information ...... 76
Table 6: Mesh 3 Grid Information ...... 78
Table 7: Mesh 4 Grid Information ...... 84
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LIST OF FIGURES
Figure 1: FAU's Ocean Current Turbine Testbed Diagram ...... 52
Figure 2: Guerra's Simplified Design ...... 53
Figure 3: Coordinate System ...... 54
Figure 4: Noise levels felt at a point of observation positioned at spherical coordinates
(100 m, 45º, 45º) ...... 55
Figure 5: Actual Turbine Geometry vs. Simplified Geometry ...... 56
Figure 6: Difference between Theoretical and Numerical Velocity Profiles at the location
of the blades ...... 57
Figure 7: 2-Dimensional Axis-Symmetric Cylinder Study; Geometry ...... 58
Figure 8: 2-Dimensional Axis-Symmetric Cylinder Study; Grid #1, 6,790 nodes ...... 59
Figure 9: 2-Dimensional Axis-Symmetric Cylinder Study; Case #1 Velocity Contour with
Boundary Layer Plots ...... 60
Figure 10: 3-Dimensional Cylinder Study; Geometry Iso-View ...... 61
Figure 11: Geometry of Cylinder with Hemisphere End Caps and Mast ...... 62
Figure 12: Mean Velocity Profile for Cylinder with End Caps and Mast at Location of
Blades ...... 63
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Figure 13: Length Scale at Location of Blades ...... 64
Figure 14: Original Turbine Geometry ...... 66
Figure 15: Geometry of the Turbine Modeled ...... 67
Figure 16: Turbine Coarse Grid Spacing, Mesh #1 ...... 69
Figure 17: Velocity Contour at Location of Blades ...... 71
Figure 18: Velocity Contour with Specified Lines of Interest ...... 72
Figure 19: Convergence Independence, Mesh #1, Lines ...... 73
Figure 20: Convergence Independence, Mesh #1, Circles ...... 74
Figure 21: Turbine Mesh #2 Grid Spacing ...... 75
Figure 22: Convergence Independence, Mesh #2, Lines ...... 77
Figure 23: Convergence Independence, Mesh #2, Circles ...... 78
Figure 24: Turbine Mesh #3 Grid Spacing ...... 80
Figure 25: Convergence Study, Mesh 3, Lines ...... 81
Figure 26: Convergence Study, Mesh 3, Circles ...... 82
Figure 27: Turbine Mesh #4 Grid Spacing ...... 83
Figure 28: Convergence Study, Mesh 4, Lines ...... 85
Figure 29: Convergence Study, Mesh 4, Lines ...... 86
Figure 30: Grid Independence Study, Lines ...... 87
Figure 31: Grid Independence Study, Circles ...... 88 ix
Figure 32: Unsteady Lift for One Blade, Theoretical vs. Numerical...... 89
Figure 33: Orientation of the Observer with respect to the Turbine ...... 90
Figure 34: Unsteady Acoustic Pressure, One Blade, Theoretical vs. Numerical ...... 91
Figure 35: Sound Spectral Levels for Numerical and Theoretical Results ...... 92
Figure 36: Typical Ocean Noise Levels...... 93
Figure 37: Flow Direction for Varying Angle of Attack ...... 94
Figure 38: Stall Angle, Angle of Attack Analysis ...... 95
Figure 39: Unsteady Lift, Varying Angle of Attack ...... 96
Figure 40: Acoustic Presssure, Varying Angle of Attack ...... 97
Figure 41: Sound Spectral Levels, varied angle of attack ...... 98
Figure 42: Unsteady Lift, Chord Reduction ...... 99
Figure 43: Sound Pulse, Chord Reduction ...... 100
Figure 44: Spectral Levels, Chord Reduction ...... 101
Figure 45: Unsteady Lift, 3 Blades ...... 102
Figure 46: Sound Pulse, 3 Blades ...... 103
Figure 47: Unsteady Lift, 5 Blades ...... 104
Figure 48: Sound Pulse, 5 Blades ...... 105
Figure 49: Spectral Levels for 1 Blade and 3 Blades ...... 106
Figure 50: Unsteady Loading Comparison with number of blades ...... 107 x
Figure 51: Skewed Propeller Design [16] ...... 108
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CHAPTER 1: INTRODUCTION
Hydrokinetic energy is produced by harnessing the kinetic energy of a body of water. The available kinetic energy of the Florida Current has potential to supply Florida with much needed clean, renewable electricity [10]. Although harnessing energy from the
Florida Current has been considered for decades, no commercial scale system has been demonstrated or installed [10]. Florida Atlantic University’s Southeast National Marine
Renewable Energy Center (SNMREC) is currently collaborating with university and industry partners to research, fabricate, and test promising hydro-kinetic power technologies. SNMREC has applied to the Bureau of Ocean Energy Management,
Regulation and Enforcement for a lease to deploy an experimental demonstration device about 12 miles off the coast of Fort Lauderdale [9]. Since, no ocean current turbine system has ever been installed or operated in the Florida Current there is no technical or environmental knowledge-base.
The environmental impacts of this project need to be taken into serious consideration. This thesis will approximate acoustic noise levels and evaluate their potential impact on marine mammals. Acoustics and the marine life impacts have been of great concern for many years and much research and information is available. There are many case studies performed on marine animals and mammals to determine unsafe levels of acoustics. The ocean is a relatively high noise environment. Principal natural sound
1 sources include seismic, volcanic, wind, and even biotic sources. Whales and dolphins in particular have evolved ears that function well within this context of high natural ambient noise. The aquatic ear must tolerate sound pressures in water that are ~60 times greater than are required in air. [3] Actual studies with threshold information will be discussed in great detail later.
In order to determine if marine life will be affected by the acoustics of the underwater turbine the noise levels need to be calculated. Calculating these noise levels requires an understanding of underwater propellers. This can be achieved by using the
Ffowcs Williams and Hawkings equation, and using the process that Guerra [13] outlined in his thesis, the equation is transformed into a usable tool in calculating these noise levels from a water turbine. It was determined by Guerra that the primary source of the noise comes from the unsteady lift fluctuations experienced by the blade [13].
Calculating the noise levels of the actual turbine requires the use of a
Computational Fluid Dynamics model. By modeling the actual turbine within a CFD program (ANSYS Workbench) the velocity profiles of the flow into the turbine can be obtained and then put into the code developed by Guerra. Once the noise levels have been calculated they can be used to estimate the impact on marine mammals.
This thesis will first examine previous work and studies that pertain to the analysis of determining the acoustics generated from underwater turbines. This will lead into the chapter that explains the differences between previous work, and the analysis performed in this thesis. The following chapter, Chapter 5, will begin the in depth process of examining computational fluid dynamics and its application is relevant to this thesis.
2
Chapter 5 will also explain how the data will be verified, and examine simplified geometry cases. After the validation process, the results will be examined, and the acoustic noise and unsteady loading results will be analyzed. Characteristics of the turbine will be modified and these results analyzed, in order to determine significant changes. These results will all be compared against ambient noise levels on the ocean, and will ultimately determine any potential impacts on marine mammals.
3
CHAPTER 2: LITERATURE REVIEW
2.1. ACOUSTIC IMPACTS ON MARINE LIFE
One of the biggest hurdles for the progress in developing Ocean Energy is satisfying the requirements of regulatory agencies, and most of these agencies require environmental impact studies. When putting man made devices into the ocean it is crucial to understand how the device will impact the marine life. Sound is a key element for survival and hearing is a key component of communication, mate selection, feeding, and predator avoidance for most marine life. Dolphins and Whales devote three fold more neurons to hearing than any other animal [3]. Being able to calculate the acoustics generated and understanding how the acoustics will impact the marine life is also important. There is no habitat, except space, that is soundless.
In the mid 1970’s, it was estimated that noise from human related activity was increasing in coastal areas and shipping lanes at 10dB per decade. Given our ever increasing activity in all seas and at all depths, this figure is not surprising. It may even be too conservative [3]. It is no wonder why so much time and research is devoted to marine life and acoustics. Unfortunately, the same reasons that make marine mammals acoustically and auditorally interesting also make them difficult research subjects [3].
4
There are two fundamental issues to bear in mind for the auditory as well as any sensory system. One is that sensory systems and therefore perception are species specific. The ear and what it can hear is different for each species. The second is that they are habitat dependent. In terms of hearing, both of these are important [3].
