ENSC 388 PROJECT 1
Assigned date: Sep.24, 2009
Due date: Oct 29, 2009
The project should be completed individually. The report should be typed and be
accompanied with a CD including your code. It should not exceed 11 pages,
appendices extra, if needed.
Total mark is 50, that is 5% of your final mark. Innovative ideas or
engineering recommendations have 10 bonus marks.
The Compressed Air Car (Air Car) has been claimed as the true car of tomorrow,
with the same mileage and zero emissions as a fuel-cell car without the dangers
currently associated with hydrogen. Air Cars are powered by air turbines and
driven by compressed air, which is stored in a tank under high pressure, typically
30 𝑀𝑃𝑎 (4500 𝑝𝑠𝑖 or 300 𝑏𝑎𝑟). Schematic of the compressor unit and the Air Car
are shown in Fig. 1.
Regulator Valve
Air Car
𝑊𝑐𝑜𝑚𝑝
4
𝑄𝑎𝑐
5
1
Air Tank
3
Turbines
2
Compressor
Air-cooler
Tires
Figure 1. Schematic of the Air Car and air compression process.
The compressor unit (compressor and air-cooler) is not a part of the car.
M. Bahrami
ENSC 388
Project 1
1
The overall process can be described as below:
Air is compressed from ambient condition (state 1) under a polytropic process,
𝑃𝑉 𝑛 = 𝐶𝑜𝑛𝑠𝑡., in a compressor. Pressure ratio (𝑟𝑝 = 𝑃2 /𝑃1 ) of the compressor and
the ambient temperature can vary from 50 to 300 and −10 ℃ to 40 ℃,
respectively. Air is then cooled in an air-cooler to the ambient temperature (state 3)
and stored in the vehicle air tank. Volume of the tank is 300 𝐿 . The compressed air
is transferred to the turbines to produce work and is discharged to the atmosphere.
As a result of this process, the pressure in the tank drops gradually and heat
transfer occurs from the surrounding to the tank, hence the compressed air can be
assumed to remain at the ambient temperature. At the inlet of each turbine, a
regulator valve is installed which maintains a constant pressure of 10 𝑏𝑎𝑟
(state 4). Assume isentropic expansion: 𝑃𝑉 𝑘 = 𝑐𝑜𝑛𝑠𝑡. The process continues until
the tank pressure reaches 10 𝑏𝑎𝑟. At this state the mass of the air remaining in the
tank is negligible.
Your job is to determine:
a) The amount of work needed to fill the tank, 𝑊𝑐𝑜𝑚𝑝 [𝑘𝐽], the heat transfer in
the air-cooler, 𝑄𝑎𝑐 [𝑘𝐽], the amount of work produced in turbines to move the
car, 𝑊𝑡𝑢𝑟𝑏 [𝑘𝐽], mass of air stored in the tank, 𝑚𝑡𝑎𝑛𝑘 and the total efficiency
of the Air Car, 𝜂. Consider constant ambient temperature and pressure, 𝑇1 =
25℃, 𝑃1 = 1 𝑏𝑎𝑟 and pressure ratio, 𝑟𝑝 = 300 in this part. Also consider
𝑛 = 1.51 for the polytropic processes in the compressor and 𝑘 = 1.4 for
ideal expansion in the turbines.
b) Assume: the car net mass is 𝑚𝑐𝑎𝑟 = 380 [𝑘𝑔], the cruising speed is
𝑉𝑐 = 60 [𝑘𝑚/ℎ𝑟] (in a flat road), with two passengers on board; each,
𝑚𝑝 = 80 𝑘𝑔. Find the maximum distance (Δ𝑋𝑚𝑎𝑥 ), this car can travel for
one air tank. Consider constant friction coefficient, 𝑓 = 0.1 for the friction
resistance between tires and the road. Also the drag coefficient is 𝐶𝐷 = 0.25
and the car frontal area is 𝐴𝑓 = 2.2 [𝑚2 ].
Hint: You can consider an averaged mass, 𝑚𝑡𝑎𝑛𝑘 /2, for the air tank mass for
the duration of Δ𝑋𝑚𝑎𝑥 .
