CFD Analysis of Rotor Blade of Helicopter

CFD Analysis on the Main-Rotor Blade ofa Scale Helicopter Model using Overset

Meshing

CHRISTIAN RODRIGUEZ

Masters’ Degree ProjectStockholm, Sweden August 2012

Abstract C.Rodriguez Helicopter Aerodynamics

Abstract

In this paper, an analysis in computational fluid dynamics (CFD) is presented on a helicopter scalemodel with focus on the main-rotor blades.

The helicopter model is encapsulated in a background region and the flow field is solved using StarCCM+. A surface and volume mesh continuum was generated that contained approximately seven mil-lion 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 inter-polation method between cells.

An implicit unsteady flow solver, with an ideal gas and a SST (Mentar) K-Omega turbulence modelwere used. Hover and forward cases were examined. Forward flight cases were done by changing therotor shaft angle of attack αs and the collective pitch angle θ0 at the helicopter freestream Mach numberof M = 0.128, without the inclusion of a cyclic pitch motion. An additional flight case with cyclic pitchmotion was examined at αs = 0 and θ = 0.

Each simulation took roughly 48 hours with a total of 96 parallel cores to compute. Experimentaldata were taken from an existing NASA report for comparison of the results. Hover flight coincided wellwith the wind tunnel data. The forward flight cases (with no cyclic motion) produced lift matching theexperimental data, but had difficulties in producing a forward thrust. Moments in roll and pitch startedto 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 us-ing CFD does work. Adding a cyclic pitch motion at θ0 = 5 and αs = 0 successfully removed the rolland pitching moment from the results.

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Nomenclature C.Rodriguez Helicopter Aerodynamics

Nomenclature

Symbols

αs : Rotor shaft angle of attack - deg

β0 : Blade coning angle - deg

βc : Longitudinal flapping angle - deg

βs : Lateral flapping angle - deg

θ0 : Collective pitch angle - deg

θ1 : Built in twist angle distribution, positive nose up - deg

θc : Lateral cyclic pitch - deg

θs : Longitudinal cyclic pitch - deg

µ : Rotor advance ratio, VΩR

µ : Dynamic viscosity - Pa · s

ρ : Density - kg/m3

Ψ or ψ : Blade/rotor azimuth location - deg

Ω : Rotor angular velocity - rad/s

CD : Rotor drag coefficient for the main-rotor

CL : Rotor lift coefficient for the main-rotor

Cl : Roll moment coefficient for the main-rotor

Cm : Pitch moment coefficient for the main-rotor

CQ : Torque moment coefficient for the main-rotor

A : Reference area - m2

a : Semi-major axis of ellipse - m

b : Semi-minor axis of ellipse - m

cp : 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

MR12 : Molar mass of Freon (R12) - kg/kmol

p : Pressure - Pa

pav : Average surface pressure over all blades. - Pa

Pr : Prandtl number

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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

Vtip : 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

fpressure : Pressure force vector - N

f shear : Shear force vector - N

I : Identity Matrix

nD : 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

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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 measuredin 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 usingwireframe and surface features.

Gyroscopic precession: Phenomena that occur in rotating bodies in which an applied force is mani-fested 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 movingobject 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 marchingsolution to the steady state, the magnitude of the residuals and their rate of decay are often used as afigure of merit.

Quasi-Steady State: A time-dependent condition in which acceleration effects can be neglected, andhence, 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 ) areunchanging over time.

Swash plate: Helicopter rotor device that transforms inputs via the helicopter flight controls intomotion of the main rotor blades.

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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 isable to decrease/increase the mesh density.

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Introduction C.Rodriguez Helicopter Aerodynamics

Contents

1 Introduction 71.1 Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Theory 82.1 Governing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Momentum theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Helicopter flight controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Meshing methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Overset mesh introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Project brief 123.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Purpose and goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Method I - CAD modelling 13

5 Method II - Meshing 155.1 CAD model to computational domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2 Generating surface and overset mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.3 Volume mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.4 Supercomputer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6 Method III - Simulations 186.1 Physics model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186.2 Aerodynamic coefficients and moving average . . . . . . . . . . . . . . . . . . . . . . . . . 186.3 Stripped version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196.4 Complete helicopter configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.4.1 Hover flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.4.2 Forward flight without cyclic pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.4.3 Forward Flight with cyclic pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7 Main results 237.1 Flight simulations in Hover Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237.2 Flight simulations in forward flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8 Discussion 258.1 General discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258.2 CAD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258.3 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9 Conclusion 28

References 30

A Appendix A 31

B Appendix B 37B.1 Hover stripped version results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37B.2 Hover complete results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B.3 Forward flight no cyclic pitch results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41B.4 Forward flight cyclic pitch results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

C Appendix C 47

D Appendix D 51

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Introduction C.Rodriguez Helicopter Aerodynamics

1 Introduction

The need to modernize combat efficiency in military defense technology is growing rapidly along withtodays technical advances. Unmanned Aerial Vehicle (UAV) have a significant role in the future develop-ment of aerial reconnaissance. Their main priority is to minimize human risks in hazardous environmentthrough reconnaissance or in support missions. The lighter UAV classes (approximate 5-10 kg) are rel-ative portable and easy to assembly when needed. However, current small scaled UAVs are increasingboth 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 Quadcopter1

or Saab Aeronautics own helicopter UAV, Skeldar (Naval Technology, 2011 [2]) are a few projects whichhave been under development under the recent years. Increasing interest from Saabs side has led to moreadvanced analysis in rotor aerodynamics. Current mathematical models used in Saab are trivial in theform of propeller disc models and blade element theory. Increasing demands from flight mechanic modelshas led to a desire to improve the methodology for complex, unsteady flow fields that exist in theseapplications. To keep Saabs’ UAV projects in constant development, flight mechanics and aerodynamicsimprovements are needed.

Computational Fluid Dynamics (CFD) is a powerful tool which is used extensively in aerodynamicapplications. It provides the numerical solutions to the governing Navier-Stokes Equations throughoutthe flow region. The method gives the possibility to simulate and analyze complex problems withoutloosing the integrity of the problem due to simplified flow models. Saab made it possible to write thisthesis in the field of aerodynamics using CFD as the main tool. They want to extend the understandingin unsteady flow analysis using CFD for rotational systems, which could be implemented into futurehelicopter-UAV projects.

1.1 Guidelines

Section 2 gives a brief introduction to fundamentals of fluid dynamics, the understanding of helicopterflight controls and the basics of meshing. Section 3 explains how the idea came about in writing a thesis onhelicopter aerodynamics, and the purpose and goals behind it. The report proceeds by presenting how thehelicopter schematic underwent the transformation to a computer aided design (CAD), in section 4. Thiscontinues on with the computational part of report (section 5), giving description of the challenges thatare identified showing how the model went from a CAD-model to a discretized volume mesh generatedin Star CCM+. This is then followed by the analysis and simulations on the rotor blade monitoringforce and moment coefficients predicted on the helicopter at hover and forward flight. The results arethen 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 tablesfound in the Appendices are marked with a letter in their reference to easily distinguish them in thereport, e.g Fig. B.5 and Tab. A.1.

