UNIVERSITY OF CALGARY INFLUENCE OF GROUND EFFECTS ON BODY FORCES FOR BI-COPTER UAV. Daniel Norton A THESIS

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1 UNIVERSITY OF CALGARY INFLUENCE OF GROUND EFFECTS ON BODY FORCES FOR BI-COPTER UAV by Daniel Norton A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN MECHANICAL ENGINEERING CALGARY, ALBERTA January, 2017 c Daniel Norton 2017

2 Abstract The Navig8 TM are a family of dimensionally similar Unmanned Aerial Vehicles (UAVs) designed for high-speed autonomous flight in confined spaces. The Navig8 UAVs generate their lift through the use of dual shrouded fans, and are capable of controlling the pitch of their bodies while hovering. The use of shrouded fans increases the efficiency of the Navig8, which allows the UAV s design to have smaller fans while simultaneously decreasing its power usage. The autonomous control of a Navig8 UAV requires an understanding of the forces acting on its body while operating in close proximity to the ground, which is known as the ground effects region, as well as the forces acting on their fans and shrouds. Computational Fluid Dynamics (CFD) simulations were used to determine the forces acting on the Navig8 UAV s body, fans, and shrouds as a function of height and dihedral angle using a dimensionally-similar model. Heights were defined as the distance from the bottom of the shroud to the ground, and dihedral angles were defined as the difference between the fan s axis of rotation and vertical. Positive dihedral angles direct flow away from the UAV s body. Heights ranged from a maximum of 7.0 fan diameters to a minimum of 0.75 fan diameters. Dihedral angles ranged from a maximum of 8 degrees to a minimum of 0 degrees. The simulated results were compared to the results calculated from existing methods to estimate body and fan forces while operating in the ground effects region. Recommendations were made to the design and operation of the Navig8 based upon the results. The simulated forces acting on the Navig8 s body were found to have two primary competing sources: 1) fountain forces and 2) suck-down forces. Fountain forces are caused by the flow from the two fans impacting the ground and creating wall jets. These wall jets intersecting each other beneath the UAV s body then fountain into the body which results in an upwards force. Suck-down forces are caused by a vortex forming between the downwards flow from the fan and the upwards fountain flow. This results in a general downwards force i

3 on the body. Suck-down forces are primarily important at altitudes below 1.5 fan diameters, where the gradient of body lift with respect to height is positive, which results in unstable operation. Body lift peaks at approximately 25% of the combined fan and shroud lift out of ground effects at an altitude between 1.1 and 1.5 fan diameters. The body forces decrease from their peak with increasing altitude and drop below 5% by an altitude of 3.8 fan diameters. Increasing the dihedral angle of the fans increases the maximum altitude for which body forces are significant, but has no noticeable impact on the maximum body forces. The change in fan lift varied by less than 2% and the change in shroud lift varied by less than 3% within the experimental range of heights and dihedral angles. The simulated body forces did not agree with those calculated from available estimation methods. Simulated body forces were higher in magnitude than the estimated body forces from available methods, and these methods were unable to properly account for the dominance of suck-down forces at elevations below 1.5 fan diameters.

4 Acknowledgements I would like to thank my supervisor Dr. Alex Ramirez-Serrano and my co-supervisor Dr. Robert Martinuzzi for all of their help, guidance, and support throughout this thesis. You ve made me a better engineer and researcher than I was when I entered this program. I would also like to thank my colleagues at the AR 2 S lab at the University of Calgary for instantly making me feel welcome and at home, and my parents for giving me the chance to get to where I am today. This thesis is dedicated to my wife, Michelle Campbell. This thesis wouldn t have happened without you. Thank-you for always bringing out the best in me. iii

5 Table of Contents Abstract Acknowledgements Table of Contents List of Tables List of Figures List of Symbols i iii iv vii viii xi 1 INTRODUCTION Motivation The Navig8 Family of UAVs Forces acting on Navig Objective of the Thesis Organization of the Thesis BACKGROUND AND LITERATURE REVIEW Lift Generated from a Rotating Fan Effects of Shroud on a Lift Fan Performance Benefits of Shrouded Fans Safety Benefits of Shrouded Fans Acoustic Effects of Shrouded Fans Ground Effects Predicting Ground Effects for Rotating Lift Fans Shrouded Fans in Ground Effects Single Jet-Induced Body Forces Forces due to Wall Jet Flow Entrainment Multiple Jet Induced Body Forces Body Forces in Ground Effect for Multiple Lift Jets Estimating Body Forces using Kotansky s Method Estimating Body Forces using Kuhn s Method Effects of Body Shape Effects of Lift Improvement Devices Limitations on Predicting Body Forces PROBLEM DEFINITION Problem Statement Comparison of Results against Existing Methods of Prediction Scope Contribution iv

6 4 METHODOLOGY Solution Approach Model Setup Model Simplifications Model Dimensions Model Constraints Assumptions and Limitations Symmetry Planes Fan Modelling Power, Lift, and Flow Rate Relations Experimental Domain Limits of Experimental Domain Design Space Investigation Method Estimating Body Forces in Ground Effects Estimating GE Body Forces based on Kuhn s Method Estimating Fountain Forces based on Kuhn s Method Limitations and Modifications to Fountain Force Estimation based on Kuhn s Method Estimating Suck-down Forces based on Kuhn s Method Limitations and Modifications to Kuhn s Suck-down Force Estimation Estimating GE Body Forces based on Kotansky s Method Estimating GE Fountain Forces based on Kotansky s Method Limitations and Modifications to Fountain Force Estimation based on Kotansky s Method Estimating GE Suck-down Forces based on Kotansky s Method Limitations and Modifications to Suck-down Force Estimation based on Kotansky s Method Estimating Fan Forces in Ground Effects Shroud Forces in Ground Effects SIMULATION IMPLEMENTATION Software CFD Environment and Model Model Meshing Boundary Conditions and Fluid Properties Turbulence Modelling Wall Region Modelling Fan Model SIMULATION VERIFICATION Domain Size Independence Fan Model Invariance Symmetry Plane Independence Solver Residuals and Monitors Convergence Solver Fluctuations v

7 6.4 Domain Force and Momentum Balance Grid Independence RESULTS AND DISCUSSION Normalization of Lift GE Body Forces as a Function of Height and Dihedral Angle Discussion of Body Forces Suck-down Forces at Low Altitudes Estimating Ground Effects and Body Forces Body Force Estimation Methods based on Kuhn s Method Fountain Force Estimate Suck-down Force Estimate Total Body Forces Estimate Body Force Estimation based on Kotansky s Method Fountain Force Estimate Suck-down Force Estimate Body Forces Estimate Fan Forces Fan Lift Discussion of Fan Lift Fan Horizontal Forces Shroud Forces Shroud Lift Shroud Horizontal Forces CONCLUSIONS AND FUTURE WORK Conclusions Future Work Physical Validation and Testing Recommended Modifications Bibliography 119 A Grid Independence 123 B Reynolds-Averaged Navier-Stokes Equations and Turbulence Modeling 125 B.1 Navier-Stokes Equations B.2 Reynolds-Averaged Navier-Stokes (RANS) Equations B.3 Turbulence Models and The Problem with Closure B.4 k ω SST Turbulence Model B.4.1 Wilcox k ω Model B.4.2 Baseline k ω and Blending Function B.4.3 Shear Stress Transport (SST) k ω Turbulence Model C The Law of the Wall and y vi

8 List of Tables 4.1 Simulation Model Dimensions and their Basis Experimental Domain Combinations of Height and Dihedral Angle for Simulations Variables, Equations, and Definitions to Estimate Fountain Force based on Kuhn s Method [1] Variables, Equations, and Definitions to Estimate Suck-down Force based on Kuhn s Method [1] Variables and Equations used to Estimate Fountain Forces Based on Kotansky s Method Variables and Equations used to Estimate Suck-down Forces Based on Kotansky s Method Mesh Sizing Criteria Meshing Methods Boundary Conditions Properties of Air used in CFD Simulations Comparison between Uniform Power Density and Uniform Thrust Density Fan Models on Identical Meshes at Height = 0.75 D, θ = 8 degrees Force-Momentum Balance for Models at Minimum and Maximum Combinations of Height and Dihedral Angle Simulation Order of Accuracy for Fan Lifts Simulation Order of Accuracy for Shroud Lifts Simulation Order of Accuracy for Body Lifts Normalized Body Lift (%) as a function of Height and Dihedral Angle Normalized Fan Lift as a function of Height and Dihedral Angle Normalized Shroud Lift as a function of Height and Dihedral Angle B.1 Constant Values for Wilcox k-ω Turbulence Model vii

9 List of Figures and Illustrations 1.1 Bell-Boeing V-22 Osprey [2] Regions of Fountain and Suck-down Forces while Operating in GE Prototype of the Navig8 UAV Definitions of Height H and Dihedral Angle θ Primary Forces Acting on Navig8 while Hovering Airfoil Lift Shrouded Fan in Region of Ground Effect (from Schade Figure 2 [3]) Effect on Height on Thrust for Shrouded Lift Fan Submerged in Wing in Ground Effects (from [4]) Simplified Model of Navig8 Used for Simulations Shroud and Fan Model (all dimensions in inches) Dimensions for Fountain and Suck-down Force Calculations for Kuhn s Method [1] Fig Additional body Dimensions for Fountain and Suck-down Force Calculations from [5] Figure Dimensions and Origin of Suck-down Force for Method based on Kotansky s Method (from [5] Fig. 65) Domain used for CFD Simulations Example of Mapped Face Mesh on Shroud Domain Size Dependence for Fan Lift, Shroud Lift, and Body Lift as a Function of Height and Dihedral Angle Monitor of Body Lift Convergence for Height = 0.75 D, θ = 8 degrees Monitor of Shroud Lift Convergence for Height = 0.75 D, θ = 8 degrees Streamlines showing Recirculation between Shroud and Body at Height = 0.75 D, θ = 8 degrees Total Lift Comparison between Two Independent Fan-and-Shroud Assemblies (Benchmark) against Navig8 Spaced Fan and Shroud Assemblies with and without the presence of the UAV s Body Normalized Body Lift as a Function of Height and Dihedral Angle Body Lift Gradient With Respect To Height as a function of Height and Dihedral Angle Body Lift Gradient with respect to Dihedral Angle as a function of Height and Dihedral Angle Location Used to Plot Pressure on Bottom of UAV Body at Plane of Symmetry Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Heights for θ = 0 degrees Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Heights for θ = 8 degrees viii

10 7.8 Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Dihedral Angles for Height = 3.0 D Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Dihedral Angles for Height = 0.75 D Streamlines Coloured by Velocity at Height = 0.75 D, θ = 8 degrees Pressure Contours on Bottom of UAV Body at Height = 0.75 D and θ = 8 degrees Circulation as a function of Inverse Swirling Strength at Height = 0.75 D, θ = 0 degrees Circulation of Vortex Beneath UAV Body as a Function of Height and Dihedral Angle Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 0.75 D, θ = 0 degrees Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 1.1 D, θ = 0 degrees Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 1.5 D, θ = 0 degrees Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 0.75 D, θ = 8 degrees Vorticity in z-direction for Height = 0.75D, θ = 8 deg Equation-derived Fountain Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height Equation-derived Suck-down Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height Equation-derived Body Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height Equation-derived Fountain Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height Equation-derived Suck-down Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height Equation-derived Body Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height Change in Normalized Fan Lift in GE for Vertically-Oriented Fans as a function of Height Normalized Fan Lift as a function of Height and Dihedral Angle Normalized Fan Horizontal Force as a Function of Height and Dihedral Angle Normalized Shroud Lift as a Function of Height and Dihedral Angle Shroud Pressure Contour at Height = 0.75 D, θ = 8 degrees Shroud Shear Stress Contour showing Areas of Flow Separation at Height = 0.75 D, θ = 8 degrees ix

11 7.31 Normalized Shroud Horizontal Force as a Function of Height and Dihedral Angle x

12 List of Symbols, Abbreviations and Nomenclature Latin Symbols Definition B Constant from Law of the Wall, 5.1 C C T D f F H K L n p q S U u i u τ u + V x i w W y + Greek Symbols Constant Thrust Coefficient Diameter Body force per unit mass Force Height Source Lift Surface Normal Pressure Volumetric Flow Rate Spacing between centerline of fans Mean velocity Velocity in direction i Friction velocity Dimensionless velocity Volume Direction vector in direction i Power Watts, unit of power Dimensionless wall distance Definition xi

13 δ δ ij ε Γ Error, Percent Kronecker Delta Error, Absolute Value Circulation κ von Karman s Constant, 0.41 µ Dynamic viscosity µ t Eddy viscosity ω ω θ τ ij Subscripts ave B F f Turbulent specific dissipation rate Vorticity Dihedral angle Reynolds Stress Tensor Definition Average Property of the Body Property of the Fan fountain force i Direction index; i = 1..3 j Direction index not necessarily equal to i; j = 1..3 L x S s Superscripts Abbreviations AR Dimensional distance, typically Chord length Distance x Property of the Shroud suck-down force Property in the far-field Definition Definition Advance Ratio xii

14 AR 2 S CF D CS CV Const db Deg Dia Eq n GE GBE GW E GP S in lbf LIDs RAN S Re RM S SST U AV U of C V T OL V/ST OL W RT Autonomous Reconfigurable/Robotics Systems Computational Fluid Dynamics Control Surface Control Volume Constant Decibels Degrees Diameter(s), 1 Diameter = 16 in Equation Ground Effects Ground Body Effects Ground and Wall Effects Global Positioning System Inches Pounds Force Lift Improvement Devices Reynolds Averaged Navier Stokes Reynolds number Root Mean Square Shear Stress Transport Unmanned Aerial Vehicle University of Calgary Vertical Take-Off and Landing Vertical / Short Take-Off and Landing With Respect To xiii

