Study and Design of an Axial Fan

IN

DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2020 ,

Study and Design of an Axial Fan

Safran Engineering Services / Airbus Helicopters

ALEXIS DORANGE

Study and Design of an Axial Fan

Safran Engineering Services / Airbus Helicopters

Alexis Dorange

Master’s Degree Project Master in Aerospace Engineering

Academic supervisor and examiner:

Evelyn Otero Sola Company supervisor:

Jean-Christophe Coquillat

KTH Royal Institute of Technology

Aeronautical and Vehicle Engineering Department

SE-100 44, Stockholm, Sweden

Abstract

The cooling system is a crucial part for helicopter operations. Without

it, hovering flight could not be operated. The cooling system for the main

gearbox of a helicopter is composed of radiators and a fan. A fan is an

aerodynamic body and as such it can be improved in terms of aerodynamic

efficiency. Therefore di↵erent parameters need to be taken into account when

designing a new axial fan to have good aerodynamic performance. Simula-

tions have been carried out to investigate the e↵ects of these parameters and

come up with an optimal design based on the study requirements. The fan

has to enable the cooling system to evacuate an amount of thermal power so

that the helicopter can take o↵ with high outside temperatures. This optimal

design has shown an increase of the mass flow rate up to a factor of about

two for a given pressure loss compared to the original fan.

Referat

Kylsystemet ¨ar en avg¨orande del f¨or en helikopters drift. Utan den kan

helikoptern inte hovra. Kylsystemet f¨or huvudv¨axeln hos en helikopter best˚ ar

av radiatorer och en fl¨akt. En fl¨akt ¨ar en aerodynamisk kropp och kan d¨arf¨or

f¨orb¨attras g¨allande aerodynamisk e↵ektivitet. D¨arf¨or m˚ aste olika parame-

trar ¨overv¨agas n¨ar man utformar en ny axialfl¨akt f¨or att f˚ a god aerody-

namisk prestanda. Simuleringar genomf¨ordes f¨or att unders¨oka e↵ekterna

av dessa parametrar och komma fram till en optimal utformning baserad p˚ a

unders¨okningskraven. Denna optimala utformning har visat en ¨okning av

massfl¨odet upp till en faktor p˚ a cirka tv˚ a f¨or en given tryckf¨orlust j¨amf¨ort

med den ursprungliga fl¨akten.

Acknowledgements

I wish to thank Mr. HONNORAT, project leader, for welcoming me in his department for this project. I wish to thank particularly Mr. COQUILLAT for mentoring me and guide me throughout this project with good advice, for trusting me to do the best I could and achieve the target fixed. For helping me when I needed help, whether in the professional or the personal domain.

I also thank Mr. SERR for helping me during the trainee, for his expertise in the helicopter domain and for his joy everyday that makes everyone want to work. I wish to thank both of them to have trusted me with this tremendous project and motivated me when I had hard times. I also want to thank Mr.

BARRAUD for helping me with CAD software when I was struggling. I

want to thank Mr. DELECROIX, Mr. BLANCHARD and Mr. BIANCO

for my integration during the first month of my trainee period. I also want

to thank all the people in the department for welcoming me and integrate

me so quickly in the team. It has been a real pleasure to work with such a

devoted and competent team. Finally I wish to thank Ms. OTERO SOLA

for her advice, for the help provided and for her time and attention.

Contents

1 Introduction 1

2 Background 3

2.1 Safran Engineering Services . . . . 3

2.2 Airbus Helicopters . . . . 4

2.2.1 History . . . . 4

2.2.2 H130 . . . . 6

2.3 Basics of aerodynamics . . . . 6

3 Methodology 9 3.1 CFD Tools . . . . 9

3.1.1 Governing equations . . . . 9

3.1.2 The Case Study . . . 10

3.1.3 Turbulence model . . . 12

3.1.4 Wall Treatment . . . 12

3.2 Mesh realization and control . . . 14

4 State Of The Art 18 5 Parameter investigation 22 5.1 Parameter definition . . . 22

5.2 Blade thickness . . . 24

5.3 Blade angle . . . 25

5.4 Number of blades . . . 26

5.5 Chord distribution . . . 27

5.6 Deflection . . . 27

5.7 Twisting law . . . 28

6 Fan Design Analysis 29 6.1 Low Power Consumption Based Design . . . 29

6.2 High Mass Flow Rate Based Design . . . 30

6.2.1 New shape of the hub . . . 31 6.3 CFD Correction . . . 31

7 Mechanical Sizing 33

7.1 Beam Theory . . . 33 7.2 Finite Element Analysis . . . 34

8 Conclusion 35

List of Figures

2.1 Safran Engineering Services Logo. . . . 3

2.2 Eurocopter EC665 Tigre. . . . 4

2.3 Eurocopter logo. . . . 4

2.4 Airbus Helicopters logo. . . . 5

2.5 H160 first pre series exemplar and military model ”Gu´epard”. 6 2.6 H130 in flight . . . . 6

2.7 Airfoil nomenclature [1]. . . . 7

2.8 Aerodynamic forces [2]. . . . 8

3.1 Domain of Computation. . . 11

3.2 Torque and axial force created on the fan by air. . . 11

3.3 An example of local impermeability. . . 14

3.4 Skewness theory illustration with the ideal cell size (green), and the current cell created by the meshing tool (purple). . . . 15

