design and fabrication of a miniature turbine for power generation...
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Design and Fabrication of a Miniature Turbine for Power Generation on
Micro Air Vehicles
Preliminary Design Report
Team 02008 Arman Altincatal Srujan Behuria Carl Crawford
Dan Holt Rob Latour
Department of Mechanical Engineering Kate Gleason College of Engineering
Rochester Institute of Technology 76 Lomb Memorial Drive
Rochester, NY 14623-5604
Executive Summary This report summarizes the progress made by the Miniature Turbine Senior Design Team. The goal of this project is to design, fabricate, and test a miniature turbine built to power small vehicles such as a micro air vehicle (MAV). MAV’s are vehicles less than six inches in size and are used for surveillance and scouting. Due to the small size of MAV’s, weight is a key design parameter. The batteries alone can account for more than 50% of the weight of the entire vehicle. A miniature turbine has been proposed as a replacement for batteries on these and other small vehicles. The turbine would not only produce power for the electrical systems but mechanical power for mechanical systems as well which removes the need for a motor. By decreasing the weight of power systems, MAV’s will be able to carry more instrumentation, fly longer, and be better able to complete their mission. The team used the Engineering Design PlannerTM methodology to design the miniature turbine. The first five facets of this process have been completed. The first facet or chapter of the report, recognizing and quantifying the need, discusses the goals, motivation, and background for the project. The second chapter presents an overview of four concepts the team has developed. The next section presents the feasibility assessment the team conducted for the four concepts. The fourth chapter presents a detailed description of the goals of the project as well as several safety and design practices. The fifth section, which is the analysis, is the bulk of the report. It describes the analyses that have been done to design the miniature turbine. The last chapter of this report summarizes the current status of the project, describes the experiments that will be performed next quarter, and presents the plan for finishing the project on schedule and within budget. The preliminary design documents, which include a technical data package of the miniature turbine, have also been completed. Through this design process, the idea of a miniature turbine evolved. The final design consists of three plates, which house the turbine, bearings, and flow paths. The flow paths are formed by channels milled into the plates. Air enters the casing through a fitting that is located on the same axis as the turbine. Three bolts fasten the plates together. These bolts also connect the supports that attach the faceplate of the motor to the turbine casing. When fabricated, the turbine should spin at a minimum speed of 50,000 rpm and produce at least 5 watts of power, but hand calculations show the turbine may reach speeds up to 100,000 rpm and produce up to 15 watts of power. The final design of the miniature turbine is shown in drawings included in the technical data package. The package has both assembly drawings as well as part drawings. Testing will be done next quarter on both dental turbines and the turbine presented in this paper. This will be done to validate that the fabricated turbine meets the design objectives and specifications as well as to show improvement over a commercially available turbine of the same size, such as a dental turbine.
Table of Contents
Executive Summary.................................................................................................................. 2 Table of Contents...................................................................................................................... 3 List of Illustrations.................................................................................................................... 5 1.0 Recognize and Quantify the Need ................................................................................ 6
1.1 Project Mission Statement ........................................................................................ 6 1.2 Product Description .................................................................................................. 6 1.3 Scope Limitations ..................................................................................................... 9 1.4 Stake Holders .......................................................................................................... 10 1.5 Key Business Goals ................................................................................................ 10 1.6 Top Level Critical Financial Parameters ................................................................ 11 1.7 Financial Analysis................................................................................................... 11 1.8 Primary Market ....................................................................................................... 12 1.9 Secondary Market ................................................................................................... 12 1.10 Order Qualifiers ...................................................................................................... 12 1.11 Order Winners......................................................................................................... 12 1.12 Innovation Opportunities ........................................................................................ 13 1.13 Background Research ............................................................................................. 13
2.0 Concept Development................................................................................................. 17 2.1 Control System Concept ......................................................................................... 17 2.2 Multiple Jets Concept ............................................................................................. 19 2.3 Cooling Generator Concept .................................................................................... 21 2.4 Light Weight Material Concept .............................................................................. 22
3.0 Feasibility Assessment................................................................................................ 23 3.1 Control System Feasibility...................................................................................... 23 3.2 Multiple Jets Feasibility.......................................................................................... 26 3.3 Cooling Generator Feasibility................................................................................. 27 3.4 Light Weight Material Feasibility........................................................................... 28 3.5 Feasibility Conclusion ............................................................................................ 30
4.0 Performance Objectives and Specifications................................................................ 31 4.1 Design Objectives ................................................................................................... 31 4.2 Performance Specifications .................................................................................... 32 4.3 Design Practices Used by the Team........................................................................ 34 4.4 Safety Issues............................................................................................................ 34
5.0 Analysis of Problem and Synthesis of Design............................................................ 36 5.1 Casing Design ......................................................................................................... 36
5.1.1 Flow Passages ................................................................................................. 37 5.1.2 Nozzle ............................................................................................................. 40 5.1.3 CFD Analysis.................................................................................................. 45
5.1.3.1 Introduction................................................................................................. 45 5.1.3.2 Analysis....................................................................................................... 48
5.1.4 Bearings and Shaft .......................................................................................... 58 5.1.4.1 Bearing Life ................................................................................................ 58 5.1.4.2 Shaft Design................................................................................................ 58
5.2 Power Generation.................................................................................................... 59 5.2.1 Generator Selection......................................................................................... 60 5.2.2 Electrical Load Connection to Generator ....................................................... 63
5.2.2.1 Brushed DC Motor...................................................................................... 63 5.2.2.2 Brushless DC Motor ................................................................................... 63
5.2.3 Voltage Regulation ......................................................................................... 65 5.3 Structural Design .................................................................................................... 65 5.4 Analysis Conclusion ............................................................................................... 66
6.0 Future Plans ................................................................................................................ 68 6.1 Experimentation...................................................................................................... 68 6.2 Schedule.................................................................................................................. 72 6.3 Budget ..................................................................................................................... 73
7.0 Conclusion .................................................................................................................. 74 References............................................................................................................................... 76 Appendix................................................................................................................................. 77
List of Illustrations Figure 1.1: Initial Sketch of Miniature Turbine………………………………………………... ..8Figure 1.2: Flow Chart………………………………………………………………...……….. ..9Figure 1.3: Capstone Turbine……………………………………………..……………………. 13Figure 1.4: Working Microturbine………………………………...…………………………… 15Figure 1.5 MIT’s Microturbine Design…………………….………………………………….. 16Figure 1.6 Stanford’s Microturbine……………………………………………………………. 16Figure 2.1: Casing design with Multiple Jets………………………………………….………. 20Figure 5.1 Casing Design………………………………………………………………………. 37Figure 5.2: Mass Flow vs. Inlet Pressure for T1=255K to 305K…………….………………… 42Figure 5.3: Force on Nozzle Due to Flow……………………………..……………………….. 43Figure 5.4: Mass Flow vs. Inlet Pressure for T1 = 255K to 305K…………………...………… 44Figure 5.5: Force on Nozzle Due to Flow……………………………………………………… 44Figure 5.6: Geometry………………………………………………………………………….. 48Figure 5.7: Static Pressures (Pa)……………………………………………..………………… 50Figure 5.8: Static Pressures (Pa) 10°……………………………………….…………………... 51Figure 5.9: Static Pressures (Pa) 20°………………………………………...…………………. 51Figure 5.10: Static Pressures (Pa) 45°……………………………………...………………….. 51Figure 5.11: Geometry…………………………………………………….…………………… 51Figure 5.12: Geometry…………………………………………………….…………………… 52Figure 5.13: Velocity Vectors (m/s)…………………………………………………………… 52Figure 5.14: Velocity Vectors (m/s)…………………………………………………………… 53Figure 5.15: Geometry……………………………………………………….………………… 54Figure 5.16: Static Pressure (Pa)……………………………………………………………….. 54Figure 5.17: Velocity Vectors (m/s)……………………………………………………..…….. 54Figure 5.18: Entropy Contours (kJ/kg.K)……………………………………………………… 54Figure 5.19: Static Pressure (Pa)…………………………………………………….…………. 55Figure 5.20: Velocity Vectors (m/s)…………………………………………..……………….. 55Figure 5.21: Geometry………………………………………………...………………………. 56Figure 5.22: Static Pressure (Pa)………………………………………………………………. 56Figure 5.23: Dynamic Pressure (Pa)……………………………………………………...……. 56Figure 5.24: Velocity Vectors (m/s)…………………………………………………...………. 56Figure 5.25: Bridge Rectifier………………………………………………………..…………. 64Figure 5.26: Voltage Regulator……………………………………………………..…………. 65Figure 5.27: Entire Assembly………………………………………………………………….. 66Figure 6.1: Experimental Setup…………………………………………………….………….. 70
1.0 Recognize and Quantify the Need
1.1 Project Mission Statement
The Miniature Turbine Senior Design Team is to design and fabricate a working
prototype in conjunction with graduate work being done at the Rochester Institute of
Technology. This prototype will be used as a proof of feasibility for a new avenue of
research being conducted at the University. A secondary goal of the project is to power
future Micro Air Vehicles (MAVs) also being developed at RIT.
1.2 Product Description
One of the most significant problems facing MAVs and other small autonomous
vehicles is the weight of conventional batteries to power motors, controls, navigations,
and other auxiliary systems. Background research and preliminary calculations show
that a miniature turbine/generator run on compressed nitrogen will have a higher power
to weight ratio then current chemical batteries. A miniature turbine would be used in
the same way as a battery; the only modification needed would be an exhaust port.
Since the turbine is run on compressed nitrogen, the exhaust gas will be inert and lower
than room temperature. Therefore, it will not be harmful to any surrounding
componentry or the environment.
Since the Miniature Turbine is to be used on future MAVs it will be designed to
interface properly with a future MAV system by meeting the power requirements of the
motor, servos, receiver, and camera. See Appendix A for electrical specification of the
2003 RIT MAV. Weight is a critical parameter; therefore, the Miniature Turbine Team
should design the prototype to be as light as possible.
The distribution of work between the Senior Design Team and the Graduate
Research will be as follows:
Senior Design Team:
Casing around Turbine
Generator Selections
Flow paths / Nozzle
Electronics, Controls
Shaft and Bearings
CFD Analysis
Reliability
Graduate Work:
Fuel Tanks
Starter
Turbine Design
Shared Responsibilities
Data Acquisition System
Design of Experiments and
Testing
A future goal of the Miniature Turbine project is to scale it down to a Micro
Electrical Mechanical System (MEMS) size. Therefore, the team should design the
prototype with the idea that it can be constructed in two dimensions and MEMS
fabrication techniques will be used to build a microturbine in the near future.
Current work is being done at a number of schools on microturbines (MEMS size
turbines). These schools have put significant time and resources into designing and
building a working microturbine, but they still face many challenges. The University of
Wisconsin is the only group to have fabricated a microturbine that produced power, but
their design only produced 17 millieWatts. This is not nearly enough to power a MAV.
Therefore, the goal of this project is to build a miniature turbine, or a turbine that is
about an order of magnitude bigger than a microturbine. This miniature turbine should
produce enough power for a MAV and be a first step towards RIT’s research on a
microturbine.
This project has numerous potential applications. In the short term, the Miniature
Turbine will be used in MAV’s and other autonomous vehicles being designed at RIT.
Both the Department of Defense (DoD) and the Forest Service are very interested in
using MAV’s for surveillance. The DoD would like MAV’s to be a short-range, hand-
launched tool for ground troops in military conflicts. The Forest Service is looking for
MAV’s to fly into and around forest fires to record information such as temperature,
speed of fire movement, and location. Long-term applications of a Miniature Turbine
include any device that uses electric power and needs to be lightweight. One example
is ground based micro robots, which could be made lighter by using a miniature turbine
instead of a battery.
Figure 1-1: Intial Sketch of Miniature Turbine
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A sketch of the turbine and fuel tank is shown in Figure 1.1. The turbine will be
of the Pelton Wheel type (similar to a water wheel), so the figure accurately represents
how the turbine will be oriented to the inlet and exit of the fuel. Figure 1.1 also shows
the shaft that will connect the turbine to the generator. An overview of how the
different components of the Miniature Turbine will be assembled is given Figure 1.2.
The figure also shows how the mechanical and electrical systems will be integrated.
Figure 1.2: Flow Chart
Input Signal
Power OutElectronics
Gen - Set
Casing OutTurbine
Controls
Casing InStarter Fuel Tank
1.3 Scope Limitations
The prototype Miniature Turbine shall be fully designed by the end of RIT’s
winter quarter and be fabricated and assembled by the end of spring quarter.
At the end of Winter Quarter, 20023, the senior design team will hold a Preliminary
Design Review. At this review they will be responsible for:
��Drawing Package
��Quotes for Vendors
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��Budget
At the end of Spring Quarter, 20024, the senior design team will present the working
prototype. At this presentation they will be responsible for:
��Working Prototype
��Final Report / Binder
��Initial testing done on the turbine and generator
The senior design team shall not be responsible for the following:
��Impeller Design
��Fuel Tanks, therefore compressed air can be used for initial runs
��Starter
1.4 Stake Holders
The main stakeholders are the students working on the team and the faculty
connected to the project. Other stakeholders are students of the MAV team, other
schools working on small turbines, future users of MAV’s (military, forest service), and
future employers of the students working on the project.