15 Chapter 1 INTRODUCTION Unmanned Aerial Vehicles (UAVs) are defined as aircraft that are designed to fly without a human on-board. These aircraft may be piloted by a person remotely or be self-piloted by an on-board computer. UAVs, also commonly known as drones, have significant advantages over manned aircraft. The lack of human occupants allows for UAVs to be substantially smaller and less expensive than traditional aircraft and allows them to operate safely in areas that would otherwise be hazardous to human health or inaccessible. Of special interest are UAVs that are capable of flying in confined spaces and/or in close proximity to infrastructure where the aerodynamic effects of the ground or walls cannot be ignored. Aircraft that are heavier than air typically generate their lift either through a fixed wing or a rotating wing, such as a helicopter. Fixed wing aircraft such as passenger planes generate lift by creating a low pressure region on the top of their wings while in forward motion. They have higher efficiency than rotary wing aircraft, but they need to maintain forwards motion in order to continue generating lift. On the other hand, rotary wing aircraft do not need to maintain forward motion in order to generate lift and maintain altitude. The ability to hover and take-off vertically provides them with substantial advantages in flexibility and maneuverability; however, they are less efficient and have a reduced range when compared to fixed wing aircraft. Some hybrid designs exist between fixed wing and rotary wing aircraft, notably the Bell-Boeing V-22 Osprey shown in Figure 1.1. The V-22 uses two large rotating propellers to provide thrust. These propellers are capable of rotating relative to the airframe of the V-22, which allows the aircraft to take off and land vertically or hover. The rotors can then rotate to a horizontal orientation to transition the V-22 into a normal fixed wing 1

16 aircraft which generates its lift from the fixed wings. Other similar unmanned systems exist on a smaller scale, such as the Quantum TRON from Quantum Systems [6]. Some jet powered aircraft such as the Harrier and Harrier-II are capable of directing their jets downwards to allow for Vertical Take-Off and Landing (VTOL). Other transitional UAVs exist that include separate systems for VTOL and a fixed-wing flying mode, such as the Airbus Quadcruiser [7] and the transitional aircraft from Latitude Engineering [8]. This study focuses on the Navig8 TM family of UAVs developed by 4Front Robotics TM and the Autonomous Reconfigurable/Robotic Systems (AR 2 S) lab at the University of Calgary which is a VTOL capable UAV designed specifically for high-speed flight in confined spaces. The Navig8 UAVs generate their thrust though two shrouded-fans and are capable of controlling the body s pitch while in hover by modifying its centre of mass or through the use of a low-thrust, high-moment fan located at its tail. Figure 1.1: Bell-Boeing V-22 Osprey [2]. 2

17 1.1 Motivation The need to fly in close proximity to the ground or walls while operating in confined spaces requires either the prediction in real time of any additional forces generated on the UAV while operating in this region, or the minimization of these forces to an extent that the UAV s controller can mitigate the resulting effects. The additional forces that an aircraft experiences while operating in close proximity to the ground or walls are referred to as Ground Effects (GE) and Wall Effects (WE) respectively. A well-known and well-studied GE is an increase in lift for rotating fans [3, 9, 10, 11]. A common method to predict the GE is through the method of images, which treats the ground as a mirror plane so that an equal and opposite lift source is located equidistantly from the ground. The fan itself is often modeled as a source or dipole [11, 12]. The source model is the most common; however it lacks directionality. Modelling the fan as a dipole can account for directionality and also estimate the effects of operating in close proximity to walls [12]. VTOL aircraft are also susceptible to additional forces acting on the body of the aircraft; while forces such as drag and lift are present at any altitude, additional forces act upon the body while operating in close proximity to the ground or the walls. Two particularly important forces for a multi-jet VTOL aircraft are fountain forces and suck-down forces [13]. The regions on the body for which fountain and suck-down forces are dominant are shown in Figure 1.2. Fountain forces (denoted by F f ) create a region of high pressure (P > P ) in the centre of the bottom of the UAV s body, while suck-down forces (denoted by F s ) create regions of low pressure (P < P ) on the outer portions of the bottom of the UAV s body. When the flow from each lift fan intersects the ground, it disperses radially around its stagnation point and forms a wall jet. The flow from intersecting wall jets is redirected into a fountain. If this fountain intersects the body of the aircraft then additional forces act on the aircraft which are referred to as fountain forces [1, 5, 13, 14]. Unlike traditional ground effects, fountain forces do not act through the centre of the lift fans, and instead act on the 3

18 F s Regions F f Region P<P P>P Figure 1.2: Regions of Fountain and Suck-down Forces while Operating in GE body of the aircraft. The centre of lift and magnitude for fountain forces vary depending on the flight conditions such as the velocity of the UAV, crosswind velocity, or the relative thrust of the fans. This dependency on flight conditions make fountain forces less predictable and, consequentially, more difficult to compensate for in real-time. Two alternate explanations exist for the cause of the suck-down forces shown in Figure 1.2: 1) the forces are caused by flow entrainment into wall jets formed as the downwash impacts the ground [5]; or 2) the forces are caused by the formation of vortices between the fountain and downwash region [1]. The net result is a region of negative pressure acting on the UAV s body. Each potential cause leads to different methods of predicting suck-down forces. The accuracy of each cause and their respective methods are investigated in Chapter 7. Like fountain forces, suck-down forces do not generally act through the UAV s centre of mass and can induce moments on the body of the UAV. Suck-down forces and fountain forces act on the body in opposite directions, with fountain forces increasing lift and suck-down forces decreasing lift. This implies that one force may dominate the other over different ranges, and it becomes difficult to predict which force will dominate. Understanding the range and dominance of each force is necessary to be able to 4

19 properly control the aircraft throughout its operating range. UAVs are typically controlled in one of two ways: by a human controlling the vehicle remotely, or by an autonomous on-board computer or autopilot system. It is common for UAVs to have some component of autonomous control, even for remotely-controlled or human-piloted aircraft. For example, a UAV may be pre-programmed to hover in place if an operator does not apply any input. We will refer to such systems as computer assisted remotely piloted aircraft in the context of this thesis. Other UAVs can be programmed to follow pre-programmed routes, maintain their position while hovering, or return to their launch position using GPS or other sensor feedback [15]. 1.2 The Navig8 Family of UAVs The Navig8 TM family of UAVs were developed by 4Front Robotics TM and the AR 2 S lab at the University of Calgary. These UAVs are designed specifically to fly in areas that are difficult or inaccessible to traditional aircraft [16]. This includes flying through confined spaces such as inside buildings or mines. The Navig8 aircraft are dual shrouded-fan Vertical Take-Off and Landing (VTOL) UAVs which are able to fly in close proximity to the ground and walls. The dual shrouded-fan design, combined with an adjustable centre of mass or a low thrust tail propeller, make the Navig8 UAVs capable of pitched-hover and take-off and landing from both stationary and/or moving inclined surfaces. A prototype of the Navig8 is shown in Figure 1.3. Each of the two fans of the Navig8 UAV is surrounded by a shroud that increases the lift for a given input power while simultaneously providing some protection for and from the fan blades [17]. The Navig8 is unique in that it is also capable of controlling the pitch of its body in hover by modifying its centre of gravity. Pitch-hover can also be achieved through the use of a small propulsion source located on the tail of the UAV which creates a moment with a minimal amount of overall force. Having full control of the pitch orientation allows 5

20 Figure 1.3: Prototype of the Navig8 UAV. the Navig8 to operate in confined spaces that would otherwise be impassible for a typical UAV. Unlike single rotor aircraft, the dual-fan Navig8 aircraft are subjected to fountain forces while operating in the ground effects region. These forces are extremely difficult to predict, especially in uncontrolled environments. The strength and centre of lift for fountain forces are unstable, and are dependent on many variables including: the height of the fans above the ground, the dihedral angles of the fans (also referred to as the splay angle), the height of the body above the ground, the air velocity through the fans, the crosswind velocity, the velocity of the UAV, the texture and orientation of the ground, the effects of nearby walls, and the shape of the UAV s body. The variables of interest for the purposes of this thesis are the height of the UAV (H) and the dihedral angle (θ) (Figure 1.4). The height was studied to determine the effects on the Navig8 as it operates at various elevations within the ground 6

21 effects region. Dihedral angle was studied to determine whether varying the dihedral angle could improve the performance of the Navig8 while operating in the ground effects region. z x θ y x z y H Figure 1.4: Definitions of Height H and Dihedral Angle θ Forces acting on Navig8 The Navig8 is subjected to numerous forces while operating, including: forces acting on the the fans (F X,F and F Y,F ), forces acting on the shrouds (F X,S and F Y,S, forces due to gravity (F Y,g ), and two forces acting vertically on the body: fountain forces (F Y,f ) and suckdown forces (F Y,s ). The primary forces acting on the Navig8 while hovering are shown in Figure 1.5. Gyroscopic forces from the fans are not included in the scope of this thesis. Additional external forces that may act upon the Navig8 include drag and disturbances such as crosswinds, projectile impacts, and ground and wall effects. 7

22 Figure 1.5: Primary Forces Acting on Navig8 while Hovering 1.3 Objective of the Thesis The objective of this thesis is to identify and investigate the region in which ground effects, and Ground Body Effects (GBE) in particular, are significant for Navig8. These will be investigated as a function of the UAV s height above the ground, herein referred to as the height (H) of the UAV, and the dihedral angle of the fans, herein referred to as the dihedral angle (θ). The findings will be compared against previously developed estimations methods to determine if these methods are applicable to the Navig8. The work aims to provide guidance on how closely-spaced bi-copter VTOL vehicles in general are affected by ground effects and discusses methods to identify and mitigate these forces if desired. 8

23 1.4 Organization of the Thesis The organization of this thesis is as follows: Chapter 2 reviews and discusses the state-of-the-art in research and engineering which is related to the development of bi-copter VTOL aircraft with an emphasis on the Navig8. This overview includes a discussion on predicting ground effects for rotary fans using the method of images while modelling the fan as a source or dipole, the effects of shrouds on lift fans, and previous research into fountain and suck-down forces. Chapter 3 describes the problem to be investigated in detail. This chapter includes a description of the independent variables and results of interest, as well as how the simulation data will be compared to existing estimation methods. Chapter 4 describes the methodology used to investigate the problem. Chapter 5 details the simulation setup procedure including information on the software used and the parameters used at each stage of setup, solving, and post-processing. Chapter 6 describes the methods used to verify the results of the simulations. The verification checks include domain size independence, fan model invariance, solution monitor convergence, force and momentum balance checks, and grid independence. Chapter 7 details and discusses the results of the simulations, which are then compared to expected results from literature. Significant results are noted, and the limitations of the simulations and available estimation methods are discussed. Chapter 8 summarizes the conclusions of the simulations. The key findings are discussed, and recommendations are made for future work. 9

24 Chapter 2 BACKGROUND AND LITERATURE REVIEW 2.1 Lift Generated from a Rotating Fan The Navig8 UAVs generate their lift through the use of two rotating lift fans, commonly referred to as propellers. The propeller s blades act as airfoils. The lift of the airfoil can be explained through the Kutta-Joukouski Theorem [18]. The Kutta-Joukouski theorem states that the lift of a body L can be calculated according to Equation 2.1: L = ρu Γ (2.1) Where ρ is the fluid density, u is the relative velocity of the airfoil to the surrounding fluid, and Γ is the circulation around the airfoil. Figure 2.1 shows the required parameters to calculate the circulation Γ. Figure 2.1: Airfoil Lift. For a 2-D cross-section, the circulation can be calculated as either 10

25 Γ = u d l = ω da (2.2) c s The vorticity ω in Equation 2.2 is the curl of the velocity field of the fluid, with the units of rad/s. It defines the local rate of rotation of the fluid. Vorticity is defined as: ω = u i (2.3) The variable c in Equation 2.2 defines a closed path around the airfoil and s defines the surface bounded by the closed path. The bounding contour c must be located far enough from the airfoil for the flow to be considered irrotational in order for it to fully bound the circulation. 2.2 Effects of Shroud on a Lift Fan The Navig8 UAV uses shrouded (also known as ducted) fans. A shroud is a cylindrical body which surrounds the fan blades. They are typically shaped as a ring airfoil to increase the overall thrust of the aircraft for a given fan power. The use of a shroud provides a number of benefits for small UAVs which are capable of offsetting the disadvantage of additional weight. These advantages can be classified into 3 categories: performance, safety, and acoustics Performance Benefits of Shrouded Fans The use of a shroud can improve the overall performance of a fan, particularly at low Mach numbers. Wind tunnel tests on micro air vehicles have shown that shrouded fans are able to produce up to 94% additional thrust for a constant power, or reduce the power consumption by up to 62% for a given thrust [17]. For a UAV, the reduction in power consumption can be used to increase both the UAV s range and operating speed. Ducted fans with rotors ranging from 6.3 inches to 37.8 inches in hover have approximately 30% higher thrust coefficients than open rotors for set tip speeds with various tip 11

26 shapes and tip clearances [19]. The effects of shrouds while operating under edgewise flow were also investigated [19]. Fans and shrouds were vertically oriented in a wind tunnel, and exposed to lateral wind loading. Under these conditions, shrouded fans could produce nearly 3 times the lift of an open rotor, with the total lift increasing with crosswind velocity for the shrouded fans. The use of shrouded fans on a quadrotor micro UAV with 6.6 cm diameter rotors was found to increase the overall lift capacity of the UAV by 15% after accounting for the additional weight of the shrouds [20]. However, the use of shrouds increased the drag and pitching moments by a factor of when exposed to edgewise loading. The results from the micro UAV testing were found to be scale-invariant through comparisons with the results of a UAV with 24.1 cm rotors [20] Safety Benefits of Shrouded Fans The safety benefits of a shroud are perhaps the most obvious for small UAVs operating in confined spaces and in close proximity to people. The shroud prevents the tips of the fan blades from laterally impacting their surroundings. This helps to reduce the possibility of injury to persons proximal to the drone, and also helps to prevent damage to the UAV itself. These benefits are particularly important while operating in confined spaces which requires operating in close proximity to environmental obstacles Acoustic Effects of Shrouded Fans While noise reduction is not often the primary objective of adding shrouds to fans, the use of shrouds can substantially reduce noise levels when compared to an equivalent open rotor [21]. The total noise generated by a lift fan is a function of numerous variables including, but not limited to, tip speed, the number of blades, and blade geometry. There is an increase in noise levels at multiples of the blade passing frequency for fans with evenly spaced blades. The use of a shroud has been shown experimentally to reduce noise levels for fans operating 12