1www.aeroquad.com

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Theory C.Rodriguez Helicopter Aerodynamics

2 Theory

2.1 Governing equation

The Navier-Stokes equation are the fundamental governing equations for compressible viscous and heatconducting flows. It is obtained by applying Newton’s Law of Motion to a fluid particle and is calledmomentum equation (Eq. (2.2)), which is followed by the energy equation (Eq. (2.3)) and the massconservation equation, also known as continuity equation (Eq. (2.1)). Usually, the term Navier-Stokesequation is used to refer to these three equations. These equations interprets the physics behind the fluiddynamics and are mathematical statements of three physical principles upon which all of fluid dynamicsare 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, momentumand energy in non-conservative form:

∂ρ

∂t+ ρ (u · ∇) + ρ∇ · u = 0 (2.1)

∂u

∂t+ (u · ∇) u +

1

ρ∇p =

µ

ρ

[∇2u− 1

3∇ (∇ · u)

](2.2)

∂p

∂t+ (u · ∇) p+ γp∇ · u = (γ − 1) [(τ · ∇) · u +∇ · (k∇T )] (2.3)

where the shear stress tensor τ for Newtonian fluid is:

τ = µ[∇u + (∇u)

T]− 2

3µ (∇ · u) I (2.4)

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 ac-tuator 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 flowthrough the rotor is considered one dimensional, quasi-steady, incompressible and inviscid. Due to thefact that viscous effects are neglected, no viscous drag or momentum diffusion are present. The actuatordisc supports the thrust force which is generated by the rotating blades, and for power to insure a thrustgeneration, a torque is supplied through the rotor shaft. Compressibility correction can be done in themodel, however this can only be done to a certain extent.

The approach for this mathematical method is straight forward and gives sufficient results. This theoryis trivial and can be solved analytically to examine the influence of the propeller performance withoutneeding to solve the Navier-Stokes equations. However, when it comes to rotor aerodynamics the mo-mentum theory is insufficient in terms of accuracy. The method is not valid for examining helicopterflight 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 independentlyflap and lead/lag with respect to the hub plane (HP) under the influence of aerodynamic forces. Inaddition, a pitch bearing is integrated in the blade design to allow the blades to feather, giving them the

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ability to change their blade or pitch angle θ (Fig. D.7). To control the overall lift, the pitch angle forall blades is collectively altered by changing the blade pitch an equal amount, resulting in an increaseor decrease in lift. To perform a maneuver such as tilting forward (also called pitch), or tilting it side-ways (roll), the angle θ of the main rotor blade is altered cyclically during rotation, thereby producingdifferent amounts of lift at different points over the helicopter disc. The flapping hinge creates an angleβ (Fig. D.6) between the blade and HP, which allows each blade to freely flap up and down in a periodicmanner 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 ofthe main rotor blades.

As the helicopter leaves the ground, there is nothing that keeps the engine from spinning the heli-copter body. Without anything counteracting this movement, the body of the helicopter will spin in theopposite direction to the main rotor. By adding a tail rotor to the helicopter, it produces a counteractingforce. By producing thrust in a sideways direction, this critical part counteracts the rotors desire to spinthe body. To increase or decrease the thrust, the pitch angle can be altered collectively, just as themain-rotor.

Figure 2.1: Schematic showing the three motion of the rotor blade, which includes flapping, lead/lag andfeathering. (Leishamn, 2000 [4])

Consider now a flight case where the rotor operates in vacuum, in which no aerodynamic forces arepresent. In the absence of aerodynamic forces the rotor takes up an arbitrary orientation in inertialspace. As a result, the main-rotor acts as a gyroscope. Including aerodynamic forces produces a flappingmoment about the hinge, which causes the rotor to precess to a new orientation until the aerodynamicdamping causes equilibrium to be obtained once again. This phenomena is called gyroscopic precessionand 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 counterclockwisematter. To give a forward cyclic command, the natural assumption is that the rotor blade needs tohave more positive pitch at 6 o-clock rather than at 12 o-clock, giving the rotor more lift at the backrather than the front, pitching the helicopter forward. However because of gyroscopic precession, the liftactually occur 90 later in the rotation (at 3 o-clock or ψ = 90), thereby rolling the helicopter to theleft and not pitching it forward. Therefore, in order to give a forward cyclic forward command, more liftis 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 isaltered 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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The flapping motion can be described as harmonically constant and periodic (sine and cosine) terms, asexpressed in Eq. (2.5). β0 is referred as the coning angle, a constant angle independent of ψ.

β = β0 + βc cos(ψ) + βs 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 angleand θ1 is defined as the built in twist angle along the rotor blade. Using Leishman [4] definition, thecyclic flapping angles are defined as longitudinal flapping angle βc and lateral flapping angle βs. Thesubscript c denotes a motion with pure cosine cyclic motion opposed to s which denotes the pure sinusmotion. As for the cyclic pitch angles, the therm θc control the lateral orientation and θs controls thelongitudinal 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 commandof θc 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 maximumforce/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 quitestraightforward, in order to analyze the flow, the continuous flow domains are split into smaller discretesubdomains (Anderson, 1995 [5]), as shown in Fig. 2.2. For a continuous domain, each flow variableis defined at every point, in such domain we can for instance define the pressure as, p = p(x) at anygiven point at 0 < x < 1. In the discrete domain on the other hand, each flow variable is definedonly at certain grid points. Taking the same example as before, the pressure for a discrete domain isdefined as, pi = 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 theapproximative version of the governing equations: finite elements (FEM), finite difference (FDM) andfinite volume (FVM). To give a proper image of the fluid flow in the complete domain, care must betaken to ensure continuity of solution across the general interfaces between two subdomains. The subdo-mains 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, structuredgrids and unstructured grids. The term ”structure” emphasizes to the way the grid information is allo-cated. In a structured grid, the typical character is that the mesh have a regular connectivity, meaningthat 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 thatit allows a given cell neighbour to easily be identified and efficiently accessed, which gives very fast CFDcodes. However, this limits the possibility to refine or add additional cells in a certain area, and it maybe difficult to compute an uniform grid to complex shapes.

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An unstructured grid on the other hand, does not follow an uniform pattern. As oppose to the structuredgrid, 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 neigh-bouring cells and hence, use up more memory (Innovative CFD, 2007 [6]). However, the trade off isthat it allows for a freedom in constructing the CFD grid, it can add resolution where it is needed, anddecrease the resolution where it is not. Common cell types are hexahedrals, tetrahedrals, or prism layersfor 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. Thereare numerous types of overlapping grids but the one of interest here is so called Chimera grid or, as itis known in SCCM+, Overset mesh. This is one of SCCM+ (v7.02) new features and the main reasonwhy this software was chosen. Previous versions have not included the possibility to create simulationsof interaction between moving objects in a volume mesh continuum before. Close interactions and casesof objects with extreme ranges of motion has been almost impossible to render. Using the overset meshcapability gives the freedom for users to generate individual local meshes, which allows objects to bemoved 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 representthe acceptor cells. (b) The background region showing a cutout of the overset region which is represented in redcolor. (CD-adapco, 2012 [7])

A volume mesh is a set up by a large number of active cells, the big difference when using oversetmeshes arises from the use of acceptor cells. Seen in Fig. 2.3 is a scalar field representation of a 2D wingprofile for both the background region and overset region. The inactive cells (red coloured with the value1) removes or rather ”cuts out” the background cells overlapping other regions, leaving a hole for thecells for the moving regions. To identify the cell types the cells have been assigned values; inactive cellshave 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 theoverlapping regions (CD-adapco, 2012 [7]). In SCCM+ there are two interpolation options, linear in-terpolation and weighted interpolation. The latter works in a way that the interpolation factors areinversely proportional to the distance from acceptor cell center, resulting in the largest contributiongiven by the closet cell.