1.5 Key Business Goals
The Team will be successful when they have fabricated a working Miniature
Turbine that produces power. If this has been done then:
��The students on the team will have learned how to work on a multidisciplinary team
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��A proof of concept will have been completed and further funding can be requested for
future prototypes.
��The MAV team will have a new power source available to them.
1.6 Top Level Critical Financial Parameters
��The generator shall be reusable, i.e. the generator cannot be destroyed by the speed of
the turbine through the normal operation of the turbine up to 15 minutes.
��All testing and demonstrating will be done with compressed air. However, since air
and nitrogen have very similar properties the turbine will be designed for both
gases. Integration of turbine/fuel tanks will be done at a later point as part of a
graduate project.
1.7 Financial Analysis
A $2000 budget has been proposed for the Miniature Turbine Project. This budget
shall include:
��Generator
��Electronics
��Casing Material
��Any needed components to complement the DAQ systems in either the
Instrumentation Lab or the Windtunnel
��Couplings for turbine and generator shaft
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1.8 Primary Market
The primary market of the Miniature Turbine is the future MAV teams at RIT.
This consists of both the students on the team, the faculty connected to the team, and
any competitions the team attends.
1.9 Secondary Market
The initial secondary markets are the Department of Defense, the Forest Service,
and the commercialization of MAV’s for private use.
1.10 Order Qualifiers
The Miniature Turbine Team shall fabricate and assemble a prototype that will
produce at minimum enough power for the current MAVs. The team will also do
experimentation to verify the power produced and efficiency of turbine.
1.11 Order Winners
The following are goals of the project if time and budget permit:
��Be lighter than a battery that produces the same power, i.e. have a better power to
weight ratio.
��Be reliable.
��The prototype is easy to use and reuse.
��Have an automated control system.
��Verify that Engineering Design Models agree with prototype
��Computational Fluid Dynamics analyses will also be performed to aid in casing
design.
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1.12 Innovation Opportunities
Potentially the Miniature Turbine could be used anywhere a lightweight power
source is required. Eventually, Micro Turbines could be integrated directly into
electronics. This would allow the user to only have to replace or recharge the fuel tank.
This would make the electronics lighter and more portable, cheaper, and more
environmentally friendly.
1.13 Background Research
The word micro is used very loosely in the turbine industry. For microturbines,
the main difference depends on whether an academic institution or industry is using the
word micro. In academia, the word micro usually refers to a Micro Electrical
Mechanical System (MEMS) where very specialized fabrication techniques have been
created to work on the micron scale. A number of these very small micro turbines are
being developed and will be outlined below. In industry, where turbines are designed
awatts, a micro turbine is a turbine that produces less
than five hundred kilowatts. On the smaller end of
this very large gap is where the microturbine
presented in this paper lies.
The
to produce up to a thousand meg
current leader in industry of
micro
Figure 1.3: Capstone Turbine
turbines is the company Capstone, Inc. This
company builds turbines down to 30 KW range.
These turbines are used for a variety of applications
such as power generation for manufacturing plants
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and powering city buses. Figure 1.3 shows one of Capstone’s models. These turbines
can run on a several fuels including natural gas, propane, and diesel.
In recent years, a number of institutes have been working on MEMS sized
turbines.
successful fabrication of a microturbine that produced
powe
The first group to work on a microturbine using silicon fabrication techniques
was the researchers at AT&T Bell Laboratories (Mehregany, et al., 1987). They were
able to fabricate a turbine that was 900 �m in diameter and turned at approximately
24000 rpm. The smallest turbine they fabricated was 600 �m in diameter and 40 �m
thick. The AT&T team was focused more on showing that turbines can be built at this
size than in fabricating a turbine for power generation, so they did not attempt to attach
the turbine to a generator.
The first and only
r was done by a joint project between the University of Wisconsin and Motorola
(Wiegele, 1996). Their design produced 17 millieWatts with the turbine shown in
Figure 1.4. They integrated the turbine rotor and the generator rotor into one part. This
significantly decreased the size and complexity of the design. The turbine was able to
run up to 70,000 rpm with a backpressure of 29.7 kPa. The rotor required 4.6*10^-3 N-
m/m to turn. Although they were able to produce power through an innovative design,
the amount produced is not sufficient to power a MAV.
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Figure 1.4: Working Microturbine
Most of the academic research on microturbines has used a compressed gas to
power the turbine. Groups at the Massachusetts Institute of Technology and Stanford
University are currently researching the use of a different power source. The MIT
project is being sponsored by DARPA and was started in the early nineties. They are
currently using liquid hydrogen as a fuel and are predicating the use of hydrocarbons in
the future. Significant numbers of papers have been published on their work as well as
several patents. MIT’s design, show in Figure 1.5, assembles the generator,
compressor, fuel manifold, combustion chamber, and turbine into a one cm x one cm x
three mm package. The microturbine is designed to produce 10-20 Watts of power at a
speed of around one million rpm. The use of hydrocarbons for fuel could produce up to
a hundred watts of power.
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Figure 1.5 MIT’s Microturbine Design
Stanford’s work on micro gas turbines has been focused on MEMS fabrication
techniques. Recently they have developed a process called Mold Shape Deposition
Manufacturing (Mold SDM). Using this process, they have been able to create the
complex shapes shown in Figure 1.6. These rotors are made out of silicon nitride, so
they are extremely strong. Testing showed that a 12mm blade was able to spin up to
456,000 rpm.
Figure 1.6 Stanford’s Microturbine
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2.0 Concept Development
The Miniature Turbine Senior Design group developed a large list of possible
ideas on ways to power a Micro Air Vehicle during a brainstorming session. This list,
which is available in the Concept Development Section of the Engineering Design
Planner Binder, has twenty-four ideas. These ideas were further discussed,
consolidated, and voted on. The top five chosen were an air miniature turbine, solar
power, windmill, nuclear reaction, and rocket. After discussing the feasibility of these
ideas and based on work that has already been done, the group decided to focus on the
air miniature turbine. Brainstorming was then done on ideas for the air-powered
turbine. Twenty-one ideas were presented, four of which the team decided to further
investigate based on a vote taken by the team. These four were utilizing a
control/feedback loop incorporating either a variable nozzle or solenoid valve, multiple
jets impacting the turbine, using exhaust air to cool generator, and using lightweight
materials to reduce weight. Group drawing was then used to start developing these
ideas. After the basic concept of each idea was developed, each person in the group
took one of the ideas to further develop them. Each of these ideas is presented in more
detail below.
2.1 Control System Concept
A control system incorporating a feedback loop to regulate the output terminal
voltage of the generator was investigated. A permanent magnet dc motor will be
utilized as a generator in this miniature turbine proof of concept. The inducted voltage
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at the terminals of the generator will be directly proportional to the mechanical speed of
rotation of the generator’s shaft.
The demand of the generator’s electrical load will affect the rotational speed
of its shaft. As the electrical load on the generator is increased, the shaft’s speed of
rotation will decrease. Because the generators output voltage is dependent on the
rotational speed, an increased load will also result in a decreased voltage supplying the
load.
It is desirable to maintain a constant output terminal voltage on the generator,
which will be driving the electronic components of the MAV. Using a permanent
magnet dc motor as a generator, the only way to vary the output voltage is to vary the
shafts speed of rotation. Therefore, in order to maintain a constant generated voltage as
the generators electrical load is increased, more mechanical power will need to be
supplied to the generator to maintain a constant speed of rotation.
As mentioned above the voltage at the generators output will only remain
constant if the rotational speed is held constant. Varying the output power of the
generator’s prime mover, the air-powered miniature turbine, will change the speed of
the turbine / generator shaft with a no-load condition on the generator. An increased
airflow to the turbine will increase its power output and consequently increase the
speed of the turbine. Conversely, decreasing the flow to the turbine will result in a
lower turbine speed. Using this method the speed of the generator shaft may be
effectively controlled.
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A feedback loop will be required to vary the airflow to the turbine’s input
nozzles. If the airflow to the turbine is controlled, the terminal voltage of the generator
can be regulated as desired. To control the airflow to the turbine a variable solenoid
valve or a variable flow nozzle may be utilized. A solenoid valve would control the
turbine flow by varying the electrical potential difference across the valves electrical
terminals. A change in voltage across the terminals would result in a change in the
valves position, achieving airflow control to the turbine as desired. A variable flow
nozzle could achieve airflow control to the turbine in a similar manner. As seen in the
drawings presented in the Concept Development section of the Engineering Design
Planner Binder, a screw valve driven by a servomotor would increase or decrease the
flow through the turbine’s nozzle.
The speed of rotation of the generators shaft, which is given by the generator’s
terminal voltage, can be used as a feedback signal to control the solenoid valve or
variable nozzle. The control signal, which would be passed back to the control systems
input through a negative feedback loop, can be the generator’s output voltage itself.
The feedback signal would enter a summing node, which would be built using an
operational amplifier to implement negative feedback. The feedback compensator
would take the feedback signal and use it to vary the voltage across the terminal of the
solenoid, or to power the servomotor to vary the nozzle position.
2.2 Multiple Jets Concept
Another concept proposed by the design team is the idea of having multiple
jets impacting the impellers to maximize the performance of the miniature air turbine.
In order to make use of this concept the casing, which is the material surrounding of the
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turbine, was to be designed to have several jets directed at the turbine as seen in Figure
2.1. Since each jet produces a certain amount of momentum resulting in torque on the
shaft, each additional jet increases the total torque produced by the turbine. One
possible configuration is to use four inlets, one on each quadrant of the circular
geometry of the casing, facing perpendicular to one another. Figure 2.1 illustrates this
proposed casing design.
F
Impeller
Inlet 2Inlet 1
Turbine
�
+
It is observed
add to each other rath
was to increase the torq
while maintaining the
Jet Momentum
igure 2.1 Casing design with Multiple Jets
Inlet 3
Inlet 4
from Figure 2.1 that the introduced flow at the four inlets would
er than conflict with one another. The purpose of this concept
ue produced by the turbine by increasing the net mass-flow rate
rotational balance of the turbine. Since the power produced is
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directly proportional to the torque produced, as the torque increases the power
increases. One negative aspect of the concept is since there are four jets, the air (or
fuel) is used up faster, so a larger fuel tank is required.
2.3 Cooling Generator Concept
One concept developed by the team was to use the turbine’s exhaust gas to cool
the generator. As power is produced, the generator is expected to heat up. If it can be
kept cool, higher speeds will be attainable, which would result in greater power
production. To accomplish this, ducts are connected to the turbine outlet and are used
to direct the cool exhaust flow to the generator. Cooling fins placed on the surface of
the generator casing would improve the cooling efficiency.
The gas used to drive the turbine is compressed air at a pressure greater than 50
psi. The enthalpy for a gas is a function of temperature. As the air moves through the
turbine, that enthalpy is converted into work. The decrease in enthalpy will cause a
decrease in temperature. The only concern is that the turbine will generate enough heat
due to the friction of the air impacting the blades to warm the air before it gets to the
generator. If that happens, the air will not help cool the generator. If the air becomes
too warm, it could cause the generator to heat up quicker than without the air. The
added cost for the cooling fins and air ducts would be minimal compared to the overall
cost of the product. This concept would be easy to implement into the design of the
turbine.
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2.4 Light Weight Material Concept
Keeping in mind that this design is intended for use in MAV’S, an important
concept that needs to be integrated into this design is the use of lightweight materials in
the fabrication of the turbine. The basic idea of this concept is that the miniature turbine
needs to be extremely light in weight Hence, incorporating the use of lightweight
materials in the design stages is extremely important to the project and must be
accomplished in the initial stages.
The team prepared a list of the materials that can be used to make the various
parts of the miniature turbine and to incorporate the lightweight concept when
researching for possible materials. The team also realized that besides weight several
other factors including strength, stresses, manufacturability, cost of material and cost to
manufacture play a vital role in the material selection process. There is a trade-off in
these properties for various materials. For example, silicon nitride is light and had other
properties required by the team, but the cost was too high to fit within the team’s
budget. After looking at various materials, the team prepared a list of materials and
found that aluminum is the most viable option for most of the parts that are to be
designed. There is also an option of looking into certain types of steel that are lighter
than aluminum but it is to be constantly remembered that the lightest possible materials
with the other specified properties are to be considered when selecting materials.
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3.0 Feasibility Assessment
The four concepts presented in the previous section are the results of team
brainstorming and initial investigation. Once each idea had been clearly defined and
well understood by all members of the team, a feasibility assessment was conducted on
each concept by the team. The feasibility assessment was governed by the twelve-
question assessment guide provided in the Design Planner package. This assessment
looked at technical, economic, market, schedule, and performance factors affecting the
completion of the project. Each question was compared to the project baseline, which
is the miniature turbine as described in the Needs Assessment. These questions were
graded on a scale of zero to three, with a score of two representing the same as
baseline, zero being unfeasible, and three being the most feasible. The team used these
factors to rank the four concepts and decide which direction the team wanted to move.
The feasibility of each concept is described below.
3.1 Control System Feasibility
The Control System Concept was compared to a baseline of not utilizing a
control scheme. The 12 questions are broken into five subgroups and are discussed in
the following.
