A medium duty truck running on a turbo diesel engine with a

A medium duty truck running on a turbo diesel engine with a 12’ x 6’ (interior dimensions) freezer compartment needs to generate 350 HP at standard highway speeds. The diesel engine has a cutoff ratio of 2.1 and diesel is mixed with incoming air at a ratio of 14.5 air-fuel, on a mass basis. This ratio is also known as the A/F ratio of a diesel cycle. Diesel has a calorific value of 44,800 kJ/kg of fuel. The exhaust from the engine is routed through a small turbine to generate some extra power before rejecting the exhaust at atmospheric temperature and pressure i.e. 25°C and 1 atm. The isentropic efficiency of the turbine is 80%.

A. Design your engine and turbine combo so as to have the highest efficiency possible. Find the optimal values of the following based on this criterion:

1. Compression ratio of the engine (cannot go beyond 18 due to difficulty in manufacturing)

2. Highest temperature of the cycle (cannot go beyond 2200°C to prevent NOx emissions)

3. Pressure ratio of the turbine (cannot go beyond 3 due to restrictions in size)

4. Displacement volume of the engine (no restrictions but the biggest engines are around 16 L)

B. Assume that the space inside the freezer is completely occupied by air at 35°C. If you can only fit in small compressors with pressure ratios of 2.5 into your freezer compartment, design a multistage refrigeration cycle with the above compressors to achieve the highest efficiency possible for the given load. The outside temperature is assumed to be constant at 25°C. The compressors should never come in contact with refrigerant that is not superheated vapor because liquid refrigerant can corrode the compressor blades.

C. Redesign your engine and turbine keeping in mind that while the power requirement is still 350 HP in steady driving on highways, the freezer now consumes a chunk of that power and the engine might need to be upgraded to maintain maximum efficiency.

Solution

solution:

for part A

1)here if we choose cylinder with displacement volume Vd=.016 m3 then amount of air sucked during suction sytroke si given by

PaVd=Ma*RTa

Pa=1.01325*10^5 N/m2

Ta=298 K

R=287

Vd=.016 m3

we get that

Ma=.01895 kg/s

2)here A.f ratio is

Ma/Mf=14.5

Mf=1.3072*10^-3 kg/s

Mg=Ma+Mf=.0202572 kg/s

3)where for cut off ratio 2.1

we get for constant pressure

T3/T2=V3/V2=2.1

T3=2200+273=2473 k

T2=1177.61 k

here for given maximum compression ratio 18 we get temperature as

T2/T1=(V1/V2)^(k-1)

k=1.4

V1/V2=18

T1=370.58 k

4)here diesel engine is turbocharged engine hence turbine work will drive compressore to increased temperature of inlet charged to 370.58 k from 298 k

hence equation becomes

ma*Cv(T1-Ta)=Mg*cv(T4-Ta)

on putting value we get that

T4=365.89 k

6)hence number of cylinder required to produce 350 HP power is given as follows

W=Qs-Qr

W=Mg[1.005(T3-T2)-.718(T4-Ta)]

W=25.38 Kw

hence number of cylinder required are

n=350*.746/25.3846=10.28 =11 cylinder of 16 litre capacity