The results of previous research show that the frequencies of water turbine noise are expected to be in the very low frequency range. Good lower frequency hearing appears to be confined to larger species in both the cetaceans and pinnipeds. Most pinniped species (types of seals) have peak sensitivities between 1-20 kHz. Only the elephant seal has shown to have good to moderate hearing below 1 kHz. Marine mammals as a group have functional hearing ranges of 10Hz to 200 kHz with best thresholds near 40-50 dB re 1 μPa. This can be compared with a healthy human ear that has a maximum frequency range of 20 Hz to 20 kHz. There is a significant difference between sounds in water versus sound that travels through air. The speed of sound is not invariable; it depends upon the density on the medium (water or air). In water sound speed is 4.5 times faster and at each frequency, the wavelength is 4.5 times greater than air. The consensus of the data is that virtually all marine mammal species are potentially impacted by sound sources with a frequency of 300 Hz or higher. Relatively few species are likely to receive significant impact for lower frequency sources. The species that currently are believed to be likely candidates for low frequency acoustic impact are most mysticetes (types of whales) and the elephant seal [3].
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2.2. WIND TURBINE NOISE
Wind Turbines generate two different types of noise: aerodynamic and mechanical. Mechanical noise is generated by the turbines’ internal gears. Fortunately, utility scale turbines are usually insulated to prevent mechanical noise from proliferating outside the nacelle or tower [5]. Mechanical noise may contain discernable tones which makes it particularly noticeable and irritating. Aerodynamic noise is generated by the blades passing through the air. The output power of aerodynamic noise is related to the ratio of the blade tip speed to the speed of sound. Depending on the turbine model and the wind speed, the aerodynamic noise may seem like buzzing, whooshing, pulsing and even sizzling. Turbines with their blades downwind of the tower are known to cause a thumping sound as each blade passes the tower. The noise from two or more turbines may combine to create an oscillating or thumping “wa-wa” effect [5].
2.3. MARINE PROPELLER NOISE
Similar to wind turbines, marine propellers have been around for many years and there is much information and research readily available. There are four types of noise that can be produced by a propeller; displacement noise, which is due to the water displaced by the rotating blade; fluctuation load noise, which is caused by non- uniformities in the incoming flow causing unsteady blade loading; cavity noise caused by periodic fluctuation of the cavity volumes in the wake behind the marine vehicle and cavitation noise caused by the sudden collapse process associated with cavitation bubbles
[5]. Cavitation of the marine propeller is the prevalent source of underwater sound in oceans and is often the dominant noise source of a marine vehicle [6].
6
For the case of water turbines which will initially be deployed at a depth of approximately 10 meters, their cavitation number is.
[Equation 1] ( ) ( )( )( )
Where:
Po- is a characteristic pressure level
Pv- is the vapor pressure
Utip- is the tip velocity of the blade roughly calculated using tip speed ratio
TPR=4.62 [4].
Cavitation occurs for σ0= 0.1 or less and so the water turbine will not cavitate. Since cavitation does not occur the process of calculating the noise is greatly simplified.
The non-cavitating noise from an underwater propeller can be represented as the solution of the wave equation if the distribution of sources on the moving boundary (the blade surface) and the flow field is known. Ffowcs Williams and Hawkings derived the governing differential equation by applying the Lighthill acoustic analogy to bodies in motion [6]. The Ffowcs Williams-Hawkings equation addresses three types of noise source terms which are monopole, dipole, and quadrupole terms. For underwater turbines with low tip Mach numbers the noise is dominated by the dipole term which can be calculated from the unsteady blade loads.
2.4. OCEAN CURRENT TURBINE TESTBED
Florida Atlantic University’s Southeast National Marine Renewable Energy
Center has designed a small-scale ocean current turbine system. This system consists of a 7 permanently anchored mooring and Telemetry Buoy (MTB) with a gravity anchor, and
Ocean Current Turbine Testbed (OCTT) and a twin-hull Observation Control
Deployment Platform (OCDP) , as shown in Figure 1 [10].
The Ocean Current Turbine Testbed is a 20 kW open-blade axial flow horizontal- axis underwater turbine design, driven by a 3 meter diameter 3-blade rotor. It is intended for use in ocean currents that average 1.7 m/s, but the peak operating velocities are 1.5 m/s and 2.5 m/s with a rotational velocity of 50 RPM. It is to be moored to the ocean bottom at a depth of 330 meters on the Miami terrace. It is to operate in a maximum sea state of 6, but typically in sea state of 4 or less. The turbine will operate at a depth of 30 meters.
The upstream truss mounted on the turbines plays an important role in the production of the loading noise because it induces disturbances on the incoming velocity of the blades [13]. This structure can also develop vortex shedding, which causes an especial type of unsteady loading noise known as blade vortex interaction (BVI), causing a very loud “thumping” noise [11].
2.5. PREVIOUS WORK
Julian Guerra based his thesis on developing a mathematical model that would estimate noise levels of the Ocean Current Turbine Testbed. He noted that wind turbines and propellers produce both harmonic and broadband noise. However, his work focused on the harmonic noise, more specifically the harmonic noise generated by velocity deficit profiles formed upstream of the blades. He left the unsteady loading noise created by vortex shedding off the structure, blade vortex interaction (BVI) to be considered as a 8 topic of study for future works. He categorized his thesis into sections that outlined his process for calculating the noise levels created form the turbine and the attached structures.
2.5.1. SIMPLIFIED TURBINE
Guerra used a number of assumptions and simplifications to be able to derive simpler mathematical expressions that can later be adjusted as needed to tailor the characteristics that are specific to the turbine. Figure 2 shows the simplified design he assumed for his calculations [13]. The estimation of the loading noise levels of the OCCT assumed high aspect ratio blades, which is defined as the ratio of the span to the blade chord. This high aspect ratio indicates that a two-dimensional strip theory approach is valid [13]. He also assumed that the blades are thin (thickness to chord ratios of less than
0.1) because the blades could then be modeled as flat plates confined to the rotor disk plane. The implementation of this model is based on the assumption that the results for loading noise levels are qualitatively similar for blades whose cross-sections are either thin, flat plates, or real hydrofoils [12]. These assumptions will prove to be useful when the equations for calculating the noise levels are being derived.
2.5.2. RADIATED SOUND
The Ffowcs Williams and Hawking’s wave equation gives a method to calculate the sound generated rotating blades in an otherwise stationary fluid [6]. The dipole term relates the radiated acoustic pressure field generated by the rotor blades due to the unsteady loading on the blade. It describes the dominant source of sound generation by
9 water turbines. On this basis, the simplified Ffowcs Williams and Hawking’s equation in terms of the dipole term gives the acoustic pressure expressed as [11]:
( ) ∫ [ ] [Equation 2] | |
Where,
x - The position of the observer, x = [x1,x2,x3]
t – The observer’s time
r- The distance between acoustic source and observer
| | √( ( )) ( ( )) ( )
y - The position of the noise source
τ – Emission Time
γ - The radius of the point source element
φ - The time dependent azimuthal location
Pij – The surface stress tensor
Mr – The Mach number in the radiation direction
S – The surface of the blade
For Water Turbines, unsteady variations of the drag are small compared to those of the lift [11]. So, only the fluctuating forces in the direction perpendicular to the rotor will be important. The ratio of the chord to the acoustic wavelength is less than one, so
10 the load distributions in the chordwise direction can be neglected and the noise sources can be modeled as a rotating line source [13]. Further simplification is obtained by noting that in the acoustic far field, the propagation effects dominate the space derivatives [11].
The distance in between the observer and the source creates a time delay effect, and this relationship is shown in figure 3. There is a difference in time from when the source emits sound and when the sound is heard. The relationship between the observer’s time, t, and the emission time, τ*, is
[Equation 3]
Where, r/c0 is the time the acoustic wave takes to propagate at the speed of sound from the source element to the observer. It is necessary to convert the time differential of the observed field into an expression evaluated at emission time [13]. Taking the derivative of equation 2 and changing to the partial derivative with respect to the emission time, the acoustic pressure equation is transformed into the time history of the acoustic field, and is proportional to the unsteady lift variation on the blade.
