Experimental Approach to the Feasibility of an Axially-Stacked Propeller System

Home , Blade pitch, Propeller (aeronautics)

A thesis submitted to the

Graduate School of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE (M.S.)

in the School of Aerospace Systems

of the College of Engineering and Applied Science

University of Cincinnati

July 2014

Schuyler Nichols

B.S., Aerospace Engineering, University of Cincinnati

Committee Chair: Shaaban Abdallah, Ph.D. ABSTRACT

The aerospace industry is experiencing an ever increasing demand for cheaper, quieter, and more efficient propulsion systems. This demand has placed much pressure on engineers to further explore the uses of existing technology to levels that in times past did not seem possible, due to limited technology capabilities. One form of research that has re-gained much attention in the past couple decades is the use of propeller driven systems. Propellers are unique in the sense that they can be manipulated in many ways to fit the needs of a certain demand. The intention of this thesis is to use an experimental approach to expand on this line of thinking in the form of a single shaft, axially stack propeller system. This experimentation is intended to explore the propulsion effects of this said system.

The experiment itself was run using two common R/C aircraft propellers mounted on a single shaft that was attached to an electric motor. The axial distance between the propellers was increased at each new stage of the experiment, during which downward force was monitored and recorded at designated RPM’s of the motor. At each axial distance, as well as each RPM setting, the propellers were also adjusted to designated relative angles to one another. Overall, the experiment was broken down into three phases. The first phase used two propellers of equal diameter and pitch. The second phase used a smaller diameter propeller stacked on top of a larger diameter propeller, with each propeller having the same pitch. The third phase used a larger diameter propeller stacked on top of a smaller diameter propeller, once again with each propeller

i having the same pitch. For all three configurations, the relative angle between the propellers was varied from 0° to 135°, at increment s of 45°.

For the most part, the results of the experiment can most effectively be explained by the Actuator Disc Theory, seeing that the before mention third phase of the experiment performed the most efficiently, as opposed to the second phase, which performed the least efficiently.

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ACKNOWLEDGMENTS

I would first like to recognize and express my gratitude to my advisor, Dr. Shabban

Abdallah, who has always remained patient with me and consistently helped guide me in the right direction, even during times that were inconvenient to him.

My appreciation also goes out to all the other Aerospace Faculty and Staff members who have assisted me during this long process of research, study and compilation of this thesis. I am forever grateful for all assistance I was so freely given to help complete this thesis, no matter how small.

A special thanks goes out to Mark Cerrezin and Dave Lang for their technical assistance, as well as Mohammed Shaheen for his assistance with CFD related issues.

I would also like to thank my loving Parents who have consistently believed in me and cheered me on in my endeavors since the day I was born. I have always been mindful of my Mother’s prayers in my behalf and have truly felt the Lord blessing me throughout all my endeavors.

Finally, I would like to thank my wife and my son for their patience, love, and support. I am forever indebted to my wife for the sacrifices she has so willingly made in order to make it possible for me to reach my academic goals.

TABLE OF CONTENTS

ABSTRACT ...... i

ACKNOWLEDGMENTS ...... iv

LIST OF SYMBOLS ...... x

LIST OF FIGURES ...... vii

Chapter 1 ...... 1

1.0 Introduction ...... 1

1.1 Motivation ...... 2

1.2 Propeller Basics ...... 4

1.3 Aerodynamic Approaches to Propeller Analysis and Design ...... 6

1.4 Systems with Similar Configurations ...... 11

1.4.1 Contra-Rotating Propeller Systems ...... 11

1.4.2 Wind Farms and Tandem Wind Turbines ...... 13

Chapter 2 ...... 20

2.0 Experimental Setup ...... 20

2.1 Experimental Procedure ...... 25

2.2 Experimental Uncertainty ...... 28

2.2.1 Scale Uncertainty ...... 28

2.2.2 Air Density Uncertainty ...... 29

2.2.3 RPM Uncertainty ...... 30

2.2.4 Uncertainty in the Mean ...... 31

Chapter 3 ...... 33

3.0 Effect of the Support Plate ...... 33

3.1 Effect of Relative Angles Between Propellers ...... 38

3.1 Effect of Axial Distance Between Propellers ...... 39

3.2 Miscellaneous Observations ...... 40

3.3 Discussion ...... 41

Chapter 4 ...... 46

4.0 Conclusions ...... 46

REFERENCES ...... 48

APPENDIX A ...... 51

APPENDIX B ...... 67

LIST OF FIGURES

Figure 1: Axially Stacked Propeller ...... 2

Figure 2: Parts of a Propeller ...... 4

Figure 3: Propeller Blade Cross Section ...... 5

Figure 4: Propeller Pitch and Slip ...... 6

Figure 5: Propeller Stream Tube ...... 8

Figure 6: Blade Element Method ...... 10

Figure 7: Contra-Rotating Propeller ...... 11

Figure 8: Example of Velocity Triangle of Contra Rotating Propellers ...... 13

Figure 9: Wind Turbine Farm Arrangement ...... 14

Figure 10: Co-Rotating and Counter-Rotating Tandem Wind Turbines ...... 16

Figure 11: Dual Contra-Rotating Wind Turbine ...... 18

Figure 12: Thin Electric Propellers ...... 20

Figure 13: Bodine Electric 3317 Motor ...... 21

Figure 14: Bodine Electric 3921 Controller ...... 22

Figure 15: Frame Assembly ...... 22

Figure 16: Virtual Measurements and Control Model VW-330A-C Scale ...... 23

Figure 17: Overall Setup ...... 24

Figure 18: Tektronix TDS 1002B Frequency Counter ...... 25

Figure 19: Propeller Configurations ...... 25

Figure 20: Relative Angle Between Propellers ...... 27

Figure 21: Scale Uncertainty v.s. Scale Output ...... 28

Figure 22: RPM Uncertainty v.s. RPM ...... 31

vii

Figure 23: Thrust v.s. Distance from Support Plate ...... 35

Figure 24: FloeEFD Cartisian Grid ...... 36

Figure 25: Flow into propeller (FloEFD Simulation) ...... 37

Figure 26: "5x5 over 7x5" Propeller Configuration Stream Tube ...... 41

Figure 27: "7x5 over 7x5" Propeller Configuration Stream Tube ...... 43

Figure 28: "7x5 over 5x5" Propeller Configuration Stream Tube ...... 44

viii

LIST OF EQUATIONS

Equation 1: Momentum Theory ...... 9

Equation 2: Blade Element Theory ...... 10

Equation 3: Propeller Thrust ...... 29

Equation 4: Peak Frequency Variation ...... 30

Equation 5: Mean Value Uncertainty ...... 32

LIST OF SYMBOLS

Symbol: Description:

Coefficient of Thrust C

D Diameter

Propeller Diameter D

dD Drag

dL Lift

dT Thrust

f Frequency

N Number of Data Values

n Rotational Speed (rev/s)

ppm Parts Per Million

R Radius

r Radial Distance from Axis of Rotation

Hub Radius r

T Total Thrust

Maximum Thrust Value T

Minimum Thrust Value T

u Externally Induced Velocity Vector

Advanced Velocity V

Resultant Velocity V

Freestream Velocity Vector V

v Rotor Induced Velocity Vector

Velocity of Incoming Airflow v

Additional Velocity, Acceleration by Propeller ∆v

W Total Velocity Vector

Z Number of Propeller Blades

α Angle of Attack

β Inflow Angle

∆f Peak Frequency Variation

Ω Rotational Speed (rad/s)

ωr Rotational Speed

Air Density ρ

Subscript:

a Air Quantity

Chapter 1

Background Information

1.0 Introduction

The main objective of this thesis is to physically evaluate a specific type of propeller system in order help determine its feasibility.

Since the dawn of controlled flight, the propeller has been a main source of propulsion for aircraft of all shapes and sizes, and for many decades was the source of much research. It seemed that the speed at which propeller design progressed was limited only by what technology could provide in terms of material and manufacturability.

With the advent of the jet age, extensive research on propellers seemed to fall by the wayside for more than fifty years, in favor of the faster and more powerful method of jet propulsion.

