The Pennsylvania State University. The Graduate School. College of Engineering IMPLEMENTATION OF BLADE ELEMENT THEORY IN

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering IMPLEMENTATION OF BLADE ELEMENT THEORY IN CFD ANALYISIS OF EDGEWISE DUCTED FAN VEHICLES A Thesis in Aerospace Engineering by Jason M. Halwick 2012 Jason M. Halwick Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2012

2 The thesis of Jason M. Halwick was reviewed and approved* by the following: Dennis K. McLaughlin Professor of Aerospace Engineering Thesis Co-Advisor Jules W. Lindau Head, Adv. Fluid-Thermal Modeling Dept. Applied Research laboratory Thesis Co-Advisor George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT Ducted fans have received renewed interest in recent years for a variety of potential missions including both civil and military STOVL applications. The design of these vehicles includes many challenges related to the influence of the ducts. Considered in this work, is a dual ducted fan vehicle in edgewise forward flight. This class of vehicle has been shown to exhibit significant separation over the ducts, causing distortion of the rotor inflow and performance. Current methods of modeling the flow field around these vehicles and their performance have proven to be lacking in regards to a design environment. High fidelity, unsteady solution methods are far too computationally and time expensive while simplified actuator disk models fail to incorporate the necessary physics of the shrouded rotor. To alleviate these problems, a computational method which couples a momentum source CFD code to a blade element theory rotor performance prediction code has been developed and validated. The coupled method was shown to have adequately resolved the dominate flow field phenomena in and around the ducts of the model, in particular the recirculatory, separation region over the front duct. Good agreement with experiment was found in the characteristics of both the inflow and outflow of the front fan in forward flight. The aerodynamic force predictions demonstrated the ability to adequately predict performance at low forward speeds and hover. At the highest advance ratio of 0.24, however, the prediction under-predicted lift by 30%. While, the coupled method was able to outperform the simplified momentum source approach and converge to a solution faster than a fully resolved rotor solution, improvements can be made. A more precise rotor model is required to improve the accuracy of the performance prediction. This is supported by the sensitivity of the coupled method solution to the lift and drag coefficients of the airfoil section used. A strong correlation was found between sectional lift data utilized by blade element theory and the resulting coupled method lift predictions.

4 iv TABLE OF CONTENTS LIST OF FIGURES... vi LIST OF TABLES... xi NOMENCLATURE... xii ACKNOWLEDGEMENTS... xiv Chapter 1 Introduction Background Current Modeling Methodology Objectives Thesis Overview... 5 Chapter 2 Description of Model Wind Tunnel Model PSU D1A Fuselage Rotors Computational Model CAD Model Momentum Source Mesh Rotor Model Fully Resolved Rotor Mesh Chapter 3 Overview of Previous Work Wind Tunnel Experiments Hover Forward Flight Computations Momentum Source Calculations Fully Resolved Rotor Comparison of Experiment and CFD Chapter 4 Computational Approach Review of Blade Element Momentum Theory Momentum Theory Blade Element Theory Blade Element Momentum Theory Coupling BET to CFD Obtaining Inflow Velocities from CFD Calculating Rotor Forces Formatting Forces for CFD Definition of Residual... 60

5 v Chapter 5 Results of Coupled Solution Validation of BET Coupled BET-CFD Solutions Flow Field Results Force Results Convergence Comparison to Previous Work Flow Field Comparison Force Comparison Sensitivity of Solutions to Airfoil Properties Use of NACA Use of NACA C L Dependence C d Dependence Chapter 6 Summary and Conclusions Dual Ducted Fan Model Coupled BET-CFD Method Development and Validation Sensitivity of the Computational Solution Suggestions for Future Work References Appendix A Airfoil Data A.1 Airfoil Coordinates A.2 Airfoil Lift & Drag Coefficients Appendix B Rotor Measurements Appendix C Codes C.1 Blade Element Momentum Theory MATLAB Code C.2 InterpFormat FORTRAN Code C.3 Blade Element Theory Code C.3.1 Input Files C.3.2 Blade Element MATLAB Code C.4 Force Relaxation MATLAB Code C.5 Body Force Format FORTRAN Code

6 vi LIST OF FIGURES FIGURE 1-1:HONEYWELL T-HAWK MICRO AIR VEHICLE (MAV) (2)... 2 FIGURE 1-2: DUCTED FANS EMPLOYED FOR LIFT PRODUCTION... 2 FIGURE 2-1 MODEL PSU D1A: (A) ISOMETRIC VIEW, (B) TOP VIEW, (C) SIDE VIEW... 9 FIGURE 2-2: MA 10X7 ROTOR GEOMETRY: (A) CHORD DISTRIBUTION, (B) MAX THICKNESS DISTRIBUTION, (C) TWIST DISTRIBUTION FIGURE 2-3: CAD MODEL OF PSU D1A: (A) TOP VIEW, (B) SIDE VIEW, (C) ISOMETRIC VIEW FIGURE 2-4: AIRFOIL SECTION USED IN CAD MODEL FIGURE 2-5: MOMENTUM SOURCE OVERSET MESH: (A) SLICE THROUGH HORIZONTAL PLANE, (B) SLICE THROUGH VERTICAL PLANE, (C) FUSELAGE SURFACE MESH FIGURE 2-6: MOMENTUM SOURCE MESH, MODEL IN HAMMOND WIND TUNNEL FIGURE 2-7: AIRFOIL COMPARISON: D1A ROTOR AND GOE FIGURE 2-8: BLENDED AIRFOIL SECTION PROPERTIES FOR RE = 70,000: (A) LIFT COEFFICIENT, (B) DRAG COEFFICIENT FIGURE 2-9: MA 10X5 MOD.A ROTOR MODEL PROPERTIES: (A) LOCAL CHORD DISTRIBUTION, (B) LOCAL PITCH DISTRIBUTION FIGURE 2-10: FULLY RESOLVED ROTOR MESH: (A) SURFACE MESH, (B) TOP VIEW, (C) FRONT ROTOR FIGURE 3-1: EXPERIMENTAL MEASUREMENT LOCATIONS WITHIN FRONT DUCT FIGURE 3-2: EXPERIMENTAL COORDINATE SYSTEM FIGURE 3-3: INFLOW & OUTFLOW VELOCITY MAGNITUDES IN FRONT DUCT IN HOVER FIGURE 3-4: LIFT IN HOVER FOR A RANGE OF RPM FIGURE 3-5: SEPARATION OVER FRONT DUCT LIP ALONG THE CENTERLINE, -10 ANGLE OF ATTACK, ADVANCE RATIO OF

7 vii FIGURE 3-6: SEPARATION OVER FRONT DUCT LIP ALONG THE CENTERLINE, -10 ANGLE OF ATTACK, ADVANCE RATIO OF FIGURE 3-7: INFLOW VELOCITY MAGNITUDES IN FRONT DUCT AT A WIND TUNNEL SPEED OF 6.1 M/S FIGURE 3-8: INFLOW VELOCITY MAGNITUDES IN FRONT DUCT AT A WIND TUNNEL SPEED OF 10.7 M/S FIGURE 3-9: OUTFLOW VELOCITY MAGNITUDES IN FRONT DUCT AT A WIND TUNNEL SPEED OF 6.1 M/S FIGURE 3-10: OUTFLOW VELOCITY MAGNITUDES IN THE FRONT DUCT AT A WIND TUNNEL SPEED OF 10.7 M/S FIGURE 3-11: EXPERIMENTAL FORCES FOR RANGE OF WIND TUNNEL VELOCITIES, (A) LIFT, (B) DRAG FIGURE 3-12: MOMENTUM SOURCE PRESSURE AND VELOCITY CONTOURS AT 18.3 M/S, 6000 RPM, 0 ANGLE OF ATTACK: (A) FUSELAGE SURFACE STATIC PRESSURE, (B) DOWNSTREAM VELOCITY FIGURE 3-13: MOMENTUM SOURCE PRESSURE CONTOURS ON VERTICAL SYMMETRY PLANE AT 18.3 M/S, 6000 RPM: (A) STATIC PRESSURE CONTOUR, (B) TOTAL PRESSURE CONTOUR WITH PARTICLE PATHS FIGURE 3-14: MOMENTUM SOURCE CALCULATED FORCES: (A) TOTAL LIFT, (B) NET DRAG FIGURE 3-15: INSTANTANEOUS VIEW OF FULLY RESOLVED STATIC PRESSURE SURFACE CONTOURS AT 18.3 M/S, 6000 RPM, 0 ANGLE OF ATTACK: (A) TOP VIEW, (B) BOTTOM VIEW FIGURE 3-16: FULLY RESOLVED ROTOR CALCULATION VERTICAL FORCE TIME HISTORY FIGURE 3-17: COMPARISON OF MOMENTUM SOURCE AND FULLY RESOLVED CALCULATED FORCES: (A) TOTAL LIFT, (B) NET DRAG FIGURE 3-18: FLOW FIELD COMPARISON FOR ADVANCE RATIO OF 0.24: (A) SMOKE WIRE FLOW VISUALIZATION AT -10 ANGLE OF ATTACK, (B) MOMENTUM SOURCE TOTAL PRESSURE CONTOUR ON VERTICAL SYMMETRY PLANE AT -5 ANGLE OF ATTACK FIGURE 3-19: TOTAL LIFT COMPARISON FOR EXPERIMENT AND CFD FIGURE 3-20: NET DRAG COMPARISON FOR EXPERIMENT AND CFD... 44

8 viii FIGURE 4-1: BASIC APPROACH TO CFD BET COUPLING FIGURE 4-2: HOVER ROTOR SLIPSTREAM (23) FIGURE 4-3:BLADE ELEMENT DIAGRAM FIGURE 4-4: COUPLED BET-CFD BLOCK DIAGRAM FIGURE 4-5: VELOCITY INTERPOLATION BLOCK DIAGRAM FIGURE 4-6: BLADE ELEMENT THEORY CODE BLOCK DIAGRAM FIGURE 4-7: FORCE RELAXATION CODE BLOCK DIAGRAM FIGURE 4-8: BODY FORCE FORMAT CODE BLOCK DIAGRAM FIGURE 5-1: BEMT INDUCED INFLOW OVER NON-DIMENSIONAL RADIUS, WITHOUT TIP LOSS FIGURE 5-2: HOVER SIMULATION WITHOUT TIP LOSS FOR 6000 RPM: (A) INFLOW VELOCITY MAGNITUDE, (B) THRUST DISTRIBUTION FIGURE 5-3: BEMT INDUCED INFLOW OVER NON-DIMENSIONAL RADIUS, WITH TIP LOSS FIGURE 5-4: HOVER SIMULATION WITH TIP LOSS FOR 6000 RPM: (A) INFLOW VELOCITY MAGNITUDE, (B) THRUST DISTRIBUTION FIGURE 5-5: STATIC PRESSURE COEFFICIENT CONTOURS ON VERTICAL SYMMETRY PLANE FOR 6000 RPM, 0 ANGLE OF ATTACK, (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-6: TOTAL PRESSURE COEFFICIENT CONTOURS ON VERTICAL SYMMETRY PLANE FOR 6000 RPM, 0 ANGLE OF ATTACK: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-7: VELOCITY MAGNITUDE CONTOURS ON HORIZONTAL PLANE ABOVE ROTOR PLANE FOR 6000 RPM, 0 ANGLE OF ATTACK: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S (D) 18.3 M/S FIGURE 5-8: BLADE ELEMENT LOCAL ANGLE OF ATTACK (DEG.) FOR 6000 RPM: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S (D) 18.3 M/S... 75

9 ix FIGURE 5-9: BLADE ELEMENT NON-DIMENSIONAL DISCRETIZED THRUST OVER ROTOR DISK FOR 6000 RPM: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-10: NON-DIMENSIONAL, VOLUMETRIC THRUST INPUT INTO CFD FOR 6000 RPM: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-11: NON-DIMENSIONAL, VOLUMETRIC FORCE IN X DIRECTION INPUT INTO CFD FOR 6000 RPM: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-12: NON-DIMENSIONAL, VOLUMETRIC FORCE IN Y DIRECTION INPUT INTO CFD FOR 6000 RPM: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-13: FORCES ON MODEL CALCULATED BY COUPLED METHOD AT 6000 RPM, 0 VEHICLE ANGLE OF ATTACK FIGURE 5-14: FORCE HISTORY FOR COUPLED METHOD SOLUTIONS: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-15: RESIDUALS FOR COUPLED METHOD SOLUTIONS: (A) HOVER, FORWARD SPEEDS: (B) 6.1 M/S, (C) 10.7 M/S, (D) 18.3 M/S FIGURE 5-16: LOW SPEED FLOW FIELD COMPARISON: (A) SMOKE WIRE VISUALIZATION, Μ=0.065, -3 AOA, (B) TOTAL PRESSURE CONTOUR, Μ=0.08, 0 AOA FIGURE 5-17: HIGH SPEED FLOW FIELD COMPARISON: (A) SMOKE WIRE VISUALIZATION, Μ=0.24, -10 AOA, (B) TOTAL PRESSURE CONTOUR, Μ=0.24, 0 AOA FIGURE 5-18: INFLOW VELOCITY MAGNITUDE COMPARISON IN FRONT DUCT FOR 6000 RPM, 6.1 M/S WIND TUNNEL SPEED FIGURE 5-19: OUTFLOW VELOCITY MAGNITUDE COMPARISON IN FRONT DUCT FOR 6000 RPM, 6.1 M/S WIND TUNNEL SPEED... 90

10 x FIGURE 5-20: EXPERIMENTAL AND COUPLED CFD FLOW ANGULARITY COMPARISON FOR 6000 RPM, 6.1 M/S WIND TUNNEL SPEED: EXPERIMENTAL VECTORS IN GREEN, CFD IN BLUE & RED FIGURE 5-21: LIFT RESULT COMPARISON TO PRIOR WORK FIGURE 5-22: DRAG RESULT COMPARISON TO PRIOR WORK FIGURE 5-23 NACA 4412, GOE 527 AIRFOIL COMPARISON FIGURE 5-24 AIRFOIL PROPERTY COMPARISONS, NACA 4412 & GOE 527, RE=70,000: (A) LIFT COEFFICIENT, (B) DRAG COEFFICIENT FIGURE 5-25: LIFT SENSITIVITY, NACA 4412, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-26: DRAG SENSITIVITY, NACA 4412, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-27: NACA 4314, GOE 527 AIRFOIL COMPARISON FIGURE 5-28: AIRFOIL PROPERTY COMPARISON, NACA 4314 & GOE 527: (A) LIFT COEFFICIENT, (B) DRAG COEFFICIENT FIGURE 5-29: LIFT SENSITIVITY, NACA 4314, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-30: DRAG SENSITIVITY, NACA 4314, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-31: LIFT COEFFICIENT COMPARISON, C L DEPENDENCE FIGURE 5-32: LIFT SENSITIVITY, C L DEPENDENCE, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-33: DRAG SENSITIVITY, C L DEPENDENCE, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-34: DRAG COEFFICIENT COMPARISON, C D DEPENDENCE FIGURE 5-35: LIFT SENSITIVITY, C D DEPENDENCE, 6000 RPM, 0 ANGLE OF ATTACK FIGURE 5-36: DRAG SENSITIVITY, C D DEPENDENCE, 6000 RPM, 0 ANGLE OF ATTACK

