MCD4140 Assignment

Posted 2021-12-01 xifua

MCD4140 Assignment 1 of 8
MCD 4140: Computing for Engineers
Assignment
Trimester 1, 2019
Status: Individual
Hurdle: There is no hurdle on assignment
Weighting: 10%
Word limit: No limit
Due date: By 12.00pm on Monday 6/05/2019 via Moodle (Week 10).
INSTRUCTIONS
This assignment should be completed INDIVIDUALLY. Plagiarism will result in a mark of zero. Plagiarism
includes letting others copy your work and using code without citing the source. If a part of your code is
written in collaboration with classmates, say so in your comments and clearly state the contributions of each
person.
NOTE: Your MATLAB code will be checked for plagiarism – DON’T RISK LOSING ALL 10 MARKS BY COPYING
SOMEONE ELSE’S CODE (OR BY ALLOWING SOMEONE ELSE TO COPY YOURS).
Download the assignment template files from Moodle and update the m-files named Q1a.m, Q1b.m, etc…
with your assignment code. DO NOT rename the m-files in the template or modify run_all.m. Check your
solutions to Q1 and Q2 by running run_all.m and ensuring all questions are answered as required. Do not
use close all, clear all, clc in any individual mfiles.
SUBMITTING YOUR ASSIGNMENT
Submit your assignment online using Moodle. Read the “Assignment upload instructions.pdf” to prepare
your ZIP file for submission. Your ZIP file (not .rar or any other format) must include the following
attachments:

代做MCD4140作业、MATLAB编程作业代写、代写MATLAB课程设计作业
a. Solution m-files for assignment tasks (e.g. run_all, Q1a.m, Q1b.m, etc.)
b. Any additional function files required by your m-files (e.g. heun.m, falseposition.m, etc.)
c. All data files needed to run the code including the input data provided to you (e.g. data1.txt,
data2.csv, etc.)
d. A completed cover sheet
Your assignment will be marked in your usual computer lab session during Week 11. YOU MUST ATTEND TO
HAVE IT MARKED. IF YOU DO NOT ATTEND, YOUR ASSIGNMENT MARK WILL BE ZERO. YOUR ZIP FILE WILL
BE DOWNLOADED FROM MOODLE DURING WEEK 10 AND ONLY THESE FILES WILL BE MARKED. We will
extract (unzip) your ZIP file and mark you based on the output of run_all.m on a Windows-based system. It is
your responsibility to ensure that everything needed to run your solution is included in your ZIP file. It is also
your responsibility to ensure that everything runs seamlessly on a Windows-based system (especially if you
have used MATLAB on a Mac OS or Linux system). Windows OS computers are available in the computer labs
on campus for testing. The assignment will not be downloaded to your individual laptops for marking.
MARKING SCHEME
This assignment is worth 10% (1 Mark = 1%) of the unit mark. Your assignment will be graded using the
following criteria:
MCD4140 Assignment 2 of 8
1) run_all.m produces results automatically (additional user interaction only if asked explicitly)
2) Your code produces correct results (printed values, plots, etc…) and is well written.
3) Coding interview performance
CODING INTERVIEW RUBRIC
As part of the marking process, your demonstrator will spend a few minutes interviewing you to gauge your
understanding of the assignment code. The purpose of this is to ensure that you have contributed to the
assignment and understand the code.
You will be assigned a score based on your interview and your code mark will be penalized if you are unable
to explain your submission.
Category Description Penalty
No understanding The student has not prepared, cannot answer even the most basic
questions and likely has not even seen the code before. 100%
Trivial
understanding
The student may have seen the code before and can answer something
partially relevant or correct to a question but they clearly can’t engage in a
serious discussion of the code
30%
Selective
understanding
The student gives answers that are partially correct or can answer
questions about one area correctly but another not at all. The student has
not prepared sufficiently
20%
Good understanding
The student is reasonably well prepared and can consistently provide
answers that are mostly correct, possibly with some prompting. The
student may lack confidence or speed in answering.
10%
Complete
understanding
The student has clearly prepared and understands the code. They can
answer questions correctly and concisely with little to no prompting. 0%
ASSIGNMENT HELP
1) You can use function files you‘ve written in your labs
2) You can ask questions in the Discussion Board on Moodle
3) Hints and additional instructions are provided as comments in the assignment template m-files
4) Hints may also be provided during lectures
5) The questions have been split into sub-questions. It is important to understand how each sub-question
contributes to the whole, but each sub-question is effectively a stand-alone task that does part of the
problem. Each can be tackled individually.
6) It is recommended that you break down each sub-question into smaller parts too, and figure out what
needs to be done step-by-step. Then you can begin to put things together again to complete the whole.
7) The m-file templates contain comments and sections only as a guide. You do not need to follow its
structure.
8) Bold text has been used to emphasize important aspects of each task. This does not mean that you should
ignore all other text.
MCD4140 Assignment 3 of 8
QUESTION 1 [6 MARKS]
Background:
Flows around cylinders of various cross-sections continue to engender a significant amount of engineering
research interest due to its ubiquitous nature in society. Examples include bridge spans and pylons, high-rise
buildings, pipelines, heat exchangers and oil platforms. When fluid (such as air or water) flows around such
bodies, a wake develops which may become unstable and lead to a development of vortex streets. An
example of the vortex street formed by clouds flowing past an island is illustrated in Figure 1. Additional
information including images and animations can be found here.
Figure 1. Kármán vortex street caused by wind flowing around the Juan Fernández Islands off the Chilean
coast.1
The vortices that develop are capable of containing large amounts of energy which can cause damage to
neighbouring structures on impact. Therefore, engineers and scientists study the wake dynamics behind these
bodies with the aim of suppressing the vortex shedding. There are some cases where vortex shedding is
encouraged as to dissipate heat from a heated wall for example. Thus, it is crucial to determine when these
flows transition from a laminar state to vortex-shedding state.
A non-dimensional parameter commonly used to characterise such flows is given by the Reynolds number, Re.
The Reynolds number describes the ratio between inertial to viscous forces. That is, a small Reynolds number
flow is typically laminar as it is dominated by viscous forces. Higher Reynolds number flows become
susceptible to vortex shedding and ultimately turbulence.
Brief:
You, the engineer, have performed experiments in a water channel involving flow past a circular cylinder. All
flows are started from Re = 60 and then impulsively changed to either Re = 40, 45, 50, 55 or 65. The lift force
on the cylinder is measured as soon as Re is changed (i.e. at time equal zero) and this is recorded in the text
files fy_re<X>.dat where <X> represents the Re value. Each file contains:
1. [column 1] Time, t
2. [column 2] Lift force, Fy
It is clear from the flow visualisation in Figure 2 that the flow transitions from a laminar flow to a vortexshedding
state somewhere between Re = 40 and Re = 65. The lift force information can be used to predict the
critical Reynolds number, which describes the point of transition from laminar to vortex-shedding flow. You
are to complete the following tasks to determine the critical Reynolds number.