First, a feasibility assessment relating to the technical aspect of the control
scheme was conducted. The senior design team has the basic skills necessary to
implement the control scheme, however, some areas of the design would require
consulting an expert outside of the team. Any outside assistance needed could be
received from an R.I.T. Electrical Engineering faculty member. Any necessary
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electrical components needed to implement the control scheme are readily available on
the market. However, preliminary research raised concern that a variable solenoid
adequate for the concept may be difficult to obtain. In addition, to implement the
alternative control method utilizing a variable nozzle as discussed in the concept
development would require design and testing by the Senior Design Team. A variable
nozzle such as the one required for this project is not available on the market. The
technical assessment received a score below baseline.
Next, an assessment was done relating to economic feasibility. The team’s
budget would be able to support this concept, however, if it were to fail, the concept
would be viewed as a waste of resources. The utilization of a control scheme would be
an added feature to the project, and would not be effected by the future national or
global economy. The economic assessment received a score slightly below baseline.
The next assessment conducted relates to the market in which the concept
would be introduced. The proof of concept project can be successfully completed
without implementing a control scheme; therefore, inclusion of the control scheme
would not have a high market demand as viewed from the project’s objectives. The
R.I.T. engineering department is putting significant resources into MEMS development.
The department would likely support future development. The market assessment
received a score equivalent to baseline.
The next assessment dealt with the teams schedule constraints. The concept
could be implemented during the allotted time; however, concept failure would be
interpreted as an improper allocation of resources. Research is currently being
conducted at various universities on similar projects as discussed in Section 1.1.3,
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Background Research. A working miniature turbine utilizing a control scheme would
be viewed as a research success if completed before competing researchers. The
schedule assessment received a score slightly below baseline.
The final assessment investigated the concept feasibility with respect to
performance. A miniature turbine utilizing a control scheme would go beyond the
requirements specified in the Needs Assessment. In addition, the miniature turbine
project can be successful without implementing this concept. At this time, the team is
aware of no significant regulatory hurdles. The control scheme would be designed for
the current miniature turbine project and would serve no useful purpose in other
applications outside of this project. The performance assessment received a score
above baseline.
The Control Scheme Concept Feasibility Assessment yielded an average score
of 1.92. This average score can be interpreted that the feasibility of the control scheme
concept is slightly lower than the baseline design. The senior design team decided not
to further pursue the control scheme concept at this time. The Miniature Turbine
Project will be used as a proof of concept for a new avenue of research being conducted
at the University. The proof of concept can be successful without utilizing the control
scheme concept. The Feasibility Assessment questions led the team to believe the
team’s resources are better utilized at this stage of the design in more productive
activities. The control scheme concept is left as an avenue of future development of the
Miniature Turbine project once the feasibility of the overall turbine design has been
assessed.
25
3.2 Multiple Jets Feasibility
The design team had evaluated the multiple jet concept by comparing it to the
baseline model which consisted of single jet. The discussion topics to evaluate this
concept were its technical, economical, marketing, scheduling and performance
strengths and weaknesses. The technical background required to produce the multiple-
jet concept was evaluated as being at the same level as the baseline model. This meant
that if a single jet model could be built, then a multi jet model could also be built. The
economic issues were also discussed and estimated that the concept was not at a higher
standing than the baseline. The team had sufficient resources to complete the concept
although its future impact on the economy was questionable. Marketing values of the
concept were also discussed by the design team. The multi jet design predicted a
market value that was greater than a single jet baseline model. The schedule to
complete the concept was agreed on that it was at the same level as the baseline
concept. The team decided that the sooner the concept was designed and tested, the
better its chances of creating a market value greater than its baseline. Finally, the
design team discussed the feasibility of the concept’s performance. It was concluded
that the multi jet design would have better performance than the baseline model in
terms of its efficiency for torque generation due to an increase in the mass-flow rate.
Therefore, greater torque suggested greater power generation, which surpassed the
customer’s expectations and needs.
In completion of the feasibility assessment of the concept, the team obtained an
average value, shown in Appendix B, that described the concept’s technical,
economical, marketing, scheduling and performance strengths and compared it to the
26
baseline. Overall, it was observed that the multi jet concept enhanced the design.
Therefore, the team decided to modify the design by using multiple jets.
3.3 Cooling Generator Feasibility
The concept of using the turbine exhaust to cool the generator compared well
to the baseline design in all of the feasibility factors. Technically, the team members
have an adequate background in heat transfer and fluid dynamics to analyze the cooling
fins on the generator. All of the parts needed for this concept are readily available. A
problem may come up with finding cooling fins that would fit the curvature of the
generator casing. This part may have to be fabricated by the team. Since the part
would need a curved profile, manufacturing it would be difficult for the team. The
materials and parts needed to direct the exhaust flow over the generator are rather
inexpensive compared to the overall budget for the project. However, it would increase
the overall cost of the turbine without adding much to the overall value. Cooling the
generator would increase the speed that the turbine is able to spin. The increase in
speed leads to more power production. Because of this, adding a cooling system would
increase the market value of the finished product. In terms of RIT, the heat transfer
work required to analyze this concept fits the direction the school wants it’s research to
purse. The extra analysis needed for this concept would delay the finish date of the
overall design, but the increased time would be minimal. The team should be able to
finish the extra analysis in the allotted time. However, any delay could allow another
school to get ahead of RIT in terms of miniature turbine technology. As far as
performance, this concept exceeds the baseline design. The added power derived from
the generator cooling would exceed the needs of our customer. The finished product
27
will be able to produce more power than is needed for the MAV, so it could be carried
over to other applications. Any product that requires a lightweight power source could
make use of the miniature turbine.
After reviewing the feasibility assessment on this concept, the team decided to
defer the decision to incorporate the concept into the design of the turbine until the
spring. At the time, the team was not certain if the generator would need cooling to
operate at the design speeds. If cooling is not needed, the added analysis, time, and
money would be wasted since it is not required for the final product. Once the
generator is tested, the team will know if cooling is needed. The design for the cooling
system is very simple, so will be easy to add at a later date.
3.4 Light Weight Material Feasibility
The feasibility of using light weight materials was investigated based on the five
factors outlined previously and compared to a baseline of the entire turbine being made
out of a standard carbon steel such as 1018 steel. Technically the team has the ability
to work with superior materials; therefore, the feasibility was same as the baseline. The
team has the basic competence required for any materials that it is to use in the future
except for the use of exotic materials like silicon alloys, titanium, etc. Since the team
decided on the fact that it was not going to use something expensive, the materials are
readily available. Economically, this concept was worse than the baseline concept
because if the team is going to use extremely light materials other than aluminum, it is
going to cost a lot more. Although, looking towards the future, this concept can have a
higher value as the world is looking towards lighter materials and they are becoming
cheaper and easier to acquire. Market-wise, this concept scored above the baseline
28
concept because the lighter the miniature turbine, the more useful it will be to bigger
market. RIT is also moving towards the MEMS area and this concept fits in well with
programs being started by the school. From a schedule standpoint, the concept fit in
well with the baseline concept. It may take longer if the team uses better and expensive
materials due to time taken to research on these materials, but it should not take much
longer than steel. The window of opportunity in the market for this concept is infinite.
No matter how light the team makes it (within budget), the turbine can always be
lighter.
Lastly, this concept is also above the baseline concept in the performance area.
The turbine has to be light and the materials need to have other important properties
such as a specified strength. The main customer for this product is the RIT MAV team
and if the Miniature turbine team uses the appropriate materials within the scope of this
project, then it will exceed all of the MAV team’s expectations.
Thus, it can be concluded from the feasibility assessment that the use of
lightweight materials is essential when fabricating the turbine and is feasible in most
aspects. Taking all these factors into account the team decided to incorporate the
concept into the design of the miniature turbine. The importance of weight in this
system has already been emphasized and it has been decided that weight plays an
extremely important role in this project. Also, after the team looked at all the feasibility
aspects, it seemed that the use of light weight materials will not only be feasible but
will prove to extremely profitable and advantageous to all involved in this project.
29
3.5 Feasibility Conclusion
Based on the analysis presented above, the team was able to examine each
concept and decide whether the idea should be further developed. The scores of each
concept and a radar chart can be seen in Appendix B. The team decided to continue to
develop both the multiple jet concept and the lightweight material concept. Both seem
to be feasible based on the analysis and both would better enable the team to meet the
customer requirements. After looking at using the exhaust gas to cool the generator, it
was decided that the team should wait until it was needed before more time was spent
developing the idea. Based on the feasibility analysis the team decided the control
system concept was not needed to meet the customer requirements and therefore the
idea should be left for future teams to develop.
30
4.0 Performance Objectives and Specifications
The team acknowledged the fact that certain objectives and specifications have to
be determined so the team can measure the performance of the miniature turbine. These
objectives and specifications are discussed briefly in this chapter.
4.1 Design Objectives
There are a number of design objectives that required the attention of the team.
These objectives have to be specified in order for the team to have a list of goals and
aims to achieve. These objectives are listed below
1) The most important objective or goal that the team has to achieve is the production
of power by the miniature turbine. This goal lies in the core of the project and the
design elements must include this objective at every phase.
2) Another objective is to design the miniature turbine for future use by Miniature Air
Vehicles. The miniature turbine has to light in comparison to the batteries that are
currently being used by MAV’S. In addition, the size of the turbine plays an
important part as it needs to be fitted into MAV’S.
3) An important objective that has been incorporated into the design of the turbine is
for the generator to withstand the speed of the turbine. This is important for
efficient and effective functioning of the miniature turbine and to prevent the
destruction of the generator.
4) The team will also ensure that enough torque is produced by the miniature turbine
to turn the generator. This objective is also important in the design of the
miniature turbine and is essential for its successful and effective performance.
31
5) Another design objective that the entire team agreed upon is that the miniature
turbine generator should run for at least fifteen minutes. Effective functioning of
the miniature turbine is not the sole goal of the team, but also effective
functioning for a required time is necessary since MAV’S need to run for fifteen
minutes or more.
6) An additional objective is to conduct experiments to find the power produced
mechanically by the turbine and the power produced electrically by the generator.
These experiments are vital in order for the team to successfully analyze the
efficiency of the turbine.
7) Another objective that the entire team thought was essential was that the miniature
turbine generator should be reusable.
4.2 Performance Specifications
The team decided that a number of performance specifications need to be
met in order for the project to be successful. These specifications are based on the
minimal requirements of the miniature turbine to be designed by the team. Therefore,
the final product needs to be able to meet these minimal requirements so that the basic
objectives of the project are fulfilled. These specifications have been kept in mind when
designing the turbine. They are listed below.
A) TURBINE SHALL PRODUCE 5 WATTS OF POWER
The miniature turbine has been designed to produce a minimum amount of
power. This is an important specification as the miniature turbine is being
designed for possible future use by MAV’s through the replacement of batteries to
32
generate power. Therefore, the team will strive to design the product to meet this
requirement. If this power requirement is not achieved, the team will redesign and
rebuild to reach this requirement.
B) TURBINE BLADES SHALL SPIN AT A MINIMUM OF 50,000 RPM
In order for the miniature turbine to produce the set amount of power, the
turbine blades need to rotate at a certain speed that forms the basis for this
performance specification. Thus, the team will design to obtain this minimum
required speed.
C) GENERATOR TEMPERATURE SHALL BE LESS THAN 125�C AFTER
15 MINUTES
The generator needs to be maintained below a certain temperature so that it can
continue to function properly. Exceeding this temperature may damage the
generator. Thus, it is essential that this fact be incorporated into the design of the
turbine. If this specification appears to be a problem, then the team will
implement the concept discussed previously of using the exhaust gas to cool the
generator.
D) MINIMUM TORQUE TO BE PRODUCED BY TURBINE SHALL BE
0.021 oz-in or 1.48�10^-4 Nm
This is another requirement that needs to be met by the miniature turbine to
facilitate the successful completion of the project and hence, requires attention
during the design stages of the project. This minimum amount of torque produced
by the turbine will enable it to further produce the specified power.
33
4.3 Design Practices Used by the Team
The team discussed a number of design practices to be considered when designing
the miniature turbine. A list of these practices is provided below.
1) Design for Manufacturability – The team has designed the miniature turbine such
that the parts that are designed in a customized manner to fit the requirements of
the team’s design can be manufactured by using a machine at the institute.
2) Design for Re-Usability or Re-manufacturing – The team has designed the turbine
such that the turbine can easily be disassembled and parts of it can be reused.
3) Design for Assembly – The design of the turbine is such that a number of
assemblies and sub-assemblies exist in order to make the entire assembly process
easier.
4) Design for Low Cost – The team designed the miniature turbine such that the cost
of making the turbine is kept to a minimum. There are no extra or unnecessary
parts and the materials were selected after a cost benefit analysis process.
5) Design for Efficiency – The team has designed the miniature turbine to make it as
efficient as possible within the scope of the project.
4.4 Safety Issues
The team found no set safety standards for this project as it is an experiment being
conducted by the institute rather than an industrial process. Also, the comparatively
miniature size of the turbine does not hold many possible risks for the team. Although
34
there are several safety issues that need to be addressed. These issues are discussed
briefly in this section.
1) The most important safety issue is the fact that the turbine blades will be rotating
at an approximate speed of 50,000 and hence, members of the team must be
extremely careful while performing any tests on the turbine as it may cause slight
injuries. This will be done by performing tests in a sealed plexi-glass container
and by wearing safety goggles.
