Fluid-Structure Interaction and Rotor-Stator Noise

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Literature Review

The acoustic noise caused by fluid interactions with solid bodies is a well-researched field. Theoretical and experimental research has led to a solid understanding of the basic mechanisms by which fluids can cause structures to radiate noise. The turbomachinery industry has led the drive to apply these results to reducing the noise generated by a rotor wake. Thus, the flow control techniques of trailing- and leading-edge blowing have been introduced. The trailing-edge blowing technique has been extensively tested in air, but has not been widely implemented in water vehicles. The leading-edge blowing technique is the newest method and has not yet been widely tested. The following sections give a summary of the previous research, both experimental and theoretical, performed in all three of these areas.
 

Fluid-Structure Interaction and Rotor-Stator Noise

One of the principle methods of noise generation in a fluid machine is the sound produced by the unsteady forced response of rotor blades and stator vanes to the surrounding fluctuating flowfield. These fluctuating forces on the rotor blades and stator vanes produce an acoustic pressure field described by Equation 1.1, which resembles that of a dipole. Two dominant causes of these dipole sources are the rotor wake impinging on the downstream stators and to a lesser effect the potential field of the stators extending upstream to interfere with the rotor.2 Woodward and Balombin confirmed the effects of the rotor-stator interaction on the radiated noise by examining the change in sound pressure level with and without downstream struts to support the motor. They found that adding struts within downstream of the rotor showed an increase of 10 dB at the BPF tone. The amount of noise generated depended directly on the distance between the rotor and the stators. The smaller the distance, the more tonal noise occurred. However, the addition of struts did not change the broadband noise or the higher harmonics of the BPF.3
The forcing on downstream bodies, in this case an exit guide vane (EGV), is caused by the non-uniform flowfield from the rotor. The momentum deficit that is inherent in a viscous wake causes an upwash velocity on the EGV. As the wake passes by the stationary EGV the blade is subjected to a fluctuating upwash velocity, see Figure 2.1, which translates into a fluctuating reaction force exerted by the EGV onto surrounding fluid. The fluctuating force is the source for acoustic pressure radiation described by Equation 1.1. The implication of this relationship is that the impact on acoustic radiation can be approximated experimentally by the force imparted on a structure. Goldstein derived a method to compute the tonal component of this fluctuating interaction force from a known impinging wake flow field, thus enabling an analytical estimation of the forcing on a blade in some circumstances.4
The rotor wake is a result of the viscous effects of the fluid as it passes by the moving rotor blade.5 However, the blade-wake interaction can be approximated as an inviscid interaction in most turbomachines because the viscous effects do not significantly impact the behavior of the wake interaction with the downstream stator. This means that analytical approximations can use the simpler Euler equations to model the interactions as well as the more complicated Navier-Stokes equations.6 These analytical models are confirmed by experiments on the radiated noise from turbomachines. For most of such turbomachines, the rotor/stator stage is housed inside of a duct, which significantly impacts the radiated acoustic noise. The shape and size of the duct determines the frequencies that are able propagate through the duct and out to the far field. In addition, the interaction creates specific circumferential modes that are determined by the blade count of both the rotor and the stator. These circumferential modes that are created and allowed to propagate to the far field constitute the tonal noise that is measured experimentally.7 This tonal noise can be reduced by either acoustic treatments in the duct or reduction of the initial wake interaction.
The rotor-stator interaction problem has been well researched throughout the past years. In this time, several different techniques for reducing the effects of the interaction on performance and radiated acoustic noise have been researched. Since the rotor-stator interaction is one of the major sources of noise in high speed gas turbines and aircraft engines7, most of this research has been performed in air. However, in many cases techniques that show improvement in aerodynamic applications will also show benefits in hydrodynamic applications. One of these methods of noise reduction is known as active noise control (ANC), which operates by using additional noise sources to cancel out or reduce the propagation of the rotor-stator interaction tones to the far field. Sawyer et al. used acoustic sources mounted on the stator vanes to match the tones radiated from the wake interaction. This configuration showed a reduction in radiated sound pressure level of 10 dB over all of the motor operating speeds, with larger reductions present at certain operating point. Hall and Woodward used experimental results to estimate the reduction of perceived noise given the removal of the certain radiated tones via active noise control. This research found that the removal of the BPF tone by active noise control would yield a reduction in radiated noise level of 2-3 dB.8 This technique shows the most effectiveness in ducted propulsors where the duct allows the ANC to cancel the rotor-stator interaction noise before the sound leaves the duct to propagate into the far field. However, ANC does require extensive equipment, such as acoustic drivers and power amplifiers, that can add additional weight and complexity to the propulsor.
Another means of reducing the noise generated by the rotor-stator interaction is the application of active aerodynamic means to change the nature of the interaction between the wake and the solid body. One of these means is an actuated flap that serves as a control of the unsteady lift on the airfoil. Since the unsteady lift force exerted on the blade is the cause of most of the radiated tonal noise, reducing the magnitude of this unsteadiness should reduce the radiated noise. Simonich et al experimentally tested this technique using a single stator positioned downstream of a simple two bladed propeller. The flap on the trailing edge of the stator would actuate in response to the incoming wakes in order to achieve a lift force on the stator that remained constant. Using this technique, a 10 dB reduction was found at certain frequencies as well as a reduction of the peak to peak acoustic pressure by a factor of 2.9 Minter and Fleeter also showed positive results applying this technique to both a single stator vane and a three vane cascade. The upstream and downstream propagating modes showed maximum decreases of 9 and 6.5 dB, respectively.10 While this method is beneficial, the mechanisms required for actuating the flap adds weight and complexity to the turbomachine.
Passive means of reducing the rotor-stator interaction can provide some of the same benefits as the active means, yet without the need of additional mechanical components. Alteration of the geometry of the turbomachine is a type of passive treatment of the rotor-stator interaction. First, since the rotor wake diffuses as it propagates downstream, increasing the axial distance between the rotor and stator reduces the velocity deficit felt by the stator.11 Reducing the velocity deficit reduces the force imparted to the blade and thus the radiated noise. Kantola and Gliebe found that applying an increase in rotor stator spacing of 0.5 to 2.3 times the rotor chord length yields a reduction in the BPF tone sound level of 3 dB.12 However, increasing the axial distance requires a longer turbomachine; an increase in length also causes an increase in the total weight of the propulsor. In many cases, the propulsor size and weight are intended to be a small as possible in order to meet design constraints, thus increasing the size creates detrimental effects on the design. Other passive techniques designed to reduce turbomachine noise include reducing the rotor tip clearance and adding lean to the stators. Hughes et al. showed that the decreasing the rotor tip clearance in a 22 blade turbofan simulator increased the performance of the fan while decreasing the radiated broadband noise. However, the rotor-stator interaction tonal noise increased for the smaller tip clearances, possibly due to the interaction of the rotor tip with the boundary layer on the duct wall.13
The use of lean and sweep in the stator design reduces the noise radiated due to rotor wake- stator interaction by changing the radial variation of the incoming flow. This causes a phase shift of the unsteady upwash velocity which distributes the interaction energy across higher order acoustic modes. By energizing the higher order modes as opposed to the lower modes the energy created by the wake interaction can be channeled into the higher modes that are cut off by the duct. Elhadidi and Atassi used analytical techniques to confirm that the application of leaned stators will reduce the radiated noise. However, this passive technique was only found to be effective for lower mode numbers.11 Woodward et al. experimentally tested this theory on a row of 42 stators driven by an 18 blade rotor. Using a 30o sweep and lean angle, a reduction of both broadband and tonal was observed; the broadband noise indicated the most significant reduction of 4 dB as opposed to the 3 dB reduction of BPF tonal noise.14
Many different flow control techniques have been researched to determine their effectiveness in controlling rotor-stator interaction. The passive techniques involve no moving parts or alteration of the flow due to fluid injection. Some such passive techniques include using lean on the stators to change the strength of the BPF and its harmonics, increasing the axial spacing between the rotor and the stator, and changing the tip clearance to reduce either tonal or broadband radiated noise. These passive techniques do not have the mechanical complexity of the active techniques; however, the passive techniques outlined here have not shown the same magnitude of noise reduction as some of the active techniques. In addition to the active noise control and active lift control, there is a flow control technique that uses momentum injection to reduce the rotor-stator interaction. This technique is known as active flow control. There are two main types of active flow control; both types will be explained in the following sections. Application of these techniques in experiment has shown the potential for larger noise reduction than some passive techniques without the complexity of the mechanical actuators needed for active lift control.