3.5 Example of a skewness correction. . . 15

3.6 Section of the volume mesh when cutting horizontally the do- main of computation at the middle of the fan. . . 16

3.7 Continuity, velocity, energy, k and epsilon residuals. . . 16

4.1 Given CAD (left) and more accurate (right) CAD of the stan- dard fan of the H130. . . 19

4.2 Complete fan (rotor, stator and grid) design with CAD (left) and simplified for CFD computation (right). . . 19

4.3 Target point, working curve of the original fan and aim of the study (thick red line). . . 20

4.4 Comparison between CFD computations and test on the orig- inal fan. . . 20

4.5 Comparison of turbulence models in Ansys on the original fan. 21 5.1 Airfoil of the original fan. . . 22

5.2 Thickness and curvature of an airfoil. . . 23

5.3 Blade angle and twist t of a fan blade. . . 23

5.4 Velocity triangle for the H130 fan. . . 24 5.5 E↵ect of the blade thickness on the mass flow rate and the

power consumed. . . 24 5.6 E↵ect of the blade angle on the mass flow rate and the power

consumed by the fan. . . 25 5.7 Evolution of mass flow rate (left) and efficiency (right) with

respect to the AoA at fixed pressure losses PL1 and PL2. . . . 26 5.8 E↵ect of the number of blades, namely 6 (T1C1 6B) and more

than 6 (T1C1 B1) on the mass flow rate and power consumed by the fan. . . 26 5.9 E↵ect of chord distribution on the mass flow rate and power

consumed by the fan. With T2 the original chord distribution and T2 Chord the new chord distribution. . . 27 5.10 E↵ect of the deflection on the mass flow rate and power con-

sumed by the fan. . . 27 5.11 E↵ect of twisting law on the mass flow rate and power con-

sumed by the fan. . . 28 6.1 Fan performance for a design based on low power consumption. 29 6.2 Fan performance for a design based on high mass flow rate. . . 30 6.3 Fan performance for a design based on high mass flow rate

with a new hub. . . 31 6.4 Corrected final design fan performance. The full lines being

CFD results and the dashed the test and the scaled final design. 31

7.1 Geometry simplification of a fan blade. . . 33

Nomenclature

Abbreviations

AH Airbus Helicopters AoA Angle of Attack

CAD Computer-Aided Design

CETIAT Centre Technique des Industries A´erauliques et Thermiques CFD Computational Fluid Dynamics

MRF Multiple Reference Frame N-S Navier-Stokes

RANS Reynolds-Averaged Navier-Stokes SES Safran Engineering Services

Symbols

↵ Angle of Attack Blade Angle

⌧ Stress Tensor D

Dt Material derivative r¨ Divergence Operator

⌘ Efficiency

g Body acceleration

q Heat flux

u Flow velocity B Partial Derivative

⇢ Density

C D Drag Coefficient C L Lift Coefficient

D Drag

E Total Energy per unit of mass

L Lift

p Pressure

q Mass Flow Rate

Re y Turbulent Reynolds number

t Time

y ^` Dimensionless wall distance

Chapter 1 Introduction

Cooling systems are of various forms and for numerous applications : power plants, engines, electric systems, etc. The objective of a cooling system is to cool down an electronic or a mechanical device, such as an engine. A cooling system comprises a closed loop of fluid which cools down the device by exchanging heat with it, and a radiator which cools down the fluid with air. Moreover this last exchange is accelerated by a fan.

On light helicopters, a cooling system regulates the temperature of hot parts like the engine, the main gearbox and other components. The system is composed by radiators and a fan. Due to the capacity of a helicopter to fly in hover, without any relative wind, the cooling fan has to ensure a fresh air flow through the radiators in all weather conditions otherwise the engine risks to be overheated. The radiators are placed after the air intake at the top cover of the machine. Following these radiators is the fan that blows directly into the main transmission box.

As part of the continuous improvement of its product range, Airbus He- licopters is seeking to improve the cooling system for the main gearbox and engine on the H130 helicopter. The standard fan of the H130 is a commer- cial fan built for trucks in the USA. It was sufficient at the beginning but constant power improvements have led to an overheating when the outside atmospheric temperature is too high, preventing the helicopter to even take o↵. In this project , the axial cooling fan of the H130 is studied in order to deal with the temperature limitations. However, the stator and the electronic command of the fan will stay the same so the study is limited to the blades and hub of the fan.

The approach used for the study is divided in several steps. First the

original fan is characterized to identify its current performance and the one

that needs to be fulfilled. Then a parameter study is carried out with Com-

putational Fluid Dynamics (CFD) simulations to assess the impact of these

parameters on the fan. Based on this analysis, an optimal design is defined and then characterized through calculations.

The report starts with a general background on the companies involved,

the helicopter under consideration and the basics of aerodynamics. Then the

CFD based methodology is presented, followed by the parameter investiga-

tion, the design analysis, and some conclusions.

Chapter 2 Background

This chapter provides a brief history of the companies involved in this project, namely Safran Engineering Services, where the project has been carried out, as a subcontractor for Airbus Helicopters. The H130 helicopter considered in this analysis is presented, followed by a brief background to aerodynamics.

2.1 Safran Engineering Services

Safran Engineering Services (SES) is part of the Safran group and a sub- sidiary of Safran Electrical & Power. The company provides hi-tech engi- neering services to the aerospace, energy and ground transport industries.

Figure 2.1: Safran Engineering Services Logo.