11 xi LIST OF TABLES TABLE 2-1: DUAL DUCTED FAN DESIGN PARAMETERS... 8 TABLE 2-2: MOMENTUM SOURCE CFD SPECIFICATIONS TABLE 2-3: FULLY RESOLVED ROTOR MESH SPECIFICATIONS TABLE 3-1: EXPERIMENTAL MEASUREMENT LOCATIONS WITHIN FRONT DUCT TABLE 5-1: COMPARISON OF BET HOVER THRUST AND EXPERIMENTAL LIFT RESULTS AT 6000 RPM TABLE A-1: GOE 527 AIRFOIL COORDINATES TABLE A-2: PSU D1A AIRFOIL COORDINATES TABLE A-3: NACA 4412 AIRFOIL COORDINATES TABLE A-4: NACA 4314 AIRFOIL COORDINATES TABLE A-5: BLENDED LIFT AND DRAG COEFFICIENTS, RE=7E TABLE A-6: BLENDED AIRFOIL COEFFICIENTS, RE=7E4, MODIFIED DRAG TABLE A-7 NACA 4412 AIRFOIL COEFFICIENTS, RE=7E TABLE A-8: NACA 4314 AIRFOIL COEFFICIENTS, RE=7E TABLE B-1: MASTER AIRSCREW 10X5 ROTOR MODEL TABLE B-2: MASTER AIRSCREW 10X7 ROTOR MEASUREMENTS TABLE B-3: MASTER AIRSCREW 10X5 MOD. A ROTOR MODEL

12 xii NOMENCLATURE Rotor Area Rotor Far Wake Area Center Body Length Blade Element Momentum Theory Blade Element Theory Section Drag Coefficient Section Lift Coefficient Static Pressure Coefficient c BET Local Blade Chord Duct Chord Computer Aided Design Computational Fluid Dynamics Drag Duct Diameter Force Vertical Force Max Thickness of Fuselage Center-Body Along the Centerline of the Model Overall Max Thickness of Fuselage Center-Body Lift Mass Flux Number of Blades Number of Azimuthal Positions Number of Radial Positions Rotor Radius Radial Position

13 xiii Root-Mean-Square-Deviation Rotor Slipstream Surface Thrust Duct Thickness BET Local Relative Total Velocity BET Local Relative Vertical Velocity BET Local Relative Tangential Velocity Unmanned Aerial Vehicle Velocity Vector Induced Velocity Wind Tunnel Velocity Work Rotor Far Wake Velocity Body Fixed X-axis Body Fixed Y-axis Body Fixed Z-axis α θ μ ρ φ ψ BET Local Angle of Attack BET Local Pitch Angle Advance Ratio Air Density BET Local Inflow Angle Azimuthal position

14 xiv ACKNOWLEDGEMENTS Above all I would like to thank my family, especially my parents, Allison & Mike, and my brother Ryan, for their endless support and encouragement. They have inspired me to achieve my goals and more. I would like to express my gratitude toward my advisor Dr. McLaughlin for giving me the opportunity to work on this project. With his guidance I have developed skills and knowledge that will stay with me throughout my career. I would also like to thank my thesis co-advisor, Dr. Lindau, for his assistance and support. Without his expertise this thesis would not have been possible. Also deserving recognition are my officemates and friends, Leighton El Monty Myers, Kevin Chit Chat Brennan, Brian the Ginger Wallace, Kylie Home Dawg Flickinger and Russell Graduated Third in the Class Powers 1, who have helped keep me sane when sanity was scarce. Whether it was bouncing ideas off of them, learning from their expertise or providing me a therapeutic distraction, their friendship has been invaluable. 1 List is comprised of officemates at time of thesis writing. Listing is in geographical order and does not indicate or imply varying levels of friendship. List of friends is not exclusive. If you feel your name should appear then please add in available space, nickname required. Results may vary. Restrictions may apply.

15 For the Glory of Old State

16 1 Chapter 1 Introduction 1.1 Background Interest in the benefits of shrouding a rotor and the optimization of their design stems back to the first half of the previous century (1). This propulsor configuration seeks to obtain an augmentation of the thrust of a rotor by taking advantage of the induced velocity field and forcing it through a duct or annular airfoil. The use of shrouded rotors or ducted fans has attracted interest for a wide range of uses in both commercial and military applications. Modern applications of ducted fans include helicopter anti-torque devices, referred to as fantails or fenestrons, and a myriad of UAVs (Unmanned Aerial Vehicles) intended for military use. These vehicles employ ducted fans to take advantage of several characteristics unique to this rotor configuration. Ducted fan devices allow for higher efficiencies as compared to isolated rotor of the same diameter. This allows the ducted rotor to obtain higher thrusts for a given required power or to lower power requirements for a given thrust, compared to the isolated rotor. As a result of this, a rotor can be replaced with a ducted fan with a smaller diameter and achieve the same thrust. These advantages are very useful for small UAVs intended for surveillance and also rotorcraft applications for urban environments were safety and FOD (Foreign Object Debris) issues are of concern. The majority of the ducted fans UAVs currently in use utilize a ducted fan for both lift and forward propulsion and rely on vectoring of the duct outflow or pitching the vehicle for forward propulsion. An example of these vehicles is shown in Figure 1-1. Here, the single ducted

17 fan is responsible for the lift required to keep the vehicle aloft and maneuvering. The control vanes under the duct are used to vector the outflow to achieve directional control. 2 Figure 1-1:Honeywell T-Hawk Micro Air Vehicle (MAV) (2) Current developments in ducted fan vehicles are focusing on applications to higher speed, forward flight. In this configuration the ducted fans are used primarily as lifting devices and propulsion is provided by a separate device. Several vehicles utilizing this concept have been explored in recent years including conceptual fan-in-wing vehicles, the Urban Aeronautics AirMule, shown in, and the Lockheed Martin F-35B, shown in, which is currently in production. The AirMule is a dual ducted fan vehicle where the fans are the primary lifting devices and the F- 35B uses a ducted fan to provide STOVL capabilities to a multirole jet fighter aircraft. (a) Urban Aeronautics Airmule (3) (b) Lockheed Martin F-35B (4) Figure 1-2: Ducted Fans Employed for Lift Production

18 3 However, in forward flight the duct begins to negatively affect the flow through the fan and adversely influences efficiency (5) (6). As the forward speed increases separation occurs over the front lip of the duct as demonstrated in Myers et al. (7). Here the duct lip shape was identified as a driving influence on the separation behavior of the duct by Graf et al. (6). This separation over the front lip of the duct induces drag and reduces rotor performance by distorting the inflow and reducing the mass flow through the duct. The ducted fan vehicle at the focus of the research efforts here was designed to study the effects of forward flight on the fans and the flow field through the ducts. The model is a dual ducted fan vehicle in a tandem configuration similar to the Urban Aeronautics Airmule (3). 1.2 Current Modeling Methodology Computational tools are a valuable resource in the design and analysis of aerospace vehicles. The use of computational fluid dynamics (CFD) allows the aerodynamic behavior of a vehicle to be modeled and its performance predicted. This allows the designer the opportunity to refine a configuration before constructing prototypes and performing testing. This approach saves time and money while allowing the designer a detailed insight into the design. However, this requires the complex physics of fluid flows to be adequately modeled. Ducted fans, as mentioned previously, experience a great deal of complicated flow phenomena due to the influence of the ducts as well as the dynamics of the rotating rotor. The interaction between the duct and the rotor is a major concern and focus of ducted fan analysis, the ability to capture this interaction accurately is essential to modeling ducted fan vehicles. Several methods have been employed to model these systems, from simple vortex models to complex, unsteady, fully resolved rotor solutions.

19 4 The unsteady, fully resolved rotor method is the ideal method by which ducted fans can be analyzed. This method allows for detailed calculations of the real-time effects of the rotor and its interactions with the duct. However, this method is prohibitively expensive computationally, limiting its availability for routine design tasks (8) (9). The goal in ducted fan modeling then, has been simplifying the model to allow for an efficient solution without neglecting the fundamental physics of the problem. Modeling the duct using potential flow methods is one way of simplifying the problem. However, the potential flow solutions were found to lack the ability to properly handle the flow phenomena over the duct, primarily the separation (9) (10). The use of a viscid flow solver allows the flow over the duct to be adequately resolved and the problem then becomes modeling the fan. To simplify this, the rotor forces are input into the CFD as momentum sources, modeling the rotor as an actuator disk. To model the fan and calculate thrust, momentum theory is often used. However, momentum theory cannot model the swirl effects without detailed a priori knowledge of the flow (11) and fails to model the effects of forward flight (9). Blade element theory (BET) has seen success in modeling the fan with more fidelity. Blade element theory allows the rotor model to resolve forward flight effects and interactions between the rotor, duct and fuselage (9). This results in a physically relevant non-uniform rotor thrust distribution which is seen to influence the flow field calculation through the duct (12). 1.3 Objectives Seeing the benefits of BET in modeling the rotor in application to a laminar Navier- Stokes CFD solution led He and Xing (9) to conclude that coupling the fan and duct aerodynamic interaction had the potential to enhance modeling efforts. A similar approach was used to model a

20 5 fantail anti-torque device using an Euler equation CFD method and blade element theory by Alpman (13). This thesis seeks to demonstrate the utility of this approach by coupling blade element theory to a Reynolds Averaged Navier-Stokes CFD solution. The coupled method will take advantage of a momentum source method CFD approach where the fan is modeled as an actuator disk using force input from a BET rotor model. The method will be validated using experimental results and compared to other CFD analysis methods. This will allow the time and computational cost savings to be weighed against the accuracy of the solution. The intention of these efforts is to provide another option in the design and analysis of ducted fans and enable engineers to analyze design choices in timely manner without unnecessary cost. 1.4 Thesis Overview The thesis is organized into the remaining chapters: Chapter 2: Description of Model An overview of the wind tunnel model used for experimentation and the computational meshes used for the CFD analysis. A description of the rotor model used in BET is also included. Chapter 3: Overview of Previous Work This chapter presents an overview of the experiments conducted on the wind tunnel model and used as validation for the coupled method as well as the previous CFD anaylsis performed on the vehicle.

21 6 Chapter 4: Computational Approach Here a review of momentum theory and blade element theory is provided. Also the manner in which the CFD is coupled to the BET rotor model is explained. The codes used to do this are also presented. Chapter 5: Results of Coupled Solution The flow field and aerodynamic force results from the coupled method are analyzed and discussed. These results are compared to experiment and to prior CFD modeling attempts. The sensitivity of the coupled method to BET input is discussed. Also included is a demonstration of the BET validation with the performance of a hover rotor. Chapter 6: Summary and Conclusions The results and findings of the thesis are summarized and suggestions for future work and the development of both the coupled method and ducted fans are discussed.

22 7 Chapter 2 Description of Model The design of the Penn State dual ducted fan model was an evolution of single ducted fan vehicle research conducted by Leighton Myers as discussed in his MS thesis (14). The model was designed to resemble a 1/10 th scale conceptual UAV medevac. The goal of the design was to enable a study of the vehicle aerodynamics and of the flow field in and around the ducts; the model is strictly a wind tunnel model. To allow for comparisons to other past and present dual ducted fan designs, the model was kept generic in shape and function while retaining a layout similar to the Urban Aeronautics AirMule (3). The important geometric characteristics of this wind tunnel model, referred to as PSU D1A, will be explored in section 1 of this chapter. Having performed some initial performance studies on the wind tunnel model, it was determined that the use of CFD would be an informative endeavor. A CAD model was then produced by researchers at the Penn State Applied Research Laboratory (ARL) based on the geometry of PSU D1A. The CAD model was used to develop two separate meshes for the analysis, one where the fan is replaced by an actuator disk and a second where the rotor itself is resolved. These will be explained more thoroughly in section 2 of this chapter. The computational model and accompanying meshes were the focus of this thesis and supported the development of the computational methods described in the coming chapters.

23 8 2.1 Wind Tunnel Model PSU D1A Fuselage The wind tunnel model is a dual ducted fan model intended for edgewise forward flight. The ducts are arranged in forward aft tandem configuration with a solid center-body. The shape of the model s fuselage is a generic design meant to be similar to existing ducted fan designs. Important design parameters for this fuselage configuration include: length of the center-body (distance from the tip of the forward rotor to the tip of the aft rotor), a, the duct chord, c D, duct diameter, D D, the maximum thickness of the center-body along the centerline of the model, hcenterline, the overall maximum thickness of the center-body, hmax, the max duct thickness, t, the placement of the rotors within the duct, Rotor Depth, possible inclination angles of the rotors, and approximate cargo capacity. These design parameters are listed for the PSU D1A and several other dual ducted fan designs that were publically available in Table 2-1. Length measurements have been non-dimensionalized as. Vehicle a/d c D /D PSU D1A AirGeep II NASA Parlett UA AirMule UA/Bell X-Hawk Table 2-1: Dual Ducted Fan Design Parameters h CENTERLINE / D D h MAX /D D Duct t/c D Rotor Depth/c D Angle of Rotor Inclination ±10 (capable) Approximate Cargo Capacity[m 3 ] N/A N/A N/A N/A N/A

24 9 The model consists of a steel frame and PVC ring sub-structure overlaid with foam. This foam was then hand shaped to form the fuselage and encased in a fiberglass reinforced epoxy resin to improve strength and surface smoothness. The finished wind tunnel model, PSU D1A, can be seen in Figure 2-1. More details about the design and construction of this model can be found in (15). Also additional information about the electronics and setup of the model are discussed in Ryan Hook s Master of Science Thesis (16). (a) Isometric View (b) Top View (c) Side View Figure 2-1 Model PSU D1A: (a) Isometric View, (b) Top View, (c) Side View

25 Rotors The rotors chosen for use in the dual ducted fan model are commercially available, offthe-shelf 10 inch diameter [25.4 cm], three bladed rotors with 7 inches of pitch produced by Master Airscrew. Two rotors of the same model were used, each with a different direction of rotation, one tractor and one pusher, to enable a counter-rotating configuration. These rotors were chosen based on the previous single ducted fan research performed by Leighton Myers (14), using a Master Airscrew, three bladed, 10 inch diameter, 5 inch pitch rotor. A higher pitched rotor was desired for the dual ducted fan model (D1A) to increase rotor thrust capability. In order to fit and operate the rotors in the wind tunnel model, the rotors were trimmed and balanced. The rotors tips were made square and trimmed to a final rotor diameter of 23.8 cm [9.37 in], resulting in a nominal tip gap of ~2%. To balance the rotors, a balancer was used and weight was either removed or added to each blade by sanding the blades or adding whiteout to the tips, respectively. The chord, maximum thickness and pitch of each rotor were recorded using a caliper and protractor. The results of this study are shown in Figure 2-2. The properties are shown for both the forward and aft rotors at locations near the hub, mid-span and near the tip and plotted against the radial location. These properties were used to aide in the design and modeling of the computational models of this vehicle. Of distinct importance is the pitch distribution, which approaches a local pitch at the tip of about 14 with a tip chord of about 1.3 cm [0.5 in] which is an important property for Reynolds Number considerations.