( ) [ ( ) ] [Equation 4] ∫ ( )
Where,
x - The position of the observer, x = [x1, x2, x3]
r- The distance between acoustic source and observer
γ - The radius of the point source element
Mr – The Mach number in the radiation direction
11
c0 – The speed of sound in sea water
L - The Lift per unit span
Linear Interpolation methods are required to evaluate the observed signatures at a fixed point from the time history of the source on the blade [13].
2.5.3. UNSTEADY LIFT NOISE
The periodic noise of non-cavitating propellers and water turbines operating at low speeds depends mostly on the unsteady blade loads [13]. The unsteady load variations can be divided into unsteady drag and lift for non-cavitating propellers operating in a non-uniform flow. The unsteady lift fluctuations are the dominant source of noise and are induced by small velocity variations that cause a small change in the angle of attack [13].
Sears established an expression for the lift distribution of a rigid airfoil passing through a sinusoidal gust. It was assumed that the flow about the airfoil was two- dimensional. Given the high aspect ratio of the OCTT it is not unreasonable to assume that the flow past the blade can be described as the flow over each cross section making it two-dimensional, so Sear’s theory can be used.
The expression for the Sear’s lift distribution passing through a sinusoidal gust is proportional to the upwash velocity and Sear’s function:
( )
( ) ( ) ( ) [Equation 5] ( ) ( )
Where,
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σ – Non-Dimensional Frequency used in Sear’s function
C – The chord of the foil
λ – Wavelength of Sinusoidal gust
(2) (2) H1 (σ), H0 (σ) - Cylindrical Hankel functions of the Second Kind
The unsteady flow encountered by the blade will be since it repeats each blade revolution a periodic gust profile can always be formed by superposition of sinusoidal gusts. Using this result Guerra showed that the lift per unit span can be represented by,
( ) ∑ | ( )| ( ( ) ) [Equation 6]
Where,
σ – Non-Dimensional Frequency used in Sear’s function
( )
Ue – Incoming gust velocity
C – The chord of the foil
Wn – Fourier Coefficient (defined in equation 14)
S(σn) – Sear’s Function
β(σn) – Phase of the Sears function
– Angular Speed of the Blade
13
τ – Emission Time
φ - The time dependent azimuthal location
This is the total lift produced on any rigid airfoil by a vertical gust of any arbitrary profile, which is proportional to the upwash and the Sear’s function [13].
Since, w(τ) is symmetrical about the ordinate its Fourier series can be represented as [13],
( ) ∑ ( ) [Equation 7]
which, implies φ is zero from equation 6, and where
∫ ( ) ( ) ( ∫ ( ) ( ) ) [Equation 8] ⁄
Approximating the integration yields the Fourier coefficients of the vertical velocity on a rigid flat plate passing through a sinusoidal gust were shown to be [13]:
( ∑ ( ) ( )) [ ( ( ))] [Equation 9]
The matlab routine (ifft) is used to calculate the coefficients.
2.5.4. VELOCITY DEFICITS AND UPWASH VELOCITY
The expression for the total lift depends on the Fourier coefficients of the velocity normal to the blade. These coefficients are derived by finding the upwash velocity that causes a lift perturbation on the blade while passing through the wake formed by an upstream structure. The velocity profile originates at the upstream structure and is modeled in Guerra’s work by using the results of Wygnanski, Champagne and Marasli’s
14 for two-dimensional, turbulent, small deficit wakes created by wake generators of different shapes [14].
2.5.5. NOISE LEVEL CALCULATION
The simplified Ffowcs Williams and Hawking’s equation for the acoustic pressure requires the time derivative of the lift per unit span equation.
(∑ ( )( ) ( ) [Equation 10]
Substituting this back into the acoustic pressure equation yields,
( ) (∑ ( )( ) ( )) ∫ [ ] [Equation 11] ( )
Where the Fourier Coefficients are calculated using,
( ∑ ( ) ( )) [Equation 12]
With these equations the noise levels can be calculated for a simplified water turbine. First, the Fourier coefficients for the upwash velocity are calculated. Because of the time delay effect from the distance in between the source and observer, the position of the observer needs to be established. Then, the lift’s time derivative needs to be determined and combined with equation 4. The time history of the acoustic field will be to calculate the frequency time spectrum from the signal by combining the positions established with the Ffowcs Williams and Hawking’s equation.
( ) ( ) ( ) ∑ [( ) ( ) ( ) ( )] ( ) [Equation 13] ( ) ( ) ( )
The span step is defined as,
15
[Equation 14]
Where,
– Turbine Radius
B- The number of Subsections
The relationship of the average power in the acoustic radiated sound signal can be described by using Parseval’s theory. This theory explains that p’(t) is either given by the time average of the squared magnitude of the signal, or by the sum of the squared magnitudes of its Fourier Coefficients [13]. The power spectrum is obtained by taking the square of the Fourier coefficients of the acoustic pressure time history p’(t). The Fourier
Coefficients of the acoustic pressure time history are defined as,
∑ ( ) ( ) [Equation 15]
These coefficients are found the same way as in equation 9. The power contained in any limited frequency range is obtained by the summation of the power spectral
2 density over that range, and will be equal to the sum of the Fourier coefficients |pn| , whose frequency lies in the range of interest [13]. The average power can then be described as the following,
∫ | ( )| ∑ | | ( ) [Equation 16]
16
To convert these levels to decibels the source level (SL) and the intensity level
(SE) need to be taken into consideration. This relationship is shown below in equation 17.
( ) ( ) [Equation 17]
Combining the results from equation 16 and 17, the source level power spectrum is presented on a decibel scale and corrected for the transmission losses to obtain the effective source levels.
| | (√ ) ( ) [Equation 18]
2.5.5 DISCUSSION
Through his work Guerra determined that the noise source levels are well above the ambient noise levels in the ocean at very low frequencies (< 20 Hz), figure 4, which indicates that the acoustic pulses generated during the operation of the hydrokinetic turbines will certainly be heard in the vicinity of the turbine. However, at high frequencies, the noise levels are well below the ambient noise levels in the ocean [13].
Noise source levels decrease with range as 6 dB per doubling of distance and so the turbine noise level will not be a significant source of sound at larger distances from the turbine. However, the very low frequency nature of the sound may make it particularly audible, and of more significance than similar sound levels at higher frequencies. Guerra compares the source levels of these results to those of the ocean and it was concluded that
17 the acoustic pulsations generated under this conditions would be heard in the ocean but only at low frequencies.
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CHAPTER 3: REVISED ANALYSIS
The study and development of Fluid Dynamics is a balance of three different approaches to the subject; experimental, theoretical, and most recent being numerical. Up until a couple decades ago, most scientists and engineers were only using the first two approaches. Guerra used theory in obtaining his results. In doing so, he made some assumptions and simplifications to ease the calculation of his data analysis. This chapter will explain the differences between Guerra’s theoretical model for the structure geometry, and the numerical modeling of the actual turbine discussed in this thesis.
3.1.1 SIMPLIFIED TURBINE VS. ACTUAL GEOMETRY
The biggest difference is that Guerra used a simplified turbine design, where this thesis uses the actual geometry of the turbine structure. Guerra used a theoretical model for the structure for his results. The difference between the geometries used can be seen in figure 5.
The difference in the geometries has a significant effect on the upwash velocity profiles, which is the velocity profile used to calculate the lift forces, acoustic pressures, and ultimately the sound levels. The difference between the two geometries and the resulting upwash velocities is shown in figure 6. The updated velocity does have the structure on the bottom, where Guerra’s geometry has the structure on the top. Figure 6
19 shows upwash velocities where the structure is in the same location for comparison purposes.
Guerra assumed the structure to be solid. Section 2.5 of this thesis explains in great detail the use of this assumption and the availability of turbulent, small-deficit wake theories. Figure 6 shows a significant difference in the upwash velocities because of the assumption Guerra used. The actual structure of the turbine allows for more uninterrupted flow, where the solid structure assumption creates more disturbances in the flow.
3.1.2 SMALL-DEFICIT WAKE THEORY
Guerra used the work of Wygnanski, Champagne, and Marasli in creating his velocity deficit profiles. While this model for establishing velocity deficits is well established, the application to a complex structure, such as the OCCT turbine structure, is unprecedented.
The work of Wygnanski, Champagne, and Marasli “On the large-scale structures in two-dimensional, small-deficit, turbulent wakes” is slightly limited in the sense that they only observed the wake generation of specific simple shapes, and objects. This work establishes a general equation for the mean flow field in a small-deficit, plane wake
(equation 19).