The French company is born from the merger of Teuchos and Labinal’s Engineering and Technology division. Labinal Power Systems was a major company in the aeronautic sector and was created in 1921 specialised in design, production and implementation of electric wires in the aeronautic sector.

Safran Engineering Services is selling its expertise in the following do- mains: electrical systems, aerostructures, mechanical and software systems and On-board electronic systems.

Today, SES employs more than 3,700 people on 19 sites in 10 countries,

working as a subcontractor for most of the major aerospace companies. SES’s

customers are mainly in the aeronautics sector, but they are also present in the automotive, energy, rail and space industries in companies such as:

Airbus, Airbus Helicopters, Dassault Aviation, PSA... [3]

2.2 Airbus Helicopters

2.2.1 History

Airbus Helicopters is the world’s leading manufacturer of civil helicopters and one of the leading manufacturers of military helicopters. It was cre- ated under the name Eurocopter in 1992 from the merger of the helicopter divisions of the French company A´erospatiale (SNIAS) and the German com- pany Deutsche Aerospace (DASA). In 2000, the merger of Daimler Chrysler Aerospace with the Spanish company Construcciones Aeron´auticas gave birth to EADS. Eurocopter joined the group in 2014 with Airbus, Cassidian and Astrium. Eurocopter becomes a wholly owned subsidiary of EADS and car- ries out a number of major co-operations such as the Tiger combat helicopter, or broader co-operation with the Germans, French, Italians and Dutch for the European NH90 transport helicopter program.

Figure 2.2: Eurocopter EC665 Tigre.

Figure 2.3: Eurocopter logo.

Since January, 1 ^st 2014 the EADS Group has changed its name to Airbus

Group. This choice of communication lies in a desire to strengthen collabo-

ration between the di↵erent entities of the Airbus group and to rely on the

strong reputation of the Airbus name in order to find new markets for all

activities. On January, 7 ^th 2014 Eurocopter changed its name to Airbus

Helicopters.

Figure 2.4: Airbus Helicopters logo.

The head office of Airbus Helicopters Division is located in Marignane, France. It employs about 12,000 workers, including 3,000 subcontractors [4].

Airbus division Helicopters is the world’s leading manufacturer and exporter of civil helicopters. The group’s mission is to design, produce and market high-tech helicopters for military, parapublic (ministries other than the army) and civil customers. The company also provides related services (after-sales service, training, etc.). The helicopter’s advantages are its ability to take o↵ and land vertically, to access cramped areas and to move slowly in all directions. Its high manoeuvrability allows it to adapt to specific situations such as:

‚

Combat: reconnaissance, anti-tank combat, support and protection of ground troops, transport of troops or equipment.

‚

Firefighting

‚

Civil transport (sightseeing flight) and VIP transport

‚

Evacuation of people in distress, on land, sea or mountain

‚

Oversight of police and customs services

‚

The transport of goods

‚

Lifting of construction equipment

The success of Airbus Helicopters is based on a very wide range of prod- ucts and the reliability of its aircraft. The Group’s products account for 30%

of the world’s entire helicopter fleet. The company’s latest product is the

H160, a new medium-tonnage helicopter. It features design elements and

modern engine technology. It stands out in particular for its exceptional

maneuverability and excellent acoustic performance. The pre-series model

has been in circulation since the beginning of 2019 and orders have already

been received. The military version of this aircraft, the H160M, christened

Gu´epard, was officially presented at the last International Paris Air Show at

Le Bourget. The first flight has been announced for 2023.

Figure 2.5: H160 first pre series exemplar and military model ”Gu´epard”.

2.2.2 H130

The H130 is a member of Airbus’ Ecureuil family, which represents 42% of Airbus’ in-service fleet and has accumulated more than 33 million flight hours worldwide. There are more than 646 H130s operated in 50 countries. The H130 is an intermediate single-engine helicopter with three blades on the main rotor tailored for passenger transportation, sightseeing and VIP duties, medical airlift, law enforcement and surveillance missions. It has a cabin up to 7 passengers and a range of 617 km and a fast cruise speed of 128 knots (237km/h [5] ). As the best-selling helicopter of the company the continuous improvement is common on this helicopter so all components need to be carefully investigated to adapt to those upgrades.

Figure 2.6: H130 in flight

2.3 Basics of aerodynamics

In this study the aerodynamic of the fan will be changed so a quick overview

of aerodynamic forces and vocabulary is provided.

Figure 2.7: Airfoil nomenclature [1].

An airfoil is described by its geometry Fig 2.7: the upper surface and lower surface, the leading edge which is the point at the front that has the maximum radius and corresponds to the stagnation point. The trailing edge is defined at the other end of the airfoil. The chord c, Fig 2.8, is the line defined between the leading and the trailing edge. The mean camber line is the line defined midway between the upper and lower surfaces; it depends on the thickness and camber. The angle of attack ↵ is the angle between the relative wind direction U ₈ , Fig 2.8, and the chord line [6].

The aerodynamic force is the force that the fluid is applying on the body

in which it is submerged due to the relative motion between the body and

the fluid, Fig 2.8. Depending on the chosen axes one can distinguish di↵erent

sets of components of the resultant aerodynamic force R. With respect to the

body axes, the two components are the normal force N and the axial force

A, perpendicular and parallel to the airfoil chord line respectively. Moreover,

the lift L, and the drag D, are the components of the aerodynamic force in

the freestream axes where the lift is the force perpendicular to the direction

of freestream velocity U ₈ and the drag is parallel to the relative freestream

velocity [7].

