CFD Analysis on the Main-Rotor Blade of a Scale Helicopter Model using Overset Meshing CHRISTIAN RODRIGUEZ

Transcription

1 CFD Analysis on the Main-Rotor Blade of a Scale Helicopter Model using Overset Meshing CHRISTIAN RODRIGUEZ Masters Degree Project Stockholm, Sweden August 2012

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3 Abstract C.Rodriguez Helicopter Aerodynamics Abstract In this paper, an analysis in computational fluid dynamics (CFD) is presented on a helicopter scale model with focus on the main-rotor blades. The helicopter model is encapsulated in a background region and the flow field is solved using Star CCM+. A surface and volume mesh continuum was generated that contained approximately seven million polyhedral cells, where the Finite Volume Method (FVM) was chosen as a discretization technique. Each blade was assigned to an overset region making it possible to rotate and add a cyclic pitch motion. Boundary information was exchanged between the overset and background mesh using a weighted interpolation method between cells. An implicit unsteady flow solver, with an ideal gas and a SST (Mentar) K-Omega turbulence model were used. Hover and forward cases were examined. Forward flight cases were done by changing the rotor shaft angle of attack α s and the collective pitch angle θ 0 at the helicopter freestream Mach number of M = 0.128, without the inclusion of a cyclic pitch motion. An additional flight case with cyclic pitch motion was examined at α s = 0 and θ = 0. Each simulation took roughly 48 hours with a total of 96 parallel cores to compute. Experimental data were taken from an existing NASA report for comparison of the results. Hover flight coincided well with the wind tunnel data. The forward flight cases (with no cyclic motion) produced lift matching the experimental data, but had difficulties in producing a forward thrust. Moments in roll and pitch started to emerge. By adding a cyclic pitch successfully removed the pitch and roll moments. In conclusion this shows that applying overset meshes as a way to analyze the main-rotor blades using CFD does work. Adding a cyclic pitch motion at θ 0 = 5 and α s = 0 successfully removed the roll and pitching moment from the results. 1

4 Nomenclature C.Rodriguez Helicopter Aerodynamics Nomenclature Symbols α s : Rotor shaft angle of attack - deg β 0 : Blade coning angle - deg β c : Longitudinal flapping angle - deg β s : Lateral flapping angle - deg θ 0 : Collective pitch angle - deg θ 1 : Built in twist angle distribution, positive nose up - deg θ c : Lateral cyclic pitch - deg θ s : Longitudinal cyclic pitch - deg µ : Rotor advance ratio, V ΩR µ : Dynamic viscosity - Pa s ρ : Density - kg/m 3 Ψ or ψ : Blade/rotor azimuth location - deg Ω : Rotor angular velocity - rad/s C D : Rotor drag coefficient for the main-rotor C L : Rotor lift coefficient for the main-rotor C l : Roll moment coefficient for the main-rotor C m : Pitch moment coefficient for the main-rotor C Q : Torque moment coefficient for the main-rotor A : Reference area - m 2 a : Semi-major axis of ellipse - m b : Semi-minor axis of ellipse - m c p : Specific heat capacity at constant pressure - J/(kg K) d : Diameter of the volumetric control - m h : Height of the volumetric control - m γ : Ratio of specific heats k : Thermal conductivity - W/(m K) l : Length of overset boundary - m M : Freestream Mach number M : Blade tip Mach number M R12 : Molar mass of Freon (R12) - kg/kmol p : Pressure - Pa p av : Average surface pressure over all blades. - Pa P r : Prandtl number 2

5 Nomenclature C.Rodriguez Helicopter Aerodynamics R : Rotor radius - m r : Spanwise distance along the blade radius measured from the rotational center - m r : Radius of the overset boundary (Stripped version) - m T : Temperature - K V tip : Blade tip velocity - m/s V : Freestream velocity - m/s Vectors τ : Stress tensor - Pa. a : Non-dimensional unit vector defining the component of the moment vector f pressure : Pressure force vector - N f shear : Shear force vector - N I : Identity Matrix n D : User specified direction vectors r : The distance/position of the cell relative to some point - m u : Velocity vector - m/s. Subscript/Superscript c : Cosine cv : Complete version f : Faces ref : Reference s : Sine sv : Stripped version vc : Volumetric control Abbreviations ARES : Aeroelastic Rotor Experimental System CAD : Computer Aided Design CFD : Computational Fluid Dynamics FDM : Finite Difference Method FEM : Finite Element Method FVM : Finite Volume Method HP : Hub Plane NASA : National Aeronautics and Space Administration NACA : National Advisory Committee for Aeronautics NFP : No Feathering Plane RPM : Revolutions per minute 3

6 Nomenclature C.Rodriguez Helicopter Aerodynamics RAM : Random-access memory SCCM+ : Star CCM+ SMA : Simple Moving Average TPP : Tip Path Plane UAV : Unmanned Aerial Vehicle Glossary Acceptor cell: Interpolating cells that exchange information with background and overset cells. Boundary: Surfaces that surround and define a region. Base size: A characteristic dimension of the size of your mesh prior to your model used measured in a length unit. Catia V5: Software engineering tool for use of computer aided design products. Cells: Subdomains of the discretized domain using the Finite Volume Method discretization. Chimera grids: Synonym to Overset grids. Faces: Interface or surface that make up cells boundaries. Generative Shape Design: wireframe and surface features. Workbench in Catia V5 that allows the user to model shapes using Gyroscopic precession: Phenomena that occur in rotating bodies in which an applied force is manifested 90 in the direction of rotation from where the force was originated. Hexahedral cell: Cell which is composed of six squared faces. Interface: Connect regions with each other, makes it possible for quantities to pass between regions. Nodes: Parallel server computers that are part of Saabs Aeronautics Cluster. Overset Mesh: Overset Mesh allows the user to generate an individual mesh around each moving object which then can be moved at will over a background mesh. (CD-adapco, 2012 [1]) Prism layers: Orthogonal prismatic cells that are located next to wall boundaries. Residual plot: To validate and compare the relative merits of different algorithms for a time marching solution to the steady state, the magnitude of the residuals and their rate of decay are often used as a figure of merit. Quasi-Steady State: A time-dependent condition in which acceleration effects can be neglected, and hence, treated as a steady state problem. This can include time periodic solutions. Regions: Volume domains in space that are surrounded by boundaries. Star CCM+: Computer software in which CFD simulations are executed. Steady State: A system in a steady state condition implies all properties (eg: ρ, p, V and T ) are unchanging over time. Swash plate: Helicopter rotor device that transforms inputs via the helicopter flight controls into motion of the main rotor blades. 4

7 Nomenclature C.Rodriguez Helicopter Aerodynamics Polyhedral cell: Cell which is composed of 12 pentagonal faces. Tetrahedral cell: Cell which is composed of 4 triangular faces. Volumetric Control: A surface or volume mesh based on an arbitrary volume where the user is able to decrease/increase the mesh density. 5

8 Introduction C.Rodriguez Helicopter Aerodynamics Contents 1 Introduction Guidelines Theory Governing equation Momentum theory Helicopter flight controls Meshing methodology Overset mesh introduction Project brief Background Purpose and goal Method I - CAD modelling 13 5 Method II - Meshing CAD model to computational domain Generating surface and overset mesh Volume mesh Supercomputer Method III - Simulations Physics model description Aerodynamic coefficients and moving average Stripped version Complete helicopter configuration Hover flight Forward flight without cyclic pitch Forward Flight with cyclic pitch Main results Flight simulations in Hover Mode Flight simulations in forward flight Discussion General discussion CAD models Meshing Simulations Conclusion 28 References 30 A Appendix A 31 B Appendix B 37 B.1 Hover stripped version results B.2 Hover complete results B.3 Forward flight no cyclic pitch results B.4 Forward flight cyclic pitch results C Appendix C 47 D Appendix D 51 6