Within the last couple of decades, the constant issues of increasing fuel prices and the never ending demand for cheaper forms of propulsion has once again made the propeller a subject of great interest. The demand for cheaper propulsion has sometimes brought with it the requirement of a more simplified approach to existing technology. Existing propeller systems such as contra-rotating blades, or constant speed propeller systems, are very complex and can be costly to produce, and costly to maintain. By comparison, an axially stacked propeller system on a single shaft is a much simpler system that has much potential.

In this study I will use an experimental approach to determine the feasibility of this before mentioned axially stacked propeller system. Since I am not attempting to accommodate any particular aircraft design, I am left with the luxury of using readily available off the shelf propeller designs to perform my study. The study will consist of two propellers that are stacked some axial distance along a single shaft, as seen in figure 1.

Figure 1: Axially Stacked Propeller

For this study I will confine my evaluation of this concept by using only two bladed propellers.

1.1 Motivation

Most propeller research appears to more or less be focused on single rotor systems that fall within the realm of blade geometry, blade pitch, and number of blades. The main reason for this is because by keeping the system confined to a single rotor system, one is able to avoid the extra cost, complexity, and weight that come with multi

2 propeller systems, such as the contra-rotating propeller. As I thought about the contra rotating propeller, my attention continued to focus on the overwhelming complexity of the dual shafts and gear box that are required to make such a system work. I began to wonder if there was any way that a multi-rotor system could remain simple, yet still be able to produce an increase in performance when compared to a single rotor system.

The only way that I could conceive of avoiding dual shafts and gearboxes was to avoid the contra rotating system all together, and simply place two propellers on a single rotating shaft that are set at some axial distance between one another. I was sure that I was not the only person to think of such an idea, so I figured the available literature on the subject would be abundant. However, much to my surprise, this was not the case.

In my extensive search to find anything on the subject, I managed to come across a study that was performed by Knesnik [8] .

By using a modified blade element/momentum solver to perform the aerodynamic analysis, Knesnik was able to evaluate the performances of a 2-bladed propeller, 4- bladed propeller, and an axially stacked propeller, each at their highest desirability conditions. By comparing the results, Knesnik was able to prove that the axially stacked propeller system did in fact outperform the 4-bladed propeller in thrust and efficiency, at least theoretically.

With seeing such promising results from Knesnik, as well as the fact that any further literature on the subject of axially stacked propellers is scarce at best, I decided to take the concept that Knesnik had presented and perform an experimental validation.

However, unlike Knesnik who included an acoustic analysis in his study, my research

3 will be completely focused on the thrust aspect of performance improvement. The focus on acoustic performance will be performed separately in a future study.

1.2 Propeller Basics

Before one can fully appreciate the information that this thesis provides, one must first understand the basics of what a propeller is and how it works.

To put it simply, the propeller is what converts an engine’s work into a force that can be used. This is basically achieved by generating thrust from an engine’s horsepower in order to push or pull an airplane forward. The “Blade” is one of the limbs of the propeller that extends from the hub to the tip, as seen in figure 2. Propellers typically have a minimum of two blades, but can number up to several blades on certain propeller designs. The “Hub” is the center part of the propeller that carries the blades and is fitted directly onto an engine’s shaft. The “Shank” is the part of the blade that begins to become very thick as you get closer to the center of the propeller. The “Tip” is the part of the blade that is the farthest away from the center of the propeller. The

“Leading Edge” is the part of the blade that cuts through the air when the propeller is spinning. The opposite edge of the blade is of course called the “Trailing Edge”. The

“Blade Back” is the surface of the blade that can be seen if one was to be standing in front of an airplane. The “Blade Face” is the part of the blade surface that can be seen if one was to be standing behind an airplane.

Figure 2: Parts of a Propeller [1]

If we were to take several different propeller designs and slice a 2-dimensional cross section from one of the blades on each propeller, we would notice that there are certain features that are common to every blade. The “Chord Line” is the direct distance between the leading edge and trailing edge of the blade. The “Blade Angle” is the angle between the chord line and the plane that is perpendicular to the axis of rotation. The “Angle of Attack” is the angle between the chord line and the relative direction of the oncoming wind. The “Camber” is the asymmetry between the curvatures of the face of the blade and the back of the blade.

As seen in figure 3, the 2- dimensional cross section of a propeller blade also appears to resemble the airfoil of an airplane wing. This resemblance is not a coincidence by any means and actually plays a very important role in the how a propeller works.

Figure 3: Propeller Blade Cross Section In general, the propeller is a series of airfoils that are rotating about an axis. When said airfoils rotate through the air they create a lifting force that is very much like the lifting force of a wing that forces an airplane into the air. However, due to the horizontal

5 axis that a propeller is mounted onto relative to an aircraft’s fuselage, this said lifting force is called “thrust” and is the force that pulls or pushes an aircraft forward.

The overall motion of the propeller with respect to the air is much like a cork screw that is being driven into the cork of a bottle. The distance that a propeller moves forward from a single revolution is known as the “geometric pitch”, as shown in figure 4.

However, in the real world there are several factors, which we will not get into, that cause a number of inefficiencies in a propeller’s performance. Because of these inefficiencies the geometric pitch from a propeller’s rotation is almost never achieved.

The actual forward distance that a propeller achieves from a single revolution is known as the “effective pitch”. The difference between the geometric pitch and the effective pitch is what is known as the “slip”.

Figure 4: Propeller Pitch and Slip [1]

1.3 Aerodynamic Approaches to Propeller Analysis and Design

First of all, it is not my intention to provide in depth presentation of the propeller analysis and design, but rather a glimpse into some of the more popular methods that have been developed and are still used today.

Mathematical models have long been used as a method of analysis and design of propellers, even before the airplane was ever brought onto the scene. The reason for this was because the propeller had already been the main source for marine propulsion for quite some time and the demands for ever more efficient propellers systems for boats continues to this day. With the advent of the airplane propeller and the fact that it works on the same concept as marine propellers, these useful mathematical models were quickly adapted to the realm of aircraft propeller design as well.

One of the oldest and most widely used modeling methods is a simple1- dimensional approach known as the “Momentum Theory” (Rankine 1865 & Froude

1885), or the “Actuator Disk Theory”, which uses the following assumptions: 1.) The flow is ideal (inviscid and steady); 2.) The propeller is seen as a disk to represent an infinite number of blades, each with an infinite aspect ratio; 3.) The propeller produces thrust with no rotation in the slipstream.

As seen in the figure 5, the stream tube is the most common way to illustrate the propeller when working with the Momentum Theory. The propeller is represented as an actuator disk with air moving along the stream tube and passing through the disk

(neglecting compressibility).

Figure 5: Propeller Stream Tube

On a side note, the stream tube’s bizarre shape is caused by “conservation of mass” principles as the air becomes accelerated by the propeller. Due to the fact that the mass of air passing through the stream tube must be constant, the increase in velocity leads to a contraction of the stream tube that is passing through the propeller disk. In addition to the stream tube contraction, the propeller also adds a swirl component to its outflow (wake). The amount of swirl that occurs is dependent upon the rotational speed of the engine, and is a major factor that eats up energy, which is not available for thrust anymore. Well-designed propellers typically loose about 1-5% of their power from the swirl effect. The swirl angle can cause non symmetrical flow conditions on anything that may be operating behind the propeller.

In its simplest form, the thrust of the propeller depends upon three main factors: 1.) the density of the air; 2.) the acceleration of the air; 3.) the volume of air accelerated per unit of time. Based on the stated assumptions of the momentum theory, the thrust can be expressed by the following equation.

∆ (1) = ∗ ∗ + ∗ ∗ ∆

where: T is the total thrust

Dp is the propeller diameter

va is the velocity of the incoming air flow

∆va additional velocity, acceleration by propeller

ρa density of air

By examining equation 1, we can clearly see that the thrust increases when the propeller diameter increases or when the density of the air increases. The acceleration of the propeller depends on the velocity, thus it is generally not true that increasing the velocity increases the thrust. But it can be said, that increasing the additional velocity, increases the thrust.

The downside of the momentum theory is that it provides no information as to how the propeller blades should be geometrically designed in order to produce a given thrust. Also, the profile drag losses are ignored. On the other hand, the “Blade Element

Theory” (Froude 1878) is based on the assumption that each element of a propeller blade can be considered an airfoil segment. Lift and drag are then calculated from the resultant velocity acting on the individual airfoil. The thrust of the rotor is obtained by simply integrating the individual contribution of each element along the radius of the propeller blade.

