Homework answers / question archive / School of Engineering, Discipline of Mechanical Engineering and Mechatronics, pp

School of Engineering, Discipline of Mechanical Engineering and Mechatronics, pp

Mechanical Engineering

Share With

---

School of Engineering, Discipline of Mechanical Engineering and Mechatronics, pp. 1–12

Assignment 2: Air-conditioner simulation and safety system design

MCHA3400

Semester 1 2023

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

Introduction

Air conditioners are widely used for cooling in both residential and commercial applications. In this assignment, you are tasked to construct a dynamic simulation of an air conditioner unit being installed in a industrial environment with the purpose of cooling a switch room. You are additionally required to write a functional description and validation tests for the air conditioning system.

The layout of the installed system is shown in Figure 1. Power is delivered to the air conditioner

unit via a power contactor (industrial switch). When the contactor is in the closed position, 415V

is supplied to the compressor, driving the unit. When the contactor is in the open position, the air

conditioner is stopped. Three temperature sensors and a pressure sensor are installed throughout the

air conditioner so that it can be continually monitored for safe operation.

Figure 1: Overview of the air condition system proposed for installation.

Submission instructions

Assignment 2 is due at 11:59pm, Friday 5th May. Your submission will consist of a software and a

written component.

Software submission: Problem 1 requires you to create several simulations in Matlab. Your simulation files should be labelled as per the file names indicated throughout this document. Files with

names different from those specified will be ignored.

Written submission: Your written solutions should be collected into a single .pdf file with the

name assignment2 written.pdf. For task 1, you are required to include labelled output plots from

your simulations in your written submission. Your solution to task 2 should also be included in the

written solution. Please ensure that your solutions are neatly presented and organised in the correct

order within your document. Examples of acceptable submissions include:

• Neatly handwritten on paper and scanned to a pdf,

2

MCHA3400 — Embedded Systems Engineering

• Neatly handwritten on a tablet (e.g., Surface, iPad) and saved to a pdf,

• Typed in a word processor (e.g., MS Word with equation editor) and exported to a pdf,

• Typeset in LATEX and compiled to a pdf.

If you written submission cannot be easily read, it will receive a grade of 0.

Warning

Don’t submit your initial working-out. Rewrite your solutions neatly in a logical order!

Hint

Submission format: Add both your written and software solutions into a single .zip file called

studentNumber studentName assignment2.zip1 and submit this file to Canvas for assessment. Your

final .zip folder should include the following files:

studentNumber StudentName assignment2

air conditioner simulation

convectionFuncs

thermalFuncs

Task 1 condenser.m

Task 1 airCon.m

Task 1 fullSystem.m

assignment2 written.pdf

(root directory)

Figure 2: Expected workspace directory tree after completing the assignment.

1The expressions studentNumber and studentName should be replaced with your student number and name, respectively.

3

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

Task 1: Simulation of an air conditioner (75%)

In this task, you will develop a dynamic simulation of an air-conditioner system. A simple overview

of a refrigeration cycle is depicted in Figure 3. The main stage of the cycle are described below:

1. A refrigerant in vapour phase enters a compressor which results in high pressure and high

temperature gas.

2. The high pressure refrigerant vapour is passed through a condenser which extracts heat from the

refrigerant and radiates it to the ambient outside air. This causes the refrigerant to condense

into a liquid, still at a high pressure.

3. The liquid refrigerant passes through an expansion device, reducing the pressure of the refrigerant. The drop in pressure causes the temperature to drop and the liquid refrigerant becomes a

mixture of gas and liquid.

4. The cooled refrigerant is passed through an evaporator where heat is exchanged with the environment. This stage causes the remainder of the refrigerant to boil, putting the refrigerant back

into a vapour phase.

Figure 3: Abstraction of a single stage refrigeration cycle.

In order to construct your simulation, you will utilise the convection bond graph functions developed

during your labs. Before starting, copy the convectionFunctions and thermalFunctions folder (and

contained functions) into your assignment 2 working directory.

We will now construct a new macro element, called HXmacro, to describe the dynamic behaviour of

the heat exchangers used in the air conditioner. The bond graph representation of the new macro

element is shown in Figure 4.

