CFD Analysis of Rotor Blade of Helicopter

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

CHRISTIAN CHRISTIAN RODRIGUEZ RODRIGUEZ

Masters’ Degree Project Stockholm, Sweden August 2012

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 between cells. An implicit unsteady flow solver, with an ideal gas and a SST (Mentar) K-Omega turbulence model were were used. Hov Hover er and forward cases cases were examined. examined. Forward orward flight cases were were done by changing changing the rotor shaft angle of attack α attack  α s  and the collective pitch angle θ angle  θ 0  at the helicopter freestream Mach number of  M   M  = 0.128, without the inclusion of a cyclic pitch motion. An additional flight case with cyclic pitch motion was examined at α at  α s  = 0 and θ and  θ  = 0 . ◦

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Each Each simula simulatio tion n took roughly roughly 48 hours hours with a total total of 96 parall parallel el cores cores to com compute pute.. Experim Experimen ental tal 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 experimenta experimentall data, but had difficulties difficulties in producing producing a forward forward thrust. Moments 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 at  θ 0  = 5 and α and  α s  = 0 successfully removed the roll and pitching moment from the results. ◦

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Nomenclature

C.Rodriguez

Nomenclature Symbols αs  : Rotor shaft shaft angle of attack attack - deg β 0  : Blade coning coning angle angle - deg β c  : Longitudina Longitudinall flapping angle - deg β s  : Lateral Lateral flapping flapping angle - deg θ0  : Collectiv Collectivee pitch angle - deg θ1  : Built in twist twist angle distribution, distribution, positive positive nose up - deg θc  : Lateral Lateral cyclic pitch pitch - deg θs  : Longitudina Longitudinall cyclic pitch pitch - deg advance ratio, ratio, µ  : Rotor advance

V  

ΩR

Dynamic viscosity viscosity - Pa · s µ  : Dynamic ρ  : Density - kg/ kg/m3 Ψ or ψ or  ψ  : Blade/roto Blade/rotorr azimuth location location - deg Ω : Rotor angular angular velocity velocity - rad/s C D  : Rotor drag drag coefficient coefficient for the main-rotor C L  : Rotor lift coefficien coefficientt for the main-rotor C l  : Roll moment moment coefficient coefficient for the main-rotor main-rotor C m  : Pitch Pitch moment coefficient coefficient for the main-rotor C Q  : Torque moment moment coefficient coefficient for the main-rotor main-rotor A  : Reference area - m 2 a  : Semi-major axis of ellipse - m b  : Semi-minor Semi-minor axis axis of ellipse - m c p  : Specific heat heat capacity capacity at constant pressure pressure - J/ J/(kg · K) d  : Diameter Diameter of the volumetric volumetric control control - m h  : Height Height of the volumetric volumetric control control - m γ   : Ratio of specific specific heats heats k  : Thermal Thermal conductivit conductivity y - W/(m · K) l  : Length Length of overset overset boundary boundary - m M   M   : Freestream Mach number number M  : M  : Blade tip Mach Mach number number M R12  : Mola Molarr mass of Freon Freon (R12) - kg/ kg /kmol  p   p   : Pressure - Pa  pav  : Average Average surface surface pressure pressure over all blades. blades. - Pa P r  : Prandtl Prandtl number number 2

Helicopter Aerodynamics

Nomenclature

C.Rodriguez

Helicopter Aerodynamics

R  : Rotor radius - m r  : Spanwise Spanwise distance distance along the blade radius measured measured from the rotational rotational center center - m r  : Radius Radius of the overset overset boundary boundary (Stripped version) version) - m T   T   : Temperature emperature - K V tip m/s tip  : Blade tip velocity - m/ V  : Freestream reestream velocit velocity y - m/ m /s Vectors   : Stress Stress tensor - Pa. Pa.

τ  

a  : Non-dimens Non-dimensional ional unit vector defining defining the component component of the moment vector vector f pressure : Pressure Pressure force vector vector - N f shear : Shear Shear force force vector vector - N I  : Identity Identity Matrix Matrix nD  : User specified specified direction direction vectors r  : The distance/pos distance/position ition of the cell relative relative to some point - m u  : Velocity elocity vector - m/ m/s. Subscript/ Subscript/Superscript c  : Cosine cv : cv  : Complete Complete version version f   f   : Faces ref   ref   : Reference Reference s   : Sine sv : sv  : Stripped Stripped version version vc  vc   : Volumetric control

Abbreviations ARES : Aeroelastic Aeroelastic Rotor Experimen Experimental tal System CAD : Computer Computer Aided Aided Design CFD : Computation Computational al Fluid Dynamics Dynamics FDM : Finite Differe Difference nce Method Method FEM : Finite Finite Element Element Method Method FVM : Finite Volume Volume Method Method HP   : Hub Plane NASA : National National Aeronautics Aeronautics and Space Administrati Administration on NACA : National National Advisory Committee Committee for Aeronautics Aeronautics NFP : No Feathe Feathering ring Plane Plane RPM : Revolutio Revolutions ns per minute minute 3

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:   Workbench in Catia V5 that allows the user to model shapes using wireframe and surface features. 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

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.

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Introduction

C.Rodriguez

Helicopter Aerodynamics

Contents 1 Introduction 1.1 Guidelines   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theory 2.1 Governing equation . . . . . . . . . 2.2 Momentum theory . . . . . . . . . 2.3 Helicopter flight controls  . . . . . . 2.4 Meshing methodology . . . . . . . 2.4.1 Overset mesh introduction .