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Project Brief C.Rodriguez Helicopter Aerodynamics

3 Project brief

3.1 Background

This master thesis was conducted by the author with supervision from Mattias Hackstrom at Saab.Before starting the project, a great amount of time was spent on formulating the problem descriptionand 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 CFDresults. We eventually found a NASA-report (Noonan et al. 2001 [8]) about rotor blade concepts onslotted 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 partsusing Catia V5. (2) The experiments done in the NASA-report had similar test cases that we wanted toconduct 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 analysisfor rotating systems using CFD. Previous analysis done by Saab did not include the rotating blades inthe volume mesh continuum but rather model it as an infinitesimally thin actuator disc. This methodworks to a certain extent but is a simplified model, which lacks accuracy in more advance helicoptermodels such as rotor configurations with cyclic pitch settings.To improve the computational tools for helicopter aerodynamics using CFD, a new method needed tobe introduced. The approach that we decided on were to include the rotating blades in the volume meshcontinuum using SCCM+ Overset mesh methodology. The steps included in the analysis are as followedbelow:

1. A stripped down version containing two rotor blades with the exclusion of the fuselage and addi-tional 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 C.Rodriguez Helicopter Aerodynamics

4 Method I - CAD modelling

The helicopter was modeled after Langley’s ARES-model (Aeroelastic Rotor Experiment System) usingCatia V5’s Generative Shape Design. Langley’s rotorcraft (Fig. 4.1) is primarily designed to performanalysis on stability, performance and dynamic loads evaluation of new rotor concepts. It has a stream-lined fuselage shape that encloses the control systems together with the drive system, and the rotor isdriven by a variable-frequency synchronous motor, with a power of 47 hp giving it an output of 12 000RPM. The model includes four blades with a built in twist angle θ1 and has also a collective and cyclicpitch control, which can be altered using the inbuilt swash plate. In addition, the model did not includea 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 anddrag are determined from the measured balance normal and axial forces. Moments such as yawing, rolland tip are measured by the balance moment component. The balance is stationary with respect to therotor shaft and pitches together with the fuselage. It is located at the balance centroid which can beseen in Fig. 4.1.

The ARES-model is kept in place using a sting that is attached to the wind tunnel floor, making itpossible to perform experiments on different angle of attack αs.

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 wasselected for the tip region (r/R ≥ 0.85). Between 0.80 ≤ r/R ≤ 0.85, a smooth transition betweenthese inboard and outboard airfoil shapes were done. In addition, the blade included a spanwise twistθ1 distribution of 8 which can be found in Fig. A.4. Tab. A.1 and A.2 shows the design coordinatesfor RC(4)-10 and RC(6)-08.

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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 theNASA report. Since it had little contribution to the aerodynamic forces the search for the original de-sign was left out. Instead an arbitrary hub geometry with similar dimensions to the original design wascomputed, 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 thirdimage 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 theAppendices in Fig. D.1.

This 3-view schematic enabled us to to compute a 3D-model by setting up wireframes to form andshape the fuselage. To achieve the shape along the body, cross sectional profiles were inserted at givenpoints 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.

2Langley Research Center was not authorized to leave out detailed schematics of the ARES-model to personnel whowere not US citizens.

14

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 requirementsare to be taken in consideration: (1) A sealed surface of the model must be computed meaning that freeedges are not allowed. (2) No internal geometry or components need to be modelled when doing theexternal flow analysis. (3) Overlapping/pierced surfaces or floating points (non-manifold vertices) arenot 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. Whenthe CADpart-files were imported to SCCM+ for the first time, the software allotted names to therespective boundaries on its own. For the desired purpose we combined the defaulted boundaries toour own preference, different boundaries of the helicopter model were then defined. By specifying theparts 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. theleading edge of the rotor blade. Boundaries included are the fuselage, hub, roof, roof edge, the bladesand the fins with additional edges. The boundaries can be seen in the Appendices in Fig. C.4 andFig. 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 (providedby Catia V5). Ideally, the imported surface should fulfill the requirements mentioned in previous sectionbut this was not the case. Errors occasionally occur when a new CAD model is imported for the firsttime to SCCM+. The Surface repair tool gave the ability to identify, isolate and fix errors on the givenboundary. The helicopter model had some minor issues regarding a few overlapping parts, but wereeasily fixed by the Surface Repair Tool.

The surface of the helicopter model was meshed using unstructured triangular elements, where thesize of each triangle was defined by the base size. It is a characteristic dimension and was scaled relativeto the size of the helicopter model. It is specified after an arbitrary length unit given by the user, in thiscase the base size was set to a value of 0.001 m.

15


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 relativeto 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 surfacewhile the minimum size acted as the lower bound limit. Seen in Tab. 5.1 surfaces with curvature suchas the rotor blades or fin edges (Fig. 5.2) have smaller mesh sizes unlike the larger and flatter surfaceslike the fuselage or freestream box. The next step was to divide the computed boundaries into differentregions. All stationary boundaries such as the fuselage, fins, and the freestream box were included inthe background region. The boundaries with a moving reference such as the main-rotor received theirown overset region, which was placed inside the background region. Since each blade needed to have theability to include a cyclic pitch motion, an overset region was assigned to each blade, giving the modela total of four separate overset regions. The size of the overset region varied depending on the differentflight 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) wasthe choice as discretization technique. A volume mesh was computed using polyhedral cells. Using thiscell type was preferable to the typical tetrahedral cells. An advantage in using the polyhedral cells isthat it uses five times fewer cells compared to the tetrahedral mesh, thus decreasing the computing timeand 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


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 thick-ness of 100 % and respectively 200%, relative to the base size. The cell interpolation in the overlappingregions used a distance-weighted interpolation, which is the preferred choice when using an unstructuredgrid setup.

Figure 5.3: The prism layers on one of the rotor blades, consisting of 10 layers with a prism layer thickness of0.002 m (200 % of the base size).

To make the overset regions work properly a few requirements had to be fullfilled: (1) Between thewall boundaries of the overset and the background meshes, there should always be at least 4-5 cells ineach 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 notallowed to overlap with each other. (3) The cells of the overlapping region should have the same sizeon both the background and overset meshes, this was done using controlled volumes called volumetriccontrol. 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 twoLinux-based subclusters identified as Skylord and Darkstar. Skylord is built up by 40 HP ProLiantDL160 G5 computer servers, with each server containing two quad-core processors3 and 16 GiB of RAM.Darkstar contain 70 supermicro-based computer servers, with two single-core processors4 and 2 GiB ofRAM. Each computer server is abbreviated as a node and the computation time can vary depending onthe number of nodes chosen and the choice of subcluster used. Darkstar was part of a previous generationcluster, giving it a slower performance compared to Skylord.

A total of 15 separate simulations were conducted with each simulations needing 10 inner iterationsin each time step, giving a total of roughly 5000 iterations. The first five simulations were for experi-mental purposes and were done to examine and analyze the behaviour of the overset meshes. While asimulation can take several weeks to converge on a conventional PC desktop, the supercomputer did thetask in just under 48 hours. The time needed to reach the desired stopping criteria greatly depended onthe number of nodes that were available during each simulation, more on this in the discussion section.