9 Introduction C.Rodriguez Helicopter Aerodynamics 1 Introduction The need to modernize combat efficiency in military defense technology is growing rapidly along with todays technical advances. Unmanned Aerial Vehicle (UAV) have a significant role in the future development of aerial reconnaissance. Their main priority is to minimize human risks in hazardous environment through reconnaissance or in support missions. The lighter UAV classes (approximate 5-10 kg) are relative portable and easy to assembly when needed. However, current small scaled UAVs are increasing both in size and weight which has led to new/alternative methods to get them airborne. Vertical start and landing capabilities are essential properties for UAVs. Concepts like the Quadcopter 1 or Saab Aeronautics own helicopter UAV, Skeldar (Naval Technology, 2011 [2]) are a few projects which have been under development under the recent years. Increasing interest from Saabs side has led to more advanced analysis in rotor aerodynamics. Current mathematical models used in Saab are trivial in the form of propeller disc models and blade element theory. Increasing demands from flight mechanic models has led to a desire to improve the methodology for complex, unsteady flow fields that exist in these applications. To keep Saabs UAV projects in constant development, flight mechanics and aerodynamics improvements are needed. Computational Fluid Dynamics (CFD) is a powerful tool which is used extensively in aerodynamic applications. It provides the numerical solutions to the governing Navier-Stokes Equations throughout the flow region. The method gives the possibility to simulate and analyze complex problems without loosing the integrity of the problem due to simplified flow models. Saab made it possible to write this thesis in the field of aerodynamics using CFD as the main tool. They want to extend the understanding in unsteady flow analysis using CFD for rotational systems, which could be implemented into future helicopter-uav projects. 1.1 Guidelines Section 2 gives a brief introduction to fundamentals of fluid dynamics, the understanding of helicopter flight controls and the basics of meshing. Section 3 explains how the idea came about in writing a thesis on helicopter aerodynamics, and the purpose and goals behind it. The report proceeds by presenting how the helicopter schematic underwent the transformation to a computer aided design (CAD), in section 4. This continues on with the computational part of report (section 5), giving description of the challenges that are identified showing how the model went from a CAD-model to a discretized volume mesh generated in Star CCM+. This is then followed by the analysis and simulations on the rotor blade monitoring force and moment coefficients predicted on the helicopter at hover and forward flight. The results are then gathered from the simulations and the paper concludes the significant results from the CAD design, meshing and simulations. Throughout the report unfamiliar words or phrases will appear in italic style, note that a brief explanation can be found in the Nomenclature (under Glossary). Figures and tables found in the Appendices are marked with a letter in their reference to easily distinguish them in the report, e.g Fig. B.5 and Tab. A

10 Theory C.Rodriguez Helicopter Aerodynamics 2 Theory 2.1 Governing equation The Navier-Stokes equation are the fundamental governing equations for compressible viscous and heat conducting flows. It is obtained by applying Newton s Law of Motion to a fluid particle and is called momentum equation (Eq. (2.2)), which is followed by the energy equation (Eq. (2.3)) and the mass conservation equation, also known as continuity equation (Eq. (2.1)). Usually, the term Navier-Stokes equation is used to refer to these three equations. These equations interprets the physics behind the fluid dynamics and are mathematical statements of three physical principles upon which all of fluid dynamics are based on: Mass is conserved Newtons second law Energy is conserved Below are the governing equations (Rizzi, 2011 [3]) which includes the conservation of mass, momentum and energy in non-conservative form: ρ + ρ (u ) + ρ u = 0 t (2.1) u t + (u ) u + 1 ρ p = µ [ 2 u 13 ] ρ (2.2) p + (u ) p + γp u = (γ 1) [(τ ) u + (k T )] (2.3) t where the shear stress tensor τ for Newtonian fluid is: [ ] τ = µ u + ( u) T 2 µ ( u) I (2.4) 3 Together with the ideal gas law this gives six scalar equation for six dependent variables, the density ρ, cartesian velocities u = (u, v, w) T, temperature T and the pressure p, plus the gas property parameters, ratio of specific heats γ, dynamic viscosity µ and the thermal conductivity k. 2.2 Momentum theory The fundamental assumption in the theory is that the rotor is modelled as an infinitesimally thin actuator disc, inducing a constant velocity along the axis of rotation. According to Leishman (2000) [4] momentum theory is applied in rotating systems such as propellers, turbines, fans and rotors. The flow through the rotor is considered one dimensional, quasi-steady, incompressible and inviscid. Due to the fact that viscous effects are neglected, no viscous drag or momentum diffusion are present. The actuator disc supports the thrust force which is generated by the rotating blades, and for power to insure a thrust generation, a torque is supplied through the rotor shaft. Compressibility correction can be done in the model, however this can only be done to a certain extent. The approach for this mathematical method is straight forward and gives sufficient results. This theory is trivial and can be solved analytically to examine the influence of the propeller performance without needing to solve the Navier-Stokes equations. However, when it comes to rotor aerodynamics the momentum theory is insufficient in terms of accuracy. The method is not valid for examining helicopter flight controls and the reason for it will be explained in the next section. 2.3 Helicopter flight controls An important feature of helicopter rotors is that articulation in the form of flapping and lead/lag hinges (see Fig. 2.1). These are incorporated in the root of each blade, which allow the blades to independently flap and lead/lag with respect to the hub plane (HP) under the influence of aerodynamic forces. In addition, a pitch bearing is integrated in the blade design to allow the blades to feather, giving them the 8

11 Theory C.Rodriguez Helicopter Aerodynamics ability to change their blade or pitch angle θ (Fig. D.7). To control the overall lift, the pitch angle for all blades is collectively altered by changing the blade pitch an equal amount, resulting in an increase or decrease in lift. To perform a maneuver such as tilting forward (also called pitch), or tilting it sideways (roll), the angle θ of the main rotor blade is altered cyclically during rotation, thereby producing different amounts of lift at different points over the helicopter disc. The flapping hinge creates an angle β (Fig. D.6) between the blade and HP, which allows each blade to freely flap up and down in a periodic manner with respect to azimuth angle ψ (Fig D.5) under the action of these varying aerodynamic loads. The swash plate makes it possible translate these inputs from the helicopter flight controls to motion of the main rotor blades. As the helicopter leaves the ground, there is nothing that keeps the engine from spinning the helicopter body. Without anything counteracting this movement, the body of the helicopter will spin in the opposite direction to the main rotor. By adding a tail rotor to the helicopter, it produces a counteracting force. By producing thrust in a sideways direction, this critical part counteracts the rotors desire to spin the body. To increase or decrease the thrust, the pitch angle can be altered collectively, just as the main-rotor. Figure 2.1: Schematic showing the three motion of the rotor blade, which includes flapping, lead/lag and feathering. (Leishamn, 2000 [4]) Consider now a flight case where the rotor operates in vacuum, in which no aerodynamic forces are present. In the absence of aerodynamic forces the rotor takes up an arbitrary orientation in inertial space. As a result, the main-rotor acts as a gyroscope. Including aerodynamic forces produces a flapping moment about the hinge, which causes the rotor to precess to a new orientation until the aerodynamic damping causes equilibrium to be obtained once again. This phenomena is called gyroscopic precession and plays a central role in the helicopter flight controls. Picture a helicopter seen from above, the nose is pointed forward (12 o-clock or ψ = 180, see Fig. D.5) and the tail is pointed backwards (6 o-clock or ψ = 0 ). The blades are rotating in a counterclockwise matter. To give a forward cyclic command, the natural assumption is that the rotor blade needs to have more positive pitch at 6 o-clock rather than at 12 o-clock, giving the rotor more lift at the back rather than the front, pitching the helicopter forward. However because of gyroscopic precession, the lift actually occur 90 later in the rotation (at 3 o-clock or ψ = 90 ), thereby rolling the helicopter to the left and not pitching it forward. Therefore, in order to give a forward cyclic forward command, more lift is applied on the blade at 9 o-clock and less on the blade at 3 o-clock. To summarize the above, to control the lateral motion of the rotor (rolling/tilting sideways), lift force is altered at 6 and 12 o-clock. To control the longitudinal motion of the rotor (pitching/tilting forward), lift force is altered at 3 and 6 o-clock. 9

