The Pennsylvania State University The Graduate School College of Engineering NOISE GENERATION MECHANISMS IN SHORT DUCTED ROTORS

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering NOISE GENERATION MECHANISMS IN SHORT DUCTED ROTORS A Thesis in Aerospace Engineering by V Santhosh Padala c 2011 V Santhosh Padala Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2011

2 The thesis of V Santhosh Padala was reviewed and approved by the following: Kenneth S. Brentner Professor of Aerospace Engineering Thesis Advisor Philip J. Morris Boeing/A.D. Welliver Professor of Aerospace Engineering George A. Lesieutre Professor and Head, Aerospace Engineering Signatures are on file in the Graduate School.

3 Abstract Ducted rotors are commonly used in helicopters as a tail rotor and in unmanned air vehicles for improved performance and safety. Proposed fan-craft vehicle designs also have ducted rotors as the primary lifting device. In addition to the conventional fan blades, ducted rotors have additional structural components such as struts and vanes to support the duct. As compared to the open rotor, these structures cause obstructions in the flow field and hence generate additional noise. Due to the current aircraft noise regulations, it becomes necessary to study the effects of the additional structural components on the noise generated by the rotor blades. This information will also assist in an optimum design for a quieter ducted rotor. To calculate noise from these additional sources, an unsteady blade loading model is used as input for noise calculations. This model is computationally inexpensive as compared to the full unsteady Navier-Stokes calculations and captures the physics as obtained in the present work. The sources from unsteady loading have been superimposed with the thickness and loading noise sources, in PSU-WOPWOP to obtain the total noise. The current study shows that the noise generation due to the struts and vanes is very important at low Mach numbers and contributes significantly to the total rotor noise. Parametric studies that highlight the effect of the unsteady loading parameters on the noise levels are examined in this thesis. iii

4 Table of Contents List of Figures List of Tables List of Symbols Acknowledgments vii ix x xii Chapter 1 Introduction to Shrouded Rotors Early attempts Shrouded tail rotors Fancraft Motivation for research Chapter 2 Noise prediction strategies Sources of noise Methods of noise prediction Early prediction theories Ffowcs Williams-Hawkings Equation Formulation 1A Current noise prediction method Chapter 3 Computational methods for ducted fan aerodynamics Overview of methods used in modeling ducted fan aerodynamics iv

5 3.2 ANSYS CFX solution Computational setup Flow field description Input to PSU - WOPWOP Chapter 4 Unsteady loading noise computation Introduction to unsteady rotor aerodynamics Concepts of unsteady rotor blade aerodynamics Velocity deficit formulation Steady response Indicial Response Comparison of Küssner and Quasi-Steady responses Input to PSU - WOPWOP Chapter 5 Ducted fan noise results Sources of noise from steady CFD Effect of tip Clearance on noise Scattering of Unsteady loading noise Total Noise Unsteady loading noise Resolution study Spatial Resolution Temporal Parametric studies Varying wake width Varying velocity deficit Multiple struts Varying tip clearance Chapter 6 Conclusion Summary of the thesis Future work possibilities Appendix A Steady Noise Calculation Of Ducted Rotors 67 v

6 A.1 ANSYS FLUENT Settings For Moving Mesh A.1.1 FLUENT input file A.2 Running in Cocoa A.3 ANSYS FLUENT To PSU-WOPWOP Converter Program Manual. 74 A.3.1 Algorithm of the code A.3.2 Input and Output parameters of the code Appendix B PSU-WOPWOP namelist file 77 Appendix C Unsteady Loading Noise Calculation 95 C.1 Unsteady Blade Loading Code Structure C.2 Input Parameters and Output Options C.3 PSU-WOPWOP Namelist For Unsteady Loading Bibliography 100 vi

7 List of Figures 1.1 Different types of ducted rotors (a) The Hiller Platform VZ -1 (b) The Nord 500 (c) istar9 (d) HoverEye (Ref. [5]) Shrouded tail rotor helicopter (Ref. [2]) Comparison of Thrust vs pitch for conventional and shrouded tail rotor helicopters (The helicopter is SA 340/341 Gazelle (Ref. [7])) Comparison of Horsepower vs True airspeed for conventional and fenestron helicopters (This helicopter is SA 340/341 Gazelle (Ref. [7])) Experimental SPL vs Frequency (Ref. [8])) X-Hawk of the Urban Aeronautics(Ref. [9]) Figure showing relative axial positions of the rotor, stator and transmission shaft of the ducted tail rotor configuration (Ref. [8]). The transmission shaft is represented by the circle with chords. The rotor and the stator cross-section is shown in the figure SPL from different noise generating mechanisms at an observer location that is 45 0 to the rotor axis(ref. [8]) Noise prediction approach Noise sources region of duct. The portion of the duct in blue represents the source region Experimental and computational ducted fan (Ref. [21]) Different components of the flow domain (Ref. [21]) Velocity vectors in the flow domain (Ref. [21]) Pressure Contours on the blade and shroud (Ref. [21]) PSU-WOPWOP Results Figure showing various sources of tip and trailed vortices ( Ref. [23]) Basic parameters used in strut wake (modified from Ref. [25]) Change in C l vs azimuthal angle (blade starts from downward vertical postion) (Ref. [25]) vii

8 4.4 The blade wake configuration (blade starts from downward vertical postion) Comparison of steady and Küssner response for a quarter revolution of the blade Lift coefficient history (Ref. [25]) Loading history. PSU - WOPWOP input Acoustic Pressure History. PSU - WOPWOP output SPL(dB) vs frequency. PSU - WOPWOP output inch Ducted Fan Steady observer grid Contributions of various steady noise sources: OASPL comparison OASPL Comparison for different tip clearances The duct used for scattering analysis Comparison of Incident and Scattered SPL Observer grid for steady, unsteady and total noise comparison Overall sound pressure level of steady, unsteady and total noise Effect of radial step size on SPL Effect of azimuthal step size on Unsteady loading, Acoustic pressure and Sound Pressure Level. 1.5, 3 and 6 are the number of timepoints per degree of revolution Observer positions for parametric studies Velocity deficit azimuthal history for 20%c and 40%c wake widths SPL vs Frequency for varying wake width Effect of Velocity Deficit (D v ) on Acoustic Pressure Effect of Velocity Deficit (D v ) on SPL Effect of wake width on OASPL Strut configurations of the ducted rotor. The rectangles represent wake regions. The dashed line is a blade Comparison of SPL (db) for increasing number of struts Effect of tip clearance on Acoustic pressure Effect of tip clearance on SPL C.1 Figure representing blade and wake region positions. The circular region is the rotor disk. The thin rectangle inside the circle is the wake region. -.. line represents the mid line of the wake region viii

9 List of Tables 3.1 Important parameters used in the CFD calculation performed using ANSYS CFX. * Position with respect to duct leading edge Parameters used in the unsteady analysis. Calculations were performed by varying wake width and velocity deficit in their respective range as shown in the table. Induced velocity is obtained from the ANSYS CFX calculation Parameters used in scattering analysis ix

10 List of Symbols B t D v ψ t ψ 0 C d D r T R t Strut wake width Maximum velocity deficit Instantaneous azimuthal position with respect to a reference line(usually the horizontal x-axis if plane of rotation is XY). Please see figure 4.2 for a better perspective. Angle traveled by the blade from entry of strut wake to the then center of strut wake. Please see figure 4.2 for a better perspective. Drag coefficient Diameter of the cylinder radius Time period of 1 revolution of a rotor radius of tip Abbreviations SPL OASPL BPF BPFH CFD Sound Pressure Level (reference pressure of Pa) Overall Sound Pressure Level (reference pressure of Pa) Blade Passage Frequency Blade Passage Frequency Harmonic Computational Fluid Dynamics x

11 GUI FEBLOCK Graphical User Interface Finite Element Block format (default format in Tecplot) xi

12 Acknowledgments I would like to thank Professor of Aerospace Engineering Dr. Kenneth S. Brentner for providing me this opportunity to conduct this research. I am indebted to Professor of Aerospace Engineering Dr. Cengiz Camci and Dr. Ali Akturk for proving valuable research data in this project. I would also like to thank Professor Philip Morris for thesis related coursework and for reviewing my thesis. I am very lucky to be in the company of my bright colleagues and friends Dr. Seongkyu Lee, Mr. Jacob S. Zentichko, Mr. Jeswanth Mentey, Mr. Pavanakumar Mohanamuraly, Ms. Swati Saxena, Dr. Steven Miller and many more. I greatly appreciate the ideas and inputs I had received from my colleagues especially Dr. Seongkyu Lee. I would also like to thank my close friends who are mostly in Aerospace Engineering for encouraging me in tough times and for sharing my happiness. xii

13 Dedication I would like to dedicate my thesis to my parents and sister for their unconditional support and love throughout my life. xiii

14 Chapter 1 Introduction to Shrouded Rotors Any rotor configuration consisting of a blade hub embedded in a short duct can be called a shrouded rotor. In such configurations, the duct chord is of the order of the blade radius, and hence these rotors are referred as short ducted rotors. The major features of such a configuration are lower power for a given total (duct and rotor blades) thrust and a safer configuration in comparison to an open rotor. These rotors are used as a means of propulsion in uninhabited aerial vehicles (UAV), fan in wing airplanes and fancraft. They are also used as an anti-torque rotor in the standard helicopter. Such anti-torque devices are called fenestrons. Well known aircraft that use ducted rotors include the Hiller Flying Platform (Ref. [1]), the Eurocopter Dauphin (Ref. [2]), the RAH 66 Comanche (Ref. [3]), and the X - Hawk (Ref. [4]). In such configurations, apart from the rotor itself there are additional components like struts, vanes, transmission shaft and support structures that house the rotor in the duct. These components may be present upstream or downstream of the rotor thereby affecting the dynamics of the flow. The primary goal of this thesis is to understand the effects of these additional components on the acoustics of the rotor configuration. Section 1.1 describes the early rotor configurations that used ducted rotors. Section 1.2 discusses the advent of shrouded tail rotors and reasons for their choice over a conventional tail rotor. Section 1.3 briefly illustrates the Fancraft concept, that is an ongoing research program, which has not yet reached production stage. Section 1.4 emphasizes the importance of this work and the road map for the rest of the thesis.

