AIRCRAFT COOLING SYSTEMS CLASS NOTES FOR MECHANICAL ENGINEERING
AIRCRAFT COOLING SYSTEMS
CLASS NOTES FOR MECHANICAL
ENGINEERING
Inside the aircraft, a cooling system
is required to maintain comfortable
conditions. It may on
the ground or in the air. Different
cooling systems are used. These are
Simple, boot strap, generative and
reduced ambient cooling systems.
ANALYSIS OF AIRCRAFT COOLING SYSTEMS

Simple Cooling System
Refrigerant is air in all the systems of the aircraft cooling systems.
FIG. LINE DIAGRAM OF SIMPLE AIRCRAFT COOLING SYSTEM
Fig. Simple Aircraft Cooling on Temperature Entropy Chart
Mathematical analysis of Simple Aircraft Cooling System
Properties of air are
c_{P} =1.005 k J/kg ^{0}c
c_{v }=0.714 k J/kg ^{0}c
γ = 1.4 =C_{p}/C_{v}
R_{air}=287 k J/kg K
1kWh =3600 k J
1HPh = 2650 k J
Say V is the velocity of aircraft in m/s
Bringing moving air to rest is ram effect. Due to ramming effect, there is a temperature rise of
(i) 4^{0}C at 325 km/h
(ii) 16^{0}C at 650 km/h
(iii) 40^{0}C at 1000 km/h
(iv) 63^{0}C at 1300 km/h
T_{1} is the absolute stagnant ambient temperature of air (outside the aircraft)
Let T_{2} is the stagnant absolute temperature of air after ram compression
T_{2} = T_{1} + V^{2}/2000 x c^{p}
M is Mach number.
where M is Mach number=v _{aircraft}/v _{sound}
T2/T1= 1 + ((γ –1)/2)M^{2}
Let T_{2’} is the stagnant absolute temperature of air after ram compression
Assumption T_{2}=T_{2’}
Firstly p_{1} is the atmospheric pressure outside the aircraft
Secondly p_{2} is the actual stagnation pressure after ram effect
Thirdly p_{2′ } is the theoretical pressure after ramming effect
Find p_{2′ } from p_{2′}/p1 = (T_{2′}/T_{1})^{γ}
Then find p_{2} from η^{ram = (p2 –p1) / (p2′ –p1) }
Assume η^{ram } as 80 % if not given.
NOTE: Efficiency of ram is expressed in terms of pressures. Efficiency of all other units (compressor, turbine, heat exchanger effectiveness) is expressed in terms of temperatures.
(ii) Calculation of T3′ and T3
T3’ is the theoretical temperature after compression in the main compressor
T3 is the actual temperature after compression in the main compressor
T3’/T2 = ( p3/p2)^{ (γ—1)/γ}
η _{main comp} = (T3’—T2)/ (T3—T2)= Theoretical temp rise/ Actual temp rise
Assume η _{main comp} as 80 % if not given.
Find T3
(iii) Calculation of T4 after the HEAT EXCHANGER
Find temperature T_{4, }after the heat exchanger from effectiveness of the heat exchanger. Assume it 80 % if not given.
Є_{HEX} =( T3—T4)/( T3 — T2) = Actual temp drop/Theoretical temp drop possible
(iv) Calculation of temperatures T_{5 }and T_{5’} _{ }
T_{5}’ is the theoretical temperature at the outlet of turbine
T_{5} is the actual temperature after the turbine
p_{3} = p_{4}
p_{5} = p_{5′} is pressure inside the cabin of the aircraft
Assume cabin pressure p_{5}=p_{5′} = 1.1 bar if not given.
T5^{’}/T4 =(p5/p4)^{γ1/γ}
η_{Turbine} = T5 – T4/(T5^{’}—T4) = Actual temp drop/theoretical temp drop
Assume η_{Turbine} as say 80 % if not given
(v) CALCULATION OF THE COOLING EFFECT, N
N = 1 Cp (T _{cabin} –T_{5})
T_{cabin} = 22 to 27^{0}C = 295 to 300 K, comfortable temperature
(vi) CALCULATION OF THE NET WORK DONE, W _{net}
W _{ram} = 1.C_{p} (T2—T1) kJ/kg
Wc_{omp} = 1.C_{p} (T3—T2) kJ/kg
W _{Turbine} = 1.C _{p} (T 4—T 5) k J/kg
W _{net} = W _{ram} + W c_{omp} –W _{Turbine}
Generally _{ }W _{ram} is neglected.
W _{net} = W _{comp} –W _{turbine}
= 1 c _{p} (T 3T 2) –1 c _{p} (T 4–T 5)
(vii) CALCULATION OF COP
COP = N / W _{net}
(viii) CALCULATION OF MASS FLOW RATE OF AIR
m^{.} = TR x 211/ N kg/min
(ix) CALCULATION OF VOLUMETRIC DISPLACEMENT OF MAIN COMPRESSOR, V_{3}
Volumetric displacement of a compressor is always at the inlet of the compressor.
p _{3}^{ } x 100 V _{3} = m. R T _{3}
(x) CALCULATION OF VOLUMETRIC DISPLACEMENT OF TURBINE
It is always at the outlet of the turbine.