( ) [Equation 19]
This equation is a function of the velocity scale, and length scale. The length scale and velocity scale are dependent on Wygnanski coefficients and the use of the virtual origin. Wygnanski, Champagne, and Marasli established a table of suggested Wygnanski
20
Coefficients and virtual origin locations for various shapes, sizes, and objects. The model
Guerra used for his work mirrors the wake generator example of a flat plate, and used the coefficients for the flat plate wake generator. However, since the study that Wygnanski,
Champagne, and Marasli performed was specific to the shapes, sizes, and objects of their study, the coefficients can be tweaked for larger or smaller objects, and virtual origin distances. Their study observed cylinders of sizes ranging from 1/16 inches to 3/16 inch, screens of different solidity, symmetrical airfoil, and flat plates with or without a flap at different frequencies. Unfortunately, not a lot of data exists on the mean wake growth, and confirming the coefficients that Guerra used would require the use of experimental data.
3.1.3 ANGLE OF ATTACK
Another significant difference between the works of Guerra and this thesis is the varying of the angle of attack. Guerra assumed a free-stream velocity in the direction normal to the turbine blades. This thesis modeled different cases with a varying angle of attack and discusses the differences from changing this angle. The angle of attack on turbines plays a significant role in the determining the lift and drags forces experienced.
The simplified Ffowcs Williams and Hawking’s equation (equation 4), shows the dependence on the lift forces. If the angle of attack varies so will the lift forces. More details on this can be found in section 6.2.
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CHAPTER 4: COMPUTATIONAL FLUID DYNAMICS METHOD AND
VALIDATION
4.1 INTRODUCTION
The use of Computational Fluid Dynamics (CFD) has been around for decades, and as computer become more and more optimized, the accuracy and complexity of numerical modeling increases. This chapter will first explain the CFD analysis methods and turbulence models used. The process for the computational fluid dynamic analysis will then be discussed. Simplified cases were run, and the results and discussions for those will lead up to the results and analysis from the turbine analysis.
Fluid dynamic analysis is a combination of theory, numerical data, and experimental data. Numerical data needs to be verified, just like any of the other forms of data generation. Deploying a turbine of this nature is unprecedented, and therefore lack of data creates a problem. Simplified cases were first analyzed in order to determine the correct process to achieve the most accurate results. Simplified geometries were analyzed and the data verified by using well established theories and experimental data. The same processes for modeling the simplified geometries lead to the most accurate process used to get the best obtainable results without having the experimental data for comparison.
This process is explained in more detail, and the results afterward.
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4.2 COMPUTATIONAL FLUID DYNAMICS
Computational fluid dynamics (CFD) is a process used in fluid mechanics that uses numerical modeling and algorithms to solve and analyze fluid flow problems.
Navier-Stokes equations are the basis for most flow problems. Reynolds-averaged
Navier-Stokes equations are used in non-linear, turbulent flows. Turbulent flow is of particular interest because of the random fluctuations that occur in turbulent flow.
The most common turbulence models are the k-ω, k-ε, Spalart-Allmaras,
Reynolds stress model (RSM), and Scale-adaptive simulation (SAS). Each turbulent model has benefits and limitations. The standard k-ε model is based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). They have been found to work fairly well for a wide range of wall bounded and free shear flows and, with constant modifications being performed, this has been deemed the industry standard. The k-ω turbulent model is based on the Wilcox k-ω model using two equations to solve for turbulent viscosity and empirically derived. This model has been shown to have inaccuracies outside the shear layer. The Spalart-Allmaras model is a one equation model designed primarily for aerospace applications involving wall-bounded flows and high Mach number flows. The Reynolds stress model is the most elaborate of all the
RANS (Reynolds Averaged Navier-Stokes equations) based turbulence models. This model has the greatest potential to give accurate predictions for complex, high swirl, and stress-induced flows because of the robustness of the equations used for this model.
The modeling of the pressure-strain and dissipation rate terms is particularly challenging, and often considered to be responsible for compromising the accuracy of
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RSM predictions [7]. The Scale-Adaptive Simulation (SAS) is an improved URANS formulation, which allows for the resolution of the turbulent spectrum in unstable flow conditions [7]. This model is best at producing accurate results for large scale unsteadiness that resembles large eddy simulation model results while maintaining accuracy in stable regions. Each model has strengths and weaknesses and only through running the models will allow the determination of the best model.
Boundary conditions are necessary when solving the hydrodynamic equations because they define the surfaces of the model. The particular boundaries used in ANSYS
FLUENT are unique to the problem conducted; depending on which boundaries are used will affect the data. For the velocity inlet boundary the velocity and scalar properties of the flow at inlet boundaries are defined. Only the velocity component normal to the control volume face contributes to the inlet mass flow rate. For this particular model there are two options for the outlet boundary condition that can be used, outflow and pressure outlet. The Outflow boundary condition in ANSYS FLUENT is used to model the flow exit where the details of the flow velocity and pressure are not known prior to solving the flow problem. The Pressure Outlet is used to define the static pressure at flow outlets. The use of a pressure outlet boundary condition instead of an outflow condition often results in a better rate of convergence when backflow occurs during iteration. Wall boundary conditions are used to bound fluid and solid regions. In viscous flow, the no- slip boundary condition is enforced at walls by default, but you can specify a tangential velocity component in terms of the translational or rotational motion of the wall boundary, or model a “slip” wall by specifying the shear. Similar to wall boundary
24 condition the symmetry boundary condition can be used to model zero-slip walls in viscous flows.
4.3 SIMPLIFIED CASES
The OCCT turbine can be modeled within ANSYS FLUENT and all the characteristics of the flow can be output as data to be analyzed. The OCCT Turbine model was created as a SolidWorks assembly and will be input into ANSYS Workbench for modeling. The lack of data creates a problem. As mentioned before any data obtained from numerical modeling methods need to be verified by using other types of methods.
Before modeling the geometry of the turbine, it is necessary to run some models with a simplified design to establish a process for verification.
The use of simplified geometries will generate patterns in the numerical modeling analysis. These pattern built the standards for the verification process. This verification process is the process used to obtain the most accurate results with the use of any other data for verification. This process starts with a really simple geometry and progresses towards a more complex geometry. The simplified geometries will be verified by using well established theories and studies. The aspects of these simplified cases will be used when modeling the turbine geometry.
4.3.1 TWO DIMENSIONAL AXIS-SYMMETRIC STUDY
The first simplified geometry was just a cylinder geometry, and can be seen in figure 7. The nature of the geometry allowed for two-dimensional axis-symmetric analysis. The analysis laid the ground work for the rest of the geometries analyzed. For
25 example, the boundary conditions, and convergence criterion from the simplified geometries will be the same ones used in the more complex geometries. Eventually, the more complex geometries will establish the proper grid spacing, boundary conditions, and under-relaxation factors.
Flat plate flows have been the topic of many studies and this made it simple to validate the data for the geometry of the 2-dimensional axis-symmetric cylinder study, which can be seen in figure 7. A relatively coarse mesh with a bias about the y-axis was the first grid spacing modeled. This mesh is shown in figure 8 and contains approximately 6,000 nodes. A node is a cross section of data that will be evaluated. A node can be compared to a pixel on a photo; the more pixels the better quality of the photo. The number of nodes will allow for a more detailed understanding of how the flow behaves. The element size is the distance in between nodes and was determined by estimating the size of the boundary using 1/7th Power theory.
( )( )( ) [Equation 21]
The 2-dimensional axis-symmetric cylinder study was modeled using the k-ε turbulence model. Second Order spatial discretization methods were used in solving the turbulence and flow equations. The inlet boundary used was the velocity-inlet option and the outlet boundary used was the outflow option. Where the fluid meets the solid is what is known as the wall boundary and the no-slip option was used. The boundary opposite of the wall at the top of the flow was designated as symmetry, which assumes zero-shear.