2) The team must also be careful while handling the turbine due to the chances of
infliction of minor shocks caused by the generation of electrical power by the
turbine.
3) The parts of the miniature turbine have many sharp edges. The members of the
team must be careful to avoid being cut on these small pieces.
4) Most importantly, all members of the team must follow all machine shop safety
guidelines during the fabrication of any part.
35
5.0 Analysis of Problem and Synthesis of Design
The analysis of the miniature turbine looked at several different aspects of the
design. The team split up the analysis into three main sections: the design of the casing
around the impeller, the electrical power generation, and the design of the structure
connecting the casing and motor together. The design of the casing was complicated by
the small size of the impeller geometry. This forced the team to design based on
available fabrication techniques, which greatly limited the complexity of the casing. As
the casing design progressed a number of areas were investigated including the head
loss in the flow passages, the design of a nozzle to increase the velocity of the air
striking the impeller, a computational fluid dynamics (CFD) analysis on the flow in the
impeller cavity, and an investigation of the fatigue of the bearings and shaft. The next
section presents the analysis of the electrical part of the miniature turbine. The
generator selection is discussed in detail as well as the design of circuitry needed to
convert the output AC power into DC power for the MAV componentry. The final
section discusses how the miniature turbine will be packaged and the connection of the
motor and impeller.
5.1 Casing Design
The turbine casing is constructed from three aluminum plates fastened together by
three bolts. These plates house the turbine, bearings, flow passages, and nozzles.
Gaskets are used between the plates to prevent air leakage.
The compressed air enters the top of the casing through a 1/16” ID NPT air hose
fitting. The flow is then split by a channel in the top plate and directed through the
36
flow passages to the two inlet nozzles. The air then flows through the turbine housing
and exits out the two exhaust ports on the bottom of the casing. Figure 5.1 shows an
exploded view of the casing assembly.
Figure 5.1 Casing Design
5.1.1 Flow Passages
Due to size limits in the casing, two flow passages are used in the casing to split
the airflow and direct it to the two inlet nozzles. These two passages must be identical
in size and shape so the inlet pressures and velocities at the two nozzles are equal.
Early concepts had the air enter the casing through the side to minimize pressure loss,
but the design would not allow for two paths that would be of equal length and have the
same number of turns. The team then began to develop the concept utilizing a top
mounted air fitting. This concept used air passages that have more bends and longer
passages and therefore greater pressure losses, however both flow passages are
identical. Since the passages, and therefore the losses are equal, the conditions at the
nozzles will be identical.
To form the passages, a three-plate casing was developed. In the plates,
horizontal channels will be milled into the surfaces as well as drilled holes to create the
37
passages. The milled channels create a square passage. The fourth wall is the face of
the neighboring plate.
The passages are designed to be simple ducts. In order to do this, the channels
and holes had to be designed so that they would not accelerate or diffuse the flow. The
air fitting has a 1/16” (1.58 mm) inner diameter, which is an area of 0.003 in2 (1.96
mm2). All of the other passages are designed to have the same cross sectional area. In
order to construct a smooth channel, the square passage needed to be the same width as
the diameter of the holes. Because of this, the channels were made to be 1.58 mm wide
by 1.25 mm deep.
Since the air fitting is mounted axially to the turbine, the paths need to route the
airflow around the turbine housing. To do this, three 90° bends were used. The first
bend is a T-junction that splits the inlet flow into the two passages. A square channel
then brings the air outside of the radius of the turbine housing. The second bend directs
the flow into 1/16” holes that bring the flow to the bottom plate. The third bend directs
the flow into the nozzle. See the technical data package for drawings of the plates and
how they are assembled.
To determine how the flow passage design affects the flow properties, a head loss
calculation was done. To calculate the total head loss, the following equation (equation
5.1) was used:
�
phhh orlmajorltotall�
��� min,,, Equation 5.1
In this equation, �p is the change in pressure and � is the density of the air. The
major head loss is due to friction in the flow passages, and minor head loss is due to
bends in the flow. In order to calculate the losses, the air was assumed to be an ideal
38
gas. This assumption is valid since the operating temperature is greater than twice the
critical temperature of 133K and less than five times the critical pressure of 546.8 psi.
Also, the flow was assumed to be fully developed and turbulent with a Reynolds
number in the order of 105. Under these conditions, the major head loss is
2
2
,V
DLfh majorl � Equation 5.2
where L is the length of the passage, D is the diameter, and V is the average velocity of
the flow. In the case of the square channels, the hydraulic diameter needed to be
calculated. For a rectangular duct with a width b and a height h, this is found by the
equation
� �hbbhDh�
�
24 Equation 5.3
The friction factor, f, is a function of the Reynolds number, Re, and the
smoothness of the pipe. Since the ducts are machined into the casing, they are assumed
to be a smooth pipe. The Reynolds number is defined as
�
� DV�Re Equation 5.4
where�� is the viscosity of the air. The viscosity of a gas can be found as a function of
temperature using the Sutherland correlation. For air, the viscosity is defined as
K4.110Ksm
kg10458.1 1/26
2/3
�
��
�
�
�
�
S
xb
TSbT
�
Equation 5.5
The previous equations yielded a viscosity of 1.62x10-5 N s/m2. The Reynolds
number for the square channels is 2.30x105 and for the circular holes is 1.16x105.
39
Based on these values, a friction factor of 0.0245 can be found for the square channel
and 0.027 for the circular hole. The chart used to determine this can be found in the
Appendix as Fig. D.2.
The major head loss was calculated as 259.37 J/kg
The minor head loss was found in a similar way. It is defined as
2
2
min,V
DLfh e
orl � Equation 5.6
where Le/D is a function of the deflection angle in the bend of the duct. Using figure
D.1 with a 90° deflection angle, a value of 60 is found. From these values, the minor
head loss was calculated to be 5512.5 J/kg for all three bends.
The major and minor head losses yield a total head loss of 5771.87 J/kg, which
equates to a pressure drop of 7.89 psi. See appendix D for details of these calculations.
5.1.2 Nozzle
The nozzle concept started with the nozzle being manufactured as a separate piece
and placed into the casing. In order to generate the highest velocity possible at the
nozzle exit, a converging-diverging design was considered. Since the small scale of the
nozzle makes it very difficult to manufacture, a search was performed to find a
commercially available nozzle suitable for the project. After an extensive search, a
small number of applicable nozzles were found.
The most promising product found was made by an Israeli company called
Miniature Tools. These nozzles, made for water blasting, have orifice sizes as small as
0.01” (0.254 mm) and are rated for pressures up to 35,000 psi. One desirable aspect of
this nozzle was that it was made as a carbide insert. This would make it very easy to be
40
incorporated into the casing. Other nozzles found would need some further design
work to mount them into the casing. The only negative aspect of the design was the
fact that it was a simple converging nozzle. The highest attainable exit velocity with
this type of nozzle is Mach 1. Once the flow reaches that velocity, it will be choked
and will not accelerate further. A converging-diverging design would allow the flow to
accelerate past Mach 1.
The team decided that the velocity limitation was acceptable for the design. Since
the force exerted on the impeller blade from the air jet is a function of inlet velocity, the
highest attainable velocity is desirable. Even though higher velocities are attainable
with a converging-diverging nozzle design, a velocity of Mach 1 will provide enough
force to drive the turbine. The nozzle was then analyzed to determine the mass flow as
well as the reaction force generated by it. For this analysis, it was assumed that the
flow was at steady state, the air is an ideal gas, and the flow through the nozzle is
isentropic. Using these assumptions, the mass flow rate is
exitexitexit
exitexitexitexit VA
RTp
VAm �� �� Equation 5.7
where pexit, Texit, Aexit and Vexit are the pressure, temperature, area and velocity at the
nozzle exit, respectively and R is the ideal gas constant. To maximize the efficiency of
the turbine, the diameter at the nozzle exit was assumed to be 1 mm. This would make
the air jet the same size as the turbine blade. Because of the converging nozzle design,
the exit velocity was assumed to be Mach 1. The relation
RTMV �� Equation 5.8
41
was used to find the exit velocity. A spreadsheet was created to calculate the mass flow
at various inlet temperatures and pressures. These plots can be seen in figure 5.2.
0.0005
0.001
0.0015
0.002
0.0025
0.003
20 40 60 80 100 120
Inlet Pressure (psi)
Mas
s Fl
ow (k
g/s)
T1 = 255
T1 = 265
T1 = 275
T1 = 285
T1 = 295
T1 = 305
Figure 5.2: Mass Flow vs. Inlet Pressure for T1=255K to 305K
A control volume analysis was then done to calculate the force that the flow
exerts on the nozzle. The following equation was used:
exitexitinletinletexitnozzle APAPVmF ��� � Equation 5.9
A plot of Force vs. Inlet Pressure is shown in figure 5.3.
42
0
0.2
0.4
0.6
0.8
1
1.2
1.4
20 40 60 80 100 120
Inlet Pressure (psi)
Forc
e (lb
f)
Figure 5.3: Force on Nozzle Due to Flow
After further discussion, it was decided that since a contoured nozzle could
not be found commercially and would be difficult and expensive to manufacture, the
team would machine the nozzle directly into the casing. Not only does this result in
fewer parts, but it eliminates the need for the team to design a way to secure the nozzle
into the casing. The overall cost of the turbine is also reduced because the nozzle does
not need to be purchased by an outside vendor. This design has a square shaped nozzle
with a 1.58 mm X 1.25 mm inlet and a 0.7 mm X 1.25 mm outlet. Plots of the mass
flow vs. inlet pressure and force on the nozzle vs. inlet pressure can be seen in figures
5.4 and 5.5. These plots show an increase in the mass flow from the Miniature Tools
nozzle. This increased flow causes an increase in reaction force. However, since the
nozzle is machined directly into the casing, this force does not need to be balanced in
order to keep the nozzle in place.
43
0
0.001
0.002
0.003
0.004
0.005
0.006
20 40 60 80 100 120
Inlet Pressure (psi)
Mas
s Fl
ow (k
g/s)
T1 = 255
T1 = 265
T1 = 275
T1 = 285
T1 = 295
T1 = 305
Figure 5.4: Mass Flow vs. Inlet Pressure for T1 = 255K to 305K
0
0.05
0.1
0.15
0.2
0.25
0.3
20 40 60 80 100 120
Inlet Pressure (psi)
Forc
e (lb
f)
Figure 5.5: Force on Nozzle Due to Flow
44
5.1.3 CFD Analysis
5.1.3.1 Introduction
Fluent is a commercially available software that uses Computational Fluid
Dynamics (CFD) to analyze and solve 2D and 3D flow fields. CFD uses
conservation of mass, conservation of energy and transport equations, otherwise
known as Navier-Stokes equations, at points in the flow field to calculate pressures,
velocities, temperatures and other flow characteristics based on specified boundary
conditions. There are two main sections to complete the CFD analysis.
The first section is gambit, a pre-processor where the geometry is built,
meshed and the boundary entities are defined. The model is built based on a xyz
coordinate system. Points, edges, faces and volumes are created to form the
geometry. The geometry is then carried through Boolean operations such as
splitting, uniting or subtracting to obtain a physical connection between intersecting
parts. Once the geometry configuration has been established, it is a good practice to
connect all the points, lines (edges), and faces to avoid mesh complications. One
can locate the critical areas in the geometry by obtaining the location of the shortest
edge. This technique will be useful to visualize where the meshing operation might
fail. The next operation in pre-processing is meshing the geometry. Knowing the
model’s unit scale, one must choose appropriate size intervals at the critical regions
and stretch the mesh at the less critical regions. Gambit provides structured and
unstructured meshing techniques. Structured mesh uses quadrilateral elements
while unstructured mesh uses triangular elements. Unstructured mesh is used for
geometries that have significant obstructions. The use of structured mesh is
45
recommended to minimize the maximum element skew level. It is important to
check the element skew level upon completion of mesh. Desired maximum element
skewness for a typical 3D model with an unstructured mesh is 85% or below.
Values greater than 95% might affect the computational results. The final step for
completing the pre-processing section is to define the boundary entities. For
example: inlets, outlets, boundaries that will behave as walls, rotating fluid regions,
stationary solid regions, etc. Finally, the meshed model is exported to be used in
the post-processing section.
The second part of a CFD analysis uses Fluent, a post-processor where the
meshed geometry is imported and the boundary conditions are defined so that the
model can be solved. Typically, the imported geometry is scaled to the appropriate
unit that it was built in. Then the domain is reordered to reduce or simplify the
bandwidth of the matrix formed to solve the model. The user must then setup the
operating conditions, such as the reference working pressure, gravitational effect,
and working temperature condition. The solver is chosen based on the flow
characteristic. There are two types of solvers that Fluent uses. The Coupled solver,
typically used for compressible flow (M>0.3), and the segregated solver, usually
used for incompressible flow (M<0.3). The segregated solvers solve each of the
transport equation separately, whereas coupled solvers solve all the transport
equations simultaneously. The working fluid’s materialistic properties are defined
in the materials panel. Fluent has capabilities of running different types of working
fluids or gases depending on the desired design operation. Viscous effects can be
modeled by different turbulence models provided by Fluent. Standard �
46
(turbulence kinetic energy-turbulence dissipation rate) model is a widely used
turbulence model that uses two equations. It is an empirical model, however the
approximations obtained are reasonably accurate. Boundary conditions are defined
at locations where the fluid is entering, leaving, or rotating in the domain. Unless
appropriate boundary conditions are defined, the results will not be correct.
