Consider an ideal air-standard diesel cycle in which the state before the compression process is 95 kPa, 290 K, and the compression ratio is 20. Find the maximum temperature (by iteration) in the cycle to have a thermal efficiency of 60%?

Question

Accepted Answer

Diesel cycle: [latex]P _1=95 \,kPa ,\quad T_1=290 \,K , \quad v _1 / v _2=20, \quad \eta_{ TH }=0.6[/latex]

Since the efficiency depends on [latex]T _3 ext { and } T _4[/latex], which are connected through the expansion process in a nonlinear manner we have an iterative problem.

[latex]\begin{aligned}& T _2= T _1\left( v _1 / v _2 ight)^{ k -1}=290(20)^{0.4}=961.2 \,K \& v _1=0.287 imes 290 / 95=0.876 \,m ^3 / kg = v _4, \& v _2= v _1 / CR =0.876 / 20=0.0438 \,m ^3 / kg \& v _3= v _2\left( T _3 / T _2 ight)=0.0438\left( T _3 / 961.2 ight)=0.0000456 T _3 \& T _3= T _4\left( v _4 / v _3 ight)^{ k -1}=\left(\frac{0.876}{0.0000456 T _3} ight)^{0.4} \Rightarrow T _4=0.019345 T _3^{1.4}\end{aligned}[/latex]

Now substitute this into the formula for the efficiency

[latex]\begin{aligned}\eta_{ TH } & =0.60=1-\frac{ T _4- T _1}{ k \left( T _3- T _2 ight)}=1-\frac{0.019345 imes T _3^{1.4}-290}{1.4\left( T _3-961.2 ight)} \\Rightarrow & 0.019345 imes T _3^{1.4}-0.56 imes T _3+248.272=0\end{aligned}[/latex]

Trial and error on this non-linear equation in [latex]T_3[/latex]

3050 K: LHS = +1.06 3040 K: LHS = -0.036,

Linear interpolation [latex]T_3[/latex]= 3040 K

Question 12.CSGP.128: Consider an ideal air-standard diesel cycle in which the sta......

Related Answered Questions

Verified Answer:

Repeat Problem 12.67, but assume variable specific heat. The ideal gas air tables, Table A.7, are recommended for this calculation (and the specific heat from Fig. 5.10 at high temperature). ...

Verified Answer:

Verified Answer:

Repeat Problem 12.29 when the intercooler brings the air to T3= 320 K. The corrected formula for the optimal pressure is P2 = [ P1 P4 (T3 /T1 ^)n/(n-1)]^1/2 see Problem 9.241, where n is the exponent in the assumed polytropic process. ...

Verified Answer:

Reevaluate the combined Brayton and Rankine cycles in Problem 12.114. For a more realistic case assume the air compressor, the air turbine, the steam turbine and the pump all have an isentropic efficiency of 87%. ...

Verified Answer:

Find the temperature after combustion and the specific energy release by combustion in Problem 12.92 using cold air properties. This is a difficult problem and it requires iterations. The worlds largest diesel engine has displacement of 25 m³ running at 200 RPM in a two stroke cycle producing ...

Verified Answer:

Consider a gas turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each compressor stage and each turbine stage is 8 to 1. The pressure at the entrance of the first compressor is 100 kPa, the temperature entering each compressor is 20°C, and the ...

Verified Answer:

Repeat Problem 12.31, but assume that the compressor has an efficiency of 82%, that both turbines have efficiencies of 87%, and that the regenerator efficiency is 70%. ...

Verified Answer:

Redo the previous problem for a large stationary Brayton cycle where the low T heat rejection is used in a process application and thus has a non-zero exergy. ...

Verified Answer:

The conversion efficiency of the Brayton cycle in Eq.12.1 was done with cold air properties. Find a similar formula for the second law efficiency assuming the low T heat rejection is assigned zero exergy value. ...

Verified Answer: