代写Introduction to Thermodynamics and Fluid Mechanics帮写Matlab语言程序

日期：2024-03-13 11:43

Department if Mechanical Engineering

Introduction to Thermodynamics and Fluid Mechanics

Individual Coursework

Release date: March 4th. Deadline: March 15th at 2pm

This is the only piece of coursework for MECH0005. You will need to read the information below and answer all the questions which cover both thermodynamics and fluid mechanics. This coursework is worth 30% of your final grade.

You need to explain your answers (using full sentences) and pay attention to the way they are presented, with proper descriptions and diagrams where appropriate. Please see the guidance and marking rubric at the end of this document for more information on this assessment and how you will be assessed. There is a five page limit for your answer (including any references used), and you should not copy out the questions again within your submitted answer. We expect this assessment to take you approximately 8 hours. Submissions in pdf format are to be made through the “Coursework submission portal” under the “Assessments” tab.

Background

Modern aviation has made significant benefits to mankind including allowing affordable travel be-tween many countries, increasing trade around the world and boosting the economy by generating many direct and indirect jobs. However aviation contributes to 2.5% of the global CO2 emissions and therefore finding methods of reducing this footprint are vital. This is a complex engineering exercise and this coursework will explore some of the thermodynamics and fluid mechanics concepts from MECH0005 applied to a Cessna aircraft which is shown in figure 1. This small lightweight aircraft can be considered an ideal case study in how thermodynamics and fluid mechanics prin-ciples can affect an aircraft’s performance. The two scenarios that will be covered are (i) take off (Question 1) and (ii) cruising at altitude (Question 2). Question 3 will explore the engineering challenges associated with using hydrogen as an aviation fuel.

Figure 1: Photograph of a cruising Cessna airplane.

Useful information

In this coursework you will be required to carry out calculations. Below are the variables which are given explicitly however you will be expected to search the internet for variables which are not given explicitly (e.g. speed of sound at an sea level).

Wind tunnel experiments

? Wind speed: 200 kph

? Chord length of aerofoil section: 0.8 m

? Angle of attack: 15o

? Altitude: sea level

? Radius of wind tunnel measurements: 2 m

Full scale airplane (take off)

? Airplane speed: 100 kph

? Wing surface area: S “ 16 m2 (chord length 1.6 m? effective wing span 10 m)

? Angle of attack: 15o

? Altitude: sea level

? Total mass of plane (excluding fuel): 660 kg

Full scale airplane (cruising)

? Altitude: 2450 m

? Compression ratio of engine: 8.5

? Engine displacement: 5.24 litres

? Maximum temperature in engine cycle: 2000 K

? Propulsive efficiency: 0.8

? Power generated by engine: 72.2 kW

? Fuel heat of combustion: ?hfuel “ 43.5 MJ/kg

? Mass flow rate of fuel mf = 0.005 kg/s

? Total aircraft drag coefficient (based on wing surface area) CD = FD/(2/1ρU2S) = 0.032

? The ratio of specific heat capacities is a constant γ “ 1.4

Figure 2: Schematic of the aerofoil section at an angle attack α in the wind tunnel with the steady incident flow U from left to right. The dashed line is the location of the data points where velocity and pressure are measured.

Take Off

Introduction

To gain an understanding of the forces on the airplane, a section of the Cessna wing is tested in a wind tunnel. The aerofoil is placed in a wind tunnel at a steady and uniform. speed U. The lift force (FL) (per unit span) is known to be dependent on the following variables:

f(ρ, μ, c, L, U, α),                        (1)

where ρ is the density of the air, μ is the dynamic viscosity of air, c is the speed of sound in air, L is the chord length of the aerofoil, U is the incident speed and α is the angle of attack.

The Reynolds Transport Theorem applied to momentum is

                  (2)

where Fa={FD, FL}, are the forces on the aerofoil (with the drag force acting along the x-axis and the lift force acting along the y-axis) and Fp = {Fpx, Fpy} are forces due to the pressure.

The time averaged velocity (u = {u, v}) and gauge pressure (p) is determined in the wind tunnel experiments at various azimuthal locations for —π < θ < π and a constant radius R = 2 m, in the flowfield as shown in the Figure 2. Note that these are provided in the attached excel file with the four columns giving (i) azimuthal location (θ), (ii) horizontal velocity (u), (iii) vertical velocity (v) and (iv) pressure (p).

Question 1

(a) Apply dimensional analysis to the dependent variable FL (per unit span) given the above independent variables in (1). Write down the functional relationship and name the common dimensionless groups. Calculate the dimensionless groups (in the functional relationship) for the full scale plane at take off and in the wind tunnel experiments and comment on your findings. State clearly any additional data used for your calculations. [3 marks]

(b) Apply the methodology that was taught in the lectures for Reynolds Transport Theorem, to obtain integral expressions for the lift coefficient per unit span CL = FL/(2/1ρU2L) on the aerofoil in the wind tunnel, in terms of the azimuthal location θ, velocity components ({u, v}) and pressure (p). State and justify any simplifications to equation (2). [3 marks]

(c) Plot the azimuthal variation for the terms (i) ρv(u ¨ ?n), and (ii) Fpy. Copy and paste the Matlab code for this plot into your submission. [2 marks]

(d) By numerically integrating the profiles in (c), confirm that the lift coefficient is approximately CL ? 1.6 indicating the contribution from the two terms in Question 1 (c). Copy and paste the Matlab code for these calculations into your submission. [2 marks]

(e) Assuming that the lift coefficient in the wind tunnel is the same as the lift coefficient of the full scale plane at take off, what is the mass of fuel such that there is a ratio of lift force to plane weight of 1.5, at take off? [2 marks]

Note: marks will be lost if no Matlab code is given for (c) and/or (d).