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7 7 8 8 8 8 10 11

3 Project brief  12 3.1 Background   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Purpose and goal   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Method I - CAD modelling

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5 Method II - Meshing 5.1 CAD model to computational domain 5.2 Generating surface and overset mesh   . 5.3 Volume mesh . . . . . . . . . . . . . . 5.4 Supercomputer . . . . . . . . . . . . .

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6 Method III - Simulations 6.1 Physics model description . . . . . . . . . . . 6.2 Aerodynamic coefficients and moving average 6.3 Stripped version . . . . . . . . . . . . . . . . 6.4 Complete helicopter configuration . . . . . . . 6.4.1 Hover flight   . . . . . . . . . . . . . . . 6.4.2 Forward flight without cyclic pitch   . . 6.4.3 Forward Flight with cyclic pitch . . .

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7 Main results 23 7.1 Flight simulations in Hover Mode  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 7.2 Flight simulations in forward flight   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8 Discussion 8.1 General discussion 8.2 CAD models . . . 8.3 Meshing   . . . . . . 8.4 Simulations . . . .

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25 25 25 26 26

9 Conclusion

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References

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A Appendix A

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B Appendix B 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  . . .

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37 37 39 41 44

C Appendix C

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D Appendix D

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6

Introduction

1

C.Rodriguez

Helicopter Aerodynamics

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.1.

1

www.aeroquad.com

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Theory

2

C.Rodriguez

Helicopter Aerodynamics

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 •   Energy

second law

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 ∂ u 1 µ 1 ∇2 u − ∇ (∇ · u) + (u · ∇) u + ∇ p = ∂t ρ ρ 3



(2.1)



∂p + (u · ∇) p + γp∇ · u = (γ  − 1)[(τ   · ∇) · u + ∇ · (k ∇T )] ∂t where the shear stress tensor τ    for Newtonian fluid is:

 

(2.2) (2.3)

2 = µ ∇u + (∇u)T  − µ (∇ · u) I   (2.4) 3 Together with the ideal gas law this gives six scalar equation for six dependent variables, the density ρ, T  cartesian velocities u  = (u,v,w) , temperature T   and the pressure p, plus the gas property parameters, ratio of specific heats γ , dynamic viscosity µ  and the thermal conductivity k. τ  

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

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. ◦

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◦

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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.

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Theory

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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) = θ0  + θ1 (r) + θc cos(ψ) + θs sin(ψ)

(2.6)

where θc and θs   are angles that control the cyclic motion. θ0   is the constant collective pitch angle and θ1  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 θc  control the lateral orientation and θs   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  θs   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. 2.2.   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(xi ) 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.

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Theory

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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). 2.4.1

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

Project Brief

3

C.Rodriguez

Helicopter Aerodynamics

Project brief

3.1

Background

This master thesis was conducted by the author with supervision from Mattias Hackstr¨om 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.   2001 [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.

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Method CAD Modelling

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Helicopter Aerodynamics

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 12 000 RPM. The model includes four blades with a built in twist angle θ1  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. 4.1. 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 θ1  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)-08. ◦

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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 Center2 , 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.

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Method Meshing

5 5.1

C.Rodriguez

Helicopter Aerodynamics

Method II - Meshing 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.5.

5.2

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 0.001 m.

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Parts

Target size %

Minimum size %

Fin 1-2

600

25

Fin Edge 1-2

10

150

Freestream box

25000

25000

Fuselage

1600

200

Hub

600

25

Overset Region

1500

1500

Top part (fuselage)

1600

200

Top part edge (fuselage)

400

50

Rotor 1-4

600

150

Rotor Edge 1-4

10

150

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 0.001 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.

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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 

0.002 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 4

Intel Xeon E5462 quad core 2.8 GHz, 6 MiB level 2 cache. Intel Xeon single core processors 3.4 GHz, 2 MiB level 2 cache.

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Method Simulations

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Helicopter Aerodynamics

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 23.04 m 2 (248 ft2 ), see Fig. 3.1.   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 /m3 (0.006 slugs/ft3 ) at a temperature and pressure of 293 K and 61495 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 follows5 : f  pressure + f f shear · nD f  C L  =  C D  =





f 

 2 ρref  Aref  V ref 

5

(6.1)

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.

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Eq. (6.1) gives a dimensionless force in which the user specifies the direction using the unit vector nD . 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. Aref    is defined as the main-rotor disc area, and V ref  denotes the tip velocity of the blades.

 r f  f  ×

C l  =  C m  =  C Q  =

 pressure f 

+ f f shear

f 

 a ·

 2 R ρref Aref V ref  ref 

(6.2)

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 nD   (for the force coefficient) but instead defines the roll, pitch and torque moment coefficient. rf  is the position of each face  relative to the reference point x0  of the moment vector. The pressure- and shear- force vector are defined as; f  pressure = ( pf  + p ref )af  and f f shear = −τ   · af . Where pf    is the f  face pressure, af  is the face area vector, pref   is the reference pressure, which was set to pref   = 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. SM A =

6.3

xM  + xM  1 + xM  2  + .... + xM  n −

−

(n−1)

−

 

(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 rsv = 0.5 m and lsv = 1.6 m, as seen in Fig. 6.2. 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.

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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