27 at constant speeds, especially high frequency noise [22]. However, if the flow over the shroud separates before entering the fan blades, a shrouded fan can produce approximately twice the amount of noise of an unshrouded fan [21]. A study on the acoustic effects of 5 shrouded fans [21] found that, on average, sound pressure levels of shrouded propellers were half that of identical unshrouded propellers when the flow remained attached throughout the shroud, which equates to a 3dB reduction. However, if the flow separated from the shroud before passing over the propeller then the sound pressure levels doubled relative to those of unshrouded propellers. This is an effective increase of 6dB over the sound pressure level of a properly functioning shrouded fan. Reducing fan tip speed also results in a substantial decrease in fan noise [23]. If the performance benefits of using a shroud are taken into account, then a shrouded propeller will have even lower noise levels at equal thrust levels. The increased efficiency allows a shrouded fan to operate at a lower speed or have a reduced fan diameter and be able to generate the same amount of lift. Both of these effects will in turn reduce the overall amount of noise generated in addition to the direct noise level reduction through the use of shrouds. 2.3 Ground Effects The additional loads acting on an aircraft when it is in close proximity to the ground are collectively known as Ground Effects (GE). Rotating lift aircraft such as helicopters create additional lift while operating in close proximity to the ground [24, 9], provided that the flow over the blades does not separate. There are two primary methods to compare the effects of the ground to operating in farfield: comparing the relative thrust ( Tg T ) while operating at constant power, or comparing the required power ( Wg W ) to achieve a constant thrust value. 13

28 2.3.1 Predicting Ground Effects for Rotating Lift Fans Previous research on lift fans in ground effects has shown that the additional lift generated by the ground can be predicted analytically by reflecting the lift fan across the ground [24]. The practice of using the ground as a mirror to create an image of the fan below the ground is known as the method of images. The imaged flow field acts to reduce the velocity through the fan. For a fan operating at constant power, this decrease in velocity results in an increase in thrust. The traditional technique used for the method of images replaces the fan with a model of a source [11]. For a stationary lift fan at height Z and with radius R operating at constant power, the thrust ratio between a lift fan operating in ground effects and in the free field can be estimated as: T g T = 1 (2.4) 1 R2 16Z 2 The method of images can also be used to predict the effects of a rotor lift aircraft in forward flight [11]. For a lift rotor travelling forward at V i and with an induced downwash velocity v i, the thrust ratio for operating in ground effects compared to operating in the free field can be estimated as: T g T = 1 R2 16Z 2 1 ( 1 + V i 2 vi 2 ) (2.5) In Equation 2.5, when the aircraft forward velocity V i is much less than the induced downwash velocity v i, the equation reduces to Equation 2.4. The method for estimating the ground effects by modelling the fan as a source and the ground as a mirror plane is a common method that forms the basis for estimating the ground effects for rotating lift fans. The exact means to estimate the lift generated by the source has been modified and improved multiple times [25, 26]. A deficiency of Equation 2.5 is that it does not account for the complexity of flow interactions which occur under low advance ratios while under ground effects. For helicopters 14

29 and similar aircraft, the Advance Ratio AR is defined as the ratio of the aircraft s forward velocity over the tip speed of the blades: AR = V ωr (2.6) The various flow regimes are also dependent on the thrust coefficient for the propeller, which is generally a function of the propeller s design. The thrust coefficient can be calculated as: C T = T ρπr 2 (ωr) 2 (2.7) Ground effects regimes are dependent on the normalized advance ratio AR [25]: 2 AR = AR (2.8) C T For normalized advance ratios of AR < 1, there is a region of recirculation in front of the fan which imparts a substantial downward flow through the front of the lift fan. This in turn reduces the overall lift of the fan in comparison to a rotor in hover, as estimated by Equation 2.5. The lift continues to decrease until the wake of the fan passes behind the fan and no longer creates a region of recirculation, which occurs at normalized advance ratios of approximately AR 1. The normalized advance ratio at which this transition occurs is dependent upon the size of the room in relation to the fan blades [27]. For example, when the diameter of the helicopter blades is approximately half the width of a wind tunnel used for testing, the transition occurred at approximately AR 1.6 [27, 25]. Another limitation of Equation 2.5 is that modelling the fan with a source model removes the ability to model directionality. This lack of directionality prevents the model from being able to predict the effects of inclination on a stationary lift fan operating in ground effects, which is of particular importance to multi-rotor aircraft where the rotors are not necessarily mounted vertically. The use of a dipole model instead of a source model allows for the effects of inclination for stationary rotors in ground effects to be estimated [12]. The dipole model also allows for the estimation of the effects of operating in proximity to both the ground and 15

30 walls by modelling the ground and wall as mirror planes [12]. The use of a dipole model was found to hold for a shrouded fan [12]. This observation does not take into account the lift generated by the shroud itself, and only holds for the lift generated by the fan. The effects of swirl was determined to be negligible in a previous study on shrouded fans with the tangential velocity being approximately 2% of the axial velocity of the fan [12]. The ability to predict ground effects for inclined shrouded fans is restricted to an operating range in which the flow over the blades does not separate [12]. Shrouded fans typically have their blade angles optimized for operating out of ground effects and have steeper blade angles than those of unshrouded fans [3]. These fans experience flow separation (stalling) earlier when operating in ground effects, which can cause a rapid decrease in lift [3]. Decreasing the angle of the fan blades can delay the onset of fan separation, which increases the lift in ground effects, but decreases the performance during normal operation Shrouded Fans in Ground Effects The overall change in lift for a shrouded fan in ground effects is difficult to predict, as lift generally rises for the fan blades while in ground effects, while the lift for the shroud decreases [28]. The net change in lift is dependent on the configuration of the shroud, and fan-in-wing models have notably different results than isolated fan and shroud configurations [3, 28]. The majority of shroud lift is generated by accelerating air over the upper lip of the shroud, which creates a region of low pressure [4, 29]. As the velocity through the fan decreases as the shrouded fan nears the ground, the lift generated by the shroud decreases. Ground effects for a shrouded fan can result in either a net increase or decrease in lift, with the net effect being dependent on the overall configuration [3]. In particular, the net effect of the ground is dependent on the blade angle of the fan blades. It was found that when the blade angle was optimized for far-field hover performance, ground effects reduced the net lift of the blades and shroud. The loss in lift was due to the blades stalling while in close proximity to the ground. When shallow blade angles were used, there was a net 16

31 increase in lift while operating in ground effects. However, the decreased blade angle results in reduced performance while operating out of ground effects. The difference can be seen in Figure 2.2 from Schade [3]. Ground effects begin to onset at a height of approximately fan diameters depending on the fan configuration. Whether the net change in lift is positive or negative is also dependent on the configuration [3]. Figure 2.2: Shrouded Fan in Region of Ground Effect (from Schade Figure 2 [3]). The the total lift generated shrouded propeller submerged in a wing operating in ground effects decreases with decreasing height for some fan-in-wing configurations [4]. At heights less than 0.75 fan diameters the total static thrust decreases rapidly, and even becomes negative for heights below 0.4 diameters [4]. Figure 2.3 from [4] shows the relation between height and thrust for a shrouded fan-in-wing in GE. The rapid decrease in lift is at least partially due to suck-down caused by flow entrainment into wall jets, which is discussed in Section The forces acting on a single shrouded fan operating in ground effects can be estimated by using a dipole model for the fan [12]. The dipole model adds directionality to the model so that it can predict the effects of inclination on the fan. In addition to the normal ground forces, the dipole model is capable of predicting additional forces acting normal to the wall or the ground, which can represent up to 15% of the fan lift. However, this model is not capable of predicting separation from the fan blades or the shroud, which was noted to be 17

32 Figure 2.3: Effect on Height on Thrust for Shrouded Lift Fan Submerged in Wing in Ground Effects (from [4]). significant in other studies [3, 28]. 2.4 Single Jet-Induced Body Forces Body forces are defined for this thesis as the forces acting on the body of the UAV resulting directly from the flow-field of the lift fans while operating in hover. Notably, they exclude any drag forces acting on the UAV either through its own propelled motion or crosswinds. There are two sources of body forces which can act on a VTOL UAV with a single lift fan: entrainment in the fan s outlet stream while operating in or out of ground effects, causing a general downwards force; and entrainment into the wall jet while operating in ground effects, causing a general downwards force[1, 13]. The high local velocity of the fluid in the wall jets or in the fan s outlet stream induces motion in the nearby fluid due to viscosity, which results in a local decrease in pressure. The lift losses due to flow entrainment in the fan s exit stream are dependent on the shape of the body and the height of the body to the fan s exits [1, 13]. The losses due to 18

33 entrainment are generally less than 2% of the total lift for a flat bottomed aircraft Forces due to Wall Jet Flow Entrainment The suck-down forces from wall jets are caused by flow becoming entrained into the wall jet while the aircraft is operating in ground effects. This causes a region of low pressure on the lower surfaces of the aircraft, which sucks the aircraft towards the ground [13]. These forces are dependent on the overall geometry but can become very strong, even overpowering the lift generated by the lift fans. For example, a study on a fan submerged in a wing found that at an altitude of approximately 0.4 fan diameters, the fan in wing produced essentially no net lift, and produced negative lift at lower altitudes [4]. (Figure 2.3). The suck-down pressures on bodies located at the same height above the ground as the jet exit can be estimated as a function of the distance between the bottom of the body and the ground to the exponent of 2.3 [30]. The suck-down forces are related to the distance between the body and the top of the wall jet instead of to the ground [13]. This relation holds for circular, rectangular, and triangular shaped bodies until the wall jet intersects the body. If the wall jet intersects the body of the aircraft, a trapped vortex forms and the suck-down force increases substantially [1]. 2.5 Multiple Jet Induced Body Forces The mechanism for multiple jet suck-down forces is more complicated than those for single jets. For aircraft with multiple lift fans, there are two additional sources of significant body forces: flow fountaining from intersecting wall jets impacting the UAV s body and causing a general upwards force [5, 13], and a vortex forming between the fountain flow and the downwards flow from the fans, creating a region of low pressure and downwards force on the body [1]. The additional lift from fountain forces usually, but not always, dominates the suck-down caused by the vortices forming between the lift fans and the fountain [13]. 19

34 For the Navig8 UAV, suck-down forces due to wall jets are not significant due to the entire body being located between the two lift fans [1]. 2.6 Body Forces in Ground Effect for Multiple Lift Jets There are two competing body forces acting on a UAV similar to Navig8 while operating in close proximity to the ground: fountain forces and suck-down forces. These two forces act in opposite directions, with fountain forces increasing lift and suck-down forces decreasing lift. The strength of each force varies with altitude. Two methods to estimate the fountain and suck-down forces acting on the body were compared against the simulation data. These estimation methods are referred to by the first authors on their respective papers: Kotansky s method [5] and Kuhn s method [1] Estimating Body Forces using Kotansky s Method A fountain flow is formed when wall jets from multiple fans or jets intersect, and the resulting flow is directed upwards. If the fountain intersects the body of the UAV, it creates a region of high pressure which increases lift. The forces caused by fountaining flow impacting the body are only present during operation in the ground effects region. The formation and nature of the fountain is dependent on the arrangement and type of lift fans on the UAV [5]. The need to accurately predict these fountain forces have previously been discussed by numerous reports [5, 31, 32, 33]. The main methods of prediction focused on calculating the fountain s momentum as it impacts the aircraft s body, and the centre of its location [5, 33]. Correction factors are calculated and used to account for momentum that is dissipated along the route [5, 31]. The general calculation procedure for estimating fountain forces based on conservation of momentum is as follows: 1. Calculate the velocity and momentum flux for each jet 20

35 2. Determine the locations of stagnation points on the ground for each jet 3. Determine the momentum flux distribution around each stagnation point 4. Determine the points and/or lines of stagnation between the wall jets 5. Calculate the angle of departure for the fountain flow from its points / lines of stagnation between wall jets 6. Calculate the location and momentum flux of any fountains which intersect with the aircraft s body 7. Determine the fraction of the momentum flux which transfers into a force on the body of the aircraft. Importantly, these calculations require experimentally determined coefficients in order to be useful [5, 31]. The approach detailed above was used to create software that is able to predict the fountain forces acting on the aircraft [5]. Further work to experimentally validate and improve Kotansky s method was completed by Kotansky and Glaze [14]. A jet spacing of 12.8 jet diameters was used for their validation at a height of 5 jet diameters. Kotansky and Glaze [14] found that the stagnation line between two jets could be predicted using their Momentum flux density method which states that the stagnation line between the fans occurs when the momentum flux density is equal between the two wall jets. The momentum flux density method assumes that the momentum of the wall jets dissipates proportionally to r 2 instead of linearly with radius. Kotansky s method for estimating suck-down forces is based upon the entrainment of fluid into the fountain flow. The velocity of the air being drawn into the fountain is the hypothesized cause of the suck-down forces. 21

36 2.6.2 Estimating Body Forces using Kuhn s Method An alternate method for estimating body forces is described by Kuhn [1], which includes estimations methods for closely spaced fans. Kuhn s method is based on determining the area of the body on which the fountain acts, and uses a pressure coefficient C P to calculate the total forces acting on the body. This method employs correction factors for the shape of the body s contours, the spacing between fans, the distance that the body spans between the fans, and the effects of Lift Improvement Devices which act to reduce vortex-based suck-down forces. Kuhn s method [1] also details the total forces acting on the aircraft s body as a summation of all components, and it accounts for the change in lift due to entrainment, wall jet entrainment, fountain forces, and vortices induced by the fountain. The main limitations of Kuhn s method are the lack of corrections for non-vertically oriented nozzles, and the fact that the method does not account for differences in altitude when the body is lower than the fans. Kuhn s method was also not tested with shrouded fans. Regardless of these limitations, Kuhn s method is used as a basis against which to compare the simulation results of this study. Kuhn s method for estimating suck-down forces is based upon the formation of vortices between the fountain and the fan s downwash. These vortices create regions of low pressure and suck-down forces on the bottom of the UAV s body [1]. The height at which these vortices form is unclear/uncertain, and no basis is given for estimating the vortex onset height Effects of Body Shape The use of rounded edges on the bottom of a UAV s body decreases the magnitude of suckdown forces [1]. Only the curvature of the lower edges along the sides of the aircraft were noted to affect suck-down forces, while the edges along the front and rear of the aircraft did 22