26 Pitch [deg.] Chord [in.] Max Thickness [in.] (a) Chord Distribution Front Rotor Aft Rotor Radial Location [in.] (b) Max Thickness Distribution Front Rotor Aft Rotor Radial Location [in.] (c) Twist Distribution Front Rotor Aft Rotor Radial Location [in.] 4 5 Figure 2-2: MA 10x7 Rotor Geometry: (a) Chord Distribution, (b) Max Thickness Distribution, (c) Twist Distribution 2.2 Computational Model CAD Model Having produced the wind tunnel model by hand, there was no computer-aided design (CAD) model or layout for the ducted fan fuselage. In order to produce a computational model that was geometrically similar, and therefore relevant for comparison, researchers at Penn State ARL relied on a series of measurements and photographs to reproduce the wind tunnel model s

27 design features. The final model of the dual ducted fan is shown in Figure 2-3 along with a computational model of the rotors. 12 (a) Top View (c) Isometric view (b) Side View Figure 2-3: CAD Model of PSU D1A: (a) Top View, (b) Side View, (c) Isometric View The CAD model is complete with a model of the motors and rotor hubs for use in both of the CFD meshes and also a model of the rotors used in experiments for use in the fully resolved CFD calculations. Missing from the CAD model are the motor mounts and mounting struts. The mounting struts are of particular concern as they may have an effect on outflow swirl, acting as a crude stator vane. However, this has not been addressed. A study of the geometric similarity between the CAD and wind tunnel models was performed and reported close similarity with minimal differences in any of the significant vehicle parameters. The study was performed using a precision dial indicator traverse setup. The details and specific results of the study were reported on in Hook (16). The rotor model is based on the measurements from Figure 2-2 and utilizes an approximated airfoil shape, as derived from the tip airfoil of the Master Airscrew rotor, as shown

28 13 in Figure 2-4. This airfoil is approximately 16% thick with 5.5% camber. The coordinate file for this airfoil can be found in Appendix ## and was obtained by digitizing an image of the rotor tip airfoil from SolidWorks. Figure 2-4: Airfoil section used in CAD Model Momentum Source Mesh The momentum source mesh is a simplified representation of the dual ducted fan model. In this mesh the resolved fan blades are replaced with a computational mesh resolving the rotor sweep volume only, allowing the input of body forces, which will be discussed in later chapters. The mesh is a block-structured and overset mesh with over five million cells and is used in a steady flow solution, the list specifications can be seen in Table 2-2. Table 2-2: Momentum Source CFD Specifications Calculation Type Number of Blocks Number of Cells Number of Points Steady RANS 239 5,006,016 5,564,571 Several views of this mesh can be seen in Figure 2-5. Here it can be seen that the rotors are absent from the mesh, however the hub pieces and motors are present. Rotor sweep volume occupies a space which is of the same height as the hub and approximates the actual rotor radius with a tip gap. This region can be clearly seen in the horizontal and vertical plane cross-sections. On the horizontal cross-section the rotor sweep volumes occupy nearly the entirety of the forward and aft ducts and, and no grid overlap occurs within this region, making force specification and input straightforward.

29 14 (a) Slice Through Horizontal Plane (b) Slice Through Vertical Plane (c) Fuselage Surface Mesh Figure 2-5: Momentum Source Overset Mesh: (a) slice through horizontal plane, (b) slice through vertical plane, (c) fuselage surface mesh In order to more accurately simulate the experimental test conditions, the meshes were made to represent the Aerospace Engineering Department s Hammond Wind Tunnel test section with dimensions of 91.4 cm [36 in] in height by 60.9 cm [24 in] wide. Figure 2-6 shows the momentum source fuselage mesh within the computational domain representing the Hammond tunnel. The momentum source mesh forms the basis for the computational work presented in this thesis and supported not only initial CFD efforts as explained in chapter 3 but also the improved BET coupled method which is the focus of this thesis and will be explored in greater detail in the coming chapters.

30 15 Figure 2-6: Momentum Source Mesh, Model in Hammond Wind Tunnel Rotor Model In order for the BET CFD coupled solution to work properly, a model of the rotor was necessary. In Subsection it was shown that the ARL CAD model of the dual ducted fan model contained an approximation of the airfoil used on the physical wind tunnel model, PSU D1A. This airfoil, as presented in Figure 2-4, was selected as the airfoil section to be used in the blade element calculations. It was also found that this airfoil was nearly identical to another airfoil: GOE 527. The Gottingen 527 airfoil is, like the D1A rotor airfoil a flat bottomed foil with 5.5% camber and is about 16% thick. Figure 2-7: Airfoil Comparison: D1A rotor and GOE 527

31 16 XFOIL (17) was used to obtain lift and drag coefficient data for both airfoils at a Reynolds Number of 70,000. However, using XFOIL, difficulty was encountered in determining coefficient data for either airfoil for any useful range. It was suspected that the airfoil coordinates found for the Gottingen airfoil and those digitized from SolidWorks for the D1A rotor airfoil had inadequate resolution, appearing far too rough to XFOIL. To alleviate this several functions available with XFOIL were taken advantage of. First, the two airfoil shapes were blended together at equal weightings using the INTE command. The objective of this operation was to alleviate any local deviations or error in the curvature of either airfoil by interpolating the surfaces with a like surface and achieve a smoother airfoil shape. The second operation on the airfoil included a smoothing of the calculated velocity distribution. Any remaining roughness of the airfoil shape was minimal but still negatively affected the results and convergence of the XFOIL routine. It was found that smoothing the velocity distribution, using the SMOO command within the.qdes routine, at any problematic angles of attack greatly improved convergence. This was done primarily at angles around the zero lift angle and stall. Having improved the airfoil shape and established a procedure to obtain the data from XFOIL, the blended airfoil was run through an angle of attack sweep at a Reynolds Number of 70,000. The resulting lift and drag coefficients are shown in Figure 2-8. The airfoil has a max lift coefficient of about 0.8 at a stall angle of attack of nearly 11 and a lift coefficient at 0 angle of attack of about 0.11 due to it camber. The drag coefficients show a drag bucket ranging from about -2 to +5 angles of attack with a minimum drag coefficient of 0.54 which is larger than was anticipated. These properties were then extrapolated into a larger angle of attack range of ±180 using the spreadsheet AirfoilPrep_v2p2.xls developed by the National Renewable Energy Laboratory (NREL) (18). This spreadsheet takes the lift and drag data and extrapolates the lift using a sinusoidal fit to existing data and estimating drag using a flat plate assumption. The full list of airfoil data used for this airfoil is shown in Appendix A.

32 Lift Coefficient Drag Coefficient 17 (a) Lift Coefficient (b) Drag Coefficient Angle of Attack [deg] Angle of Attack [deg] Figure 2-8: Blended Airfoil Section Properties for Re = 70,000: (a) Lift Coefficient, (b) Drag Coefficient Having selected an airfoil and obtained relevant lift and drag data, the properties of the rotor blades themselves must be established. The necessary properties required to model the rotors in blade element theory are the local chord and pitch (or twist) distribution of the blades. Fortunately there were two sets of data produced by the ducted fan team for Master Airscrew (MA) rotors. The first were measurements of the MA 10x7 rotors used in the dual ducted fan model, PSU D1A, shown in Figure 2-2. The second set was a description of a lower pitch MA 10x5 rotor produced by Leighton Myers for use in single fan ducted fan research, a listing of these data can be found in Appendix B. The D1A rotor data, while an accurate measurement of the used rotor, was unfortunately very sparse. The MA 10x5 measurements had much more resolution and were used to supplement the known information. To do this, the MA 10x5 data was modified to closely match the properties at known locations resulting in a rotor model referred to as MA 10x5 Mod.A. This rotor model preserves the distribution of the properties found in the MA 10x5 rotor while adjusting the actual values to match the known properties of the D1A rotor blades. The results of this are shown in Figure 2-9 and are compared to the D1A rotor, they can also be found in Appendix B.

33 Local Pitch [deg.] Local Chord [cm] (a) Local Chord Distribution (b) Local Pitch Distribution Figure 2-9: MA 10x5 Mod.A Rotor Model Properties: (a) Local Chord Distribution, (b) Local Pitch Distribution The shown airfoil section and rotor blade properties comprise the completed rotor model. This model is assumed to be valid for the entire blade. The assumption was made for two reasons: the first was a lack of detailed airfoil section information from Master Airscrew and the second, simplicity. Though the airfoil section does in fact change radially over the blade, the change is only significantly at the inner radial station near the blade root. As the lift generation of this region is small due low tangential velocities, discrepancies in the sectional properties are assumed to have only minor effects. D1A Rotor MA 10x5 Mod.A Radial Station [cm] Radial Station [cm] D1A Rotor MA 10x5 Mod.A 18

34 Fully Resolved Rotor Mesh The second CFD mesh developed by Penn State ARL adds resolved rotors to the momentum source mesh described in subsection (19). Here the CAD rotor model shown in subsection with the CAD model of the fuselage is also meshed and rotated in real time within the fuselage. This increases the complexity and fidelity of the calculation, creating a dynamic overset mesh requiring over 12 million computational cells that must be run as an unsteady case, the specifications of the mesh can be seen in Table 2-3. Table 2-3: Fully Resolved Rotor Mesh Specifications Calculation Type Number of Blocks Number of Cells Number of Points Unsteady RANS 309 ~12x10 6 ~13x10 6 Figure 2-10 shows several views of the fully resolved mesh and highlights both the similarities and the differences with the momentum source mesh previously described. The fuselage mesh remains unchanged from the momentum source mesh. Also unchanged is the size and shape of the computational domain, the ducted fan is placed in a model of the Hammond Wind Tunnel as it was with the momentum source mesh. The difference, and the source of the added complexity, is the overset rotating rotor meshes. In the surface mesh and top view of Figure 2-10 both rotors can be seen within the fuselage, with a counter-rotating orientation. In the view of the front rotor in the same figure the topology of the rotor meshes is highlighted.

35 20 (a) Surface Mesh (b) Top View (c) Front Rotor Figure 2-10: Fully Resolved Rotor Mesh: (a) Surface Mesh, (b) Top View, (c) Front Rotor

36 21 Chapter 3 Overview of Previous Work Work on the dual ducted fan model has been done over a several year period and grew out of single ducted fan research. The goal of the research was to better understand not only the performance of a dual ducted fan vehicle but also the flow physics in and around the ducts. This was done with a mixture of experiments and CFD. The experiments consisted of both flow measurements and a force and moment study of varying flight regimes. The CFD looked to replicate these conditions and provide additional insight while exploring the validity of CFD methods in dual ducted fan design and analysis. 3.1 Wind Tunnel Experiments The wind tunnel experiments took place in two wind tunnel facilities with the majority of the hover experiments taking place in a hover stand outside of the wind tunnel. The wind tunnel facilities utilized for the experiments were the Hammond Building Wind Tunnel and the Academic Projects Building (APB) Wind Tunnel. Both wind tunnels are closed return, low speed, atmospheric facilities. The Hammond wind tunnel has a 61 cm [2 ft] wide by 91 cm [3 ft] tall test section with a mean turbulence intensity of 0.7 percent. The APB wind tunnel has a test section which is 101 cm [3.25 ft] tall and 148 cm [5 ft] wide with a turbulence intensity of.045% at 150 ft/s (20). The force and moment measurements were taken with two different force balances, one a platform balance in the Hammond wind Tunnel and the other a pyramid type balance in the APB facility. The flow field measurements were taken using two different types of pitot probes. The

37 22 first is a five-hole pitot probe which provided a large amount of the data for flow velocities and direction within the duct. The second probe, a kiel probe, provided data in regions where the fivehole probe failed to adequately resolve flow direction due low velocity magnitudes. Measurement of the flow velocity and direction were taken exclusively in the front duct, both above and below the rotor. Figure 3-1illustrates the position of the flow measurements within the front duct. The labels in parentheses indicate an outflow data point and 180 is defined as the front of the vehicle. Table 3-1quantifies the locations of these measurements with radial and azimuthal positions along with their distances from the center of the duct. For further detail on the facilities, equipment, setup and calibration; please refer to Hook (16). Figure 3-1: Experimental Measurement Locations within Front Duct

38 23 Table 3-1: Experimental Measurement Locations within Front Duct Point Label Type Longitudinal Distance (cm) Lateral Distance (cm) % Radius Azimuthal Angle (deg) A Inflow B Inflow C Inflow D Inflow E Inflow F Inflow G Inflow H Inflow I Inflow J Outflow K Outflow L Outflow M Outflow N Outflow O Outflow P Outflow Q Outflow R Outflow The coordinate system used for all flow field measurements is shown in Figure 3-2. Here the flow in the Z direction is defined as positive when traveling downward through the duct. The x-axis, X b, is aligned with the fuselage longitudinal axis such that velocities directed to the rear of the model are considered positive. The resultant Y axis is shown and preserves a right handed system. This coordinate system was chosen such that the dominate flow are in the positive direction. This includes the wind tunnel onset flow which flows towards the rear of the vehicle simulating forward flight and the flow through the duct which is ideally downward for production of thrust.

39 24 X b Y b Z b Figure 3-2: Experimental Coordinate System Hover The experiments to determine flow velocities through the duct in hover were performed out of the wind tunnel in a hover stand which ensured the model was unaffected by ground effects. The velocities were taken around the azimuth as discussed in the previous section. Figure 3-3 displays the results of this survey in terms of both inflow and outflow velocity magnitudes at roughly 70% radius around the duct azimuth. For both the inflow and the outflow, the velocities around the duct azimuth are fairly consistent. The inflow sees some distortion in the front of the duct at the 150 and 210 azimuthal stations. This is believed to be due to the locations of the measurements being at a larger radial station, 78% radius, than the other measurements. The outflow velocities show similar trends and are larger than the inflow which is to be expected and required for the production of thrust. These trends also stay consistent for both RPMs, with velocity magnitudes increasing with RPM.

40 Velocity Magnitude [m/s] Inflow 4k RPM 4 Inflow 6k RPM 2 Outflow 4k RPM Outflow 6k RPM Azimuthal Angle [deg] Figure 3-3: Inflow & Outflow Velocity Magnitudes in Front Duct in Hover A survey of lift force in hover was performed over a range of RPMs. Figure 3-4 shows the results of this survey. The survey was conducted in the APB wind tunnel on the pyramid force and moment balance, operating out of ground effect, with both fans running the same RPM. As such, the lift force presented represents the total of the thrust of each rotor and any lift force on the fuselage. The lift was found to vary with the square of the angular speed of the rotor. The maximum RPM tested was 10,000 RPM, which is the maximum achievable by the model and corresponds to a tip Mach number of The maximum thrust produced at this rotor RPM is 35.6 N.

