Abstract
The fist compressed air vehicles were built by Andraud and Tessié du Motay in
Paris between 1838 and 1840. Since then the idea has been tried again and
again, but has never reached commercialization. In recent years the French
developer MDI has demonstrated advanced compressed air vehicles. However,
the claimed performance has been questioned by car manufacturers and
automobile expert. Basically, when referred to ambient conditions, the relatively
low energy content of the compressed air in a tank of acceptable volume is
claimed to be insufficient to move even small cars over meaningful distances.
On the other hand, another air car developer claims to have driven 184 km on
one 300 Liter filled with air at initially 300 bar pressure. Obviously, there are
issues to be resolved, not by heated debates, but by an analysis of the
thermodynamic processes involved. This is the aim of this study.
The results indicate that both sides are correct. At 20°C a 300 Liter tank filled
with air at 300 bar carries 51 MJ of energy. Under ideal reversible isothermal
conditions, this energy could be entirely converted to mechanical work.
However, under isentropic conditions (no heat is exchanged with the
environment) not more than 25 MJ become useful. By multi-stage expansion
with inter-stage heating the expansion process is brought closer to the
isothermal ideal.
The analysis is extended to the compression of air. Again, the ideal isothermal
compression is approached by multi-stage processes with inter-cooling. By this
approach energy demand for compression is reduced to acceptable levels and
system pressure and temperature are kept within safe limits.
The results of this analysis seem to indicate that the efficiency of the four-stage
expansion process is acceptable, while even a four-stage air compression with
inter-cooling is associated with significant losses. However, the overall energy
utilization could be increased if the waste heat generated during the air
compression process would be used for domestic water and space heating.
It seems that there is some justification for continuing the development of
compressed air cars. However, it would be useful to establish the performance
of such vehicles by an endurance race under controlled conditions
in the presence of the general public
1. Introduction:
The air flow of a compressed air car is schematically shown in Figure 1. The
following two questions need to be answered.
3. Air Compression
Three compression processes are illustrated in a pressure-volume diagram
(Figures 2) and a temperature-entropy diagram (Figure 3). Both presentations
are commonly used for thermodynamic analyses.
The fist compressed air vehicles were built by Andraud and Tessié du Motay in
Paris between 1838 and 1840. Since then the idea has been tried again and
again, but has never reached commercialization. In recent years the French
developer MDI has demonstrated advanced compressed air vehicles. However,
the claimed performance has been questioned by car manufacturers and
automobile expert. Basically, when referred to ambient conditions, the relatively
low energy content of the compressed air in a tank of acceptable volume is
claimed to be insufficient to move even small cars over meaningful distances.
On the other hand, another air car developer claims to have driven 184 km on
one 300 Liter filled with air at initially 300 bar pressure. Obviously, there are
issues to be resolved, not by heated debates, but by an analysis of the
thermodynamic processes involved. This is the aim of this study.
The results indicate that both sides are correct. At 20°C a 300 Liter tank filled
with air at 300 bar carries 51 MJ of energy. Under ideal reversible isothermal
conditions, this energy could be entirely converted to mechanical work.
However, under isentropic conditions (no heat is exchanged with the
environment) not more than 25 MJ become useful. By multi-stage expansion
with inter-stage heating the expansion process is brought closer to the
isothermal ideal.
The analysis is extended to the compression of air. Again, the ideal isothermal
compression is approached by multi-stage processes with inter-cooling. By this
approach energy demand for compression is reduced to acceptable levels and
system pressure and temperature are kept within safe limits.
The results of this analysis seem to indicate that the efficiency of the four-stage
expansion process is acceptable, while even a four-stage air compression with
inter-cooling is associated with significant losses. However, the overall energy
utilization could be increased if the waste heat generated during the air
compression process would be used for domestic water and space heating.
It seems that there is some justification for continuing the development of
compressed air cars. However, it would be useful to establish the performance
of such vehicles by an endurance race under controlled conditions
in the presence of the general public
1. Introduction:
The air flow of a compressed air car is schematically shown in Figure 1. The
following two questions need to be answered.
Question A
How much compression energy is needed to fill the tank with air at final
pressure (300 bar = 30 MPa), but ambient temperature (20°C = 293.15K)?
The compression process is treated as polytropic change of state. The
compression from the initial air volume V1 to the final tank volume V2 = V3 is
followed by heat removal at constant tank volume V3 from (p2,T2) to (p3,T3=T1),
i.e. back to the original ambient temperature T1. The final conditions (p3,T3=T1)
can also be reached by an ideal isothermal compression from (p1,V1). The
technical work input by isothermal compression Wt13 is equal to the final energy
content of the tank irrespective of the chosen path of polytropic compression
and isochoric cooling. The energy input is related to the thermodynamics of the
compression process. The lower limit is obtained for isothermal, the upper for
isentropic compression while polytropic case are located between the two.