37 not appear to have a significant impact on body/suck-down forces [1]. Kuhn s method [1] includes a correction factor to reduce fountain forces based on the radius of curvature of the edges. The correction factor K r which applies to the Navig8 is calculated as: ( ) r 2 K r = (2.9) e where r is the radius of curvature of the lower edges on the sides of the aircraft s body and e is the distance from the centreline of the UAV to the centreline of the fan. K r is bounded with a maximum value of 1 for r e 0.05, and decreases rapidly with increasing r Effects of Lift Improvement Devices Lift Improvement Devices (LIDs), also known as strakes, can be used to increase fountain lift on the body at the lowest altitudes [1]. LIDs are vertical extensions around the perimeter of the body which extend below the bottom of the body. Their primary purpose is to increase fountain lift at the lowest altitudes by reducing the suck-down forces [1]. The Navig8 UAV does not currently include LIDs in its design Limitations on Predicting Body Forces The capacity to predict fountain forces is currently limited due to the complexity of the flow fields involved. Small perturbations and asymmetries can lead to substantial differences in the fountain formation [34]. A ground obstruction near the stagnation line between the two wall jets that is approximately equal to the boundary layer thickness has a noticeable effect on the upwards velocity and inclination of the fountain [13]. Fountain flows also become unstable at close fan spacing and at low altitudes. At fan spacing ratios S/D 3, where S is the distance between the fan centrelines and D is the diameter of the fans, two jets function similarly to a single larger jet [34]. In experiments at altitudes of H/D = 1, where H is the height of the jet above the ground, the fountain formation was unstable for fan spacing ratios of S/D = 4 and 7 [34]. 23

38 The angle of the fans relative to the ground also plays a significant role in the stability of the fountain formation. Rotating both fans in their common plane by 4 degrees in parallel is enough to eliminate most of the fountain formation between the fans [34]. The effects of the UAV s body descending beneath the fans and the use of shrouded fans are not discussed in the methods presented by either Kotansky or Kuhn. 24

39 Chapter 3 PROBLEM DEFINITION The Navig8 UAVs are designed to fly in confined spaces where they will regularly be exposed to ground effects. Their design differs from single-rotor aircraft in that the fans, shrouds, and body will all be exposed to different ground effects which become significant over different operating ranges. All aircraft have to operate in the ground effects region at some point during operation. This occurs only during take-off and landing for many aircraft, but having an understanding of the forces acting on the aircraft at all elevations is beneficial for the proper control and design of the aircraft. The use of a dihedral angle for the fans allows for the Navig8 to rapidly correct for lateral disturbances without first inducing body roll. This is particularly important while operating at high-speed in confined spaces where maneuverability is essential. Understanding what effects, if any, the dihedral angle has on body forces while operating in ground effects can be used to improve the design UAVs with a positive dihedral angle. All simulations in this thesis can be considered to occurring under ideal operating conditions. The flows patterns and UAV are perfectly symmetrical, the ground is perfectly smooth, and the effects of transient effects are not considered. This means that the simulated body forces in this thesis are expected to exceed those in reality. This understanding can be used to bound the body forces during normal operation for use with a control system, which could be used to improve the controller s performance while operating in ground effects. Methods are available in the literature to estimate the change in lift due to ground effects for constant-power fans both with and without a shroud. These methods involve replacing the fan with either a source model [11] or a dipole model [12]. The source model and the dipole 25

40 model both treat the ground or walls as a mirror plane, and use the influence of a mirrored source or dipole to predict the effects of the ground [11, 12] and walls [12]. The source model is the traditional method for estimating fan ground effects; however, this method lacks any directionality [11]. The lack of directionality makes the source model unable to account for the effects of an inclined fan or a fan operating in proximity to a wall. A dipole model adds directionality to the fan s model [12]; however, the strength of the dipole needs to be calibrated to match the effects of the fan [12]. The source and dipole model are both limited in their ability to estimate ground effects for shrouded-fans at altitudes below approximately fan diameters, where fan and shroud flow separation are problematic [3]. The change in lift of the shroud decreases as the velocity of the flow through the shroud decreases; however the exact change in lift due to ground effects is specific to the fan and shroud combination. The shroud lift decreases rapidly if the flow separates from the shroud, and the height of onset of flow separation depends on the geometry of both the fan and shroud. Two methods to estimate body forces in ground effects are available in literature: 1) a method developed by Kotansky [14]; and 2) a method developed by Kuhn [1]. Body forces are generally undesirable because they do not act on the body in a steady location nor through the UAV s centre of mass. Kotansky s method was developed for VTOL aircraft with widely-spaced fans or jets [5]; thus their estimations are limited for closely-spaced fans and very close proximity to the ground. The equations from Kotansky s method assume that the distance between fans is significantly greater than the distance between the body and the ground, and that the distance between fans is significantly greater than the fan diameter. Conversely, Kuhn s method does not require that the spacing between fans is substantially larger than the fan diameter or the height above the ground [1]. Neither Kuhn s nor Kotansky s methods have allowances for the difference in altitude between the bottom of the UAV s body and the fans, 26

41 the use of shrouded fans, or non-vertical fans. The result of this work will allow for better control of dual shrouded-fan UAVs with closely-spaced fans while operating in ground effects. It could be used to allow for an optimal selection of dihedral angle during the design of the UAV, or to develop an equation which is capable of predicting the body forces acting on the UAV while operating in ground effects. 3.1 Problem Statement Determine the effects of height and dihedral angle on body lift with a secondary interest in fan and shroud lifts for a UAV which is dimensionally similar to the Navig8 UAV family while operating in the ground effects region. 3.2 Comparison of Results against Existing Methods of Prediction In this study, the simulation results for the change in fan lift while in ground effects are compared to the estimated ground effects of a source model [11]. Differences between the estimated lift from the source model and the simulation results will be investigated. The effects of height and dihedral angle on shroud lift are dependent on the shroud geometry, but flow separation from the shroud is a concern. The potential for flow separation and the causes of this separation are investigated. The available estimation methods for body forces from both Kotansky [5] and Kuhn [1] will be compared against the simulations results. These methods were both developed to predict the body forces acting on a multi-fan aircraft while operating in ground effects. The underlying assumptions of each method will be investigated to determine their effect on UAVs which are dimensionally similar to the Navig8. The underlying assumptions for the causes of fountain and suck-down forces are investigated and discussed. Differences between 27

42 the existing estimation methods and the simulation results are examined and discussed. 3.3 Scope In this study, the height of the UAV is measured from the bottom of the shroud, which corresponds to the vertical centre of the body, to the ground. A minimum height of 0.75 fan diameters (D) is used to exclude operating heights where separation from the fan and shroud blades becomes probable. A maximum height of 7 D is used, which was determined to be out of the range of ground effects by iteratively increasing the elevation of the model. A maximum dihedral angle of 8 degrees of fan and shroud rotation was used for this thesis, which directs flow away from the body. A minimum dihedral angle of 0 degrees was used. Negative dihedral angles were not considered. The effect of operating in proximity to walls was not considered for this thesis. The use of a single wall removes the ability to use the symmetry plane in simulations, which doubles the solution time required for each simulation. Thus, the implementation of a variable wall distance would entail a substantial increase in both the simulation time and the number of simulations required. The distance of the UAV from the walls and ceiling is considered to be infinite for the purposes of this study. Therefore, the effects of the size of the room and the potential to develop vortices within the room in which the UAV is operating are not considered in this study. Fine details of the UAV s body shape, such as the curvature of the edges, lift improvement devices, and body contours were excluded for simplicity. The effects of body edge curvature and lift improvement devices are discussed in and 2.6.4, respectively. 3.4 Contribution The primary contributions of this thesis are as follows: 28

43 The body forces acting on a UAV which is dimensionally similar to the Navig8 aircraft are determined as a function of height and dihedral angle. Existing methods to estimate body forces are compared to the simulation results and evaluated. The onset of significant body forces is investigated as a function of height and dihedral angle. The two primary sources of body forces (fountain forces and suck-down forces) are investigated and compared. The origins of the forces and their range of significance are identified and discussed. Fan lift is determined as a function of height and dihedral angle. The simulated fan lift is compared to theoretical values by estimating the change in fan lift using a source model. Deviations between the simulation data and estimations are discussed. Shroud lift is determined as a function of height and dihedral angle. Significant secondary flow patterns around the UAV are identified and discussed. Recommendations are made to improve the design and operation of Navig8 by taking into account the results from simulations from the existing literature. 29

44 Chapter 4 METHODOLOGY 4.1 Solution Approach A simplified version of the Navig8 Model E-16 was used for Computational Fluid Dynamics (CFD) modelling over a set range of heights above the ground and dihedral angles. Critical dimension and relations were maintained throughout the simulations. The simulation results were then compared against the results generated from existing methods to estimate fan and body forces while operating in Ground Effects (GE). This chapter describes in further detail the methodology employed in this study, including the model setup, the assumptions and limitations inherent to the model, the methods for modelling the behavior of the fans, as well as the methods for estimating fan and body forces in ground effects. 4.2 Model Setup Model Simplifications The model of the Navig8 UAV used in computer simulations was simplified in order to capture the relevant flow patterns and forces while minimizing computational time and removing superfluous information. The Navig8 prototype body was replaced with a rectangular body for modelling purposes, while maintaining the same overall length, width, and approximate height of the UAV. This simplification was used in order to increase the generality of the simulated body forces and to allow for comparison against existing methods to estimate body forces. Correction factors for body features such as the body curvature can then be applied to allow the results to be applicable to other body shapes [1]. The simplified model used is shown in Figure 4.1 and 30

45 the dimensions are specified in Figure 4.1: Simplified Model of Navig8 Used for Simulations. A general momentum source of uniform thickness was used for the fan model. This model creates a force in the direction normal to the fan. The physical properties of the fan, such as the blades, fan hub, tip clearance, and attachment shaft are ommitted. For additional details on the fan model used, see 4.4. The shroud was modelled according to the design by Trek Aerospace [35] for 4Front Robotics Ltd. for use with a 16 diameter propeller. The shroud model was simplified by removing the openings required to attach the fan to the body of the UAV. A 0.5 in thick section was used as a momentum source to simulate the effects of the fan. Figure 4.2 shows the general dimensions and the layout of the fan model within the shroud. 31

46 SHROUD FAN BLADE Figure 4.2: Shroud and Fan Model (all dimensions in inches) Model Dimensions The dimensions of the simplified Navig8 UAV model used in all CFD simulations are shown in Figure 4.1 and given in Table 4.1, while the dimensions of the modelled fan and shroud assembly are shown in Figure 4.2 and also given in Table 4.1. Descriptions and the basis for each of the dimension variables are included in Table

47 Table 4.1: Simulation Model Dimensions and their Basis Dimension Description Value Basis X B Body Width 11.5 in Width required to match gap between fan and body for Navig8 Z B Body Length in Maintains distance between fan centreline and tail of the Navig8 Y B Body Height 9 in Double shroud height Y S Shroud Height 4.5 in Trek Aerospace [35] D S Shroud Throat Diameter 16 in Trek Aerospace X 1 X 2 Distance between fan centre and UAV centreline Gap Between Shroud and Body 16.7 in (425 mm) Navig m (1.73 in) Navig8 Y F Fan Thickness 0.5 in Approximate thickness of fan blades Y 1 Offset from top of Shroud to top of fan blades 0.5 in Approximate height of fan blades within shroud Model Constraints In addition to the dimensions listed in Table 4.1, the model setup contains dimensional constraints that are used to relate the relative locations of parts. These constraints and their basis are as follows: The top of the shroud is at an equal height to the top of the UAV s Body. This is the approximate existing relation between the shroud and body, and maintains centre of lift above centre of mass for the UAV. The centre of rotation for the shroud and the fan dihedral angle is located at the top centre of the shroud. This position maintains a constant minimum distance between the shroud and the body. 33

48 4.3 Assumptions and Limitations Certain simplifications were used on the model in order to expedite the convergence of simulations due to computing limitations, and to allow for more generic results that may be applicable to a wider range of UAV models Symmetry Planes Two symmetry planes were used in the simulations to reduce the model size and decrease convergence time. One symmetry plane vertically bisects the aircraft longitudinally. A second symmetry plane, orthogonal to the first plane, vertically bisects the model through the centre of the fans. The use of these symmetry planes results in the model s body extending equally fore and aft of the fans, but allows for the simulations to converge within a reasonable amount of time. The required domain size, computational time, and computer resources are reduced by a factor of 4 through the use of the symmetry planes. The results from the model generated through the use of symmetry planes was compared to the results from a simulation without any symmetry planes at a height of 7 fan diameters with vertical fans. The difference in fan and shroud lifts between the two models were minimal, and differed by less than 1% between models. 4.4 Fan Modelling A constant power fan model with a uniform thrust distribution was used to produce a constant 1 kw of total hydraulic power for the full-scale model. The total lift generated by the fans and shrouds is approximately 100 N of lift. For the 1/4 model used in the CFD simulations, the fan model had a specified 250 W of power. 34

49 4.4.1 Power, Lift, and Flow Rate Relations The lift generated by the fan L F is calculated by integrating the pressure gradient in the vertical direction throughout the control volume: L f = CV p dv (4.1) y If the change in pressure is uniform throughout the fan, then the hydraulic power w is defined as the change in pressure p multiplied by the volumetric flow rate q: w = pq (4.2) For a constant power fan, the fan s lift L f is inversely proportional to the fan s volumetric flow rate q. 4.5 Experimental Domain The experimental domain was investigated as a function of two independent variables: the height of the aircraft above the ground (H), and the dihedral angle of the fan (θ). The height of the aircraft is defined as the distance from the bottom of the aircraft s shroud (which corresponds to the centre of the UAV s body) to the ground, while the dihedral angle is defined as the angle of rotation of the fan s central axis from vertical, with positive angles discharging away from the aircraft s body. All heights were normalized by the fan diameter to allow for comparisons between dimensionally similar UAVs, which is typical practice for estimating ground effects [11, 12] Limits of Experimental Domain The experimental domain s maximum and minimum heights were selected to reflect the range in which body forces were present while remaining within heights that were reliable for the fan model. Ground effects were iteratively found to be negligible at heights of 7 fan 35

50 diameters or greater for this model. In addition, the equations used by Kotansky in their prediction method of fountain forces [5] were tested at a height of 7 fan diameters. The minimum height of 0.75 fan diameters was selected due to the limitations of a shrouded fan operating in Ground Effects. Multiple studies [3, 4] have shown that shrouded fans which are optimized for far-field performance undergo performance degradation and separation at heights below 0.75 fan diameters, as shown in Figure 2.3. The fan model used in this thesis is not able to predict separation from the fan blades; therefore, a minimum height of 0.75 fan diameters was used. The dihedral angle of the fans range from vertical (0 degrees) to a maximum of 8 degrees. Negative angles were not considered Design Space Investigation Method A variation of the Box-Behnken design method was used to investigate the design space. The Box-Behnken method normalizes the minimum and maximum values for each property to -1 and 1 respectively. Sample points are taken at the centre of the model (0, 0) and along the sides, e.g. ( 1, 0). The corners of the domain, e.g. (1, 1) are not normally sampled using Box-Behnken design. The centre of the domain is oversampled for physical experiments to determine the degree of randomness within the sample points. The data points are then used to create response surfaces. For this thesis, the corners of the domain were also sampled. No points were oversampled since computer simulations are deterministic and do not contain random variation. The combinations of heights and dihedral angles employed for the simulations of this study are shown in Table 4.2. The intersections of the heights and angles that were modelled are marked with an X. 36

