16.50 Propulsion Systems
Spring 2011
Quiz 2 May 18, 2011
Two hours, open book, open notes
TRUE-FALSE QUESTIONS
Justify your answer in no more than two lines.
4 points for correct answer and explanation
2-3 points for a correct answer with only partially c
16.50 Propulsion Systems
Spring 2012
Homework : Mean-Line Compressor Design
a) At the compressor inlet (station 2), the flow area is:
(1)
The mean radius (same everywhere) is:
(2)
Hence:
(3)
Using and :
Blade heig
16.50 Propulsion Systems
Spring 2012
Homework : Supersonic Internal-Compression Inlet
a) Geometry for the design condition:
Apply the continuity equation between stations 1 and 2:
(1)
Similarly, apply continuity between stations t and 2
16.50 Propulsion Systems
Spring 2012
Homework 7: Exploration of Velocity Ratios
a) For equal core and bypass velocities, according to the notes, we must have:
(1)
For maximum thrust (maximum as well), we choose:
(2)
Using , we calculate:
16.50 Propulsion Systems
Spring 2012
Homework 3: Two-Position Nozzle
a)
(1)
(2)
(3)
Solving for and :
For the inner bell:
Therefore, the exit Mach number is given by:
The area ratio is then:
16.50 Propulsion Systems
Spring 2012
Homework 6: Off-Design Performance of Small Turboprop Engine
a) At the end of climb, , we have , and .
Also, . Finally,
.
Force balance along and transverse to the
trajectory:
From equation (2),
We are give
16.50 Propulsion Systems
Spring 2012
Quiz 1 March 18, 2011
One hour, open book, open notes
TRUE-FALSE QUESTIONS:
Give an explanation for your answer in no more than 2 lines. For each question,
Right answer, valid explanation
Right answer, bad explanation
16.50 Propulsion Systems
Spring 2012
Homework 5: Thermochemistry Exploration Using CEA Code
The CEA output is very detailed and takes a total of 12 pages, so only one case (equilibrium, O/F=2.6)
will be displayed here. The results are for , using RP-1 fue
16.50 Propulsion Systems
Spring 2012
Homework 2: Chemical vs. Electrical Thrusters
a) Chemical:
We start outside the sphere of influence (SOI) of Earth, and end outside the SOI of Mars, so no escape
or capture are involved. The whole motion is under the S
16.50 Propulsion Systems
Spring 2012
Homework 4.1: Solid Propellant Rocket
1a) Normal operation mass balance:
(1)
Transient operation after port opening:
(2)
Define:
(3)
(4)
(5)
(6)
In terms of these variables, equation (2) becomes:
16.50 Propulsion Systems
Year Unspecified
Quiz 1
One hour, open book, open notes
TRUE-FALSE QUESTIONS (50%)
Please include a 1-2 line explanation for each of your answers.
Statement
1. If one takes a given rocket, with a fixed chamber pressure, and replac
16.50 Propulsion Systems HWK #1
Preliminary design of a Satellite launcher
We wish to produce a first-order design of a 3-stage launch vehicle to place a 3 kg.
nanosatellite in a circular equatorial of 500 km. altitude. Launch will be from the
Equator, in
16.50 Homework 10 Solution
a) Calculate the degree of reaction and the flow angles at the stator and rotor exits . Draw the velocity triangle
to scale. Also, sketch the blade shapes of the stator and rotor.
;
;
b) Calculate the velocity entering t
16.50 Propulsion Systems
Spring 2012
Homework 1: Preliminary Design of a Satellite Launcher
a) Velocity Calculations:
Point A: Start of ascent trajectory
Point B: Apogee of ascent trajectory
Conservation of Angular Momentum:
Rearranging becomes:
(1)
16.50 Lecture 4
Subjects: Hyperbolic orbits. Interplanetary transfer.
(1) Hyperbolic orbits
p
, but now we have >1, so that the
1 + ! cos "
radius tends to infinity at the asymptotic angle ! " = # $ cos $1 (1 / % ).
The trajectory is still described by r
16.50 Lecture 7
Subject: Modeling of rocket nozzles; effects of nozzle area ratio.
In the last lecture we saw how the throat area of the nozzle controls the mass flow rate. Now
we will explore the effects of the shape of the nozzle downstream of the throa
16.50 Lecture 15
Subject: Ablative cooling
By ablation we mean the recession of a surface due to heating, usually by a hot gas.
It is the key process for
a)
b)
c)
d)
Re-entry heat shields
Solid propellant nozzles
Rocket case insulation
Fire-proofing skysc
16.50 Lecture 14
Subjects: Heat Transfer and Cooling
Because the combustion temperatures in most rocket engines are far beyond the
levels tolerable by most common structural metals, the walls of the combustion
chambers and nozzles must be cooled. The high
16.50 Lecture 8
Subjects: Types of Nozzles; Connection of flow to nozzle shape.
Types of Nozzles
The axisymmetric convergent-divergent "bell" nozzle that has been used as the example to
this point is the standard for rocket nozzles, for several reasons:
1
16.50 Lecture 10
Subjects: Models for rocket engines; Flow of reacting gases
Models for Rocket Engines
In Lecture 6 we described in general terms a set of models we might use to describe the
various features of rocket engines, making the point that no one
16.50 Lecture 13
Subject: Rocket casing design; Structural modeling
Thus far all our modeling has dealt with the fluid mechanics and thermodynamics of
rockets. This is appropriate because it is these features that
16.50 Lecture 11
Subject: Reacting Gases (continued); Temperature dependence of specific heats.
Reacting gases (continued)
We were at the point in the last lecture of solving for the composition in the combustion
chamber.
If we set Tc and Pc, we can solve
16.50 Lecture 9
Subject: Solid Propellant Gas Generators; Stability; Grain designs
We have thus far discussed two models for the nozzle flow in rocket engines, the Channel
Flow Model and the Two Dimensional Isentropic Model. Now we will introduce a model
16.50 Lecture 12
Subject: Nozzle flow of reacting gases
In the last two lectures we discussed the phenomena that occur in the combustor, and how to
estimate the properties of the gas in the (near) stagnation state there. Suppose now that we
have determine
16.50 Lecture 5
Subjects: Non-Chemical rockets; Optimum exhaust velocity
1) Non-chemical rockets
A shared characteristic of all non-chemical propulsion systems is that the energy and
propellant mass are separate initially
Chemical
Chemical
Energy
mass
.
m
16.50 Lecture 3
Subjects: Orbital mechanics; Single force center
The most usual application of rocket engines is to propel vehicles under conditions where
the behavior of the vehicle is largely determined by the gravitational attractions of one or
more bo
16.50 Lecture 1
Subjects: Rocket Equation; Gravity Loss; Optimum Acceleration.
1) Rocket Equation
A rocket is a propulsive device that produces a thrust force F on a vehicle by ejecting
mass a high relative velocity c. This force is simply equal to the ra
16.50 Lecture 6
Subject: Modeling of Thermal Rocket Engines; Nozzle flow; Control of mass flow
Though conceptually simple, a rocket engine is in fact physically a very complex device and
difficult to represent quantitatively by mathematical models. But th
16.50 Lecture 2
Subjects: Rocket staging; Range of aircraft; Climb & Aceleration
1) Rocket Staging
The reason for staging is to avoid having to accelerate empty tanks. Assume for
simplicity only two stages; one does not want to stage either too early (and