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Aerospace propulsion 3

1. JP4 fuel heating value QR = 45,000kJ/kg

When mass of fuel = 200t, the range= ...

AAE 339 Aerospace
Propulsion Summer 2020
Homework Assignment 3
1. Given that an airliner has a range of 6000 miles using 200 tons of JP4 fuel, and its dry weight
(with no fuel) is 800 tons. Estimate the range of the aircraft burning (a) the same mass of
liquid hydrogen fuel, and (b) the same volume of liquid hydrogen fuel. Use the range
formula in Hill, page 152 Eq. 5.19, but note that there should be parentheses around [ln
(m1/m2)], so that the range formula is:
s = (QR/g) ηo (L/D) [ln (m1/m2)]
The dry mass of the aircraft is 800 tons.
Assume that the flight speed is varied so that the L/D and the overall efficiency remain the
same for the different fuel types.
JP4
Density = 800.0 kg/m3 Heating value = 45,000 kJ/kg
Liquid Hydrogen
Density = 70.8 kg/m3 Heating Value = 120,900 kJ/kg
2. Consider an ideal ramjet engine. Plot the specific thrust, TSFC, and fuel/air ratio as a
function of Mach number (range: 0 < M < 7) for the following input data.
Tatm = 216.7 K
γ = 1.4
Cp = 1005 J/kg-K
QR = 42800kJ /kg
(a)
To4 = Tmax = 1500 K
(b)
To4 = Tmax = 2000 K
(c)
To4 = Tmax = 2500 K where To4 = combustor outlet stagnation temperature.
3. A turbojet engine works on an open cycle that is closely related to the Brayton cycle. The
main difference is that the air is expanded in the turbine so that the work output exactly
matches the compressor work input. Additional expansion is then accomplished in a nozzle
to produce a high exhaust velocity jet for thrust.
In this assignment, we will analyze the open-cycle turbojet cycle using the procedures given
in class for the Brayton cycle. For simplicity, we will study the case of static sea-level thrust,
i.e., the jet engine is stationary, which means that the air intake velocity into the engine is
negligibly small. You may use these additional assumptions:
1
•
•
•
•
Reversible adiabatic processes for the compressor, turbine and nozzle expansion.
Combustion is modeled as constant pressure heat-addition. Neglect the mass of fuel
added.
Potential energy differences are negligible throughout and kinetic energy is negligible
everywhere except the nozzle exit.
Take air to be a perfect gas with constant specific heats, R=287 J/kg-K and γ =1.4.
(1) The intake air at the compressor inlet is at the ambient conditions of 300 K and 0.1 MPa.
If the compressor has a pressure ratio of 30, what is the compressor exit temperature?
How much work input does the compressor require?
(2) The constant pressure heat addition process has an exit temperature of 1500 K. How
much heat is added in the burner?
(3) The turbine expands the air until the work extracted exactly equals the compressor work
input. What is the exit temperature of the turbine? What is the exit pressure?
(4) The air from the turbine outlet is then further expanded in a nozzle in a reversible
adiabatic expansion down to the ambient pressure of 0.1 MPa. What is the exhaust
temperature? Determine the exhaust velocity. Note that there are no work or heat
transfers in the ideal nozzle expansion and that kinetic energy is not negligible at the
nozzle exit.
(5) Determine the nozzle exhaust velocity using the Isentropic Tables (handout). Note that
the nozzle inlet temperature is the same as the stagnation temperature because the
velocity is negligible at that location. Verify that your answer agrees with that in Part 4.
(6) Represent the above turbojet cycle in a T-s diagram. Mark out all the states and
processes.
(7) Defining the kinetic energy of the exhaust jet as the useful work output of the jet engine,
calculate the efficiency of the engine.
(8) Speculate on how the efficiency may be improved. You may wish to use some of the
