ME503 Project
Due 8 May 2025, 11:59 pm
The goal of this project is to give you an opportunity to apply your
newly-acquired skills as an engineering thermodynamicist to the
analysis and design of a practical device: an aircraft jet engine. Moreover, this project is designed to serve as a study guide for the final
exam. The purpose of many engineering systems is to convert disordered internal energy into more useful electrical or mechanical
energy. Most such systems involve a working fluid, such as water
or air, which is circulated through the system in a cycle. Note that
in steam power plants, for example, the cycle is closed, but in gas
power systems, such as an aircraft jet engine, the cycle is open. An
open cycle is not, strictly speaking, a thermodynamic cycle, since a
given mass of working fluid is not brought back to its original state,
even though the mechanical parts of the system may operate in a
cyclic fashion. In some sense, open cycles may be thought of as being
closed by the atmosphere.
Figure 1: A jet engine
You are charged with the task of performing a preliminary thermodynamic analysis of an aircraft jet engine. A jet engine provides
thrust by accelerating relatively small amounts of air to very high
velocities. You can show (after studying fluid mechanics!) that the
thrust, T, generated by a jet engine is given by
T = ṁ (|Vexit | − |Vinlet |)
where ṁ is the mass flow rate of air passing through the engine, |V |
is the velocity vector magnitude, and the subscripts denote exit and
inlet velocity vectors, respectively. A jet engine often is modeled as
operating on an (ideal) open Brayton cycle (one in which all of the
me503 project
work delivered by the turbine goes into driving the compressor). Referring to the schematic of the jet engine in the figure below, we see
that the air (i.e. the working fluid) entering the engine is first slowed
in a diffuser before being compressed in the compressor. The warm,
high-pressure air leaving the compressor then enters the combustor.
Following combustion, which occurs at nearly constant pressure,
the hot air is expanded first through a turbine and then through a
subsonic-supersonic nozzle, where the air exits the engine at speed
|Vexit |, we will model the jet engine as a cycle consisting of various
components across which a processes occurs. The components and
their process steps are as follows (we neglect the diffuser):
1. 1 → 2: compressor
2. 2 → 3: combustor
3. 3 → 4: turbine
4. 4 → 5: nozzle
5. 5 → 0: atmosphere (to close the cycle as described above)
The model to be used is ideal gas with constant specific heat (take
R ≃ 287 J/kg/K, and cv ≃ 715 J/kg/K). Each process is steadystate, constant properties and velocity at each inlet and exit, and no
potential energy change. The only kinetic energy change occurs in
the nozzle.
Find:
1. an expression for the specific work of the compressor assuming
isentropic (adiabatic and reversible) compression.
2. an expression for the specific enthalpy change across the combustor assuming q is added to the system by the combustion of jet
fuel.
3. an expression for the specific work of the turbine assuming isentropic (adiabatic and reversible) expansion of the heated air in the
turbine.
4. an expression for Vexit of the nozzle.
5. the air density assuming the airplane is flying at an elevation of
approximately 10 km, with a pressure of 30 kPa and temperature
of 215K.
6. the air temperature leaving the compressor assuming P2 /P1 = 50.
2
me503 project
7. the specific compression work for these conditions using the properties of air above. Is this positive or negative? Why?
8. the air temperature exiting the turbine, if the inlet temperature to
the turbine is 1300K and the specific work of the turbine equals the
specific work of the compressor. Assume the pressure entering the
turbine is P2 , i.e., the combustor operates at constant pressure.
9. the air pressure exiting the turbine.
10. Vexit if the air pressure and temperature exiting the nozzle are
P = 70 kPa and T = 250 K, assume the velocity entering the nozzle
is 50 m/s. Note that you will need a factor of 1000 if working in
kJ.
3