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Once the boundary conditions are established, the fluid dynamic and turbulence equations are solved within FLUENT. The solver will continue to iterate towards a solution until the desired convergence criterion are met. The accuracy of the results will depend on how small the convergence criteria are for each equation. The convergence criterion for the first case was set to 10-6 for all equations. The data was analyzed by comparing the results to theoretical boundary layer plots. The results for this case, shown in figure 9, were displayed as a velocity contour with the theoretical boundary layer superimposed along with the δ99 boundary layer. The δ99 boundary layer is the area within the flow where,
( ) [Equation 22]
It can be seen in figure 9, that the theoretical data and the numerical data obtained from the model are very close. The purpose of this study is to determine the ideal grid size and type, and therefore, this process was then repeated four more times using different grid method types and sizes. The geometry remains the same for all grid cases along with the use of the same turbulence model.
As the geometry becomes more complex the ability for the solver to iterate towards the convergence criteria will require the use of either changing the model or the use of model options. Most of the turbulence models are empirically based and have embedded coefficients known as under-relaxation factors which are also used to ease the convergence if necessary. These factors should be used cautiously and can dramatically affect the accuracy if used incorrectly.
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From the 2-dimensional cylinder axis-symmetric study the 2-dimensional axis- symmetric cylinder with hemisphere end caps study began. This analysis mirrors the analysis used in the cylinder study. Except, that the convergence was harder to achieve
The grid study for the 2-dimensional axis-symmetric cylinder with end caps analyzed six different grid types and sizes. The conditions established in the flat plate study were mirrored for this study with the exception of the outlet boundary which was changed from outflow to pressure outlet for the specified case. This change was necessary because of the behavior of the convergence.
Both studies showed the importance of the convergence criteria and grid spacing.
The most accurate results were found after the grid independence study for the cylinder study. The cylinder geometry, which is the simplest of the geometries, was basically a boundary flow problem. Results for the cylinder with end caps study were more complex, and not only was grid spacing important but achieving the convergence criteria was crucial. A grid with a smaller amount of nodes achieved similar results in the data verification stages. This is because the data from the smaller node size grid was able to achieve more convergence then the grid with more nodes.
4.3.2 THEE-DIMENSIONAL SIMPLIFIED GEOMETRY STUDY
Building from the 2-dimensional axis-symmetric studies, the 3-dimensional studies continues the process leading up to the modeling of the actual underwater turbine.
We begin with the geometry of the 3-dimensional cylinder, as shown in figure 10.
Different 3-dimensional grid methods were analyzed in this study. The velocity profile was taken along the axis of the cylinder shaft. Boundary layer theory was used to verify 28 the data. Just like before, the grid-spacing models that produced the most accurate results came from the models that met convergence independence. The models with the finest grid spacing did not necessarily produce the most accurate results.
The next step in the process was the study of the 3-dimensional cylinder with hemisphere end caps. The greatest challenge was achieving convergence. Different grid methods and sizes were also analyzed, but the determining factor for this study was the convergence criterion. This study required the most manipulation of the under relaxation factors and conditions of the flow. The methods used for this study created the basis for the hemisphere with end caps and the mast study.
The cylinder with hemisphere end caps and mast geometry proved to be the most interesting of the simplified geometries. The geometry is shown in figure 11. The data was verified using Small Deficit Wake theories based on the work of Wygnanski,
Champagne, and Marasli.
Similar to the previous studies, the initial grid spacing was coarse with default convergence criteria. The grid spacing was reduced to increase the nodes and with each grid reduction there was a convergence criteria study performed. The data was verified using theory from the work of Wygnankski, Champagne, and Marasli.
The results of this study are shown in figure 12, which show the mean velocity profiles of all the different grid sizes. Where, the theoretical mean velocity profile was calculated using the following equation,
( ) [Equation 23]
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Where η is the ratio of the y position and the length scale,
[Equation 24]
The theoretical length scale was calculated using the theory from Wygnanski,
Champagne, and Marasli. Figure 13 shows that there is a difference from the theoretical data and the numerical data. Table 1 show the difference in the different mesh cases shown in the figure. The ideal mesh comes from the grid case with the smallest convergence criteria, but not the finest grid meshing. This study shows the importance in the convergence criteria. So, being able to achieve convergence criteria is just as important as having a fine enough grid.
4.4 VALIDATION PROCESS
As already stated the lack of experimental data proves to be most undesirable.
This section will discuss the process used to create the most accurate results without the use of experimental data. Simplified geometries have been analyzed, and because of the abundance of proven data available the results were verified. The characteristics of the modeling process were pulled from the simplified geometry cases, and common factors help create the process in which the turbine was modeled. The first observation was that convergence independence needed to be met, and if convergence was not achieved then the results were less accurate. It was proven that it is better to have coarser grid spacing and achieve complete convergence independence, then to have finer grid spacing, without the proper convergence. As the geometry became more complex, proper convergence was harder to achieve. This leads to the second observation, that finer grid spacing did
30 not necessarily mean more accurate results. This is why the process below will start with a coarse grid, and perform convergence independent studies simultaneously as the grid independent studies are being performed. The process is a balance of find the best grid spacing, and achieving convergence independence.
This process was established to ensure that the best results can be achieved without the use of experimental data. The geometry is either created or imported into the
ANSYS software. Using Boolean subtraction method the control volume for the fluid flow was created. The initial grid was created using a relatively coarse spacing scheme. A convergence independent study was performed, making sure that the ideal convergence was achieved. ANSYS uses a default value of 10-3, and this number has already proven to be not sufficient enough for accurate results. A grid independent study was performed with a convergence independence study being performed on each grid. The velocity profile at selected locations were taken and used to verify the data.
Once the ideal grid was found, second order analysis was performed. This was performed after the grid study, because second order analysis takes a significant amount of time to run and combined with time constraints. This is the ideal process, and the process used to obtain the data used for acoustic and load analysis.
4.5 ACTUAL TURBINE
The simplified geometries helped determine grid sizes, under-relaxation factors, and provided a process to validate the data needed for the actual turbine modeling. A convergence independence study was initially completed on the actual turbine geometry.
Once convergence independence was achieved, grid independence was next in being 31 completed. The second-order analysis was performed and the results analyzed. The results of this study lead to the optimal data set and converted to MATLAB. Finally the data was compared to Guerra’s code for comparison purposes.
4.5.1 DESIGN CONSIDERATIONS
The actual turbine is shown in figure 14. This geometry is very complicated, and shows every nut and bolt on the turbine. For modeling purposes the geometry was slightly simplified, which is shown in figure 15. The geometry file was a surface body
SolidWorks file. ANSYS geometry and meshing programs require solid body geometry to be imported for three-dimensional modeling. All the surfaces needed to be repaired and translated to a solid body. Repairing the geometry was a tedious process, and eliminating a lot of the extremely small details made this process more endurable. The geometry was extremely detailed, and all of the bolts and screws were removed, because they were going to be de-featured anyway with the grid creation. The control volume was created as a cylinder around the turbine. The boundary conditions used for the numerical analysis are shown in table 2.
4.5.2. CFD METHOD
As outlined previously, the process in which the turbine was modeled began with the importing of the geometry into the ANSYS program. Workbench was used for this process. For the initial grid spacing, a convergence independence study was performed.
The initial grid analyzed, labeled mesh #1, was relatively coarse spacing with just over 71,000 nodes, shown in figure 16. The specifications of the mesh are shown in table
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3. The velocity profiles were analyzed at the location just before where the blades would be, which can be seen in figure 17. Six different lines were used for analyzing the velocity profiles of the local velocity, and their locations are shown in figure 18. These lines were used for all the convergence studies, and were normalized against the tip velocity and total radius of the blade.
Using this coarse mesh allowed for quick convergence, and to work out any problems that were encountered with using the actual turbine geometry. Figure 19 shows the velocity profiles along the 3 lines. Figure 19 shows that convergence independence was achieved. Just to make sure that these profiles were best represented; velocity profiles with constant radius were taken at different locations. The results of these circles are shown in figure 20, and were normalized against the tip velocity, and the period. Just like with the lines, the circles also show that convergence was achieved.
The next grid size, labeled mesh #2, was determined by using the default fine meshing option within FLUENT. This resulted in a grid with approximately 164,000 nodes as shown in figure 21. The specifications of this mesh are displayed in table 4. The convergence of this grid spacing was smoother than the coarse grid spacing. This is represented in figure 22. At the convergence criteria of 10-5, convergence independence was already reached. Figure 22 shows similar results where convergence independence was obtained at a larger convergence criterion. The profiles about constant radius, for the circles, are displayed in figure 23. At this point in time the grid independence study began, but will be discussed in detail following the convergence independence studies for each mesh.