Figure 2.8: Aerodynamic forces [2].

They are defined as:

# L “ Ncos↵ ´ Asin↵

D “ Acos↵ ` Nsin↵ (2.1)

From these forces are calculated the lift and drag coefficients that depends on the geometry and on the fluid characteristics:

C L “ 2L

⇢SU ₈ ² ; C D “ 2D

⇢SU ₈ ² (2.2)

With ⇢ is the density of the fluid, S is the wing surface area and U ₈ is the

freestream velocity.

Chapter 3

Methodology

This chapter goes through the theory behind CFD and the models used in this trainee. It also explains the domain used and the quantities measured.

3.1 CFD Tools

3.1.1 Governing equations

CFD codes solve the continuity, momentum and energy equations. These coupled partial nonlinear di↵erential equations are in general not easy to solve numerically and analytical solutions are available for only very few limited cases. The equations in case of incompressible fluid which will be the case for this study are the following [8].

$ ’

’ ’

’ ’

’ ’

&

’ ’

’ ’

’ ’

’ % B⇢

Bt ` r ¨ p⇢uq “ 0 Continuity

⇢ Du

Dt “ ´r ¨ p ` r ¨ ⌧ ` ⇢ g Momentum Bp⇢Eq

Bt ` r ¨ p⇢EVq “ r ¨ p⌧ ¨ Vq ` ⇢g ¨ V ` r ¨ q Energy

(3.1)

Where ⇢ is the density of the fluid, u is the Eulerian velocity vector of a fluid particle, ⌧ is the viscous constraints tensor, p is the pressure, g is an exterior surface force, E is the total energy per mass unit and q is the heat flux.

The first equation is the continuity equation and comes for the mass

conservation. The second is the Cauchy momentum equation or momentum

conservation equation and comes from the second Newton law. The third

equation is the energy equation and come from the global energy of the system.

The system 3.1 is a system of non-linear partial di↵erential equations.

The non-linearity occurs in the material derivative in the momentum equa- tion. In order to solve it, boundary conditions are fixed. The CFD packages use various numerical methods based on a mesh [9]. Finite-element methods require a 2D or 3D mesh and are very flexible in terms of geometry and mesh elements. At each mesh element, a base function is used. This base function should locally describe the solution of (or part of) the governing equation to be approximated. The finite-element method aims to minimize the di↵erence between the exact solution and the collection of base functions [10]. How- ever, problems in the fluid-mechanics area are generally governed by local conservation. For instance, the continuity equation dictates the local con- servation of mass. Local conservation is not necessarily a property of the finite-element method, since the di↵erence between the base functions and the exact solution is minimized globally. Most of the CFD packages are using Finite Volume Method for the mesh since it is based on local conservation.

To solve the equations numerically with the finite volume method, the en- tire computational domain is divided into ‘small’ sub-volumes, so-called cells.

Employing Gauss’ law, the partial derivatives expressing a conservation prin- ciple, such as r¨u, can be rewritten at each cell as an algebraic contribution.

The governing equations are reformulated, at each computational cell, into a set of linear algebraic equations. These equations are solved in an iterative manner afterwards. The price for this so-called discretization of the domain is the introduction of a numerical error into the solution [11].

For this simulation the Reynolds-Averaged Navier-Stokes (RANS) equa- tions are solved to simplify the turbulence modelling and computations. They are time-averaged equations of motion. The method is based on the decom- position of every variable into the mean value and the fluctuating value of the variable. Moreover the derivation of a mean value is equal to zero, so this decomposition will greatly help to solve the equations.

3.1.2 The Case Study

In order to compute the new designs that will be made the CFD package

Ansys Fluent which solves the RANS equations is used. For the simulation

to give satisfactory results an appropriate domain needs to be created. Here

it is a tube long enough before the fan for the air to stabilize and after the

fan for the flow to converge toward a stable flow. To simulate the rotation

of the fan the MRF (Multiple Reference Frame) meshing option in Ansys is

used. The MRF is a steady-state approximation in which rotational and/or

translational speeds can be assigned to cell zones. It does not account for the relative motion of a moving zone around other zones, in this case the mesh remains fixed for the computation. It can be compared to freezing the motion of the moving cell zone in a specific position and computing the instantaneous flow field with the moving zone in that position [12]. To calculate the mass flow rate the pressure loss is imposed thanks to a parameter that will fix the pressure at the pressure inlet and outlet. As the rotation is simulated thanks to the MRF, the other surfaces will be set as walls. This gives the following domain:

Figure 3.1: Domain of Computation.

The result is a fairly light mesh of around 15 million elements in 2D, at the scale of the company which is used to have 50 millions elements mesh in 2D. The computation is realized in few hours thanks to the company means, which are clusters of thousand cores dedicated to performing calculations.

For this study the AH process requires to use RANS equations and a k ´ ✏ turbulence model which is commonly used in this kind of simulations.

Figure 3.2: Torque and axial force created on the fan by air.