insights gained from the Brayton cycle analysis as well as consider the nozzle expansion
process.
Lecture 9
Introduction to Chapter 5, The Gas Turbine Engine Cycle
Rayleigh flow example: Scramjet combustor analysis
Performance Parameters • Efficiency
• Thrust
• Range
SCRamjet
Combustor
example:
Suppose the air-force is interested in the use of
hydrogen fuel in a scramjet combustor as a mean
of high-speed air-breathing propulsion
Assume:
Complete mixing and
combustion
Find:
Turbojets, Turbofans, Turboprops
Turbojet Thrust
Single-Stream Air-Breathing Engine
T above is ‘net thrust’
For static tests, u = 0, T is ‘gross thrust’
Difference is ‘ram drag’: Fn = Fg – mau
If pe ~ pa, and fuel flowrate is neglected
Simple Thrust Equation
Performance
Specific Thrust
Thrust Specific
Fuel Consumption
where
kg/N-hr or lb/lbf-hr
Ramjets
0.2
2
Turbojets
0.1
1
Turbofans 0.05
0.5
Efficiency
Work produced/heat energy supplied
In the engine:
Fuel energy is converted to mechanical energy
with efficiency ht
Mechanical energy is converted to useful thrust
with efficiency hp
Overall Efficiency:
ho = useful work done on vehicle
energy supplied by fuel
Power
Mechanical power (work/time) is DKE/time
Chemical power is
Thrust power is
Conservation of Energy
Power
Fuel Power
(chemical energy/time)
Thermal Efficiency
Jet Power
(kinetic energy/time)
Propulsion Efficiency
Thrust Power
(work/time)
Power
Fuel Power
Jet Power
Thrust Power
Overall Efficiency
Thermal Efficiency
Jet Power
Fuel Power
Propulsion Efficiency
Thrust Power
Jet Power
Max when ue=u
or Zero Thrust!
Overall Efficiency
Thrust Power
Fuel Power
Average ho ~ 0.30
Max when u=ue/2
Turbofan
Substitute
Energy Balance
Specific Thrust
Turbofan Efficiencies
Aircraft Range
How far can an airplane fly, and why?
L
T
D
Force balance for an aircraft in
steady level flight
W
Lecture 11
Chapter 5, The Gas Turbine Engine Cycle, cont
Performance Parameters - Efficiency, Thrust, Range
the Brayton Cycle
Engine Design - Goals
• Meet required thrust thought flight envelop
- aircraft: takeoff, climb, cruise,…
- spacecraft: launch, orbit transfer, planetary mission,…
• High efficiency
- minimize amount of fuel (energy input) required to
provide delivered thrust (energy output)
• Constraints
- materials limitations (max temperature, stress,…)
- low emissions: NOx, soot, toxics, …
- other: size, lifetime, manufacturability, maintainability
Gas Turbine Engines
Brayton Cycle
Open-Cycle
Closed-Cycle
Ideal Brayton Cycle
1-2 : Isentropic compression (in a compressor)
2-3 : Constant pressure heat addition
3-4 : Isentropic expansion (in a turbine)
4-1 : Constant pressure heat rejection
Closed-Cycle Gas Turbine
neglect kinetic and
potential energies
q1
q2
Closed-Cycle Gas Turbine
Treating air as an ideal gas with constant specific heat (‘cold-air-standard’
analysis) with isentropic compression and expansion, and constantpressure heat transfer:
Closed-Cycle Gas Turbine
T1
cycle = 1 −
T2
cycle = 1 −
1
P2
P1
−1
How to improve efficiency?
- Increase pressure ratio rp=p2/p1, increase specific heat ratio
For aero-propulsion, pressure ratio is practically limited
- weight
- compression temperature
Pressure Ratio and Temperature Ratio
Area under each curve represents specific work, w
1: low pressure ratio, large q, low thermal
2: moderate pressure ratio, less q, higher w than (1)
3: high pressure ratio, least q, high thermal , lower w than (2)
Specific Work-Optimized
Pressure Ratio
p2
T3 2( −1)
=
p1 opt T1
Real Brayton Cycle
Ideal
Real
Irreversibilities:
- Pressure drop in heat exchanger
- More work input to compressor
- Less work output from turbine
Real Gas
Turbine Cycle
Diffusion and
compression
Component Parameters
Component
Effect
Symbol
Diffuser
Total pressure recovery
pd
Compressor
Efficiency
Fan
Efficiency/bypass ratio