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The velocity profile curves shown in the previous mesh examples were ridged in the area of the 20-50% of the blade radius area, and for this reason the next grid spacing the growth rate was adjusted. The specifications of the third mesh, labeled mesh #3, are displayed in table 5, and the grid spacing is shown in figure 24. The growth rate represents the increase in element edge length with each succeeding layer of elements [8].
Using the growth rate of 1.15 results in a 15% increase in element edge length with each succeeding layer of elements; was used instead of the default of 20%. This adjustment was an attempt to create a smoother curve for the velocity profiles. The results are shown in figure 25 and figure 26 for the line and circle velocity profiles respectively.
It is shown that the curve is smoother and that increasing the growth rate reduced the rigidness of the curve. However, the increase of the growth rate increased the number of nodes and generated a finer grid map. This increase of nodes leads to a decrease in the convergence. This decrease in convergence will be discussed later in the grid independence study analysis.
The decrease in the convergence criterion lead to the creation of the next grid and contained approximately 180,000 nodes. This grid is labeled mesh #4, and is shown in figure 27. The spacing for this grid was chosen as a middle ground from in between the second and third grid spacing, in hopes that convergence independence and grid optimization could be achieved. The characteristics of this grid are shown in table 6.
The convergence independence study for this grid began with the lines, and is displayed in figure 28. The profiles for the circles are shown in figure 29. It can be seen that the lines almost reach complete convergence independence.
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At this point, the grid independence study will be discussed. The plots for this study represent the same data values for the converged plots for each grid, and the line plots are seen in figure 30. The plots for the circle profiles are displayed in figure 31.
This figure shows the importance of the convergence. The third grid, labeled mesh 3, did not reach complete convergence independence and the line for this grid does not correlate with the other lines. The normalized velocity profiles are somewhat consistent with each other, and it was determined that the fourth grid spacing was the most ideal grid spacing.
The velocity profile for the fourth grid will be the data used for the unsteady lift, and acoustic analysis.
4.5.3 DATA INTEGRATION
Incorporating the data for the unsteady loading and acoustic analysis is an important step and the following section outlines how the data was integrated for the acoustical analysis. Guerra established a process that takes a velocity profile and translates that information to unsteady loading, and ultimately creates the acoustic information. Guerra used a theoretical upwash velocity profile in his analysis as outlined from the work of Wygnanski, Champagne, and Marasli. The velocity profiles taken from the CFD analysis were used as the upwash velocities for this thesis.
The flow velocity is a function of the radius, γ, and the angle, θ. Where the velocity can be defined as,
( ) ( ) [Equation 25]
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Guerra calculated the perturbation velocity, Ut, using small wake deficit theory, and from that he calculated the upwash velocity, as seen in equation 17. This thesis used the numerical data taken from FLUENT as the upwash velocity.
[Equation 26]
The Fourier series will be represented as,
( ) ∑ ( ) [Equation 27]
and the Fourier coefficients as,
∫ ( ) ( ) [Equation 28]
The Fourier coefficients were calculated by taking the inverse Fast Fourier
Transform function, ifft(), from the velocity profile taken at the blades normal to the direction of the flow. Inverse fast Fourier transform (ifft) returns the inverse discrete
Fourier transform (DFT) or a vector or matrix with a fast Fourier transform (FFT) algorithm. If a matrix is being evaluated, ifft returns the inverse DFT of each column of the matrix. The Matlab function ifft() will be used to the evaluate Wn.
( ( )) [Equation 29]
The angular speed of the blades can be written as,
[Equation 30]
Where,
T – The period in seconds, T=M τ
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[Equation 31]
M- The number of Fourier coefficients
τ- Time step
4.5.4 COMPARISON TO GUERRA’S CODE
The validation process outlines a process that can be used to generate data in the absence of other data for verification purposes. Chapter 3 outlines the differences between the work of Guerra and the work of this thesis. There was a significant different in the upwash velocities, and this difference will significantly affect the unsteady loading, and acoustic results.
The theoretical upwash velocities were created from the work of Wygnanski,
Champagne, and Marasli. Their theory concluded that using equation 32 would generate the correct wake deficit behind a structure.
( ) [Equation 32]
Where, u0 is the velocity scale and η is defined, in equation 33, as the ratio of y over the length scale.
[Equation 33]
The comparison between the theoretical and numerical velocity profiles are shown in figure 6. Guerra’s work was for an ideal turbine, with many assumptions used to complete his work. Although his data is available for comparison, it cannot be used as a tool for data verification.
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CHAPTER 5: ACOUSTIC NOISE ESTIMATES AND UNSTEADY LOADING
This chapter will bring together all of the components of the turbine flow and the calculation of the unsteady lift, acoustic pressure, and sound levels. The Ffowcs,
Williams, and Hawking equation relates the acoustic pressure from the perturbations of the flow around the turbine to the lift fluctuations experienced on the blades. The data from the upwash velocity profile at the location of the blades is used to calculate the
Fourier coefficients. The lift per unit span is calculated using Sear’s unsteady lift distribution of a rigid airfoil passing through a sinusoidal upwash gust and the upwash
Fourier coefficients.
5.1 UNSTEADY LOADING RESULTS
The Fourier coefficients of the upwash velocity are calculated using the inverse fast Fourier transform function within MATLAB as outlined in section 4.5.3 of this thesis. These coefficients along with Sear’s function, equation 5, According to Sear’s,
( ) ( ) ( ) [Equation 34]
Combining equation 35 with the total lift results in equation 36.
∑ (∑ ( ) ( ) ( ( )) ( )) [Equation 35]
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Figure 32 shows the plot of the total unsteady lift coefficient against the omission time, τ, by the period, T, for both the numerical data taken from the CFD modeling and the theoretical data created by Guerra for the simplified turbine design.
The theoretical unsteady loading is significantly higher than the numerical. This is expected because Guerra assumed a simplified geometry design of the structure of the turbine. His results reflect the velocity profile of a solid structure, when in fact the structure contains beams. The numerical results reflect the actual geometry of the structure. These results prove most interesting, and will reflect in the acoustic analysis.
The lower values for the lift perturbation will create lower fluctuations in the pressure, and ultimately lower the sound levels.
5.2 ACOUSTIC RESULTS
The Ffowcs Williams and Hawkings equation gives a method to calculate the acoustic sound levels. The equation for the acoustic pressure time history from the unsteady lift is given in equation 11. This equation has already been evaluated at the emission time with respect to the observer’s position. The observer’s position is defined by equations 36 and 37.
[Equation 36]
( ( )) ( ( )) ( ) [Equation 37]
The acoustic pressure time history, p’(t) takes all the perturbation pressures arriving at the point of observation at a time regardless of location of the point source where the perturbation originated. The time history of p’(t) is shown in figure 34.
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As expected the numerical acoustic pressure perturbation are significantly lower than the theoretical values. As explained earlier, the theoretical values were taken from a geometry that assumed the structure of the turbine to be solid, when the structure is not.
This translates to lower velocity fluctuation downstream of the structure. The lower fluctuations create smaller acoustic pressure fluctuations.
When it comes to sound, it is usually measure in decibels which relates the sound intensity as a function of power ratio that gives the difference between 2 sounds. In order to calculate the decibels, the power levels need to be calculated. The power levels are found by using Parseval’s theorem, equation 16. Where pn is calculated by using the perturbation pressure,
∫ ( ) ( ) [Equation 38]
When converting to decibels it is necessary to understand the relationship of the source level (SL) with the intensity level (SE). The intensity level due to an excess perturbation or radiated pressure at any range r from a compact source in a homogenous lossless medium is obtained from the source level [13].The intensity level is the sound pressure level of the radiated perturbation pressure, and is defined in equation 17.Using algebraic manipulation the sound level equations is created, and shown in equation 18.
Figure 35 shows the noise spectrum levels for the actual turbine geometry data, and compares it to the theoretical results established by the Guerra for the Idealized turbine.
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The sound levels are still lower than the theoretical values. However, these results are most useful when compared to the ocean noise levels. The ocean is a noisy place, and the noise levels from the turbine need to be louder than the noise levels in the ocean. An example of typical ocean shipping noise levels is shown in figure 36 [13]. Even at the highest end of the spectrum of the ocean noise, the low frequency noise would still be audible, but at high frequencies the sound levels were well below the ambient levels. The sound levels at very low frequencies are audible under these conditions, but it would be interesting to see how the results would vary if the conditions or the characteristics of the turbine flow would change.
