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

1. 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 ⁰c

c_v =0.714 k J/kg ⁰c

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) 4⁰C at 325 km/h

(ii) 16⁰C at 650 km/h

(iii) 40⁰C at 1000  km/h

(iv) 63⁰C at 1300 km/h

T₁ is the absolute stagnant ambient temperature of air (outside the aircraft)

Let T₂ is the stagnant absolute temperature of air after ram compression

T₂ = T₁ + V²/2000 x c^p

M is Mach number.

where M is Mach number=v _aircraft/v _sound

T2/T1= 1 +  ((γ –1)/2)M²

Let T_2’ is the stagnant absolute temperature of air after ram compression

Assumption T₂=T_2’

Firstly p₁ is the atmospheric pressure outside the aircraft

Secondly p₂ 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′/T₁)^γ

Then find p₂  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 T₅ and T_5­’  

T₅’ is the theoretical temperature at the outlet of turbine

T₅ is the actual temperature after the turbine

p₃ = p₄

p₅ = p_5′ is pressure inside the cabin of the aircraft

Assume cabin pressure p₅=p_5′ = 1.1 bar if not given.

T5^’/T4 =(p5/p4)^γ-1/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 –T₅)

T_cabin = 22 to 27⁰C = 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 3-T 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 T₄ after the HE I.

Є_{HE I} = (T₃ – T₄)/(T₃ –T₂),

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’/T₄ =( p_5’ /p₄)^(γ—1)/γ

Determination of temperature T₅

η_{comp II} = (T₅ –T₄)/ (T_5’ –T₄)

Determination of temperature T₆ after the second heat exchanger

Є_{HE II} = (T₅ – T₆)/(T₅ –T₂)

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’/T₆ =( p_7’ /p₆)^(γ—1)/γ

Determination of actual temperature T₇ after the turbine

_{η (turbine)} = (T₇ –T₆)/ (T_7’ –T₆)

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 –T₂)

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 ( V₂^.) of compressor 1 at the INLET OF COMPRESSOR

P ₂   x  100 V₂^.  = m^. R T₂

Determine volumetric capacity ( V₄^.) of compressor 2 at the INLET OF COMPRESSOR

P ₄   x  100 V₄^.  = m^. R T₄

Determine volumetric capacity ( V₇^.) of turbine at its outlet

P ₇   x  100 V₇^.  = m^. R T₇                                                                                   

  _{(b). Bootstrap without evaporative cooling}

_{Fig. Boot Strap Aircraft Cooling System Without Evaporator on T-s 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  T₅ 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 ex-changer 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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