Figure 6: Blade Element Method

where: dT is the thrust

dL is the lift

dD is the drag

VA is the advanced velocity

ωr is the rotational speed

VR is the resultant velocity

α is the angle of attack

β is the inflow angle

The thrust force of a blade is obtained by integrating the dT over the radius ( R), and the total thrust force ( T) is found by multiplying the number of blades ( Z) by the blade thrust force, as shown in equation 2.

= = − (2)

Over time the Momentum Theory and the Blade Element Theory were eventually combined in an attempt to help reduce the difficulties in calculating the induced

10 velocities. This combined theory became known as what is called the “Blade Element

Momentum Theory”.

In more recent modern times the capabilities of computing power have greatly opened the doors to using more and more complex CFD (Computation Fluid Dynamics) techniques to help determine the performance of a propeller. Due to the complexity of these CFD methods I will not go into detail of the inner workings. However, these CFD methods may include but are not limited to, Vortex Lattice Methods, Boundary Element

Solvers, as well as Lifting Line and Lifting Surface Methods.

1.4 Systems with Similar Configurations

1.4.1 Contra-Rotating Propeller Systems

Contra-Rotating propellers (CRP) consist of two propellers that are in tandem with one another, as seen in figure 7. The two propellers operate on two separate shafts that are connected to a gear system that spin the propellers opposite directions.

Figure 7: Contra-Rotating Propeller [Courtesy of diydrones.com]

The CRP has been a very attractive propeller system for many years, especially among Russian and British aircraft designs. Much of the interest in CRP designs comes from the system’s ability to improve propulsive efficiency by reducing the amount rotational kinetic energy losses from the lead propeller. Depending on the source, improved efficiencies have been reported to be within the 6% to 20% when compared to single propeller designs.

In order to achieve the greatest efficiency, most literature that is referenced seems to suggest that the axial distance between propellers has to remain relatively close in order to most effectively counteract the kinetic energy losses from the lead propeller, although none of the literature seemed to give any reasoning as to why they chose the values of axial distances that were used. Unfortunately, this limitation on axial distance also helps feed the problem of noise levels from the blade interactions, which are considerable higher when compared to a single propeller.

Most of the referenced literature was primarily focused on 2-D and 3-D numerical design methods to perform the analysis using mainly the pitch of the propellers (figure

8) to adjust the relative velocities at the rotors, and ultimately achieve the desired efficiency of the system.

Figure 8: Example of Velocity Triangle of Contra Rotating Propellers [8]

When compared to the “axially stacked propeller system”, which is the focus of this thesis, the CRP has only a few similarities. They are both systems that require tandem propellers that are at an optimal axial distance between one another, as well as require the rear propeller to deal with the induced velocities and swirl coming off of the lead propeller (i.e. the pitch of the propellers). However, the CRP is considerably more complex having two counter-rotating shafts and a gear system. The fact that the tandem propellers in a CRP system rotate in opposite directions also means that the propeller interactions are going to be very different than what the proposed “axially stacked propeller system” sees.

1.4.2 Wind Farms and Tandem Wind Turbines

Wind farms consist of organized patterns or arrays of multiple wind turbines. Due to the multiple wind turbines operating within a confined area, the performance of the wind turbines operating downwind in the array are greatly affected by wake interferences located within the near and far wake regions of the upstream rotors. Ideally, wind farm designers try to space turbines far enough apart to minimize the any wake interferences 13 from the lead turbines. Minimizing the wake interference from the lead turbines allows the trailing turbines to draw as much energy from the oncoming flow as possible. In addition to downwind spacing, most modern wind farms also utilize the concept of a staggered layout which also utilizes crosswind spacing to help increase the overall power production of the array.

Figure 9: Wind Turbine Farm Arrangement [22]

The downward spacing of wind turbines by far has seen the greatest amount of research. As before mentioned, once the freestream flow passes through the leading wind turbines, wake interferences are immediately generated for the trailing wind turbines to deal with. These wake interferences create a velocity deficit in the freestream velocity, which end up greatly hindering the power generation of the trailing wind turbines, sometimes by as much as 30%. Because of this, the velocity deficit recovery becomes an important factor in making sure the greatest amount of energy can be harvested from the trailing turbines. The amount of distance needed for the

14 freestream velocity to recover is crucial when trying to determine the spacing needed between wind turbines. The diameter (D) of the wind turbine rotors is the key variable, as all downwind distances are determined as a multiple of the rotor diameter. When considering past research that has been conducted on the matter, most studies have shown that up to 50% of the velocity deficit is rapidly recovered at a distance of 2D.

From that point the recovery gradually increases to roughly 70% when a distance of around 6.5D reached. From that point on, the recovery becomes very slow.

Interestingly enough, studies have also shown that freestream flows that have higher turbulence levels tend to have a faster recovery of the velocity deficit. Most modern offshore wind turbine designs have utilized similar research and generally end up having spacing between 6 – 10 rotor diameters.

Crosswind spacing is another factor that is considered in modern wind turbine farms. Although I will not go too much into depth on the subject, I will say that crosswind spacing has been proven to improve the overall power input of a wind turbine farm.

Depending on the downwind and crosswind spacing configuration, research has shown that the difference in total power production can be as high as 10% - 12% when compared to an aligned turbine layout.

Ultimately the goal is to produce as much power out of each wind turbine as possible, which according the Betz limit is theoretically around 59%. However, in reality most well designed wind turbines are only able to achieve around 40% - 50%.

Another goal of a wind turbine farm is to generate as much power as possible within the given area that the wind turbine farm is confined to, which is especially true for on-shore wind farms that typically do not have the luxury of excessively large areas

15 that off-shore wind turbine farms are able to utilize. This can be a bit of a challenge due to the spacing requirements that have been mentioned beforehand. However, one configuration that has received some attention is the concept of counter rotating wind turbines.

Figure 10: Co-Rotating and Counter-Rotating Tandem Wind Turbines [19]

The appeal of reducing the downwind distance between wind turbines is once again based on the Betz theory. As before mentioned, the Betz theory states that only about

59% of the total energy from the freestream velocity can be extracted by a single rotor system, but for a dual rotor system the Betz limit is increased to about 64%. In order to take advantage of this increased energy extraction, the distance between the two wind turbines would have to be considerably lower to the point that the downwind turbine would be forced to operate within near wake region of the lead turbine. Counter-rotating configurations are very advantages in this situation for the reason that by counter rotating the turbines, the downwind turbine is able to extract more energy from the flow

16 swirl component coming off of the lead turbine, whereas the downwind turbine for a co- rotating configuration are almost entirely limited to extracting energy from the freestream velocity coming off of the lead turbine. A study completed by Wei, Wei,

Ahmet and Hui [19] showed that at a downwind spacing of about 0.7D, the counter- rotating turbines produced about 20% more power when compared to the accompanying co-rotating configuration. However, they also found that at a downwind spacing of about 6.5D, the advantages of the counter rotating turbines became almost negligible

Due to the fact that counter rotating configurations tend to produce the highest power output at shorter downwind distances between turbines, some wind turbine designs have adopted the dual rotor concept (figure 11), and in fact have been proven to produce very similar results. Using this dual rotor concept, Al-Abadi, Ertunc, Epple,

Koerbel, and Delgado [24] were able to produce a similar trend that was previously talked about for Wei, Wei, Ahmet and Hui [19] . By using three bladed Clark-Y profile propellers as wind turbines, not only did Al-Abadi, Ertunc, Epple, Koerbel, and Delgado’s results show that the counter-rotating configuration produced a high power coefficient, but the axial distance between rotors that produced the highest power coefficient was at 0.5D.

Figure 11: Dual Contra-Rotating Wind Turbine [17]

However, there is a point at which the downwind distances between propellers becomes too short. As Shen, Zakkam, Sorensen and Appa [15] found in there numerical study of a counter-rotating wind turbine using Nordtank 500 kW rotors, when the incoming wind speed was set at 10 m/s, a large fluctuation in power began to occur when the downwind spacing reached about 0.05D. This doesn’t mean that all counter-rotating configurations would start to experience power fluctuations at 0.05D, but it does prove that there is a limit as to how close the rotors in counter-rotating system can be before the advantages of power extraction are lost.