Question B
How much mechanical energy can be recovered by expanding the compressed
air in an air motor?
The expansion from (p3,T3=T1) to (p4=p1, T4<T1) is also considered to be
polytropic. For an ideal isothermal expansion the entire reversible isothermal
technical work input Wt13 could be recovered by a reversible process. However,
in reality less energy is converted to technical work by the real expansion.
Again, the polytropic process is worse than an isothermal, but better than an
isentropic expansion.
After the extraction of expansion work the air is exhausted at low temperatures.
In an overall energy balance the heat taken from the ambient to restore initial air
temperatures is less than the heat released during air compression because of
the non-ideal processes involved.
There are technical options for compression and expansion. The following
analysis will suggest useful clues for the design of a compression-expansion
system for air cars with acceptable driving performance that make good use of
the electric energy needed to compress the air.
2. Reference Conditions
Reference conditions:
Normal pressure p0 = 760 mmHg = 1.01325 bar = 0.101325 MPa
Normal temperature T0 = 0°C = 273.15 K
Air density at NTP ρ0 = 1.2922 kg/m3
Initial conditions ("1"):
Ambient temperature T1 = 20°C = 293.15K
Ambient pressure p1 = 1 bar = 0.1 MPa
Air density ρ1 = 1.1883 kg/m3
Original air volume V1 = V3 * p3/p1 = 90 m3 (before compression)
Mass of air m1 = V1 * ρ1 = 106.95 kg
Final conditions inside filled tank ("3"):
Tank volume V3 = 300 Liter = 0.3 m3
Air temperature T3 = T1 = 20°C = 293.15 K
Pressure in air tank p3 = 300 bar = 30 MPa
Air density ρ3 = 356.49 kg/m3
Mass of compressed air m3 = V3 * ρ3 = 106.95 kg = m1 (check)
Final conditions after expansion ("4"):
Air pressure p4 = 1 bar = 0.1 MPa
3. Air Compression
Three compression processes are illustrated in a pressure-volume diagram
(Figures 2) and a temperature-entropy diagram (Figure 3). Both presentations
are commonly used for thermodynamic analyses.
3. Isothermal Compression
During the idealized reversible isothermal compression process the temperature
is considered to remain unchanged. The initial temperature T1 is also the final
temperature T3. All compression heat must be removed during the compression
process by heat exchange with the environment (e.g. by transfer to a colder
medium). In reality this is impossible for practical system designs.
The technical work required for filling the tank with air from (p1,T1) to (p3,T3=T1)
under isothermal conditions is
Wt13 = W13 = p1 * V1 * ln(p3/p1)
= p1 * V1 * ln(V1/V3) (1)
4. Polytropic Compression Followed by Isochoric Cooling
The polytropic change of state follows the isentropic laws. However, the
isentropic coefficient (γ = 1.4 for air) is replaced by a polytropic coefficient n.
The value of the coefficient n may vary between 1.4 for isentropic and 1.0 for
isothermal expansions. Air is treated as an ideal gas.
In the isentropic case, no heat is neither exchanged with the environment nor
generated internally by friction or poor aerodynamics, while in the polytropic
case some heat is exchanged with the environment or available form internal
friction losses. The isothermal case is the second idealized limit for real
compression or expansion processes. However, a polytropic compression
process is always associated with an increase of entropy as seen in the T-s-
Diagram (Figure 3).
The technical work required for polytropic air compression from initial (p1,V1) to
final (p2,V2) with V2 = V3 is given by the following equation:
Wt12 = m * cp * (T2 – T1)
= p1 * V1 * n/(n-1) * [(V1/V3)^(n -1) – 1] (2)
The intermediate pressure p2 and temperature T2 are obtained from
p2 = p1 *(V1/V3)^n (3)
and T2 = T1 * (V1/V3)^[(n-1)/n] (4)
Finally, a thermodynamic efficiency of compression can be defined as the ratio
of useful energy in the tank to the total technical work required to fill the tank
with compressed air.
ηth = Wt13 / Wt12 (5)
The following significant results are obtained for different polytropic coefficients:
The results clearly indicate that the compression has to proceed close to the
isothermal limit. Low energy input, reasonable temperatures and acceptable
efficiencies cannot be obtained under isentropic conditions. The problems are
solved with multi-stage compression and air cooling between stages. The
analysis does not include real gas effects and mechanical or electrical losses.
5. Four-Stage Compression
A four-stage compression process is now analyzed. Heat is removed by three
intercoolers between stages 1 to 4 and between the final stage and the tank.
The polytropic compression process is started with air under normal conditions
(p1 = 1bar, T1 = 20°C). For all following stages the inlet air temperature is
assumed to be cooled to 20°C. In practice, this can only be accomplished by
heat transfer to a cold medium.
0 comments:
Post a Comment