51 Table 4.2: Experimental Domain Combinations of Height and Dihedral Angle for Simulations. Height (Diameters) (Normalized) Dihedral Angle (Degrees) (Normalized) X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 4.6 Estimating Body Forces in Ground Effects The change in lift for the UAV s fans and body while operating in GE were estimated using two separate available methods and compared against the simulation results. The first method was developed by Kuhn [1] while the second method was developed by Kotansky [5]. Both methods involve different methods of estimating body forces and have different limitations. 37

52 4.7 Estimating GE Body Forces based on Kuhn s Method Kuhn s method [1] is one of two methods used to estimate the forces acting on the UAV s body. Kuhn s method determines pressure coefficients for fountain forces and suck-down forces acting on the body. Each force component is considered to be independent, and net change in lift is equal to the sum of the components, as shown in Equation 4.3 from [1]. The variables L, L f and L s represent the change in total change in lift, and the change in lift due to fountain and suck-down forces respectively. The variable T is the UAV s thrust out of ground effects. L T = L f T + L s T (4.3) Estimating Fountain Forces based on Kuhn s Method The change in lift due to fountain forces, L f, is calculated as: T L f T = C p,f S f 2A j K r (4.4) The variables in Equation 4.4 are defined in Table 4.3, while the dimensions w, e, d, x 0, and y are defined graphically in Figure 4.3. The variable y is used in suck-down calculations only Limitations and Modifications to Fountain Force Estimation based on Kuhn s Method The method for calculating fountain forces described in has three substantial limitations for estimating fountain forces for the Navig8 model: The definition of X 0 does not account for cases where the body half-width w is less than half the spacing e between fans; The calculations do not contain a correction factor for when the body descends below the height of the bottom of the shrouds; 38

53 Figure 4.3: Dimensions for Fountain and Suck-down Force Calculations for Kuhn s Method [1] Fig The calculations do not contain a correction factor for non-vertical fans. used: In order to address these deficiencies, the following modifications and restrictions are The definition of X 0 is modified to equal the body half-width w instead of the half-distance e between fans; The distance from the ground h is measured from the bottom of the body to the ground instead of from the bottom of the shroud to the ground; Only vertically oriented fans are considered for comparative purposes Estimating Suck-down Forces based on Kuhn s Method The suck-down forces are estimated using the equations and variables listed in Table 4.4 in addition to the variables used in Table 4.3. Kuhn s method of estimating suck-down 39

54 forces assumes that a stable vortex forms beneath the UAV s body at some height [1]. Two equations for estimating suck-down forces are given: one for estimating suck-down force coefficients at heights above the onset of a stable vortex (C p,ave,s,high ), and one for estimating forces at heights below the onset of a stable vortex (C p,ave,s,low ). The onset height of the stable vortex is absent from Kuhn s method. The fractional change in lift due to suck-down forces, L s /T, is thus the average suckdown pressure coefficient C p,ave,s multiplied by the ratio of the effective suck-down area, divided by the total jet area for two round jets with equal thrust. 40

55 Table 4.3: Variables, Equations, and Definitions to Estimate Fountain Force based on Kuhn s Method [1]. Variable Definition Eq n from [1] ( ) 1 K r from [1] r e Correction factor for body curvature s effect on fountain lift for lengthwise fountains S f 4X 0 Y 2.36 from [1] Cross-sectional area of fountain X 0 e (when e/d 1.5) 2.38 from [1] h Half-width of region of positive fountain pressure Height measured from the bottom of the shroud to the ground Defined in [1] Y f Body half-width at the front jet Defined in[1] Y r Body half-width at the rear jet Defined in [1] ( ) 0.5 f from [1] w e h f 3.7(NP R) 0.5 ( ) 0.2 ( ) 0.6(NP R) 0.6 e d w e Height of the top of stable fountain 2.45 from [1] S 4wy Defined in [1] Cross-sectional area of the body ( ) 0.72 ( ) 0.5 ( ) 0.25 ( C p,ave,f,low 0.16 S Aj e d Y f +Y r 2d Pressure coefficient when h h f ( ) 0.72 ( ) 0.5 ( ) 0.25 ( S e Y C p,ave,f,high 0.16 f +Y r A j d 2d Pressure coefficient when h > h f w e w e ) 0.5 ( ) 0.5 ( h e h e ) f 2.42 from [1] ) f ( ) 3 h f 2.46 from [1] h 41

56 Table 4.4: Variables, Equations, and Definitions to Estimate Suck-down Force based on Kuhn s Method [1] Variable Definition Eq n from [1] T l Thrust of the local jet, = T/2 for symmetrical jets Defined in [1] S x 4wY 2X 0 Y Defined in [1] The effective area of suction pressure, difference between the geometric area and half the fountain area S f H s h D p D e NP R ( 0.8 ) Y /d 2.52 from [1] D p Effective diameter of the planform area of interest (in this case, the area of the UAV s body) Defined in [1] D e = 2d Defined in [1] Effective diameter of the combined area for two identical round jets K s,inb ( ) 1 ( ) 0.15 S e 0.3 A j d 2.53 from [1] ( ) 1 ( S K s,high A j ( ) 0.34 ( S g 0.38 A j e d e d ) 0.5 ( ) 0.36 ( Y d w e ) from [1] ) 0.25 ( ) 0.15 Y 2.59 from [1] d C p,ave,s,low K s,inb H g s 2.48 from [1] Pressure coefficient at low heights C p,ave,s,high K s,high H 1.8 s 2.49 from [1] Pressure coefficient at high heights L s T C p,ave,s S x 2A j T l T/ from [1] 42

57 4.7.4 Limitations and Modifications to Kuhn s Suck-down Force Estimation In addition to the limitations previously discussed in for fountain forces, there are the following additional limitations placed on the suck-down calculations: The definition of the effective diameter of the planform D p is assumed to be the diameter of a circle with an equivalent area to the area of the UAV s body; No limitations or effects are given for the planform aspect ratio; The transition height where the equations transfer from low to high is not specified. This corresponds with the onset height of a stable vortex forming beneath the body; A step discontinuity occurs at the transition from the low to high pressure coefficients. The step discontinuity in pressure coefficients between the low and high heights limits the ability of this method to accurately predict the suck-down force throughout the entire range of operating heights. 4.8 Estimating GE Body Forces based on Kotansky s Method An second approach to estimating the body forces was developed by Kotansky [5]. This method is based on conserving momentum in a control volume around the body and fountain. Like the method described in 4.7, the effects of fountain forces and suck-down forces are considered to be independent Estimating GE Fountain Forces based on Kotansky s Method The fountain forces are estimated by determining the fraction of the fountain flow which impacts the UAV s body, and then using these results to determine the net change in fountain 43

58 momentum. This in turn is used to estimate the upwards force on the body. The estimation method is based on the work of the McDonnell Aircraft Company and Kotansky [5]. The variables and equations listed in Table 4.5 are used to estimate the fountain forces acting on the UAV: Table 4.5: Variables and Equations used to Estimate Fountain Forces Based on Kotansky s Method. Variable Definition Source R j Radius of fountain See Figure 4.4 V j Velocity of jet at radius R j See Figure 4.4 x 0 Width of fountain jet See Figure 4.4 S Distance between wall impingement points Definition from [5] h Distance between bottom of body and ground Definition from [5] R 0 h + S 2 See Figure 4.4 y Distance from fountain measured parallel to fountain s See Figure 4.4 centreline R (R0 2 + y 2 ) 1/2 Definition from [5] Distance to a point the given point on the body being impacted by the fountain and the fountain s origin K t Eq. 90 Constant for determining the half-velocity boundary of the fountain x 5 K t (R R j ) Eq. 90 from [5] With of the fountain with half of its original velocity as a function of radius Continued on next page 44

59 Variable Definition Source ξ x x 0 x 5 Eq. 93 from [5] ξ 1.763ξ Eq. 97b from [5] ξ L, Xi T Limits for integration for ξ, evaluated at limits of body Definition from [5] witdh M j 2πρR j V 2 j X j Definition from [5] Total annular momentum of the fountain jet ȳ y normalized by R 0 Definition from [5] F z π ȳ 0 [tanhξ 1 3 tanh3 ξ ] ξ L (ȳ) ξ T (ȳ) (1+ y 2 ) 3/2 dȳ Eq. 97a from [5] Vertical force coefficient acting on half of the UAV s body normalized by M j C N 2 F z Eq. 98 from [5] Total vertical force coefficient acting on half of the UAV s body normalized by M j F z C N M j Definition from [5] Total vertical body force Limitations and Modifications to Fountain Force Estimation based on Kotansky s Method Kotansky s estimation method for fountain forces has a number of limitations which may restrict the ability of this model to accurately predict fountain forces acting on the Navig8 model. The most significant of these include: The method assumes that S >> D je. Experimental testing in the original study showed poor correlation for S D je 4; 45

60 Figure 4.4: Additional body Dimensions for Fountain and Suck-down Force Calculations from [5] Figure 64. The method assumes that R 0 >> R j. At lower altitudes this assumption does not hold; Of these limitations, the requirement for S D je > 4 is a requirement that is not met by the Navig8 UAV due to its configuration. Despite these limitations, the results from simulations are compared against these predictive methods to determine if body forces can be estimated with a reasonable degree of accuracy Estimating GE Suck-down Forces based on Kotansky s Method A suck-down force acting on the UAV s body is estimated based on the entrainment of air into the fountain and wall jets formed on the bottom of the UAV s body. The airflow into a control volume around the fountain and body s bottom which is induced by the velocity of 46

61 the fountain jet is used to estimate a 1-dimensional inflow velocity, which results in a region of negative pressure. Figure 4.5 shows the general mechanism as well as the dimensional variables used to estimate the magnitude of the suck-down force. Figure 4.5: Dimensions and Origin of Suck-down Force for Method based on Kotansky s Method (from [5] Fig. 65). The additional variables and equations not shown in Figure 4.5 or Table 4.5 are included in Table 4.6. Table 4.6: Variables and Equations used to Estimate Suck-down Forces Based on Kotansky s Method. Variable Definition Source b Length of body aligned with fountain centreline Definition from [5] c width of body perpendicular to fountain centreline Definition from [5] Continued on next page 47

62 Variable Definition Source [ ( ) ( ) ] 2 K (R 0 + c)ln b/2 b/2 2 R 0 + +c/2 R 0 +c/2 + 1 Eq. 110 from [5] A L 14 ( [ ( ) b/2 (R 0 H)ln R 0 + H + b 2 ln [ (R 0 +c/2)+ (R 0 H)+ ] (R 0 +c/2) 2 +(b/2) 2 (R 0 H) 2 +(b/2) 2 ( ) ] 2 b/2 R 0 H + 1 ) b+c H Eq. 112 from [5] 2 Area of air entrainment beneath 1/4 of body A W 14 bc Eq. 113 from [5] 4 Area of 1/4 of body bottom F S A W 14 A 2 L 14 [ρv 2 ( x j R j )K 2 ] Eq. 115 from [5] Total Suck-down force acting on 1/4 of the aircraft s body [ C s bc (b+c) 2 H 2 ] K 2 Eq. 117 from [5] Suck-down force coefficient for full UAV body normalized by total radial jet momentum flux Limitations and Modifications to Suck-down Force Estimation based on Kotansky s Method Like Kuhn s method, Kotansky s method to estimate suck-down forces does not include correction factors for bodies descending beneath the exits of the shrouds, nor does it include correction factors for the dihedral angle of the fans. Kotansky s method does not assume that a vortex forms beneath body of the UAV for suck-down force calculations. The difference in approach to estimating suck-down forces between Kuhn s and Kotansky s methods are investigated in the results of this thesis. 48

63 4.9 Estimating Fan Forces in Ground Effects The additional lift due to GE for the fans was estimated using Equation 2.4 from Cheeseman [11]. Over the range of simulated fan heights, it is expected that the total change in lift should remain within approximately 1% of the far-field lift. By limiting the dihedral angle to 8 degrees or less, the lift force of the fans is essentially identical to that of vertical fans by the small angle approximation. The use of the small angle approximation introduces less than 1% in error in lift. It is expected that the horizontal force of the fan and shroud will vary linearly with dihedral angle if the flow patterns remain constant. The simulated fan lifts are compared against the estimated values. The estimated change in fan lift is essentially negligible throughout the operating domain, and any differences between the measured and estimated fan lifts will be discussed Shroud Forces in Ground Effects The change in shroud forces while operating in GE is dependent on the geometry of the fans and shrouds. There is not an available method to estimate the change in shroud lift; therefore, the shroud lifts will be plotted as a function of height and dihedral angle to identify any trends. 49

64 Chapter 5 SIMULATION IMPLEMENTATION 5.1 Software The simplified UAV model described in was simulated using ANSYS R software. AN- SYS DesignModeler TM was used to build the UAV model and simulation environment, AN- SYS Meshing TM was used to build the meshes, and ANSYS CFX R version 16.2 was used to set up and run the simulations. A Solidworks R model of the shroud was supplied by Trek Aerospace R and imported into DesignModeler. The completed simulations were postprocessed using ANSYS CFD-Post TM CFD Environment and Model Figure 5.1 shows the CFD environment and model used as a basis for the simulations described in this thesis. One quarter of the UAV was modeled inside a cylindrical environment that was designed to have a consistent meshing scheme for all combinations of height and dihedral angle. The domain in Figure 5.1 is sub-divided into an inner and outer region, with the inner region having a radius of 5 fan diameters at base of the shroud. The inner domain is further sub-divided into 3 regions to refine the meshing: a lower region which extends from the ground to the region near the UAV; a region in close proximity to the UAV which requires a tetrahedral mesh; and an upper region that extends upwards to the domain s upper boundary. The simulation domain was designed to adapt to the height and dihedral angle of the UAV. The height of the lower domain varies to adjust to the height of the UAV. The inner domain (including the lower, near UAV, and upper regions) rotates with the dihedral angle so that the primary direction of flow through the fan remains aligned with the mesh. The 50