Trailing Edge Blowing

The trailing edge blowing technique has been applied in many different fields. The primary application has been for acoustic noise reduction in turbomachines. The viscous wake formed by an airfoil moving through a fluid has a region of low momentum that propagates downstream from the rotor. As the wake progresses downstream it interacts with downstream objects, such as an exit guide vane, causing fluctuating pressures of the structure surface.15 These pressures radiate acoustic noise from the blade. Trailing edge blowing (TEB) means the application of flow control to the blade trailing edge to energize the low momentum section of the wake. Figure 2.2 shows an illustration of the effects of trailing edge blowing on the rotor wake that would impinge on downstream bodies. Often TEB involves momentum injection to fill in the deficits that are formed by the flow of fluid around a rotor blade. The momentum is added in the form of fluid ejected from the trailing edge of the airfoil.16

Abstract.
Acknowledgements
1 Introduction
1.1 Need of hydroacoustic noise reduction.
1.2 Main Causes of Underwater Propulsor Noise
1.3 Flow Control Methods for Reducing Hydrodynamic Noise
1.4 Thesis Outline
2 Literature Review.
2.1 Fluid-Structure Interaction and Rotor-Stator Noise
2.2 Trailing Edge Blowing
2.3 Leading Edge Blowing
3 Experimental Assembly.
3.1 Assembly and Facility Overview.
3.2 Rotor Assembly.
3.3 Exit Guide Vane Assembly.
3.4 Flow Control Configurations
4 EGV Flow Control Results
4.1 Assessing Force Measurement Variability
4.2 Leading Edge Blowing Configuration Results
4.3 Tangential Blowing Results.
4.4 Summary and Conclusions of EGV Flow Control Results
5 Self-Pumping Rotor Results.
5.1 Case 1 Flow Control Results
5.2 Case 2 and 3 Flow Control Results
5.3 Summary of Self-Pumping Rotor Tests.
6 Conclusions
6.1 Results and Conclusions
6.2 Suggested Future Work
Appendix 
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Experimental Investigation of Flow Control Techniques To Reduce Hydroacoustic Rotor-Stator Interaction Noise

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