1 https://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_vortex_street
MCD4140 Assignment 4 of 8
Figure 2. Axial vorticity contours of flow past a circular cylinder for Re=40 (top) and Re=65 (bottom).
Q1a
In the Q1a.m file, read in the data for Re = 40, 45, 50, 55 and 65 and store it into a 3D matrix using a for loop.
Be aware that there is header information.
A 3D matrix can be thought of as multiple 2D matrix planes stacked in the 3rd dimension. Consider matrix M
which is a 3-by-3-by-6 matrix. An illustration of its decomposition into six 2D matrix planes is shown below:
Plane 1:
M(1,1,1) M(1,2,1) M(1,3,1)
M(2,1,1) M(2,2,1) M(2,3,1)
M(3,1,1) M(3,2,1) M(3,3,1)
Plane 2:
M(1,1,2) M(1,2,2) M(1,3,2)
M(2,1,2) M(2,2,2) M(2,3,2)
M(3,1,2) M(3,2,2) M(3,3,2)
Plane 3:
M(1,1,3) M(1,2,3) M(1,3,3)
M(2,1,3) M(2,2,3) M(2,3,3)
M(3,1,3) M(3,2,3) M(3,3,3)
Plane 4:
M(1,1,4) M(1,2,4) M(1,3,4)
M(2,1,4) M(2,2,4) M(2,3,4)
M(3,1,4) M(3,2,4) M(3,3,4)
Plane 5:
M(1,1,5) M(1,2,5) M(1,3,5)
M(2,1,5) M(2,2,5) M(2,3,5)
M(3,1,5) M(3,2,5) M(3,3,5)
Plane 6:
M(1,1,6) M(1,2,6) M(1,3,6)
M(2,1,6) M(2,2,6) M(2,3,6)
M(3,1,6) M(3,2,6) M(3,3,6)
Examples of matrix addressing is provided below:
M(2,2,1) will address element corresponding to row 2, column 2, plane 1.
M(1,3,4) will address element corresponding to row 1, column 3, plane 4.
M(:,2,6) will address elements corresponding to all rows, column 2, plane 6.
M(:,:,3) will address elements corresponding to all rows, all columns, in plane 3.
MCD4140 Assignment 5 of 8
In figure(1)2
, plot the lift force against time on linear axes for each Re in a 3-by-2 subplot arrangement as
follows:
[panel 1] Re = 40 [panel 2] Re = 45
[panel 3] Re = 50 [panel 4] Re = 55
[panel 5 + 6] Re = 65
The plot characteristics for all subplot panels are black continuous lines. The title of your subplot windows
should correspond to the Re of the data.
*You should have one figure window by the end of this task.
Hint: Use sprintf() to import data and to title the subplots.
Q1b
In the maxima.m file, complete the function to determine a specified number of maxima turning points in the
data that is supplied to the function.
Q1c
In the Q1c.m file, use the function you wrote in Q1b to determine the first 350 maxima turning points in the
lift force data for each Re. The maxima turning points represent the amplitude measure of the flow. In
figure(2), plot the amplitude against time on logarithmic axes for each Re in a 3-by-2 subplot arrangement
as follows:
[panel 1] Re = 40 [panel 2] Re = 45
[panel 3] Re = 50 [panel 4] Re = 55
[panel 5 + 6] Re = 65
The plot characteristics for all subplot panels are red continuous lines with circles. The title of your subplot
windows should correspond to the Re of the data. A legend is not required.
*You should have two figure windows by the end of this task.
Q1d
In reviewing the plots (on logarithmic scales) created in Q1c, you notice that the initial trend of the amplitude
against time data is relatively linear. This suggests that the data follows the power model
where α and β are coefficients.
In the Q1d.m file, you are required to identify the timespan (starting from 0) where the amplitude data for all
Re illustrates a linear trend. A SINGLE timespan should be used for all Re. You are to determine this timespan
through observation. On the existing plots of figure(2), plot the linear segments of the amplitude against time
data using red circles with a continuous line for each Re.
*You should still have two figure windows by the end of this task.