65 Figure 5.1: Domain used for CFD Simulations. outer domain boundaries remain stationary at a constant radius of 13 fan diameters Model Meshing The model meshing criteria were selected so that they could remain constant for all combinations of height and dihedral angles. A tetrahedral mesh was used in the region near the UAV, while a hexahedral mesh was used for the remainder of the domain. Each of the regions shown in Figure 5.1 have their own mesh sizing conditions. Three different levels of grid refinement were used for each combination of height and dihedral angle. The distance between nodes was decreased at a constant ratio of 3 2 for a grid independence check, which results in an effective doubling of the number of nodes and is discussed in more detail in 6.5. Inflation layers were used for all near-wall regions to improve the simulation s ability to simulate pressure gradients and flow separation. The first node nearest the wall was selected to maintain y + < 2 for all walls. y + is referred to as the dimensionless wall distance, and is discussed in detail in Appendix C. Using a maximum y + value of 2 or less locates the node 51

66 nearest to the wall in the viscous portion of the boundary layer and allows for the boundary layer to be directly modeled if a sufficient number of nodes are used. Additional details on the near-wall region modelling are discussed in The mesh sizing criteria used for the simulations are shown in Table 5.1. Each combination of height and dihedral angle used the same mesh sizing in order to improve comparability between models. Table 5.1: Mesh Sizing Criteria. Mesh Size (m) Mesh Description Coarse Medium Fine Global Max Sizing Global Min Sizing 9.28E E E-6 Global Growth Rate 1.13 Shroud Inflation First Node Height: 1E-5 Inflation Layer Thickness: 15 nodes Inflation Layer Growth Rate: 1.2 UAV Body Inflation Layer First Node Height: 5E-5 Inflation Layer Thickness: 15 nodes Inflation Layer Growth Rate: 1.2 Ground Inflation Layer Inflation Layer Thickness: 1.27E-3 Inflation Layer Nodes: 5 Inflation Layer Growth Rate: 1.2 Shroud Face Sizing 1.70E E E-3 Tet Core Region Sizing 4.00E E E-2 Upper Hex Core Region Sizing 6.00E E E-2 Continued on next page 52

67 Mesh Size (m) Mesh Description Coarse Medium Fine Outer Region Sizing 8.00E E E-2 UAV Body Face Sizing 5.00E E E-3 Fan Region Sizing 5.00E E E-3 Lower Hex Core Edges Number of Divisions (all inner core edges parallel to ground plane) Lower Hex Core Region Sizing 6.00E E E-2 In addition to the mesh sizing in Table 5.1, meshing style controls were used to dictate the type of mesh being built in each region. A sweep method was used to mesh all of the volumes outside of the region near the UAV. This method maps a face on one side of the hexahedron and sweeps that mesh through the volume. Mapped face meshes were specified on all the UAV and shroud walls. This method places a regular and approximately uniform mesh on the faces. The use of mapped faces on the UAV body and shrouds resulted in a more uniform mesh which improved convergence. Figure 5.2 shows an example of the mapped face meshing on the shroud. Table 5.2 lists the specified meshing methods used in the simulations. Table 5.2: Meshing Methods. Mesh Region Method Used Notes Outer Region Sweep Method Upper Inner Core Sweep Method Lower face is source Ground Inner Core Faces Mapped Faces Lower Hex Core Body Sweep Method UAV Faces Mapped Faces Shroud Faces Mapped Faces 53

68 Figure 5.2: Example of Mapped Face Mesh on Shroud Boundary Conditions and Fluid Properties All CFD Simulations in this thesis share common boundary conditions. These boundary conditions, along with their mathematical constraints and the locations in which they were used are summarized in Table 5.3. Symmetry boundaries impose two conditions on the flow: 1) the normal velocity u n = 0, and 2) all normal gradients φ n = 0. The opening boundary used at the outer edges of the domain have specified constant pressure of 0 Pa(g) and the velocity and turbulent gradients normal to the boundary are zero. This does not mean that the flow itself is normal to the boundary. The walls are specified as no-slip walls, so that the velocity at the wall, u wall = 0. The fan blades are specified as a general momentum source with a constant change in pressure normal to the fan blades, i.e. p x = Constant. The operating fluid for all simulations was dry air at 25 C at kpa with constant properties. The density and dynamic viscosity used are included in Table

69 Table 5.3: Boundary Conditions. CFX Boundary Type Constraints Locations Used Symmetry u n = 0 XY Plane φ n =0 YZ Plane Opening p = C Environment Boundaries (zero gradient velocity and turbulence) φ n = 0 Wall (No slip) u wall = 0 Shroud Walls General Momentum Source p x = C Body Walls Ground Fan Blades 5.2 Turbulence Modelling Table 5.4: Properties of Air used in CFD Simulations. Air Property Value Units Density (ρ) kg m 3 Dynamic Viscosity (µ) Ns m 2 The Shear-Stress Transport (SST) k ω model was used to model turbulence for all simulations. The SST k ω model functions similarly to the k ɛ turbulence model in the free stream while improving its accuracy in the near-wall region [36]. The SST k ω model is also better at simulating regions of adverse pressure gradients and predicting the separation point from a surface [36]. This is particularly important in determining whether the flow is separating from the shroud walls, which is required to accurately simulate the shroud lift. Additional information on the turbulence model used and the differences between the SST k ω model and its alternatives are included in Appendix B. 55

70 5.2.1 Wall Region Modelling The SST k ω model requires the near-wall region to be modeled in order to accurately simulate the wall shear-stress and to predict separation [36]. This was done by placing the first node into the viscous sub-layer of the flow near walls. A maximum y + value of 2 was used throughout the simulations, and 15 nodes were placed within the boundary layer for both the shroud and the body. Additional details on y + are included in Appendix C. It is recommended to use a maximum y + value of 2 and a minimum of 10 nodes within the boundary layer when using the SST k ω model [37]. 5.3 Fan Model The fan blades region shown in Figure 4.2 were modeled as a 3D general momentum source extending to the walls of the shroud. The blade model has a thickness of 0.5 in while its bottom is elevated by 1 in from the throat of the shroud. Locating the fan in the throat of the shroud was found to limit the simulation s convergence during preliminary simulations. The fan model was extended to the wall in order to remove any effects caused by the fan s tip clearance. The thrust force generated by the fan is equal to the sum of the change in momentum of the fluid and the change in pressure across the fan integrated over the control surface. This is expressed in Equation 5.1: F j = CS P n j ds + In Equation 5.1, the variables are defined as follows: CS ρu j (u j n j ) ds (5.1) F j = force in the j-direction P = pressure at the fan s surface n j = surface normal in j-direction 56

71 u j = velocity in j-direction CS = Control Surface A fan model with a constant hydraulic power of 1 kw over a full UAV was used to create a general momentum source which simulated the fan. This produced approximately 100 N of lift for a full-scale model between the fans and shrouds. The thrust generated from a constant-powered fan in direction j is found by dividing the fan power w F by the velocity u, i.e.: F j = w F u j (5.2) This relation was used to create a general momentum source in CFX. In CFX, the strength of a general momentum source K j is specified as a change in pressure per unit length, i.e.: K j = P x j (5.3) The total force exerted by the general momentum source is calculated by iterating the general momentum source over the volume of the fan: F j = V P x j dv (5.4) A uniform force distribution was used for the fan model. This was done by calculating the volume-averaged velocity through the fan u j,ave in the direction of interest, and using this volume-averaged velocity to calculate K j. Equation 5.5 describes the fan model used for the simulations in this thesis: ( ) w F K j = abs u j,ave V fan (5.5) where K j is the specified strength of the general momentum source, w F is the total power of the fan, u j,ave is the average fan velocity in the j-direction, and V fan is the volume of the fan model. A local fan-coordinate system was used, with the positive y-direction being normal to the fan blades and oriented generally upwards. In Equation 5.5, the negative absolute value 57

72 in the j-direction was used in Equation 5.5 to ensure that the source would consistently add momentum in the downwards direction. This was required in order to prevent the source from changing direction in the case of flow separation or recirculation within the fan model. 58

73 Chapter 6 SIMULATION VERIFICATION The simulation data presented in this thesis were verified to eliminate and account for potential sources of modelling error. The following properties were checked as part of the verification procedure: Domain size independence Fan model invariance Symmetry plane independence Solver residuals and monitors convergence Domain force and momentum balance Grid independence Physical validation of the experiment was not completed, and is recommended for future work. All simulations are limited by the assumptions used throughout this thesis, including steady-state operating conditions, perfect surface roughness, perfectly uniform fan thrust, and an infinitely large environment. 6.1 Domain Size Independence The effects of the overall domain size on the forces acting on the UAV were investigated. The domain size independence was checked by sequentially increasing the height and radius of the domain by a factor of 1.3, which approximately doubles the volume of the domain. Consecutive domain sizes were checked at the combinations of minimum and maximum 59

74 height and dihedral angle. Fan lift, fan velocity, and shroud lift were monitored for domains with a radius and height above the UAV of 10, 13, and 17 fan diameters (D). Body lift was compared at a height of 0.75 fan diameters and was negligible (Lift <0.1N) at the maximum height of 7.0 D. Figure 6.1 compares the lifts and velocities for each domain size normalized by the results of the largest domain for all combinations of minimum and maximum height and dihedral angle. (a) Height = 7D, θ = 0 Deg (b) Height = 7.0D, θ = 8 Deg (c) Height = 0.75D, θ = 0 Deg (d) Height = 0.75D, θ = 8 Deg Figure 6.1: Domain Size Dependence for Fan Lift, Shroud Lift, and Body Lift as a Function of Height and Dihedral Angle. Figures 6.1a and 6.1b show the fan lift, shroud lift, and fan velocities at a height of 7.0 D for θ = 0 and 8 degrees, respectively. The fan lift and velocities for the domain size of 13 D are within 1% of those from 17 D. Shroud lifts differ by 2% or less between domain sizes of 13 D and 17 D. Figures 6.1c and 6.1d show the fan, shroud, and body lifts as well as the fan velocities 60

75 at a height of 0.75 D for θ = 0 and 8 degrees, respectively. Figure 6.1c shows that all properties agree within 1% and converge with increasing domain size. Figure 6.1d shows that the shroud and body lift have some dependence on the domain size. The shroud lift differs by approximately 3% between domain sizes of 13 D and 17 D, while the body lift is not asymptotically converging for changing domain size. This may be due to some dependence on the domain size, or fluctuations occurring in the solution. The solver fluctuations are discussed in A domain with a height and radius of 13 D was used for the resulting simulations because of its balance between acceptable accuracy and solution speed. 6.2 Fan Model Invariance Two alternative methods of modelling a constant-power fan were compared on identical meshes. The first fan model had a constant power with uniform thrust density, which was created by dividing the power by the fan s average normal velocity. This is expressed in Equation 6.1, where u j,ave is the volumetric-averaged velocity normal to the fan and P x j the strength of the general momentum source: is P x j = w F u j,ave (6.1) These results were compared to a constant power fan model with a uniform power density, as shown in Equation 6.2: P x j = w F u j (6.2) The difference between Equation 6.1 and 6.2 is the treatment of the fan velocity for each node. Equation 6.1 averages the velocity throughout the fan, which results in a lower power density in regions of low velocity and a uniform thrust density throughout the fan. Equation 6.2 uses the local velocity to calculate the strength of the general momentum source. This 61

76 results in a uniform power density, but dramatically increases the thrust near the walls to maintain a constant power. The additional thrust near the walls artificially suppresses flow separation, and is not representative of typical fan behavior. Each fan model was run for a total of 2000 iterations on identical meshes. The results for the model at height = 0.75 D, θ = 8 degrees are shown in Table 6.1. All monitored properties agree within < 1%. The uniform thrust-density fan model from Equation 6.1 was ultimately selected because of its better response in the near-wall region and the negligible difference between the two models in overall performance. Table 6.1: Comparison between Uniform Power Density and Uniform Thrust Density Fan Models on Identical Meshes at Height = 0.75 D, θ = 8 degrees. Property Uniform Power Density Uniform Thrust Density Fan Lift Shroud Lift Fan Avg Velocity Body Lift Ground Origin Pressure Ground Under Fan Pressure Ground Under Body Pressure Total Ground force Symmetry Plane Independence The simulations used throughout this thesis contain two symmetry planes: one dividing the domain longitudinally through the body and a second vertically bisecting the fans. The lift of the fans and shrouds was compared between models at height =7.0 D and θ =0 degrees, both with and without the symmetry planes, in order to ensure that the results were not 62

77 affected from the use of these symmetry planes. The difference in total lift for the fan and shroud between the models with and without symmetry planes was approximately 0.1%. This difference is negligible for the purposes of this thesis. 6.3 Solver Residuals and Monitors Convergence A residual target of 1E-6 was used for all simulations. The residual target was not always achieved due to a fluctuation in the solution which is described in All residuals converged within 1E-4 and most simulations converged within 1E-5. A typical solution required approximately iterations to converge. Multiple properties were monitored during convergence to ensure that the results had stabilized within a bounded range. The monitored properties for all simulations are as follows: Body lift Environment boundary force in vertical direction Fan thrust Fan lift (fan thrust in vertical direction) Fan velocity Ground force Shroud lift Point pressures: Pressure at ground origin Pressure at ground under UAV s body (located 425 mm from origin along YZ-symmetry plane) 63

78 Pressure at ground under UAV s fan (located 425 mm from origin along XY-symmetry plane) Solver Fluctuations There is a residual fluctuation remaining in the solver that prevented complete convergence for the majority of the simulations. Figures 6.2 and 6.3 show the convergence of monitors for the body and shroud lift respectively at height = 0.75 D and θ = 8 degrees. These are the two properties and the combination of height and dihedral angle which showed the highest degree of domain dependence in 6.1. Figure 6.2: Monitor of Body Lift Convergence for Height = 0.75 D, θ = 8 degrees. The range of fluctuating properties is denoted using error bars in the figures in Chapter 7. Most of the simulations which experienced small fluctuations were found to have near 64

79 Figure 6.3: Monitor of Shroud Lift Convergence for Height = 0.75 D, θ = 8 degrees. grid independent fan lift and body lift, with solutions asymptotically converging towards a finite value and peak-to-peak fluctuations of less than 1%. The peak-to-peak fluctuations in body lift in Figure 6.2 are approximately 2% of the average body lift, while the shroud lift convergence in Figure 6.2 fluctuates by approximately 1%. The hypothesized cause of these fluctuations is a region of recirculation between the shroud and body. Figure 6.4 shows the recirculation region between the shroud and body at height = 0.75 D and θ = 8 deg using streamlines. This recirculation pattern is typical for all combinations of height and dihedral angle. These streamlines show that some airflow exits the bottom of the shroud and recirculates upwards between the body and the shroud before re-entering the fan. This creates a feedback loop between the strength of the recirculation and the thrust of the fan, 65