Figure 3: Schematic of the real power cycle for the Cessna engine.

Cruising at altitude

Introduction

Cessna aircraft can use a naturally aspirated spark ignition engine where a typical power cycle of a spark ignition engine presented in figure 3. This question is about analysing the power generated by the engine and the resistive power due to aerodynamic drag.

Question 2

(a) Approximate the power cycle in figure 3 to an air standard cycle (utilise the knowledge developed from theory/lecture notes on gas power cycles). Identify the key processes that govern this cycle and describe them. [3 marks]

(b) Plot the T - s and P - V diagrams indicating clearly the temperature, pressure and volume at each stage (show your working). You can assume that the temperature and pressure of the air at inlet is ambient for that altitude. Briefly articulate the differences between the real cycle and the idealised cycle. [3 marks]

(c) Assuming that 60 kg of fuel is used for cruising, calculate the steady speed of the aircraft and its range (assuming zero wind speed). Assume that the changing mass of the plane does not affect performance. State clearly any additional data used for your calculations. [3 marks]

(d) Using the data in this document, calculate the (i) the thermal efficiency of the actual Cessna engine, (ii) the thermal efficiency of the power cycle in (a) and (iii) the thermal efficiency of a Carnot engine operating between the maximum and minimum temperatures of the power cycle in Question 2 (a). Comment on your findings. [3 marks]

Outlook to the future

Commercial aircraft, which are much heavier than the Cessna considered here, usually operate on a Brayton cycle. To address the emissions associated with combustion, using hydrogen has been tipped as a potentially more environmentally friendly fuel. For an extensive review of hydrogen usage in the aviation industry see Yusaf et al. (2024).

Question 3

By referencing four scientific journal publications, describe in your own words, two engineering challenges of using hydrogen as fuel for gas turbine engines. [6 marks]

Note: There is a 300 word limit for this question. If you can keep your total submission (for the three questions) to within five pages, an figure can also be included here.

Bibliography

Yusaf, T., Mahamude, A.S.F., Kadirgama, K., Ramasamy, D., Farhana, K., Dhahad, H.A. & Talib, A.R.A. 2024 Sustainable hydrogen energy in aviation - A narrative review. Int. J. Hydrogen Energy. 52, 1026–1045.

Glossary

? The thermal efficiency (ηthermal) is the ratio of the net rate of work output of the engine to the net rate of energy that was supplied to the engine.

? The propulsive efficiency (ηpropulsive) is the ratio of the actual propulsive power to the net rate of work output of the engine.

? The span is the length of an aerofoil or wing.

? Engine displacement is a measurement of the total volume of all of an engine’s cylinders.

Guidance on completing this coursework

1. This coursework falls under AI category 1. There should be no AI tools used for this course-work.

2. Equations should be appropriately formatted. Be careful of notation; vectors are bold and scalars are not.

3. Solutions need to be explained in words (e.g. stating conservation laws or stating/justifying simplifications). Show all your working. Just the solution will get no marks. Please refer to the marking rubric under ‘technical analysis’.

4. Always re-read your answers, look again at the question, and ask yourself whether you have answered the specific question that was asked.

5. Hand drawn figures: be clear to indicate control volumes (using dashed lines), control sur-faces, unit normal vectors, components in the cycle etc. Labels should be in good handwriting with a fontsize that is easily readable.

6. The technical language in Question 3 should be concise and precise. A consequence of language not being precise is that the meaning of the sentences can become ambiguous. Please refer to the marking rubric, which is also on Moodle under this coursework assignment tab.

7. You may want to adopt a ’SEE’ method to your writing, which stands for ’Statement’, ’Explanation’ and ’Evidence’. That means making a statement, explaining in detail the consequences of that statement and then providing some evidence to support your comment (this could be in the form. of a calculation or journal reference).

8. Choose an appropriate and consistent method of referencing the scientific journals.

9. Do not use Wikipedia. Also, websites should not be used as they can be taken down or moved. Scopus, pubmed etc. are not journal references.

10. In technical reports there should be no use of ”I”, ”we”, ”us” etc.

11. If you are taking a figure from the web, this needs to be referenced. The figure also needs to be annotated by you, it is not good enough to just copy a figure into your coursework.

12. This coursework is an individual effort and any collaboration is not authorised. If you don’t acknowledge the work or ideas of others, you could be penalised for Academic Misconduct.

Individual Coursework