2 Note that figure(H) makes H the current figure, forces it to become visible, and raises it above all other figures on the
screen. If Figure H does not exist, and H is an integer, a new figure is created with handle H.
MCD4140 Assignment 6 of 8
Q1e
It turns out that the β coefficient represents the growth rate of the flow. That is, a negative β coefficient
represents a laminar flow whereas a positive β coefficient represents a vortex-shedding flow.
In the Q1e.m file, curve fit the linear segments using a power model to determine the coefficients α and β
for each Re. In figure(3), plot β against Re using black diamonds and turn on the grid.
*You should have three figure windows by the end of this task.
Q1f
In the Q1f.m file, fit polynomials of order 1 to 5 to β against Re. Plot these polynomials as continuous lines in
figure(3) using colour specifications ‘rbkgm‘. Additionally, determine the critical Re value for each polynomial
fit and plot these as diamonds in figure(3) using colour specifications ‘rbkgm‘. Use any appropriate rootfinding
method to determine the critical Re. The legend may contain duplicate entries (as provided in the mfile).
Lastly, use fprintf() to print a list of values similar to the following:
Polynomial Re_c
*You should still have three figure windows by the end of this task.
MCD4140 Assignment 7 of 8
QUESTION 2 [4 MARKS]
The rate of change of temperature of an object is directly proportional to the difference in temperature
between the object and its surrounding, such that it is described by:
where T represents the temperature, t represents the time, Ts represents the surrounding temperature and k
is a constant.
Q2a
In the Q2a.m file, calculate the temperature of an object from t=0 to t=60 units, assuming T(0) = 0.3, k=0.5
and Ts = 2. Do this using Euler‘s method and Heun‘s method with a time step of 3.5 units.
In figure(4), plot the temperature against time solutions – Euler as a blue line and Huen‘s as a red line. Use
fprintf() to describe why the solution using Euler‘s method differs greatly to Heun‘s method.
Q2b
In the Q2b.m file, calculate the temperature of a point on the plate from t=0 to t=60 units for k=[0.1, 0.5, 1, 2],
assuming T(0) = 0.3 and Ts = 2. Do this using the midpoint method with a time step of 1 unit.
In figure(5), plot temperature against time for each k value. Use the RGB values defined in the ‘colourmap‘
variable as provided in the m-file to colour solutions from the smallest k to the largest k (top row to the
bottom row).
Q2c
The temperature profile on a plate that is 17m long
(∈ [7,10]) and 9m wide ( ∈ [1,8]) is illustrated in
the figure on the right. The temperature profile on the
plate is described by:
The average temperature of the plate can be calculated
through:
In the Q2c.m file, calculate the average temperature of the plate using the composite Simpson‘s 1/3 rule
using 99 points in each direction (x and y). Start by evaluating the inner integral along the x dimension for
each value of y. The resulting values can be integrated along the y dimension. Use fprintf() to print a
statement containing the average temperature to 4 decimal places.
*You should still have three figure windows by the end of this task.
MCD4140 Assignment 8 of 8
Hint: You may want to create a function file for the composite Simpson‘s 1/3 rule that accepts vectors. i.e. the
function header declaration may be: I = comp_simp13_vector(a,b), where I is the integral and (a,b) are
the points you are integrating.
Poor Programming Practices [-2 Marks]
(Includes, but is not limited to, poor coding style or insufficient comments or
unlabeled figures, etc.)
(END OF ASSIGNMENT)

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