Due to the fact that tandem wind turbines utilize two separate shafts rotating at different speeds, as well as the fact that the flow is driving the rotors and not vice versa, there is really not much useful information that can be applied to the “axially stacked propeller system” that is being proposed in this thesis. However, given the fact that the axial distance between wind turbines is a large factor in how much power can be

18 extracted from a freestream flow, it stands to reason that the axial distance between the propellers on the proposed system will probably be a contributing factor of thrust performance as well. How much of a factor is of course the big question.

Chapter 2

Method of Approach

2.0 Experimental Setup

Because there are such a large number of propeller choices that could be used in an experimental setting, each with varying degrees of complexity depending on the type of performance that is being focused on (i.e. speed, thrust, etc.), it was decided that only common propeller designs that are used within the electric motor UAV industry would be utilized in this experiment. These common propeller designs helped to maintain a cheap and simple experimental setup, as well as help maintain a representation of a plausible real world scenario. After much consideration, it was determined that both the APC 7x5E (7” DIAMETER x 5” PITCH) and APC 5x5E (5”

DIAMETER x 5” PITCH) Thin Electric Propeller designs (figure 12) were the best option.

Although one propeller has a larger diameter than the other, it was desired that both propellers have the same pitch to maintain as much similarity as possible.

Figure 12: Thin Electric Propellers

The full experiment consisted of two Thin Electric propellers that were axially stacked at varying distances along an aluminum shaft that was connected to an electric motor. Each shaft varied in length depending on the desired axial distance between propellers, which also took into account the thickness of the propeller hubs. The shafts were precision machined to make sure there would be minimal balancing issues during operation, but also to match the diameter of the of the propeller hubs. However, due to the relatively small diameter of each shaft (.500” diameter), the danger of a shaft becoming unbalanced from minor vibrations at higher RPM’s was a growing issue as the shaft lengths became longer. Because of this problem the experiment was limited to using a maximum axial distance of 4” between propellers.

The electric motor that was used in this experiment was a Bodine Electric 3317

Motor (figure 13), which has a rating of 10,000 RPM’s.

Figure 13: Bodine Electric 3317 Motor

This particular motor was chosen for two reasons. The first reason was that it provided enough horsepower (1/3 hp) to avoid any torque load issues when the propellers were spinning at higher RPM’s. The second reason was because the power to the motor has

21 to pass through a Bodine Electric 3921 Controller (figure 14) which guaranteed constant and stable power to the motor, which in turn helped to avoid and fluctuations in RPM’s.

Figure 14: Bodine Electric 3921 Controller

The motor was bolted to the bottom side of an 8”x8.5” plate that was part of a specially made aluminum frame, with the shaft passing through a hole in the center of the plate, as seen in figure 15.

Figure 15: Frame Assembly

The motor was oriented in such a manner that the shaft holding the propellers was positioned vertically upward, with the propellers configured to produce a downward force when spinning. It is also worth noting that the propeller closest to the plate surface was set at 2.5”. This distance was deliberately set in order to provide a large enough gap between the plate and the propeller, as well as avoid making the shaft too long in order to avoid balancing issues from stirring of the shaft.

The aluminum frame was then placed onto a Virtual Measurements and Control

Model VW-330A-C scale (figure 16), which was chosen for its high load capacity, as well as its 2 gram resolution capability.

Figure 16: Virtual Measurements and Control Model VW-330A-C Scale

The weight of the aluminum frame coupled with the weight of the motor ensured that there would be no slippage from the effects of the torque from the motor, or vibration, provided the propeller shaft was properly balanced.

Figure 17: Overall Setup

Due to the fact that the 1-10 dial settings of the RPM control on the 3921 controller are not in sync with a linear ramp up of 1000-10000 RPM’s, an Eddy Current probe was mounted .020” away from the spinning shaft. The probe was then connected to a

Tektronix TDS 1002B frequency counter (figure 18) to provide an actual RPM reading at each dial setting.

Figure 18: Tektronix TDS 1002B Frequency Counter

2.1 Experimental Procedure

The experiment was carried out in a systematic manner as to cover two separate variables: 1.) axial distance between propellers, 2.) relative angle between propellers,

These said variables were tested using three separate propeller configurations, as shown in figure 19.

Figure 19: Propeller Configurations

Before each experiment was performed, the desired propeller configuration was set-up on the shaft, after which the aluminum frame was properly placed onto the scale, as seen in figure 17. Once everything was in place, the scale was turned on and the output reading was set to Kilograms (kg), after which the scale was then zeroed out.

In order to create a base to compare the data from the axially stacked propeller experiments, the first experiments that were ran consisted of a single APC 7x5E propeller being ran at the dial settings 1-9 on the 3921 controller. At each dial setting the motor was allowed to run for at least ten seconds, after which a scale reading was recorded. This same process was repeated using a single APC 5x5E propeller. Once the first set of base data was collected, the second set of base experiments was performed.

The second set of base experiments were meant to replicate four bladed propellers by simply stacking two APC 7x5E propellers directly on top of each other at 90 degrees from one another. The same process that was used in the first base experiments was again followed to collect the needed data. This same process was repeated using an

APC 7x5E directly stacked on top of an APC 5x5E, then with an APC 5x5E directly stacked on top of an APC 7x5E.

The first set of regular experiments was performed using two axially stacked APC

7x5E propellers (figure 19a). The axial distance between propellers was fixed at 1”, 2”,

3”, and 4” accordingly. At each axial distance, the relative angle between the two propellers were set accordingly at 0°, 45°, 90°, an d 135°, in a manner shown in figure

20.

Figure 20: Relative Angle Between Propellers

Once again, each individual setup was run at dial settings 1-9, at which the motor was allowed to run for at least ten seconds, after which a scale reading (kg) was recorded.

The second set of regular experiments were performed in the same manner as the first regular set, but instead using an APC 5x5E on the bottom and an APC 7x5E on the top, as shown in figure 19b.

The third set of regular experiments were again performed in the same manner as the first regular set, but instead using an APC 7x5E on the bottom and an APC 5x5E on the top, as shown in figure 19c.

To gain a better understanding of the execution process of the experiment, as well as how data was collected, please refer to the raw data sheets in Appendix B of this thesis.

2.2 Experimental Uncertainty

2.2.1 Scale Uncertainty

Despite making sure that the calibration of the VW-330A-C Scale was current, there is still the overall issue of the accuracy of the scale itself. Due to the fact that the scale’s maximum capacity of 50 kg is relatively high, the resolution capability comes out to be only .002 kg. Given that the scale readings at lower RPM’s could be as low as

.002 kg means that the percent of uncertainty in the scale can actually reach almost

100%, and will only get lower as the scale output becomes higher, as illustrated in figure

20. The appropriate scale uncertainty at each data point is reflected in the final results.

100

0.1 Uncertainty (%) Uncertainty

0.01

0.001 0.001 0.01 0.1 1 10 100 Scale Output (kg)

Figure 21: Scale Uncertainty v.s. Scale Output

2.2.2 Air Density Uncertainty

Given that the experiment took place over a period of three months, the atmospheric conditions during experimentation varied from day to day. These variations in atmospheric conditions would have had at least a minor effect on the air density that the experiment was being performed in, and because of this I must account for this variation in the final results.

The facility that the experiment was conducted in was climate controlled at a relative humidity of 23% ±2%, and a temperature of 24° C ±2° C. The altitude of the facility above sea level is 182 m. By looking up the history of atmospheric pressure for the local area during the days the experiment was conducted, it was found that the pressure range always fell between 10282 kg/m^2 and 10382 kg/m^2. This information was then input into an aviation air density calculator to provide the minimum and maximum air density values during the entire period of experimentation, which turned out to be 1.2770 kg/m^3 and 1.3004 kg/m^3.

Using the equation for Propeller Thrust (equation 3), as well as the published values of the thrust coefficients from the APC website, the thrust was able to be calculated for both the maximum and minimum air density values at 1000 through

10000 RPM.

(3) =

where: T is the total thrust

Dp is the propeller diameter

CT is the coefficient of thrust

n is the propeller speed in rev/s

ρa is the density of the air

Using the calculated thrust values for the 7x5 and 5x5 propellers, the percent difference between the maximum and minimum thrust values were calculated for each of the two propellers. As it turns out, the percent difference for both propellers at each

RPM was consistently at 1.799%. This 1.799% is what is used as air density uncertainty in the final results.