3Intel Xeon E5462 quad core 2.8 GHz, 6 MiB level 2 cache.4Intel Xeon single core processors 3.4 GHz, 2 MiB level 2 cache.

17

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-sectionalarea of 23.04 m2 (248 ft2), see Fig. 3.1. According to the NASA-report (Noonan et al, 2001 [8]) allwall interference were significantly small, thereby excluding all wall disturbances in our analysis. In thecomputational 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 studiedwith the assurance of minimum wall interference. Due to the small aerodynamic disturbances the stingcontributes 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 thismedium are for its high molecular weight and low speed of sound. As a result of this, the medium givesthe matching of a model-scale Reynolds number and Mach number to full scale values. The nominaldensity conducted in the wind tunnel experiment was 3.06 kg/m3 (0.006 slugs/ft3) at a temperature andpressure of 293 K and 61495 Pa, respectively. In Tab. D.1 (located in the Appendices) the gas propertiesof Freon 12 is presented in more detail. These values were acquired using the software F-Chart (F-ChartSoftware, 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 followingphysical 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 themodel, meaning that the rotor blades did not have a weight or experienced any inertia. The blades weremodelled 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 ofnumerous force- and moment-coefficient for the blades. As seen in Eq. (6.1), the force coefficients aredefined as follows5:

CL = CD =

∑f

(fpressuref + fshearf

)· nD

ρrefArefV 2ref

(6.1)

5The definition of the force and moment coefficient in helicopter aerodynamics is slightly different compared to aeroplaneaerodynamics. In our case, a factor of one half is omitted from the denominator.

18


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 asthe freestream velocity. For lift, the direction is specified normal to that direction. Aref is defined asthe main-rotor disc area, and Vref denotes the tip velocity of the blades.

Cl = Cm = CQ =

∑f

[rf ×

(fpressuref + fshearf

)]· a

ρrefArefV 2refRref

(6.2)

Similar equation goes for defining the moment coefficient as seen in Eq. (6.2). a is the vector defining theaxis direction through an arbitrary point x0 in which the moment is taken. It defines the same propertiesas nD (for the force coefficient) but instead defines the roll, pitch and torque moment coefficient. rfis the position of each face relative to the reference point x0 of the moment vector. The pressure- andshear- force vector are defined as; fpressuref = (pf + pref )af and fshearf = −τ · af . Where pf is theface pressure, af is the face area vector, pref is the reference pressure, which was set to pref = 0. Thedisc radius Rref is included to acquire a dimensionless property. The aerodynamic forces and angles aredefined 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 datais 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 wasdone by regulating the number of n data points included in the SMA. Adding this made it easier todetermine the results from the plots, damping the fluctuation that are formed.

SMA =xM + xM−1 + xM−2 + ....+ xM−(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 setupincluded a stripped down version of the complete helicopter configuration, containing two rotor bladesand the main hub. The fuselage and the additional rotor blades were excluded to reduce the total numberof cells in the volume mesh. By narrowing down the number of cells, we managed to reduce the timeit took to generate the grid and the computed results, reducing the computation time from 48 hours tounder 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 andlsv = 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 mentionedearlier).

A cylindrical shaped volumetric control was added, it is an arbitrary volume were the user have theability to control the cell size for a specific surface/volume. This was added in the background mesh tomatch the cell size of the overset region in order to make a cutout for the overlapping regions possible. Ithad a dimension of rvc = 4 m and hvc = 1.4 m and the cell size was set to 3000 % of the base size whichcorresponded to a length of 0.03 m. In Fig. C.6 a scalar representation describing the model, with thevolumetric control surrounding blades (and the overset regions) The total cell count landed in around 5million cells.

19


Figure 6.2: Stripped version two blades removed and with no fuselage present. The blades are surrounded bylarge 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 additionalrotor blades were added to the previous model, with some modifications. The overset regions had to beresized and reshaped to an elliptical shaped cross section in order to give room to the fuselage and theadditional rotor blades (and their corresponding overset regions). Now that the fuselage were added tothe model, it proved to be difficult to shape overset boundaries that did not intersect with the fuselage orhub. For practical reasons the hub and top part were removed from the fuselage (Fig. C.9 and C.10). Thenew elliptical shape, shown in Fig. 6.3, had the dimensions of semi-major axis a = 0.1 m and semi-minoraxis 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 lengthof lcv = 1.4 m. The size of the overset region had to be large enough to encapsulate the rotor blade butsmall 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 suc-cessful cutout of the four overlapping regions. The volumetric control was added but with a thinner discshape (dcv = 3.3 m and hcv = 0.35 m), and the cell size was reduced to 1500 % (0.015 m). The final cellcount 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 oversetregions have been considerably reduced.

20


6.4.1 Hover flight

Data were obtained in hover flight with three collective pitch settings, θ0 = 5 θ0 = 10 and θ0 = 12. Theblade rotated at 640 RPM which corresponded to a nominal blade tip Mach number of MT = 0.627. Thelift- CL, drag- CD and torque-coefficients CQ were calculated using Eq. (6.1) and (6.2), with the referencevalues, ρref = 3.06 kg/m3 Vref = 96.443 m/s, Aref = 6.406 m3 and Rref = 1.428 m. These were takenfrom the the disc area, disc radius and tip velocity of the main rotor. The torque is rotating around thelocal z-axis located 102 cm from the fuselage nose. Appendix B shows the different aerodynamic forcesand moments that were monitored.

6.4.2 Forward flight without cyclic pitch

When the hover flight was completed the next step was to analyze the flight performance in forwardflight. A freestream flow was introduced to the simulation and was chosen so that the advance ratiowas set to µ = 0.2, which corresponded to a freestream Mach number of M = 0.128. As opposed toan actual/real flight case, the helicopter would need to alter the collective pitch cyclically to produce athrust vector forwards. But for this simulation no cyclic pitch was added. This did indeed affect thepitching and roll moment of the helicopter. For this purpose, two additional monitors, Cl and Cm wereadded to the simulations. Four cases were examined θ0 = 5 and θ0 = 10 at an rotor shaft angle ofattack αs = 0, and θ0 = 5 and θ0 = 10 at αs = −4.