12 Theory C.Rodriguez Helicopter Aerodynamics The flapping motion can be described as harmonically constant and periodic (sine and cosine) terms, as expressed in Eq. (2.5). β 0 is referred as the coning angle, a constant angle independent of ψ. β = β 0 + β c cos(ψ) + β s sin(ψ) (2.5) The blade pitch motion has similar characteristic motion as the flapping motion and is described as: θ(r, ψ) = θ 0 + θ 1 (r) + θ c cos(ψ) + θ s sin(ψ) (2.6) where θ c and θ s are angles that control the cyclic motion. θ 0 is the constant collective pitch angle and θ 1 is defined as the built in twist angle along the rotor blade. Using Leishman [4] definition, the cyclic flapping angles are defined as longitudinal flapping angle β c and lateral flapping angle β s. The subscript c denotes a motion with pure cosine cyclic motion opposed to s which denotes the pure sinus motion. As for the cyclic pitch angles, the therm θ c control the lateral orientation and θ s controls the longitudinal orientation. This can seem a bit confusing, but as mentioned earlier a rotor has exact 90 force and displacement phase lag. Therefore, to control the lateral orientation a cyclic pitch command of θ c is applied giving a maximum force/displacement occurring 90 later, giving a lateral cyclic motion. By similar argument, the application of θ s controls the longitudinal orientation giving a maximum force/displacement 90 later, resulting in a longitudinal cyclic motion. 2.4 Meshing methodology In this section the aim is to explain the basic idea in how to create a mesh (also known as a grid), rather than deriving the mathematical principle behind the methodology. The approach of CFD is quite straightforward, in order to analyze the flow, the continuous flow domains are split into smaller discrete subdomains (Anderson, 1995 [5]), as shown in Fig For a continuous domain, each flow variable is defined at every point, in such domain we can for instance define the pressure as, p = p(x) at any given point at 0 < x < 1. In the discrete domain on the other hand, each flow variable is defined only at certain grid points. Taking the same example as before, the pressure for a discrete domain is defined as, p i = p(x i ) where i = 1, 2, 3...N. As for the governing equation, these too are discretized and Figure 2.2: Difference between continuous and discrete flow domains. solved in each and every subdomain. There are three types of methods that can be used to solve the approximative version of the governing equations: finite elements (FEM), finite difference (FDM) and finite volume (FVM). To give a proper image of the fluid flow in the complete domain, care must be taken to ensure continuity of solution across the general interfaces between two subdomains. The subdomains are usually refereed as elements or cells, and the collection of all cells are known as a mesh or a grid. There are several different type of grids but the group in which they can be categorized in are, structured grids and unstructured grids. The term structure emphasizes to the way the grid information is allocated. In a structured grid, the typical character is that the mesh have a regular connectivity, meaning that it follows an uniform grid pattern. A cartesian structured grid can be comprised of square elements (2D) or hexahedral elements (3D), which are orthogonal in space (Fig. D.2). The benefits of this is that it allows a given cell neighbour to easily be identified and efficiently accessed, which gives very fast CFD codes. However, this limits the possibility to refine or add additional cells in a certain area, and it may be difficult to compute an uniform grid to complex shapes. 10

13 Theory C.Rodriguez Helicopter Aerodynamics An unstructured grid on the other hand, does not follow an uniform pattern. As oppose to the structured grid, the cell at a given location n has no relation to the cell next to it at location n+1. Consequently, the unstructured solver has to be more robust and needs more computational power to find the neighbouring cells and hence, use up more memory (Innovative CFD, 2007 [6]). However, the trade off is that it allows for a freedom in constructing the CFD grid, it can add resolution where it is needed, and decrease the resolution where it is not. Common cell types are hexahedrals, tetrahedrals, or prism layers for 3D cases (Fig. D.3) Overset mesh introduction Overlapping mesh is a type of multi-block grid that uses multiple grids that overlap each other. There are numerous types of overlapping grids but the one of interest here is so called Chimera grid or, as it is known in SCCM+, Overset mesh. This is one of SCCM+ (v7.02) new features and the main reason why this software was chosen. Previous versions have not included the possibility to create simulations of interaction between moving objects in a volume mesh continuum before. Close interactions and cases of objects with extreme ranges of motion has been almost impossible to render. Using the overset mesh capability gives the freedom for users to generate individual local meshes, which allows objects to be moved at will over a background mesh. (a) (b) Figure 2.3: From left to right: (a) The overset region, yellow color represent the active cells and the blue represent the acceptor cells. (b) The background region showing a cutout of the overset region which is represented in red color. (CD-adapco, 2012 [7]) A volume mesh is a set up by a large number of active cells, the big difference when using overset meshes arises from the use of acceptor cells. Seen in Fig. 2.3 is a scalar field representation of a 2D wing profile for both the background region and overset region. The inactive cells (red coloured with the value 1) removes or rather cuts out the background cells overlapping other regions, leaving a hole for the cells for the moving regions. To identify the cell types the cells have been assigned values; inactive cells have a value of 1, acceptor cells have a value of -2 and active cells have a value of 0. Boundary information is exchanged using acceptor cells that work as interpolating donors cells in the overlapping regions (CD-adapco, 2012 [7]). In SCCM+ there are two interpolation options, linear interpolation and weighted interpolation. The latter works in a way that the interpolation factors are inversely proportional to the distance from acceptor cell center, resulting in the largest contribution given by the closet cell. 11

14 Project Brief 3 C.Rodriguez Helicopter Aerodynamics Project brief 3.1 Background This master thesis was conducted by the author with supervision from Mattias Hackstro m at Saab. Before starting the project, a great amount of time was spent on formulating the problem description and researching literature for the subject. A crucial issue was to find wind tunnel experimental data, oriented in helicopter aerodynamics that could be used as guidance, and to compare the computed CFD results. We eventually found a NASA-report (Noonan et al [8]) about rotor blade concepts on slotted airfoils in the rotor blade tip region. The report was primarily chosen for two main reasons: (1) the fuselage and rotor blade geometry was available (Fig. 3.1), which made it possible to design the parts using Catia V5. (2) The experiments done in the NASA-report had similar test cases that we wanted to conduct in our analysis. Figure 3.1: Aeroelastic rotor experimental sytem (ARES) test bed in Langley Transonic Dynamics Tunnel. (Noonan et al, 2001 [8]) 3.2 Purpose and goal The main goal with this thesis was to find a method that can improve the understanding of flow analysis for rotating systems using CFD. Previous analysis done by Saab did not include the rotating blades in the volume mesh continuum but rather model it as an infinitesimally thin actuator disc. This method works to a certain extent but is a simplified model, which lacks accuracy in more advance helicopter models such as rotor configurations with cyclic pitch settings. To improve the computational tools for helicopter aerodynamics using CFD, a new method needed to be introduced. The approach that we decided on were to include the rotating blades in the volume mesh continuum using SCCM+ Overset mesh methodology. The steps included in the analysis are as followed below: 1. A stripped down version containing two rotor blades with the exclusion of the fuselage and additional stationary parts, in hover mode (rotor advance ratio µ = 0). 2. Complete helicopter configuration in hover mode ( µ = 0) with different collective pitch settings. 3. Complete helicopter configuration in forward flight (µ > 0) with no cyclic pitch motion. 4. Complete helicopter configuration in forward flight (µ > 0) with included cyclic pitch motion. 12

15 Method CAD Modelling C.Rodriguez Helicopter Aerodynamics 4 Method I - CAD modelling The helicopter was modeled after Langley s ARES-model (Aeroelastic Rotor Experiment System) using Catia V5 s Generative Shape Design. Langley s rotorcraft (Fig. 4.1) is primarily designed to perform analysis on stability, performance and dynamic loads evaluation of new rotor concepts. It has a streamlined fuselage shape that encloses the control systems together with the drive system, and the rotor is driven by a variable-frequency synchronous motor, with a power of 47 hp giving it an output of RPM. The model includes four blades with a built in twist angle θ 1 and has also a collective and cyclic pitch control, which can be altered using the inbuilt swash plate. In addition, the model did not include a vertical fin and a tail rotor (Noonan et al, 2001 [8]). Rotor forces and moments are measured using a six-component strain gauge balance. Rotor lift and drag are determined from the measured balance normal and axial forces. Moments such as yawing, roll and tip are measured by the balance moment component. The balance is stationary with respect to the rotor shaft and pitches together with the fuselage. It is located at the balance centroid which can be seen in Fig The ARES-model is kept in place using a sting that is attached to the wind tunnel floor, making it possible to perform experiments on different angle of attack α s. Figure 4.1: Schematic of the ARES-model test bed. All dimensions are in cm. (Noonan et al, 2001 [8]) The rotor blade (Fig. 4.2) consisted of two airfoil section geometries. At the inboard region (r/r 0.80) the section was the 10-percent-thick RC(4)-10. The 8-percent-thick airfoil section RC(6)-08 was selected for the tip region (r/r 0.85). Between 0.80 r/r 0.85, a smooth transition between these inboard and outboard airfoil shapes were done. In addition, the blade included a spanwise twist θ 1 distribution of 8 which can be found in Fig. A.4. Tab. A.1 and A.2 shows the design coordinates for RC(4)-10 and RC(6)

16 Method CAD Modelling C.Rodriguez Helicopter Aerodynamics Figure 4.2: Schematic on the main-rotor blade. All dimensions are in cm. (Noonan et al, 2001 [8]) The next step was to assemble the blades to the hub. The hub geometry was not included in the NASA report. Since it had little contribution to the aerodynamic forces the search for the original design was left out. Instead an arbitrary hub geometry with similar dimensions to the original design was computed, as shown in Fig. A.6. The need of a detailed schematics was of great importance, for a successful design of the fuselage. The NASA-report only provided images with a sketching (Fig. 4.1) of the side and front view. A third image of the top view was needed to design the fuselage. By contacting Langley Research Center 2, they managed to provide us with a complementary image of the top view, which can be found in the Appendices in Fig. D.1. This 3-view schematic enabled us to to compute a 3D-model by setting up wireframes to form and shape the fuselage. To achieve the shape along the body, cross sectional profiles were inserted at given points along the body. Connecting them together with wireframes eventually gave the skeleton base. Spline functions made it possible to get the desired smooth surfaces needed for the fuselage. 2 Langley Research Center was not authorized to leave out detailed schematics of the ARES-model to personnel who were not US citizens. 14