2.2.3 RPM Uncertainty

Although there were no fluctuations in the RPM at each dial setting of the 3921 controller, the overall accuracy of the Tektronix TDS 1002B Frequency Counter is still a factor that introduces uncertainty in the data. The accuracy of the TDS 1002B frequency counter is rated at ±51 ppm, and by using equation 4, we are able to determine the peak frequency variation ( Df) for the frequency at each dial setting of the

3921 controller.

× (4) ∆ =

where: Df is the peak frequency variation

f is the frequency

ppm is “parts per million”

The rotational speed for the experiment fell between 5.5 Hz and 177 Hz, so the frequency uncertainty can easily be plotted to show the trend in the variations for that

30 frequency range. However, since this experiment is utilizing RPM instead of Hertz as the rotational speed, we will need to multiply both the frequency and the frequency variation by 60 in order to plot the uncertainty at each RPM, as shown in figure 22.

These Uncertainties are what are used to show the RPM uncertainty in the final results.

RPM Uncertanty v.s RPM 0.6

0.5

0.4

0.3

0.2 RPM RPM Uncertainty

0.1

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM

Figure 22: RPM Uncertainty v.s. RPM

2.2.4 Uncertainty in the Mean

In order to gain an overall view of how the axial distance affects the thrust of the propeller system, the results of the relative angles at each axial distance will be averaged. This averaging creates another uncertainty that must also be accounted for in the final results. Since there are only four sets of data at each axial distance, I am forced to use a simple statistical analysis tool (equation 5) to determine the uncertainty of the mean thrust values.

∆ = (5) √

where: DTavg is the uncertainty in the mean thrust

Tmax is the largest thrust value in the data set

Tmin is the smallest thrust value in the data set

N is the number of data values in the set

Once the values of uncertainty are determined for each of the mean values, those same values are what are used as the averaging uncertainty in the final results.

Chapter 3

Results and Discussion

3.0 Effect of the Support Plate

Due to some concerns about the support plate partially blocking the flow entering into the propeller, two additional tests were performed to investigate the blockage effect on the propeller, the first test being experimental and the second test being computational. In the first test, the same experimental procedure that was explained in

Chapter 2 for a single propeller was used, except in this case the distance between the support plate and the single propeller was varied from 2.5 to 6.5 inches, and the measured results for the thrust are compared to the manufactured published data from the APC website, as shown in figure 23. It is observed that a small increase in the thrust occurs as the distance from the support plate becomes greater, indicating that the effects of the plate blockage decreases as the propeller gets further away. However, the experimental results at every distance appear to have higher thrust values at higher

RPM’s than the APC published data for static thrust. The reason for this is clearly due to differences in experimental setup, and unfortunately the manufacturer does not provide details in this regard. However, given that the curve trends are still similar indicates that the support plate is not causing any major issues.

By use of FloEFD software, the second test shows the computed thrust of the propeller without the plate blockage at 10000 RPM, as well as the thrust data of the propeller with the plate blockage at 10000 RPM and 2.5 inches from the propeller, as shown in figure 24. The two main reasons why it was decided to use FloEFD was

33 because it provided a more robust Cartesian grid to work with, as well as the fact that an inlet velocity of zero could be used to better simulate static thrust. A solid-works part file of the propeller was imported for the geometry. An external flow was defined, and the global rotation for the propeller geometry was set about the –ve y-axis. An angular velocity of 166.77 rad/s (10,000 RPM) was specified, with air being the fluid of choice.

A grid independence study was performed with the varying grid levels within the program. When the grid independence study was completed, the grid level of choice ended up being grid level four, with 437463 grid cells (see figure 24). The conditions in front of the constructed domain were set as ambient. However, in order to prevent back flow behind the propeller, as well as provide flow uniformity in front of the propeller, the size of the domain around the propeller was adjusted to five propeller lengths on every side of the propeller geometry except behind the propeller, which was given ten propeller lengths. Before the program was run, the convergence criteria was set to monitor the thrust force and stop at 10 -3. When the FloEFD program was finally run for both cases, the results showed a slightly higher thrust without the plate blockage versus the propeller with the plate blockage, as seen in figure 25. It is important to note here that the propeller used in the FloEFD simulation is different than that of the propellers used in the experiment, due to the fact that efforts to obtain the propeller geometry were not successful. However, both sets of data from the experiment and simulation indicate only a minor effect from the plate blockage on the propeller performance.

Figure 23: Thrust v.s. Distance from Support Plate

Figure 24: FloEFD Cartesian Grid

Figure 25: Flow into propeller (FloEFD Simulation)

3.1 Effect of Relative Angles Between Propellers

The effects of relative angle between propellers were a bit different for each of the three propeller configurations. The “5x5 over 7x5” configuration seemed to be the configuration that was most effected by propeller relative angles, given that the data curves for each relative angle are the most spread out at each axial distance (see plots

1-4 in appendix A) when compared to the other two configurations. What is also interesting is the fact that the data curves seem to become slightly more spread out as the axial distance becomes greater. However, due to the fact that almost all the curves for each relative angle fall at least slightly within the uncertainty bands of one another, these observations may not be an accurate assessment.

The “7x5 over 7x5” configuration seemed to be less effected by propeller relative angles than what was observed for the “5x5 over 7x5” configuration (see plots 9-12 in

Appendix A). In this case the data at 1” axial distance seems to be the only time that that the relative angles had a noticeable effect on the data, seeing as it is the only case that the data curves between relative angles are spread out to any considerable degree, whereas the data curves at the higher axial distances remaining tightly grouped, indicating that the difference in relative angles had little to no effect at the higher axial distances.

The “7x5 over 5x5” configuration seemed to be the configuration that was the least affected by the propeller relative angles (see plots 5-8 in Appendix A). No matter what the axial distance was, the data curves for each relative angle appeared to always be tightly grouped, well within the error band of one another, which once again indicates little to no difference in the effects from each relative angle.

3.1 Effect of Axial Distance Between Propellers

Instead of providing thrust plots for each relative angle at each axial distance, I decided to take a simpler approach by taking an average of the four relative angles at each axial distance. The reasoning for this is the fact that the data curves for the relative angles between propellers at each axial distance almost always fall within the uncertainty band of one another, or at least close to it, we should be able to get away with taking an average of the curves to provide a general trend for each axial distance.

By doing so we are able to narrow the data down to three plots, and in my opinion, provide a much clearer picture of how the axial distance affects the thrust performance

(see plots 13-15 in Appendix A).

The information provided by plots 13-15 is fairly easy to decipher, and a few points of interest can quickly be spotted. One of the most noticeable points of interest can be observed in the 5x5 over 7x5 configuration, as well as the “7x5 over 7x5” configuration.

It seems in both configurations that no matter what axial distance the propellers have between each other, the thrust performance is never really able to exceed the performance of the “90° Stacked” base case. This t rend is quite a bit more vivid for the

“5x5 over 7x5” configuration, whereas the trend for “7x5 over 7x5” configuration seems to hug the curve of the “90° Stacked” base case a l ot more. On the contrary, the “7x5 over 5x5” configuration proves to show just the opposite, where the thrust performance at every single axial distance seems to match or exceed the thrust performance of the

“90° Stacked” base case.

3.2 Miscellaneous Observations

As the experiments were being performed, the output readings on the scale consistently jumped around, and it required a lot of patience to catch the output reading when the scale would finally settle for a few moments. However, it was observed that as the distance between propellers increased, the erratic behavior would become less and less prevalent. Interestingly enough, the scale’s erratic behavior was very minimal when the “90° Stacked” base cases were being perfor med, and almost non-existent when the single propeller base cases were being performed. What is even more interesting is that the amount of erratic behavior between one type of propeller configuration and another was quite different. The “7x5 over 5x5” propeller configuration by far had the least amount of erratic behavior. Whereas the “7x5 over

7x5” and “5x5 over 7x5” configurations were plagued with erratic behavior, probably more so for the “5x5 over 7x5” from a personal observation point of view. On a further note, during the erratic moments, the readings from the scale would often peak at a level that was at times about 3% higher than the steady output. Once again, this was more so for the “5x5 over 7x5” configuration, but especially for the “7x5 over 7x5” configuration.