6.4.3 Forward Flight with cyclic pitch

The purpose behind this simulation was to show the possibilities in adding cyclic pitch using the oversetmeshes. Looking at the previous flight case, the ARES-system experienced roll and pitching momentswhen no cyclic pitch was added. This was expected since the rotor blades were no longer experienc-ing uniform lift distribution in the retrieving and advancing side of the main-rotor. To remove theseunwanted moments the cyclic pitch was added to the main-rotor. Noonan’s NASA-report [8] did notmention what cyclic pitch configuration they used in their experimental setup. Without knowing thelateral (θc) and longitudinal (θs) 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 tothe model. This came down to three separate analysis were the first had a pure longitudinal cyclicmotion (θs = −1 and θc = 0) and the second had a pure lateral cyclic motion (θs = 0 and θc = −1).The third simulation used a combination of the lateral and longitudinal angles, and by using the resultsfrom the simulations with pure motion, the cyclic pitch angles θc and θs were calculated. Using a simplelinear equation system between the roll and pitching moment the equation was expressed as shown inEq. (6.4) and Eq. (6.5):

Cl = Cl,(θ=0) + Cl,θsθs + Cl,θcθc (6.4)

Cm = Cm,(θ=0) + Cm,θsθs + Cm,θcθc (6.5)

The additional variables Cl,θs , Cl,θc , Cm,θs , and Cm,θc showed how much increase/decrease the roll andpitching moment were affected when the pure cyclic motion were included. The aim was to find θc and θswhere no roll or pitching moment occurred (Cl = 0 and Cm = 0). The following variables are expressedas:

Cl,θs =Cl,(θs=−1) − Cl,(θ=0)

−1(6.6)

Cl,θc =Cl,(θc=−1) − Cl,(θ=0)

−1(6.7)

Cm,θs =Cm,(θs=−1) − Cm,(θ=0)

−1(6.8)

Cm,θc =Cm,(θc=−1) − Cm,(θ=0)

−1(6.9)

21


Cl,(θ=0) and Cm,(θ=0) were values in which the cyclic pith motion was not included (θs = 0 and θc = 0).Cl,(θs=−1), Cl,(θc=−1), Cm,(θs=−1) and Cm,(θc=−1) are defined as the roll and pitching moment valueswhen the lateral and longitudinal cyclic pitch motion was added. The value −1 denoted the change inθs and θc for respective pitching and roll moment.

The flapping and lead/lag angles were not included to reduce the complexity of the cyclic pitch mo-tion. The flapping angle was instead replaced by a constant blade coning angle that was set to β0 = 2.With a limited time for computing the simulations, the decision was made on including the cyclic pitchon only one of the previous test cases. The flight case that was chosen had a collective pitch angle ofθ0 = 5 at αs = 0.

22

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+.

7.1 Flight simulations in Hover Mode

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012−0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

Lift

Coe

ffici

ent C

L [−]

Torque Coefficent CQ

[−]

Hover Flight Characteristics CL vs C

Q

Spline functionNasa Report ResultComputational results

θ0 = 10°

θ0 = 12°

θ0 = 5°

Figure 7.1: Hover results showing CL vs CQ.

23

Main Results C.Rodriguez Helicopter Aerodynamics

7.2 Flight simulations in forward flight

−0.014 −0.012 −0.01 −0.008 −0.006 −0.004 −0.002 0 0.002−0.001

0.001

0.003

0.005

0.007

0.009

0.011

0.013

Lift

Coe

ffici

ent C

L [−]

Drag Coefficient CD

[−]

Forward Flight Main Results CL vs C

D

Exp data αs = 0°

Exp data αs = −4°

No Cyclic Results αs = 0°

No Cyclic Results αs = −4°

With Cyclic Results αs = 0° θ

0 = 5° θ

0 = 5°

θ0 = 10°

Figure 7.2: Forward flight results showing CL vs CD.

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014−0.001

0.001

0.003

0.005

0.007

0.009

0.011

0.013

Lift

Coe

ffici

ent C

L [−]

Torque coefficient CQ

[−]

Forward Flight Main Results CL vs C

Q

Exp data αs = 0°

Exp data αs = −4°

No Cyclic Results αs = 0°

No Cyclic Results αs = −4°

With Cyclic Results αs = 0° θ

0 = 5°θ

0 = 5°

θ0 = 10°

Figure 7.3: Forward results showing CL vs CQ.

24

Discussion C.Rodriguez Helicopter Aerodynamics

8 Discussion

8.1 General discussion

Supercomputer: The time to compute the simulations depended highly on which sub-cluster thatwas used. Each Skylord-node had a total of 8 cores per node (2x4) unlike Darkstar which only had 2cores (2x1). Even though each Darkstar-node had better performance (per processor), Skylord had thepossibility in using four times more cores for parallel computing that gave a faster overall performance.With a time step of 0.001 s, and with 10 inner iterations on each time step, each run took approximately1-4 days to compute depending on the number of available nodes. With a total of 96 cores (12 nodes x8 cores) in Skylord, the time to compute was not more than 48 hours. A rule of thumb states that eachcore should have at least 100 000 volume cells for calculations, which corresponded to 70 cores for ourcase (our model had 7 million cells).We decided on having 96 cores since the model had four overset meshes that needed computational powerto cut out the overlapping regions. Since other users needed to use the supercomputer, the possibility foracquiring available nodes led to simulations that went idle until slots opened up. It was hard to predictwhen the nodes were available, therefore the number of simulations were reduced from 25 (which wasthe intended number of simulations) to 15.

Overset meshes: When examining how the overset meshes worked at first, difficulties emerged whenthe four blades shared one large overset region. Previous simulations that were done proved to cut outthe overlapping regions faster, with one large region. This is since less time is spent in cutting out theoverlapping region and time in exchanging information between the interpolating cells. Since the bladesshared one large overset region the disadvantage with this method is that it constrains the blades intobe altered separately.The benefits of having separate overset regions is that; (1) The regions are independent of each other, giv-ing the possibility to move or rotate the blades without affecting the other regions.(2) Greater flexibilitycompared to standard meshing, overset meshes does not require any mesh modification after generatingthe 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 whatwe excepted when examining the results. As shown in Fig. B.18 and Fig. B.19, adding a θc angle con-trolled the roll moment, and adding a θs angle controlled the pitching moment. Comparing these resultswith the theory in section 2.3, the results did not show any indication of a 90 phase lag. Since eachblade was considered having no weight, the blades did not experience any inertial effects, thereby thegyroscopic precession was not applied for our model. The aerodynamic forces that were computed arestill valid, on the contrary, if wanting to apply the main-rotor to a flight mechanical model, then ourmodel 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 tothe actual ARES-model. This model did not state the geometry used for the horizontal stabilizer, sowe decided on using an arbitrary wing profile, NACA-0012 (Abbott and von Doenhoff, 1959, p.113 andp.321 [12]). The purpose of having the body was to redirect the flow field and to change the pressuregradient under the the main-rotor. Note that the results showed in Appendix B did not include theaerodynamic forces contribution of the fuselage and horizontal the stabilizer.Noonan’s NASA-report [8] did not provide enough detail schematics regarding the hub. When examiningthe NASA-report, it stated that tares were determined throughout the test ranges meaning that the hubdid not contribute at all to the aerodynamic forces reported. Both deadweight and aerodynamic hubtares 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 theaerodynamic forces, however it affected the redirection of the flow field at the rotor conjunction, whichmanage to emerge few vortices, as seen in Fig. C.3.

25


8.3 Meshing

Polyhedral cells: According to Peric and Ferguson (2005) [9] there are several benefits in polyhedralcells opposed to other conventional method such as tetrahedral and hexahedral cells. One downside withtetrahedral cells are that they are more restricted in cell stretching, which leads to much larger number ofcontrol volumes. Considering that tetrahedral cells only have four neighbours, computing gradients canbe more problematic. Giving the fact that a major advantage of polyhedral cells are that they have manyneighbouring faces (approximately around 10), which give gradients better approximation compared totetrahedral cells.The polyhedral cells were the preferred choice to use on the rotating blades. For a cartesian hexahedralcells, they have three optimal flow directions (six faces) which tend to constrain the accuracy whendealing with rotating flow fields. For a polyhedral with 12 faces have six directions, which together witha 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 themaster thesis. Increasing the number of cells would likely increase the time it spent on computing theresults, but presumably also improve the accuracy. As an alternative solution, higher cell resolutionwere addressed to the moving boundaries e.g the blades and regions close to the blade. This kept thecell count down and decreased the time to compute, but retained the accuracy in the solution. A gridindependence study was outside the scope of this thesis, the focus was not to optimize the grid but rathermake it work properly.