17 Method Meshing C.Rodriguez Helicopter Aerodynamics 5 Method II - Meshing 5.1 CAD model to computational domain To successfully compute a surface and volume mesh for the ARES-model three fundamental requirements are to be taken in consideration: (1) A sealed surface of the model must be computed meaning that free edges are not allowed. (2) No internal geometry or components need to be modelled when doing the external flow analysis. (3) Overlapping/pierced surfaces or floating points (non-manifold vertices) are not allowed to be present in the model (Fig. 5.1). (a) (b) (c) Figure 5.1: Errors that occurred when importing the CADpart-file. From left to right: (a) Pierced surfaces (b) Free edges (c) Non-manifold vertices Before the model went through the remeshing, boundaries had to be specified for each part. When the CADpart-files were imported to SCCM+ for the first time, the software allotted names to the respective boundaries on its own. For the desired purpose we combined the defaulted boundaries to our own preference, different boundaries of the helicopter model were then defined. By specifying the parts to different boundaries allowed us to change custom mesh size on specified areas of the helicopter. Boundaries with curvature needed finer mesh density to properly compute the given shape e.g. the leading edge of the rotor blade. Boundaries included are the fuselage, hub, roof, roof edge, the blades and the fins with additional edges. The boundaries can be seen in the Appendices in Fig. C.4 and Fig. C Generating surface and overset mesh Surface meshing was done in three steps: (1) Repairing the surface using SCCM+ Surface repair tool. (2) Creating a surface mesh and (3) creating the overset region for each blade. The first step for generating a mesh was to import a surface description from the CADpart-files (provided by Catia V5). Ideally, the imported surface should fulfill the requirements mentioned in previous section but this was not the case. Errors occasionally occur when a new CAD model is imported for the first time to SCCM+. The Surface repair tool gave the ability to identify, isolate and fix errors on the given boundary. The helicopter model had some minor issues regarding a few overlapping parts, but were easily fixed by the Surface Repair Tool. The surface of the helicopter model was meshed using unstructured triangular elements, where the size of each triangle was defined by the base size. It is a characteristic dimension and was scaled relative to the size of the helicopter model. It is specified after an arbitrary length unit given by the user, in this case the base size was set to a value of m. 15

18 Method Meshing C.Rodriguez Helicopter Aerodynamics Parts Target size % Minimum size % Fin Fin Edge Freestream box Fuselage Hub Overset Region Top part (fuselage) Top part edge (fuselage) Rotor Rotor Edge Table 5.1: Triangular element sizes where the target and minimum length size are presented. These are relative to the base size which has an arbitrary length of m. There were two additional parameters that played an important role in controlling the mesh size, namely, the target size and the minimum size. The target size is the desired edge length on the surface while the minimum size acted as the lower bound limit. Seen in Tab. 5.1 surfaces with curvature such as the rotor blades or fin edges (Fig. 5.2) have smaller mesh sizes unlike the larger and flatter surfaces like the fuselage or freestream box. The next step was to divide the computed boundaries into different regions. All stationary boundaries such as the fuselage, fins, and the freestream box were included in the background region. The boundaries with a moving reference such as the main-rotor received their own overset region, which was placed inside the background region. Since each blade needed to have the ability to include a cyclic pitch motion, an overset region was assigned to each blade, giving the model a total of four separate overset regions. The size of the overset region varied depending on the different flight cases done. This will be explained in a later section. 5.3 Volume mesh To divide the domain into a number of control volumes (cells), the Finite Volume Method (FVM) was the choice as discretization technique. A volume mesh was computed using polyhedral cells. Using this cell type was preferable to the typical tetrahedral cells. An advantage in using the polyhedral cells is that it uses five times fewer cells compared to the tetrahedral mesh, thus decreasing the computing time and process power to compute the meshes and simulations (Peric and Ferguson, 2005 [9]). In our case, the number of polyhedral cells span between 4 to 7 million cells depended on the different simulation cases. The volume mesh also included prism layers, orthogonal prism cells located next to the wall bound- Figure 5.2: The rotor blade showing surfaces with high curvature gives finer surface mesh. 16

19 Method Meshing C.Rodriguez Helicopter Aerodynamics aries such as the main-rotor and fuselage. There are five prism layers for the non-rotating boundaries (fuselage, fins and hub) and 10 layers for the rotating blades (Fig. 5.3), and these have a prism layer thickness of 100 % and respectively 200%, relative to the base size. The cell interpolation in the overlapping regions used a distance-weighted interpolation, which is the preferred choice when using an unstructured grid setup. Figure 5.3: The prism layers on one of the rotor blades, consisting of 10 layers with a prism layer thickness of m (200 % of the base size). To make the overset regions work properly a few requirements had to be fullfilled: (1) Between the wall boundaries of the overset and the background meshes, there should always be at least 4-5 cells in each mesh. (2) The overset mesh is not allowed to cross the boundaries of the background region unless, it lies completely within the solution domain. This also goes for multiple overset regions, these are not allowed to overlap with each other. (3) The cells of the overlapping region should have the same size on both the background and overset meshes, this was done using controlled volumes called volumetric control. However, this feature is more of a request rather than a requirement for accuracy reasons. 5.4 Supercomputer Each CFD simulation was computed using Saab Aeronautics supercomputer. It is divided into two Linux-based subclusters identified as Skylord and Darkstar. Skylord is built up by 40 HP ProLiant DL160 G5 computer servers, with each server containing two quad-core processors 3 and 16 GiB of RAM. Darkstar contain 70 supermicro-based computer servers, with two single-core processors 4 and 2 GiB of RAM. Each computer server is abbreviated as a node and the computation time can vary depending on the number of nodes chosen and the choice of subcluster used. Darkstar was part of a previous generation cluster, giving it a slower performance compared to Skylord. A total of 15 separate simulations were conducted with each simulations needing 10 inner iterations in each time step, giving a total of roughly 5000 iterations. The first five simulations were for experimental purposes and were done to examine and analyze the behaviour of the overset meshes. While a simulation can take several weeks to converge on a conventional PC desktop, the supercomputer did the task in just under 48 hours. The time needed to reach the desired stopping criteria greatly depended on the number of nodes that were available during each simulation, more on this in the discussion section. 3 Intel Xeon E5462 quad core 2.8 GHz, 6 MiB level 2 cache. 4 Intel Xeon single core processors 3.4 GHz, 2 MiB level 2 cache. 17

20 Method Simulations C.Rodriguez Helicopter Aerodynamics 6 Method III - Simulations 6.1 Physics model description The test section of the tunnel measured 4.88 m (16 ft) square with cropped corners and a cross-sectional area of m 2 (248 ft 2 ), see Fig According to the NASA-report (Noonan et al, 2001 [8]) all wall interference were significantly small, thereby excluding all wall disturbances in our analysis. In the computational domain, the helicopter was placed in a cubical box with the dimensions 20 x 20 x 20 m. The box region represented the freestream flow (Fig. 6.1) and allowed the helicopter model to be studied with the assurance of minimum wall interference. Due to the small aerodynamic disturbances the sting contributes to, it was not necessary to include it in the model. Instead of air as medium, Freon 12 (R12) was applied as test medium. The benefits of having this medium are for its high molecular weight and low speed of sound. As a result of this, the medium gives the matching of a model-scale Reynolds number and Mach number to full scale values. The nominal density conducted in the wind tunnel experiment was 3.06 kg/m 3 (0.006 slugs/ft 3 ) at a temperature and pressure of 293 K and Pa, respectively. In Tab. D.1 (located in the Appendices) the gas properties of Freon 12 is presented in more detail. These values were acquired using the software F-Chart (F-Chart Software, 2012 [10]). Figure 6.1: Freestream background region containing the helicopter model and its additional overset meshes. To conduct this type of analysis an appropriate physics model was needed for usage. The following physical models were chosen to simulate the flow field around helicopter-model: implicit unsteady flow, ideal gas properties of freon, and a turbulent flow using a SST (Menter) K-Omega turbulence model. To reduce the complexity of the main-rotor blades, gravitational properties were not included in the model, meaning that the rotor blades did not have a weight or experienced any inertia. The blades were modelled as stiff blades, thereby removing structural properties such as aeroelasticity from the analysis. 6.2 Aerodynamic coefficients and moving average In this section, the variables for simulation that were monitored will be presented. These consists of numerous force- and moment-coefficient for the blades. As seen in Eq. (6.1), the force coefficients are defined as follows 5 : ( ) f pressure f + ff shear n D C L = C D = f ρ ref A ref V 2 ref 5 The definition of the force and moment coefficient in helicopter aerodynamics is slightly different compared to aeroplane aerodynamics. In our case, a factor of one half is omitted from the denominator. (6.1) 18