15 2 Figure 1.1. Different types of ducted rotors (a) The Hiller Platform VZ -1 (b) The Nord 500 (c) istar9 (d) HoverEye (Ref. [5]) 1.1 Early attempts Early attempts at using the ducted fan vertical take off and landing (VTOL) concept can be traced to the Hiller Flying Platform of U.S. Army and the French Nord 500 [5]. The Hiller Flying Platform is based on NACA engineer Charles Zimmerman s kinesthetic theories. This vehicle is based on the idea that a persons natural balancing reflexes can control a small aircraft. Hiller Helicopters made the first prototypes for the Office of Naval Research(ONR) and the U.S. Army. As shown in the Figure 1.1, this aircraft consists of a duct enclosing contra-rotating coaxial two bladed propellers powered by two 44 hp Nelson H-59 engines (Ref. [1]). This was the first successful manned ducted fan aircraft. In this aircraft 40% of the lift was produced by the duct and the remaining 60% from the thrust of the contra-rotating propellers. Further development of this vehicle ended due to limited forward speed capability and the problem with adverse pitching moments.

16 3 The state-owned French manufacturer, Nord, designed the Nord 500 for verifying and understanding tilt duct propulsion concepts. This aircraft consists of two 5 - bladed propellers surrounded by ducts. There are four control vanes which were used for yaw and pitch control by differential and collective tilt respectively. The ducts could tilt along with the wing. Roll control in hover was achieved by differential thrust and pitch control by collective duct tilt. At that point of time, noise studies were not done in great detail and hence little acoustic data is available. In these configurations the focus was on performance and efficiency more than rotor noise. This research was followed by the shrouded rotors. These are described in the next section. 1.2 Shrouded tail rotors The conventional helicopter has a tail rotor in order to compensate the torque from the main rotor and provide yaw control. The tail rotor of a conventional helicopter operates in a complex flow environment. Apart from the relative wind, it has to encounter the vortices of the main rotor and wake of the fuselage. The tail rotor can be damaged while maneuvering very close to the ground especially in places with tall trees. Additionally the ground personnel are at risk of getting injured while operating close to the helicopter. Also the conventional tail rotor is a significant source of noise exceeding the main rotor noise levels at higher frequencies. A desire to avoid some of these problems associated with conventional tail rotors prompted the fenestron tail rotor design. A fenestron is a fan in fin configuration as shown in Figure 1.2. It consists of a rotor placed in a duct. The duct chord is equal to the thickness of the fin. Support struts (see Figure 1.2(b)) hold the rotor blades assembly in its position. There is a transmission shaft that imparts power to the rotor. Additionally the rotor configuration may have stator vanes downstream of the blades. The number of blades in fenestrons is usually higher than conventional tail rotors and they may be unevenly spaced. This is a measure to distribute acoustic energy among multiple harmonics which leads to a lower total noise level (Ref. [6]). The first flight of a helicopter with a shrouded tail rotor was performed in 1968

17 4 (a) CEV Dauphin 6075 (b) Closer view of tail rotor Figure 1.2. Shrouded tail rotor helicopter (Ref. [2]) on the Gazelle helicopter designed by French state-owned Sud Aviation. This was soon followed by the Dauphin helicopter originally manufactured by Aerospatiale, the Eurocopter EC135 in 1990s and the RAH-66 Comanche developed by Boeing/Sikorsky also in the 1990s. Figure 1.3 shows a comparison of tail rotor thrust as a function of tail rotor blade pitch between open and shrouded tail rotors. The

18 5 Figure 1.3. Comparison of Thrust vs pitch for conventional and shrouded tail rotor helicopters (The helicopter is SA 340/341 Gazelle (Ref. [7])) Figure 1.4. Comparison of Horsepower vs True airspeed for conventional and fenestron helicopters (This helicopter is SA 340/341 Gazelle (Ref. [7])) thrust from the blades of a fenestron is less than an open tail rotor. But the thrust from the duct and blades put together exceeds that of the open tail rotor. This results in greater yaw control for the pilot. It also reduces loading on the blade resulting in reduced structural stress. Another advantage of having a fenestron is lower power consumption at higher airspeeds. Figure 1.4 shows that at higher airspeeds the power required for a fenestron is lower than that of a conventional tail rotor, whereas at lower airspeeds and hover the opposite is true (for more details see Ref. [7]). Noise quality is an important parameter in the design of a fenestron configuration. The presence of the upstream obstructions, higher number of blades and the presence of shroud are important sources of noise in hover. Uneven blade spacing (Ref. [6]), increasing number of blades and reduced angular speed are some of the

19 6 Figure 1.5. Experimental SPL vs Frequency (Ref. [8])) measures taken to reduce noise. Studies on the effects of additional components like struts or vanes on noise from fenestrons can be found in Roger [8]. Figure 1.5 shows SPL vs Frequency for a full scale 11 bladed Dauphin tail rotor. As shown in the figure, it is a short ducted rotor. The observer location is 45 degrees to the axis of rotation of the rotor. At a blade pitch of 32 degrees the thrust produced by the rotor is significant. From the figure it is clear that most of the frequencies fall in the audible range. Apart from Roger, there are not many studies available on the effects of additional components like struts or vanes on noise of short ducted rotors. In the next section, a futuristic VTOL vehicle called a fancraft will be discussed. 1.3 Fancraft Medical evacuation in urban areas and urban warfare are fast becoming important helicopter missions in this century. The ability to land and take off vertically

20 7 Figure 1.6. X-Hawk of the Urban Aeronautics(Ref. [9]) has been available for many years but the enviroment in urban areas restricts the mobility of such vehicles. Fancraft technology is an attempt to offer the kind of capabilities required for operations in confined areas. Fancraft have packaged ducted fan configurations with a unique vane control system for lateral control stability and robust wind gust performance. The X-Hawk is a proposed tandem lift fan as shown in the Figure 1.6 (Ref. [9]). It is powered by turbine engines and has two ducted fans at the rear that provide propulsion for forward translation (Ref. [4]). The pilot can translate in three directions while remaining horizontal at all times. This is the kind of maneuverability required in the obstacle rich confined areas in an urban canyon. The projected top speed of this vehicle is 130 kts. For details on the proposed performance and specifications please see Ref. [4]. The X-Hawk is not currently in production; although it is being studied and tested. By looking at this vehicle we can see that it has many vanes. These obstructions can create non-uniformities in flow which might be a potential source of noise. There are no noise studies available at this time. 1.4 Motivation for research As mentioned before, the ducted rotor has additional components like struts and vanes, unlike conventional open rotors. These components can pose additional levels of noise. As seen from Figure 1.5, these additional components lead to a broad spectrum. Hence there is a need to understand the phenomena and also

21 8 develop the capability to design suitable rotors. In order to understand the noise generation mechanisms in the ducted rotor, this research used a two step method for calculation of total noise. The aerodynamics of the problem has been split into steady and unsteady parts. The flow and acoustic calculations are made in the steady mode when the configuration does not have struts or vanes. In the unsteady part, the changes in the loading of the blade that occur due to the presence of the struts or vanes and the corresponding noise, are calculated. These two calculations are superimposed in the time domain to obtain the total noise. Their contributions to the total noise have been analyzed. In addition, the effects of various parameters on the noise levels are also studied. In the next chapter the sources of noise for such configurations will be outlined. The strategy adopted for calculation of noise is explained in detail in Chapter 2. The implementation details of each phase of the procedure: i.e., steady and unsteady calculations, are explained in Chapter 3 and 4 respectively. Chapter 5 contains results of the computational experiments performed for the selected configuration. These experiments are aimed at understanding the effect of design parameters on the noise levels. Appendix A illustrates the script files used for running ANSYS FLUENT calculations. These files can be used to run a parallel ANSYS FLUENT simulation without the GUI. This Appendix also contains a manual of a code that converts the exported ANSYS FLUENT data to PSU- WOPWOP format. Appendix B has the details of the namelist file (input file for PSU-WOPWOP) used for calculating total noise. Appendix C has details of the algorithm used in the calculation of unsteady loading, and the corresponding namelist file for acoustic calculation.

