Mathematics-in-Action
Engine Design Workshop
Ian Halliwell
Senior Research Scientist
Avetec Inc, Springfield, Ohio
July 21, 2008
Contents
1. The Role of Mathematics in the Design of Gas Turbine Engines
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Mathematics, Science & Engineering
The Preliminary Design Process
Detailed Design
Complex Calculations
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Flow around Aircraft & inside Engines
Cycle Models for Jet Engines
2. How a Gas Turbine Engine Works
3. Gas Turbine Engine Configurations
4. Engine Design Workshop
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1. The Role of Mathematics in the Design of
Gas Turbine Engines
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The Role of Mathematics: From Molecules to Moon Landings (1)
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We all use mathematics everyday for a variety of mundane purposes
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On a much higher level, mathematics forms the fabric of today’s technology-based
society
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Making change, telling time
Science & technology
Commerce
Defense
Computers
Electronics
Design & manufacturing processes
Medicine
We use mathematics to model concepts that we cannot grasp in any other way
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Small scale objects, such as atoms & molecules
Very large-scale objects, such as our solar system and universe
Very complex systems, such as a gas turbine engine cycle or the flow field inside a compressor
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The Role of Mathematics: From Molecules to Moon Landings (2)
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Small stuff!
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Bigger stuff!
CFD Grid of a Stator & Rotor in a Turbine
Mars – Earth Transfer Orbit
Prediction of Rotor Pressure Distribution
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Mathematics, Science & Engineering
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While mathematics may be considered as a separate subject in its own right, it
also plays a vital role as a tool in science & engineering.
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Scientists discover and explain natural phenomena, often expressing them in
theoretical or mathematical terms.
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Mathematicians describe scientific phenomena and help us to understand
them using mathematical theories. Some examples are:
– Electricity
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Engineers turn concepts into hardware that is able to be used for the benefit of
everyone.
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Simple Calculations
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In aircraft design we can calculate the thrust needed from the engines to accelerate down the runway
and take off
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Balancing forces horizontally:
T  D  M dV
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Balancing forces vertically:
R  Mg  L
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Combining the two gives:
M dV
Where
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dt
dt
  R
  T  D   Mg  L
M = aircraft mass
dV/dt = aircraft acceleration
μ = runway coefficient of friction
R = undercarriage reaction force = Mg – L
g = gravitational acceleration
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Cycle Models for Jet Engines
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A cycle deck can calculate the value of
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every flow property (mass flow rate, temperature, pressure, velocity, etc)
at every station within the engine
at every operating condition
at every point on the aircraft mission.
It can also estimate the performance of every component (fan, compressor, turbine,
exhaust nozzle, etc.) and the fuel consumption.
GE CFM56–5C Turbofan Engine
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How an Airplane Flies
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There are four forces acting on an airplane in flight:
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Lift acts upwards
Weight acts downwards
Thrust acts forwards
Drag acts backwards
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At a constant altitude the lift balances the weight
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At a steady speed the thrust balances the drag
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Lift is produced by air flowing over the wings
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The air moves faster over the upper surface than over
the lower surface
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This results in a lower pressure on the upper surface
(the suction surface) than that on the lower surface
(the pressure surface)
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Thrust is produced by the engine(s)
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Drag is produced by friction of the air over the
airplane
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We all know where the weight comes from!
Forces on an Airplane in Flight
An Airplane Wing – Streamlines & Forces
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2. How a Gas Turbine Engine Works
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How a Jet Engine Works
The
SUCK
SQUEEZE
BANG
BLOW
process!