21 Method Simulations C.Rodriguez Helicopter Aerodynamics Eq. (6.1) gives a dimensionless force in which the user specifies the direction using the unit vector n D. If the desired force coefficient is to compute the drag, the direction is specified as the same direction as the freestream velocity. For lift, the direction is specified normal to that direction. A ref is defined as the main-rotor disc area, and V ref denotes the tip velocity of the blades. C l = C m = C Q = f [ ( r f f pressure f ρ ref A ref V 2 ref R ref )] + ff shear a Similar equation goes for defining the moment coefficient as seen in Eq. (6.2). a is the vector defining the axis direction through an arbitrary point x 0 in which the moment is taken. It defines the same properties as n D (for the force coefficient) but instead defines the roll, pitch and torque moment coefficient. r f is the position of each face relative to the reference point x 0 of the moment vector. The pressure- and shear- force vector are defined as; f pressure f = (p f + p ref )a f and ff shear = τ a f. Where p f is the face pressure, a f is the face area vector, p ref is the reference pressure, which was set to p ref = 0. The disc radius R ref is included to acquire a dimensionless property. The aerodynamic forces and angles are defined in Fig. D.4 which is found in the Appendices. Simple moving average (SMA) is a tool to smoothen the plots computed in the analysis. Old data is dropped as new data comes available causes the average to move along the time axis (Eq. (6.3)). Prediction indicated that the results had some disturbances and needed to be smoothen out. This was done by regulating the number of n data points included in the SMA. Adding this made it easier to determine the results from the plots, damping the fluctuation that are formed. (6.2) SMA = x M + x M 1 + x M x M (n 1) n (6.3) 6.3 Stripped version The purpose of this test case was to examine the behaviour regarding the overset regions. The setup included a stripped down version of the complete helicopter configuration, containing two rotor blades and the main hub. The fuselage and the additional rotor blades were excluded to reduce the total number of cells in the volume mesh. By narrowing down the number of cells, we managed to reduce the time it took to generate the grid and the computed results, reducing the computation time from 48 hours to under 24 hours, which gave us the possibility to edit the model in a faster paste when errors occurred. Each blade was assigned to a cylindrical shaped overset region, with the dimensions r sv = 0.5 m and l sv = 1.6 m, as seen in Fig In addition, the shaft connecting the hub to the blades were removed, the purpose being that the regions were not allowed to cross any background boundaries (as mentioned earlier). A cylindrical shaped volumetric control was added, it is an arbitrary volume were the user have the ability to control the cell size for a specific surface/volume. This was added in the background mesh to match the cell size of the overset region in order to make a cutout for the overlapping regions possible. It had a dimension of r vc = 4 m and h vc = 1.4 m and the cell size was set to 3000 % of the base size which corresponded to a length of 0.03 m. In Fig. C.6 a scalar representation describing the model, with the volumetric control surrounding blades (and the overset regions) The total cell count landed in around 5 million cells. 19

22 Method Simulations C.Rodriguez Helicopter Aerodynamics Figure 6.2: Stripped version two blades removed and with no fuselage present. The blades are surrounded by large cylindrical shaped overset regions. 6.4 Complete helicopter configuration The next step was to introduce the rest of the additional boundaries. The fuselage and two additional rotor blades were added to the previous model, with some modifications. The overset regions had to be resized and reshaped to an elliptical shaped cross section in order to give room to the fuselage and the additional rotor blades (and their corresponding overset regions). Now that the fuselage were added to the model, it proved to be difficult to shape overset boundaries that did not intersect with the fuselage or hub. For practical reasons the hub and top part were removed from the fuselage (Fig. C.9 and C.10). The new elliptical shape, shown in Fig. 6.3, had the dimensions of semi-major axis a = 0.1 m and semi-minor axis b = 0.05 m at 0 < r/r < 0.1 and a = 0.2 m and b = 0.1 m at 0.1 < r/r < 1.0, with the total length of l cv = 1.4 m. The size of the overset region had to be large enough to encapsulate the rotor blade but small enough to prevent overlapping of the background and overset regions. As the previous setup a volumetric control was addressed to the background region to insure a successful cutout of the four overlapping regions. The volumetric control was added but with a thinner disc shape (d cv = 3.3 m and h cv = 0.35 m), and the cell size was reduced to 1500 % (0.015 m). The final cell count for the complete helicopter version increased from 5 to 7 million cells. Figure 6.3: The complete helicopter model containing the fuselage and the the two additional blades. The overset regions have been considerably reduced. 20

23 Method Simulations C.Rodriguez Helicopter Aerodynamics Hover flight Data were obtained in hover flight with three collective pitch settings, θ 0 = 5 θ 0 = 10 and θ 0 = 12. The blade rotated at 640 RPM which corresponded to a nominal blade tip Mach number of M T = The lift- C L, drag- C D and torque-coefficients C Q were calculated using Eq. (6.1) and (6.2), with the reference values, ρ ref = 3.06 kg/m 3 V ref = m/s, A ref = m 3 and R ref = m. These were taken from the the disc area, disc radius and tip velocity of the main rotor. The torque is rotating around the local z-axis located 102 cm from the fuselage nose. Appendix B shows the different aerodynamic forces and moments that were monitored Forward flight without cyclic pitch When the hover flight was completed the next step was to analyze the flight performance in forward flight. A freestream flow was introduced to the simulation and was chosen so that the advance ratio was set to µ = 0.2, which corresponded to a freestream Mach number of M = As opposed to an actual/real flight case, the helicopter would need to alter the collective pitch cyclically to produce a thrust vector forwards. But for this simulation no cyclic pitch was added. This did indeed affect the pitching and roll moment of the helicopter. For this purpose, two additional monitors, C l and C m were added to the simulations. Four cases were examined θ 0 = 5 and θ 0 = 10 at an rotor shaft angle of attack α s = 0, and θ 0 = 5 and θ 0 = 10 at α s = Forward Flight with cyclic pitch The purpose behind this simulation was to show the possibilities in adding cyclic pitch using the overset meshes. Looking at the previous flight case, the ARES-system experienced roll and pitching moments when no cyclic pitch was added. This was expected since the rotor blades were no longer experiencing uniform lift distribution in the retrieving and advancing side of the main-rotor. To remove these unwanted moments the cyclic pitch was added to the main-rotor. Noonan s NASA-report [8] did not mention what cyclic pitch configuration they used in their experimental setup. Without knowing the lateral (θ c ) and longitudinal (θ s ) cyclic pitch angles, an alternative method needed to be used. The approach was to examine how the main-rotor would react if a pure cyclic pitch was inserted to the model. This came down to three separate analysis were the first had a pure longitudinal cyclic motion (θ s = 1 and θ c = 0 ) and the second had a pure lateral cyclic motion (θ s = 0 and θ c = 1 ). The third simulation used a combination of the lateral and longitudinal angles, and by using the results from the simulations with pure motion, the cyclic pitch angles θ c and θ s were calculated. Using a simple linear equation system between the roll and pitching moment the equation was expressed as shown in Eq. (6.4) and Eq. (6.5): C l = C l,(θ=0) + C l,θs θ s + C l,θc θ c (6.4) C m = C m,(θ=0) + C m,θs θ s + C m,θc θ c (6.5) The additional variables C l,θs, C l,θc, C m,θs, and C m,θc showed how much increase/decrease the roll and pitching moment were affected when the pure cyclic motion were included. The aim was to find θ c and θ s where no roll or pitching moment occurred (C l = 0 and C m = 0). The following variables are expressed as: C l,θs C l,θc C m,θs C m,θc = C l,(θ s= 1) C l,(θ=0) 1 (6.6) = C l,(θ c= 1) C l,(θ=0) 1 (6.7) = C m,(θ s= 1) C m,(θ=0) 1 (6.8) = C m,(θ c= 1) C m,(θ=0) 1 (6.9) 21

24 Method Simulations C.Rodriguez Helicopter Aerodynamics C l,(θ=0) and C m,(θ=0) were values in which the cyclic pith motion was not included (θ s = 0 and θ c = 0). C l,(θs= 1), C l,(θc= 1), C m,(θs= 1) and C m,(θc= 1) are defined as the roll and pitching moment values when the lateral and longitudinal cyclic pitch motion was added. The value 1 denoted the change in θ s and θ c for respective pitching and roll moment. The flapping and lead/lag angles were not included to reduce the complexity of the cyclic pitch motion. The flapping angle was instead replaced by a constant blade coning angle that was set to β 0 = 2. With a limited time for computing the simulations, the decision was made on including the cyclic pitch on only one of the previous test cases. The flight case that was chosen had a collective pitch angle of θ 0 = 5 at α s = 0. 22