22 Chapter 2 Noise prediction strategies This chapter explains the noise prediction strategy adopted in this thesis. In order to formulate the strategy, the sources of noise and the applicable methods are required. Section 2.1 explains the sources of noise considered in this thesis. Section 2.2 presents an overview of applicable methods for predicting noise from these sources. The focus is on the methods that calculate loading noise. Section 2.3 explains the strategy adopted to calculate the individual noise and the total noise of the ducted fan used in this research. 2.1 Sources of noise The complicated flow environment of a ducted fan results in many sources of noise, which have distinct mechanisms. Considering the operating conditions (low tip Mach number) of the ducted fan in this research, the major sources of noise are thickness noise, loading noise and broadband noise. Thickness and loading noise together are known as rotational noise and are related to linear aerodynamic theory. Thickness noise is produced due to the displacement of the fluid by the moving blades. Loading noise is generated from the force acting on the fluid due to the moving surface. The noise calculated from these sources will be termed steady noise because they do not vary with blade azimuth when the blade loading is also steady. On the other hand, broadband noise is generated from non-deterministic sources of loading such as turbulent flow near the blade surface, free stream turbulence, tip vortex formation, laminar

23 10 vortex shedding, trailing edge noise, blade wake interaction, etc., which vary with blade azimuth, radial position and time. Broadband noise sources have not been considered in the present work. Apart from the sources on the blade, the presence of the duct around the blade causes scattering of the incident blade noise. The ducts used in turbomachinery are typically long and the familiar duct theory (Ref. [10]) can be used (ducts are assumed to be infinitely long or very long). In this approach, the convected wave equation is solved by imposing a rigid wall boundary condition and assuming that the duct is infinite. This assumption means that transverse dimensions of the duct are smaller than the longitudinal dimensions. However, that is not the case for the configurations studied in this research. In fact in some cases the duct radius is more than the length of the duct. So duct theory is not applicable here and another approach is required for modeling. The significant noise sources in the duct are present on the inner surface of the duct that is closer to the rotor blades. This is because, this inner surface region of the duct is subjected to periodic loading due to the movement of the rotor blades. Periodic loading can be a substantial source of noise. This periodic loading data is obtained from CFD. The noise calculated using this loading data is the scattering of incident blade noise. The presence of the struts or vanes upstream of the rotor causes flow distortion which ultimately impinges the rotor blades. There is usually a decreased inflow velocity due to the obstruction. This decreased inflow velocity results in a change in loading on the blades. This change in loading will occur only when the portion of the blade is in the wake of the strut or vane. Hence this loading is unsteady and will also depend on the radial location of the blade region being considered. To summarize the sources considered in this thesis are thickness noise, loading noise, scattering of rotor blade noise and unsteady loading noise. 2.2 Methods of noise prediction Some of the methods of noise prediction that are important with respect to the calculation of noise for short ducted fan configurations are discussed in this section.

24 Early prediction theories In the pre Ffowcs Williams-Hawkings era, loading noise prediction methodology was based on acoustic theories developed for propellers. Gutin theory (Ref. [11]) of propeller and rotor noise is the first theoretical result for rotating blade noise calculation. In this theory the blade load distribution is constant. Using this theory, amplitudes of various harmonics at a given observer location can be calculated. Noise from fluctuating blade loads is not accounted in this calculation. A methodology and results for noise radiation from periodic fluctuations in blade loading was given by Wright and Lowson (Refs. [12, 13]). The amplitude of various harmonics at a given observer location for a periodic blade loading distribution is calculated using this method. According to this theory the amplitude of a single harmonic depends on all loading harmonics. The results from their calculations predict that sound from unsteady loading can dominate the sound field more than steady loading (Ref. [14]). This theory was important around that time because it was applicable to various helicopter related phenomena like vortex shedding, asymmetric loading from forward flight, impulsive loading etc. The relation of operating conditions to harmonics is not well established in this method. This is one of the major drawbacks of this method. Roger (Ref. [8]) proposed a loading noise calculation method based on Lowson s theory. This method was applied for calculating noise from the ducted tail rotor of a helicopter in hover condition. Three noise generating mechanisms were considered in the analysis: Rotor noise due to ingestion of atmospheric turbulence Unsteady loading on the rotor blade due to the presence of downstream transmission shaft. Unsteady loading on the stator vanes due to average velocity deficit from the presence of upstream rotor blades. The configuration used in this analysis is shown in Figure 2.1. Some of the results of this analysis are shown in Figure 2.2. The peaks in the figure are points of Blade Passage Frequencies. The dots represent the calculated spectrum from

25 12 the respective sources. The calculation of acoustic pressure in this paper (Ref. [8]) is based on Lowson s classical result. Figure 2.1. Figure showing relative axial positions of the rotor, stator and transmission shaft of the ducted tail rotor configuration (Ref. [8]). The transmission shaft is represented by the circle with chords. The rotor and the stator cross-section is shown in the figure. Consider the second mechanism. The loading on the blades is altered due to the presence of a downstream shaft. The change in the loading depends on the distance between shaft and the blades. This change in loading will be unsteady because the loading is changed in the vicinity of the transmission shaft which exists only at a particular azimuthal position. Figure 2.2(b) shows the SPL vs Frequency due to this source. The noise prediction is good only at the BPFH. Consider the third mechanism. The presence of the blades upstream is an obstruction to the incoming flow to the vanes. This results in reduction in velocity of incoming flow. This reduction is termed as average velocity deficit. This reduction in velocity occurs only when the blade passes the stator. In the time between two blade passages the incoming flow attempts to return to full velocity. Essentially this is a periodically varying vertical gust impinging on the stator vanes. Apart from the reduced velocity, there may vortices convecting downward, inflow turbulence etc. But the contribution to loading from velocity deficit is much higher than other sources. Figure 2.2(a) shows SPL vs Frequency for this source. In this case the prediction is better at frequencies other than the BPFH. The acoustic contribution from unsteady loading on the rotor due to the pres-

26 13 ence of the transmission shaft is mainly at the BPF (Figure 2.2(b)). The contribution due to unsteady sources (Figure 2.2(a))on stator vanes is significant for a wider range of BPF s and hence much more important than the loading on rotor blades. This velocity deficit based loading can also occur on the rotor blades if there are upstream struts or vanes which is the configuration considered in the present thesis. (a) Sound Pressure level from unsteady sources on a stator (b) Sound Pressure level from flow distortion due to transmission shaft Figure 2.2. SPL from different noise generating mechanisms at an observer location that is 45 0 to the rotor axis(ref. [8]) Ffowcs Williams-Hawkings Equation The Ffowcs Williams-Hawkings (FW-H) equation is the most general form of Lighthill s acoustic analogy. It includes effects of general types of surfaces and motions. In this approach the Navier-Stokes equations have been rearranged into an inhomogeneous wave equation with a quadrupole source distribution in the volume surrounding the body and monopole and dipole source distributions on the surface of the body.

27 14 The FW-H equation can be written in differential form as 2 p ( x, t) = t {[ρ 0v n + ρ(u n v n )]δ(f)} x i {[ P ij ˆn j + ρu i (u n v n )]δ(f)} + 2 x i x j [T ij H(f)] (2.1) where P ij = (p p 0 )δ ij, or gauge pressure, T ij = ρu i u j σ ij + (p c 2 ρ )δ ij is the Lighthill stress tensor, 2 is the wave operator, p is the acoustic pressure, f = 0 is the moving data surface, c and ρ 0 are speed of sound and density of air in unperturbed medium, u n is the velocity of fluid normal to the data surface, v n is the velocity of surface in the direction of the normal to the surface, and ˆn j is the outward unit normal vector at a point on the surface. Equation 2.1 is a FW-H equation for a permeable data surface. It accounts for the quadrupole noise sources inside the data surface through the surface source terms. For the present configuration the dominant sources are thought to be present on the blade and duct surfaces; hence, quadrupole noise sources can be neglected. Therefore only thickness and loading noise sources will be evaluated. The data surface is the blade surface in which case u n = v n. Equation 2.1 is then reduced to: 2 p T = t {ρ 0v n δ(f)} 2 p L = x i {pˆn j δ(f)} (2.2) The subscripts in acoustic pressure in equation 2.2 indicate thickness and loading components respectively. The viscous stress term (σ ij ) in Lighthill stress tensor is neglected. From Equation 2.2 it is understood that the thickness noise depends on the geometry and angular velocity of blade. On the other hand, loading noise depends on the geometry of the blade and gradient of pressure distribution. This equation is converted to an integral form using a Green s function by which the thickness and loading noise components can be predicted.