41 Lift [N] Rotor RPM Figure 3-4: Lift in Hover for a Range of RPM Forward Flight The aerodynamics of an edgewise ducted fan are not well understood or demonstrated and therefore the forward flight study comprises the majority of the previous work. Using the hover experiments as a baseline for comparison, a series of flow field surveys and lift and drag measurements were done on the PSU D1A model in a forward flight condition. In forward flight it was expected that separation would develop over the front lip and this would contribute to a highly distorted inflow to the fan. The measurements were taken to capture conditions at, primarily, two advance ratios (μ): 0.08 and Here advance ratio is defined according to Equation 3.1 as the ratio of tunnel speed to rotor tip speed. (3.1)

42 27 Flow field Measurements Flow visualizations were done in order to obtain a qualitative understanding of the flow phenomena. The visualizations were obtained using the smoke wire technique where oil is evaporated off a heated wire; this was done over the centerline of the model. These visualizations demonstrated that the inflow was in fact distorted with significant separation over the front lip. Figure 3-5 shows the visualization at an advance ratio of 0.08 and a vehicle angle of attack of -10. A clear region of separated and stagnant flow can be seen just behind the front lip, extending nearly a third of the duct. As the advance ratio is increased, the separation region enlarges as evidenced by Figure 3-6 which shows the flow visualization at an advance ratio of 0.24 and an angle of attack of -10. Here the separation region has grown to over half of the duct and the streamlines do not cross the rotor plane until aft of the rotor hub. This region of separation indicates a loss of fan effectiveness and a source of drag. Figure 3-5: Separation over Front Duct Lip along the Centerline, -10 Angle of Attack, Advance Ratio of 0.08

43 28 Figure 3-6: Separation over Front Duct Lip along the Centerline, -10 Angle of Attack, Advance Ratio of 0.24 Velocity measurements were taken in the same manner and at the same locations as the hover measurements in order to obtain a quantitative description of the forward flight flow field. The five-hole pitot probe and kiel probe were inserted through the duct while the model was in the wind tunnel at an angle of attack of -10. Considering the findings of the flow visualizations, the combination of the two probes proved useful as the five-hole probe was ineffective in the highly turbulent separation region where the kiel probe was able to retain accuracy. The data from the two probes were aggregated together and presented in the figures below. Figure 3-7 shows the velocity magnitudes at the inflow plane of the front duct at a wind tunnel speed of 6.1 m/s. Here a RPM sweep was done to obtain data at 0, 4000 and 6000 RPM. Most of the data shown in at the 70% radial position with one measurement at 30%, labeled as point E in Figure 3-1and Table 2-1. The duct velocities are found to be small at zero RPM and increase as RPM is increased, as seen in the hover experiments. The velocity magnitudes increase from the rear of the fan toward the front of the fan until the region between 150 and 210 is reached where a large decrement in velocity magnitude is seen. Comparing the 6000 RPM data from Figure 3-7 to the flow visualization from Figure 3-5, both representing an advance ratio of 0.08, the measurements confirm the presence of a reduced velocity region at the front third of the fan.

44 Velocity Magnitude [m/s] 70%R 6k RPM 30%R 20 70%R 4k RPM 30%R 18 70%R 0 RPM 30%R Azimuthal Angle [deg] Figure 3-7: Inflow Velocity Magnitudes in Front Duct at a Wind Tunnel Speed of 6.1 m/s As the wind tunnel velocity increases, and hence the advance ratio, flow visualization suggests that the separation region will also grow in severity. The inflow velocity magnitudes at a wind tunnel speed of 10.7 m/s in Figure 3-8 confirm this. These results mirror the results at a wind tunnel speed of 6.1 m/s except that the difference between the maximum and minimum velocities seen above rotor has grown. At an advance ratio of 0.24, 4000 RPM at 10.7 m/s wind tunnel velocity, this difference is 9 m/s or 77.5% of the max where at μ=0.08 it is 8.1 m/s or 50.3% of max velocity magnitude. Clearly, as corroborated by the flow visualization in Figure 3-6, not only has the separated region grown in size but the separation off the front lip has caused a greater distortion in the inflow velocities to the ducted rotor. 29

45 Velocity Magnitude [m/s] 70%R 6k RPM 20 30%R 18 70%R 4k RPM 16 30%R 14 70%R 0 RPM Azimuthal Angle [deg] Figure 3-8: Inflow Velocity Magnitudes in Front Duct at a Wind Tunnel Speed of 10.7 m/s Having studied the nature of the inflow velocity field, a survey of the outflow characteristics was also performed. Here it was found that the features seen in the inflow, namely the effects of the lip separation, are also seen in the outflow. At a wind tunnel speed of 6.1 m/s, a region of reversed flow is encountered as demonstrated by Figure 3-9 at the front of the fan just aft of the lip at from the 150 azimuthal station to the 210 station. This indicates that not only is there reduced inflow to the fan at these locations but also a low pressure region under the rotor causing flow to enter the bottom of the duct and flow upwards through the duct. A low pressure region under the rotor disk indicates a substantial loss of lifting capability and effectiveness in this flight condition. The outflow in the aft two thirds of the duct are fairly consistent, especially at the 6000 RPM, 0.08 advance ratio condition, where the outflow velocity magnitude at the 180 and 30% radial location is nearly 13 m/s, closely matching the other points, despite the reversed flow at the 70% radial, 180 position. 30

46 Velocity Magnitude [m/s] %R 6k RPM 30%R 70%R 4k RPM 30%R 70%R 0 RPM 30%R Azimuthal Angle [deg] Figure 3-9: Outflow Velocity Magnitudes in Front Duct at a Wind Tunnel Speed of 6.1 m/s Increasing the wind tunnel speed induces a growth in the reversed flow region under the rotor. Figure 3-10 shows the outflow measurements at a wind tunnel speed of 10.7 m/s and an angle of attack of -10. Here, similar to the results at 6.1 m/s, the front of the fan is experiencing reversed flow. However, this region has grown to include the 118 and 240 azimuthal stations, leaving only the rear of the fan with significant, clean outflow velocities. Comparing advance ratios, at a wind tunnel speed of 10.7 and an RPM of 6000 (μ=0.15) and a wind tunnel speed of 6.1 m/s and 4000 RPM (μ=0.12) a similar pattern emerges. Here the front of the fan is dominated by the lip separation with very low or reversed velocities with significant loss seen on the advancing and retreating sides of the rotor. However, in both cases the front, 30% radial location retained a strong velocity magnitude. Looking at the largest advance ratio, 0.24 (4000 RPM with a wind tunnel speed of 10.7 m/s), the front two thirds of the measurement locations experienced either a negative or greatly reduced velocity magnitude. This is confirmed by the flow visualization shown in Figure 3-6 where the streamlines were ingested into the rotor in the rear of the fan.

47 Velocity Magnitude [m/s] %R 6k RPM 30%R 70%R 4k RPM 30%R 70%R 0 RPM 30%R Azimuthal Angle [deg] Figure 3-10: Outflow Velocity Magnitudes in the Front Duct at a Wind Tunnel Speed of 10.7 m/s A curious result of the velocity magnitude survey in both inflow and outflow is the behavior of the flow at the front of the fan. In the flow visualizations, it was suggested that the front of the fan would see little inflow. However, significant velocity magnitudes were measured in the inflow plane at the front of the fan, although noticeably reduced. The outflow measurements show that at these same locations, under the same conditions, the flow velocities are negative or near zero. This results in a situation where a position at the front of the duct experiences a downward velocity at the inflow plane and either zero velocity or upward velocity at the outflow plane. This result indicates a large amount of angulation of the flow through the duct (16) and further demonstrates the complexity of the duct flow. From the study of the flow field around and through the front duct of the dual ducted fan model, it can be concluded that while the duct provides some benefits, both aerodynamic and safety, it can also be a liability to rotor performance. The measurements and visualizations demonstrate that the front duct front lip design is crucial to rotor performance and greatly affects the flow field into the fan and warrants additional attention and study (16).

48 33 Force Measurements Lift and drag measurements of the dual ducted fan model, D1A, were taken in forward flight to compliment the flow field measurements. The results of these experiments are shown in Figure 3-11 for a range of wind tunnel velocities at an angle of attack of 0. The lift force displayed here is the total lift which is fuselage lift plus rotor thrust. The lift results display a parabolic increase in total lift with tunnel speed. At low tunnel speeds, the lift force approaches the hover lift force. As the wind tunnel speed increases, the mass flow into the duct increases resulting in more thrust as well as an increase in fuselage lift consistent with that of a lifting body, which is also parabolic. Increasing wind tunnel speed is not the only way to increase lift however. An equal or greater increase in total lift force is seen by increasing rotor RPM from a given condition that wind tunnel speed. As the rotor RPM is increased the rotors perform more work on the incoming flow and likewise produce more thrust by better turning the flow into the duct. The drag force presented in Figure 3-11 is considered the net drag or drag on the fuselage less any component of thrust in the drag direction. The drag force results indicate a much more linear rise in response to increased tunnel speed as compared to the lift results. In fact at 6000 RPM the increase in drag from 10.6 m/s to 20 m/s in less than the rise from 3 m/s to 10 m/s. Also of note, the increase in drag due to an increase in RPM increases as the wind tunnel speed is increased. This is due to a component of the drag called momentum drag or ram drag (21). This is the component of drag due to the flow turning into the duct. This action requires the momentum of the oncoming flow to being redirected into the duct which requires a force, a force that acts on the fuselage as drag. As the rotors turn flow at a higher rate and produce a greater thrust, as seen in the lift results, the drag due to this increased flow turning also increases. Still, at lower speed the effects of the wind tunnel speed in increases profile drag dominate the drag results as seen in a greater drag increase due to tunnel speed increase rather than RPM.

49 Total Lift [N] Net Drag [N] (a) Lift Exp 8k RPM Exp 6k RPM Wind Tunnel Velocity [m/s] (b) Drag Exp 8k RPM Exp 6k RPM Wind Tunnel Velocity [m/s] Figure 3-11: Experimental Forces for Range of Wind Tunnel Velocities, (a) Lift, (b) Drag 3.2 Computations After developing a basic understanding of the characteristics of the dual ducted fan via experimentation, a computational approach was pursued to study the dual ducted fan flow physics in greater detail. The computational study was performed by Penn State ARL and consisted of two types of computations differing in their level of modeling fidelity. The first was a simplified model which replaced the rotor with momentum sources, modeling its effects with known forces. The second method fully resolved the rotor within the mesh, calculating rotor forces in real time. These results were also detailed at the 2010 Powered Lift Conference (19). The CFD utilized the OVER-REL (22) flow solver which is an in-house ARL Reynolds- Averaged Navier-Stokes (RANS) equation solver that has undergone development for over 15 years and validated for a large variety of configurations. The code solves the pseudocompressible form of the RANS equations (22). The governing equations are solved in their integral form and discretized for cell centered finite volumes on hybrid block-structured and

50 35 overset meshes of hexahedral cells (22). The overset grid communication is handled by the grid processor SUGGAR (22). The results of the CFD were then compared to the experiments to determine the effectiveness of CFD analysis techniques in ducted fan vehicles Momentum Source Calculations The momentum source calculations utilized the mesh shown in section 2.2.2, running a steady RANS calculation. Here the rotors are not included in the mesh topology. Rather the rotors are modeled as an actuator disk by a distribution of momentum sources. In this calculation then, the rotor sweep volume is resolved along with the bulk rotor effects to achieve a time averaged solution. To determine the forces required for input into the calculation, the forces measured in the hover experiments were used. To use the hover experiments, three assumptions needed to be made. First it was assumed the thrust in hover could be evenly attributed to each rotor, such that the forward and aft rotors produce the same thrust. Secondly it is assumed that for a given RPM the fans produce the same thrust at any forward speed. Third, it was assumed that these forces could be distributed through the rotor sweep volume as a constant distribution of momentum sources. Through these simplifying assumptions the momentum source model was assembled and run. Figure 3-12 shows the results of a simulation run for 6000 RPM, 18.3 m/s wind tunnel speed and 0 angle of attack. Here the rotor forces, taken from the hover experiments were 5.39 N per fan, evenly distributed over the rotor sweep volume. Figure 3-12 (a) shows the static pressure contours over the fuselage surface. Here high static pressure coefficients are seen on the front lip and the rear of both of the ducts, indicating areas of drag creation due to the high forward velocity. Also low pressure regions are seen over the top of the ducts demonstrating the benefits

51 36 of the duct where lift is derived from the fuselage due to the low pressure regions induced by the fan. Figure 3-12 (b) presents the contours of the downstream, x direction, velocity. Here the orange contours represent the free-stream forward velocity of 18.3 m/s. Clearly noticeable here is the flow field around the vehicle is dominated by flow which has been slowed, including a substantial wake and a large stagnation region at the front of the front duct. The duct flows are also dominated by slowed and often reversed flow. The front duct is colored completely blue, indicated a negative x -velocity. This represents flow that has entered the duct and reversed direction. The same effect is seen in the front portion of the aft fan. (a) Fuselage Surface Static Pressure (b) Downstream Velocity Figure 3-12: Momentum Source Pressure and Velocity Contours at 18.3 m/s, 6000 RPM, 0 Angle of Attack: (a) Fuselage Surface Static Pressure, (b) Downstream Velocity Figure 3-13 aides in understanding these effects. Here a view of a simulation at 6000 RPM and 18.3 m/s is shown through the vertical symmetry plane. Figure 3-13 (b) shows the total pressure coefficient contours on the vertical symmetry plane for a -5 angle of attack with overlaid particle paths. In this graphic, consistent with Figure 3-12(b), there is a region of recirculating particles in the front of the front fan (colored red) and the front of the blue fan (colored blue). Clean flow showing a total pressure jump (colored orange and red) are seen only in the rear of both fans, with the recirculating region being much larger in the front fan.