25 Main Results C.Rodriguez Helicopter Aerodynamics 7 Main results The results computed are presented in the following figures which can be found in the Appendix B: Hover Performance (Stripped version)... B.1-B.4 Hover Performance (Complete version)... B.5-B.8 Forward performance (No cyclic pitch)... B.9-B.14 Forward performance (With cyclic pitch)... B.15-B.19 The results below are represented here as the main results computed in Star CCM Flight simulations in Hover Mode Hover Flight Characteristics C L vs C Q Spline function Nasa Report Result Computational results Lift Coefficient C L [ ] θ 0 = 10 θ 0 = θ 0 = Torque Coefficent C [ ] Q Figure 7.1: Hover results showing C L vs C Q. 23

26 Main Results C.Rodriguez Helicopter Aerodynamics 7.2 Flight simulations in forward flight Forward Flight Main Results C L vs C D Lift Coefficient C L [ ] Exp data α s Exp data α s = 4 No Cyclic Results α s No Cyclic Results α s = 4 θ 0 = 10 With Cyclic Results α s θ 0 = 5 θ 0 = Drag Coefficient C [ ] D Figure 7.2: Forward flight results showing C L vs C D. Forward Flight Main Results C L vs C Q Lift Coefficient C L [ ] θ 0 = 5 θ 0 = 10 Exp data α s Exp data α s = 4 No Cyclic Results α s No Cyclic Results α s = 4 With Cyclic Results α s θ 0 = Torque coefficient C Q [ ] Figure 7.3: Forward results showing C L vs C Q. 24

27 Discussion C.Rodriguez Helicopter Aerodynamics 8 Discussion 8.1 General discussion Supercomputer: The time to compute the simulations depended highly on which sub-cluster that was used. Each Skylord-node had a total of 8 cores per node (2x4) unlike Darkstar which only had 2 cores (2x1). Even though each Darkstar-node had better performance (per processor), Skylord had the possibility in using four times more cores for parallel computing that gave a faster overall performance. With a time step of s, and with 10 inner iterations on each time step, each run took approximately 1-4 days to compute depending on the number of available nodes. With a total of 96 cores (12 nodes x 8 cores) in Skylord, the time to compute was not more than 48 hours. A rule of thumb states that each core should have at least volume cells for calculations, which corresponded to 70 cores for our case (our model had 7 million cells). We decided on having 96 cores since the model had four overset meshes that needed computational power to cut out the overlapping regions. Since other users needed to use the supercomputer, the possibility for acquiring available nodes led to simulations that went idle until slots opened up. It was hard to predict when the nodes were available, therefore the number of simulations were reduced from 25 (which was the intended number of simulations) to 15. Overset meshes: When examining how the overset meshes worked at first, difficulties emerged when the four blades shared one large overset region. Previous simulations that were done proved to cut out the overlapping regions faster, with one large region. This is since less time is spent in cutting out the overlapping region and time in exchanging information between the interpolating cells. Since the blades shared one large overset region the disadvantage with this method is that it constrains the blades into be altered separately. The benefits of having separate overset regions is that; (1) The regions are independent of each other, giving the possibility to move or rotate the blades without affecting the other regions.(2) Greater flexibility compared to standard meshing, overset meshes does not require any mesh modification after generating the initial mesh, thus offering the ability to have for instance a cyclic pitch motion. Gyroscopic Precession: The effects when adding a longitudinal/lateral cyclic pitch was not what we excepted when examining the results. As shown in Fig. B.18 and Fig. B.19, adding a θ c angle controlled the roll moment, and adding a θ s angle controlled the pitching moment. Comparing these results with the theory in section 2.3, the results did not show any indication of a 90 phase lag. Since each blade was considered having no weight, the blades did not experience any inertial effects, thereby the gyroscopic precession was not applied for our model. The aerodynamic forces that were computed are still valid, on the contrary, if wanting to apply the main-rotor to a flight mechanical model, then our model would need to include weight and inertia to properly model the gyroscopic phenomena. 8.2 CAD models Fuselage and hub: The computed CAD part had several design aspects that deviated compared to the actual ARES-model. This model did not state the geometry used for the horizontal stabilizer, so we decided on using an arbitrary wing profile, NACA-0012 (Abbott and von Doenhoff, 1959, p.113 and p.321 [12]). The purpose of having the body was to redirect the flow field and to change the pressure gradient under the the main-rotor. Note that the results showed in Appendix B did not include the aerodynamic forces contribution of the fuselage and horizontal the stabilizer. Noonan s NASA-report [8] did not provide enough detail schematics regarding the hub. When examining the NASA-report, it stated that tares were determined throughout the test ranges meaning that the hub did not contribute at all to the aerodynamic forces reported. Both deadweight and aerodynamic hub tares were removed from the wind tunnel data. As for the case in our model, removing the top part of the fuselage and hub had little effect on the aerodynamic forces, however it affected the redirection of the flow field at the rotor conjunction, which manage to emerge few vortices, as seen in Fig. C.3. 25

28 Discussion C.Rodriguez Helicopter Aerodynamics 8.3 Meshing Polyhedral cells: According to Peric and Ferguson (2005) [9] there are several benefits in polyhedral cells opposed to other conventional method such as tetrahedral and hexahedral cells. One downside with tetrahedral cells are that they are more restricted in cell stretching, which leads to much larger number of control volumes. Considering that tetrahedral cells only have four neighbours, computing gradients can be more problematic. Giving the fact that a major advantage of polyhedral cells are that they have many neighbouring faces (approximately around 10), which give gradients better approximation compared to tetrahedral cells. The polyhedral cells were the preferred choice to use on the rotating blades. For a cartesian hexahedral cells, they have three optimal flow directions (six faces) which tend to constrain the accuracy when dealing with rotating flow fields. For a polyhedral with 12 faces have six directions, which together with a larger number of neighbours leads to a more accurate solution with a lower cell count. Volume and Surface meshing: The final cell count of seven million cells suited the size of the master thesis. Increasing the number of cells would likely increase the time it spent on computing the results, but presumably also improve the accuracy. As an alternative solution, higher cell resolution were addressed to the moving boundaries e.g the blades and regions close to the blade. This kept the cell count down and decreased the time to compute, but retained the accuracy in the solution. A grid independence study was outside the scope of this thesis, the focus was not to optimize the grid but rather make it work properly. The volume mesh included prism layers to accurately capture the flow field at the surface of the mainrotor and fuselage. Numerical diffusion is greatly minimized when the flow is aligned with the mesh. With the use of prism layers, the accuracy greatly increases as a result to the intended consequence of aligning the flow with the mesh (CD-adapco, 2012 [7]). Seen in Fig. C.9 and Fig. C.10, the hub and the top part of the fuselage were removed. The decision for this was based on the blades overset meshes. As mentioned in section 5.3, the wall boundaries at the overset and background meshes needed at least 4-5 cells in each mesh. Since the background boundaries (hub and top fuselage) and the overset boundaries were at close proximity, the resolution of the boundaries were forced to increase to fulfil the requirement. To keep the number of cells down, the hub and top part of the fuselage were removed for practical reasons. 8.4 Simulations The convergence history for the simulations can be found in Appendix B which shows the monitored aerodynamic properties on the main-rotor. As mentioned earlier, the fuselage, hub and the horizontal stabilizer were not included in the analysis of the forces and moments, only the rotor blades were included in the results. The number of datapoints included for the SMA were between points depending on the flight case. Some plots had larger fluctuations and therefore needed higher number of points. Some results, such as in Fig. B.17 had a few spikes in their plots. The simulations encountered problems at these time steps and the calculations stopped. To continue the calculations, the time step had to be adjusted by increasing/decreasing it by s. As a consequence, large spikes appeared in the results to adjust the new time step. Collective pitch angle: At the early stages of the master thesis we decided to select θ 0 angles between 0 and 10. Looking at the results indicated that we chose relative low values for the collective pitch (θ 0 = 5, 10, 12 ). These values were based on the same configuration used in the Skeldar UAV, which have blades with low built in twist angle. Looking at the results in Fig. 7.1, it clearly shows that higher θ 0 values where used in the experimental wind tunnel setup. Having a collective pitch extending between 10 to 20 is consider high values (Leishman, 2000 [4]), but since the blades for the ARES-model had a high (negative) built in pitch angle (Fig. A.4), using angles at these regions seemed reasonable. Hover flights case: Looking at the convergence history for C L for the stripped version in Fig. B.1, the lift force is pointing downwards giving it a negative lift. This was predicted since the built in twist angle θ 1 had a distribution between 7 < θ 1 < 1, giving the major part of the blade a negative lift (when θ 0 = 0 ). Another aspect in mind was the size of the overset regions, which were reduced considerable. 26