28 Formulation 1A To solve the Ffowcs Williams-Hawkings equation, PSU-WOPWOP (Ref. [15]) uses a time-domain integral formulation developed by Farassat (Ref. [16]). This formulation excludes the quadrupole term of the FW-H equation and is valid for any rigid-body surface motion: p ( x, t) = p T ( x, t) + p L( x, t) (2.3) where the thickness contribution p T 4πp T ( x, t) = f=0 + f=0 is calculated from [ ] ρ0 ( v n + vṅ) ds ret r(1 M r ) 2 [ ρ 0 v n (rṁr + c(m r M 2 )) r 2 (1 M r ) 3 and the loading contribution p L is calculated from 4πp L( x, t) = 1 c c f=0 f=0 f=0 [ ] L r r(1 M r ) 2 [ Lr L M r 2 (1 M r ) 2 [ ] ret ds ds ret L r rṁr + c(m r M 2 ) r 2 (1 M r ) 3 ] ] ret ret ds ds (2.4) (2.5) Here, L i = pˆn j (2.6) v n is the velocity of surface in the direction of normal of the surface. The derivation of equations 2.4 and 2.5 can be found in Refs. [16, 17]. The integrand on the right hand side of these equations is evaluated at the retarded time. The retarded time is the time at which the sound source emits the signal so that it reaches the observer at the current time. All the integrands in the calculation of thickness noise require

29 16 the normals and coordinates of points on the data surface as a function of time. In the case of the loading noise calculation, apart from normals and coordinates, only the pressure distribution on the data surface as a function of time is required. The data surfaces in the current problem are the blade and inner duct surface. The duct as a data surface is explained in more detail in the next section. 2.3 Current noise prediction method In the current work, Formulation 1A (Equations 2.4 and 2.5) of FW-H equations is used. The aerodynamics of the problem are split into steady and unsteady parts (See Figure 2.3). The steady aerodynamics consists of the rotor configuration without the upstream struts or vanes. Loading on blades and duct, and fluid displacement by blade (thickness noise) constitute steady noise. In the unsteady aerodynamics the loading on the blade is unsteady. The loading and geometric data from these sources is then used as input to PSU-WOPWOP to obtain the total noise. Steady loading noise requires blade loading (i.e. surface pressure) from a CFD calculation (described in Chapter 3). The rotor blade surface pressure distribution from the CFD calculation is converted to PSU-WOPWOP input. The surface pressure distribution does not vary with time. But the rotor blade is a moving data surface and the movement is simulated in PSU-WOPWOP. (a) CFD (b) Unsteady loading Figure 2.3. Noise prediction approach In this steady configuration, the loading on the inner duct surface closer to the blade (the blue part of the duct shown in Figure 2.4) has a periodic variation in

30 17 Figure 2.4. Noise sources region of duct. The portion of the duct in blue represents the source region. time. This is the only region of the duct that generates substantial noise. The CFD calculation is a steady calculation hence the loading on the duct is available for one time point. In order to create a periodic variation in duct loading, the source region of the duct rotates with the same angular velocity as the blade in PSU- WOPWOP. This simulation results in calculation of steady loading noise from the duct. The presence of struts or vanes upstream results in interrupted inflow velocity in the rotor disk. This effect is simulated in the unsteady part of the problem. Using the varying inflow velocity, the change in loading on the rotor blades is calculated. The blade is represented as chordwise compact, which is modeled in PSU-WOPWOP as a compact patch. A compact patch is a line formed by joining the quarter chord locations of each spanwise section of blade. Loading time history is calculated at every point in the compact patch. This loading time history depends on location and dimensions of the upstream obstructions, and inflow velocity into the rotor disk. The inflow velocity into the rotor disk is obtained from CFD. In this analysis mean value of inflow velocity in the rotor plane is used for all spanwise locations. The movement of the compact patch and loading history are both calculated and converted to PSU-WOPWOP input using the unsteady loading code (Appendix C). The effects of various parameters on the unsteady noise calculation is explained in Section 5.4. The loading and geometry data for all these sources can be loaded into one input namelist file (see Appendix B). Each of the sources can be analyzed separately or can be summed with other sources. In order to calculate the total noise all the sources are included. The duct periodic loading was simulated by rotating the

31 18 duct at the angular velocity of the blade, which results in additional thickness noise from the duct. A duct data surface which has inverted normals and zero loading is added to the PSU-WOPWOP namelist file to counter the additional thickness noise from the duct. A compact patch is a line; hence, no thickness noise is generated from unsteady rotor blade loading. The next chapter explains the steady aerodynamics details and the related sound field calculation procedure.

32 Chapter 3 Computational methods for ducted fan aerodynamics Loading noise of a rotor configuration is calculated from the loading distribution on the rotor blades and duct, which are a function of spatial position and time. The flow domain of a ducted fan has complex geometry involved. The flow is affected by rotors, which are continuously spinning and also by the stationary duct. Both these structures provide lift for the ducted fan configuration. Hence the pressure distribution on these surfaces is extremely important. The goal is to generate the loading data accurately and cost (time) effectively. In Section 3.1, the methods usually employed in the steady loading data calculation are addressed. Section 3.2 explains the steady aerodynamics results obtained using ANSYS CFX software. In addition, the procedure for noise calculation using PSU-WOPWOP is explained in Section Overview of methods used in modeling ducted fan aerodynamics Some of the computational methods used in solving the flow field of a ducted fan, will be discussed in this section. These computational methods include momentum balance, potential flow methods and momentum source models. These methods are listed in Ref. [18].

33 20 In case of the momentum balance methods, the fan is treated as an actuator disk with constant inflow and outflow(ref. [18]). The fluid flow is along the duct axis. The pressure on each side of the rotor disk is assumed constant over its area. These assumptions simplify the flow features and hence the computations are simple and fast. The variation in loading near the tip is not accounted for in this method. The blade twist distribution over the span, duct thickness along its chord, etc. are not used as input. These are important geometrical features that influence the loading and hence the computations made through these methods are not accurate. This analysis is good to gain insight into the possible loading distribution, and the computed flow field may be used as an input for more advanced methods. In potential flow methods (Ref. [18]), the flow is considered to be inviscid, irrotational and incompressible. The geometry of the blade is taken into consideration in these methods. Both two dimensional and three dimensional analyses can be done using this approach. The loading distribution on the blade can be obtained in this method. But critical flow features that can affect loading such as tip losses and the duct boundary layer are not modeled due to the underlying assumptions. The flow features predicted by potential methods include the mutual effects of the blade influencing the duct and the duct influencing the blade. These features are important for parametric studies, from a design point of view, and for acoustic calculations. The momentum equation governs the balance of the rate of change of momentum and the external forces experienced by the fluid element. In the momentum source model (Ref. [18]), the rotation of the blade is included in the governing equation in the form of force exerted on the fluid by the moving blades. The components of the force exerted on the fluid are included in the source terms of scalar momentum equations. These source terms are dependent on the derivatives of angle of attack, blade location, angular velocity of rotor, airfoil distribution and characteristics to name a few. The force on the fluid is exerted by the blade only for the fraction of time it spends at that blade element. Complete Navier-Stokes equations are solved throughout the flow field with additional source terms (momentum sources) for fluid elements that are near the blade. So this method takes as input the blade geometry and also accounts for most of the flow physics. Apart from momentum balance and potential flow methods, the commercial

34 21 solvers ANSYS FLUENT and ANSYS CFX (Refs. [19, 20]) offer additional methods for solving the flow field of a ducted fan. The appropriate method is chosen based on the interactional aerodynamics of blade and shroud, and accuracy requirements. Apart from a good solution these solvers have reasonable scalability while running in parallel. The ANSYS CFX solution is discussed in the next section. 3.2 ANSYS CFX solution Dr Ali Akturk and Prof. Cengiz Camci constructed an experimental 22 inch ducted fan (Figure 3.1). Dr Ali Akturk (Ref. [21]) has performed both experimental and computational analyses for this fan. The results included in the current thesis are hover calculations with no upstream obstructions; hence, the flow is relatively simple. The computational analysis has been performed using ANSYS CFX. AN- SYS CFX (Ref. [20])is a finite volume based commercial solver used widely in turbomachinery related fluid applications Computational setup The computational model used for the calculation is shown in Figure 3.1(b). In this analysis, the incompressible flow field around the ducted fan is solved in a periodic domain. The Reynolds-Averaged Navier Stokes equations were solved using a k ω two equation turbulence model developed by Wilcox (Ref. [20]). The important parameters of this calculation are shown in Table 3.1. Tip clearance 1.71% 3.04% Angular velocity (Ω) 2400 rpm 2400 rpm tip Mach number (M) tip radius (R t ) m m hub radius (R h ) m m blade chord (c) m m duct chord m m blade position* 27.73% 27.73% Table 3.1. Important parameters used in the CFD calculation performed using ANSYS CFX. * Position with respect to duct leading edge. Figure 3.2 shows the various subdomains of the flow field. There is a stationary

35 22 (a) Experimental model (b) Computational model Figure 3.1. Experimental and computational ducted fan (Ref. [21]) inlet region, a rotating region in the vicinity of the fan blades, and a stationary outlet region. The rotating domain consists of the fan blades and middle section of the duct (below the duct lip to a little above the duct trailing edge). In this domain the moving reference frame equations are solved. In the stationary domain the regular equations are solved. The Stage type interface model has been used in passing data between the two domains moving relative to each other. This model performs a circumferential averaging of flow variables before using them to

36 23 compute fluxes (Ref. [21]). Figure 3.2. Different components of the flow domain (Ref. [21]) The direction of fluid flow changes from inward to outward on the side surface of the domain (Figure 3.2). Hence an opening boundary condition is applied. This boundary condition allows the fluid to cross the boundary surface in either direction. The upper face of the stationary inlet region has pressure inlet and the lower face of the stationary outlet has pressure outlet boundary conditions, respectively. The walls of the duct that are not part of the rotating domain have no slip boundary condition. The duct wall that is part of the rotating domain has a counter-rotating angular velocity. For more information about the implementation of these boundary conditions, please see Ref. [21].

