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R.C
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**Long Post**
1. Homework Statement
The Mazda MX5 (2001-2005) comes with two engine sizes, 1.6 litre and 1.8 litre which are rated as 110 bhp and 146 bhp respectively at 6,500 rpm. You are required to choose one of the two engine sizes and analyse the system with a view to improving the power output of the vehicle.
Aspects to consider during the analysis:
· What energy is input into the engine and what losses could be reasonably expected?
· Need to identify the value of the total power generated by the engine; brake horsepower does not provide a value for the total power.
· Constraints on compression ratio resulting in loss of power due to excessive heating
· Significant engine redesign is a costly option and manufacturers tend to prefer less radical, incremental improvements
Temperature =Kelvin, Pressure =Pa, Volume = ##m^3##
I'm hoping you will all understand my notation if I say that for this Otto Cycle T1 & P1 are the temperature and pressure at the inlet to the combustion chamber and hence the temperature and pressure at point 1. so for point 2: T2 & P2 etc...
$$T_2=T_1*\frac{V_1}{V_2}^{1.4-1}$$
$$V_2=\frac{V_1}{Compression Ratio}$$
$$P_2=P_1*\frac{V_1}{V_2}^{1.4}$$
$$V_3=V_2$$
$$P_2=P_1*\frac{T_3}{T_2}^{\frac{1.4}{1.4-1}}$$
$$T_4=T_3*\frac{1}{Compression Ratio}^{1.4-1}$$
$$V_4=V_1$$
$$P_4=P_3*\frac{1}{Compression Ratio}^{1.4}$$
So once these were found I went on to find:
$$Mass_{air}=\frac{P_1*V_1*28.97}{8314*T_1}$$
$$Heat_{in}=Mass*C_v*(T_3-T_2)$$
$$Heat_{Rejection}=Mass*C_v*(T_4-T_1)$$
$$Net Work=Heat_{in}-Heat_{Rejection}$$
$$Cycle Efficiency=\eta_{Cycle}=\frac{Net Work}{Heat_{in}}$$
$$Carnot Efficiency=1-\frac{T_1}{T_3}$$
I'll split this section into a few parts; firstly I'll state my assumptions so far, then I'll show you what data I have (it's limited :[ ), then I'll probably have lost the will to live and simply congratulate anyone who has read up to the end. Nevertheless! Here we go:
To begin I'll outline a few assumptions I have made so far, therefore they will be subject to change to analyse my problem in more depth later, but for now I'm looking at an Otto Cycle where:
1. The processes are steady.
2. Neglect potential and kinetic energy effects.
3. All processes are ideal.
4. Air is an ideal gas with constant specific heat.
5. Using a cold air standard air approximation (is this the right phrase? Where air properties are assumed at a constant Cp & Cv etc...)
6. I have also assumed the air at inlet is at STP
7. I would like your assistance on this assumption if you would be so kind, I have assumed the temperature at the highest point of combustion is 2100K. This is only from gathering a few (non-peer reviewed!) sources together and guesstimating, also in a seminar problem this is the temperature given (yes I have tried to work through the same seminar problem to help me here already). Is this reasonable? All I seem to come across is the temperature of the piston surfaces when looking for data rather than the air during combustion.
8. Exactly the same circumstances as for number 7 except for a compression ratio of 9.4.
What I have so far: Just looking at the 1.6L engine
At the moment I have an excel spreadsheet which outlines the temperature and pressure at each point in the Otto Cycle. Using the equations above I have T1=273, T2=718, T3=2100, T4=857, P1=101325 P2=2333972, P3=99872857, P4=4335792, V1=V4=0.0016, V2=V3=0.0001702(approx).
Heat in = 1913
Heat Rejection = 781
Net Work = 1132
Cycle Efficiency = 0.59
Carnot = 0.86
So now I have an engine whose efficiency is less than that of the Carnot efficiency, great, it theoretically should work...
My problem is I'm not sure where to go from here, ,and where does the horsepower of the engine come into this? I was wondering if I should be working backwards from the engine horsepower but I have no idea how I would do this. I'm almost certain that to optimize this the ideal situation may be to use a turbo to increase air volume of to play with compression ratios (I'm no car genius so please keep jargon to a minimum).
I'm really struggling here, I'd appreciate any help you can give. Please give values in SI units, or at least state what units you are using.
Also, Kudos for reading this far!