29 Discussion C.Rodriguez Helicopter Aerodynamics The current size was not necessary due to the fact that according to Star CCM+ (2012) [7], the wall boundaries at the overset and background meshes needed no more then 4-5 cells in each mesh to properly work. Proceeding to the complete helicopter model a collective pitch was added, giving the main-rotor a positive lift force. At θ 0 = 5 the lift force was relative low, due to the fact that some regions on the blade (at the blade tip region) still had a a negative built in pitch angle, giving it a negative lift. Increasing θ 0, gave larger values of the lift and torque that increased linearly (seen in Fig. 7.1). Fig. B.5 to Fig. B.8 illustrates that with increasing θ 0, the aerodynamic properties converged faster to a (quasi) steady-state condition. Helicopter forward flight (No cyclic motion): As for the flight cases with α s = 0 shown in red circles in Fig. 7.2 and 7.3, the results were consistent when comparing it to the experimental data. The drag and torque however deviated with increasing θ 0. A real flight case with α s = 0 would never be possible since a forward thrust would never be possible to obtain. This case should therefore be seen as more an experimental wind tunnel case, where the model is stationary and a freestream flow is affecting it. For the simulation where θ 0 = 10 at α s = 4, the lift coefficient decreases with about units, indicating that the main-rotor has developed a thrust component. This is shown in the computed results in Fig. 7.2, which clearly shows that C D has a negative value giving it thrust forward (positive value gives drag resistance, while a negative value give thrust). However, the thrust has a very low value compared to the experimental data which has comparably 40 times bigger forward thrust than the CFD results. This can be due to the fact that the cyclic pitch motion was not included in the analysis, giving the drag resistance an increased value. However this can not be concluded since simulations with cyclic pitch motions were not done at these flight regions. Helicopter forward flight (with cyclic motion): Looking at Fig. B.18 and Fig. B.19, the pitch and roll moment were successfully removed with the configuration θ 0 = 5 at α s = 0. Examining the pure longitudinal cyclic motion showed that adding a negative θ s gave a positive roll moment. This showed that θ s needed to be a positive value to induce a negative roll moment. Fig. B.18 showed that the roll moment was already close to zero, meaning that a small positive value of θ s was needed. The lateral cyclic motion indicated that adding θ c = 1 reduced the pitching moment. This did not entirely remove the pitch moment which Fig. B.19 illustrates. Therefore increasing θ c (negatively), the pithing moment was reduced. From this and with Eq. (6.4) and Eq. (6.5) it was found that C l and C m equals zero for θ s = and θ c =

30 Conclusion C.Rodriguez Helicopter Aerodynamics 9 Conclusion Applying the overset meshes to perform CFD analysis on the rotating blades worked properly. Assigning each blade an overset region gave the possibility to include a cyclic pitch motion. This would not be the case if all four blades shared one large overset region. Having independent overset regions needed more computational power to successfully cut out the overlapping regions. With only one overset mesh however, leads to less time to cut out the overlapping regions, thereby reducing the time it takes to compute the simulations. This came down to a tradeoff between computational power versus computational time. By adding the cyclic pitch motion at θ 0 = 5 and α = 0, the roll and pitching moment were successfully removed from the results with small interference effects on C L. With this to say, including an additional flapping angle is possible by modifying the existing model. This will contribute into helping to understand cyclic pitch motion in further CFD investigations. The main-rotor showed good results in hover and forward flight cases (with no cyclic motion) which closely matched the experimental data. At higher collective pitch angles the aerodynamic values fluctuated more but converged faster to its quasi-steady state. The flight case with the setting θ 0 = 10 at α s = 4 gave drag results that deviated 10 times more compared to the size of the experimental values. This led to a discussion regarding how much the lack of a cyclic pitch affected the drag, giving the possibility in future investigations on examining the affect in including cyclic pitch motion. It is a bit misleading to say that CFD with overset meshes is a better method than momentum theory, we merely found an alternative CFD method for analyzing helicopter aerodynamics. One important aspect is that using overset meshes gives more freedom in anlyzing non-uniform lift analysis e.g cyclic pitch motion. This cannot be done with momentum theory and is therefore the biggest advantage of overset meshing. 28

31 Acknowledgement C.Rodriguez Helicopter Aerodynamics Acknowledgement I wish to thank Prof. Arne Karlsson of the Royal Institute of Technology. The people in Saab Aeronautics, Mattias Hackström and Nenad Jankovic for giving me this opportunity to write my master thesis here in Saab. For assistance and support I want to thank Per Weinerfelt and Lars-Erik Berg for providing me the theory and tools for this thesis. And of course, thank you for all support from my family and friends, special thanks to Norah Sakal who helped me get in touch with Saab Aeronautics. I want to give my sincere gratitude to Marie Malmgren who constantly motivated me throughout this thesis, and reminded me to never settle for less, I thank you. 29

32 Appendix A C.Rodriguez Helicopter Aerodynamics References [1] CD-adapco, 2012 Overset Mesh specifications, Website Last retrieved [2] Naval Technology, 2011 Skeldar UAV article, Website Last retrieved [3] Arthur Rizzi, 2011 Aerodynamic Design a Computational Approach Stockholm, KTH Department of Aeronautical and Vehicle engineering [4] J. Gordon Leishman, 2000 Principles of Helicopter Aerodynamics Cambridge University Press [5] John D. Anderson Jr, 1995 Computational Fluid dynamics, The basics with applications McGraw-Hill inc, ISBN [6] Innovative CFD, 2007 Making Sense of CFD Grid Types, Website Last retrieved [7] CD-adapco, 2012 Star CCM+ (Version 7.02) [Computer software] Last retrieved [8] Kevin W. Noonan, William T. Yeager Jr, Jeffrey D. Singelton, Matthew L. Wilbur and Paul H. Mirick, 2001 Wind Tunnel Evaluation of a Model Helicopter Main-Rotor Blade With Slotted Airfoils at the Tip NASA TP , 2001 [9] Milovan Peric and Stephen Ferguson, 2005 [Article] The advantage of polyhedral meshes Dynamics, p.4-5 [10] F-Chart Software (2012) F-chart (Version 6.76) [Computer software] Last retrieved [11] Fig.D.1, Langley Research Center, 2001 Images containing top view of ARES-model Last retrieved [12] Ira H. Abbott and Albert E. von Doenhoff, 1959 Theory of wing sections: including a summary of airfoil data. Dover Publications 30

33 Appendix A C.Rodriguez Helicopter Aerodynamics A Appendix A Blade geometry and CAD-model 0.3 Root Chord RC(4) Figure A.1: Root chord. 0.3 Tip Chord RC(6) Figure A.2: tip chord. 31

34 Appendix A C.Rodriguez Helicopter Aerodynamics 0.3 Horiziontal Stabilizer NACA Figure A.3: Horizontal Stabilizer. 2 Rotor Blade Twist Built in twist angle distribution θ 1 [deg] r/r [ ] Figure A.4: Built in twist angle distribution θ 1. 32

35 Appendix A C.Rodriguez Helicopter Aerodynamics Upper surface Lower surface Station Ordinate Station Ordinate Table A.1: Design Coordinates for RC(4)-10 Airfoil. [8] 33

36 Appendix A C.Rodriguez Helicopter Aerodynamics Upper surface Lower surface Station Ordinate Station Ordinate 0, , Table A.2: Design Coordinates for RC(6)-08 Airfoil. [8] 34

37 Appendix A C.Rodriguez Helicopter Aerodynamics Additional CAD images Figure A.5: Isometric view of the rotor blade. Figure A.6: Isometric view of the hub with the additional connecting shafts. 35

38 Appendix A C.Rodriguez Helicopter Aerodynamics Figure A.7: Side view of the final CAD-model designed after Langleys ARES- helicopter model. Figure A.8: Isometric view of the final CAD-model designed after Langleys ARES- helicopter model. 36

39 Appendix B C.Rodriguez Helicopter Aerodynamics B Appendix B Simulation convergence history B.1 Hover stripped version results 0 Hover Flight Comparison (Stripped Version) Lift Coefficient C L [ ] Computational plot θ 0 =0 Moving Average plot Time t [s] Figure B.1: Stripped hover version showing C L vs t for the main-rotor Hover Flight Comparison (Stripped Version) Computational plot θ 0 Moving Average plot Drag Coefficient C D [ ] Time t [s] Figure B.2: Stripped hover version showing C D vs t for the main-rotor. 37