37 Flow field description Figure 3.3 shows the velocity vectors from a cross-sectional view of the flow domain. Figure 3.3(a) shows the cross-sectional view of the total flow domain. There is a high concentration of points near the rotor region. (a) Overview (b) Rotational domain (c) Vortices in the tip region Figure 3.3. Velocity vectors in the flow domain (Ref. [21]) Figure 3.3(b) shows a magnified view of the domain near the rotor region. In this view the rotating domain can be seen. It starts from below the duct lip and extends a little above the trailing edge of the duct. These figures are plotted using Dr. Akturk s data (Ref. [21]). Figure 3.3(c) shows a further magnified look at the domain. The formation of

38 25 the tip vortex just before the tip region of the blade is visible in this figure. The tip vortex convection may have been impeded by the duct boundary layer and a very low tip clearance. The flow is not separated and it looks like a well-converged solution (for more details on the flow please see Ref. [21]). (a) (b) Figure 3.4. Pressure Contours on the blade and shroud (Ref. [21]) Figure 3.4 shows pressure contours of the blade and shroud region for the two tip clearances 1.71% and 3.04%. The figures of both tip clearances are plotted using Dr. Akturk s data (Ref. [21]). The difference in pressure contours for the

39 26 two tip clearances occurs at the tip and, at the region of shroud close to the tip. The difference is mostly a change in intensity rather than distribution. The low pressure region on the upper side of the blade is because of the high velocity on the upper surface. The interaction between the shroud and the blade in the case of the lower tip clearance is more than the higher tip clearance case. This causes a higher amplitude low pressure region for the tip clearance of 1.71%. 3.3 Input to PSU - WOPWOP In Section 2.3 it was explained that the dominant sources of noise are on the blade and duct surfaces. Hence the pressure distribution on these surfaces and the coordinates and normals of the grid points on these surfaces are required for acoustic calculations. The CFD results obtained from CFX can be written out in a variety of formats. The results in this research are viewed in CGNS if Tecplot (Ref. [22]) is to be used for flow visualization. From Tecplot, the CFD results are converted to FEBLOCK format for each individual component (blade, duct etc). Accordingly coordinates and pressure on each component are written in a separate file. This separation will help in comparison of different sources of noise. If noise from one single source is to be calculated then only that particular component is loaded in PSU-WOPWOP for calculation. A converter program (Section A.3) is used to convert the FEBLOCK format data into geometry and loading files that are the inputs to PSU-WOPWOP. In this program the normals at every node are calculated and this data along with the coordinates are written to the geometry file. The loading file consists of pressure data only ([15]). The geometry and the loading files written out by the converter program is read by PSU-WOPWOP for acoustic calculation. The CFD result is a steady calculation for 1/8 of the duct and one blade. In PSU-WOPWOP the components can be translated or rotated by keeping the pressure constant. So the blade and duct data is read 8 times (because there are 8 blades), and each time it is rotated by an increasing multiple of In this way the blades, duct and pressure distribution are imported in PSU-WOPWOP. Since this is a steady calculation the solution for the total configuration is present

40 27 only for a single timepoint. Now since the noise sources are rotating, the rotation of blade and duct has to be simulated in PSU-WOPWOP for the accurate noise computation. (a) Acoustic pressure (b) Sound pressure level Figure 3.5. PSU-WOPWOP Results Apart from setting the actual motion of blades and duct in PSU-WOPWOP, the observer grid can be specified. Figure 3.5(a) shows acoustic pressure time history over one rotation of the blade at an observer point 2R from the axis of rotation in the plane of rotation. Here total implies the steady configuration which consists of the 8 blades and the rotating domain of the duct. It has 8 peaks which is expected because there are 8 blades. Figure 3.5(b) shows sound pressure level for the total steady configuration. Some important points regarding the steady noise calculation: The rotor and the duct have steady loading data in their respective domains. Hence both are rotated at the angular velocity of rotor in PSU-WOPWOP. The duct needs to be rotated to generate the pressure time history of the steady CFD data. This rotation of the duct alters the thickness noise of the rotor because the noise from rotation of the duct is superimposed with the

41 28 noise from blade rotation. Therefore to cancel the thickness noise signal from the duct (which is erroneous), another duct with inward normals is added as an additional source. This additional duct source will exactly cancel the thickness signal from the original duct. The additional duct source does not have loading data; hence, it does not contribute to the loading noise. The thickness noise from the rotor blades and total steady loading noise from duct and rotor blades is given as output by PSU-WOPWOP. The unsteady loading and the process leading to the acoustic computation from unsteady loading will be explained in the next chapter.

42 Chapter 4 Unsteady loading noise computation In the ducted rotor configurations that have been described in Chapter 1, it is observed that many of the configurations have support struts and other obstructions upstream of the flow. These obstructions, based on location (upstream) and dimension, cast their wake on the rotor blades at certain azimuthal positions. This causes a drastic reduction and gradual recovery of loading force over the time the rotor blade passes by the wake of the obstruction. The modeling of unsteady blade loading is explained in this chapter. 4.1 Introduction to unsteady rotor aerodynamics The rotor airloads prediction is of primary importance to an aircraft designer. The design, although primarily influenced by the steady loads acting on the aircraft, should also take into account the unsteady phenomena for a robust design. There are many important unsteady phenomena like flutter, buffeting, transient flows and gusts, which are major hindrances in aircraft performance. These phenomena are unavoidable and must be dealt with. The major sources of unsteadiness arise from the blades themselves and parts of rotor configuration that are placed upstream and downstream of the rotor. These parts must be of appropriate dimensions and close enough to the rotor plane. The sources from a blade wake that may affect the blade airloads are shown in

43 30 Figure 4.1. Figure showing various sources of tip and trailed vortices ( Ref. [23]) Figure 4.1. The figure shows the wake of a blade consisting of a vortex sheet leaving the trailing edge of the blade. Apart from trailing edge vortex sheet, there are also tip vortices that, from experimental observations, are known to be fully rolled up(with in a few degrees of rotation) and contain vorticity that is stronger than the trailed vorticity. Also shown in Figure 4.1, the tip vortex from previous blade passes near the current blade. This feature is a distinct attribute of rotating blades as compared to the fixed wing case. The contribution from the next blade is important and is termed as the near shed wake (See Ref. [23] for more details). In the present analysis it is assumed that there is no blade pitching or flapping. Hence, the sources of unsteadiness arising from the blade itself have been neglected. The focus of the current thesis is the influence of other parts of the ducted rotor system geometry on the blade loading.

44 31 The presence of obstructions to the flow downstream of the rotor understandably does not cause major impact on the blade loading unless they are very close and there is a potential flow effect. But the vanes or struts present upstream of the rotor can alter the flow field in three ways. The wake of these obstructions can have 1) reduced velocity, 2) turbulence, and 3) vortex shedding from the obstruction. The primary effect will be the velocity deficit (Ref. [24]) depending on the dimensions and distance of the obstruction from rotor blades. As a blade passes through the wake it will experience a sharp decrease in inflow velocity which is followed by a recovery of the inflow velocity. This change in velocity occurs over a short period of time. The change in the inflow velocity will result in perturbations in angle of attack, which will in turn effect blade loading history. The perturbations in angle of attack are small and the flow is fully attached. Under these conditions, the most fundamental approach to modeling the unsteady aerodynamics is an extension of 2D thin airfoil theory. At the blade element level the perturbations in local angle of attack (AoA) and velocity field are modeled as a function of time. The angle of attack variations are small, and hence linear (based on the assumptions of thin airfoil theory). So the unsteady airloads manifest as a change in amplitude and phase. The quasi-steady loads are obtained by calculating the loading on the rotor in the absence of obstructions. In this state the loading on the rotor is steady. The unsteady airloads are calculated as a perturbation from these quasi-steady loads and are small in comparison. The methods employed in calculations are semi-analytical, numerical and essentially 2D in nature. These methods serve as a way to realize the potential of unsteady effects and also describe certain key features of the physics involved. These methods are faster than conventional CFD methods and hence can be used as preliminary design tools. 4.2 Concepts of unsteady rotor blade aerodynamics Reduced frequency (k) and reduced time (s) are two important parameters used in the description of unsteady aerodynamics (Ref. [23]). Reduced frequency is a

45 32 measure of the degree of unsteadiness. From dimensional analysis it can be shown that the force on an airfoil of chord c is a function of Reynolds number (Re), Mach number (M) and reduced frequency. The reduced frequency is defined as, k = ωb V (4.1) where ω is the angular frequency of airfoil oscillation, b is the airfoil semi-chord and V is the velocity of the airfoil. The flow is steady for k = 0. If 0 < k < 0.05, the flow is quasi-steady. Quasi-steady means that the changes with respect to time are small and can be ignored for load calculations. For values of k higher than 0.05 the problem is regarded as unsteady. The airfoil velocity varies across the span of the blade; hence k values are higher towards the hub and lower at the tips. So the unsteady effects have to be accounted for with varying frequencies across the span of the blade for an accurate evaluation. The other parameter, reduced time (s) represents the distance traveled by the airfoil in semi-chords. s = 2 c t 0 V dt (4.2) where c is blade chord length. The quantification of unsteady airloads is easier when reduced time parameter is used as an input especially for airfoils operating in gusts. In order to use 2D thin airfoil theory for unsteady calculations there are certain limitations and assumptions: The frequency of unsteady sources is small compared to the frequency at sonic velocity of airfoil. This means that reduced frequency is small. Since the analysis is performed at the blade element level, spanwise effects are ignored. All unsteady effects are measured as changes in AoA. 4.3 Velocity deficit formulation As explained in the introduction (Section 4.1), the obstructions upstream of the blades cast a region of reduced velocity on the rotor disk. When the blades en-