•The inlet captures the air and slows it down (SUCK)
•The compressor pressurizes the air (SQUEEZE)
•The combustor heats the air by mixing fuel with & burning the mixture (BANG)
•The turbine extracts work from the hot gas to power the compressor (BLOW)
•The exhaust nozzle converts high temperature & pressure into high velocity to produce thrust
(BLOW continued)
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Comparison of Gas Turbine & Piston Engines
Gas
Turbine
Engine
Internal
Combustion
Engine
SUCK
SQUEEZE
BANG
BLOW
In a Gas Turbine Engine – the processes each take place in a different component
In an Internal Combustion Engine – the processes all happen in the same place
The thrust required to propel an airplane can be produced by:
•Accelerating a small amount of air very hard
or
•Accelerating a large amount of air relatively gently
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The choice of high or low jet velocity depends on the engine application
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A regional jet with 50 passengers flies at about Mach 0.8 or 500 feet per
second at 30,000 feet altitude
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An F-16 fighter flies at about Mach 2 or 1500 feet per second at 40,000 feet
altitude
The jet velocity must be higher than the speed of the aircraft but not too much higher!
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Today, we will design a new engine for this airplane.
Boeing 777-200LR
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3. Gas Turbine Engine Configurations
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Different engines are used at different speeds
and altitudes
Engine Types & Range of Application
(1 knot = 1.152 miles/hour = 1.689 feet/sec)
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Types of Gas Turbine Engines
Simple Turbojet
Turboprop
Turboshaft
Turbofan
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Gas Turbine Engine Configurations (1)
A Simple Turbojet
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Example of a Simple Turbojet
Teledyne Continental J402 Turbojet Missile Engine (640 lbf Thrust)
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Gas Turbine Engine Configurations (2)
A Twin-Spool Unmixed High Bypass Ratio Turbofan
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Example of a High Bypass Ratio Turbofan
CFM56 High Bypass Ratio Turbofan (30,000 lbf thrust)
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Gas Turbine Engine Configurations (3)
A Twin-Spool Low Bypass Ratio Turbofan
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Example of a Low Bypass Ratio Turbofan
F110-GE-129 Low Bypass Ratio Turbofan (29,000 lf thrust)
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Gas Turbine Engine Configurations (4)
An Apache Longbow (Boeing AH-64D) Helicopter
T700-GE-701C Turboshaft
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Gas Turbine Engine Configurations (5)
GE 36 Unducted Fan
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Gas Turbine Engine Configurations (6)
Rolls Royce Pegasus
McDonnell Douglas Harrier AV-8B
A Lift Fan
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Gas Turbine Engine Configurations (7)
If we fly fast enough to generate the pressure we need by “ramming” the air into the
front of the engine, we can eliminate the fan, compressor and turbines!
A Ramjet
We use another type of engine to reach a speed & altitude at which the ramjet can
be turned on.
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Gas Turbine Engine Configurations (8)
A Variable Cycle Engine
F-22 Raptor
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4. Engine Design Workshop
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The Design Competition
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In the design program you will be asked to design new engines to power the Boeing 777
airplane for a mission that carries 300 passengers from New York - JFK to London Heathrow. The engines are turbofans. The design program already knows how much
thrust the airplane needs at both take-off and cruise conditions. This will then be divided
equally between two engines. High efficiency and low weight are the most important
characteristics.
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Your job is to re-engine Boeing's 777 airliner with new, quiet, clean engines that meet the
new noise and emissions requirements.
Boeing 777 200ER
The NASA website: http;//www-psao.grc.nasa.gov/education/engine engineering
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Running the Design Program
There are four major design variables that you can change. These are:
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Airflow
Fan Pressure Ratio (from station 2 to station 21)
Overall Pressure Ratio (from station 2 to station 3)
Combustor Temperature (at station 4)
Airflow
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Airflow
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The airflow entering the engine at the fan face is one of the parameters used in this
problem to determine the size, weight, and performance of your turbofan.
The dimensions and weights of all components in the engine are directly related to
airflow.
Increasing or decreasing the airflow causes the engine to grow larger or smaller
respectively.
Specifying a higher airflow can increase the thrust of the engine, but its weight, size, and
aerodynamic drag are increased as well!
The units used to describe airflow are pounds per second (lb/s).