1. Homework Statement
The Mazda MX5 (2001-2005) comes with two engine sizes, 1.6 litre and 1.8 litre which are rated as 110 bhp and 146 bhp respectively at 6,500 rpm. You are required to choose one of the two engine sizes and analyse the system with a view to improving the power output of the vehicle.
Aspects to consider during the analysis:
· What energy is input into the engine and what losses could be reasonably expected?
· Need to identify the value of the total power generated by the engine; brake horsepower does not provide a value for the total power.
· Constraints on compression ratio resulting in loss of power due to excessive heating
· Significant engine redesign is a costly option and manufacturers tend to prefer less radical, incremental improvements
Homework Equations
Temperature =Kelvin, Pressure =Pa, Volume = ##m^3##
I'm hoping you will all understand my notation if I say that for this Otto Cycle T1 & P1 are the temperature and pressure at the inlet to the combustion chamber and hence the temperature and pressure at point 1. so for point 2: T2 & P2 etc...
$$T_2=T_1*\frac{V_1}{V_2}^{1.4-1}$$
$$V_2=\frac{V_1}{Compression Ratio}$$
$$P_2=P_1*\frac{V_1}{V_2}^{1.4}$$
$$V_3=V_2$$
$$P_2=P_1*\frac{T_3}{T_2}^{\frac{1.4}{1.4-1}}$$
$$T_4=T_3*\frac{1}{Compression Ratio}^{1.4-1}$$
$$V_4=V_1$$
$$P_4=P_3*\frac{1}{Compression Ratio}^{1.4}$$
So once these were found I went on to find:
$$Mass_{air}=\frac{P_1*V_1*28.97}{8314*T_1}$$
$$Heat_{in}=Mass*C_v*(T_3-T_2)$$
$$Heat_{Rejection}=Mass*C_v*(T_4-T_1)$$
$$Net Work=Heat_{in}-Heat_{Rejection}$$
$$Cycle Efficiency=\eta_{Cycle}=\frac{Net Work}{Heat_{in}}$$
$$Carnot Efficiency=1-\frac{T_1}{T_3}$$
The Attempt at a Solution
I'll split this section into a few parts; firstly I'll state my assumptions so far, then I'll show you what data I have (it's limited :[ ), then I'll probably have lost the will to live and simply congratulate anyone who has read up to the end. Nevertheless! Here we go:
To begin I'll outline a few assumptions I have made so far, therefore they will be subject to change to analyse my problem in more depth later, but for now I'm looking at an Otto Cycle where:
1. The processes are steady.
2. Neglect potential and kinetic energy effects.
3. All processes are ideal.
4. Air is an ideal gas with constant specific heat.
5. Using a cold air standard air approximation (is this the right phrase? Where air properties are assumed at a constant Cp & Cv etc...)
6. I have also assumed the air at inlet is at STP
7. I would like your assistance on this assumption if you would be so kind, I have assumed the temperature at the highest point of combustion is 2100K. This is only from gathering a few (non-peer reviewed!) sources together and guesstimating, also in a seminar problem this is the temperature given (yes I have tried to work through the same seminar problem to help me here already). Is this reasonable? All I seem to come across is the temperature of the piston surfaces when looking for data rather than the air during combustion.
8. Exactly the same circumstances as for number 7 except for a compression ratio of 9.4.
What I have so far: Just looking at the 1.6L engine
At the moment I have an excel spreadsheet which outlines the temperature and pressure at each point in the Otto Cycle. Using the equations above I have T1=273, T2=718, T3=2100, T4=857, P1=101325 P2=2333972, P3=99872857, P4=4335792, V1=V4=0.0016, V2=V3=0.0001702(approx).
Heat in = 1913
Heat Rejection = 781
Net Work = 1132
Cycle Efficiency = 0.59
Carnot = 0.86
So now I have an engine whose efficiency is less than that of the Carnot efficiency, great, it theoretically should work...
My problem is I'm not sure where to go from here, ,and where does the horsepower of the engine come into this? I was wondering if I should be working backwards from the engine horsepower but I have no idea how I would do this. I'm almost certain that to optimize this the ideal situation may be to use a turbo to increase air volume of to play with compression ratios (I'm no car genius so please keep jargon to a minimum).
I'm really struggling here, I'd appreciate any help you can give. Please give values in SI units, or at least state what units you are using.
Also, Kudos for reading this far!