4

MCHA3400 — Embedded Systems Engineering

Figure 4: Bond graph of the HXmacro element.

It is assumed that the CSmacro element has a constant volume. Because of this, the HX macro

element is described by two states—entropy and mass.

Task 1.1: HXmacro element (25%)

• Construct a Matlab function in the convectionFuncs folder called HXmacro output which computes the fluid outputs of the HXmacro element (as indicated by the causality in Figure 4) based

on the current state. The function should have the following inputs and outputs:

Inputs Outputs Description

HX state HX state = [S m]

>

is the current state of the HXmacro element.

S and m are the entropy and mass of the fluid contained in the

HXmacro element, respectively.

fluid name Name of the fluid being pumped (must be a valid CoolProp fluid)

HX params Structure containing the parameters of the HXmacro element.

P in Pressure of the upstream fluid.

h down Specific enthalpy of the downstream fluid.

P down Pressure of the downstream fluid.

The HX params input is a structure with the elements

Element Description

H Thermal conductivity of the heat exchanger walls [WK−1

]

V Volume of the heat exchanger [m3

]

Use your CSmacro outputs function within your HXmacro output function. Recall that the

CSmacro outputs function requires a state inputs of the form CS state = [S, V, m]>.

Tip

• Construct a Matlab function in the convectionFunctions folder called HXmacro deriv.m that

computes the derivatives of the HXmacro states given the current states and inputs. The function

should have the following inputs and outputs:

5

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

Inputs Outputs Description

HX state HX state = [S m]

>

is the current state of the HXmacro element.

S and m are the entropy and mass of the fluid contained in the

HXmacro element, respectively.

h up Specific enthalpy on inlet flow

dm up Mass flow rate into the element

dm down Mass flow rate out of the element

T ext Temperature from the external thermal power bond [K].

fluid name Name of the fluid being pumped (must be a valid CoolProp fluid)

HX params Structure containing the parameters of the HXmacro element.

dHX state The time derivative of the HXmacro state vector dHX state =

[dS dm]

>

. dS and dm are the time derivatives of entropy and mass

of the HXmacro element, respectively.

dS ext Entropy flow rate on external thermal power bond [J/kg/K/s]

Use your CSmacro deriv function within your HXmacro deriv function.

Tip

Figure 5 shows a bond graph of the condenser sub-system, consisting of a HXmacro element for the

heat exchanger and an RS element for the expansion device. Use the orifice function which was

developed in Lab 5 to evaluate the CCR of the RS element.

Figure 5: Bond graph of the condenser sub-system.

• In your root directory, create a Matlab script called Task 1 condenser.m. In that script, create

a simulation for the system depicted in Figure 5. Use the following parameters for the system:

Parameter Value

condenser params.H 138.3627

condenser params.V 0.8 × 10−3

[m3

]

orifice params.A up 0.1 × 10−4

[m2

]

orifice params.A down 0.0046 × 10−4

[m2

]

fluid name “R410A”

• Using the ode23s solver with a relative tolerance of 1×10−6

, simulate the system for 100 seconds.

Initialise the condenser states with entropy Scond = 177.1135 [J/K] and mass 0.1178 [kg]. The

inputs into the system are given as follows:

Input Value

T ext 35.0 [?C]

h in 4.571 × 105

[J/kg]

dm in 0.018 [kg/s]

P out 0.9 × 106

[P a]

6

MCHA3400 — Embedded Systems Engineering

• Using the subplot command, generate a plot showing the temperature, pressure and mass of

the refrigerant within the condenser vs time. For reference, the pressure within the condenser

should agree with Figure 6.

0 20 40 60 80 100

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

Pressure [Pa]

106

Figure 6: Output of the condenser pressure.

There is a bug in the CoolProp libraries that can cause a PropsSI call to fail when given

specific entropy and density as inputs (the input pair required for evaluation of the requested plots). In your CSmacro output and CSmacro deriv functions developed in lab 7,

you should have implemented the work-around of first evaluate the temperature using the

code

Figure 7: The temperature can be computed using a nonlinear solver.

where s and D are the specific entropy and density of the CSmacro element, respectively.