When the pilot releases the brake to begin take-off, the airflow of a B777-200ER's
GE90-85B engine is 3,120 lb/s!
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Fan Pressure Ratio
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The fan in a commercial turbofan engine is a very large, single stage, axial compressor
with a relatively low pressure ratio. This pressure ratio is defined as the pressure out
divided by the pressure in.
The fan is driven by a shaft that connects it to low pressure turbine. The main job of the
fan is accelerate the air in the bypass stream that bypasses, or goes around, the core of the
engine.
In a commercial turbofan of this size, most of the thrust comes from the bypass stream.
For a fixed design, higher values of fan pressure ratio may be achieved by increasing the
speed of the fan.
But be careful when increasing the fan pressure ratio, because the fan noise gets much
worse. The jet velocity from the bypass duct is also determined by the fan pressure ratio,
so jet noise will be affected as well.
The fan pressure ratio is a dimensionless quantity. The sea level static fan pressure ratio of
a GE90-85B engine is about 1.5.
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Overall Pressure Ratio
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The overall pressure ratio is defined as the highest pressure in the engine (at the exit of the
high pressure compressor) divided by pressure of the outside air.
In a large commercial turbofan of this kind, the core flow passes through three compression
components: the fan, the booster, and the high-pressure compressor. The product of the
pressure ratios of these individual components gives the overall pressure ratio.
There is a very complex relationship between the thrust of the engine, the amount of fuel
burned and all of the design variables. Component pressures, temperatures, flow rates,
flight speed, and other variables contribute to a turbofan's performance and fuel efficiency.
It's up to you to discover the best overall pressure ratio for your particular design! In this
design exercise, you select the fan pressure ratio, but the booster's pressure ratio is always
the same. The high-pressure compressor pressure ratio is then changed by the program to
give the overall pressure ratio you select.
The overall pressure ratio is a dimensionless quantity. The sea level static overall pressure
ratio of a GE90-85B engine is about 40.
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Combustor Temperature
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The combustor temperature is varied by the pilot, who uses the throttle to adjust the fuel
flow rate to the engines – just like an accelerator in a car. The temperature you specify in
is the temperature at the combustor exit at the engine's takeoff condition.
In a commercial turbofan of this kind, this temperature is only held for a minute or two
until the takeoff is complete and the airplane is safely at altitude. To extend hot section
component life and to reduce time between overhauls, the pilot reduces the throttle to
lower combustor temperatures for the rest of the mission.
The higher the temperature, the more energy there is in the gas, and therefore the engine
can be smaller. The maximum temperature that you specify is used to size and design
much of the turbomachinery – the fan, compressor and turbines.
Higher temperatures provide more energy for your turbines, but mean that more fuel in
consumed. Higher combustor temperatures require complex cooling methods, primarily
for the first stage of the high-pressure turbine. The turbine cooling flows and blade designs
are automatically accounted for in this exercise and are not apparent to you, but they are
there!
Keep in mind that higher temperatures require more cooling flow, which punishes the
engine by robbing the turbines of available useful work. Also keep in mind that higher
temperatures produce more NOx emissions and they are bad for the earth’s atmosphere.
The units used to describe combustor exit temperature in this game are degrees Rankine
(°R). The maximum rated temperature of many modern commercial jet engines is over
3200°R or 2740F.
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Pioneering NASA Technologies
Advanced Fan Duct Acoustic Liner
• If fan noise is a problem with your engine design, and if adjusting the fan pressure ratio
and tip speed doesn’t help much, you can try using an advanced acoustic liner material.
This can be done by checking the appropriate box in the design choices area.
• The conventional acoustic liner found in most modern commercial engines is typically a
perforated metal sheet laid atop honeycomb cavities.
• The liner available to you here is very advanced and works much better than liners of
today! Although this magical material is fictitious in our design game, NASA is
developing many innovative noise reduction technologies. But beware -- this noisereducing liner increases your engine's weight!