46 33 counter this region the change in velocity, termed as the velocity deficit, varies through the width of the wake. The velocity deficit is zero just before entering the region. It gradually increases from zero at the entry of the wake width to V D v at the center of the wake. D v is a parameter that sets the maximum velocity deficit and hence can be a value from 0 to 1.0 (complete blockage). But from experimental measurements D v is in the range 0.1 to 0.9 (Ref. [24]). V is the inflow velocity upstream of the rotor impinging on the strut or vane. This velocity is obtained from CFD calculation of the rotor configuration without the upstream obstructions. It can also be obtained from wind tunnel measurements. As the blade moves from the center to exit of wake region the velocity deficit decreases and is zero at the exit. The velocity deficit has been modeled as a cosine function by Wang and Cotton (Ref. [24]) as shown in Equation 4.3. Figure 4.2. Basic parameters used in strut wake (modified from Ref. [25]) V g = V D v 2 [ ( 1 + cos 2π ψ t π )] 2 (4.3)

47 34 Here V g is the velocity deficit within the wake of the strut. Outside the strut wake the deficit is zero (i.e the velocity of fluid is same as the induced velocity at the plane). The angle ψ t shown in the Figure 4.2 is the azimuthal position of the blade with respect to the horizontal i.e., when ψ t = 0 the blade is horizontal. The blade rotates counter clockwise and enters the strut wake at ψ t = π/2 + arcsin( Bt) and 2r leaves at ψ t = π/2 arcsin( Bt ). ψ 2r 0 is a constant equal to arcsin( Bt ). When the 2r blade is about to enter the wake, V g = 0 ( if ψ t is replaced by its entry value the cosine term becomes -1 ) and its value is zero near the exit too. The maximum value of V g occurs at ψ t = π/2 ( cos term is equal to 1). This should be the case because the blade experiences the least velocity at the center of the wake. The width of strut wake region B t and maximum value of velocity deficit D v depend on streamwise distance from the rotor and Reynolds number for the flow past the strut. Wake width and velocity deficit variations are provided by wind tunnel studies performed by Snyder and Wentz (Ref. [24]). An important finding in this study is that the deficit (D v ) depends on the boundary layer separation (laminar or turbulent). Applying linear momentum theory to Equation 4.3, a relation between C d, B t and D v is obtained (Ref. [24]): C d = B t D where C d is the drag coefficient of the strut. ( 1 3 ) 4 D v D v (4.4) 4.4 Steady response The simplest method to calculate rotor load distribution is by calculating the lift coefficient across the span of the blade. In this methodology the blade is characterized as a one-dimensional lifting line. The lift coefficient at every blade element has a linear dependence on the angle of attack as long as the variations are small (thin airfoil theory assumptions). The change in angle of attack at every spanwise location for every azimuthal position is calculated by using Equation 4.3. The following equation calculates change in lift coefficient:

48 35 Cl = Cl α V g V a (4.5) Here V a is the velocity of the airfoil at a given spanwise location and is equal to that spanwise distance times the angular velocity of the rotor. The load distribution obtained by using the lift coefficient will be similar in behavior to the velocity deficit history. Figure 4.3 shows comparison of lift coefficient for a 75% span-wise location on a wind turbine blade which has an upstream tower (Ref. [25]). The dashed line shows the change in lift coefficient calculated by using Equation 4.5. The solid line represents the change in lift coefficient by placing the wind turbine in a wind tunnel. The figure reiterates that the quasi-steady response follows the same behavior as velocity deficit and is symmetric about the center of the wake region. The blade falls in the shadow of the tower at around 90 o azimuthal position which is also the azimuthal position where the blade is at the center of the wake region, hence, the maximum change in lift. From the figure it can be understood that the quasi-steady response does not characterize the loading on the blade well enough. The experimental measurement shows that there is an asymmetry in the response about the center of the wake. The entry is sharp whereas the recovery is slow. Even if the velocity deficit parameters are changed to match the amplitude of the measured maximum change in loading, the shape of experimental response cannot be matched using steady response formulation. Another methodology is required to capture the experimental response. 4.5 Indicial Response The changes in the AoA can be processed to obtain the load distribution and time history. The operations can be performed in both reduced time (s) and reduced frequency (k) domains. The vertical gust that impinges on the rotor contains multiple frequencies. It would require analysis of every possible frequency. So a theory formulated in time domain might be more general and hence more useful (Ref. [23]). One of the fundamental approaches to solving the lift response in the time domain is using the indicial lift response. According to this methodology, if the

49 36 Figure 4.3. Change in C l vs azimuthal angle (blade starts from downward vertical postion) (Ref. [25]) response of the independent variable (AoA or V g ) and the indicial response are known then the response of the dependent variable can be calculated using the Duhamel integral. If the indicial response is φ then the output y(t) can be written using Duhamel s integral as (Ref. [23]): y(t) = f(0)φ(t) + t 0 df φ(t σ)dσ (4.6) dt where σ is a dummy variable for integration in time, and φ is the indicial response. The value of this function must be known for a large number of time steps for accurate evaluation of the output y(t). The calculation of transient lift response on an airfoil entering a vertical gust was first attempted by Küssner (Ref. [23])and completely solved by Von Kármán and Sears (Ref. [23]).

50 37 The vertical gust is described by { 0 : outside strut wake w g (r, t) = V g : inside strut wake Note:- V g has been defined in Equation 4.3. The Küssner function can be used with Duhamel superposition to compute the transient lift response. Cl = Cl α V a w g (0)ψ(s) + s 0 dw g (σ) ds ψ(s σ)dσ (4.7) There is an exponential approximation to Küssner s function ψ(s) given by Sears and Sparks (Ref. [23]): ψ (s) = 1 0.5e 0.13s 0.5e 1.0s (4.8) There is also an algebraic approximation given by Bisplinghoff (Ref. [23]): ψ (s) = In order to evaluate Equation 4.7, w g s 2 + s s s (4.9) and dw g /ds must be known at all time points. The derivative of w g is obtained by differentiating Equation 4.5. The integral can be converted from reduced time (s) to time (t) using equation 4.2. Also the exponential approximation of Küssner response function has been used in this research. The integration was performed using the trapezoidal rule because of its simplicity and reasonable accuracy Comparison of Küssner and Quasi-Steady responses Consider a single blade traveling in the counterclockwise direction from θ = 0 o position (blade vertical and facing down) as shown in Figure 4.4. Although a blade is shown in the figure, for purposes of calculation, the blade is approximated by the line formed by joining quarter chord points. For simplicity it is assumed that the induced velocity is uniform at all span wise locations. From figure 4.4 it can be understood that the blade tip will be at the center of

51 38 Figure 4.4. The blade wake configuration (blade starts from downward vertical postion) the wake region at approximately θ = 90 o azimuthal position. Figure 4.5 shows time history of change in loading using steady and Küssner response methods, for a quarter revolution of the blade centered on the strut wake region. From 225 o to 267 o the blade is not in the wake region. The blade enters the wake after 267 o and is completely submerged in the wake region around 270 degree azimuthal postion. At exactly 270 o it is at the center of the wake region. Then it exits the wake at around 273 o and is not in the influence of the wake region anymore as depicted in the quasi-steady response. In case of the quasi-steady response the variation is symmetric about the center of the wake region and the response exists as long as the blade is in the wake region. This is modeled differently using Küssner s method. Although the peak of the loading change is at 270 degrees (center of wake region), the recovery continues well after the blade leaves the wake region. Both quasi-steady and unsteady response are periodic in nature. Although in case of unsteady response, the periodic nature is obtained after a few revolutions of the blade, which should be the case in practice. Figure 4.6 (Ref. [25]) shows time history of the change in lift coefficient (C l ) using different methods. This example is for a wind turbine which has an upstream tower and the lift coefficient perturbations have been calculated at 75% span for the same flow parameters as shown in Figure 4.3. The important thing to notice in this figure is the contrast in the response from the three sources of

52 39 Figure 4.5. Comparison of steady and Küssner response for a quarter revolution of the blade data. The dashed line represents the quasi-steady method. The dotted line shows lift coefficient from experimental measurement and the solid line represents the lift coefficient from the Küssner response method. The agreement between the Küssner response and experimental data is significantly better than the agreement quasi-steady response and experimental data. The recovery part of the Küssner response (azimuthal angle around 95 degrees to 180 degrees, see figure 4.6) does not quite match up to the experimental response in magnitude probably because the velocity deficit parameters (D v, B t ) were not appropriately chosen. But, in general, the Küssner response agrees well with the experimental measurements and is used in the following calculations to predict noise. The predictions in the unsteady loading model are sensitive to specification of the wake characteristics (B t and D v ). Velocity deficit varies from 10% to 30% of the freestream value. The strut wake width depends on the type of boundary layer separation. Hence to make a prediction, all possible combinations must be calculated and a worst case scenario must be predicted.