Fluent uses iterative techniques to solve the flow fields. The solution is
typically initialized with the inlet conditions where the pressure, directional
velocities, temperature and turbulence values are entered. The solution is defined
as converged when pressure, momentum, energy, and turbulence residuals are
below a defined relative error limit. Typical values for convergence are: pressure,
momentum, and turbulence residuals below 1e-03, and energy residual below 1e-
06. The solution is controlled and stabilized by using under-relaxation factors for
the residuals. By default, Fluent assigns under-relaxation values for each of the
residuals. They are well approximated working values for most of the analyses,
however there are times that the values must be reduced or increased based on the
behavior of the solution. Under-relaxation factors can have great impact on the
solution convergence. For example, a low under-relaxation value will make the
solution stable, however it will increase the time of the convergence due to smaller
iterative steps. A high under-relaxation value will speed the convergence time, but
could make the solution unstable and diverge. Therefore, the analyst must make the
appropriate selection to stabilize the solution while maintaining a reasonable
convergence time (Fluent 6.0 User Guide).
47
5.1.3.2 Analysis
The design team performed 2D CFD analyses to conceptually visualize the
flow inside the miniature turbine’s casing. The goal of the analysis was to attain the
most efficient flow path to extract the fluid from the domain. The CFD analyses
were performed using commercially available pre-processor Gambit 2.0, and post-
processor Fluent 6.0. The team’s initial step was to validate that the CFD could be
efficiently used to solve models in small scales, such as millimeters. The team
contacted Fluent university support engineer Ashish A. Kulkarni and validated that
the software was capable of solving problems in these small scales.
Initial design of the casing and the turbine consisted of single inlet, and
single outlet with four blades mounted on the turbine. The casing was of a circular
design to help the flow gain smooth
transition from one section to the other.
The model was meshed with triangular
elements at 0.25mm interval size. The
figure below displays the initial
geometry and the mesh.
Figure 5.6 was used as an initial
design model to test the forces on the top
blade shown in the 12 o’clock position. As observed in the figure, a uniform mesh
was used throughout the geometry. The tip clearances of the blade to casing surface
were kept large in order to extract the flow easily since there was no rotation
defined for the blades. The meshed model was imported and solved in Fluent 6.0.
Figure 5.6: Geometry
48
The summary of the setup and the boundary conditions are summarized in the table
below.
Table 5.1: Summary of boundary conditions Solver Coupled Implicit Viscous Model � standard Temperature � ��(constant)
Fluid Properties
Air ��- ideal gas Cp – 1006.43J/kg.K (constant) k – 0.0242W/m.K (constant) � - Sutherland Law
Operating Conditions Pressure – 101325Pa (static)
Under-Relaxation
Solid – 0.8 (combination of pressure and momentum residuals)Turbulence Viscosity – 0.6 �- 0.3 � - 0.3
Inlet M=0.7 a= 347.22m/s Velocity Inlet – 243.05m/s
Outlet Pressure Outlet – 0Pa (gauge)
Solution Initialization
Pressure-0Pa x-velocity: 243.05m/s y-velocity: 0.1m/s z-velocity: 0.1m/s �- 0.025m2/s2 � - 0.025m2/s3
49
Figure 5.7: Static Pressures (Pa)
Using the above conditions, the
model was solved in steady state. The
static pressure contours, velocity contours,
and velocity vectors were obtained (See
Appendix F). Knowing the length of the
blade and the pressure difference between
the top blade, the force per unit depth was
calculated by Fluent to be 111.94 N/m-depth. Figure 5.7 above show the static
pressure contours in the casing. Notice that at steady state, high-pressure region is
observed at the root of the blade.
the upstream and the downstream side of
To obtain the forces on the top blade at different angles of rotation the model
was modified by rotating the blades 10°, 20° and 45° clockwise. At those
configurations the forces on the top blade was calculated as:
10°: F=142.13N/m-depth
20°: F=122.04N/m-depth
45°: F=112.82N/m-depth
The pressure contours revealed that the maximum force on the blade was at
10° configuration. This analysis was conducted to approximate the torque that
would be generated due to the forces on the blades. Assuming a 1mm depth, the
forces on the turbine blades were sufficient to overcome the estimated torque
needed by the generator. Another reason the forces on the blades were calculated
was to observe the stagnation points, which might cause structural failure.
50
Figure-5.8: Static Pressures (Pa) 10°
Figure-5.10: Static Pressures (Pa) 45°
Figure-5.9: Static Pressures (Pa) 20°
The models presented in
figures 5.8, 5.9, and 5.10 display the
gauge pressures inside the casing and
the turbine assembly. As one might
expect, the forces on the top blade
decreased as the geometry was
rotated. The pressure contours
illustrate the shift of the high-pressure regions due to the rotation. Since there were
no rotational effects in these steady-state solutions, the casing behaved as a pressure
tank. This behavior is clear in figure 5.9. Once again, the purpose of the analysis
observed above was to obtain the forces on the blades at different turbine
configurations. Therefore, pressure contours were the key components in obtaining
the forces and the stagnation points on the blades.
The mass-flux balance showed that the
total mass flow coming into the domain was not
efficiently balancing the mass flow that was
51
Figure 5.11: Geometry
exiting. One of the reasons for this problem was the location of the outlet. The
design team’s next step was to modify the geometry so that the maximum torque
could be achieved with an optimum flow performance. The multiple-jet concept
was a candidate to achieve this goal. The figures 5.11 and 5.12 show the
modifications made to the initial model that was used in the preceding analyses.
The geometry show in figure 5.11 is
similar to the initial design, with the addition of
a second inlet and outlet introduced in the lower
section. The second inlet was located at the
lower right quadrant and the outlet pertaining to
the second inlet was located at the lower left
quadrant. Figure 5.12 shows a modified version of the geometry of figure 5.11.
The outlets were relocated to extract the mass flow efficiently. The boundary layers
were also meshed at a lower interval size (0.1mm) to capture the turbulence effects.
As it is observed from the
figure 5.13, the velocity vectors do not
exit the domain effectively. In order to
obtain an optimum flow performance,
the flow entering the control volume
must exit efficiently. Any disturbed
flow in the casing will cause losses that will affect the performance of the design.
The mass-flux balance of the model shown in figure 5.13 was on the order of 1e-
02kg/s, which signified that there was still some mass-flow remaining in the
Figure 5.12: Geometry
Figure 5.13: Velocity Vectors (m/s)
52
domain. An ideal mass-flux balance would be 0 kg/s, but for these analyses the
limit was set to 1e-05 kg/s.
As it will be observed in the next sections of the analysis, the multiple-jet
concept led to flows that were more symmetrical than the single jet design.
An option that the design team had was to introduce a rotating reference
frame that would simulate a steady-state performance of the rotating blades, which
simulates actual condition of the rotating turbine. In Fluent 6.0 this approach is
referred to as Multiple Reference Frame (MRF). The model in figure 5.14 below
was used to experiment with MRF. The boundary conditions for the rotating fluid
region were defined as a moving wall with an angular velocity of 50,000rpm
(optimum rotational velocity for the generator). The inlet speed was reduced to
10m/s because the speeds that were used in earlier models exceeded the desired
rotational speed of the generator (50,000rpm). Velocity vectors illustrated in figure
5.14 show the flow behavior when rotational effects are taken into account. The
new configuration for the outlets enhanced the flow performance by extracting the
mass-flow much more efficiently. In this model the mass-flux balance was reduced
to 1e-6.
The model analyzed to the left
contained a large tip clearance to
simplifying the convergence.
Traditionally, the tip clearances in
turbines are at their minimum to
increase efficiency. Therefore, the Figure 5.14: Velocity Vectors (m/s)
53
next step taken by the design team was to modify the geometry of the turbine and
the casing to strengthen the design by reducing the tip clearance.
The model to the right, figure
5.15, is composed of eight blades
separated by 45°. The geometry was
meshed using 0.1mm interval size. The
inlet boundary condition was modified due
to the changes in the geometry. The new
inlet velocity was 28.6m/s. The rotational velocity remained at 50,000 rpm. The
results obtained from this analysis did not illustrate a symmetric flow pattern within
the structure and therefore raised the concern of the team.
Figure 5.15: Geometry
Figure 5.16: Static Pressure (Pa) Figure 5.17: Velocity Vectors (m/s)
As it is observed from both the
pressure contours and the velocity
vectors of figures 5.16, and 5.17, the
behavior of the flow was not realistic.
The team expected a symmetric pressure
and velocity distribution along the flow Figure 5.18: Entropy Contours (kJ/kg.K)
54
field. Boundary conditions were re-checked to make sure that both inlets had the
same velocity rates. The entropy contours, figure 5.18, were inspected to see if the
grid had a discontinuity, but none were observed. Finally, the team had discovered
the problem that lead to unrealistic results. The solution initialization for x-velocity
was the cause. Typically, the solution is initialized with the velocity rate observed
at the inlet. In this model, both inlets were initialized with an x-velocity of 28.6m/s.
When the solution was initialized using very low value for x-velocity (1m/s) the
results were much better. The figures 5.19 and 5.20, which are the static pressure
contours and velocity vectors, show a symmetric pressure and velocity distribution.
Figure 5.20: Velocity Vectors (m/s)
Figure 5.19: Static Pressure (Pa)
The team’s final modifications were to increase the inlet velocity slightly to
obtain a free spinning turbine and to reduce the tip clearances to an absolute
minimum. Figure 5.21 displays the geometry with reduced tip clearance. The
55
reason to reduce the tip clearance is to be able to move the air more effectively.
This in terms will increase the flow performance and hence increasing the
efficiency of the turbine. The velocity vectors displayed in figure 5.20 illustrates
that the rotation of the blades was driving the flow rather than the nozzle. This
meant that the team needed to increase the inlet velocity to make sure the nozzle
was causing the turbine to rotate.
Figure 5.22: Static Pressure (Pa) Figure 5.21: Geometry
Figure 5.23: Dynamic Pressure (Pa) Figure 5.24: Velocity Vectors (m/s)
The static pressure contours in figure 5.22 validates a free spinning turbine.
The velocity vectors in figure 5.24 illustrates that the inlet speed is driving the
rotational flow. The reduced tip clearances increased the efficiency of the turbine
56
by preventing the air from flowing around the blades. However, reducing the tip
clearances increased the tip velocities significantly. The maximum velocity
observed at the tip was approximately 104 m/s. Even though the tip velocities
increased significantly, the flow was still incompressible (M<0.3
subsonic/incompressible). To validate the grid independence, the future models
will be meshed with finer meshes at the tip clearances. All the models observed in
this analysis section are presented in detail in Appendix F.
The 2-dimensional CFD simulations helped the team to visualize and
optimize the flow inside the casing. The steady state analyses helped gain an
understanding of the forces observed at the blades. To maintain the structural
integrity of the blades the stagnation points are important key factors for the
designer. The configuration of the inlets and the outlets were obtained based on the
model performance using iterative steps. The team observed the model
performance, brainstormed the variables that would impact the efficiency, and
modified the geometry predicting better results than the previous model. The CFD
simulations were preliminary steps to design an optimization tool. The design
team’s goals for the future are to validate the 3D CFD simulations with the
experimental data, and also to optimize the existing model to obtain an ideal flow
performance. Due to close interaction between the blades and the casing, sliding
mesh technique was suggested by the Fluent technical support. The team will
explore this technique in future analyses.
57
5.1.4 Bearings and Shaft
5.1.4.1 Bearing Life
The team thought that due to the high speeds and fluctuating forces on the
bearings a fatigue analysis should be done. A number of commercial bearings were
examined with a close look at the bearings rated speed and dynamic loading. The
max speed the turbine will spin will be 100,000 rpm and the max force the bearing
will see is .00667 lbs. Standard commercial bearings are rated for this size up to
120,000 rpm and around 80 lbs of loading. Even though the turbine parameters were
well within the specifications of the bearing, the team calculated the minimum or L10
life based on Equation 5.10.
)(10 FCLa
� Equation 5.10
Where C is the load rating of the bearing provided by the manufacturer, a is a
constant equal to three for ball bearings, and F is the radial load seen by the bearing.
This gave a L10 life on the order of 1012 cycles, which is sufficiently high. This is due
to the small load being applied to the turbine. Based on this calculation and the
bearing being within the specifications given by the manufacturer, the team decided
that no further calculations were needed.
5.1.4.2 Shaft Design
The turbine shaft was designed based on Soderberg’s Line, Eqn 5.11. This is a
conservative approach but gave a final shaft diameter which was smaller then most
commercially available. The analysis was done using 316 Stainless Steel (common for
small shafts) and a factor of safety, n, of 5. The maximum torque, T, on the shaft was
58
assumed to be the maximum torque at full load required by the motor while the
minimum torque was assumed to be the no load torque of the motor. The shear stress,
�, for these torques was calculated using Eqn 5.12, where r is the radius of the shaft and
J is the polar moment of inertia. These stresses were then used to find a mean stress,
�m, and stress amplitude, �a. A modified endurance limit was then calculated based on
the surface factor, the size factor, and the load factor. The Soderberg Equation was
then used to solve for the minimum diameter.
nSS ut
m
e
a 1��
��
Equation 5.11
3
2rT
JTr
�
� �� Equation 5.12
This analysis gave a minimum diameter of 0.45 mm. This is much smaller then
the motor shaft, for that reason the shaft diameters of the turbine and the generator will
be matched.