80 preventing complete convergence. The strength of recirculation may also be changing the pressure distribution along the shroud walls in its vicinity, which would change the lift of the shroud. Figure 6.4: Streamlines showing Recirculation between Shroud and Body at Height = 0.75 D, θ = 8 degrees. 6.4 Domain Force and Momentum Balance The total forces and change in momentum flux across the external boundaries were checked to ensure that the difference between the sum of the forces and the change in momentum are negligible. For a constant volume control volume with an incompressible fluid, the sum of the forces acting on the domain are equal to the change in momentum in a given direction i: ΣF i = cs ρu i (u n)da (6.3) 66

81 Force and momentum balances were calculated at the minimum and maximum combinations of height and dihedral angles were checked to ensure that global momentum imbalances remained below 2% of the combined lift of the fan and shroud. Table 6.2 shows the force and momentum balances for the combinations of minimum and maximum heights and dihedral angles. All momentum imbalances remained within 2% of the combined lift of the fan and shroud. Table 6.2: Force-Momentum Balance for Models at Minimum and Maximum Combinations of Height and Dihedral Angle. Model Height (Dia) Model Dihedral Angle (Deg) Force / Momentum Source(Y) Value(N) Value(N) Value(N) Value(N) Fan Shroud Body SymmetryXY SymmetryYZ Ground Environment Boundary Pressure Environment Boundary Momentum Force Imbalance Imbalance (% of Lift) 0.54% -1.14% 1.07% -1.81% 6.5 Grid Independence A grid independence check was completed for all combinations of height and dihedral angle. Three simulations for each combination of height and dihedral angle were run at increasing mesh densities. This was done by decreasing the characteristic mesh length by a ratio of 3 2, as shown in Equation

82 x coarse x medium = x medium x fine = (6.4) In Equation, 6.4, x coarse,x medium, and x fine represent the node spacings for the coarse, medium, and fine mesh respectively. Appendix A contains additional details on the math behind the grid independence check procedure. Full grid independence is achieved when the solution s properties converge exponentially towards a finite value at the same order of accuracy of the solver with increasing mesh density. The solver used in all simulations is the CFX Higher Order solver, which has an order of accuracy (P value) between 1 and 2 [38]. Negative and N/A values denote solutions which did not asymptotically converge. Tables 6.3, 6.4, and 6.5 show the order of accuracy of the fan lifts, shroud lifts, and body lifts, respectively. Most simulations show some degree of grid dependence, which may be accounted for by the solver fluctuations discussed in Most fan and shroud lift values are asymptotically converging with increasing grid density at an order of magnitude near the order of accuracy of the solution. Body lift values show a higher degree of grid dependence and thus have a higher expected error associated with their values. Table 6.3: Simulation Order of Accuracy for Fan Lifts. Dihedral Angle (Degrees) Height (Diameters) N/A

83 Table 6.4: Simulation Order of Accuracy for Shroud Lifts. Dihedral Angle (Degrees) Height (Diameters) N/A Table 6.5: Simulation Order of Accuracy for Body Lifts. Dihedral Angle (Degrees) N/A -7.6 N/A N/A Height (Diameters) N/A N/A N/A

84 Chapter 7 RESULTS AND DISCUSSION The flow field formed by a two-fan UAV hovering close to the ground was simulated using the methodology presented in Chapter 5. The simulations are investigated for ground effects on fan lift, shroud lift, and body forces which include fountain forces and suck-down forces. The results of these simulations are presented and discussed. The results are then compared to the estimation methods described in 4.7 and 4.8. These estimation methods are assessed and the underlying assumptions and their potential for implementation are discussed. 7.1 Normalization of Lift The results for a single fan and shroud assembly operating out of ground effects was used as a benchmark for aerodynamic forces on the UAV to assess the significance and influence of ground effects and dihedral angle. The benchmark consists of two isolated fan-and-shroud assemblies which produce a total lift of 99.9 N. Figure 7.1 shows a comparison between the combined fan lift, shroud lift, and total lift for the benchmark case and dual-fan assemblies spaced to the Navig8 model s dimensions, both with and without the body. The total lift for Figure 7.1 is defined as the sum of the fan and shroud lift. Figure 7.1 shows that the total change in lift caused by the fan spacing and presence of the body has a minor effect on fan and shroud lift. The fan lift decreases by 1% with the fans spaced at the Navig8 model s design spacing. The shroud lift decreases by 3.8% between the benchmark and the Navig8 model with the body. 70

85 Figure 7.1: Total Lift Comparison between Two Independent Fan-and-Shroud Assemblies (Benchmark) against Navig8 Spaced Fan and Shroud Assemblies with and without the presence of the UAV s Body 7.2 GE Body Forces as a Function of Height and Dihedral Angle The forces acting on the UAV s body were simulated using the methodology described in Chapters 4 and 5 and normalized with the benchmark lift in 7.1. Figure 7.2 shows the normalized body lift as a function of height and dihedral angle (θ). Three views are shown in Figure 7.2 to improve visibility. The tabulated body lifts from Figure 7.2 are included in Table

86 (a) Normalized Body Lift (View A). (b) Normalized Body Lift (View B). (c) Normalized Body Lift (View C). Figure 7.2: Normalized Body Lift as a Function of Height and Dihedral Angle. 72

87 Table 7.1: Normalized Body Lift (%) as a function of Height and Dihedral Angle. Dihedral Angle (Degrees) Height (Diameters) The gradient of the body forces with respect to height is shown in Figure 7.3. gradient of the body lift with respect to height is primarily a function of height. The The gradient increases rapidly at heights below approximately 2 fan diameters (2D) and becomes positive at heights below approximately 1.3 D. The gradient of body forces with respect to dihedral angle is shown in Figure

88 (a) Body Lift Gradient With Respect To Height (View A) (b) Body Lift Gradient With Respect To Height as a function of Height Figure 7.3: Body Lift Gradient With Respect To Height as a function of Height and Dihedral Angle. 74

89 Figure 7.4: Body Lift Gradient with respect to Dihedral Angle as a function of Height and Dihedral Angle. 75

90 The pressure along the bottom of the body at the plane of symmetry bisecting the fans was plotted to gain additional insight into the pressure distribution. The location used for plotting pressures is indicated by the red line in Figure 7.5. Figure 7.5: Location Used to Plot Pressure on Bottom of UAV Body at Plane of Symmetry Figures 7.6, 7.7, 7.8, and 7.9 show the pressure plotted along the bottom of the UAV s body as a function of the distance from the centreline. Figure 7.6 compares the pressure plots at multiple heights for vertically oriented fans. Figure 7.7 compares the pressure plots at multiple heights for fans with a dihedral angle of 8 degrees. The pressure profiles in Figure 7.6 and 7.7 exhibit similar characteristics for all heights except for the elevations at 3.0 D 76

91 and 2.3 D. These correspond with the heights that showed the most variation in lift as a function of dihedral angle in Figure 7.2c. Figure 7.8 compares the pressure plots at multiple dihedral angles at a constant height of 3.0 D in order to determine how the pressure profile differs as a function of dihedral angle at an elevation which has a sensitivity to dihedral angle. Figure 7.9 compares the pressure plots at multiple dihedral angles at a constant height of 0.75 D, which is the region where suckdown forces are the most prevalent. 77

92 Figure 7.6: Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Heights for θ = 0 degrees. 78

93 Figure 7.7: Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Heights for θ = 8 degrees. 79

94 Figure 7.8: Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Dihedral Angles for Height = 3.0 D. 80

95 Figure 7.9: Pressure Distribution along Bottom of UAV s Body at Symmetry Plane at Multiple Dihedral Angles for Height = 0.75 D. 81

96 7.3 Discussion of Body Forces Figure 7.2 shows the normalized forces acting on the body as a function of height and dihedral angle. The body forces are primarily a function of height with a secondary dependence on dihedral angle. Figure 7.2b shows that the body forces have a low dependence on the dihedral angle θ at heights below 1.5 D and above 3.8 D. The body lift shows some dependency on θ at heights between 1.5 D and 3.8 D. The region between 1.5 D and 3.8 D shows the strongest dependence on dihedral angle, which is the region where the UAV is transitioning into ground effects. Figure 7.2c displays the model in Figure 7.2a when viewed to show the body lift as a function of θ, and primarily shows the dependency of body lift on θ for heights between 1.5 D and 3.8 D. In Figure 7.2c the line with a body lift of 10% at a dihedral angle of 8 degrees is at a height of 3.1 D. Thus, the dependence of body lift on θ is most prevalent at heights between 1.5 D and 3.8 D, where the body forces begin to increase noticeably with decreasing altitude. Increasing θ increases the height range in which body forces are non-negligible. The body forces peak around 25% of the benchmark lift at heights between 1.1 D and 2 D, regardless of dihedral angle. The body lift gradient with respect to height increases rapidly as the height decreases below 2 D. This relationship is best shown in Figures 7.2b and 7.3b. This height region poses particular control problems for the UAV, because the the total lift changes rapidly as the height changes. The UAV s ability to maintain a constant altitude becomes unstable at heights below approximately 1.5 D because the gradient of lift with respect to height is positive. A small perturbation in height for the UAV will cause the UAV to accelerate in the direction of the perturbation until a correction to the UAV s thrust is applied, the UAV impacts the ground, or the UAV travels above a height of 1.5 D. The addition of Lift Improvement Devices (LIDs) to the underside of the Navig8 s body would reduce or eliminate the suck-down forces [1]. Alternatively, a properly designed control system with methods to 82

97 increase the system s stability may allow the UAV to operate in a controllable manner at elevations below 1.5 D. Figures 7.6 and 7.7 show the pressure distribution along the bottom of the UAV s body in the XY-symmetry plane for dihedral angles of 0 and 8 degrees, respectively. These figures show that the magnitude of pressure along the bottom of the UAV s body remains low for heights of 3.8 D and greater. The body lift differs notably between the models with θ = 0 and 8 degrees at a height of 3.0 D, where the pressure is negligible for the model with a dihedral angle of 0 degrees and non-negligible for the model with a dihedral angle of 8 degrees. The maximum body pressure becomes more significant at a height of 1.5 D. The pressure remains positive across the width of the body except for the outermost edge. The maximum body forces increase substantially again at a height of 1.1 D when compared to those at a height of 1.5 D. Suck-down forces are prevalent at a height of 1.1 D, with approximately half of the UAV s body width having pressures below ambient for both dihedral angles. The total body lift at heights of 1.5 D and 1.1 D are approximately equal, despite the notably different pressure profiles. The total body lifts are tabulated in Table 7.1. The maximum body lift could be reduced by increasing the radius of curvature of the edges along the sides of the UAV s body [1]. However, significant rounding of the body s edges could increase the amount of recirculation between the body and the fans, and the presence of the body is currently obstructing the upwards fountain flow. The pressure profile at a height of 0.75 D has the highest maximum and minimum body pressures. The width of the fountain, which is the width of the positive pressure region, decreases with decreasing height for θ = 0 and 8 degrees. Figure 7.8 compares the body pressure distribution along the bottom of the UAV s body in the XY-symmetry plane at an altitude of 3.0 D. Multiple profiles are shown for the varying dihedral angles. 3.0 D is the height above the ground at which the body lift begins to differ as a function of the dihedral angle θ. The maximum body pressure and total body lift increase 83

98 with increasing θ. This force is due to a fountain forming beneath the UAV and impacting the bottom of the body. Figure 7.9 compares the body pressure distribution along the bottom of the UAV s body in the XY-symmetry plane at an altitude of 0.75 D. Multiple profiles are shown for the varying dihedral angles. All models have approximately the same fountain width, which is approximately half of the body width. The maximum pressure increases slightly with decreasing dihedral angle θ. The models with highest dihedral angles (θ = 6 8 degrees) show a rapid decrease in pressure near outer the edge of the body. All models have a local minimum pressure at approximately 0.11 m from the body s centreline. This low pressure zone may be formed by the presence of a vortex centre beneath the body. The effects of this vortex on the pressure distribution beneath the body are discussed in Suck-down Forces at Low Altitudes The mechanism behind the suck-down forces is a property of interest, especially for altitudes below 1.5 D when the body force gradient with respect to height becomes positive. Streamlines coloured by velocity for the model at a height of 0.75 D and θ = 8 degrees are shown in Figure 7.10a. Pressure is plotted at the bottom of the body for the model at height = 0.75 D and θ = 8 degrees in Figure

99 (a) Streamlines viewed from Front (b) Streamlines viewed from Top (c) Streamlines showing Recirculation between Shroud and Body Figure 7.10: Streamlines Coloured by Velocity at Height = 0.75 D, θ = 8 degrees. 85

100 Figure 7.11: Pressure Contours on Bottom of UAV Body at Height = 0.75 D and θ = 8 degrees 86

101 Figure 7.11 shows the regions of high and low pressure on the bottom of the UAV s body. The high pressure region is concentrated in the centre half of the body, while the low pressure regions are concentrated on the outer quarters. The regions of positive and negative pressure extend down the length of the body, but are concentrated in the area between the fans. Figure 7.10 shows that vortices form beneath the body between the fan downwash and fountain upwash. These vortices create a region of low pressure along the outer regions of the bottom of the UAV s body. The presence of these vortices agrees with those described in Kuhn s method for estimating body forces in 4.7. Figure 7.10b shows that the vortices extend along the length of the body, but are strongest in the region between the fans. The circulation of vortices for heights of 1.1 D and below were calculated to determine if there is a correlation between suck-down force and circulation strength as a function of height. The circulation was calculated by bounding the vortex and integrating the vorticity at the plane of symmetry. The following boundaries were used to bound the vortex: Height bounded between the ground and body bottom; Width bounded to catch all of vortex beneath body while isolating vortex at outer side of the fan; ω <= 0 to eliminate vortices rotating in the opposite direction to the main vortex; Swirling strength > 0.05rad/s. The swirling strength is defined as the imaginary portion of the complex eigenvalues of the velocity gradient tensor [39]. A minimum swirling strength was used to isolate the vortex regions from wall shear regions which have high vorticity but negligible swirling strength. The swirling strength boundary of 0.05 rad/s was determined to be in the asymptotic range of circulation as a function of swirling strength. Figure 7.12 displays the circulation as a function of inverse swirling strength at Height = 0.75 D, θ = 0 degrees, which shows that the 87