The returned value T is the temperature of the element. Once returned, use the pair T and

D for subsequent PropsSI calls.

Tip

Task 1.2: AirCon macro element (35%)

Using the HXmacro element constructed above, we can now proceed to create a simulation of an

air conditioner unit. The model will consist of two HXmacro elements to model the evaporator and

condenser, a VDM element to model the compressor and an orifice element to model the expansion

valve. A bond graph of the system to be simulated is provided in Figure 8.

7

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

Figure 8: Bond graph of a full air conditioner system.

• Write a function called airCon deriv in your convectionFunctions folder with the following

inputs and outputs:

Inputs Outputs Description

airCon state airCon state =

 

evaporator state> condenser state>

>

is the current state of the overall air conditioner system.

omega Input angular velocity for the volumetric displacement motor [rad/s]

T ext External temperature [K]

T int Internal temperature [K]

fluid name Name of the fluid being pumped (must be a valid CoolProp

fluid)

airCon params Structure containing all of the air conditioner parameters

(described below)

dairCon state Time derivative of the state vector

tau Torque of the motor

dS ext Entropy flow rate of the external thermal power bond

dS int Entropy flow rate of the internal thermal power bond

The airCon params input is a structure with the elements

Element Description

HX evap params HXmacro params structure containing the evaporator parameters

HX cond params HXmacro params structure containing the condenser parameters

expansion params orifice params structure containing the expansion device parameters

compressor params motor params structure containing the compressor parameters (see Lab 7)

Figure 9 shows a bond graph representation of an air conditioner connected to sources of temperature.

Recall that the airCon element is described by the collection of bond graph elements in Figure 8.

Your task is to simulate the system shown in Figure 9.

8

MCHA3400 — Embedded Systems Engineering

Figure 9: Bond graph of a full air conditioner system attached to temperature sources.

• Create a script in your root directory called Task 1 airCon which will be used to create your

simulation. In that file, construct a simulation for the system depicted in Figure 9. Use the

parameters detailed in the table below:

Parameter Value

HX evap params.H 71.0555

HX evap params.V 0.8 × 10−3

HX cond params.H 138.3627

HX cond params.V 0.8 × 10−3

expansion params.A up 0.1 × 10−4

expansion params.A down 0.0046 × 10−4

compressor params.nad 0.98

compressor params.nv 1

compressor params.Tm 0.9

• Simulate the system for 100 seconds using the input temperatures

Input Value

T ext 35?C

T in 25?C

For the input angular velocity, use the following values

omega(t) =

0.02 [rad/s], for t ≤ 50

0.0 [rad/s], for t > 50.

The systems initial conditions of the condenser are defined as S(0) = 176.7753, m(0) = 0.1193.

The initial conditions of the evaporator are given by S(0) = 160.5977, m(0) = 0.1051.

Use the ode23s solver with a relative tolerance of 1 × 10−4

. Generate two output plots from

your simulation. The first should show the temperature, pressure and mass within the condenser

vs time. The second should show the temperature, pressure and mass within the evaporator vs

time. In each case, use the subplot command to display the requested outputs on separate

sub-plots.

In the first instance, attempt to simulate the system with the constant input omega = 0.02

for 50 seconds. Once you have achieved this, complete the problem with the specified

time-varying input.

Tip

9

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

• The plots generated in the previous step show the temperature, pressure and mass of the evaporator and condenser outlets. For your final task, generate one more plot which shows the

temperature and pressure of the fluid at the compressor outlet vs time.

Task 1.3: Simulation with room (15%)

Your final task is to simulate the system depicted in Figure 10. This bond graph represents a room,

modelled as a solid of constant volume, being cooled by an air conditioner. The behaviour of the room

is described by the thermalCapacitor function generated in lab 5. The heat flow between the room

and external environment satisfies Newton’s law of cooling. The convectionCooling function can be

used to describe this interaction.

Figure 10: Bond graph of a full air conditioner system cooling a room.