The volume mesh included prism layers to accurately capture the flow field at the surface of the main-rotor 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 ofaligning 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 deci-sion for this was based on the blades overset meshes. As mentioned in section 5.3, the wall boundariesat the overset and background meshes needed at least 4-5 cells in each mesh. Since the backgroundboundaries (hub and top fuselage) and the overset boundaries were at close proximity, the resolution ofthe boundaries were forced to increase to fulfil the requirement. To keep the number of cells down, thehub 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 monitoredaerodynamic properties on the main-rotor. As mentioned earlier, the fuselage, hub and the horizontalstabilizer were not included in the analysis of the forces and moments, only the rotor blades were includedin the results. The number of datapoints included for the SMA were between 60-200 points dependingon 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 problemsat these time steps and the calculations stopped. To continue the calculations, the time step had to beadjusted by increasing/decreasing it by 0.0001 s. As a consequence, large spikes appeared in the resultsto adjust the new time step.

Collective pitch angle: At the early stages of the master thesis we decided to select θ0 angles between0 and 10. Looking at the results indicated that we chose relative low values for the collective pitch(θ0 = 5, 10, 12). These values were based on the same configuration used in the Skeldar UAV, whichhave blades with low built in twist angle. Looking at the results in Fig. 7.1, it clearly shows that higherθ0 values where used in the experimental wind tunnel setup. Having a collective pitch extending between10 to 20 is consider high values (Leishman, 2000 [4]) , but since the blades for the ARES-model had ahigh (negative) built in pitch angle (Fig. A.4), using angles at these regions seemed reasonable.

Hover flights case: Looking at the convergence history for CL for the stripped version in Fig. B.1, thelift force is pointing downwards giving it a negative lift. This was predicted since the built in twist angleθ1 had a distribution between −7 < θ1 < 1, giving the major part of the blade a negative lift (whenθ0 = 0). Another aspect in mind was the size of the overset regions, which were reduced considerable.

26


The current size was not necessary due to the fact that according to Star CCM+ (2012) [7], the wallboundaries at the overset and background meshes needed no more then 4-5 cells in each mesh to properlywork.

Proceeding to the complete helicopter model a collective pitch was added, giving the main-rotor a posi-tive lift force. At θ0 = 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. Increasingθ0, gave larger values of the lift and torque that increased linearly (seen in Fig. 7.1). Fig. B.5 to Fig. B.8illustrates that with increasing θ0, the aerodynamic properties converged faster to a (quasi) steady-statecondition.

Helicopter forward flight (No cyclic motion): As for the flight cases with αs = 0 shown inred 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 θ0. A real flight case with αs = 0 would never bepossible since a forward thrust would never be possible to obtain. This case should therefore be seen asmore an experimental wind tunnel case, where the model is stationary and a freestream flow is affectingit.For the simulation where θ0 = 10 at αs = −4 , the lift coefficient decreases with about 0.001 units,indicating that the main-rotor has developed a thrust component. This is shown in the computed resultsin Fig. 7.2, which clearly shows that CD has a negative value giving it thrust forward (positive valuegives drag resistance, while a negative value give thrust). However, the thrust has a very low valuecompared to the experimental data which has comparably 40 times bigger forward thrust than the CFDresults. This can be due to the fact that the cyclic pitch motion was not included in the analysis, givingthe drag resistance an increased value. However this can not be concluded since simulations with cyclicpitch motions were not done at these flight regions.

Helicopter forward flight (with cyclic motion): Looking at Fig. B.18 and Fig. B.19, the pitchand roll moment were successfully removed with the configuration θ0 = 5 at αs = 0. Examining thepure longitudinal cyclic motion showed that adding a negative θs gave a positive roll moment. Thisshowed that θs needed to be a positive value to induce a negative roll moment. Fig. B.18 showed thatthe roll moment was already close to zero, meaning that a small positive value of θs was needed. Thelateral cyclic motion indicated that adding θc = −1 reduced the pitching moment. This did not entirelyremove the pitch moment which Fig. B.19 illustrates. Therefore increasing θc (negatively), the pithingmoment was reduced.

From this and with Eq. (6.4) and Eq. (6.5) it was found that Cl and Cm equals zero for θs = 0.2462

and θc = −1.6779.

27

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. Thiswould not be the case if all four blades shared one large overset region. Having independent oversetregions needed more computational power to successfully cut out the overlapping regions. Withonly one overset mesh however, leads to less time to cut out the overlapping regions, therebyreducing the time it takes to compute the simulations. This came down to a tradeoff betweencomputational power versus computational time.

• By adding the cyclic pitch motion at θ0 = 5 and α = 0, the roll and pitching moment weresuccessfully removed from the results with small interference effects on CL. With this to say,including an additional flapping angle is possible by modifying the existing model. This willcontribute 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) whichclosely matched the experimental data. At higher collective pitch angles the aerodynamic valuesfluctuated more but converged faster to its quasi-steady state. The flight case with the settingθ0 = 10 at αs = −4 gave drag results that deviated 10 times more compared to the size of theexperimental values. This led to a discussion regarding how much the lack of a cyclic pitch affectedthe drag, giving the possibility in future investigations on examining the affect in including cyclicpitch motion.

• It is a bit misleading to say that CFD with overset meshes is a better method than momentumtheory, we merely found an alternative CFD method for analyzing helicopter aerodynamics. Oneimportant aspect is that using overset meshes gives more freedom in anlyzing non-uniform liftanalysis e.g cyclic pitch motion. This cannot be done with momentum theory and is therefore thebiggest advantage of overset meshing.

28

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 Hackstrom and Nenad Jankovic for giving me this opportunity to write my master thesis herein Saab. For assistance and support I want to thank Per Weinerfelt and Lars-Erik Berg for providingme the theory and tools for this thesis. And of course, thank you for all support from my family andfriends, special thanks to Norah Sakal who helped me get in touch with Saab Aeronautics. I want togive my sincere gratitude to Marie Malmgren who constantly motivated me throughout this thesis, andreminded me to never settle for less, I thank you.