Therefore use and find V 5
p _{5} x 100 V _{5} = m. R T _{5}
CALCULATION OF RATE OF WATER EVAPORATED FOR THE COCKPIT COOLING
(i) Calculation of cooling effect in the cockpit per kg = N = 1 C _{p} (T _{cockpit} –T 5)
(ii) Calculation of water evaporated/h for cockpit cooling m^{.} =(Cooling required/h)/Cooling effect per kg
2. Boot Strap Aircraft cooling
Fig. Line Diagram Boot Strap Aircraft Cooling System
This Bootstrap system has two compressors, two heat exchangers and one turbine. Expansion turbine also runs the second compressor. Boot strap system is of two types:
(a). System with evaporative cooling
There is a third heat exchanger. This is water cooled. It is placed after the second heat exchanger. This further cools air entering the turbine. This increases the cooling effect.
It has two compressors and two heat exchangers.
Analysis is common to simple cooling system up to point 3.
Determination of temperature T_{4} after the HE I.
Є_{HE I} = (T_{3} – T_{4})/(T_{3} –T_{2}),
Assume Є_{HE I} (effectiveness) as 80 % if not given.
Then it goes to the second compressor.
Determination of temperature T_{5’} after the second compressor
T_{5’}/T_{4} =( p_{5’} /p_{4})^{(γ—1)/γ}
Determination of temperature T_{5}
η_{comp II} = (T_{5} –T_{4})/ (T_{5’} –T_{4})
Determination of temperature T_{6 }after the second heat exchanger
Є_{HE II} = (T_{5} – T_{6})/(T_{5} –T_{2})
Assume Є_{HE II} (effectiveness) 80 % if not given.
Then it goes to the Turbine.
Determination of theoretical temperature T_{7’ }after the turbine
T_{7’}/T_{6} =( p_{7’} /p_{6})^{(γ—1)/γ}
Determination of actual temperature T_{7 }after the turbine
_{η (turbine)} = (T_{7} –T_{6})/ (T_{7’} –T_{6})
Assume efficiency of the turbine as 80 % if not given.
CALCULATE THE FOLLOWINGS:
Cooling effect per kg, N = 1 x c _{p }(T _{cabin} –T _{7})
Work input per kg in First compressor W _{c 1} = 1 x c _{p}(T _{3} –T_{2})
Specific Work used in second compressor W _{c 2} = 1 x c _{p}(T _{5} –T _{4})
Specific Work obtained from the turbine W_{T} = 1 x c _{p}(T _{6} –T _{7})
Find W _{net} = W _{c 1} + W _{c 2} –W_{T}
COP = N/ W _{net}
Determine mass flow rate of air
m^{. }N = TR x 211
where TR is the cooling capacity in tons and N is the cooling effect per kg
Determine volumetric capacity ( V_{2}^{.}) of compressor 1 at the INLET OF COMPRESSOR
P_{ 2} _{ } x 100 V_{2}^{. } = m^{.} R T_{2}
Determine volumetric capacity ( V_{4}^{.}) of compressor 2 at the INLET OF COMPRESSOR
P_{ 4} _{ } x 100 V_{4}^{. } = m^{.} R T_{4}
Determine volumetric capacity ( V_{7}^{.}) of turbine at its outlet
P_{ 7} _{ } x 100 V_{7}^{. } = m^{.} R T_{7 }
_{ (b). Bootstrap without evaporative cooling}
_{}
_{Fig. Boot Strap Aircraft Cooling System Without Evaporator on Ts Chart}
_{AB Constant pressure line p1, Ambient pressure}
_{CD constant cabin pressure line, p7 and p7′}
_{EF Constant pressure line p2 and p2′, Pressure after ram compression}
GH constant pressure line p4 and p4′, Pressure after main compression
p5 and p5′ are pressure after compressor c2.
_{As compared to case 1, last heat exchanger is absent. }
3. REGENERATIVE AIRCRAFT COOLING SYSTEM
Some air coming out of the cooling turbine does the cooling in the heat exchanger just before the turbine. In this, there is no cooling by rammed air in the first heat exchanger.
Calculations
Same calculations up to point 3 as in the case of simple system of aircraft cooling.
Now cooled air at point 5 (outlet of turbine) enters the heat exchanger for cooling.
Remember T _{5} is still unknown.
ASSUME T_{5} say= 100 ^{0 }C.
Then calculate T4 from HEX effectiveness = 0.80 = (T3 –T4)/(T3–T5)
Use T4 to calculate T5 from efficiency of turbine.
This T5 may not match with the assumed T5.
An ITERATIVE PROCEDURE minimizes the difference between assumed T5 and calculated T5.
4. Reduced Ambient Cooling System
It uses two turbines and one compressor. Turbine 1 uses rammed air. The air from turbine 1 enters the heat exchanger. Turbine 2 uses air after the heat exchanger for further cooling.
Turbine 1 has input and output points as 2 and 4.
Cooled air from turbine 1 enters the first Heat exchanger at point 4.
Heat exchanger has input at points 3 and 5.
CAUTION: RAMMED AIR IS FED TO TURBINE 1.
Turbine 2 has input and output points as 5 and 6.
Procedure of calculation is similar to the BOOT STRAP SYSTEM.
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