Overall, the “7x5 over 7x5” configuration appear to produce the largest amount of thrust, which is no surprise considering the fact that two APC 7x5E propellers are being used. However, when comparing between the “7x5 over 5x5” and “5x5 over 7x5” propeller configurations, the “7x5 over 5x5” configuration is clearly producing the higher thrust values.

In matters of efficiency, the “7x5 over 5x5” propeller configuration was by far the best performer, especially considering it was the only propeller configuration that was able to perform better than the “90° Stacked” base case, or at least consistently as good as the “90° Stacked” base case when taking the unce rtainty bands into consideration.

3.3 Discussion

I was quite baffled at the poor performance of the “5x5 over 7x5” configuration from a thrust point of view. Based on the momentum theory that was described in Chapter 1,

I was fully expecting this configuration to produce the higher amount of thrust when compared to the “7x5 over 5x5” configuration, mainly for the reason that the 5x5 propeller should have been producing a much higher level of thrust, due to the fact that it was fully exposed to the energized flow coming off the 7x5 propeller, as shown in figure 26.

Figure 26: "5x5 over 7x5" Propeller Configuration Stream Tube

However, as mentioned in in chapter 1, the swirl angle coming off of the lead “7x5” propeller was most likely causing a non-symmetrical flow to the smaller “5x5” operating behind it, which leads me to believe that having the same geometry for both propellers was probably not a good idea and the main contributing factor as to why the “5x5” propeller was not able to utilize the energized flow coming from the larger propeller in front of it, hence the poor performance of the “5x5 over 7x5” configuration. This same reasoning would also seem to explain the erratic behavior of the scale when the experiment was being performed. Even though the rear propeller was not able to consistently grasp the flow coming into it, there would be brief moments when the rear propeller would catch on and the thrust performance would peak.

The “7x5 over 7x5” configuration seemed to suffer from this same problem.

However, due to the fact that the data curves at each axial distance seem to hug the

“90° Stacked” base case curve a bit more than the “ 5x5 over 7x5” configuration, leads me to believe that the amount of issue the rear propeller was having was not quite as severe as in the “5x5 over 7x5” configuration. When considering the propeller stream tube (figure 5), we know that the flow constricts immediately behind the propeller. Since the “7x5 over 7x5” configuration uses two propellers of the same diameter, the stream tube would suggest that the outer tips of the rear propeller would not be affected by the energized flow coming off of the lead propeller, as seen in figure 27.

Figure 27: "7x5 over 7x5" Propeller Configuration Stream Tube

However, by far the majority of the rear propeller was being affected, and once again the geometry of the rear propeller was probably the main contributor to the poor effectiveness. As with the “5x5 over 7x5” configuration, the rear propeller on the “7x5 over 7x5” configuration was not able to consistently grasp the flow coming into it.

However, once again, there would still be brief moments when the rear propeller would catch on and the thrust performance shown on the scale would peak.

Following on the reasoning previously discussed, it is no wonder why the “7x5 over

5x5” configuration had the best performance. Due to the fact that the lead propeller has the smaller diameter, as well as considering the constriction of the stream tube coming off of the lead propeller, the larger “7x5” rear propeller probably only encountered the energized flow on about half of its surface area, which would have been confined to the inner diameter as well, as seen in figure 28.

Figure 28: "7x5 over 5x5" Propeller Configuration Stream Tube

The fact that a large part of the outer diameter on the rear propeller was able to perform independently from the lead propeller would seem to explain why the “7x5 over 5x5” configuration was the only configuration that was able to consistently match, or outperform the “90° Stacked” base case at every axi al distance. This would also explain why the amount of erratic behavior from the scale’s output was minimal when compared to the other two propeller configurations.

Due to the fact that a very large amount of the rear propeller in the “7x5 over 5x5” configurations was operating outside of the influence of the lead propeller clearly explains why the relative angle data curves at every axial distance are so closely grouped together. With a large part of the rear propeller operating outside of the influence of the lead propeller, the rear propeller is able to act more independently.

Thus, the relative angle between propellers matters less. This reasoning also explains why the data curves for the relative angles in the “5x5 over 7x5” configurations were

44 always the most spread out from one another. In this case the rear propeller was always operating fully within the influence of the lead propeller.

Although it appears that both relative angles between propellers and axial distance between propellers do seem to affect the overall thrust, the data is inconclusive as to which relative angle and what axial distance provides the best performance. Until another experiment can be performed with more appropriate geometries being used on the rear propeller, a solid conclusion cannot be made based on the data at hand.

Chapter 4

Conclusions

4.0 Conclusions

Three configurations were considered in this thesis. The first configuration consisted of two propellers of equal diameter and pitch (7x5 over 7x5) stacked at axial distances from one another. The second configuration consisted of a smaller propeller stacked at an axial distance on top of a larger propeller (5x5 over 7x5). The third configuration consisted of a larger propeller stacked at an axial distance on top of a smaller propeller (7x5 over 5x5). Overall, the “7x5 over 7x5” configurations produced the highest thrust values, due to the fact that two 7x5 propellers were being used.

However, the “7x5 over 5x5” configuration had the best performance, being the only configuration that was able to consistently match or out-perform the accompanying “90° stacked” propeller case.

Overall, the experimental data indicates that an optimum performance of the axial stacked propeller system requires a redesign of the rear propeller’s geometry in order to better account for the swirling flow affects coming off of the lead propeller.

Much can be learned from the information that this thesis has provided, but in the grand scheme of things I am confident that this thesis has in fact caused just as many questions to be asked as questions it has answered. Despite the limitations that were faced with this experiment there are some general questions that can be answered.

Can the axial distance between propellers affect the thrust output? Yes. Can the relative angle between propellers affect the thrust output? Yes. Is there a difference 46 between the thrust outputs of different propeller configurations? Yes. These general questions have in fact been answered, but the details within these same questions leave much to be explored. My hope is that this thesis can provide a starting point for further research into some of these details. As others work to get around the limitations that I was faced with, I am confident that there is a wide range of applications that could successfully utilize systems based on the axially stacked propeller concept.

REFERENCES

[1] U.S. Bureau of Naval Personnel, “Aircraft Propellers” 1945, Ed. of 1945, v, 237

[2] Wald, Quentin R, “The Aerodynamics of Propellers” Progress in Aerospace Sciences, ISSN 0376-0421, 2006, Volume 42, Issue 2, pp. 85 - 128

[3] Greatrix, David R, “Powered Flight: The engineering of Aerospace Propulsion” 2012, 1, ISBN 1447124847, p. 530

[4] Reaves, G; Striz, A, “A Study in Propeller Aircraft Performance Optimization” 2000, 38 th Aerospace Sciences Meeting & Exhibit, Reno, Nevada

[5] Hough, Joseph; Nagel, Robert T; Jin-Deog Chung, “Interation Between Rotors of a Counter Rotating Propeller”, AIAA, Aeroacoustics Conference, 13th, Tallahassee, FL, Oct. 22-24, 1990

[6] DAVENPORT, F. J; COLEHOUR, J. L; SOKHEY, J. S, “Analysis of counter- rotating propeller performance” , 1985, Boeing Commercial Airplane Co.,Seattle, WA and General Electric Co., Aircraft Engine Business Group, Cincinnati, OH

[7] Sasaki, Noriyuki; Onogi, Hiroshi; Murakami, Mitsunori; Nozawa, Kazuo; Soejima, Shunji; Shiraki, Akira; Aono, Takeshi; Fujimoto, Tomeo; Ishii, Norio; Onogi, Hiroshi, “Design System for Optimum Contra-Rotating Propellers”, Journal of Marine Science and Technology, ISSN 0948-4280, 03/1998, Volume 3, Issue 1, pp. 3 - 21

[8] Knesnik, Andrew S., “Feasibility Study of an Axially-Stacked, Subsonic Propeller System” , 2012, University of Cincinnati, Department of Mechanical Engineering

[9] Lowry, John T, “Fixed-Pitch Propeller/Piston Aircraft Operations at Partial Throttle” Journal of Propulsion and Power, ISSN 0748-4658, 07/1999, Volume 15, Issue 4, pp. 497 – 503

[10] Grassi, Davide; Brizzolara, Stefano; Viviani, Michele; Savio, Luca; Caviglia, Sara, “Design and analysis of counter-rotating propellers-comparison of numerical and experimental results”, Journal of Hydrodynamics, Ser.B, ISSN 1001-6058, 2010, Volume 22, Issue 5, pp. 570 – 576