29

Appendix A C.Rodriguez Helicopter Aerodynamics

References

[1] CD-adapco, 2012Overset Mesh specifications, Websitehttp://www.cd-adapco.com/news/2012/03-08_starccmv7

Last retrieved 2012-08-04

[2] Naval Technology, 2011Skeldar UAV article, Websitehttp://www.naval-technology.com/projects/skeldar-v-200-maritime-uav/


[3] Arthur Rizzi, 2011Aerodynamic Design a Computational ApproachStockholm, KTH Department of Aeronautical and Vehicle engineering

[4] J. Gordon Leishman, 2000Principles of Helicopter AerodynamicsCambridge University Press

[5] John D. Anderson Jr, 1995Computational Fluid dynamics, The basics with applicationsMcGraw-Hill inc,ISBN 0-07-113210-4

[6] Innovative CFD, 2007Making Sense of CFD Grid Types, Websitehttp://www.innovative-cfd.com/cfd-grid.html


[7] CD-adapco, 2012Star CCM+ (Version 7.02) [Computer software]http://www.cd-adapco.com/products/star_ccm_plus/index.html


[8] Kevin W. Noonan, William T. Yeager Jr, Jeffrey D. Singelton, Matthew L. Wilbur and Paul H.Mirick, 2001Wind Tunnel Evaluation of a Model Helicopter Main-Rotor Blade With Slotted Airfoils at the TipNASA TP-2001-211260, 2001

[9] Milovan Peric and Stephen Ferguson, 2005 [Article]The advantage of polyhedral meshesDynamics, p.4-5

[10] F-Chart Software(2012) F-chart (Version 6.76) [Computer software]http://www.fchart.com/


[11] Fig.D.1, Langley Research Center, 2001Images containing top view of ARES-modelhttp://www.nasa.gov/centers/langley/home/index.html


[12] Ira H. Abbott and Albert E. von Doenhoff, 1959Theory of wing sections: including a summary of airfoil data.Dover Publications

30

http://www.cd-adapco.com/news/2012/03-08_starccmv7

http://www.naval-technology.com/projects/skeldar-v-200-maritime-uav/

http://www.innovative-cfd.com/cfd-grid.html

http://www.cd-adapco.com/products/star_ccm_plus/index.html

http://www.fchart.com/

http://www.nasa.gov/centers/langley/home/index.html


A Appendix A

Blade geometry and CAD-model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1

0.2

0.3Root Chord RC(4)−10

Figure A.1: Root chord.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1

0.2

0.3Tip Chord RC(6)−08

Figure A.2: tip chord.

31


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1

0.2

0.3Horiziontal Stabilizer NACA−0012

Figure A.3: Horizontal Stabilizer.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−10

−8

−6

−4

−2

0

2Rotor Blade Twist

Bui

lt in

twis

t ang

le d

istr

ibut

ion

θ 1 [deg

]

r/R [−]

Figure A.4: Built in twist angle distribution θ1.

32


Upper surface Lower surface

Station Ordinate Station Ordinate

0 -0.0057 0 -0.0057

0.0029 0.0043 0.0047 -0.0159

0.0091 0.0132 0.0144 -0.0218

0.0235 0.0260 0.0165 -0.0227

0.0470 0.0389 0.0252 -0.0257

0.0737 0.0480 0.0356 -0.0282

0.1002 0.0537 0.0619 -0.0316

0.1261 0.0573 0.0850 -0.0323

0.1518 0.0598 0.1082 -0.0320

0.1772 0.0616 0.1321 -0.0313

0.2026 0.0630 0.1561 -0.0306

0.2278 0.0642 0.1805 -0.0303

0.2530 0.0651 0.2049 -0.0303

0.3031 0.0666 0.2295 -0.0304

0.3531 0.0674 0.2541 -0.0307

0.3781 0.0674 0.3034 -0.0314

0.4033 0.0672 0.3529 -0.0321

0.4284 0.0665 0.3777 -0.0324

0.4537 0.0655 0.4023 -0.0326

0.4789 0.0640 0.4270 -0.0326

0.5038 0.0621 0.4515 -0.0325

0.5287 0.0599 0.4760 -0.0322

0.5536 0.0573 0.5009 -0.0317

0.5785 0.0545 0.5257 -0.0310

0.6034 0.0515 0.5506 -0.0301

0.6283 0.0481 0.5754 -0.0291

0.6532 0.0446 0.6003 -0.0279

0.6782 0.0409 0.6251 -0.0267

0.7030 0.0371 0.6500 -0.0255

0.7277 0.0333 0.6748 -0.0243

0.7525 0.0295 0.6998 -0.0231

0.7772 0.0258 0.7248 -0.0219

0.8017 0.0224 0.7498 -0.0206

0.8263 0.0191 0.7749 -0.0193

0.8510 0.0161 0.8001 -0.0178

0.8757 0.0132 0.8253 -0.0162

0.9005 0.0105 0.8504 -0.0144

0.9254 0.0080 0.8754 -0.0124

0.9502 0.0057 0.9004 -0.0103

0.9750 0.0037 0.9253 -0.0081

1.0000 0.0018 0.9502 -0.0057

0.9751 -0.0032

1.0000 0.0002

Table A.1: Design Coordinates for RC(4)-10 Airfoil. [8]

33


Upper surface Lower surface

Station Ordinate Station Ordinate

0,000 -0.0040 0,000 -0.0040

0.0010 0.0005 0.0040 -0.0110

0.0030 0.0040 0.0070 -0.0128

0.0098 0.0111 0.0152 -0.0156

0.0221 0.0187 0.0279 -0.0182

0.0476 0.0276 0.0524 -0.0214

0.0748 0.0329 0.0752 -0.0234

0.0988 0.0359 0.1012 -0.0252

0.1245 0.0381 0.1255 -0.0265

0.1493 0.0398 0.1507 -0.0276

0.1747 0.0413 0.1754 -0.0286

0.2000 0.0426 0.2000 -0.0294

0.2248 0.0436 0.2252 -0.0302

0.2499 0.0444 0.2501 -0.0309

0.3001 0.0457 0.2999 -0.0321

0.3499 0.0466 0.3501 -0.0329

0.3749 0.0468 0.3751 -0.0330

0.4000 0.0468 0.4000 -0.0330

0.4250 0.0466 0.4250 -0.0328

0.4500 0.0461 0.4500 -0.0323

0.4750 0.0454 0.4750 -0.0316

0.5000 0.0444 0.5000 -0.0306

0.5251 0.0432 0.5246 -0.0296

0.5503 0.0417 0.5496 -0.0285

0.5752 0.0401 0.5748 -0.0273

0.6002 0.0382 0.5998 -0.0262

0.6255 0.0360 0.6245 -0.0249

0.6504 0.0338 0.6496 -0.0237

0.6756 0.0314 0.6744 -0.0223

0.7003 0.0288 0.6997 -0.0210

0.7256 0.0261 0.7244 -0.0196

0.7509 0.0234 0.7491 -0.0181

0.7754 0.0207 0.7746 -0.0166

0.8004 0.0181 0.7996 -0.0150

0.8254 0.0156 0.8246 -0.0135

0.8503 0.0130 0.8497 -0.0118

0.8752 0.0106 0.8748 -0.0102

0.9001 0.0082 0.8999 -0.0085

0.9250 0.0061 0.9250 -0.0067

0.9500 0.0043 0.9500 -0.0048

0.9749 0.0028 0.9750 -0.0027

1.0000 0.0010 1.0000 -0.0002

1.0000 0.0010 1.0000 -0.0002

Table A.2: Design Coordinates for RC(6)-08 Airfoil. [8]

34


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


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

Appendix B C.Rodriguez Helicopter Aerodynamics

B Appendix B

Simulation convergence history

B.1 Hover stripped version results

0 0.1 0.2 0.3 0.4 0.5−0.014

−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

0Hover Flight Comparison (Stripped Version)

Time t [s]

Lift

Coe

ffici

ent C

L [−]

Computational plot θ0 =0°

Moving Average plot

Figure B.1: Stripped hover version showing CL vs t for the main-rotor.

0 0.1 0.2 0.3 0.4 0.5−0.0002

−0.0001

0

0.0001

0.0002Hover Flight Comparison (Stripped Version)

Time t [s]

Dra

g C

oeffi

cien

t CD

[−]

Computational plot θ0 = 0°

Moving Average plot

Figure B.2: Stripped hover version showing CD vs t for the main-rotor.