5.2 Power Generation
The electrical scope of the miniature turbine senior design project includes
providing sufficient means to convert the mechanical power created by the primary
mover, the turbine assembly, into electrical power. The long-term goal of this proof of
concept is to utilize the design within the Micro Air Vehicle (MAV) program. The
electrical design was carried out with this future goal in mind. The needs assessment
dictates that the miniature turbine shall produce at a minimum enough power for the
current generation of MAV design at RIT.
59
The electrical specifications for the current R.I.T. MAV design were obtained
and may be viewed in the appendix of this report. The electrical specifications include
an electric motor, which was initially part of the MAV team’s design. The MAV team
has recently selected a gas-powered motor to replace the specified DC electric motor.
This decision by the MAV team greatly reduces the power requirements placed on the
miniature turbine design, as it will only be required to power the on-board electronics.
Eliminating the DC motor specified in the original MAV design reduces the power
requirements from approximately 8 W to approximately 3 W, as the maximum motor
draw is 5 W.
Preliminary calculations of the power capabilities of the turbine assembly predict
significantly higher power capacity than that required by the electronic components on
the MAV. Per discussions with Dr. Lyshevski of the R.I.T. Electrical Engineering
Department, the power rating of the generator should be approximately one-third the
power rating of the turbine that is being used to drive it. Realizing that the power
producing capabilities of the miniature turbine design are far greater than those required
by the current MAV, the team will strive to maximize the potential of the turbine-
generator assembly and produce the maximum amount of power attainable by the
turbine and generator assembly. This miniature turbine can be then scaled down to
produce only what is need by the MAV.
5.2.1 Generator Selection
To facilitate the conversion from mechanical to electrical power a direct current
(DC) motor will be employed, specifically a permanent magnet dc motor (PMDC). No
physical differences between a DC motor and a DC generator exist, the only distinction
60
being the direction of power flow. In a DC motor, electric power is converted to
mechanical power. Conversely, in a DC generator, mechanical power is converted to
electrical power. The fact that DC motors are two-way machines allows the motor
specifications and theory of operation to be directly applied to the same motor acting as
a generator. In this report, the term motor and generator are used interchangeably.
Wide varieties of motors have been evaluated for use as a generator in this
project. Early on in the project, the team decided on a permanent magnet dc motor. A
synchronous motor would not be an adequate means of generation. A synchronous
generator requires a DC voltage applied to the windings of the rotor, which creates an
electromagnetic field. This rotating magnetic field induces a voltage in the stationary
stator windings. Since no external dc voltage is available in this project, a synchronous
generator would not be practical, leaving a dc generator as the method of choice.
Many dc generators also require a voltage source to excite the stationary field
windings. An electromagnet field is created in the field windings and a voltage is
induced in the armature windings as they rotate through it. In this type of generator the
field can be exited externally as in a separately excited generator. The separately
excited generator requires an external power supply and is therefore not desirable for
the same reasons as explained in the synchronous generator discussion. Another
method available to excite the field is to use the voltage generated by the machine
itself. The field circuit is connected directly across the terminals of the generator in a
shunt generator, and in a series generator, the field windings are connected in series
with the generators armature. The shunt and series generator would be an adequate
61
means of generation in the project since no external power supply is required, however,
permanent magnet motors have many advantages.
A permanent magnet dc motor utilizes permanent magnets as opposed to field
windings. The permanent magnets develop the magnetic field through which the
armature will rotate, inducing a voltage in the coil terminals. In this application, the
size of the motor is a critical factor, and PMDC armature motors can be manufactured
much smaller than motors requiring field windings. These factors make the PMDC
motor a desirable choice for usage as a generator.
Two types of PMDC motors are available on the market, brushed dc motors, and
brushless dc motors. The factors taken into consideration in motor selection are output
power, speed, size, weight, and cost. A brushless dc motor has many advantages over a
brushed dc motor. The main advantage is its utilization of a permanent magnet located
on the rotor. The rotating magnet field induces a voltage on the stationary field
windings. The advantage is gained because a mechanical contact to the rotor is not
necessary. Eliminating the brushes yields extended motor lifetime because the lifetime
becomes dependent on the bearings rather than the brushes. Brushless dc motors are
also capable of running at higher speeds than the traditional brushed motor. The main
disadvantage of brushless dc motors is their high cost. Brushless dc motors also require
electronic commutation, however, that will not be a factor since the motor will be
operated as a generator.
The above factors will be taken into consideration in selection of the final
generator that will be coupled with the turbine assembly. At this stage of the design a
specific motor has not been specified, and will not be until the output characteristics of
62
the turbine are developed. In developing the generator, characteristics there are
inexpensive motors that may be purchased, and motors available for use at the RIT that
may be utilized for preliminary testing. Once preliminary testing is complete and the
turbine characteristics are developed, a motor may be acquired and integrated into the
design.
5.2.2 Electrical Load Connection to Generator
The type of circuitry needed at the output of the generators terminals will be
dependent on the final motor selection. The options are discussed in the following.
5.2.2.1 Brushed DC Motor
A brushed dc motor will not require any rectification of its output current. The
mechanical brushes will commutate the output so that current flows in only one
direction. However, the generator output will still have a ripple associated with it. The
frequency of the ripple will depend on the rotational speed of the generator. A simple
RC (resistor-capacitor) circuit may be utilized to “smooth” off the output, converting it
to true dc.
5.2.2.2 Brushless DC Motor
As stated in section 5.2.1 a brushless dc motor requires electronic commutation.
The brushless dc motor when being driven as a generator will produce an alternating
current (ac) output due to the absence of mechanical commutation. This output voltage
will need to be rectified to convert it to dc. If a brushless dc motor is employed in the
final design, a bridge rectifier will be designed to facilitate the ac to dc conversion. A
circuit model of a single-phase bridge rectifier is shown below. If a three-phase
63
brushless motor is employed the bridge rectifier circuit can be expanded to rectify each
phase. The necessity of a bridge rectifier results in a disadvantage to the utilization of
brushless dc motor. To fully rectify the generators output current will flow through two
diodes on the positive and negative cycle of the voltage. A voltage drop will be
associated with each diode, and these losses must be considered in the final design.
Another factor to consider in the selection of a brushless dc motor is the number
of phases of the stator. A three-phase motor is desirable due to 120 degrees of phase
separation, which results in a positive voltage peak every 120 degrees as opposed to
every 180 degrees in a two-phase motor. The negative aspect of a three-phase motor is
that additional rectification circuitry will be needed which will lead to additional losses.
This circuit is shown in figure 5.25.
Figure 5.25: Bridge Rectifier
In this configuration, a capacitor will serve the same purpose as discussed in the
previous section of smoothing out the output.
64
5.2.3 Voltage Regulation
As discussed in the control loop concept development, section 2.1, it will be
necessary to provide the load being driven by the generator with a constant voltage
supply. As the electrical load on the generator is varied, the output voltage will
subsequently vary due to a change of rotational speed. A method to achieve voltage
regulation will be to employ a voltage regulator circuit utilizing a zener diode. A zener
diode is designed to maintain a constant voltage across it, making it suitable for this
application. Zener diodes are available on the market with a wide range of voltage
values, so one may readily be selected to suit the circuit. A model of a voltage
regulator circuit is shown in figure 5.26.
Figure 5.26: Voltage Regulator
5.3 Structural Design
The overall structure of the turbine is designed to be small, lightweight, and
robust. A faceplate was designed for the generator to be mounted on. This plate has a
recess to align the generator with the turbine and a hole for the shaft to pass through.
Three screws are used to bolt the faceplate to the generator. The shaft of the generator
65
is attached to the turbine shaft with a plastic coupling. By making the coupling plastic,
it will be lightweight and flexible, which will allow for some misalignment. The three
bolts used to secure the plates of the casing together are also used to attach the turbine
assembly to the generator faceplate. Aluminum posts are used as spacers to ensure the
faceplate and casing have the proper distance between them and their faces are kept
parallel. A picture of the structure can be seen in figure 5.27.
Figure 5.27: Entire Assembly
5.4 Analysis Conclusion
The preceding sections presented the analysis of the miniature turbine. The final
design integrated the results from the individual analyses as well as several other
important factors. One of these factors was the experiments that will be performed on
the turbine. The experimental setup will be discussed in more detail in the next chapter,
but while designing the team had to make sure the upstream and downstream
temperature and pressure of the of the impeller could be measured as well as the shaft
speed and torque. Another factor affecting the design was the geometry of dental
turbines or handpieces. These turbines are of similar size and shape, but spin at much
higher shaft speeds and produce less torque. The team wanted to be able to use the
66
dental impeller in the casing the team designed. This specified the final dimensions for
much of the casing geometry.
The entire design of the miniature turbine is shown in Figure 5.27. For a more
detailed look at the design, see the drawings included in the technical data package
attached to this report.
67
6.0 Future Plans
At this point, the team has completed the first six facets of the miniature
turbine project. The team is now ready to begin testing the dental turbines and start
fabrication of the casing. The dental turbines are of similar size as the one presented in
this report but are designed to spin extremely fast, 300,000 to 500,000 rpm, but produce
very little torque. Since dental turbines are commercially available, the team would
like to show an improvement in their design over the dental turbines.
The team will start by performing the same tests on the dental turbine that will
eventually be performed on their design. This will do three things: 1) it will help the
learn how to take the needed measurements and 2) by comparing the results the team
gets with data from the manufacturer the team will be able to validate their experiments
and 3) it will contribute to the validation of the CFD results. The team will then place
the dental turbine impeller into the casing presented in this report. This will enable the
team to show how their casing produces more torque then the dental turbine’s casing
due to the multiple jets and how power can be generated. The final part of the project
will be taking the turbine or turbines designed by graduate work at RIT and inserting
that into the teams casing. Experimentation done on this new and novel miniature
turbine will prove this concept works and will act as a starting point for future teams to
improve upon.
6.1 Experimentation
Several experiments must be done on the miniature turbine. First, the team must
validate that the performance objectives and specifications have been met. Then, the
68
team would like to build the turbine maps the show the relationship between torque,
power, efficiency, and rpm.
Using the program “LABVIEW,” produced by National Instruments, can validate
if the performance objectives and specifications have been met. LABVIEW is a very
useful program that has invalidated the use of coding for programming and instead,
incorporats visual object-oriented programming to write programs that can perform the
same functions. In short, it has the same functions and characteristics as “C-
Programming” except that the programmer does not have to write the actual code, but
has to drag and drop icons to perform similar functions. National Instruments have also
added an extremely important feature to LABVIEW, which is DATA ACQUISITION.
This is of importance to the team, as it will help the team to perform experiments on a
dental turbine (similar in design to the team’s turbine) and gather important data from
these experiments. This data can be used to further validate the performance objectives
and specifications of the miniature turbine designed by the team.
6.2 Setup
In order for the team to validate the performance objectives and specifications, the
speed of the turbine shaft, the electrical power, the torque, and the exit temperature will
need to be measured. The team will also need to find the efficiency of the turbine.
This will be done by setting up two pressure sensors, two temperature sensors
(thermocouples), a torque sensor, a tachometer, and a power sensor. Figure 6.1 shows
the experimental setup. The air will start in a compressed air tank where the
pressure will be measured using a static pressure gage. After leaving the tank, the air
will enter a plenum where the air will settle and the temperature and pressure can be
69
Figure 6.1: Experimental Setup
measured. Once the air has left the plenum it will travel through an orifice plate, which
will measure the volumetric flow rate. Using the temperature, pressure, and volumetric
flow rate, the mass flow rate can be calculated using Equation 6.1:
QRTPm �� Equation 6.1
The mass flow rate will be used to find the mechanical power produced by the
turbine.
Once the air has exited the orifice plate, it must travel through 40 diameters of
pipe length in order to settle out the effects of the plate. From here, the air will enter
the turbine where it will spin the impeller and then exit the casing. Using the impeller
shaft, the rotation velocity and the torque of the impeller can be determined through the
use of a tachometer and torque sensor. The shaft can also be attached to an electric
motor where voltage and current, and therefore power, can be measured. The team will
also be measuring the exit temperature of the air. This will validate on of the
performance specifications, the air exit temperature must be less then 125C, and will
also provide the last piece of data needed to find the turbine efficiency.
70
The efficiency of the turbine is equal to the actual work divided by the
isentropic, or ideal, work. The actual work is equal to the torque times the rotational
velocity, both of which will be measured directly. The ideal work can be found using
one of two different methods depending on the flow conditions. If the flow entering
the turbine is compressible, defined by the Mach number being greater then 0.3, then
the ideal work can be found using the change in temperature and pressure across the
turbine as shown in Equation 6.2.
))(1(
1kk
upstream
downstreamupstream
actual
PP
T
W�
�
�� Equation 6.2
If the flow entering the turbine is incompressible, a Mach number less then 0.3, then the
ideal work can be found using the pressure and velocity in Equation 6.3.