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CHAPTER 6: TURBINE MODIFICATIONS
Changing different characteristics of the turbine flow will better simulate real world conditions. Varying the angle of attack will not only better simulate these conditions but will also give an idea on the sound levels experienced under these conditions. Increasing the number of blades and reducing the chord length by a factor of two was also investigated.
6.1 VARYING THE ANGLE OF ATTACK
Varying the angle of attack will give insight on how the unsteady lift and acoustics experienced from the turbine would are affected. The angle of attack varies from 5 degrees to 30 degrees. The direction of the flow is shown in figure 37. These angles were chosen because of the estimation for the stall angle. The stall angle should be the angle of attack that would create the most turbulence from the wake of the structure.
The calculation of this angle is represented in figure 38. Other angle directions were modeled but the difference in the flow was minimal.
The unsteady lift was affected as the angle of attack varied. Figure 39 shows how the unsteady lift varies as the angle of attack changed. With each increase of angle of attack the lift increased. Not only did the lift increase but the difference between the maximum and minimum lift forces increased.
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Since, the acoustic pressure is a function of the lift forces there was also an increase in the acoustic pressure. The effects of the structure are most noticeable as the angle increases. This can be seen in figure 40. While these results are important the significance to the acoustics are best shown in sound level comparison.
The spectral level plot, shown in figure 41, compares the sound levels for each angle of attack. The sound levels did not increase significantly, but the frequencies in which audible levels occur increased. The audible sound levels still only occur in low frequencies, but as the angle of attack increased so did the frequencies. In a real world setting if the flow were to come from the direction of the angle of attack study, the sounds created would increase with the angle.
6.2 CHORD REDUCTION
In the work of Guerra, a part of his analysis was design optimization. He analyzed different characteristics of the turbine to determine the ideal parameters of the turbine design. One of the characteristics of interest was the chord length. The chord length was reduced by a factor of 2. The unsteady loading, acoustic pressure time history, and sound levels were all compared.
The unsteady loading comparison is shown in figure 42. As expected when the chord length was reduced the unsteady lifting forces were also reduced. The sound pulse also showed a decrease in the acoustic pressure, as shown in figure 43. The sound levels reflect a slight decrease in decibels with corresponding frequencies. The spectral levels are displayed in figure 44.
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Reducing the chord significantly reduced the lifting forces, and reduced the acoustic pressure perturbations. The sound levels decreased, but only by a small factor.
Taking half the chord length created a reduction in the sound levels and therefore reducing the chord length would cause less noise to be created.
6.3 NUMBER OF BLADES
All of the data shown in chapter 5 and the previous sections are for just one blade.
In this section the difference between a turbine with one, three, and five blades will be discussed. First the unsteady lift and sound pulse with 3 blades will be discussed. Then, the unsteady lift and sound pulse with 5 blades will be discussed.
The unsteady lift for 3 blades is shown in figure 45. This figure gives visualization of the effects that 3 blades have on the unsteady lift. The sound pulse for 3 blades is shown in figure 46. The sound pulse for 3 blades is the same as the sound pulse for one blade, but tripled about the time scale. Figure 47 displays the unsteady lift for 5 blades. Just like with the unsteady lift for three blades the lift for 5 blades is the same and just repeated 5 times about the time scale. Figure 48 is the sound pulse for 5 blades.
Going from one blade to 3 blades did not change the sound levels, but just changes the unsteady lifting and acoustic pressure over the normalized time scale. This is displayed in figure 49, which is a comparison of the sound levels for 1 blade against the levels of 3 blades. The increase in the number of blades is shown in figure 50, as a comparison of the unsteady loading on 1 blade, 3 blades, and 5 blades. Due to the nature of adding pulses together, the plots move down the lift axis, but still remain zero-mean.
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CHAPTER 7: CONCLUSIONS
In-stream hydrokinetic energy is a great potential resource for harnessing clean and green energy. However, it is necessary to have full understanding of the behavior of the turbine and how it can potentially affect marine life. Environmental impact studies are performed, and analyzed to rule out any potential irreversible negative effects. The ocean is a very noisy place, and there are certain levels of acceptable noise levels. If the noise generated by the turbine is less than the ambient noise, then the turbine does not pose as a potential threat to surrounding marine life.
It is expected that the turbine will make audible noise, but only at low frequencies. There are only a few species that can hear sound at the levels of low frequency that is expected. The main species of interest are cetaceans (Whales) and pinnipeds (Seals). It is site specific as to what types of marine animals and mammals that can potentially be affected by the noise generated by the turbine.
The noise generated by turbines can be broken down into 2 categories; hydrodynamic and mechanical. As already discussed the hydrodynamic noise is discussed in great detail in this thesis. Hydrodynamic noise can further be broken down into 3 categories of noise sources; displacement noise, fluctuation noise, and cavitation.
Cavitation noise was ruled out for turbines at a depth of 10m, and the fluctuation noise was considered the noise of interest. Ffowcs Williams, and Hawkings derived a
45 differential equation that addressed these types of noise source terms. The dipole term was the only applicable term for this project.
Guerra established a method using this dipole to estimate the noise levels from the turbine. He used a number of assumptions and simplifications in his work to derive his results. He established that audible noise levels would only occur at low frequencies, and that higher frequency noise levels were well below the ambient noise of the ocean. Since,
Guerra made some many assumptions and simplifications to the turbine geometry, his results did not fully reflect the actual acoustic impacts to be expected. In this thesis CFD analysis based on the actual geometry of the turbine was used, and the actual velocity perturbations were calculated; versus Guerra’s assumed theoretical velocity profiles created from the work of Wygnanski, Champagne, and Marasli.
The computational fluid dynamic analysis was performed in the ANSYS software. The solver used was FLUENT, and the turbulent model used was the RANS based k-epsilon model. The lack of velocity profile data proved to be a challenge, but a process was established to produce the most accurate results possible without the application of other methods of data to verify. Convergence studies, and grid independence studies were performed on the actual turbine geometry to come up with the optimal grid size. Once the optimal grid size was found, second order analysis was performed. These results were then used for the unsteady loading, and acoustic analysis.
The acoustic analysis began with taking the method created by Guerra and incorporating the results from the CFD analysis. The Fourier coefficients of the upwash velocity needed to be calculated. The upwash velocity was taken directly from FLUENT
46 as an area of constant radius equal to the radius of the turbine blades at the location where the blades would be. These results were formatted, and analyzed. It should be noted that there was a significant difference in between the results calculated by Guerra and the results obtained from the CFD analysis.
First, the unsteady loading was analyzed. The unsteady lift forces experienced were much less than the forces estimated by Guerra. This was a result from his assumption that the structure of the turbine was solid. Since the structure is not solid, the lifting forces were not as large. The acoustic pressure perturbations, or the sound pulse, is a function of the unsteady lift, and therefore was also significantly less than estimated by Guerra. Ultimately, the sound levels were less than estimated by Guerra, but still audible above the ambient noise of the ocean at very low frequencies.
The angle of attack of the flow into the turbine was varied to see how changing that angle would affect the acoustic results. Changing the angle caused the structure of the turbine to create more turbulence in the flow and increased the unsteady loading, and the radiated sound. While still below Guerra’s first estimate of noise levels, the results from changing the angle of attack increased the levels at the audible frequencies.
Other turbine modifications were analyzed. Reducing the chord length resulted in a significant decrease in the unsteady loading, and acoustic pressure perturbation. The noise levels also decreased. Increasing the number of blades did not decrease forces, and therefore would not lower the sound levels.
Another potential alternative to reducing the sound levels may be found in the use of skewed turbine blades. Skewed turbine blades are a viable alternative because the 47 noise and vibrations are lower than conventional propellers. The skewed propeller sweeps back the leading and trailing edges of each blade [16], and an example of this is shown in figure 51 of a highly skewed propeller.
Skewed propellers have been the interest of studies for applications in ship and submarine propulsion. Nearly all marine propellers operate in the wake of a hull or structure, and when the blade enters the wake the angle of attack drastically changes, which causes a rapid change of pressure. This causes the unsteady loading that translates to the generation of sound, as already discussed.