52 37 Static pressure contours at an angle of attack of 0 are shown n Figure 3-13(a). The features seen on the fuselage pressure contours also can be seen in in flow field. Here high pressure regions are seen at the rear of the ducts and at the front of the vehicle. This suggests that the flow is angling into the ducts and stagnating on the fuselage center-body and the aft duct. The effects of the input momentum sources can be seen as a static pressure jump across the rotor plane. Separation effects are seen below the front section of the forward duct. The effect of this region of low pressure below the rotor can be seen in Figure 2-1(b) where the particles flowing under the vehicle are ingested into the duct. (a) Static Pressure Contour (b) Total Pressure with Particle Paths Figure 3-13: Momentum Source Pressure Contours on Vertical Symmetry Plane at 18.3 m/s, 6000 RPM: (a) Static Pressure Contour, (b) Total Pressure Contour with Particle Paths The momentum source simulations were run at several wind tunnel speeds to match the experimental conditions and at two RPMs. The lift and drag on the vehicle for each of these conditions is presented in Figure The lift is seen to have a more significant increase due an increase in RPM than wind tunnel speed, a result that was expected from the experiments. However at 6000 RPM, the lift curve levels out at higher speeds, a behavior not seen for the 8000 RPM calculation. This may be an effect of the lip separation at this high advance ratio as documented in the previous pressure contours and the flow visualization. The lip separation greatly distorts the fan inflow and causes the assumptions used for the momentum source input to

53 Total Lift [N] Net Drag [N] 38 break down, in particular the use of a constant force distribution over the rotor sweep volume. The drag curves behave as expected, with the drag for both RPM values converging at low forward speed and diverging as the forward speed is increased due to the ram drag effects previously discussed (a) Total Lift (b) Net Drag 8000 RPM 6000 RPM RPM 6000 RPM Wind Tunnel Velocity [m/s] Wind Tunnel Velocity [m/s] Figure 3-14: Momentum Source Calculated Forces: (a) Total Lift, (b) Net Drag Fully Resolved Rotor The fully resolved rotor calculations used the mesh detailed in section Where the rotors are resolved and rotated within the fuselage mesh. This allows for an unsteady RANS calculation to be performed with the rotor forces being calculated in real time as they are rotated within the duct. This calculation, while computationally expensive, yields a much higher fidelity computational solution. However, due to its high computational cost only one fully resolved computation was completed. The condition that was run represents the highest advance ratio of 0.24 at a wind tunnel speed of 18.3 m/s, 6000 RPM and 0 angle of attack. Figure 3-15 shows an instantaneous view of the of the static pressure contours on the fuselage and rotors of the dual ducted fan in the forward flight configuration tested. Visible here are the high pressure areas (colored red) on the nose of the vehicle as well as the rear of both

54 39 ducts. This is a result that was seen in the momentum sources calculations as well. The low pressure regions (colored yellow) on the top of most of the fuselage, especially the front of the front duct, is also consistent with the results from the momentum source calculation and reinforce the notion that the duct and fuselage provide benefits in lift generation. Most importantly in this simulation, however, are the rotors. Here the rotors can be seen to have very low pressure regions on the top of the blades (colored blue) with very high pressure regions on the bottom of the rotor (colored red). Also visible in the figure are the tip vortices at the blade tip and trailing from the blade acting on the duct. (a) Top View (b) Bottom View Figure 3-15: Instantaneous view of Fully Resolved Static Pressure Surface Contours at 18.3 m/s, 6000 RPM, 0 Angle of Attack: (a) Top View, (b) Bottom View The solution was calculated for a total of seven rotor revolution. The vertical force history on the rotors and the fuselage are shown in Figure Each major time division,.01 seconds, represents one rotor revolution. The first three rotor revolutions are dominated by startup transients and are not considered physical. The red line shows the lifting force on the fuselage. After the fourth rotor revolution the force begins to oscillate due to vortex shedding off the fuselage, yielding a time varying lift force. The rotor forces vary with three peaks per revolution, matching the blade passage frequency. It was found that the front fan produces more lift than the aft fan.

55 40 Figure 3-16: Fully Resolved Rotor Calculation Vertical Force Time History The resultant lift and drag as calculated by the fully resolved computations is shown in Figure 3-17compared to the momentum source results. Due to the lack of additional test points, it is not possible to draw conclusions about the trends of the data produced by the fully resolved calculation. However, it is immediately noticeable that the fully resolved result predicts a much larger lift and drag force than the relevant momentum source calculation at 6000 RPM. The forces predicted here are closer to the forces predicted by the momentum source CFD for a RPM of The cause for the lack of conformity between the two solutions is the assumptions made in running the momentum source calculations. It has been shown that the inflow field is highly distorted; the fan forces from this flow field are also non-uniform. In addition to this incorrect force distribution, it follows that the lift of the rotor will change from the hover condition. These noted differences have caused a large disparity in the predictions, the real time resolved-rotor calculation avoided these simplifying error inducing assumptions entirely.

56 Total Lift [N] Net Drag [N] (a) Total Lift (b) Net Drag M-S 8k RPM M-S 6k RPM FR 6k RPM M-S 8k PRM 5 M-S 6k PRM 5 FR 6k RPM Wind Tunnel Velocity [m/s] Wind Tunnel Velocity [m/s] 25 Figure 3-17: Comparison of Momentum Source and Fully Resolved Calculated Forces: (a) Total Lift, (b) Net Drag Comparison of Experiment and CFD Determining the accuracy of the predictions is of upmost importance. In order to determine the validity of the CFD methods in analysis of the ducted fan flow field the results of the predictions were compared to the experiments. It was previously determined that the two types of CFD did not match well for similar conditions due to the simplifications made to the momentum source calculations. In order to improve the prediction capability, the limitations of the momentum source calculation must be explored to determine what components of the momentum source computations are physically relevant. Figure 3-18 shows a comparison of the flow field for an advance ratio of 0.24 between smoke wire flow visualization at -10 angle of attack and a momentum source calculation total pressure contour at a -5 angle of attack. While the two conditions vary by angle of attack, analogous flow patterns can be seen between the two. In Figure 3-18 (b), total pressure coefficients on the vertical symmetry plane, areas of high total pressure are seen at the rear of both of the ducts. This indicates an area of clean flow through the fan that is seen in the flow

57 42 visualizations as a strong smoke discharge through the bottom of the fan at the rear of the ducts. Also seen in both of the graphics is separation over the front lip. This is seen on top of the duct into the fan where streamlines in Figure 3-18 (a) show a void over the front of the fan and ingestion of the streamlines nearly half way back into the duct. This is corroborated by the total pressure contour where the front two-thirds of the fan are engulfed in a low total pressure, separation region. In addition, a similar separation phenomenon is below the fan off the bottom of the front lip. (a) Smoke Wire Flow Visualization (b) Total Pressure Contour (M-S) Figure 3-18: Flow Field Comparison for Advance Ratio of 0.24: (a) Smoke Wire Flow Visualization at -10 Angle of Attack, (b) Momentum Source Total Pressure Contour on Vertical Symmetry Plane at -5 Angle of Attack Figure 3-19 is a comparison of the lift forces measured in the experiments and produced by both of the prediction methods at 0 angle of attack. The momentum source replicated the lift behavior fairly well at low forward speed but then significantly under predict lift at the fastest forward speed. For the top advance ratio of 0.24 at 6000 RPM and 18.3 m/s, the momentum source calculation actually predicts a lower lifting force than the next slower speed. The fully resolved rotor calculation, however, predicts the lift force very well at a similar condition with an error of only 5%. The 8000 RPM momentum source calculation also better match compared to the 6000 RPM momentum source which suggests that there is a correlation between performance of the momentum source method and advance ratio.

58 Total Lift [N] Exp 8k RPM CFD 8k RPM Exp 6k RPM CFD 6k RPM FR CFD 6k RPM Wind Tunnel Velocity [m/s] Figure 3-19: Total Lift Comparison for Experiment and CFD The drag results for the two CFD methods and the experiments are shown in Figure 3-20 for a 0 angle of attack. While the momentum source replicates the trends of the corresponding experimental data quite well, the values of the predicted drag are significantly smaller than experiment. Both the momentum source and experiment show a convergence of the 6000 and 8000 RPM drag data due to a lessening of the ram drag experienced as the wind tunnel velocity is reduced, furthermore, the ram drag is seen to increase for both data sets as wind tunnel speed increases as evidenced by the growing difference between the 6000 and 8000 RPM data. The fully resolved solution under-predicted the drag by only 3% compared to experiment and demonstrates the accuracy of the computational method. Both the experiments and the CFD results have captured the distortion of the of the inflow to the fans caused by the separation of the front lip of the front duct and the angulation of the flow into the duct due to high forward speeds. While the momentum was able to replicate these results and major flow field features very well, it was not able to accurately or consistently provide reasonable lift and drag results. It was determined that the inaccuracies were due to the simplifications made to the momentum source distribution input into the rotor sweep volumes. These simplifications did not allow the complex flow field to be adequately modeled or

59 Net Drag [N] 44 reproduced to the level required for design or analysis work. This was confirmed by the fully resolved rotor simulation which was able to accurately predict the forces on the vehicle using a detailed rotor mesh. It is then concluded that while the momentum source CFD method is adequate for a solution of the flow field in and around the duct, the rotor must be modeled with more fidelity to improve the solutions Exp 8k RPM CFD 8k RPM Exp 6k RPM CFD 6k RPM FR CFD 6k RPM Wind Tunnel Velocity [m/s] Figure 3-20: Net Drag Comparison for Experiment and CFD

60 45 Chapter 4 Computational Approach Edgewise ducted fan flows are complex flow fields dominated by separation over the ducts. In the previous chapter it was demonstrated that this separation became severe in forward flight and encompassed a large portion of the forward duct in a recirculating, separation region. Since the qualities of the inflow to the fan will affect the performance of the fan, it is assumed that the separation in forward flight will significantly affect the distribution of thrust as produced by the rotors. This assumption was reinforced by the performance of the fully resolved CFD solution over the momentum source CFD. In the momentum source CFD, the rotors were modeled using a uniform distribution of forces through the rotor sweep volume. This performed poorly in comparison to both experiment and the fully resolved rotor. It was then concluded that in order improve the fidelity of the momentum source solutions, a better rotor model must be assembled. In order to better model the rotor, a way to calculate rotor forces in response to a nonuniform inflow field is required. Not only must this method be able to handle a non-uniform inflow, it must be able to take velocity field input and produce a force output that is radially and azimuthally varied. The method utilized to do this is blade element theory (BET). Blade element theory is a modeling technique that discretizes the blade radially and models each section using a two dimensional airfoil section, obtaining a radially varied force distribution. Blade element theory is often coupled to momentum theory for a hovering rotor to allow a prediction of rotor performance by coupling the induced inflow field to rotor forces by way of a momentum balance between the inflow and the outflow. However, blade element

61 46 momentum theory (BEMT) does not consider an azimuthally varied inflow or force distribution. Therefore, momentum theory was replaced by CFD in order to obtain the velocities for the inflow to the rotor. This will allow a BET calculation of a radially and azimuthally varied force distribution. This coupling of BET and CFD is shown in Figure 4-1 where the CFD solution is run and obtained for a specific flight condition. The calculated velocities are then extracted from the CFD solution and imported into a blade element theory code. The forces calculated in the blade element theory code are then imported into the CFD code and the CFD is rerun. This loop continues until a specified level convergence is reached. Figure 4-1: Basic Approach to CFD BET Coupling This method utilized the same momentum source CFD code as used in section and the mesh described in By using the momentum source CFD and coupling it to blade element theory, computational resources are kept relatively low while achieving a higher fidelity rotor model. The computational savings relative to the fully resolved case are the result of modeling the rotor rather than resolving and rotating the rotor within the CFD solution. This method serves as a compromise between the simplistic solutions momentum source solution used in section and the fully resolved rotor solution.

62 Review of Blade Element Momentum Theory Momentum Theory Using momentum theory it is possible to predict the thrust on a hovering rotor from the induced velocity or far wake velocity. This is possible by analyzing the flow through the rotor and applying fluid dynamics conservation laws, considering the slipstream a control volume. Figure 4-2 shows this slipstream through the rotor. Using this we can construct the fundamental equations needed to determine the rotor performance. Figure 4-2: Hover Rotor Slipstream (23) In order to develop the equations describing the momentum flux through the rotor, several things need to be assumed about the flow. First it is assumed that the flow through the rotor is inviscid and incompressible. It is also considered one dimensional such that the flow will only change in the axial direction. Finally, consider the flow quasi-steady where the flow properties are constant with time.

63 48 Considering the control volume containing the rotor and its slipstream defined by the surface, S, the equation for the conservation of mass can be expressed by Equation 4.1 where is the local velocity, is the outward facing unit normal vector and is the density of the fluid. (4.1) This equation states that the mass flow into the control volume must equal the mass flow out of the control volume. Following the formulation of 4.1, an equation describing the conservation of fluid momentum can be written as Equation 4.2. ( ) (4.2) As noted by Leishman (23), the net pressure force on the fluid inside the control volume is zero for an unconstrained flow. This renders the first term in Equation 4.2 zero. Since the rotor imparts the force onto the fluid, the fluid must exert an equal and opposite force on the rotor; this is the rotor thrust, T. The equation governing the conservation of energy is shown in Equation 4.3 and demonstrated that the work performed by the rotor results in an increase in the kinetic energy of the flow through the rotor. ( ) (4.3) Applying the assumption to Equation 4.1, the mass flow through the rotor control volume can be expressed as Equation 4.4a. Performing the integration at the specified boundaries from Figure 4-2 results in the relationships found in equation 4.4b where the mass flow, as required by Equation 4.1, is constant. Here,, is the far wake area,, the far wake velocity,, the rotor area and, the induced velocity at the rotor disk.

64 49 (4.4a) (4.4b) Rotor thrust is expressed by Equation 4.5a by applying Equation 4.2 at each of the control volume boundaries. Above the rotor, section 0, experiences only quiescent flow and therefore the force on the flow here is zero. The rotor thrust is then found using the far wake conditions in Equation 4.5b. ( ) ( ) (4.5a) (4.5b) Applying a similar method to the conservation of energy in Equation 4.6 yields an expression for the fluid kinetic energy as relating to the thrust as shown in Equation 4.6b where is an expression of the power or work performed by the rotor. ( ) ( ) (4.6a) ( ) (4.6b) Utilizing the result for thrust in Equation 4.5b and the energy expression in Equation 4.6b, a relationship between the induced velocity and far wake velocity is found. Equation 4.7 shows this simple result where the far wake velocity is found to be twice the induced velocity. Following from Equation 4.4b, this indicates that the far wake area is half the rotor area. or (4.7) From Equations 4.4b, 4.5b and 4.7, Equation 4.8 is formed. This expression allows the rotor thrust to be found using the fluid density, induced velocity and the rotor area. This result is

65 the desired relationship for the purposes of rotor performance prediction. Application of this result in blade element momentum theory will be shown in a coming section. 50 ( ) (4.8) Blade Element Theory Blade element theory allows a discretization of the rotor both radially and azimuthally for the purpose of analyzing rotor performance in response to a non-uniform inflow velocity. To do this, BET models the discretized rotor section as two-dimensional airfoil sections and assumes that adjacent sections are independent and have no influence on each other. In addition to considering a non-uniform inflow, BET takes into account rotor properties such as twist as well as the airfoil properties of the blades. This allows for a study of the influence of these rotor properties and makes blade element theory an ideal method for use in rotor design and analysis. Figure 4-3shows the relationship between the flow and blade properties as well as the aerodynamic forces. It should be noted that the aerodynamic forces calculated are the sole result of the velocities as shown and are calculated assuming an averaging of one full rotor rotation. Figure 4-3:Blade Element Diagram

66 51 Only the tangential velocity,, and the axial velocity,, components are considered for the local flow velocity and the radial component is neglected. The resultant velocity can then be found using Equation 4.9. The (4.9) Using these components, the local inflow angle can be found from Equation Caution should be used in the use of the inverse tangent function with a highly varied flow field where quadrant corrects may be required. ( ) (4.10) Having the inflow angle and knowing the local pitch of the blade element allows the calculation of the effective, local angle of attack at the blade element. This result can be visual confirmed by Figure 4-3. For any given blade element, as the axial velocity increases it causes a decrease in the angle of attack. This is a significant result in that it demonstrates a negative feedback mechanism between the inflow velocity and thrust. This arises whereas the angle of attack is decreased, the lift on the blades and therefore thrust will also decrease. The importance of this will become clearer as BET is coupled with other inflow solutions. (4.11) The lift and drag can now be calculated from Equations 4.12a and 4.12b now that he angle of attack, total inflow velocity and blade properties are all known. These equations show the lift and drag in a differential, discretized form. Here the term refers to the radial step size which is equal to the spanwise (radial) width of the blade element.