c
f, b,
Turbine
Efficiency
t
Propeller
Efficiency
p
Shaft
Efficiency
Combustor
Efficiency/total pressure ratio
m
b, pb
Afterburner
Efficiency/total pressure ratio
ab, pab
Primary nozzle
Efficiency
n
Fan nozzle
Efficiency
Bypass duct
Total pressure ratio/split ratio
fn
pu, s
Bypass mixer
Total pressure ratio
pm
Exhaust
Pressure ratio
pe
Real Brayton Cycle - Compressor Process
Given:
compressor pressure ratio is 20 and
compressor efficiency is 0.80, p1=0.1 MPa
the ratio of the work required in
an isentropic process to that
required in the actual process
Real
Real Brayton Cycle - Compressor Process
Given: compressor pressure ratio is 20 and
compressor efficiency is 0.80, p1=0.1 MPa
Real
Real Brayton Cycle - Burner Process
Given
Real
Where 1-rb is the fractional pressure
loss in the combustor
Real Brayton Cycle - Turbine Process
Assume a 5% pressure loss in constant
pressure heat rejection, ie, p4/p1 = 1.05
Real
Real Brayton Cycle - Turbine Process
Assume a 5% pressure loss in constant
pressure heat rejection, ie, p4/p1 = 1.05
Real
Real Brayton Cycle - Cycle Performance
Real
Remember this Brayton cycle is ‘closed’ and is only
representative of the actual gas turbine cycle
Comparisons
Carnot Efficiency
Ideal Brayton Efficiency
Real Brayton Efficiency
representing a maximum work,
theoretical cycle
Lecture 12
Performance of Ramjets, Turbojets, and Turbofans
Engine Design Sensitivity to Flight Mach Number
Kahn, Mechanics of Jet Propulsion, 2005
Ramjet Engine
• Most efficient engine
• Simplest air breathing
engine
• Doesn’t have compressor
or turbine
• High tolerance to high
temperatures
• Ideal for very high speed
flight
X-15 with Ramjet
engine
https://www.youtube.com/watch?v=c_4UIfHNAZE
X-15 The Ultimate Flying Machine
Ramjet Engine
Diffuser
Slows down flow from supersonic to subsonic speeds
Adverse pressure gradient can be problem
Temperature Increases
Pressure Increases
Combustor
Subsonic constant pressure combustion
Nozzle
Ideal Expansion to ambient pressure
Ramjet Engine
Ramjet
Advantages:
•Low weight
•High thrust to weight ratio
•No moving parts
•Most efficient air breathing
engine
•Can reach speeds up to Mach
6.0
Turbojet
Disadvantages:
• Speed must be supersonic
• Cannot produce thrust when
engine is static
• Air must slow down to subsonic
speeds for ignition in the burner
• As air approaches Mach 6.0, it is
too hot to burn
SR-71 Blackbird
Turbojet/Ramjet Hybrid
http://www.youtube.com/watch?v=Ev8Lqm5Ngi8&f
eature=related
http://www.1000pictures.com/aircraft/special/index.htm
Importance of Shock Wave
• One way supersonic flow can be
compressed
• Fluid properties can change almost
instantaneously
• Shock appears when supersonic
flow in pipe is decelerated
http://www.physicspost.com
Importance of Shock Wave
http://www.physicspost.com
Ideal Ramjet Engine
Ideal Ramjet Thrust and Fuel Consumption
Ideal Ramjet Thrust and Fuel Consumption
Performance
Curves
1000 m/s
0.7
Question:
Why does the specific
thrust increase with
Mach number and then
decrease?
0.6
0.42
J-58 Turbo-ramjet Engine
Specifications:
Model: Pratt & Whitney J-58
Compressor: 9-stage, axial flow,
single spool
Turbine: two-stage axial flow
Thrust: 32,500 lbs. with
afterburner
Weight: approx. 6,000 lbs.
Max. operating altitude: above
80,000 ft.
J-58 Engine and Spike
J-58
Airflow
and
Temperature
https://www.youtube.com/watch?v=F3ao5S
CedIk&t=39s
J-58 Engine Testing in Afterburner
J-58 Inlet Shocks
Realistic Ramjet Cycle
Diffusers are prone to irreversibilities:
Viscous Effects
Shocks
Scramjet
https://www.youtube.com/watch?v=XV8AfgbGh5M&t=250s

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Explanation & Answer:

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Aerospace propulsion 3

1. JP4 fuel heating value QR = 45,000kJ/kg

When mass of fuel = 200t, the range= ...