Advanced Low Emissions Combustor
• If NOx emissions are a problem with your engine design, and if adjusting the combustor
temperature and/or overall pressure ratio doesn’t help much, you can try using an advanced
low-emissions combustor. This also can be done by checking the appropriate box in the
design choices area.
• Although this magical combustor is fictitious in our design game, NASA is developing
many innovative emissions reduction technologies. Of course, this low-emissions
combustor increases your engine's weight!
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Here are some suggestions if you have problems.
My Airplane Doesn't Have Enough Thrust! What Can I Do?
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One method to increase thrust is to simply increase the airflow, and therefore the size of
your engine. This is a simple "photographic scaling" of your engine. But be careful!
Simple scaling can increase the thrust of an engine, but its weight, size, and aerodynamic
drag are increased as well. Since the size and weight of the complete propulsion system
impacts the landing gear length and wing spar strength required, this effect ripples right
through the entire airplane!
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Thrust is also a function of your other design choices. Other tactics involve changing the
thermodynamic specifications of your engine cycle. You could try increasing your
combustor temperature so that there is more thrust available. Or you could increase the
overall pressure ratio or fan pressure ratio so that the bypass stream has a chance of
becoming more energetic. But be careful here as well -- higher temperatures and pressures
can adversely impact hot section component life, fuel consumption rates, emissions, and
noise, and it also may require the use of various "exotic" technologies that potentially can
be heavy, large, expensive, high-maintenance, or even have performance penalties of their
own. This will affect your ticket price!
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My Airplane Violates Your Really, Really Strict Noise Regulations! What Can I Do?
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If fan noise is a problem, you can try reducing the fan pressure ratio. Fan noise depends on
the fan pressure ratio and the fan tip speed that we use to achieve it.
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If jet noise is a problem, you can try reducing the jet velocities of your core and bypass
exhaust streams. In a turbofan, the jet velocity in the bypass stream is a function of the fan
pressure ratio; so lower your fan pressure ratio to reduce bypass jet noise. The jet velocity
of the core stream is a function of the pressure and temperature entering the core nozzle; so
you can try extracting more of the energy from the core stream via the high and low
pressure turbines by using either a high fan pressure ratio or a high overall pressure ratio.
Yes, the driving parameters do conflict with each other and you will need to balance out the
good and bad effects!
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You can also try using the advanced acoustic liner material, conveniently provided to you
by NASA technology research. Although this magical material is fictitious in our design
game, NASA is indeed developing many innovative noise reduction technologies. But
beware – this noise-reducing liner increases your engine's weight!
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My Airplane Violates Your Really, Really Strict Emissions Regulations! What Can I Do?
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The Emissions Index, EINOX, is a strong function of the combustor flame temperature and
the combustor residence time. It is also affected by combustor pressure and other flow
parameters, such as atmospheric humidity.
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The most obvious way to reduce NOx, therefore, is to reduce your combustor temperature.
However, this can lead to engines with poor performance or low fuel efficiency. Engineers
therefore attack other aspects of the problem, such as introducing clever rich-burning
and/or lean-burning zones within the combustor in order to avoid high stoichiometric flame
temperatures. Engineers also try to achieve more homogeneous combustion, avoid
combustor "hot spots," and reduce the gas residence time. These advanced combustor
designs can be used in our game by selecting the advanced low-emissions combustor
option, conveniently provided to you by NASA technology research.
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Although this magical combustor is fictitious in our design game, NASA is indeed
developing many innovative emissions reduction technologies. But beware -- this lowemissions combustor increases your engine's weight!
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Building the Engine
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When you have selected all of the design parameters you hit the “build” button and the
design code will construct your engine and produce a picture of it. Notice that the number
of stages in the HP compressor, the HP turbine, and the LP turbine will all change. These
will affect the weight and cost of the engine and both of these will show up in your
predicted ticket price!
You will be judged on ticket price for the aircraft mission.
Good luck with your design!!
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