67 52 (4.12a) (4.12b) Following the representation of these forces from Figure 4-3, the lift and drag on the blades must be transformed into the thrust and tangential force components of the rotor. This is done using Equations 4.13a and 4.13b where the relationship between the two sets of forces is trigonometric and varies with the inflow angle,. Also note that a factor,, has been applied to the thrust and tangential force equations. This represents the number of blades on the rotor and is required in order to model the rotor for one entire rotor revolution. ( ) (4.13a) ( ) (4.13b) Equations 4.13a and 4.13b represent the final force results from the blade element theory calculation and will be used in the blade element momentum theory. However, these equations are discretized only in the radial direction. Equations 4.14a and 4.14b extend the discretization into the azimuthal direction as well. To do this the factor is applied to the equation. Here the term represents the azimuthal step size and, the radian value of one rotation. This factor then represents the fraction of the rotor disk each discretized sector accounts for. These equations make the consideration of a, both, radially and azimuthally varied inflow field possible and are the form of the blade element equations used for much of this thesis. ( ) (4.14a) ( ) (4.14b)

68 Blade Element Momentum Theory Blade element momentum theory (BEMT) allows for an iterative solution to rotor performance by coupling momentum theory and blade element theory. The advantage of this method over either the two methods separately is the ability to evaluate performance knowing only the rotor geometry and properties without any inflow velocity input. This is accomplished by first considering a discretized form of the momentum theory Equation 4.8 shown in Equation 4.15 where the rotor disk is discretized into annuli. ( ) (4.15) This discretized momentum theory equation is then solved along with the thrust equation from blade element theory, Equation 4.13a. While there are multiple valid methods to couple these equations and achieve a solution, an example of a BEMT code is provided in Appendix C. In this code both thrust equations are solved independently using the same inflow and the difference between the results is used to calculate a new inflow velocity. This loop continues until the two thrust calculations converge to the same answer, where, when this occurs an induced velocity would have been found that satisfies the assumptions of both momentum theory and blade element theory. Here the calculated induced velocity will have been made to obey the governing equations of momentum theory, reflecting a mass, momentum and energy balance between the rotor inflow and far wake outflow. The aerodynamic forces produced by this induced velocity will then have been constrained to established airfoil lift and drag principle as expressed in Equations 4.13a,b from blade element theory and will be calculated as a radially varied rotor force, constant around the azimuth.

69 Coupling BET to CFD There already exists a method by which an arbitrary rotor configuration can be analyzed and designed as seen in the previous section. However, this method, blade element momentum theory, only takes rotor properties as input and calculates an induced flow field simultaneously as part of momentum theory. While this is useful for evaluating an isolated rotor, its utility is limited with respect to the design and analysis of a complete vehicle. In the evaluation of vehicle performance the outer flow around the vehicle cannot be simply modeled. The flow phenomena, and therefore the rotor behavior, involved in many vehicles, especially the ducted fan of interest here, is simply too complex to allow a successful application of a simplifying model or assumption. Therefore a method is required whereby an axially and azimuthally varied force distribution can be calculated in response to a highly distorted inflow velocity field. This will be achieved by coupling BET to a CFD code. The inflow velocities needed as input to the BET code will be extracted from the CFD results and the calculated force distribution then imported into the CFD as shown in Figure 4-1. A detailed overview of the steps involved in running this coupled method is shown in Figure 4-4. The method begins by taking restart files of a simple starting case, often an approximated hover condition, and using an interpolation routine to interpolate the velocities from the CFD files onto the BET grid. The velocities, provided in orthogonal components, are imported into the BET code. The BET code outputs the forces, again in orthogonal (X, Y, Z) components. These are then relaxed by averaging with a previous iteration of calculated forces only if the code has proceeded beyond the first iteration. These forces are then reformatted for the CFD code, OVER-REL, and are then input into the CFD code. The last step of the loop is the running of the CFD code, which at its conclusion is then used to interpolate velocities from, onto the BET grid, starting the next iteration.

70 55 Over-Rel Restart Files Interpolate Velocities onto BET Grid Blade Element Theory Relax Forces If Iteration > 1 Format Forces for Over-Rel Over-Rel Figure 4-4: Coupled BET-CFD Block Diagram In this coupled method, BET is treated much in the same way as it is in BEMT. In blade element momentum theory, BET is the primary source of rotor force information while the balance of mass, energy and momentum are dependent on another set of equations, namely, momentum theory. The assumption in the coupled BET-CFD method is that BET calculations are valid for the predicted inflow and that the CFD will effectively achieve closure. This assumption is based on how the CFD code runs and the equations that govern it. In momentum theory, it was seen that the governing equations are the conservation of mass, momentum and energy. These equations were used in BEMT to balance the force acting on the fluid through the control volume, bounding the fluid velocity. In the BET-CFD method, the CFD code is effectively replacing momentum theory. However, the governing equations are not being taken out of the iterative loop. The CFD code, OVER-REL, as a RANS code is solving, fundamentally, the same governing equations in a higher-fidelity calculation. Therefore, the rotor

71 56 performance is still bounded in the same manner as it was in BEMT, however, the BET-CFD method does not assume or simplify the inflow velocities, increasing the fidelity of the calculation by avoiding neglecting the physics of the problem Obtaining Inflow Velocities from CFD In order for the blade element routine to calculate a meaningful force distribution, the inflow velocities must be extracted from the OVER-REL results. This process is shown in Figure 4-5. To accomplish this task two codes are used: the first, interpolate_rst, performs the actual interpolation of the flow field from the OVER-REL restart file, and the second, InterpFormat, extracts the wanted information from the interpolate_rst output and formats it in a way that can be read into MATLAB. The interpolation code requires the restart files from OVER-REL which contain the flow field information from the previous OVER-REL solution and the grids onto which the velocities will be interpolated. The grids used here have the same shape and radius as the rotor sweep volume grids with a few changes. First the thickness of the grids in the axial or Z direction has been reduced and the interpolation grids were positioned above the rotor sweep volume grids. This allows for an extraction of the flow properties just above the rotor plane, which is ideal for the blade element calculation. The resolution of the grid was reduced from the rotor sweep volume grids radially to match the resolution of rotor property data, here there are 128 azimuthal positions and 16 radial positions. The result of this interpolation is a plot 3D file named plot.func. The formatting code only requires the output code from the interpolation code and extracts the relevant information: X, Y, and Z velocity components. This code then writes the

72 velocity information to a set of files with the X, Y, Z velocities for both the forward and aft fan written separately. The InterpFormat code is provided in Appendix C. 57 OVER-REL Restart Files Interpolate_rst Interpolation Grids Plot 3D properties file: plot.func InterpFormat Read plot.func Collect velocities components Writer ASCII formatted velocity files Figure 4-5: Velocity Interpolation Block Diagram Calculating Rotor Forces The rotor forces are calculated using blade element theory as detailed in section using the velocities obtained from the CFD solution as explained in the previous section. This code takes the velocity field in X, Y, Z components and the rotor properties as inputs. This code and the input files are shown in Appendix C. The block diagram of the MATLAB BET code is shown in Figure 4-6. After reading in the necessary information, the velocity is transformed into the blade element coordinate system which is in terms of radius and azimuth. The forces are calculated using the equations presented in a previous section. These forces are then transformed back into the CFD coordinate system and non-dimensionalized. The output of the BET code is

73 written as ASCII formatted, column ordered arrays written to separate files for the forward and aft fan and X, Y, Z components. 58 Read Rotor Porperties Read Inflow Velocities Transform into BET Coordinate System Calculate Forces on Blade Elements Transform into CFD Coordinate System Non- Dimensionalize Forces Write ASCII Formatted Force Files Figure 4-6: Blade Element Theory Code Block Diagram After the rotor forces are calculated from the inflow they are relaxed in a MATLAB routine, relax.m. This runs only if the BET-CFD loop iteration is greater than one as shown in Figure 4-4. Starting with the second iteration, the relaxation code reads in the current and previous iteration force distributions in all three directions. The difference is then taken of the two iteration force distributions. The amount of relaxation to be applied is determined by a relaxation factor applied to the force difference. This is then added to the previous iteration force distribution. The relaxation factor used for this thesis was 0.5, creating an average of the forces from the two iterations. The output file format is identical to the BET output files. The relaxation routine can be found in Appendix C.

74 59 Read Previous Iteration Force Distribution Read Current Iteration Force Distribution Calculate Change in Force Distribution Relaxation Factor Calculate New Force Distribution Write Force Files Figure 4-7: Force Relaxation Code Block Diagram Formatting Forces for CFD Once the force distributions have been calculated for each fan and all three components, the forces must be formatted for input into the OVER-REL CFD code, this process is shown in Figure 4-8. To do this the both the force files generated by the BET code and the rotor sweep volume grids, into which the forces are input, are read into the formatting code. Here the volume of each individual grid cell is calculated. Also the control volumes of the CFD and BET grids are compared such that the BET forces are applied radially along the correct number of CFD grid volumes. The final operation to the forces is normalization by volume. This is required by OVER-REL for the input of body forces acting on the fluid volumes. The forces are then written to files by grid block according to the plot 3D standard format.

75 60 Read CFD Grids & BET Force Files Calculate Grid Cell Volume Assign BET Forces to CFD Grid Normalize Forces by Volume Write Forces to Plot 3D force files by grid block Figure 4-8: Body Force Format Code Block Diagram 4.3 Definition of Residual To gauge the convergence of the BET-CFD loop a residual was defined based on the inflow velocity magnitudes to each fan. The inflow velocity magnitude was chosen as the metric for convergence because this is the parameter that drives the force calculation in the BET code. The forces calculated are proportional to and therefore, differences arising in the flow field will be magnified in the force calculation. It was then determined that the differences in the velocity magnitudes were a better indicator of the status of the solution. The residual, referred to as a root-mean-square-differential or RMSD, is shown in equation Here the velocity magnitudes, as interpolated from the CFD solution, are resolved into a resultant total velocity. The total velocity at the previous iteration is subtracted from the current iteration and normalized by the velocity at the current iteration. This normalized differential is then squared. This process is performed at each grid point for all radial and azimuthal locations, where is the max azimuthal coordinate and is the maximum radial

76 coordinate. The differential at each point is summed and divided by the number of points, yielding the arithmetic mean. The square root of this quantity is then taken to yield the residual. 61 [( ( ( ) ( )) ) ] (4.16) ( ) The resulting quantity is then the root-mean-square of the difference of the entire velocity field. This gives a quantitative comparison of the flow fields and a quantitative measure of the status of the coupled BET-CFD solution. It should be noted that the RMSD is not considered at the first iteration and is defined as NaN or Not a Number. For the purposes of this thesis, the residual will be used to judge the quality of the closure of the iterative loop between the CFD and BET results, not necessarily its accuracy.

77 62 Chapter 5 Results of Coupled Solution The completed BET-CFD loop was run for a variety of forward speeds at a vehicle angle of attack of 0 and a rotor RPM of 6000 in order to match several advance ratios previously investigated experimentally and to match conditions used in previous computations. An approximate hover case was also run at a forward speed of ~0.2 m/s, the forward speed was necessary due to a limitation of the CFD code. The solutions were run to 20 iterations which was found to provide an adequate level of convergence. The CFD routine used here was identical to the method from section using the grid from section 2.2.2, utilizing the OVER-REL code as developed by Penn State ARL. Within each iteration, OVER-REL was run for 2000 iterations using a CFL of 1.0 for the first 1000 iterations and 5.0 for the last 1000 iterations. Each run of the BET-CFD method was initialized using restart files from a hover condition utilizing a uniform thrust distribution identical to the solution presented in section The final series of computations shown here was the result of several studies of the accuracy and stability of the coupled method. A strong sensitivity to airfoil properties was found, which will be explored later in this chapter. The initial solutions were also found to slowly converge with oscillations in the force results. Under-relaxation was applied to the force distributions, as discussed in the previous chapter, to promote the stability and convergence of the method. With the intention of using this method as a high-level design aide, the aerodynamic force results are the primary focus and metric by which the method is evaluated. The predicted

78 vehicle performance will be explored and compared to experiment and other computational methods in addition to the results of the flow field Validation of BET The blade element theory code was tested for accuracy in its ability to reproduce the thrust of a hovering rotor at 6000 RPM. This was performed as a validation trial prior to its full implementation into the coupled method. In order to perform this test, a model of the inflow to the rotor was required. Here, two trials of this validation were run: one with a tip loss correction and one without. The inflow model was constructed using two sets of independent data. The first, shown in Figure 5-1 for an inflow without tip loss, was a radial inflow variation calculated in a BEMT code, shown in Appendix C. This calculated inflow was then normalized by the 70% radial position. The 70% radial position was selected because experimental inflow data was taken at various points around the azimuth at the 70% radial position. Taking advantage of this, an azimuthal inflow variation was constructed using the experimental hover data at 6000 RPM at the 70% radial position. Figure 5-1: BEMT Induced Inflow over Non-Dimensional Radius, without Tip Loss

79 64 The two sets of inflow data, a radially dependent distribution from BEMT and the azimuthally dependent experimental inflow magnitudes were then multiplied together to create a two dimensional, radially and azimuthally dependent inflow model. This model is shown in Figure 5-2(a) where the front of the rotor is to the left of page. In the inflow model, very low velocity magnitudes are seen in the inboard positions of the rotor near the hub. From the BEMT results, the velocity increases and plateaus out near the tip. Azimuthally, the larger velocity magnitudes are found in the front of the fan, as shown experimentally. Figure 5-2(b) shows the resultant thrust distribution from the BET code due to the inflow model. Here, the thrust is defined to be negative, indicating it is in the opposite direction of the incoming inflow velocity. Low thrust is seen near the hub, corresponding to the low inflow velocities but also the tangential velocities of the blades are low due to the small radial position. Also of note, the points at the front of the fan that experience higher velocity magnitudes have smaller thrust values. This is due to the inflow reducing the angle of attack on the blades. The highest thrust is seen near the rotor tips due to a lack of a tip loss correction. (a) Inflow Velocity Magnitude[m/s] (b) Thrust Distribution [N] Figure 5-2: Hover Simulation without Tip Loss for 6000 RPM: (a) Inflow Velocity Magnitude, (b) Thrust Distribution

80 65 Applying the same procedure for a trial with a tip loss correction, the BEMT code was rerun and the resulting radial inflow magnitude distribution is shown in Figure 5-3. This is very similar to the previously calculated inflow distribution, but here the inflow velocities are seen to decrease after the 70% radial position rather than staying relatively constant. Figure 5-3: BEMT Induced Inflow over Non-Dimensional Radius, with Tip Loss This radial distribution of inflow velocity magnitude was then normalized and multiplied by the experimental 70% radius inflow magnitude results, same as the previous inflow model. This resulted in a radially and azimuthally dependent inflow model including a tip loss correction shown in Figure 5-4(a). While the max inflow velocity magnitude in consistent with the previous model, the inflow velocity decreases out to the rotor tip. The thrust distribution calculated by BET in Figure 5-4(b) for this inflow model also included a tip loss correction. This tip loss factor caused a decrease in the thrust near the tip, yielding a more realistic thrust distribution.