2)()( 22
downstreamupstreamdownstreamupstream
actual
VVPPW
�
�
�
�
�
� Equation 6.3
For both of these equations, the downstream pressure is assumed equal to atmospheric
pressure.
Labview will gather the data from all these sources simultaneously. A
program written by the team will then plug the data into formulas provided by the
sensor manufacturers to calculate the required temperature, pressures, torque, and
rotational velocity.
71
6.3 Schedule
A schedule has been developed for the spring quarter that will keep the team on
track to finish the project on time. The schedule, shown below, has been designed to
give the team an idea of which activities it should be working on and when they should
be completed rather then to describe the day-to-day work of the team.
ID Task Name1 Fabrications - Casing Plates2 Testing - Setup3 Class 1: Intro to Detailed Design & Concurrent Engineer4 Testing - Dental5 Fabrications - Face Plate6 Class 2: Design for Safety & Compliance 7 Fabrications - Other Parts8 Class 3: Design for Manufacture & Assembly9 Fabrications - Assembly10 Class 4: Des for Quality, Reliability, and Maint. 11 Testing - Casing with Dental Impeller12 Class 5: Design for Performance – Optimization13 Class 6: Production Planning & Tool Design14 Testing - Casing with new impeller15 Final Report16 Class 8: Pilot Production17 Final Presentation18 Class 9: Transition to Commercial Production19 Class 10: Product Stewardship20 CRITICAL DESIGN REVIEW
3/14
3/21
3/28
4/4
4/114/18
5/2
5/95/16
5/19
3/9 3/16 3/23 3/30 4/6 4/13 4/20 4/27 5/4 5/11 5/18 5/25April May
72
6.4 Budget The team’s budget is shown below.
Item Part Name Part Number Material Quantity Vendor Price Line PriceCasing Fitting MT-02008-M-1-01 Brass 1 McMaster 4.75$ 4.75$
Top Plate MT-02008-M-1-02 Aluminum 0.25 McMaster 10.66$ 2.67$ Top Gasket MT-02008-M-1-03 Rubber 0.5 MSC 20.57$ 10.29$ Center Plate MT-02008-M-1-04 Aluminum 0.25 McMaster 10.66$ 2.67$ Bottom Gasket MT-02008-M-1-05 Rubber 0.5 MSC 20.57$ 10.29$ Bottom Plate MT-02008-M-1-06 Aluminum 0.25 McMaster 10.66$ 2.67$ Bearing MT-02008-M-1-07 Steel 2 McMaster 8.10$ 16.20$ Bolt MT-02008-M-1-10 Steel 3 McMaster 6.70$ 20.10$
Stuctual Post MT-02008-M-2-02 Aluminum 3 McMaster 0.95$ 2.85$ Faceplate MT-02008-M-2-03 Aluminum 0.25 McMaster 10.66$ 2.67$ Nut MT-02008-M-2-06 Steel 3 McMaster 4.42$ 13.26$
Electrical Generator MT-02008-M-2-04 ----- 1 Faulhaber 150.00$ 150.00$ Generator Bolt MT-02008-M-2-05 Steel 3 McMaster 7.94$ 23.82$ Test Motor ----- 2 In-House 3.99$ 7.98$ Zener Diode ----- 1 In-House 1.00$ 1.00$ Wiring ----- 1 In-House -$ -$ Resisters ----- 2 In-House -$ -$
Other Coupling MT-02008-M-2-07 Rubber 1 -$ -$ Shaft MT-02008-M-1-09 Stainless Steel 1 SDI 2.97$ 2.97$
Experimentation Plenum Steel 1 KMW Performance 47.40$ 47.40$ Air Supply Tubing Plastic 1 In-House -$ -$
Orifice Plate ----- 1 Lambda Squared 270.00$ 270.00$
Tachometer ----- 1 Compact Instuments 585.00$ 585.00$
Torque Measurement Device ----- 1 TDB $ - -$
Total Estimated Cost = 1,176.56$
Bill of Materials
73
7.0 Conclusion
The senior design team has completed the first six facets of the design process this
quarter. These include the needs assessment, project objectives, project specifications,
concept development, feasibility assessment, the analysis and synthesis of design and
the preliminary design documents.
The miniature turbine designed is the first step toward a working micro-turbine.
The present design is a proof of concept, which, in the future, can be scaled down to
MEMS size. The goal of the team is to develop, fabricate, and test a working turbine
capable of driving a generator and producing electrical power. The generator shall be
reusable and have a run time of at least 15 minutes.
The team developed four concepts and assessed their feasibility. The concepts
include a multiple jet design, a control system, the use of the turbine exhaust air to cool
the generator and the use of lightweight materials in the design. Although each concept
compared well with the baseline design, the team decided to proceed with the multiple
jet design and the use of lightweight materials. This decision was based upon the
results of the feasibility analysis. The team will decide on the use of a generator
cooling system after the generator can be tested to see if cooling is necessary.
An analysis of several aspects of the turbine was completed. A head loss
calculation was done to determine the pressure loss due to frictional effects in the flow
passages. In addition, the mass flow and reaction force due to the flow through the
nozzle was done. Computational fluid dynamics (CFD) software was utilized to
optimize the placement of the inlets and exhaust in the turbine housing as well as to
develop a tool for use with future designs. Mechanically, the shaft fatigue and bearing
74
life was analyzed to ensure the turbine could operate over a long lifespan. Finally, an
electrical analysis was done to select the generator that will be used for power
generation, and options were considered to convert its output to a constant dc voltage to
drive the MAV electronics.
By the end of the spring quarter, the team will have fabricated a working turbine
capable of generating electrical power. The team will conduct several experiments
designed to analyze the performance of the turbine and generator. Dental turbines will
be used to set up these experiments. The experimental results will also be used to
validate the CFD model for future use. The design team will also demonstrate the
ability of the turbine to power MAV components.
75
References
Chapman, Stephen J. Electric Machinery Fundamentals, Third Edition, McGraw-Hill, 1999. Craig, Paul. Capstone Turbine Corp. “The Capstone Turbogenerator as an
Alternative Power Source.” Society of Automotive Engineers, Inc. Electric and Hybrid Vehicle Design Studies. 1997.
Epstein, A.H. et al., “Micro-Heat Engines, Gas Turbines, and Rocket Engines”, AIAA 97-
1773, presented at 28th AIAA Fluid Dynamics Conference, 4th AIAA shear Flow Conference, Jun 29-July 2,1997, Snowmass Village, CO.
Fluent 6.0. “User’s Guide.” Online. Jan. 2003. Fox, Robert W., McDonald, Alan T. Introduction to Fluid Mechanics, 5th Ed. New York:
John Wiley & Sons, Inc. Kozak, Jeffrey. Personal interview. 6 Jan. 2003. (I don’t know if this is correct way to
reference Dr. Kozak) Kulkarni, Ashish. “Information on modeling mm scales in Fluent 6.0”. E-mail to the
support engineer. 20 Jan. 2003. Mehregany, M. Gabriel, K.J. Trimmer, W.S.N. Micro Gears and Turbines Etched from
Silicon. AT&T Bell Labs, Sensors and Actuators, V 12. Pgs 341-348. 1987. Moran, Michael J., Shapiro, Howard N. (2000). Fundamentals of Engineering
Thermodynamics, 4th Ed. New York: John Wiley & Sons, Inc. Shigley, Joseph, Mischke, Charles. Mechanical Engineering Design. McGraw-Hill, Inc. New
York, 1989, pgs 53-55, 274-301,699-710. S. Kang, J.Stampfl, A.G. Cooper and F. Prinz ,. Application of the Mold SDM Process to the
Fabrication of Ceramic Parts for a Micro Gas Turbine Engine, J.G. Heinrich (ed.), Proceedings Ceramic Materials and Components for Engines, in print, Germany, June 2000.
Wiegele, Thomas G. 1996, Micro-Turbo Generator Design and Fabrication: A Preliminary
Study, IEEE.
76
Appendix A: Micro Air Vehicle Electrical Specifications………………..…………………………….78 B: Feasibility Assessment Scores and Radar Chart…………..……………………………..79 C: Head Loss Data……………………….…………………………………………………..80 D: Nozzle Force Spread Sheet………………………………………………………………82 E: CFD Analysis……………………….……………………………………………………85 F: Shaft Fatigue Spread Sheet………….…………………………………………………..115
77
Appendix A: Micro Air Vehicle Electrical Specifications These are the electrical specifications prescribed by the RIT Micro Air Vehicle Team during the Fall Quarter of 2002.
Max Required Power For MAV : 5.98 Motor: Max Power Required* (Watts): 4.84 Quantity: 1 Spec's: Micro DC 5-2.4 Rated voltage (V) 5 No load current (mA) 35 No load speed (1/min) 21000 Stall current (mA) 2000 Stall torque (g-cm) 44.8 Max. output power (W) 2.42 Max. Efficiency (%) 75.3 * Assumes 50% efficiency
Servo: LS-2.4 digital Max Power Required (Watts): 1 Quantity: 2 Spec's: Operating voltage 3-5 V Load current <100mA
Receiver : JR R610M Micro Receiver Max Power Required (Watts): TBD Quantity: 1 Spec's:
Video Transmitter/Camera : SDX-22 2.4 GHz Wireless Video Transmitter Max Power Required (Watts): 0.135 Quantity: 1 Spec's: BATTERY OPERATED (Volts) 7 - 9 CURRENT CONSUMPTION (milliamps) 15
Video Transmitter/Camera: SDX-22 2.4 GHz Wireless Video Transmitter Max Power Required (Watts): 0.135 Quantity: 1 Spec's: BATTERY OPERATED (Volts) 7 - 9 CURRENT CONSUMPTION (milliamps) 15
78
Appendix B: Feasibility Assessment and Radar Chart Concepts T1 T2 E1 E2 M1 M2 S1 S2 P1 P2 P3 P4 Light Weight Materials 2 2 1 3 2 1 1 3 3 3 2 2 Multiple Jets 2 2 1 2 3 1.5 1.5 3 3 3 2 3 Cooling Generator 1 2 1.5 2 3 3 1 3 3 3 2 3 Control System 1 1 1 3 3 3 1 3 3 3 2 3
0
0.5
1
1.5
2
2.5
3T1
T2
E1
E2
M1
M2
S1
S2
P1
P2
P3
P4
Light WeightMaterialsMultiple Jets
Cooling Generator
Control System
79
Appendix C: Head Loss Data
Square Circular 90° bend R, m^2/s K 287 287 R, m^2/s K 287
pressure, Pa 689441.4 689441.3789 pressure, Pa 689441.4 pressure, psi 100 100 pressure, psi 100
temperature, K 255 255 temperature, K 255 width, m 0.00158 - width, m - height, m 0.00125 - height, m -
hydraulic dia., m 0.001396 0.00158 hydraulic dia., m^2 0.00158 length, m 0.007927 0.004 length, m 0.004
velocity, m/s 50 50 velocity, m/s 50 density, kg/m^3 9.420529 9.420528508 density, kg/m^3 9.420529
viscosity, N s/m^2 1.62E-05 1.6248E-05 viscosity, N s/m^2 1.62E-05 Reynolds No. 2.30E+05 1.16E+05 Reynolds No. 1.16E+05
roughness, mm 0.0015 0.0015 friction factor 0.0245 e/D 1.074684 0.949367089 Le/D 60
friction factor 0.0245 0.027 Total Total major head loss, Nm/kg 173.9231 85.44303797 259.3661 minor head loss, Nm/kg 1837.5 5512.5
Total Head Loss, Nm/kg 5771.866 Total Pressure Drop, psi 7.886679 7.89%
Figure D.1: Equivalent Length for Pipe Bend
80
Figure D.2: Friction Factor for Head Loss
81
Appendix D: Nozzle Mass Flow and Reaction Force Spread Sheets
Nozzle Mass Flow using Commercial Nozzle
T1 = 255
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa
M2 1 1 1 1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 255 K 255 K 255 K 255 K 255 K 255 K 255 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
V2 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s
mass flow 1.01E-03 kg/s 1.26E-03 kg/s 1.51E-03 kg/s 1.77E-03 kg/s 2.02E-03 kg/s 2.27E-03 kg/s 2.52E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
T1 = 265
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa
M2 1 1 1 1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 265 K 265 K 265 K 265 K 265 K 265 K 265 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
V2 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s
mass flow 9.90E-04 kg/s 1.24E-03 kg/s 1.48E-03 kg/s 1.73E-03 kg/s 1.98E-03 kg/s 2.23E-03 kg/s 2.47E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
T1 = 275
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa
M2 1 1 1 1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 275 K 275 K 275 K 275 K 275 K 275 K 275 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
82
V2 3.32E+02 m/s 3.32E+02 m/s m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s
mass flow 9.71E-04 kg/s 1.21E-03 kg/s kg/s 1.70E-03 kg/s 1.94E-03 kg/s 2.19E-03 kg/s 2.43E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
T1 = 285
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa
M2 1 1 1
3.32E+02
1.46E-03
7.92E-06
60
kPa
1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4 Nm Nm Nm Nm Nm Nm Nm/ / / / / / /R 287 287 287 287 287 287 287 kgK kgK kgK kgK kgK kgK kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 285 K 285 K 285 K 285 K 285 K 285 K 285 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
V2 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s
mass flow 9.54E-04 kg/s 1.19E-03 kg/s 1.43E-03 kg/s 1.67E-03 kg/s 1.91E-03 kg/s 2.15E-03 kg/s 2.39E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
T1 = 295
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa
M2 1 1 1 1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4 Nm Nm Nm Nm Nm Nm Nm/ / / / / / /R 287 287 287 287 287 287 287 kgK kgK kgK kgK kgK kgK kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 295 K 295 K 295 K 295 K 295 K 295 K 295 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