53 40 Figure 4.6. Lift coefficient history (Ref. [25]) 4.6 Input to PSU - WOPWOP The unsteady loading is obtained using the Küssner response. The next step is to calculate noise from these unsteady sources. The Ffowcs Williams - Hawkings equation will be used to calculate noise although the equation will be solved with Farassat s 1A formulation (refer Chapter 2 for details). The loading acoustic pressure term in this formulation is evaluated. The data surface for the calculation is a compact patch. There is no thickness hence thickness noise will not be calculated. For the loading noise calculation, coordinates of grid points, unit normals at those points and loading vectors at those points are required. There is a format for creating geometry and loading files as input to PSU-WOPWOP. For details refer to the PSU-WOPWOP manual (Ref. [15]). The effects of the parameters (like D v,b t etc.) on unsteady loading noise for a given rotor configuration will be presented in Chapter 5. In the rest of this section an example showing various parts of the unsteady noise calculation procedure will be presented. Figure 4.7 shows the unsteady loading history of a blade in the rotor. Notice

54 41 Figure 4.7. Loading history. PSU - WOPWOP input the difference in loading history at the hub and at the blade tip. Undoubtedly the maximum variation in loading increases from hub to tip. The points closer to the tip travel the fastest through the wake region. Hence the width of the loading signal at the tips is the smallest and at the hub it is highest. Also loading L = C l ( 1 2 ρv 2 a ) is dependent on the square of the airfoil velocity. Hence, the loading is higher at the blade tips. Figure 4.8 shows the time history of acoustic pressure over a single revolution. The blade passes the strut wake twice in one revolution. pulses in acoustic pressure. Hence there are two Figure 4.6 shows the Sound Pressure Level (SPL) as a function of frequency. Note that only the peaks are of importance in this figure. The peaks represent sound pressure levels at the blade passage frequency and its harmonics. The spectrum is broad and the SPL increases slightly first and then decreases gradually. This is for a single blade. When there are multiple blades and struts the scenario is different as will be explained in the next chapter.

55 42 Figure 4.8. Acoustic Pressure History. PSU - WOPWOP output These figures are only representative of the procedure involved in the calculation. They are not related to an actual configuration. The important thing to be noted here is that as long as the blade hub duct configuration is unaltered,the change in noise levels due to the upstream struts is calculated in a short time as compared to full scale CFD calculations. Typically it takes fifteen minutes on a single processor depending on the number of blades, number of struts, number of spanwise points and number of azimuthal points over the revolution of the blades. The potential of this method has been demonstrated and this method can be a preliminary design tool for acoustic based analyses. The main results for steady and unsteady loading are in the next chapter where impact of each parameter, grid points and configuration changes will be studied.

56 Figure 4.9. SPL(dB) vs frequency. PSU - WOPWOP output 43

57 Chapter 5 Ducted fan noise results This chapter contains the aerodynamic and acoustic results of the ducted fan configuration (Figure 3.1(b)). The sound field for the individual sources and total is discussed in detail in this chapter. The ducted fan developed by Drs. Akturk and Camci is as shown in the Figure 5.1. The important parameters used for the calculation are described in Table 5.1. Figure inch Ducted Fan In Table 5.1 tip clearance refers to the gap between the blade and the duct and is expressed as a percentage of duct inner radius. The blade position is expressed as a percentage of duct chord length measuring from the duct leading edge. The maximum velocity deficit (D v ) and wake width (B t ) parameters are expressed as a range. The wake width is expressed in percentage of blade chord in the range

58 45 Table 5.1. Parameters used in the unsteady analysis. Calculations were performed by varying wake width and velocity deficit in their respective range as shown in the table. Induced velocity is obtained from the ANSYS CFX calculation. Tip clearance 1.71% 3.04% Induced velocity (v i ) m/s m/s Angular velocity (Ω) 2400 rpm 2400 rpm tip Mach number (M) wake width (Bt) 20%c - 40%c 20%c - 40%c Velocity deficit(d v ) tip radius (R t ) m m hub radius (R h ) m m blade chord (c) m m duct chord m m blade position 27.73% 27.73% of 20% to 40%. Calculations have been performed for various combinations of velocity deficit and wake width values. Although the change in the induced velocity for different tip clearances is not large, there is a marked change in the pressure distribution on both blade and duct. This will result in different duct loading noise levels. This is explained in detail in Section Sources of noise from steady CFD In Chapter 3 it was explained that the noise from steady sources is computed by using the CFD calculation as an input. The sources arise from blade motion and the pressure distribution of the blades and duct surfaces. The pressure distribution on the blade remains steady but the blade itself is moving at the angular velocity of the rotor. The noise from the blade is obtained by rotating the blade surface in PSU-WOPWOP. This noise arises from acceleration (with respect to ground) of the blade (thickness noise) and movement of the blade and the forces acting on it (loading noise). The portion of the duct that falls in the rotational part of the computational domain (Chapter 3) can generate noise because of the rate of change of pressure. But the CFD data provides the pressure distribution for only a snapshot. The

59 46 noise from duct is calculated by rotating this particular portion of the duct that falls in the rotational part of the computational domain. The flow field in this part of the duct is steady in the frame of reference attached to the blade. Hence in order to compute this noise the steady solution of duct with respect to blade rotates at the same rpm as the blade. Note that the loading noise generated by the duct is the sum of the scattered signals of both thickness noise and loading noise from the rotor blades. Figure 5.2. Steady observer grid Figure 5.2 shows the observer grid used for calculating the noise levels from the individual sources in the steady configuration. Figure 5.3 shows the OASPL (db) due to steady rotational sources: thickness, blade loading and duct loading. A small observer grid is chosen for the calculation because the noise levels are low (less than 40 db) outside this region. The blade loading noise directivity extends slightly more in the axial direction as compared to thickness noise. This might be expected because blade loading is typically dominant in axial direction. The duct loading noise is slightly more intense in the radial direction than the other noise sources. Total noise in the figure is the sum of thickness, blade loading and duct loading noise. It is not very different from the individual sources and the noise levels are low. The fact that the levels are very similar to the component sources indicates that the sources are coherent in nature and there is neither complete constructive or destructive interference. The effect of tip clearance on noise levels

60 47 Figure 5.3. Contributions of various steady noise sources: OASPL comparison is studied in the next section Effect of tip Clearance on noise Two tip clearances are used in this study (1.71% and 3.04%). Figure 5.4 shows OASPL for the two tip clearances. The thickness noise for both tip clearances should be essentially the same since the blade geometry variation is not significant. The only difference is that the blade length is more in the 1.71% tip clearance case. The most noticeable difference in the two computations is the difference between the loading noise due to the duct. The rotating part of the duct contributes to this noise. This is a region that is just below the duct lip and extends until just above the duct trailing edge as explained in Chapter 3. In this region of the duct the loading changes drastically in the direction of rotation of the blade. When the blade is at the same azimuthal position as that of a point on the duct, the pressure at that point on the duct is low. As we move away from the blade in the direction of rotation, the pressure increases and reaches a maximum value (for that axial location) at midway between this blade and the next blade. The loading noise is generated because there is a fluctuation in pressure as the blades pass and leave. This magnitude of fluctuation is higher for the lower tip clearance

61 48 Figure 5.4. OASPL Comparison for different tip clearances configuration. This might be the reason for the higher duct loading noise. The difference though is not substantial and hence the total noise is nearly the same for the two configurations. 5.2 Scattering of Unsteady loading noise The presence of a body like a fuselage or sphere in an acoustic field can distort the directivity and amplitude of that field. This happens to the greatest extent if the wavelength of the incident wave is comparable or less than the dimensions of the scattering body. This means scattering should be expected to occur primarily in the high frequency range. The acoustic scattering calculations for incident unsteady loading noise have been performed by Dr. Seongkyu Lee. The calculations were made using the TIMES code developed at Penn State by Dr. Lee (Ref. [26]). The TIMES code

62 49 Figure 5.5. The duct used for scattering analysis requires the acoustic pressure gradient distribution on the scattering body. This input data is computed by PSU-WOPWOP, which in turn takes the geometry and loading data from unsteady loading code (Chapter 4). For the scattering study, a generic ducted fan configuration was used. The duct used in the scattering analysis is a body of revolution of NACA 0012 airfoil as shown in the Figure 5.5. The parameters used in the calculation are described in Table 5.2. A single blade analysis was performed because increasing the number of blades leads to higher frequencies, which makes the scattering problem computationally more challenging. This is avoided because at present a trend and a qualitative description of the noise is sought. Tip Mach number 0.2 Number of blades 1 Radius of the blade m Tip clearance 6% of blade radius Angular velocity of rotor 631 radians/second Blade passage frequency Hz Induced velocity m/s Maximum velocity deficit 0.41 Diameter of strut m (0.698 of blade chord) Wake region diameter m (1.29 of blade chord) Table 5.2. Parameters used in scattering analysis Figure 5.6 shows SPL contours of the incident and total fields displayed on an