The force on the rotation axis created by the fan which is the result of

the lift created by the blades, and the torque on the fan which is the result of

the drag created by the blades are computed in this simulation. The forces are shown on Fig 3.2. And powers can be calculated from these forces:

P aero “ F ^axis v and P nec “ T ! (3.2) where P aero is the aerodynamic power given by the force along the rotation axis created by the blades F axis and the fluid velocity along that axis v. And P nec is the necessary power to rotate the fan and is given by the torque T and the rotational speed of the fan !. This power will then be assimilated to an electric power. In Eq. 3.2, the speed v is obtained with the measured mass flow rate q and the stator surface around the fan S:

v “ q

S (3.3)

And the efficiency of the fan is:

⌘ “ P aero

P _nec (3.4)

3.1.3 Turbulence model

The k ´✏ model is a two-equation turbulence model which make it one of the simplest turbulence models. The two equations are two separate transport equations based on the turbulence energy k and the dissipation rate ✏. These two equations allow the turbulent velocity and length scales to be indepen- dently determined. Compared to the standard k ´ ✏ model, the Realizable k ´ ✏ model contains a new formulation for the turbulent viscosity and a new transport equation for the dissipation rate ✏. It is likely to provide supe- rior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation, strong streamline curvature, vortices, and rotation [13] [14].

3.1.4 Wall Treatment

The Enhanced Wall Treatment is the wall function that is going to be used for

the simulations. It is a near wall model that combines enhances wall functions

with a two-layer model. If the near-wall mesh is fine enough to be able to

resolve the viscous sublayer: y ^` « 1, then the enhanced wall treatment will

be identical to the traditional two-layer zonal model. However, the restriction

that the near-wall mesh must be sufficiently fine everywhere might cause a

very large mesh and an important computation requirement. Ideally, it is

better to have a near-wall formulation that can be used with both coarse and

fine meshes.

The Enhanced Wall Treatment is then a near-wall modelling approach that is capable of modelling with accuracy a fine near-wall mesh without significantly reducing the accuracy for wall-function meshes by combining the two-layer model with enhanced wall functions.

The viscosity-a↵ected near-wall region is entirely resolved all the way to the viscous sublayer with the near-wall model . The two-layer approach is an integral part of the enhanced wall treatment and is used to specify both ✏ and the turbulent viscosity in the near-wall cells. In this approach, the domain is divided into one viscosity-a↵ected region and one fully-turbulent region.

The separation of the two regions is determined by a wall-distance-based, turbulent Reynolds number, Re _y , defined as:

Re y ” ⇢y ? k

µ (3.5)

where y is the wall-normal distance from the nearest wall and is calculated at the cell centers with the following equation:

y ” min

~

r

P

}~r ´ ~r w } (3.6)

where ~r is the position vector at the field point, and ~r w is the position vector of the wall boundary. w is the union of all the wall boundaries involved. With this interpretation y is uniquely defined in the flow domain and is independent of the mesh topology.

In the fully turbulent region ( Re y ° 200), the k- ✏ model is employed whereas in the viscosity-a↵ected near-wall region ( Re y † 200), the one- equation model of Wolfshtein [15] is employed. In the one-equation model, the momentum equations and the k equation are retained.

To extend the method to the near-wall region, the CFD software blends the linear (laminar) and logarithmic (turbulent) laws-of-the-wall:

u ^{`</sup> “ e u <sup>`} lam ` e

u ^` _turb (3.7) where the blending function is given by:

“ ´ a py ^` q ⁴

1 ` by <sup>`</sup> (3.8)

where a “ 0.01 and b “ 5.

The software will then calculate the wall-function to apply to every region

to keep y ^` † 60 [16].

3.2 Mesh realization and control

To realize a good mesh the geometry need to be simplified first. In fact there can be some useless surfaces such as holes for screws or chamfers on surfaces.

Also some volumes can be simplified as surfaces. The domain needs to be created according to the Fig 3.1. To create a good mesh it needs to be more refined where its behaviour will change. For this case the mesh needs to be refined on the blades with even closer refinement at the leading and trailing edge. The boundary layer is meshed with the wall functions that has been described before. After meshing, the permeability of the mesh needs to be checked. In fact it can happen that some surfaces are not glued and that the nodes on both surfaces do not correspond to each other. A tool allows to join all the surfaces of the model, but it has a limitation that implies local modification by hand.

Figure 3.3: An example of local impermeability.

On Fig 3.3 it can be seen that the two surfaces has not been joined perfectly. These are two surfaces of di↵erent parts. So it has to be done by hand. After checking the permeability and repairing the potential errors, the quality of the mesh needs to be checked and it is done by checking the skewness. The skewness allow to check the quality with the following formula:

Skewness “ optimal cell size ´ cell size

optimal cell size (3.9)

Figure 3.4: Skewness theory illustration with the ideal cell size (green), and the current cell created by the meshing tool (purple).

The optimal cell is an equilateral triangle represented in green in Fig. 3.4 and the current cell is the one in purple. The 2D skewness is a value between 0 and 1. If the cell is an equilateral triangle the skewness will be 0. In this project the mesh has been generated to keep the skewness lower than 0.5.

Figure 3.5: Example of a skewness correction.

The volume mesh is an unstructured mesh with tetrahedral elements. A

section of the volume mesh is given in the following figure.

Figure 3.6: Section of the volume mesh when cutting horizontally the domain of computation at the middle of the fan.

On the figure above one can see the refinements near the surface of the fan and around the stator part on the left. The wall treatment can also be seen on the same parts. The blue zone is the MRF zone so it is refined compared to the tube in purple.

The residuals given by the computation are the following:

Figure 3.7: Continuity, velocity, energy, k and epsilon residuals.

On all the residuals one can observe that when the inlet pressure changes

it forms a spike and that every sub computation for every pressure value is

converging to a stable solution.