[11] JUNG, S; NO, T; RYU, K, “Aerodynamic performance prediction of a 30kW counter-rotating wind turbine system” , Renewable Energy, ISSN 0960-1481, 04/2005, Volume 30, Issue 5, pp. 631 – 644

[12] Wald, Quentin R, “The aerodynamics of propellers” Progress in Aerospace Sciences, ISSN 0376-0421, 2006, Volume 42, Issue 2, pp. 85 – 128

[13] Greatrix, David R, “The Propeller” Powered Flight, 2012, 2012, ISBN 1447124847, pp. 63 – 96

[14] Lee, Soogab; Lee, Seungmin; Kim, Hogeon, “Analysis of aerodynamic characteristics on a counter-rotating wind turbine”, Current Applied Physics, ISSN 1567-1739, 2010, Volume 10, Issue 2, pp. S339 - S342

[15] Shen, W Z; Zakkam, V A K; Sørensen, J N; Appa, K, “Analysis of Counter-Rotating Wind Turbines” , Journal of Physics: Conference Series, ISSN 1742-6596, 07/2007, Volume 75, Issue 1, p. 012003

[16] APC Propeller, “APC Propeller Performance Data” http://www.apcprop.com/v/downloads/PERFILES_WEB/datalist.asp

[17] Merchant, Shane; Gregg, Jason; Gravagne, Ian; Van Treuren, Ken, “Wind Tunnel Analysis of a Counter-Rotating Wind Turbine” , ASEE Gulf-Southwest Annual Confrence, 2009

[18] Yuan, Wei; Tian, Wei; Ozbay, Ahmet; Hu, Hui, “An experimental study on the effects of relative rotation direction on the wake interferences among tandem wind turbines” , Science China Physics, Mechanics & Astronomy, ISSN 1674-7348, 05/2014, Volume 57, Issue 5, pp. 935 – 949

[19] Yuan, Wei; Tian, Wei; Ozbay, Ahmet; Hu, Hui, “An experimental study on the effects of relative rotation direction on the wake interferences among tandem wind turbines” , Science China Physics, Mechanics & Astronomy, ISSN 1674-7348, 05/2014, Volume 57, Issue 5, pp. 935 – 949

[20] Sørensen, Jens N, “Wind turbine wakes and wind farm aerodynamics” , Wind Energy Systems: Optimising Design and Construction for Safe and Reliable Operation, 12/2010, ISBN 1845695801, pp. 112 - 129

[21] Pao, L.Y and Johnson, K.E, “A tutorial on the dynamics and control of wind turbines and wind farms” , 2009 American Control Conference, ISSN 0743-1619, 2009, ISBN 9781424445233, pp. 2076 - 2089

[22] Johnson, K.E and Thomas, N, “Wind farm control: Addressing the aerodynamic interaction among wind turbines” , 2009 American Control Conference, ISSN 0743- 1619, 2009, ISBN 9781424445233, pp. 2104 – 2109

[23] Laskos, Dimitrios, “Design and Cavitation Performance of Contra-Rotating Propellers” , 2010, Massachusetts Institute of Technology, Department of Mechanical Engineering

[24] Al-Abadi Ali; Ertunc, Ozgur; Epple, Philipp; Koerbel, Wolfram; Delgado, Antonio, “Development of an Experimental Setup for Double Rotor HAWT Investigation”, 2012 ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, ISBN: 978-0-7918-4472-4, pp. 1007 - 1016

[25] Hartman, Edwin P; Biermann, David, “The Aerodynamic Characteristics of Full- Scale Propellers Having 2, 3, and 4 Blades of Clark Y and R.A.F. 6 Airfoil Sections”, 1938 NACA Technical Report 640, NACA Annual Report 24, pp. 547-569

APPENDIX A

THRUST PLOTS

5 x 5 over 7 x 5 (1" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 5 x 5 over 7 x 5 Stacked (90°) 5 x 5 over 7 x 5 (1 Inch) (0°) Thrust(kg) 0.25 5 x 5 over 7 x 5 (1 Inch) (45°) 5 x 5 over 7 x 5 (1 Inch) (90°) 0.2 5 x 5 over 7 x 5 (1 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 1 52

5 x 5 over 7 x 5 (2" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 5 x 5 over 7 x 5 Stacked (90°) 5 x 5 over 7 x 5 (2 Inch) (0°) Thrust(kg) 0.25 5 x 5 over 7 x 5 (2 Inch) (45°) 5 x 5 over 7 x 5 (2 Inch) (90°) 0.2 5 x 5 over 7 x 5 (2 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 2 53

5 x 5 over 7 x 5 (3" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 5 x 5 over 7 x 5 Stacked (90°) 5 x 5 over 7 x 5 (3 Inch) (0°) Thrust(kg) 0.25 5 x 5 over 7 x 5 (3 Inch) (45°) 5 x 5 over 7 x 5 (3 Inch) (90°) 0.2 5 x 5 over 7 x 5 (3 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 3 54

5 x 5 over 7 x 5 (4" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 5 x 5 over 7 x 5 Stacked (90°) 5 x 5 over 7 x 5 (4 Inch) (0°) Thrust(kg) 0.25 5 x 5 over 7 x 5 (4 Inch) (45°) 5 x 5 over 7 x 5 (4 Inch) (90°) 0.2 5 x 5 over 7 x 5 (4 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 4 55

7 x 5 over 5 x 5 (1" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 7 x 5 over 5 x 5 Stacked (90°) 7 x 5 over 5 x 5 (1 Inch) (0°) Thrust(kg) 0.25 7 x 5 over 5 x 5 (1 Inch) (45°) 7 x 5 over 5 x 5 (1 Inch) (90°) 0.2 7 x 5 over 5 x 5 (1 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 5 56

7 x 5 over 5 x 5 (2" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 7 x 5 over 5 x 5 Stacked (90°) 7 x 5 over 5 x 5 (2 Inch) (0°) Thrust(kg) 0.25 7 x 5 over 5 x 5 (2 Inch) (45°) 7 x 5 over 5 x 5 (2 Inch) (90°) 0.2 7 x 5 over 5 x 5 (2 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 6 57

7 x 5 over 5 x 5 (3" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 7 x 5 over 5 x 5 Stacked (90°) 7 x 5 over 5 x 5 (3 Inch) (0°) Thrust(kg) 0.25 7 x 5 over 5 x 5 (3 Inch) (45°) 7 x 5 over 5 x 5 (3 Inch) (90°) 0.2 7 x 5 over 5 x 5 (3 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 7 58

7 x 5 over 5 x 5 (4" Axial Distance) 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 7 x 5 over 5 x 5 Stacked (90°) 7 x 5 over 5 x 5 (4 Inch) (0°) Thrust(kg) 0.25 7 x 5 over 5 x 5 (4 Inch) (45°) 7 x 5 over 5 x 5 (4 Inch) (90°) 0.2 7 x 5 over 5 x 5 (4 Inch) (135°)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 8 59

7 x 5 over 7 x 5 (1" Axial Distance) 0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5 5 x 5 Single 7 x 5 Single 0.45 7 x 5 over 7 x 5 Stacked (90°) 0.4 7 x 5 over 7 x 5 (1 Inch) (0°) Thrust(kg) 0.35 7 x 5 over 7 x 5 (1 Inch) (45°) 7 x 5 over 7 x 5 (1 Inch) (90°) 0.3 7 x 5 over 7 x 5 (1 Inch) (135°) 0.25

0.2

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 9 60

7 x 5 over 7 x 5 (2" Axial Distance) 0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5 5 x 5 Single 7 x 5 Single 0.45 7 x 5 over 7 x 5 Stacked (90°) 0.4 7 x 5 over 7 x 5 (2 Inch) (0°) Thrust(kg) 0.35 7 x 5 over 7 x 5 (2 Inch) (45°) 7 x 5 over 7 x 5 (2 Inch) (90°) 0.3 7 x 5 over 7 x 5 (2 Inch) (135°) 0.25

0.2

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 10 61

7 x 5 over 7 x 5 (3" Axial Distance) 0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5 5 x 5 Single 7 x 5 Single 0.45 7 x 5 over 7 x 5 Stacked (90°) 0.4 7 x 5 over 7 x 5 (3 Inch) (0°) Thrust(kg) 0.35 7 x 5 over 7 x 5 (3 Inch) (45°) 7 x 5 over 7 x 5 (3 Inch) (90°) 0.3 7 x 5 over 7 x 5 (3 Inch) (135°) 0.25