40 Appendix B C.Rodriguez Helicopter Aerodynamics Hover Flight Comparison (Stripped Version) Computational plot θ 0 Moving Average plot Torque Coefficient C Q [ ] Time t [s] Figure B.3: Stripped hover version showing C Q vs t for the main-rotor. 850 Hover Flight Comparison (Stripped Version) 900 Surface Average Pressure P av [Pa] Computational plot θ 0 =0 Moving Average plot Time t [s] Figure B.4: Stripped hover version showing p av vs t for the main-rotor, which includes the surfaces of the two blades. 38

41 Appendix B C.Rodriguez Helicopter Aerodynamics B.2 Hover complete results Lift Coefficient C L [ ] Hover Flight Comparison Computational plot at θ 0 = 5 Computational plot at θ 0 = 10 Computational plot at θ 0 = 12 Moving Average plot Time t [s] Figure B.5: Complete hover version showing C L vs t for the main-rotor. Drag Coefficient C D [ ] Hover Flight Comparison Computational plot at θ 0 = 5 Computational plot at θ 0 = 10 Computational plot at θ 0 = 12 Moving Average plot Time t [s] Figure B.6: Complete hover version showing C D vs t for the main-rotor. 39

42 Appendix B C.Rodriguez Helicopter Aerodynamics Torque Coefficient C Q [ ] Hover Flight Comparison Computational plot at θ 0 = 5 Computational plot at θ 0 = 10 Computational plot at θ 0 = 12 Moving Average plot Time t [s] Figure B.7: Complete hover version showing C Q vs t for the main-rotor. 850 Hover Flight Comparison 900 Surface Average Pressure P av [Pa] Computational plot at θ 0 = 5 Computational plot at θ 0 = Computational plot at θ = 12 0 Moving Average plot Time t [s] Figure B.8: Complete hover version showing p av vs t for the main-rotor, which includes the surfaces of the four blades. 40

43 Appendix B C.Rodriguez Helicopter Aerodynamics B.3 Forward flight no cyclic pitch results No Cyclic Pitch Flight Comparison θ 0 = 5 α s θ 0 = 10 α s θ 0 = 5 α s = 4 θ 0 = 10 α s = 4 Lift Coefficient C L [ ] Time t [s] Figure B.9: Forward flight with no cyclic pitch showing C L vs t for the main-rotor No Cyclic Pitch Flight Comparison θ 0 = 5 α s θ 0 = 10 α s θ 0 = 5 α s = 4 θ 0 = 10 α s = 4 Drag Coefficient C D [ ] Time t [s] Figure B.10: Forward flight with no cyclic pitch showing C D vs t for the main-rotor. 41

44 Appendix B C.Rodriguez Helicopter Aerodynamics Torque Coefficient C Q [ ] No Cyclic Pitch Flight Comparison θ 0 = 5 α s θ 0 = 10 α s θ 0 = 5 α s = 4 θ 0 = 10 α s = Time t [s] Figure B.11: Forward flight with no cyclic pitch showing C Q vs t. Roll Moment Coefficient C l [ ] No Cyclic Pitch Flight Comparison θ 0 = 5 α s θ 0 = 10 α s θ 0 = 5 α s = 4 θ 0 = 10 α s = Time t [s] Figure B.12: Forward flight with no cyclic pitch showing C l vs t for the main-rotor. 42

45 Appendix B C.Rodriguez Helicopter Aerodynamics No Cyclic Pitch Flight Comparison Pitching Moment Coefficient C m [ ] θ 0 = 5 α s θ 0 = 10 α s θ = 5 α s = 4 θ 0 = 10 α s = Time t [s] Figure B.13: Forward flight with no cyclic pitch showing C m vs t for the main-rotor. Surface Average Pressure P av [Pa] No Cyclic Pitch Flight Comparison θ 0 = 5 α s θ 0 = 10 α s θ 0 = 5 α s = 4 θ 0 = 10 α s = Time t [s] Figure B.14: Forward flight with no cyclic pitch showing p av vs t for the main-rotor, which includes the surfaces of the four blades. 43

46 Appendix B C.Rodriguez Helicopter Aerodynamics B.4 Forward flight cyclic pitch results Cyclic Pitch Flight Comparison at θ 0 = 5 α s Lift Coefficient C L [ ] no cyclic θ s θ c long cyclic θ s = 1 θ c lat cyclic θ s θ c = 1 long/lat cyclic θ s = θ c = Time t [s] Figure B.15: Forward flight with cyclic pitch showing C L vs t for the main-rotor Cyclic Pitch Flight Comparison at θ 0 = 5 α s Drag Coefficient C D [ ] no cyclic θ s θ c long cyclic θ s = 1 θ c lat cyclic θ s θ c = 1 long/lat cyclic θ s = θ c = Time t [s] Figure B.16: Forward flight with no cyclic pitch showing C D vs t for the main-rotor. 44

47 Appendix B C.Rodriguez Helicopter Aerodynamics Cyclic Pitch Flight Comparison at θ 0 = 5 α s Torque Moment Coefficient C Q [ ] e 05 no cyclic θ s θ c long cyclic θ s = 1 θ c lat cyclic θ s θ c = 1 long/lat cyclic θ s = θ c = Time t [s] Figure B.17: Forward flight with no cyclic pitch showing C Q vs t for the main-rotor Cyclic Pitch Flight Comparison at θ 0 = 5 α s Roll Moment Coefficient C l [ ] no cyclic θ s θ c long cyclic θ s = 1 θ c lat cyclic θ s θ c = 1 long/lat cyclic θ s = θ c = Time t [s] Figure B.18: Forward flight with no cyclic pitch showing C l vs t for the main-rotor. 45

48 Appendix B C.Rodriguez Helicopter Aerodynamics Cyclic Pitch Flight Comparison at θ 0 = 5 α s Pitching Moment Coefficient C m [ ] no cyclic θ s θ c long cyclic θ s = 1 θ c lat cyclic θ s θ c = 1 long/lat cyclic θ s = θ c = Time t [s] Figure B.19: Forward flight with no cyclic pitch showing C m vs t for the main-rotor. 46

49 Appendix C C.Rodriguez Helicopter Aerodynamics C Appendix C Star CCM+ images Figure C.1: The prism layers on the fuselage consisting of 5 layers with a prism layer thickness of m (100 % of the base size). Figure C.2: Image representing the tail surface meshing of the ARES-model.. 47

50 Appendix C C.Rodriguez Helicopter Aerodynamics Figure C.3: Image showing the scalar representation of the induced flow around the body. Figure C.4: Boundaries are defined and identified using different colors to extinguish them. Figure C.5: A close up on the boundaries with smaller surfaces such as the connecting shaft and rotor blade edge. 48

51 Appendix C C.Rodriguez Helicopter Aerodynamics Figure C.6: A scalar representation showing a cutout on the region were the overset and background region overlapp. Figure C.7: A similar figure as the previous one, but instead representing the active (yellow), inactive (red) and acceptor (blue) cells of the model. 49

52 Appendix C C.Rodriguez Helicopter Aerodynamics Figure C.8: Importing the CAD-model for the first time gave numerous errors such as pierced surfaces (red) and surfaces with free edges (green). Figure C.9: Top view of the complete helicopter representing the missing hub at the rotor conjunction. Figure C.10: Sideview of the complete helicopter showing how the new shape of the fuselage looks like without the top part. 50

53 Appendix D C.Rodriguez Helicopter Aerodynamics D Appendix D Gas Properties Gas Property Value Unit c p J/(kg K) k mw/(m K) µ µpa/s M R kg/kmol P r a freon m/s Table D.1: Freon 12 gas properties at T = 293 K and p = bar. The molar mass M R12 above gives the specific gas constant Rspecific R12 = J/(kg K), which with c p above give c v = J/(kg K) and γ = Langley Research Center Image Figure D.1: Additional top view geometry from Langley Research Center. (Langley Research Center, 2001 [11]) 51

54 Appendix D C.Rodriguez Helicopter Aerodynamics Structured versus Unstructured grid Figure D.2: Example on a structured grid using hexahedral cells. Figure D.3: Example on an unstructured grid using polyhedral cells. 52

55 Appendix D C.Rodriguez Helicopter Aerodynamics Coordinate system and Aerodynamic properties definition. Figure D.4: Definition showing positive directions of forces, angles and velocities.(noonan et al, 2001 [8]) Figure D.5: Definition of the azimuth angle.(leishman, 2000 [4]) 53

56 Appendix D C.Rodriguez Helicopter Aerodynamics Figure D.6: Flapping angle definition, showing the longitudinal flapping with the coning angle. Lateral flapping is defined the same but β c is replaced by β s and with a 90 phase shift in ψ. (Leishman, 2000 [4]) Figure D.7: Pitching angle definition.(leishman, 2000 [4]) 54