37


0 0.1 0.2 0.3 0.4 0.50.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005

0.00055Hover Flight Comparison (Stripped Version)

Time t [s]

Tor

que

Coe

ffici

ent C

Q [−

]

Computational plot θ0 = 0°

Moving Average plot

Figure B.3: Stripped hover version showing CQ vs t for the main-rotor.

0 0.1 0.2 0.3 0.4 0.5−1200

−1150

−1100

−1050

−1000

−950

−900

−850Hover Flight Comparison (Stripped Version)

Time t [s]

Sur

face

Ave

rage

Pre

ssur

e P av

[Pa]

Computational plot θ0 =0°

Moving Average plot

Figure B.4: Stripped hover version showing pav vs t for the main-rotor, which includes the surfaces of the twoblades.

38


B.2 Hover complete results

0 0.1 0.2 0.3 0.4 0.50

0.002

0.004

0.006

0.008

0.01

0.012

0.014Hover Flight Comparison

Time t [s]

Lift

Coe

ffici

ent C

L [−]

Computational plot at θ0 = 5°



Moving Average plot

Figure B.5: Complete hover version showing CL vs t for the main-rotor.

0 0.1 0.2 0.3 0.4 0.5−0.0002

−0.0001

0

0.0001


Time t [s]

Dra

g C

oeffi

cien

t CD

[−]




Moving Average plot

Figure B.6: Complete hover version showing CD vs t for the main-rotor.

39


0 0.1 0.2 0.3 0.4 0.50.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005


Time t [s]

Tor

que

Coe

ffici

ent C

Q [−

]




Moving Average plot

Figure B.7: Complete hover version showing CQ vs t for the main-rotor.

0 0.1 0.2 0.3 0.4 0.5−1200

−1150

−1100

−1050

−1000

−950

−900

−850

Hover Flight Comparison

Time t [s]

Sur

face

Ave

rage

Pre

ssur

e P av

[Pa]




Moving Average plot

Figure B.8: Complete hover version showing pav vs t for the main-rotor, which includes the surfaces of the fourblades.

40


B.3 Forward flight no cyclic pitch results

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0

0.002

0.004

0.006

0.008

0.01No Cyclic Pitch Flight Comparison

Time t [s]

Lift

Coe

ffici

ent C

L [−]

θ0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.9: Forward flight with no cyclic pitch showing CL vs t for the main-rotor.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−0.0004

−0.0003

−0.0002

−0.0001

0

0.0001

0.0002

0.0003


Time t [s]

Dra

g C

oeffi

cien

t CD

[−]

θ

0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.10: Forward flight with no cyclic pitch showing CD vs t for the main-rotor.

41


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045


Time t [s]

Tor

que

Coe

ffici

ent C

Q [−

]

θ0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.11: Forward flight with no cyclic pitch showing CQ vs t.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−0.0005

0

0.0005

0.001

0.0015


Time t [s]

Rol

l Mom

ent C

oeffi

cien

t Cl [−

]

θ0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.12: Forward flight with no cyclic pitch showing Cl vs t for the main-rotor.

42


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018


Time t [s]

Pitc

hing

Mom

ent C

oeffi

cien

t Cm

[−]

θ0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.13: Forward flight with no cyclic pitch showing Cm vs t for the main-rotor.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−1200

−1150

−1100

−1050

−1000

−950

−900

−850

−800No Cyclic Pitch Flight Comparison

Time t [s]

Sur

face

Ave

rage

Pre

ssur

e P av

[Pa]

θ0 = 5° α

s= 0°

θ0 = 10° α

s= 0°

θ0 = 5° α

s = −4°

θ0 = 10° α

s = −4°

Figure B.14: Forward flight with no cyclic pitch showing pav vs t for the main-rotor, which includes the surfacesof the four blades.

43


B.4 Forward flight cyclic pitch results

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

−0.0016

−0.0012

−0.0008

−0.0004

0

0.0004

0.0008

0.0012

0.0016

Cyclic Pitch Flight Comparison at θ0 = 5° α

s= 0°

Time t [s]

Lift

Coe

ffici

ent C

L [−]

no cyclic θs = 0° θ

c= 0°

long cyclic θs = −1° θ

c= 0°

lat cyclic θs = 0° θ

c = −1°

long/lat cyclic θs = 0.2462° θ

c = −1.6779°

Figure B.15: Forward flight with cyclic pitch showing CL vs t for the main-rotor.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−0.0002

−0.0001

0

0.0001

0.0002


s= 0°

Time t [s]

Dra

g C

oeffi

cien

t CD

[−]


c= 0°


c= 0°


c = −1°


c = −1.6779°

Figure B.16: Forward flight with no cyclic pitch showing CD vs t for the main-rotor.

44


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5e−05

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004


s= 0°

Time t [s]

Tor

que

Mom

ent C

oeffi

cien

t CQ

[−]


c= 0°


c= 0°


c = −1°


c = −1.6779°

Figure B.17: Forward flight with no cyclic pitch showing CQ vs t for the main-rotor.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

−0.001

−0.0005

0

0.0005

0.001

0.0015

0.002


s= 0°

Time t [s]

Rol

l Mom

ent C

oeffi

cien

t Cl [−

]


c= 0°


c= 0°


c = −1°


c = −1.6779°

Figure B.18: Forward flight with no cyclic pitch showing Cl vs t for the main-rotor.

45


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−0.0012

−0.0008

−0.0004

0

0.0004

0.0008

0.0012


s= 0°

Time t [s]

Pitc

hing

Mom

ent C

oeffi

cien

t Cm

[−]


c= 0°


c= 0°


c = −1°


c = −1.6779°

Figure B.19: Forward flight with no cyclic pitch showing Cm vs t for the main-rotor.

46

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 0.001 m(100 % of the base size).

Figure C.2: Image representing the tail surface meshing of the ARES-model.

.

47


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 bladeedge.

48


Figure C.6: A scalar representation showing a cutout on the region were the overset and background regionoverlapp.

Figure C.7: A similar figure as the previous one, but instead representing the active (yellow), inactive (red) andacceptor (blue) cells of the model.

49


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 withoutthe top part.

50

Appendix D C.Rodriguez Helicopter Aerodynamics

D Appendix D

Gas Properties

Gas Property Value Unit

cp 606.51 J/(kg ·K)

k 9.393 mW/(m ·K)

µ 12.357 µPa/s

MR12 120.93 kg/kmol

Pr 0.7979 -

afreon 150.73 m/s

Table D.1: Freon 12 gas properties at T = 293 K and p = 0.61494 bar. The molar mass MR12 above givesthe specific gas constant RR12

specific = 68.753 J/(kg · K), which with cp above give cv = 537.757 J/(kg · K) andγ = 1.128.

Langley Research Center Image

Figure D.1: Additional top view geometry from Langley Research Center. (Langley Research Center, 2001 [11])

51


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


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


Figure D.6: Flapping angle definition, showing the longitudinal flapping with the coning angle. Lateral flappingis defined the same but βc is replaced by βs and with a 90 phase shift in ψ. (Leishman, 2000 [4])

Figure D.7: Pitching angle definition.(Leishman, 2000 [4])

54

CFD Analysis of Rotor Blade of Helicopter

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