Chapter 4

State Of The Art

In this chapter, the original fan is analyzed and characterized showing the di↵erence between the CFD results and a test on the original fan. Note that due to confidentiality reasons, sensitive information has been omitted from the results.

As previously said the standard fan was initially designed for trucks and

is used by the company on the H130. The fan was earlier designed on

Computer-Aided Design (CAD) software thanks to surface mapping, but

its design was incorrect so the airfoil has been redesigned in order to create

a more accurate design. In addition to the fan, there are also structural

parts such as a stator and a grid that comes with the fan furnished by the

manufacturer.

Figure 4.1: Given CAD (left) and more accurate (right) CAD of the standard fan of the H130.

Figure 4.2: Complete fan (rotor, stator and grid) design with CAD (left) and simplified for CFD computation (right).

With the pressure loss in the circuit and with the characteristics of the fan given by CETIAT, namely the company which provided tests and certifica- tion for fans, the working point of the fan was found. This point is defined as the intersection of the two curves namely Pressure Loss and Working Curve Fan, see Fig. 4.3. The target working point for the new fan, called from now on simply target point, was calculated and appears as a black diamond on the figure.

The target point corresponds to the mass flow rate and pressure loss

the new fan has to achieve in order to prevent a overheating of the main

gearbox when the H130 is performing a hover flight at the maximum outside temperature specified on the requirements specification with the maximum mass onboard it can carry. This point is very important since it will be our goal when designing the new fan. In this study the goal is to change the working curve to make it intersect with the pressure loss in the circuit at the target point as show the thick red line in Fig 4.3.

Figure 4.3: Target point, working curve of the original fan and aim of the study (thick red line).

The electric circuit that powers the fan will neither be changed. So in this study we will keep the power specifications on the H130 which will give a limit in electric power. This design is simulated in order to compare the simulation results with the test results in terms of pressure loss, mass flow rate and required power. The test results are furnished by CETIAT which measured the speed and pressure on the fan to give a working curve.

Figure 4.4: Comparison between CFD computations and test on the original

fan.

One can observe that in terms of pressure loss, the simulation is close to the test for a simple model. Moreover, the CFD computation gives more linear behaviour than the test. The CFD computations show a margin of power compared to the H130 limitation. This calculation will be used as a reference to compare CFD results and real results. The final design will be therefore scaled with that di↵erence, see Sec 6.3. However, no data is available for the power consumption of the original fan so this part can no be scaled.

In the Ansys article [13] it is recommended to be careful when using the Realizable k- ✏ model with MRF, therefore a computation has been realized to compare the e↵ects. The results show that the realizable model is more accurate than the standard one, as shown in the Fig. 4.5. In fact, the computation with the realizable k- ✏ model gives closer results with respect to the CETIAT data so it will be used for all the computations.

Figure 4.5: Comparison of turbulence models in Ansys on the original fan.

Chapter 5

Parameter investigation

This chapter provides a description of all the parameters found a↵ecting the aerodynamic performance of the axial fan and how they a↵ect the perfor- mance.

5.1 Parameter definition

As we can see in Fig. 5.1, the blade airfoil used on the original fan seems to show room for improvement, so this will be firstly changed.

Figure 5.1: Airfoil of the original fan.

It then raised the question of the thickness as shown on Fig 5.2 of the airfoil which has been analyzed. Another parameter is the blade angle and the angle of attack illustrated on Fig 5.3 (left). The angle of attack can change along the blade which will create a twist as shown on Fig 5.3 (right).

This is called the twisting law of the blade and it will be also analyzed. The

e↵ect of the number of blades on the fan is also an important parameter of

the study. And deflection has been added to the blade to characterize its

e↵ect. Finally, the chord distribution along the blade was changed. For the profile of the blade several thicknesses were used: a thick one called T1, and two thinner ones T2 and T3. The measured blade angle on the original fan is called C0 and di↵erent angles C1, C2 will be tried where C1 †C0†C2. A linear and a calculated twisting law will be tested. The e↵ect of the number of blades will be compared with respect to the original configuration of six blades and we define B1 as a number of blades with B1 °6.

Figure 5.2: Thickness and curvature of an airfoil.

Figure 5.3: Blade angle and twist t of a fan blade.

C3 is the blade angle to have a zero angle of attack, calculated using the velocity triangle at the leading edge, illustrated in Fig 5.4. According to the ONERA article on design of turbomachines [17], the triangle is defined by:

$ ’

&

’ %

U ~ “ ~R ^ ~!

V ~ “ ~q{⇢S W ² “ U ² ` V ²

(5.1)

Where ~ R is the radius and ~! is the rotational speed of the fan. ~q is the mass

flow rate, ⇢ is the density of the fluid and S is the surface of fluid a↵ected by

the fan. Those quantities define the rotating speed of air ~ U and the absolute

speed of air ~ V . From these vectors is calculated ~ W , the relative speed as seen by the rotor. From this triangle we find the blade angle .

“ atan ˆ U

V

˙

(5.2)

Figure 5.4: Velocity triangle for the H130 fan.

This angle is calculated for di↵erent radius of the blade and this gives the twist distribution along the blade. This is by definition the angle distribution for a zero angle of attack.

5.2 Blade thickness

The three di↵erent thicknesses T1,T2 and T3 have been used for the analysis, with the same blade angle and same twisting law to see only the e↵ect of thickness.

Figure 5.5: E↵ect of the blade thickness on the mass flow rate and the power consumed.