81 66 (a) Inflow Velocity Magnitude [m/s] (b) Thrust Distribution [N] Figure 5-4: Hover Simulation with Tip Loss for 6000 RPM: (a) Inflow Velocity Magnitude, (b) Thrust Distribution A comparison of the thrust generated in both of these simulations and the experiments at 6000 RPM is shown in Table 5-1. Two sets of experimental data are shown here: lift in hover and rotor thrust. The hover lift is shown per fan or half of the measured lift in hover at 6000 RPM. This result, as previous presented, includes the duct lift as well as rotor thrust. To better compare to the simulations, which calculate rotor thrust only, an approximation was made. For a ducted fan, the duct can generate as much as 50% of the total lift of the vehicle (21). However, as noted by Fleming (21) an imperfect duct will generate much less than that, therefore the ducts here are expected to generate 20% to 35% of the total lift. This gives a range of valid rotor thrusts from 4.47N to 5.5N, the average being 4.99N corresponding to a duct lift of 27.5%. This average approximate rotor thrust was used to compare to the calculated thrusts from BET. The simulation without tip loss correction yielded a thrust of 5.46N or 9.4% higher than the approximate experimental value. The simulation including the tip loss factor, showed only 1% error with a predicted thrust of 5.04N. These results demonstrate the ability of blade element theory to reasonably predict rotor thrust consistent with experimental values, yielding errors of less than 10% using a modeled hover inflow.

82 Table 5-1: Comparison of BET Hover Thrust and Experimental Lift Results at 6000 RPM Experimental Hover Lift, per Fan Experimental Rotor Thrust Estimation (average) BET Simulation without Tip Loss 67 BET Simulation with Tip Loss Thrust [N] (4.99) Error to average experimental thrust estimate 37.9% % 1.00% While the predictions using a tip loss factor fared better than the prediction without a tip loss correction as compared to experiment, the tip loss factor was not used in the coupled CFD- BET method. The tip loss correction was omitted because it models an effect of rotor tip vortices on the rotor lifting capability. It is assumed that the CFD solution will sufficiently resolve these effects in the inflow velocities for the BET code, rendering the tip loss factor redundant in the coupled method. 5.2 Coupled BET-CFD Solutions Flow Field Results First, the results of the flow field and its properties in and around the duct will be explored in detail. While the vehicle performance predictions are the primary focus for evaluating the coupled method, achieving a high fidelity flow solution is critical to calculating physically relevant rotor forces. Static pressure coefficient contours on the vertical symmetry plane are shown in Figure 5-5 for a variety of forward speeds and a hover condition. The hover condition is approximated in the CFD code by using a very small forward velocity, 0.18 m/s, some effects of this can be seen in the static pressure contours. At the front lip of the front duct a small region of very low

83 68 pressure is seen. This is indicative of a separation region as demonstrated by prior experiments and computations. While some of this separation may be from flow accelerating around the duct, it is likely the small forward velocity is contributing to this effect. Much of the remainder of the flow field is as expected. The pressure jump across the rotor plane is nearly uniform across the duct cross-section due to the absence of significant inflow distortion. At forward speeds the low pressure region over the front duct expands and the pressure jump across the rotor plane becomes less uniform. The dominate feature of the forward flight results is the low pressure region extending back from the front lip of the front duct. At 6.1 m/s, this region covers nearly the front half of the front fan. As the forward speed is increased this region extends rearward until at 18.3 m/s it engulfs over two-thirds of the front fan. A similar effect is seen over the aft fan, although on a smaller scale. These areas of low pressure correspond with the expected separation region which has been shown to develop in forward flight by experiment. These regions also appear to affect the pressure below the rotor plane. Regions of drag production are readily visible in the static pressure contours. Large values of static pressure coefficient, colored in red, can be seen at the nose of the vehicle and the rear wall of both ducts. These regions of high values indicate stagnation points caused by the forward velocity, the locations of the stagnation regions in the ducts indicate high flow angularity into the rotors.

84 69 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-5: Static Pressure Coefficient Contours on Vertical Symmetry Plane for 6000 RPM, 0 Angle of Attack, (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

85 70 Further detail of the angularity and distortion of the inflow into the rotors can be seen in the total pressure contours shown in Figure 5-6 on the vertical symmetry plane for 6000 RPM, 0 angle of attack and at several flight conditions. For the hover case, where inflow distortion is low, strong total pressure coefficient values are seen from both the forwards and rear portions of both fans. Regions of low total pressure can be seen in hover near the duct walls. This is most prominent at the front lip where the low forward speed in this hover case is contributing to a small area of separated flow. As the vehicle enters forward flight, the separation region, exhibited by low total pressure colored blue, expands to cover over a third of the front fan at 6.1 m/s and nearly two thirds of the front fan at 18.3 m/s. This result mirrors the static pressure contours from Figure 5-5 and indicates that this effect is not simply a low pressure region lifting the vehicle but also a severe loss of clean flow through the duct. This loss of clean flow through the duct is evidenced by the lack of strong total pressures in the outflow as seen in the hover case. At 6.1 m/s large total pressure are only seen in the rear of the front fan and some near the 30% radial position in the front of the fan. At this speed the aft fan still experiences a large amount of clean flow. At 10.7 m/s the separation region encompasses half of the front fan and separation off the fuselage center body has increased distorting the flow into the aft fan. At the highest forward speed, 18.3 m/s, the separation off the front lip has increased to two thirds of the front duct, with clean flow seen only in the rear-most portion of the fan. The aft fan also experiences severe distortion in the inflow field. Apart from the magnitudes of the total pressure contours, the regions of high total pressure show a highly swept shape. This reinforces the notion of the flow angularity from the locations of stagnation points on the fuselage and ducts seen in the static pressure contours.

86 71 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-6: Total Pressure Coefficient Contours on Vertical Symmetry Plane for 6000 RPM, 0 Angle of Attack: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

87 72 The velocity magnitudes in the inflow plane shown in Figure 5-7 reinforce the flow patterns seen in the pressure contours and clarify the effect of a forward velocity and the inflow distortions. In hover, very little distortion of the inflow velocities is seen. A small region of reduced velocity is seen around the front of the front fan and the rear of the aft fan. This is due to separation off the ducts, as seen in the pressure contours, generated by the induced flow into the ducts. The front separation region is larger due to the small forward velocity. The front fan in hover also displays an area of increased velocity corresponding to the advancing side of the rotor. The forward speed of 6.1 m/s begins to display the expected lip separation and inflow distortion. Over the front fan, the retreating side of the fan experiences a large region of low velocities while large velocity magnitudes develop on the advancing side of the rotor, consisted with the hover case. The aft fan shows similar behavior where the velocity magnitudes increase on the advancing side of the rotor, however the aft fan experience much less distortion from separation. An area of low velocity is also seen just aft of the vehicle on the left side, indicating a possible shedding behavior. As the forward velocity increases to 10.7 m/s, the front lip separation region increases and the region of high velocity on the advancing side of the rotor begins to retreat to the rear of the fan. At 18.3 m/s forward speed, the region of low velocity has expanded still and has become more complex and irregular shaped. Only rear of the front fan ingests large velocity magnitudes at this forward speed. The aft fan inflow field has also become significantly distorted with regions of low velocity magnitudes found at both the left and right sides of the duct.

88 73 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-7: Velocity Magnitude Contours on Horizontal Plane Above Rotor Plane for 6000 RPM, 0 Angle of Attack: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s (d) 18.3 m/s

89 Force Results Figure 5-8 shows the angles of attack in degrees calculated by the blade element theory code in the front and aft fan for the four flight conditions tested. Here the rotor disks are oriented such that the rear of each fan is to the top of the page. The angles of attack are seen to vary both radially and azimuthally based on the direction of rotor rotation. The lowest angles of attack are seen on the retreating side of the rotor disk while the highest angles of attack are at the advancing side. This effect is less obvious for the hovering rotor. The hover case displays some azimuthal variation due to the low forward speed but also due to azimuthal variation of the duct design which affects the angulation of the inflow. As the forward speed increases, an area of low and negative angles of attack grows at the retreating side near the hub where angles of attack approach -15. The advancing side of the rotor experiences increasingly large angles of attack as the forward speed is increased, the maximum angles of attack is near 30 for 6.1 m/s and 10.7 m/m and increases to nearly 45 at 18.3 m/s. Radially, the angles of attack decrease out to the tip, corresponding to a decreasing local pitch angle on the blade elements due to the blade twist. The angle of attack distributions calculated in the blade element theory code also, curiously, have a lobed variation azimuthally. The source and cause of this pattern is not currently known. It is, however, observed that the lobed pattern becomes more prevalent as the forward speed and therefore the distortion of the inflow becomes more severe. Starting with the aft fan in hover, the lobing is not very prevalent, with exception to the rear, retreating quadrant of the rotor disk. At the two highest speed, 10.7 m/s and 18.3 m/s, the front fan exhibits a highly lobed angle attack result. The lobed pattern, while varied in severity, presents a potential problem and error with in the solution. The development of this pattern warrants additional investigation to determine if the effect is a flaw of the method, a neglected effect or a computational artifact.

90 75 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-8: Blade Element Local Angle of Attack (deg.) for 6000 RPM: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s (d) 18.3 m/s

91 The thrust distribution calculated from the inflow presented in section and the 76 previously presented angles of attack are presented in Figure 5-9. These forces are nondimensional and in their discretized form, which is to say the results represents as calculated in equation 4.14a. The higher thrust terms are colored in blue and are negative to represent the force on the fluid, which is equal and opposite to the force on the rotor, and conforms to the CFD coordinate system. Corresponding to the angles of attack, the highest values of thrust are found on the advancing side of the rotor disk. On the retreating side, small values of thrust (colored red) nearing zero develop near the bub. As the forward speed is increased, the distribution of thrust around the rotor disk and between the forward and aft fan changes significantly. In hover the trust does vary around the azimuth with the angle of attack, although the differences are not vastly significant in the aft fan. The distribution of thrust at 6.1 m/s is very similar between forward and aft with the aft fan retaining more thrust on the retreating side. As the forward speed is increased to 10.7 m/s and 18.3 m/s, the maximum thrust on the blade elements in the front fan begin to significantly decrease and the retreating side of the front and aft rotor disks become less effective, producing very little lifting force. The aft fan in these conditions also provides more thrust than the front fan, a result which is due to the front fan having a far more distorted inflow than the aft fan at high speeds. These thrust distributions do not change significantly on being input into the CFD code. The volumetric, non-dimensional thrust distribution input into the CFD is shown in Figure Here the forces from Figure 5-9 have been normalized by the cell volume before being input into the CFD solution. This provides some smoothing to the distribution, although a faint lobed pattern emerges to some extent, but not near the severity of the angle of attack results. This normalization also changes the relative values near the tip of the blades where in the BET results the thrust appears to approach zero, there is still significant thrust in the CFD solution.

92 77 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-9: Blade Element Non-Dimensional Discretized Thrust over Rotor Disk for 6000 RPM: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

93 78 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-10: Non-dimensional, Volumetric Thrust Input into CFD for 6000 RPM: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

94 79 Apart from the thrust of the blades, the tangential force the blades produce, essentially drag, was also calculated in the blade element theory code and input into the CFD solution. The tangential forces was broken into its constituent X and Y direction components, nondimensionalized and normalized by volume prior to being input into the CFD. The tangential rotor forces input into the CFD can be seen in Figure 5-11 and Figure 5-12 for the x and y force components, respectively. The X direction corresponds to the longitudinal axis of the vehicle and is positive to the left of the page. The y direction is aligned with the lateral vehicle axis and is positive to the top of the page. The force in the x direction is positive, colored red, for the retreating side of the rotor disk and is negative, colored blue, over the advancing side of the rotor disk. The magnitude of the X-force is larger for the advancing side, corresponding to the higher thrust and angles of attack. While the magnitude of these forces is consistent in the aft fan over a variety of forward flight speeds, the force in the front decreases as the forward flight speed increases. This is due to lower velocity magnitudes over the blade elements. The position of the maximum x-direction force is consistent throughout the forward flight, located near the root on the advancing side of the rotor. The rotor force in the y-direction varies in a similar manner to the x forces, however, the locations of the maximum and minimum have rotated within the duct. For the front fan, positive values are seen in the front of the fan and negative vales in the rear of the fan. The opposite is true of the aft fan where the rotation is reversed; the positive values are found in the rear of the fan and negative values in the front. The maximum and minimum values of y-direction rotor forces do not change significantly with forward speed. The distribution of the forces around the rotor disk also remains nearly constant between different flight conditions.