63 50 observer grid plane that passes through the rotor rotational axis. The SPL plots are for individual frequencies corresponding to wavelengths which are 2L, L, and 2L/3 respectively. Here L is the chord of the duct. The frequencies considered in the analysis are relatively high compared to the BPF. The axis of rotation of the rotor is the Z-axis in the figure and the flow direction is from the left to the right. The position of the ducted rotor configuration has been indicated in the plots by a black block. For the wavelength twice the duct chord (Figure 5.6(a)) the noise levels of the incident field are dominant along the axis of rotation. This is the trend in unsteady loading noise (Section 5.4). The incident and the total field noise levels are nearly the same over the observer grid,which indicates very little scattering. This is also the case for the other wavelengths. Apart from the change in noise levels near the plane of the rotor, there is not a significant change in either the noise levels or the directivity. This behavior may be attributed to direction of loading vectors which are along the axis of rotation. If a scattering body existed along the rotor axis the results may have been different. So in the current problem since the change in noise levels due to scattering of unsteady loading is small it is being excluded in the rest of the thesis. 5.3 Total Noise In this chapter so far the steady sources of noise and the scattering from unsteady loading noise has been presented. In this section the total noise due to both steady and unsteady loading is presented. As explained in the previous section (Section 5.2) the scattering from unsteady noise will not be included in this calculation. After looking at total noise the various parameters affecting the unsteady loading noise calculation will be explained. The total noise results have been obtained using the 22 inch ducted fan of Akturk (Ref. [21]). Throughout the thesis this configuration is used for all calculations except for the scattering of unsteady loading noise. Figure 5.7 shows the observer grid used for comparing steady, unsteady and total noise. The corresponding OASPL contours are shown in Figure 5.8. The steady calculation is for the 1.71% tip clearance configuration. The velocity deficit

64 51 (a) λ/l = 2 (b) λ/l = 1 (c) λ/l = Figure 5.6. Comparison of Incident and Scattered SPL for the unsteady calculation is Dv = 0.4 and wake deficit is Bt = 20%c where c is blade chord. Some important points from this calculation. In the near field around 1.5R the dominant noise source is the steady noise. In the rest of the acoustic field the unsteady loading noise completely dominates. The highest levels of noise are towards the rotor axis.

65 52 Figure 5.7. Observer grid for steady, unsteady and total noise comparison. This result leads to a greater investigation of unsteady loading noise. It is very important to know the factors influencing both the source and radiation of unsteady loading noise. The next section demonstrates the influence on various unsteady loading parameters on the noise levels. 5.4 Unsteady loading noise Unsteady loading noise arises from the unsteady loading on the blade due to the presence of upstream obstructions as explained in Chapter 4. The factors affecting unsteady loading noise are examined in this section. The effect of a parameter on the noise levels is observed by varying that parameter and keeping others constant. This study consists of two sections. In Section grid studies are performed. The grid spatial and temporal sizes are varied, and the effect on calculation is examined. Section consists of parametric studies on wake width, velocity deficit and number of struts Resolution study In order to measure the effects of velocity deficit(d v ) and wake width (Bt) accurately, the influence of radial and temporal step sizes must be known. In this

66 53 Figure 5.8. Overall sound pressure level of steady, unsteady and total noise section the effects of step sizes on blade loading, acoustic pressure and Sound Pressure Levels is examined Spatial Resolution In this analysis, noise calculations are performed for the radial step sizes 0.1R, 0.04R and 0.02R where R is the radius of the blade. Figure 5.9 shows the Sound Pressure Level (SPL) vs blade passage frequency (BPF) for the radial step sizes considered. The observer location is on the axis of rotation at a distance of twice the rotor radius (2R). The changes in SPL occur at higher harmonics. The changes are of the order of 3-4 db. Since the SPL at these harmonics is smaller than the fundamental by around 30 db it is not important to the OASPL. Hence a high resolution radial grid is not required for these acoustic

67 54 Figure 5.9. Effect of radial step size on SPL calculations Temporal In this section, the effect of temporal step size on noise calculations is examined. The temporal step sizes considered in the analysis are 1.5, 3 and 6 timesteps per degree of revolution. Figure 5.10 shows blade loading history, acoustic pressure time history and SPL vs blade passage frequency harmonics (NBPF). The blade loading history shown in Figure 5.10(a) is for the tip of the blade. The temporal step size affects the rotor loading near it s peak (for a blade azimuth of 90 0 ). The loading at the peak has decreased by about 1 N/m for the 6 timesteps per degree of revolution case. Apart from that, the blade loading history is approximately same for the different temporal resolutions. The observer location for acoustic calculations is a point on the rotor axis at a distance of 2R from the rotor hub. Figure 5.10(b) shows a 1 Pa change in the acoustic pressure at 0.002s for the 1.5 timesteps per degree of revolution case. This change can affect the SPL at higher frequencies. So in order to ascertain its importance there is a need to look at the SPL for each blade passage frequency. Figure 5.10(c) shows SPL vs blade passage frequency number (NBPF). The sen-

68 55 (a) blade loading vs azimuth (b) Loading acoustic pressure time history (c) SPL vs harmonics Figure Effect of azimuthal step size on Unsteady loading, Acoustic pressure and Sound Pressure Level. 1.5, 3 and 6 are the number of timepoints per degree of revolution. sitivity of SPL is higher for changes in temporal resolution as compared to the changes in spatial resolution. The changes occur for harmonics greater than 15. At these higher frequencies, the SPL is around 30 db lower than the fundamental blade passage frequency. So these changes do not substantially affect the OASPL. The important point to note from this analysis is: the 3 timesteps per degree of revolution are good for acoustic calculations. From this analyses it can be inferred that 3 timesteps per degree of revolution and 11 points per blade length are sufficient for acoustic calculations.

69 Parametric studies In this section the effects of the parameters of unsteady loading on noise levels will be examined. The observer positions are located at a distance of 2R from the blade hub at azimuthal positions 15, 45 and 90, as shown in Figure Figure Observer positions for parametric studies The parameters that are changed are wake width, velocity deficit, number of struts and tip clearance. The noise calculations are performed in the following sections by changing one of the parameters while keeping others constant Varying wake width As explained in Chapter 4, wake width is the breadth of the rectangular wake region that falls on the rotor disk. Points on the blade go through the width of the wake region, experiencing a deficit in velocity. Figure 5.12 shows the velocity deficit time history at the blade tip. Notice the difference in wake width for the two cases. This width determines the wavelength of blade loading which in turn impacts the SPL distribution across various harmonics. Three wake widths are examined : 20%, 30% and 40% c, where c is the chord length. The observer locations considered for the comparison are 15 o, 45 o and 90 o, as shown in Figure Figure 5.13 shows SPL vs frequency for the three observer

70 57 Figure Velocity deficit azimuthal history for 20%c and 40%c wake widths locations. The SPL increases as the observer azimuthal position increases from 15 o to 90 o. This is expected because noise levels are highest along rotor axis and lowest in plane. For the harmonics near the fundamental frequency the SPL is highest for the 40% c case. A closer look at the SPL plot shows that the SPL distribution itself changes with varying wake width i.e., the wider wake width(40%c) has higher SPL at the initial harmonics (1 to 10). In case of the 20%c wake width, the SPL exceeds its wider wake width counterparts at harmonics greater than 10. The increased SPL at higher harmonics may not be desirable because human hearing is more sensitive in this frequency range Varying velocity deficit In this section the effect of velocity deficit (D v ) on noise levels will be calculated. The velocity deficits considered in the analysis are 0.2, 0.3 and 0.4 because these are the commonly occurring deficits obtained from experimental studies (Ref. [24]).The observer location is 2R from the hub on the axis of rotation. Figure 5.14 shows acoustic pressure over 1/8 th of the time period (T). There are 8 blades and the periodicity of the signal is 8. In this figure the acoustic pressure changes in amplitude with velocity deficit, and the wavelength of the

71 58 (a) 2R, 15 0 (b) 2R, 45 0 (c) 2R, 90 0 Figure SPL vs Frequency for varying wake width acoustic pulse remains the same across the three deficits (D v ). The difference in SPL across velocity deficits at a given frequency is constant as shown in Figure The SPL difference across deficits is not maintained for frequencies above 26 BPF (8320 Hz). This is possibly due to numerical issues related to higher frequency calculations. For accurate SPL at higher frequencies, a highly resolved acoustic pressure signal is required. But for practical purposes, the frequencies that differ from the fundamental frequency by around 20 db can be safely ignored. This is a very important result because the design of a strut has direct impact on the noise levels, unlike the wake width in the previous section. Figure 5.16 shows OASPL contours for combinations of 2 velocity deficits (0.2 and 0.4) and wake widths (20% c and 40% c ). Please note that an increase in either the wake width or the velocity deficit results in a nearly global increase in the OASPL, especially closer to the axis of rotation of the rotor. OASPL

72 59 Figure Effect of Velocity Deficit (D v ) on Acoustic Pressure Figure Effect of Velocity Deficit (D v ) on SPL emphasizes the highest amplitude harmonics, which are the lowest frequencies in these computations; hence, the impact of changes in the higher harmonics is not evident in the figure. The noise directivity does not change significantly when the wake width or velocity deficit amplitude are changed - only noise levels are effected.

73 60 Figure Effect of wake width on OASPL Multiple struts In this section the number of struts is varied. All the struts are placed parallel to one another. Each upstream strut generates a wake which is modeled in this study. The change in SPL for the three different strut configurations is examined. All other parameters such as wake width and velocity deficit, are kept constant. (a) 1 Strut (b) 2 Strut (c) 3 Strut Figure Strut configurations of the ducted rotor. The rectangles represent wake regions. The dashed line is a blade. Figure 5.17 shows the various configurations used in the analysis. In this figure, the dashed line represents the rotor at one azimuthal angle and the sets of two parallel lines represents the struts. A single strut, 2 strut and 3 strut configurations were considered. The single strut passes through the center of the rotor disk and