102 Figure 7.12: Circulation as a function of Inverse Swirling Strength at Height = 0.75 D, θ = 0 degrees. circulation of the vortex has become asymptotic as a function of inverse swirling strength. Negative values of circulation denote a counterclockwise rotation about the z-axis. The circulation of the main vortex beneath the body shown in Figure 7.10 was plotted in Figure 7.13 as a function of height and dihedral angle for altitudes of 1.5 D and below. Figure 7.13a shows the circulation viewed as a function of height. The circulation of the main vortex increases with height, while the magnitude of the maximum suck-down pressure decreases with height. This shows that there is not a linear correlation between the vortex s circulation and the suck-down force. Figure 7.13b displays the circulation viewed as a function of dihedral angle. The magnitude of the circulation increases with increasing dihedral angle. The pressure along the bottom of the UAV s body was estimated using the stagnation pressure at the centre of the body and the induced change in pressure using the local flow velocity beneath the body. This is expressed in Equation 7.1 where P (x) is the pressure at 88

103 (a) Circulation (View A) (b) Circulation (View B) Figure 7.13: Circulation of Vortex Beneath UAV Body as a Function of Height and Dihedral Angle. the bottom of the body at distance x, P (0) is the static pressure at the bottom of the body centreline, ρ is the density of the fluid, and u(x) is the velocity in the x-direction. u(x) is measured at a vertical offset of 5 mm from the bottom of the body. P (x) = P (0) 1 2 ρu(x)2 (7.1) Figures 7.14, 7.15, and 7.16 show comparisons between the pressure profile along the bottom of the UAV s body, at the location shown in Figure 7.5, versus the pressure estimated using Equation 7.1 at heights of 0.75 D, 1.1 D, and 1.5 D, respectively, for vertically oriented fans. Figure 7.17 compares the estimated (from Equation 7.1) and simulation-derived pressures at a height of 0.75 D and a dihedral angle of 8 degrees. The estimated pressure profile closely matches the measured pressure profile at all three altitudes, except at the outer edge of the UAV s body. The matching estimated and simulated pressure profiles suggest that the primary cause of the suck-down pressure is the induced change in pressure from the horizontal velocity beneath the body of the UAV. Figure 7.18 shows the vorticity in the z-direction for height = 0.75 D, θ = 8 degrees. There is a small region of high positive vorticity at the bottom outside edge of the UAV s 89

104 body. This corresponds to the region where the estimated pressure, based on Equation 7.1, differes from the measured pressure, as shown in Figure

105 Figure 7.14: Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 0.75 D, θ = 0 degrees. 91

106 Figure 7.15: Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 1.1 D, θ = 0 degrees. 92

107 Figure 7.16: Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 1.5 D, θ = 0 degrees. 93

108 Figure 7.17: Simulation-Derived Pressure at Bottom of body vs Estimated Pressure (from Equation 7.1) as a Function of Distance from the UAV s Centreline for Height = 0.75 D, θ = 8 degrees. 94

109 Figure 7.18: Vorticity in z-direction for Height = 0.75D, θ = 8 deg 95

110 7.4 Estimating Ground Effects and Body Forces Two methods to estimate body forces while in GE were previously described in 4.7, and 4.8 based on the work of Kuhn and Kotansky, respectively. These were compared against the simulated results for the Navig8 aircraft with vertically oriented fans. The fountain, suck-down, and total force estimates were normalized by the benchmark lift. The heights used in the estimate calculations were measured from the bottom of the body and plotted against the heights above the ground, as measured from the bottom of the shroud. 7.5 Body Force Estimation Methods based on Kuhn s Method Kuhn s methods of estimating fountain, suck-down, and total body forces described in 4.7 were compared against the simulated body forces for vertically oriented fans Fountain Force Estimate Figure 7.19 shows the fountain forces estimated using the equations in 4.7 based on Kuhn s method compared to the simulated body forces. The inflection point in the estimated lift occurs at the height h f, which is the maximum estimated height of a stable fountain top as described in Table 4.3. The prediction point of the top of the stable fountain, which can be seen as a slope discontinuity in L f at a height of approximately 2.3 D trails the onset of significant body forces. The peak fountain forces estimated using Kuhn s method are significantly less than those from the simulations (15% estimated vs 25% for simulation data), and the body forces estimated using Kuhn s method begin to increase at lower altitudes than the simulated body forces. 96

111 Figure 7.19: Equation-derived Fountain Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height Suck-down Force Estimate The suck-down force estimate, based on Kuhn s method and the equations in 4.7.3, contains two height regions with separate equations [1]. However; the transition height between these regions is not defined in the available literature. It is assumed that the transition height occurs at h f, which corresponds with the maximum stable height of the fountain. The suckdown force estimates based on the equations in at low altitudes, high altitudes, and transitioning between the two at h f are shown in Figure Figure 7.20 demonstrantes that there is a discontinuity between the equations for L s,low and L s,high from 4.7.3, which are the low height and high height suck-down estimations. L s,low represents the equation for suck-down forces which are present when a vortex exists 97

112 Figure 7.20: Equation-derived Suck-down Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height. beneath the UAV s body, while L s,high estimates the suck-down without the presence of a stable vortex. No method to estimate the altitude at which a significant vortex forms is included in the original method. The two equations do not have a point of equality. Therefore, transitioning between equations causes a discontinuity in the estimated body forces. Neither L s,low nor L s,high provide accurate estimates of the suck-down forces throughout the entire range. L s,high is more accurate at predicting suck-down forces at heights over 1.5 D, where the suck-down forces are negligible. However, L s,high significantly underestimates the suck-down forces at heights below 1.5 D. In contrast, L s,low is better able to estimate the suck-down forces at heights below 1.5 D, but overestimates the suckdown forces at higher altitudes. 98

113 7.5.3 Total Body Forces Estimate The sum of the fountain and suck-down force estimations from the equations in 4.7 are compared against the simulation data in Figure The equations for L s,low and L s,high were both used to separately estimate the total body forces acting on the UAV and were compared against the UAV s simulated body forces. Figure 7.21: Equation-derived Body Forces based on Kuhn s Method compared to Simulated Body Lift as a Function of Height. Kuhn s method for estimating body forces underestimate body forces for heights below 4 D, regardless of whether L s,low or L s,high is used for estimating the suck-down forces. The gradient of body lift with respect to height remains negative for Kuhn s method except at the transition point between using L s,low and L s,high. The use of L s,low alone to estimate suck-down forces is not enough to create a positive lift gradient with respect to 99

114 height. 7.6 Body Force Estimation based on Kotansky s Method The methods used to estimate body forces described in 4.8 were calculated and compared the simulation data. The estimated body forces based on Kotansky s method normalized as described in 7.1 and compared against the simulated body forces Fountain Force Estimate The fountain forces were estimated using the equations and methods described in The force coefficient F z was calculated by discretizing the body along its length and integrating the result. The equation-derived fountain forces from Kotansky s method are compared to the simulated body forces in Figure The fountain forces calculated from the equations in underestimate the body forces from the simulations. The onset of substantial body forces occurs at a lower height for the equation-derived body forces than for the simulated data. The body forces calculated using Kotansky s method further underestimate the fountain forces for altitudes below 4 D when compared to the results calculated using Kuhn s method Suck-down Force Estimate The suck-down forces based on the equations described in are shown in Figure The estimated suck-down forces based on Kotansky s method substantially underestimate the simulated suck-down forces at low altitudes, particularly at altitudes below 1.5 D. At altitudes below 1.5 D, the simulated suck-down forces increase faster than the fountain forces, resulting in a decrease in body lift of approximately 12%. However, the suck-down forces calculed using Kotansky s method peak at about 1.5% of the benchmark lift. The basis of Kotansky s suck-down force estimate, which is the need to replace mass entrained into the 100

115 Figure 7.22: Equation-derived Fountain Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height. fountain flow, is insufficient to explain the suck-down forces at low altitudes. Kotansky s method does not consider the formation of vortices beneath the body Body Forces Estimate The sum of the estimated fountain and suck-down forces based on Kotansky s method are compared to the simulated body forces in Figure Figure 7.24 shows that the estimated body forces derived from Kotansky s method underestimate underestimate body forces throughout the experimental domain, and fail to capture the change in direction of the body force gradient with respect to height that occurs at approximately 1.3 D. Kotansky s method is less accurate than Kuhn s method at predicting 101

116 Figure 7.23: Equation-derived Suck-down Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height. body forces, although neither method is able to satisfactorily estimate body forces below 4 D. The inaccuracy of Kotansky s method was partially expected as the estimation equations assume that the diameters of the fans are substantially smaller than both the fan spacing and the height from the ground [5]. Previous research into the validity of Kotansky s method [14] found that Kotansky s method has limited accuracy at heights below 4 D and fan spacings of less than 7 D. 102

117 Figure 7.24: Equation-derived Body Forces based on Kotansky s Method compared to Simulated Body Lift as a Function of Height. 7.7 Fan Forces The lift and horizontal components of the fan force were plotted in Figures 7.26 and 7.27, respectively, as a function of height and dihedral angle to determine if a source model is capable of accurately estimating fan lift, and if the small angle approximation is able to accurately estimate the horizontal forces Fan Lift The change in lift created by a constant powered fan while operating in GE was estimated using Equation 2.4 in and normalized. At the minimum height, the estimated percent 103

118 increase in fan lift is less than 1% of the benchmark lift. Figure 7.25: Change in Normalized Fan Lift in GE for Vertically-Oriented Fans as a function of Height. Figure 7.26 shows the fan lift as a function of height and dihedral angle throughout the experimental domain. Multiple viewpoints are used for clarity. The tabulated values of normalized fan lifts shown in Figure 7.26 are included in Table Discussion of Fan Lift Figure 7.25 shows that the method for estimating fan GE using Equation 2.4 does not match the change in lift for the simulations with vertically oriented fans. The estimated change in fan lift from the source model is outside of the margin of error for L f for heights below

119 Table 7.2: Normalized Fan Lift as a function of Height and Dihedral Angle. Dihedral Angle (Degrees) Height (Diameters) D. The differences between the simulated fan lift and the estimated fan lift using Equation 2.4 may be due to the recirculation between the shroud and the body which is discussed in The total change in fan lift due to GE is small in magnitude at less than 1% of the total lift for the simulated range of heights and dihedral angles. Figure 7.26 shows that the total lift of the fans remains between 59% and 62% of the benchmark lift throughout the experimental domain. The fan lift is most consistent at low dihedral angles and high heights. Fan lift generally increases with increasing dihedral angle and decreasing altitude. The increase in lift with decreasing altitude is in line with the expected trend for a constant power source operating in GE; however, this result was not consistent for every dihedral angle. The increase in lift with increasing dihedral angle at lower altitudes suggests that there is some interference between the fan model and the rest of the UAV. 105

120 7.7.3 Fan Horizontal Forces Figure 7.27 shows the horizontal componenent of the fan forces as a function of height and dihedral angle. An estimate of the horizontal fan force is shown in Figure 7.27b using the small angle approximation. Negative horizontal forces denote a force towards the centreline of the UAV. The fan horizontal forces vary linearly with dihedral angle. Figure 7.27b shows that the horizontal fan forces estimated by the small angle approximation agree well with the simulation data. 7.8 Shroud Forces Figures 7.28 and 7.31 show the shroud lift and horizontal force as a function of height and dihedral angle, respectively Shroud Lift Figure 7.28 shows the shroud lift as a function of height and dihedral angle. The tabulated values of normalized shroud lifts from Figure 7.28 are included in Table 7.3. The shroud lift displays greater variability the fan lift both as a function of height and dihedral angle. The hypothesized cause of the variability in shroud pressure is the region of recirculation shown in Figure 7.10c. This region of recirculation causes the pressure distribution on the shroud wall to fluctuate with the strength of the recirculation. Figure 7.29 shows the region of the shroud where the wall pressure is most affected by the recirculation zone. The pressure distribution around the circumference of the shroud is relatively uniform except for the region near the body. Figure 7.30 shows the shear stress on the shroud walls in the region of recirculation. The maximum shear stress is limited to 0.5 Pa to identify regions of very low shear stress. Flow separation from the wall can be identified by areas where the shear stress approaches

121 Table 7.3: Normalized Shroud Lift as a function of Height and Dihedral Angle. Dihedral Angle (Degrees Height (Diameters) Figure 7.30 shows that the area of flow separation on the shroud is different in the region of flow recirculation shown in Figure 7.10c when compared to the rest of the shroud. There is also a region of low shear stress on the upper lip of the shroud nearest to the body. This implies that the flow may be separating from the shroud in this region. An acoustical analysis could be used to determine if the flow is separating from the fan prior to entering the fan blades, as discussed in Shroud Horizontal Forces The shroud horizontal forces as a function of height and dihedral angle are shown in Figure An estimate for the horizontal shroud forced based on the rotation of the shroud using the small angle approximation is included in Figure 7.31b. This estimate is based upon the rotation of shroud forces using the simulation at height = 7 D, θ = 0 degrees as a reference. The shroud horizontal forces shown in Figure 7.31 are weakly dependent on dihedral angle, and do not display a clear relationship with height. The shroud horizontal forces do not vary linearly with the dihedral angle, as opposed to the horizontal fan forces. There is a 107

122 slight increase in the magnitude of the simulated horizontal shroud forces as dihedral angles increase; however, this trend is not in full agreement with the expected change in horizontal shroud forces obtained by rotating the shroud using the small angle approximation. 108

123 (a) Normalized Fan Lift (View A) (b) Normalized Fan Lift (View B) (c) Normalized Fan Lift (View C) Figure 7.26: Normalized Fan Lift as a function of Height and Dihedral Angle 109

124 (a) Normalized Fan Horizontal Force (View A) (b) Normalized Fan Horizontal Force with Estimate (View B) Figure 7.27: Normalized Fan Horizontal Force as a Function of Height and Dihedral Angle. 110

125 (a) Normalized Shroud Lift (View A) (b) Normalized Shroud Lift (View B) (c) Normalized Shroud Lift (View C) Figure 7.28: Normalized Shroud Lift as a Function of Height and Dihedral Angle. 111

126 Figure 7.29: Shroud Pressure Contour at Height = 0.75 D, θ = 8 degrees 112

127 Figure 7.30: Shroud Shear Stress Contour showing Areas of Flow Separation at Height = 0.75 D, θ = 8 degrees 113

128 (a) Normalized Shroud Horizontal Force (View A). (b) Normalized Shroud Horizontal Force with Estimate (View B). Figure 7.31: Normalized Shroud Horizontal Force as a Function of Height and Dihedral Angle. 114