95 80 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-11: Non-dimensional, Volumetric Force in X direction Input into CFD for 6000 RPM: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

96 81 (a) Hover (b) 6.1 m/s Forward Speed (c) 10.7 m/s Forward Speed (d) 18.3 m/s Forward Speed Figure 5-12: Non-dimensional, Volumetric Force in Y direction Input into CFD for 6000 RPM: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

97 Forces [N] 82 The resulting aerodynamic forces and the calculated total rotor thrust are shown in Figure 5-13 for all forward velocities tested. The total thrust presented here is the sum of the thrust from the front and aft fan. This quantity does not deviate significantly from the hover value over the range of forward flight speeds. The thrust increases at the lowest forward flight speed and then decreases as the forward flight speed is further increased. This behavior is a confirmation of the previous presented thrust distributions where the thrust was seen to diminish in the front fan. The lift, shown as total vertical force, increases with forward speed, even as thrust decreases, indicating an increase in the lift on the fuselage. At the highest forward speed, 18.3 m/s, the lift is nearly double the thrust, demonstrating that he fuselage lift is nearly equal to the thrust of the rotors. This is compared to the hover condition where the rotor thrust comprises about 75% of the lift on the vehicle. As is expected, the drag rises with forward speed. However, the increase in drag becomes more gradual at the highest forward speed, a behavior in the drag result seen in previous computational results using the momentum source method Wind Tunnel Velocity [m/s] Figure 5-13: Forces on Model Calculated by Coupled Method at 6000 RPM, 0 Vehicle Angle of Attack Lift Drag Total Thrust

98 Convergence The aerodynamic forces were recorded during the course of the calculation to provide a qualitative description of the convergence of the coupled method; this is shown in Figure In each flight condition the lift, drag and thrust forces stay nearly constant after the sixth iteration. The forces in the hover and the 18.3 m/s forward flight cases settled the quickest, with the forces in the 6.1 m/s forward flight case oscillating and never truly settling. Using the definition of the residual as the root-mean-square deviation, RMSD, from equation 4.16, a quantitative description of the convergence is found. Here the residual is shown in Figure 5-15 and is considered for both the front and aft fan independently for each flight condition. In every forward flight case, the velocity field over the aft fan results in a smaller residual than the front fan. This result is indicative of the behavior of the inflow where the front fan experiences as much more distorted and complex inflow than the aft fan. The hover and 18.3 m/s forward flight case converged the fastest, as suggested by the force history results, with the residuals decreasing at least three orders of magnitudes for both the front and aft fan in both cases. The 6.1 m/s forward flight case does not converge to the level of the other solutions. Here, the residuals on the front fan decrease by little over one order of magnitude, the aft fan residuals see a two order of magnitude drop. This result reflects the oscillatory behavior of the forces observed over successive iterations. Furthermore, considering Figure 5-7(b), where shedding was suspected off the rear of the vehicle at the 6.1 m/s forward flight condition; the force history and residual results confirm an unsteady effect on the fuselage. In section 3.2.2, a similar behavior was seen within the fully resolved rotor calculations at 18.3 m/s forward speed.

99 Force (N) Force (N) Force (N) Force (N) (a) Hover Total Lift Total Fan Thrust Total Drag Iteration (b) 6.1 m/s Forward Speed Iteration (c) 10.7 m/s Forward Speed Total Lift Total Fan Thrust Total Drag Total Lift Total Fan Thrust Total Drag Iteration (d) 18.3 m/s Forward Speed Total Lift Total Fan Thrust Total Drag Iteration Figure 5-14: Force History for Coupled Method Solutions: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

100 RMSD RMSD RMSD RMSD (a) Hover Forward Fan Aft Fan Iteration (b) 6.1 m/s Forward Speed 10-1 Forward Fan Aft Fan Iteration (c) 10.7 m/s Forward Speed Forward Fan Aft Fan Iteration (d) 18.3 m/s Forward Speed Forward Fan Aft Fan Iteration Figure 5-15: Residuals for Coupled Method Solutions: (a) Hover, Forward Speeds: (b) 6.1 m/s, (c) 10.7 m/s, (d) 18.3 m/s

101 Comparison to Previous Work Flow Field Comparison In order to determine the accuracy of the solution and the validity of the force calculation the flow field calculated in the coupled method was compared to analogous flight conditions in experiment. Here, experimental measurements of flow velocity magnitude, flow angulation within the duct and flow visualization were compiled from the results of chapter 3. Figure 5-16 shows a comparison of the lowest advance ratios tested. Here the coupled calculation used is the 6.1 m/s case with an advance ratio of 0.08 at 0 angle of attack. This is compared to a similar experimental condition at an advance ratio of and -3 angle of attack. In the front duct especially, analogous flow patterns can be seen between the two graphics. In the experiment, streamlines are seen to enter the bottom of the duct with a strong wake developing out of the rear of the front duct. The rear duct does not ingest nearly as much of the smoke and therefore the wake is not as well visualized, however, flow can be seen exiting the rear duct and the distortion of the inflow streamline and the wake is minimal. The computation shows a similar result where the low total pressures in the front of front duct indicate a recirculating, separation region. The rear of the front fan then sees a strong total pressure, indicating clean flow through the rear of the fan, matching the experimental result. The aft fan in the computation also experiences little inflow distortion with strong total pressures through the duct.

102 87 (a) Smoke Wire Visualization, μ=0.065, -3 AoA (b) Total Pressure Contour, μ=0.08, 0 AoA Figure 5-16: Low Speed Flow Field Comparison: (a) Smoke Wire Visualization, μ=0.065, -3 AoA, (b) Total Pressure Contour, μ=0.08, 0 AoA A comparison of the highest advance ratio tested is shown in Figure Here both graphics show a 0.24 advance ratio condition, the computation used for comparison here was at an 18.3 m/s forward speed and 0 angle of attack. The experiment used shows the vehicle at -10 angle of attack. In the experimental flow visualization, the streamlines are seen to pass over the front portion of the duct completely and intersect the rotor in the rear of the duct. This illustrates the large separation region which envelopes the front of the fan at forward speeds. At an advance ratio of 0.24 this separation region covers nearly two-thirds of the fan with the streamlines meeting the rotor past the spinner in Figure 5-17(a). The computation matches this result only the rear third of the front duct showing strong total pressure contours, indicating a clean inflow region.

103 88 (a) Smoke Wire Visualization, μ=0.24, -10 AoA (b) Total Pressure Contour, μ=0.24, 0 AoA Figure 5-17: High Speed Flow Field Comparison: (a) Smoke Wire Visualization, μ=0.24, -10 AoA, (b) Total Pressure Contour, μ=0.24, 0 AoA Figure 5-18 shows an inflow velocity magnitude comparison between experiment and the coupled CFD method at a wind tunnel speed of 6.1 m/s and 6000 RPM. The experiments were performed at an angle of attack of -10 while the CFD is at 0 angle of attack. The measurements and the CFD results are taken at the same points with the duct seen in Figure 3-1in a plane just above the rotor. Excellent agreement is seen between the CFD and experimental results in the rear of the fan and on the advancing side of the rotor. However, the locations in the front of the duct and the 242 retreating position do not compare very well. Referring back to Figure 5-7(b), a large region of stagnated and separated flow extends from the front of the fan to the retreating side of the rotor. It is within this region that the velocity magnitudes are not predicted accurately by the CFD method. At the 30% radial position, just aft of this separated region, the measurement and prediction match very well.

104 Velocity Magnitude [m/s] 89 70%R Exp 30%R %R Coupled 30%R Azimuthal Angle [deg] Figure 5-18: Inflow Velocity Magnitude Comparison in Front Duct for 6000 RPM, 6.1 m/s Wind Tunnel Speed The velocity magnitudes in the outflow of the rotor, below the rotor plane, are shown in Figure 5-19 at the same conditions from the prior inflow measurements and predictions. Again, in the outflow, the agreement between the CFD prediction and the experimental velocity magnitudes is very good. Little error is found between the measurements and the prediction in the rear of the fan and on the advancing side of the rotor, mirroring the success of the inflow predictions. In the front of the fan, the outflow predictions fair better than the inflow predictions. Although the velocity magnitudes in the front of the fan are not predicted as well as the magnitudes in the rear of the fan, the trends are in fact accurate. Again, the velocity magnitude at the 242 azimuthal position does not match well between the prediction and the experiment and is likely due to the complex separation region engulfing the front, retreating side of the rotor.

105 Velocity Magnitude [m/s] %R Exp 30%R 18 70%R Coupled 30%R Azimuthal Angle [deg] Figure 5-19: Outflow Velocity Magnitude Comparison in Front Duct for 6000 RPM, 6.1 m/s Wind Tunnel Speed The experimental measurements also included a description of the angulation of the inflow and outflow through the duct. Streamlines from the coupled CFD solution are shown in Figure 5-20 overlaid with a depiction of these experimental velocity vectors in the vertical symmetry plane of the model within the front duct. Both the experimental and computational results are shown for 6.1 m/s forward speed and 6000 RPM, the experiments were performed at - 10 angle of attack and the computations at 0 angle of attack. Here the experimental vectors are colored green, the CFD streamlines through the inflow conditions are colored red and the streamlines through the outflow positions are colored blue. It was found that the flow angularity compares favorably between the experiment and the CFD prediction. Experimental vectors are missing from the front of the duct due to the inability to accurately measure angulation within the stagnate, separation region. The CFD shows, however, that both the inflow and the outflow streamlines enter through the bottom of the duct, demonstrating the complexity of the flow in the front region of the duct. At the front 30% radial position, the outflow vector match with experiment very well while the inflow CFD vector shows

106 91 a similar flow pattern but a differing degree of angulation. The rear of the duct displays very good agreement between the experiment and CFD angulation in both inflow and outflow, which follows the pressure and velocity magnitude results previously presented. The rear of the duct ingests a significant amount of clean flow and displays a more consistent agreement between the experiment and CFD. Figure 5-20: Experimental and Coupled CFD Flow Angularity Comparison for 6000 RPM, 6.1 m/s Wind Tunnel Speed: Experimental vectors in green, CFD in blue & red Force Comparison The total lift, fuselage lift plus rotor thrust, for the coupled CFD method is compared to the experiments, fully resolved rotor solution and the momentum source CFD in Figure 5-21 for 6000 RPM, 0 angle attack for a range of forward speeds. Good agreement is found between the coupled solution and the experiment at low forward speeds. In hover the couple solution predicts a lift of 13.17N and experiment yields 13.75N, an error of 4.2%, well within acceptable limits of engineering accuracy. However, error increases with forward velocity. At 10.7 there is 9% error between the experiment and coupled solution and approximately 30% error at 18.3 m/s between the coupled solution and the fully resolved solution.

107 Total Lift [N] 92 While the errors increase compared to the experiment, the coupled solution demonstrated the ability to capture the trend of the lifting forces on the ducted fan model. The results from the simplified momentum source CFD approach were not able to reproduce this effect and in fact decreased at the highest forward speed. This demonstrates the utility of the coupled CFD solution over a momentum source approach. The momentum source approach requires the input of an arbitrary thrust distribution; in this case a hover condition using a constant distribution of momentum sources was used. The coupled solution was able to produce a thrust distribution knowing only rotor geometry and outperformed the simplified approach Coupled Method Experiment Fully Resolved Momentum Source Wind Tunnel Velocity [m/s] Figure 5-21: Lift Result Comparison to Prior Work A comparison of the drag from the prior CFD and experimentation to the coupled method solutions are shown in Figure The results of the drag comparison are similar to the lift results. Here the coupled method was able to outperform the momentum source CFD but did not reproduce the experimental or fully resolved CFD results. Unlike the lift curve, the error in the drag prediction is more consistent over the flight conditions tested. At 10.7 m/s the error with experiment is nearly 17%. At the highest forward speed, 18.3 m/s, the error grows to 23%. The 18.3 m/s result is also seen to follow the momentum source trend more closely than the experimental trend, where the slope of the curve decreases at the highest forward speed.

108 Net Drag [N] Coupled Method Experiment Fully Resolved Momentum Source Wind Tunnel Velocity [m/s] Figure 5-22: Drag Result Comparison to Prior Work 5.4 Sensitivity of Solutions to Airfoil Properties Over the course of development and testing of the coupled CFD-BET method, the rotor model has been investigated and improved to attempt to improve the accuracy of the predictions. A critical part of this rotor model is the airfoil section used. Because the rotors used are commercial of the shelf components, their design parameters are not known in great detail. The airfoil section was among the properties not known with much confidence. This led to the study of several possible candidates for use in the rotor model. The initial airfoil used was the NACA 4412 which is a cambered, flat bottomed airfoil and was used in past ducted fan research to model Master Airscrew rotors with success. The NACA 4412 was found to be too thin for the rotors used and the NACA 4314 was selected as it is 14% thick compared to the 12% of the This was later replaced by the airfoil detailed in section 2.2.3, the GOE 527, used by the ARL computational model. In order to better quantify the effects of the airfoil section, separate lift and drag coefficient studies were also performed.

109 Use of NACA 4412 The NACA 4412 is a flat bottomed airfoil with 4% camber, 12% thickness. This differs from the airfoil used in the final coupled solutions, the GOE 527, which is 16% thick with 5.5% camber. The two airfoils are shown overlaid in Figure Figure 5-23 NACA 4412, GOE 527 Airfoil Comparison The lift and drag coefficients for both airfoils are shown in Figure The lift and drag coefficients were calculated in XFOIL at a Reynolds number of 70,000. The NACA 4412 has a much larger maximum C L as compared to the GOE 527, 1.35 vs , respectively. The NACA also has a larger lift coefficient at zero angle of attack, vs for the GOE 527. Both airfoils stall at similar angles of attack. The NACA 4412 also has a minimum drag coefficient which is half that of the GOE 527. C L (a) Lift Coefficient C d (b) Drag Coefficient NACA GOE Angle of Attack [deg] Angle of Attack [deg] Figure 5-24 Airfoil Property Comparisons, NACA 4412 & GOE 527, Re=70,000: (a) Lift Coefficient, (b) Drag Coefficient NACA 4412 GOE 527

110 Total Lift [N] 95 The coupled CFD-BET method was run using the NACA 4412 airfoil, the lift results are shown in Figure 5-25 and are compared against the final coupled solution and experiment. The lift result using the NACA 4412 is much higher than the experiment and is considerably greater than the final coupled solution, which was less than the experiment. The two runs of the coupled method differ by 45% at 18.3 m/s and by 28% at 6.1 m/s forward speed. Considering the maximum lift coefficients differ by 40%, this suggests that the lift result is dependent, not only on the maximum lift coefficient but possibly the lift curve slope as well Coupled Method 10 Experiment 5 NACA Wind Tunnel Velocity [m/s] Figure 5-25: Lift Sensitivity, NACA 4412, 6000 RPM, 0 Angle of Attack The drag comparisons between the two runs of the coupled code are shown in Figure The NACA 4412 results perform better than the final coupled solution at the lower, 6.1 m/s, forward speed. However, at 18.3 m/s the drag prediction using the NACA 4412 data is higher than the solution utilizing the GOE 527 airfoil.

111 Net Drag [N] Coupled Method Experiment NACA Wind Tunnel Velocity [m/s] Figure 5-26: Drag Sensitivity, NACA 4412, 6000 RPM, 0 Angle of Attack Use of NACA 4314 The NACA 4314 airfoil was used after re-evaluating the rotor blades and discovering the NACA 4412 was too thin. The NACA 4314 was selected due to its larger thickness, flat bottom and the point of maximum thickness being closer to the physical rotor blades on model PSU D1A. A comparison between the NACA 4314 and the GOE 527 used in the final coupled method solution is shown in Figure The NACA 4314 is 14% thick with 4% camber and a max camber location at 30% of chord. Figure 5-27: NACA 4314, GOE 527 Airfoil Comparison The lift and drag coefficients for each airfoil was obtained using XFOIL at Reynolds number, these results are shown in Figure Looking at Figure 5-28(a), the maximum lift coefficient is very similar between the two airfoils: 0.84 for the NACA 4314 and 0.80 for the GOE 527. However, the NACA 4314 stalls much sooner than the GOE yielding a