• In your root directory, create a Matlab script called Task 1 fullSystem.m. In that file, create

a simulation of the system shown in Figure 10. For the air conditioner model, use the same

parameters that were used in Task 1.2. For the room, use the following parameters:

Parameter Value

thermalCap params.S 0 6.8984 [J/K]

thermalCap params.T 0 30 [?C]

thermalCap params.c v 0.717 [ J

K·kg ]

thermalCap params.m 16.98 [kg]

thermalConvec params.h 1.8 [ W

m2K

]

thermalConvec params.A 20 [m2

]

• Simulate the system for 60 seconds using the external temperature

Input Value

T ext 30?C

Note that the internal temperature is now replaced with the temperature of the room. For the

air conditioner initial conditions, use the same values as were provided in Task 1.2. For the

inputs angular velocity, use the following input

omega = 0.01[rad/s] (1)

Use the ode23s solver with a relative tolerance of 1 × 10−4

for your simulation. Create three

output plots from your simulation. One for the both the evaporator and the condenser, each

showing the temperature, pressure and mass of the refrigerant as a function of time. Additionally,

create a third plot showing the temperature of the room as a function of time.

10

MCHA3400 — Embedded Systems Engineering

Task 2: Safety system design (25%)

The air conditioner system modelled in Task 1 is to be installed in a hazardous area on an industrial

site. A number of potential hazards related to possible failure modes of the unit have been identified.

To mitigate against potential hazards, a safety instrumented system (SIS) is to be installed which will

monitor the unit’s operation and disable the unit in the case of a hazardous event. As shown in Figure

11, a number of sensors have been proposed to monitor the unit’s operation which are connected back

to a PLC. In the case of a hazardous event, the power contactor should be opened, disabling the

device.

Figure 11: Overview of the safety instrumented system.

Temperature sensor 1 is installed to detect a dangerous high temperature at the compressor outlet. A

temperature above 140?C should trigger the SIS whereas a temperature above 120?C that persists for

more than 10 seconds should also trigger the SIS. Temperature sensor 2 and the pressure sensor 1 are

installed to detect any liquid present at the compressor intake. If liquid is detected, the SIS should

be triggered. Temperature sensor 3 is installed to detect sub-zero temperature at the evaporator.

Temperatures below 0?C can lead to freezing of the evaporator coils and, thus, should trigger the SIS.

An emergency stop (E-stop) is located near the device and, if pressed (closed), should trigger the SIS.

As per site requirements, the status of the SIS should be sent to the control room every 3 seconds.

Additionally, in the event that the SIS is triggered, the cause of the fault scenario should be relayed

to the control room. To reset the SIS, a ‘start’ command is sent from the control room to the PLC.

If none of the fault conditions are met, the contactor is closed, starting the air conditioner.

Before programming of the safety system can begin, a functional specification describing the required

behaviour of the programmable logic controller must be specified. This document is intended to be

passed onto a contractor for implementation of the safety systems.

11

School of Engineering, Discipline of Mechanical Engineering and Mechatronics

Task 2.1: Functional description (10%)

Prepare a function specification for the SIS depicted in Figure 11. Prepare two tables for your specifications. The first should outline the functional behaviour of the PLC in relation to stimuli from

the sensor. The second table should cover the reporting from the PLC to the control room. Use the

following template for your specifications:

ID Functional requirements

1.1 If the temperature at the compressor outlet (sensor 1) exceeds 140?C,

open the power contactor.

1.2 ...

ID Communication requirements

2.1 ...

Task 2.2: Validation test design (15%)

Once the function behaviour of the SIS has been formalised, validation tests for the system can be

prepared. These should be prepared before commencing work the the software solution to avoid

any bias test preparation that may occur from preparing tests after development. Using the format

provided in the following table, construct some tests for each of the provided functional requirements.

For these tests, assume that you have the ability to manipulate all of the physical inputs to the system.

Note that you may need more than one test pre functional requirement.

Spec

ID

Test

ID

Test Result Date Sign

1.1 1.1.1 Set the input stimuli to healthy levels (eg. Temp

1 = 40?C, Temp 2 = 40?C, Temp 3 = 40?C,

Pressure 1 = 2000kPa, E-stop = open),

send a ‘start’ signal to the PLC and observe

the contactor close. Increase temperature 1 to

150?C and observe the contactor open.

12