In Fig 5.5, T1 which is the thickest airfoil, gives the best mass flow rate

at same pressure loss (Fig. 5.5 left) but also requires the highest power to

rotate the fan (Fig. 5.5 right). And T3, the thinnest airfoil gives the lowest

mass flow rate but requires the lowest power. Therefore a thicker airfoil

gives better performance in terms of mass flow rate and with higher required

power. In fact the thicker the airfoil is, the higher the lift coefficient will be

resulting in an increase in terms of mass flow rate. However, a thicker airfoil will also imply more drag and by consequence more power consumption.

5.3 Blade angle

This simulation has been carried out with the same airfoil thickness and same twisting law in order to observe the e↵ect of the blade angle. The blade angle

is defined by:

↵ “ ´ 0 (5.3)

where 0 is the blade angle for zero angle of attack that has been calculated in Section 5.1 and ↵ is the angle of attack. So a big blade angle gives higher mass flow rate and higher power is required to rotate the fan since a higher angle of attack will give more lift but also more drag.

Figure 5.6: E↵ect of the blade angle on the mass flow rate and the power consumed by the fan.

In Fig 5.6 (left) with C1 °C0°C2 defined in increasing order a particular

behaviour is observed with the C2 blade angle. In fact the curve presents

waves which are the sign of local stalling on the blade so a stalling study

needs to be conducted. To perform this analysis, the software Xfoil and

the Ansys software are used. Xfoil is a 2D analysis software to study the

aerodynamic performances of airfoils. A 2D analysis has been carried out

on the airfoil for di↵erent angles of attack to study the performances and

identify the stalling of the profiles used. With CFD computations the blades

are characterized for di↵erent blade angles. The evolution of mass flow rate

and efficiency with respect to the angle of attack are studied to detect the

stalling on the blade.

Figure 5.7: Evolution of mass flow rate (left) and efficiency (right) with respect to the AoA at fixed pressure losses PL1 and PL2.

In Fig. 5.7 a phase of decrease in the efficiency and a deceleration in the linear growth of the mass flow rate can be observed. These two phases are actually starting at the same angle of attack so the same blade angle according to Eq. 5.3. For further calculations this angle will be used and called C4.

5.4 Number of blades

As for the blade angle analysis, Fig 5.8 shows that an increase in number of blades resulting in a bigger surface area, will generate lift but also more drag.

This will increase the mass flow rate and the power consumption respectively.

Figure 5.8: E↵ect of the number of blades, namely 6 (T1C1 6B) and more than 6 (T1C1 B1) on the mass flow rate and power consumed by the fan.

This analysis has been realized with T1 being the thinner airfoil, C1 being the lowest blade angle and B1 °6. From Fig 5.8 one can observe that the gap with respect to the target has been reduced by adding blades.

However we can also observe that for a small pressure loss, the design

with more blades generates a smaller mass flow rate but also a smaller power

consumption compared to the design with 6 blades. This comes from the

overlapping of blades that prevent air to follow the normal path and then goes through less surface creating less drag and lift consequently.

5.5 Chord distribution

For this study the same number of blades is kept with the medium thickness T2 and the same blade angle. The chord distribution tested is designed so that the same gap is kept along the blades of the two test cases.

Figure 5.9: E↵ect of chord distribution on the mass flow rate and power consumed by the fan. With T2 the original chord distribution and T2 Chord the new chord distribution.

From Fig 5.9, we can clearly see that the chord distribution has a minimal impact on the performance so the original chord distribution will be kept.

5.6 Deflection

For this study deflection is added on the blade at mid radius of the blade.

This study has been realized with the thick airfoil T3 and the blade angle C4 described in Section 5.3. In the T3C4 Deflect case, a deflection of 20 % of the chord is applied at mid radius.

Figure 5.10: E↵ect of the deflection on the mass flow rate and power con- sumed by the fan.

The deflection itself should not have almost any impact on the results but

we can observe a slight di↵erence. This is due to the fact that the path of

the airflow is not the same with the deflection. In fact, it will encounter the deflected part in the first place changing the local behaviour of the air. The result is that it creates less lift so makes the fan move away from the target but also less drag so less power consumed by the fan.

5.7 Twisting law

From Eq. 5.2 defining the blade angle with the velocity triangle and Eq. 5.1 defining the vectors of the triangle in Sec. 5.1, the angle that gives a zero angle of attack can be computed at every radius of the blade. The di↵erence between the angle at the tip and at the root is the twist of the blade. With these calculations an appropriate twisting law for the whole blade can be calculated. But for simplicity reasons, it can be approximated by a linear growth between the root and the tip of the blade. This study is carried out with the optimal blade angle C4 which is near the stall angle. The risk of the linear law is that it creates local stalling, worsening the performance of the blades, whereas the law calculated previously ensures the design to be at the stall angle along the blade.

Figure 5.11: E↵ect of twisting law on the mass flow rate and power consumed by the fan.

The result is that the calculated law is giving less drag so consuming less

power as can be seen on Fig 5.11 (right), and on the left part of the figure

one can see that the calculated law also creates more lift so gives a higher

mass flow rate making the design slightly closer to the target. Consequently,

this twist will be kept for all designs.

Chapter 6

Fan Design Analysis

In this chapter, di↵erent fan designs are analysed based on the previous parameter investigation. An iterative approach is used focused on di↵er- ent characteristics in order to maximise the performance of the original fan design.