V2 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s
mass flow 9.38E-04 kg/s 1.17E-03 kg/s 1.41E-03 kg/s 1.64E-03 kg/s 1.88E-03 kg/s 2.11E-03 kg/s 2.34E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
T1 = 305
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa kPa
M2 1 1 1 1 1 1 1
k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m
T1 305 K 305 K 305 K 305 K 305 K 305 K 305 K
P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa
A2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2 4.42E-07 m^2
V2 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s
6.89E+02
83
mass flow 9.22E-04 kg/s 1.15E-03 kg/s 1.38E-03 kg/s 1.61E-03 kg/s 1.84E-03 kg/s 2.08E-03 kg/s 2.31E-03 kg/s
A1 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2 7.92E-06 m^2
Nozzle Mass Flow using Designed Nozzle
T1 = 255 Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 255 K 255 K 255 K 255 K 255 K 255 K 255 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 V2 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s 3.20E+02 m/s
mass flow 2.00E-03 kg/s 2.50E-03 kg/s 3.00E-03 kg/s 3.50E-03 kg/s 4.00E-03 kg/s 4.50E-03 kg/s 4.99E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
T1 = 265 Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 265 K 265 K 265 K 265 K 265 K 265 K 265 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 V2 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s 3.26E+02 m/s
mass flow 1.96E-03 kg/s 2.45E-03 kg/s 2.94E-03 kg/s 3.43E-03 kg/s 3.92E-03 kg/s 4.41E-03 kg/s 4.90E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
T1 = 275 Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 275 K 275 K 275 K 275 K 275 K 275 K 275 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2
84
V2 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s 3.32E+02 m/s
mass flow 1.92E-03 kg/s 2.40E-03 kg/s 2.89E-03 kg/s 3.37E-03 kg/s 3.85E-03 kg/s 4.33E-03 kg/s 4.81E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
T1 = 285 Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100
Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 285 K 285 K 285 K 285 K 285 K 285 K 285 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 V2 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s 3.38E+02 m/s
mass flow 1.89E-03 kg/s 2.36E-03 kg/s 2.83E-03 kg/s 3.31E-03 kg/s 3.78E-03 kg/s 4.25E-03 kg/s 4.72E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
T1 = 295
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100 Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 295 K 295 K 295 K 295 K 295 K 295 K 295 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 V2 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s 3.44E+02 m/s
mass flow 1.86E-03 kg/s 2.32E-03 kg/s 2.79E-03 kg/s 3.25E-03 kg/s 3.72E-03 kg/s 4.18E-03 kg/s 4.64E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
T1 = 305
Pi (psi) = 40 Pi (psi) = 50 Pi (psi) = 60 Pi (psi) = 70 Pi (psi) = 80 Pi (psi) = 90 Pi (psi) = 100 Pi 2.76E+02 kPa 3.45E+02 kPa 4.14E+02 kPa 4.83E+02 kPa 5.52E+02 kPa 6.21E+02 kPa 6.89E+02 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4
R 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK 287
Nm/kgK 287 Nm/kgK
d2 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m 7.50E-04 m T1 305 K 305 K 305 K 305 K 305 K 305 K 305 K P2 5.22E+02 kPa 6.53E+02 kPa 7.83E+02 kPa 9.14E+02 kPa 1.04E+03 kPa 1.17E+03 kPa 1.31E+03 kPa A2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 8.75E-07 m^2 V2 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s 3.50E+02 m/s
mass flow 1.83E-03 kg/s 2.28E-03 kg/s 2.74E-03 kg/s 3.20E-03 kg/s 3.65E-03 kg/s 4.11E-03 kg/s 4.57E-03 kg/s A1 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2 1.98E-06 m^2
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Nozzle Reaction Force Using Commercial Nozzle T1 = 275
Pi(psi) 40 Pi(psi) 50 Pi(psi) 60 Pi(psi) 70 Pi(psi) 80 Pi(psi) 90 Pi(psi) 100 Pi 275.79 kPa 344.74 kPa 413.69 kPa 482.63 kPa 551.58 kPa 620.53 kPa 689.48 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4 R 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*Kd2 0.0008 m 0.0008 m 0.0008 m 0.0008 m 0.0008 m 0.0008 m 0.0008 m T1 275 K 275 K 275 K 275 K 275 K 275 K 275 K P2 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa A2 4E-07 m^2 4E-07 m^2 4E-07 m^2 4E-07 m^2 4E-07 m^2 4E-07 m^2 4E-07 m^2 V2 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s
mflow 0.0002 kg/s 0.0002 kg/s 0.0002 kg/s 0.0002 kg/s 0.0002 kg/s 0.0002 kg/s 0.0002 kg/s A1 8E-06 m^2 8E-06 m^2 8E-06 m^2 8E-06 m^2 8E-06 m^2 8E-06 m^2 8E-06 m^2 F 0.4667 lbf 0.5894 lbf 0.7122 lbf 0.8349 lbf 0.9576 lbf 1.0803 lbf 1.203 lbf
Nozzle Reaction Force Using Designed Nozzle
T1 = 275 Pi(psi) 40 Pi(psi) 50 Pi(psi) 60 Pi(psi) 70 Pi(psi) 80 Pi(psi) 90 Pi(psi) 100
Pi 275.79 kPa 344.74 kPa 413.69 kPa 482.63 kPa 551.58 kPa 620.53 kPa 689.48 kPa M2 1 1 1 1 1 1 1 k 1.4 1.4 1.4 1.4 1.4 1.4 1.4 R 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*K 287 N*m/kg*KT1 275 K 275 K 275 K 275 K 275 K 275 K 275 K P2 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa 101.33 kPa A2 9E-07 m^2 9E-07 m^2 9E-07 m^2 9E-07 m^2 9E-07 m^2 9E-07 m^2 9E-07 m^2 V2 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s 332.41 m/s
mflow 0.0004 kg/s 0.0004 kg/s 0.0004 kg/s 0.0004 kg/s 0.0004 kg/s 0.0004 kg/s 0.0004 kg/s A1 2E-06 m^2 2E-06 m^2 2E-06 m^2 2E-06 m^2 2E-06 m^2 2E-06 m^2 2E-06 m^2 F 0.0746 lbf 0.1052 lbf 0.1358 lbf 0.1665 lbf 0.1971 lbf 0.2277 lbf 0.2583 lbf
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Appendix E: CFD Analysis of Miniature Air Turbine Setup and Boundary Conditions for Models 1-4:
�� Single inlet and single outlet �� Mesh Interval - Triangular 0.25mm �� Inlet boundary condition: Velocity inlet at 243m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients)
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Model-1
Figure-1: Grid
Figure-2: Static Pressure Contours (Pa)
88
Figure-3: Velocity Contours (m/s)
Figure-4: Velocity Vectors (m/s)
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Model-2
Figure-5: Grid
Figure-6: Static Pressure Contours (Pa)
90
Figure-7: Velocity Contours (m/s)
Figure-8: Velocity Vectors (m/s) The model displayed in figure 8 is at a 10° clockwise rotation and the force calculated on the blade at this configuration was 142.13 N/m (width).
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Model-3
Figure-9: Grid
Figure-10: Static Pressure Contours (Pa)
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Figure-11: Velocity Contours (m/s)
Figure-12: Velocity Vectors (m/s) The model displayed in figure 12 is at a 20° clockwise rotation and the force calculated on the blade at this configuration was 122.04 N/m (width).
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Model-4
Figure-13: Grid
Figure-14: Static Pressure Contours (Pa)
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Figure-15: Velocity Contours (m/s)
Figure-16: Velocity Vectors (m/s) The model displayed in figure 16 is at a 45° clockwise rotation and the force calculated on the blade at this configuration was 112.82 N/m (width).
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Setup and Boundary Conditions for Model-5: �� Two inlets and two outlets oriented parallel to one another �� Mesh Interval – Triangular
o Casing Boundary - 0.15mm o Geometry - 0.25mm
�� Inlet boundary condition: Velocity inlet at 220m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients)
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Model-5
Figure-17: Grid
Figure-18: Static Pressure Contours (Pa)
97
Figure-19: Velocity Contours (m/s)
Figure-20: Velocity Vectors (m/s)
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Setup and Boundary Conditions for Model-6:
�� Two inlets and two reconfigured outlets �� Rotational Effects are added: = 5236 rad/s �� Mesh Interval – Triangular
o Casing Boundary - 0.1mm o Blade and Turbine Surface – 0.1mm o Geometry - 0.25mm
�� Inlet boundary condition: Velocity inlet at 10m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients)
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Model-6
Figure-21: Grid
Figure-22: Static Pressure Contours (Pa)
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Figure-23: Velocity Contours (m/s)
Figure-24: Velocity Vectors (m/s)
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Setup and Boundary Conditions for Model-7:
�� Two inlets and two outlets �� Mesh Interval – Triangular 0.1mm �� Rotational Effects are added: = 5236 rad/s �� Inlet boundary condition: Velocity inlet at 23.6m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients) �� Problem observed at the lower inlet. The pressure build up was not symmetric and it
was not realistic (See Figure-26). Therefore, entropy contours were observed to see if there was any discontinuity in the geometry.
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Model-7
Figure-25: Grid
Figure-26: Static Pressure Contours (Pa)
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Figure-27: Velocity Contours (m/s)
Figure-28: Velocity Vectors (m/s)
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Figure-29: Entropy Contours (kJ/kg.K) �� No discontinuities were observed in Figure-29 above.
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Setup and Boundary Conditions for Model-7a:
�� Two inlets and two outlets �� Mesh Interval – Triangular 0.1mm �� Rotational Effects are added: = 5236 rad/s �� Inlet boundary condition: Velocity inlet at 23.6m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients) �� Problem observed at the lower inlet was corrected by assigning lower initial condition
values for the x-velocity rate (See Figure-31 for symmetric pressure distribution). Entropy contours in Figure-32 validates once more that the grid does not have any discontinuity and that the unrealistic pressure contours observed in Model-7 were purely due to solution initialization. However, another problem observed was that the flow was driven by the rotational speed rather than the inlet speed (See Figure-33). To correct this problem the inlet velocity was increased 5m/s in the next model, which is Model-7b.
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Model-7a
Figure-30: Grid
Figure-31: Static Pressure Contours (Pa)
107
Figure-32: Entropy Contours (kJ/kg.K)
Figure-33: Velocity Vectors (m/s)
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Setup and Boundary Conditions for Model-7b:
�� Two inlets and two outlets �� Mesh Interval – Triangular 0.1mm �� Rotational Effects are added: = 5236 rad/s �� Inlet boundary condition: Velocity inlet at 28.6m/s �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients) �� Increased velocity at the inlets helped the rotational speed to be in sync with the inlet
speed (See Figure-36 and Figure 37).
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Model-7b
Figure-34: Grid
Figure-35: Static Pressure Contours (Pa)
110
Figure-36: Velocity Contours (m/s)
Figure-37: Velocity Vectors (m/s)
111
Setup and Boundary Conditions for Model-7c:
�� Two inlets and two outlets �� Mesh Interval – Triangular 0.1mm �� Rotational Effects are added: = 5236 rad/s �� Inlet boundary condition: Velocity inlet at 28.6m/s �� Decreased tip clearance �� Outlet boundary condition: Pressure outlet with 0Pa gauge pressure. �� Viscous Effects: ��� viscous model. �� Fluid: Air
�����Ideal gas Cp = 1006.43 J/kg.K k = 0.0242 W/m.K �
����Sutherland Law (3 Coefficients) �� Increased velocity at the inlets helped the rotational speed to be in sync with the inlet
speed (See Figure-36 and Figure 37).
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Model-7c
Figure-38: Geometry
Figure-39: Static Pressure Contours (Pa)
113
Figure-40: Dynamic Pressure Contours (Pa)
Figure-41: Velocity Vectors (m/s)
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Appendix F: Shaft Life Stainless steelSut = 620 MpaSy = 415 Mpa
Tmax = 0.001483 Nm tau = 32*T/(16*pi*r^3) Tmin= 0.00111225 Nm tau_max = 83730588 N/m^2
tau_min = 62797941 N/m^2d = 0.000448479 md = 0.44847927 mm
Se`= .504*Sut = 312.48 Mpa
ka = a*Sut^b a = 4.51b = -0.265
ka = 0.820716kb = 3.014971kc= 0.577
Se = ka*kb*kc*Se` = 446.1428 Mpasa = (smax-smin)/2 = 10466323 N/m^2sm= (smax+smin)/2 = 73264264 N/m^3
Soderbergsa/Se + sm/Sy = 1/n n = 5 factor of safety0.999999893 = 1
used Excel's Solver program to solve for the diameter
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