The sweeping back of each blade from a skewed propeller results in a uniform unsteady loading distribution from the wake deficit of the structure or hull. Even though the sound generated from the hydrodynamics of the OCCT turbine are low, the advantages of using skewed turbine blades go beyond reducing the hydrodynamic noise.
However, the structural integrity of the skewed propeller blades can be a concern. Also, the decrease in efficiency should be considered for the skewed blade design. The use of this design reduces the vibration and may reduce the mechanical noise from the vibrations on the shaft [16]. The reduction of mechanical noise should be of concern, because it will be the dominant source of noise coming from the turbine.
As mentioned before, turbine noise is caused by two different sources. This project addressed the hydrodynamic noise, but the mechanical noise has yet to be considered. While commercial scale turbines are usually insulated to prevent mechanical noise radiation, smaller turbines typically lack the sufficient insulation. The mechanical noise is expected to be greater than the hydrodynamic noise.
48
This work proved that the results estimated by Guerra were well above the results of the actual geometry velocity flow. His use of assumptions and simplifications created results that over-estimated the potential acoustic impacts. Computational fluid dynamic analysis allowed for modeling of the velocity flow past the actual turbine geometry.
However, even though the results were less than the results estimated by Guerra, the sound levels were still audible. In order to determine the effects of this audible noise on the marine would require additional studies on the marine life specific to the site location.
Marine life impacts are site specific and specific to the species and the hearing ranges for those species. The frequencies of the sound levels are at the very low end of the hearing ranges of pinnipeds and cetaceans. Additionally the audible sound levels are also at the low end of the chart, and other factors such as harsh sea states could drown out the noise.
It is expected that impacts associated with the hydroodynamic noise of the turbine will be minimal if any at all.
49
APPENDIX
Table 1: Table of Constants and Variables
B Number of Subsections
C Chord of the Foil
c0 Speed of Sound in Sea Water
(2) H0 (σ) Cylindrical Hankel Function of the Second Kind
(2) H1 (σ) Cylindrical Hankel Function of the Second Kind
L Lift per unit span
Mr The Mach number in the radiation direction
p'(x,t) Ffowcs Williams and Hawking's Wave Equation
P0 The characteristic pressure level
Pij The surface stress tensor
Pv The vapor pressure
r The distance between acoustic source and observer
S The surface of the blade
S(σ) Standard 2-Dimensional Sear's Function
t Observer's Time
u0 Velocity Scale
U∞ Free Stream Velocity
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Ue Incoming Gust Velocity
Ue Gust Velocity
Ut Perturbation Velocity
Utip The tip velocity of the blade roughly calculated using tip speed ratio TPR=4.62 [4] x = (x1,x2,x3) The position of the observer y = (y1,y2,y3) The position of the noise source
β(σ) Phase of the Sear's function
γ The radius of the point source element
Turbine Radius
δL/δτ Time Derivative of Lift per unit span
γ Span Step
η Ratio of y to the length scale
λ Wavelength of Sinusoidal Gust
σ Non-dimensional frequency used in Sear's function
τ Emission time
φ The time dependent azimuthal location
Angular Speed of the Blades
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Figure 1: FAU's Ocean Current Turbine Testbed Diagram
52
Figure 2: Guerra's Simplified Design
53
Figure 3: Coordinate System
54
Figure 4: Noise levels felt at a point of observation positioned at spherical coordinates (100 m, 45º, 45º)
55
Figure 5: Actual Turbine Geometry vs. Simplified Geometry
56
Figure 6: Difference between Theoretical and Numerical Velocity Profiles at the location of the blades
57
Figure 7: 2-Dimensional Axis-Symmetric Cylinder Study; Geometry
58
Figure 8: 2-Dimensional Axis-Symmetric Cylinder Study; Grid #1, 6,790 nodes
59
Figure 9: 2-Dimensional Axis-Symmetric Cylinder Study; Case #1 Velocity Contour with Boundary Layer Plots
60
Figure 10: 3-Dimensional Cylinder Study; Geometry Iso-View
61
Figure 11: Geometry of Cylinder with Hemisphere End Caps and Mast
62
Figure 12: Mean Velocity Profile for Cylinder with End Caps and Mast at Location of Blades
63
Figure 13: Length Scale at Location of Blades
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Table 2: List of Mesh number with nodes and convergence criteria
Mesh 1 52,551 10.-6
Mesh 2 102,000 10.-4
Mesh 3 102,000 10.-5
Mesh 4 102,000 5*10.-6
Mesh 5 250,000 5*10.-5
Mesh 6 419,000 5*10.-5
Mesh 7 1,270,000 10.-4
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Figure 14: Original Turbine Geometry
66
Figure 15: Geometry of the Turbine Modeled
67
Table 3: Boundary Conditions for the Turbine Model
Velocity- Inlet Inlet
Outlet Outflow
Outer Boundary Symmetry
Turbine Structure Wall- No-Slip
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Figure 16: Turbine Coarse Grid Spacing, Mesh #1
69
Table 4: Mesh 1 Grid Information
Relevance Center Coarse
Min Size 1.438E-02 m
Max Face Size 1.044E+00 m
Max Size 2.088E+00 m
Growth Rate 1.20
Nodes 71,551
Elements 404,409
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Figure 17: Velocity Contour at Location of Blades
71
Figure 18: Velocity Contour with Specified Lines of Interest
72
Figure 19: Convergence Independence, Mesh #1, Lines
73
Figure 20: Convergence Independence, Mesh #1, Circles
74
Figure 21: Turbine Mesh #2 Grid Spacing
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Table 5: Mesh 2 Grid Information
Relevance Center Fine
Min Size 3.572E-03 m
Max Face Size 3.057E-01 m
Max Size 6.114E-01 m
Growth Rate 1.20
Nodes 164,148
Elements 925,024
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Figure 22: Convergence Independence, Mesh #2, Lines
77
Figure 23: Convergence Independence, Mesh #2, Circles Table 6: Mesh 3 Grid Information
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Relevance Center Fine
Min Size 3.057E-03 m
Max Face Size 3.057E-01 m
Max Size 6.114E-01 m
Growth Rate 1.15
Nodes 229,868
Elements 1,311,840
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Figure 24: Turbine Mesh #3 Grid Spacing
80
Figure 25: Convergence Study, Mesh 3, Lines
81
Figure 26: Convergence Study, Mesh 3, Circles
82
Figure 27: Turbine Mesh #4 Grid Spacing
83
Table 7: Mesh 4 Grid Information
Relevance Center Fine
Min Size 3.057E-03 m
Max Face Size 3.057E-01 m
Max Size 6.114E-01 m
Growth Rate 1.20
Nodes 189,668
Elements 1,060,388
Refinement level 1
84
Figure 28: Convergence Study, Mesh 4, Lines
85
Figure 29: Convergence Study, Mesh 4, Lines
86
Figure 30: Grid Independence Study, Lines
87
Figure 31: Grid Independence Study, Circles
88
Figure 32: Unsteady Lift for One Blade, Theoretical vs. Numerical
89
Figure 33: Orientation of the Observer with respect to the Turbine
90
Figure 34: Unsteady Acoustic Pressure, One Blade, Theoretical vs. Numerical
91
Figure 35: Sound Spectral Levels for Numerical and Theoretical Results
92
Figure 36: Typical Ocean Noise Levels
93
Figure 37: Flow Direction for Varying Angle of Attack
94
Figure 38: Stall Angle, Angle of Attack Analysis
95
Figure 39: Unsteady Lift, Varying Angle of Attack
96
Figure 40: Acoustic Presssure, Varying Angle of Attack
97
Figure 41: Sound Spectral Levels, varied angle of attack
98
Figure 42: Unsteady Lift, Chord Reduction
99
Figure 43: Sound Pulse, Chord Reduction
100
Figure 44: Spectral Levels, Chord Reduction
101
Figure 45: Unsteady Lift, 3 Blades
102
Figure 46: Sound Pulse, 3 Blades
103
Figure 47: Unsteady Lift, 5 Blades
104
Figure 48: Sound Pulse, 5 Blades
105
Figure 49: Spectral Levels for 1 Blade and 3 Blades
106
Figure 50: Unsteady Loading Comparison with number of blades
107
Figure 51: Skewed Propeller Design [16]
108
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