6.1 Low Power Consumption Based Design

The first design is focused on low power consumption to see the margin it could have in terms of power compared to the limitation, while aiming at obtaining the best trade o↵ between low power consumption and high mass flow rate. So in this design, the blades have a low blade angle to ensure a low power consumption as seen in the previous section. From the e↵ect of the number of blades the gain of mass flow rate and the cost in power consumption of one blade was calculated, so the design was defined with a new number of blades B2 with B2 °B1, which would give good performance but also have a higher cost in power consumption. Therefore a low blade angle was used for that design to lower the power consumption. A medium thickness profile was chosen which would give moderate performance and require less power than the original part.

Figure 6.1: Fan performance for a design based on low power consumption.

It is clear from the figure above that this iteration did not give great results since it has poor performance when subjected to a low pressure loss and consume more than the original fan. After focusing on the power con- sumption, the next step aims to increase the mass flow rate.

6.2 High Mass Flow Rate Based Design

In this iteration the optimal blade angle obtained from the stalling study in Section 5.3 is used in order to have a high mass flow rate. However this angle will also bring a lot of drag so the power consumption of this fan design will be higher than the previous one. The same airfoil has been used in this analysis, namely a medium thick profile. This design has the same number of blades as in the previous analysis, namely B2.

Figure 6.2: Fan performance for a design based on high mass flow rate.

This design is clearly better in terms of mass flow rate for a given pressure loss but it is also worse in terms of drag since the blades have a higher angle.

Yet, there is a little margin in terms of power and the target in performance

has not been yet reached. So additional performance improvements needs to

be obtained. In the following section, the hub is changed.

6.2.1 New shape of the hub

In the third iteration the design is centered on a new hub. In fact, for now the air collides on a plan, so it creates local turbulence and the air which arrives on the root of the blades is not perfectly laminar preventing the root to work as it should. So in order to gain performance an eclipsed shape hub has been used which will propagate the air more properly towards the blades.

This solution gives a higher mass flow rate, improving the fan design. This design will be considered in this project as the optimal and final design.

Figure 6.3: Fan performance for a design based on high mass flow rate with a new hub.

6.3 CFD Correction

After implementing a number of improvements to the fan design, a correction needs to be applied on the CFD results with respect to the results from Section 4 on the comparison between the CFD results of the original fan and CETIAT results and as said no data on the power consumption was available for the original so there are no scaling possible in terms of power.

Figure 6.4: Corrected final design fan performance. The full lines being CFD results and the dashed the test and the scaled final design.

As shown in Fig 6.4, after correction the final design of the fan gives

an even better performance with a mass flow rate increase up to a factor

of about two for the pressure loss at the target point compared to the real

original fan (CETIAT).

Chapter 7

Mechanical Sizing

After finishing the design, the question of mechanical sizing was raised to ensure that there will not be any mechanical issue with the new design such as the blades getting broken.

7.1 Beam Theory

The beam theory is the first approach used to perform an analysis. The blade is assimilated to a parallelepiped as shown in Fig 7.1 The forces applied on a blade are the aerodynamic force and the centrifugal force. The centrifugal force will create traction and the aerodynamic force will create bending.

Figure 7.1: Geometry simplification of a fan blade.

F c “ L! ² m blade ; c “ F c

S (7.1)

Where F c is the centrifugal force and is defined by the length of the blade L,

its mass m _blade and the rotational speed of the fan !. The torsion constraint

c created by the centrifugal force is defined with the surface S “ ce and R which is the distance from the root to the centre of gravity.

The flexion is given by:

f “ RF aero

I e

2 ; I “ ce ³

12 (7.2)

Where _f is the flexion constraint and is defined with the aerodynamic force F aero and the second moment of area I.

The total constraint t is obtained by adding the two ones :

t “ c ` f (7.3)

It is compared to the limit constraint of the material. If the total constraint is below the material limit constraint the beam will not break but if it is higher the geometry needs to be changed.

In order to test this fan geometry, it has been 3D printed by powder sintering. So the total constraint needs to be compared to the powder prop- erties. With this method, a constraint was obtained inferior to the limit so the design was validated with this method and consequently the blades will not break when subjected to air.

7.2 Finite Element Analysis

The beam model has been created with many simplifications of the shape.

The CAD software that has been used to design the fan also enables to

perform a quick Finite Element Analysis. In this approach a blade is meshed

and the resultant of the two forces is applied on the centre of gravity. This

method gives a di↵erent total constraint from the last one due to the di↵erent

assumptions but it is still below the material constraint. So this study has

shown that the blades will not break while working.

Chapter 8 Conclusion

The original fan of the H130 has been investigated for further improvements.

Through a parameter investigation an optimal design has been defined with a higher blade angle, a non-linear twisting of the blades, a medium thick airfoil, a higher number of blades and an eclipsed shape hub. With this op- timal design the fan performance gets closer to the target point calculated with the H130 specifications. The gap with respect to the target point was decreased by a factor of about two compared to the original fan. Finally, a mechanical sizing study has shown that the blades will not break when the fan is working, validating the final design.

As a future work this study has proven that the study requirements were

too limiting so there is a need to find a way too change the requirements. This

could be by increasing the power given to the fan which would allow some

changes on the fan itself or on the rotational speed. It could also concern the

modification of the structural parts around the fan since the current one were

not designed for the new blade profile. These parts could also be changed to

design a bigger fan. A test should be carried out to characterize the new fan

design and after validation of the gain a series of tests should be performed

before its installation on the helicopter.

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