0.2

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 11 62

7 x 5 over 7 x 5 (4" Axial Distance) 0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5 5 x 5 Single 7 x 5 Single 0.45 7 x 5 over 7 x 5 Stacked (90°) 0.4 7 x 5 over 7 x 5 (4 Inch) (0°) Thrust(kg) 0.35 7 x 5 over 7 x 5 (4 Inch) (45°) 7 x 5 over 7 x 5 (4 Inch) (90°) 0.3 7 x 5 over 7 x 5 (4 Inch) (135°) 0.25

0.2

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 12 63

5 x 5 over 7 x 5 Thrust Average 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 5 x 5 over 7 x 5 Stacked (90°) 5 x 5 over 7 x 5 (1 Inch) (Average) Thrust(kg) 0.25 5 x 5 over 7 x 5 (2 Inch) (Average) 5 x 5 over 7 x 5 (3 Inch) (Average) 0.2 5 x 5 over 7 x 5 (4 Inch) (Average)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 13 64

7 x 5 over 5 x 5 Thrust Average 0.6

0.55

0.5

0.45

0.4

0.35 5 x 5 Single 7 x 5 Single 0.3 7 x 5 over 5 x 5 Stacked (90°) 7 x 5 over 5 x 5 (1 Inch) (Average) Thrust(kg) 0.25 7 x 5 over 5 x 5 (2 Inch) (Average) 7 x 5 over 5 x 5 (3 Inch) (Average) 0.2 7 x 5 over 5 x 5 (4 Inch) (Average)

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 14 65

7 x 5 over 7 x 5 Thrust Average 0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5 5 x 5 Single 7 x 5 Single 0.45 7 x 5 over 7 x 5 Stacked (90°) 0.4 7 x 5 over 7 x 5 (1 Inch) (Average) Thrust(kg) 0.35 7 x 5 over 7 x 5 (2 Inch) (Average) 7 x 5 over 7 x 5 (3 Inch) (Average) 0.3 7 x 5 over 7 x 5 (4 Inch) (Average) 0.25

0.2

0.15

0.1

0.05

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 RPM PLOT 15 66

APPENDIX B

RAW DATA

Single Propellers

RPM 5 x 5 Propeller Thrust (kg) 7 x 5 Propeller Thrust (kg) 330 0 0 918 0 0.002 2280 0.004 0.016 3510 0.01 0.042 5010 0.02 0.088 6480 0.036 0.16 7752 0.054 0.24 9150 0.078 0.346 10590 0.102 0.456

Propellers Directly Stacked on Each Other Angle Between Propellers 90° 90° 90° RPM 7 x 5 7 x 5 5 x 5 7 x 5 5 x 5 7 x 5 Thrust (kg) Thrust (kg) Thrust (kg) 330 0 0 0 918 0.004 0.002 0.002 2280 0.024 0.02 0.018 3510 0.074 0.054 0.05 5010 0.158 0.112 0.104 6480 0.268 0.186 0.182 7752 0.412 0.276 0.27 9150 0.596 0.408 0.394 10590 0.768 0.52 0.516

1" Vertical Distance Between Propellers Angle Between Propellers 0° 0° 0° 45° 45° 45° 90° 90° 90° 135° 135° 135° RPM 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) 330 0 0 0 0 0 0 0 0 0 0 0 0 918 0.002 0.004 0.002 0.004 0.004 0.002 0.002 0.004 0.002 0.004 0.004 0.002 2280 0.022 0.02 0.018 0.028 0.02 0.018 0.022 0.022 0.018 0.028 0.02 0.018 3510 0.066 0.054 0.046 0.076 0.054 0.046 0.068 0.056 0.048 0.078 0.056 0.048 5010 0.14 0.11 0.1 0.152 0.11 0.1 0.146 0.116 0.1 0.16 0.116 0.1 6480 0.252 0.182 0.166 0.26 0.184 0.172 0.26 0.188 0.172 0.268 0.186 0.17 7752 0.37 0.27 0.254 0.396 0.272 0.256 0.396 0.28 0.256 0.416 0.28 0.252 9150 0.556 0.406 0.37 0.594 0.406 0.372 0.574 0.412 0.368 0.598 0.414 0.374 10590 0.72 0.52 0.468 0.75 0.52 0.484 0.74 0.52 0.486 0.784 0.522 0.468

2" Vertical Distance Between Propellers Angle Between Propellers 0° 0° 0° 45° 45° 45° 90° 90° 90° 135° 135° 135° RPM 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) 330 0 0 0 0 0 0 0 0 0 0 0 0 918 0.004 0.002 0.002 0.004 0.004 0.002 0.002 0.004 0.002 0.002 0.004 0.002 2280 0.026 0.02 0.018 0.024 0.02 0.018 0.024 0.02 0.018 0.024 0.022 0.018 3510 0.076 0.058 0.05 0.076 0.058 0.05 0.078 0.058 0.05 0.076 0.056 0.05 5010 0.154 0.112 0.102 0.158 0.116 0.104 0.158 0.118 0.102 0.156 0.116 0.1 6480 0.264 0.188 0.174 0.264 0.194 0.174 0.27 0.194 0.174 0.266 0.194 0.174 7752 0.408 0.274 0.254 0.418 0.28 0.254 0.416 0.28 0.254 0.402 0.28 0.256 9150 0.588 0.416 0.38 0.606 0.42 0.372 0.604 0.426 0.378 0.598 0.424 0.372 10590 0.754 0.524 0.475 0.756 0.534 0.484 0.77 0.534 0.478 0.758 0.53 0.478

3" Vertical Distance Between Propellers Angle Between Propellers 0° 0° 0° 45° 45° 45° 90° 90° 90° 135° 135° 135° RPM 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) 330 0 0 0 0 0 0 0 0 0 0 0 0 918 0.004 0.004 0.002 0.004 0.002 0.002 0.004 0.002 0.002 0.004 0.002 0.002 2280 0.028 0.022 0.018 0.03 0.022 0.018 0.03 0.02 0.018 0.028 0.02 0.018 3510 0.08 0.056 0.05 0.08 0.056 0.052 0.08 0.056 0.05 0.08 0.056 0.05 5010 0.156 0.114 0.102 0.152 0.114 0.104 0.156 0.114 0.104 0.158 0.114 0.102 6480 0.264 0.186 0.166 0.264 0.19 0.176 0.26 0.186 0.17 0.264 0.186 0.17 7752 0.4 0.28 0.254 0.4 0.286 0.26 0.4 0.28 0.252 0.4 0.28 0.26 9150 0.574 0.402 0.38 0.582 0.41 0.368 0.584 0.408 0.378 0.582 0.41 0.382 10590 0.73 0.526 0.476 0.744 0.53 0.474 0.744 0.526 0.478 0.744 0.526 0.486

4" Vertical Distance Between Propellers Angle Between Propellers 0° 0° 0° 45° 45° 45° 90° 90° 90° 135° 135° 135° RPM 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 7 x 5 5 x 5 7 x 5 Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust Thrust (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) 330 0 0 0 0 0 0 0 0 0 0 0 0 918 0.004 0.004 0.002 0.004 0.002 0.002 0.004 0.002 0.002 0.004 0.002 0.002 2280 0.03 0.02 0.018 0.03 0.02 0.018 0.03 0.02 0.018 0.03 0.022 0.018 3510 0.08 0.054 0.05 0.08 0.056 0.052 0.076 0.054 0.052 0.078 0.056 0.05 5010 0.16 0.116 0.1 0.156 0.116 0.104 0.156 0.116 0.102 0.156 0.116 0.104 6480 0.27 0.186 0.164 0.266 0.188 0.174 0.264 0.188 0.172 0.266 0.186 0.17 7752 0.406 0.282 0.256 0.406 0.29 0.262 0.4 0.278 0.248 0.406 0.282 0.264 9150 0.576 0.406 0.382 0.576 0.412 0.372 0.576 0.408 0.374 0.58 0.41 0.38 10590 0.754 0.522 0.48 0.754 0.53 0.472 0.748 0.528 0.48 0.754 0.528 0.486