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Compressible Flow Assignment
MECH3610 Advanced Thermofluids
2024 T2
Read the following before getting started:
This assignment is to be submitted electronically through Turnitin via the 'Compressible Flow
Assignment Submission' link on Moodle before 11:59 PM, Friday 26th July 2024.
This assignment must be completed individually. Signs of collusion in the submitted report
will be treated as plagiarism and such cases will be dealt with by the school office.
This assignment can be either typed or hand-written including the use of digital ink. Regardless
of submission style, all working out and solutions must be clearly legible.
Reference to any table(s), calculator(s) or other resources must be clearly acknowledged and
snip(s) of input(s) and output(s) must be included in the assignment.
This assignment is worth 20% of your overall course grade.

Purpose: This assignment will test your understanding of the compressible flow material covered in
this course. The questions are tailored to test various concepts that you may encounter in the future as
an engineer in high-speed flow applications.

Skills: This assignment will help you practice your knowledge on the following which are essential to
your success as an engineer beyond this course:
Configurations where compressibility effects should be considered.
The design of high-speed systems and the associated parameters.
Nozzle design.
Identifying and accounting for supersonic flow phenomena.

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2024 T2 MECH3610 Advanced Thermofluids

Scenario:
Due to the growing success of developments in supersonic flight, an aerospace company you work for
is pioneering the design of a new high-speed rocket. You're tasked with various challenges in designing
and analysing the rocket's propulsion system.

Figure 1. Preliminary rocket design

Part A:
The first stage of the rocket system design is conceptualising a design that fulfils the requirements for
the propulsion system.
a. Marketing would like to present an overview of supersonic flight to an audience with a limited
understanding of aerodynamics. Prepare a brief for non-specialists on why understanding Mach
numbers and flow compressibility is crucial in high-speed aerospace applications by
differentiating between Mach 0.5 and Mach 3 flow characteristics. Limit your response to 300
words and use a diagram or chart in your response. (4 marks)

b. As part of the rocket propulsion system design using hydrogen and oxygen as propellant gases,
certain parameters have been defined by the engineering team:
Combustion chamber temperature: 4000 K
Design mass flow rate: 857.7 kg/s
Throat area of the nozzle: 0.4 m2
Mach number at the throat is sonic (M = 1)
Ratio of specific heats (γ) of the flow gas: 1.2
Molecular weight of the gas: 16 g/mol
(i) First, calculate the initial combustion reservoir pressure using the provided
parameters. (5 marks)
(ii) Your team wants to examine the impact of the throat area over a specified range. For
this, alter the throat area from 0.3 m2 to 0.5 m2 in increments of 0.05 m2 and plot the
reservoir pressures against varying throat areas to visualise the relationship. (9 marks)
Hint: It is suggested to use excel/MATLAB for your calculations.
(iii) From your plot discuss the relationship between the choice of throat area and the
required reservoir pressure. In your discussion, provide reasonings for what would
influence your team’s design decisions on these parameters based on the principles of
nozzle design. Limit your response to 300 words and you may incorporate figures and
equations to enhance your discussion. (4 marks)

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2024 T2 MECH3610 Advanced Thermofluid

Part B:
Your team has now shifted to the external geometry of the rocket system for the next design phase.

a. To aid the commercial team, your experimental testing team has designed a similarly shaped
rocket and tests it with the flow conditions shown in figure 2. At the location where the ‘X’ is
shown, the static pressure is measured to be 82.6 kPa. Assume , and are 1.005 kJ/kg.K,
0.287 kJ/kg.K and 1.4, respectively. Considering the compressibility criteria of air, determine
the velocity at ‘X’ and state any assumptions made. Additionally, quantify the percentage error
if the flow is assumed to be incompressible. (6 marks)

Figure 2. flow conditions tested.

b. A junior engineer who has only recently been recruited to the team has identified the surfaces
where they think the flow properties will be different on the external surface of the rocket. They
have labelled these surfaces with letters as per figure 3 below. You have been assigned the
responsibility of reviewing whether they have correctly labelled all the surfaces that will be
exposed to different flow conditions. Answer with either 'Yes' or 'No', documenting a
justification for your review result. (3 marks)

Figure 3. Junior Engineer - labelled geometry with flow conditions.

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2024 T2 MECH3610 Advanced Thermofluids

c. Based on your review of the junior engineer’s work in b., you are tasked with using your
knowledge of shock-expansion theory to calculate the Mach number, Prandtl-Meyer function
and pressure for all faces that will be exposed to changing flow conditions as shown in figure
3. To ease your manager's workload, summarise your findings in a table similar to Table 1
shown below. Use = 1.4 in your calculations.
(19 marks)
Table 1. Summarise your solutions in a table like this.
Face/Properties Mach number ()
Prandtl-Meyer
Function ()
Pressure ()