M. Bahrami
ENSC 388
Project 1
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c) Let the ambient temperature varies from −10 ℃ to 40 ℃, while the ambient
pressure, 1 𝑏𝑎𝑟 and 𝑟𝑝 = 300 are constant. Show that 𝑊𝑐𝑜𝑚𝑝 , 𝑊𝑡𝑢𝑟𝑏 and 𝜂
are constant. Plot 𝑄𝑎𝑐 , 𝑚𝑡𝑎𝑛𝑘 and maximum distance Δ𝑋𝑚𝑎𝑥 vs. ambient
temperature and discuss your results.
d) Perform the same analysis as part (c) when ambient temperature remains
constant (𝑇1 = 25 ℃) and the pressure ratio varies from 50 to 300.
Plot 𝑊𝑐𝑜𝑚𝑝 , 𝑄𝑎𝑐 , 𝑊𝑡𝑢𝑟𝑏 , 𝜂, 𝑚𝑡𝑎𝑛𝑘 and Δ𝑋𝑚𝑎𝑥 . Elaborate on your results.
e) Discuss potential problems with the described simplified problem and
recommend engineering solutions. For example low temperature at the
turbine exit (state 5) may lead to freezing of water content (humidity) in the
air.
Present your results using both tables and figures. Elaborate on your results; make
recommendations based on your observations and draw conclusions. What would
be the optimum working condition for the Air Car? For parts (c) and (d) you
should write a program to extract data and plot the results. You can use any of the
popular software tools, such as Maple, Mathematica, Excel, Matlab, C++, etc.
Figure 2. Air Car
(Photo from www.theaircar.com)
M. Bahrami
ENSC 388
Project 1
3
Useful Equations
- Force Balance:
𝑉𝑐 = 60 𝑘𝑚/ℎ𝑟
𝐹𝐷 = 𝜌𝐶𝐷 𝑉𝑐2 𝐴𝑓 /2
∆𝑋
W
𝐹𝑓 = 𝑓 𝑊
- Compressor and Turbine:
𝑊𝑐𝑜𝑚𝑝
𝑛𝑚𝑡𝑎𝑛𝑘 𝑅𝑇1 𝑃2
=
[( )
𝑛−1
𝑃1
(𝑛−1)⁄
𝑛
− 1] ; 𝑊𝑡𝑢𝑟𝑏
𝑘𝑚𝑡𝑎𝑛𝑘 𝑅𝑇4
𝑃5
=
[1 − ( )
𝑘−1
𝑃4
(𝑘−1)⁄
𝑘
]
- Efficiency:
𝜂=
𝐵𝑒𝑛𝑒𝑓𝑖𝑡
𝑊𝑡𝑢𝑟𝑏
=
𝐶𝑜𝑠𝑡
𝑊𝑐𝑜𝑚𝑝
- Drag and Friction Forces:
1
𝐹𝐷 = 𝜌𝐶𝐷 𝑉𝑐2 𝐴𝑓
2
𝐹𝑓 = 𝑓𝑊 = 𝑓 (𝑚𝑐𝑎𝑟 +
𝑚𝑡𝑎𝑛𝑘
+ 𝑚𝑝 ) 𝑔
2
where 𝐶𝐷 is the drag coefficient and 𝐴𝑓 is the car frontal surface area.
- Maximum Distance:
𝑊𝑡𝑢𝑟𝑏 = (𝐹𝐷 + 𝐹𝑓 )Δ𝑋𝑚𝑎𝑥
Note (1): When cruising, acceleration is zero, 𝑎⃗ = 0.
M. Bahrami
ENSC 388
Project 1
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Note (2): Neglect the initial acceleration and final deceleration in ∆𝑋𝑚𝑎𝑥
calculation.
Some assumptions you may consider:
-
Adiabatic compression and expansion.
Negligible mechanical losses.
Air as an ideal gas.
Negligible pressure losses in pipes, joints and the air-cooler.
Suggested control volumes:
Wcomp
Qac
1
Air-Cooler
COMPRESSOR
AIR
TANK
3
2
AIR TANK
Isothermal tank
mtank
T3
P3
3
Q
4
TURB
5
𝑃𝑎𝑡𝑚
Wturb
Regulator Valve
M. Bahrami
ENSC 388
Project 1
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Report Structure
It is an engineering report and should follow following structure:
- Introduction: a brief review on how Air Car works advantages and
disadvantages of the Air Car.
- Analysis:
 Justifying the assumptions and simplifications.
 Control volumes and calculations.
 Plots and tables.
 Discussions on the results.
 Recommendations and suggestions.
-
Conclusions and summaries.
M. Bahrami
ENSC 388
Project 1
6