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ENGR5003 / Week 4
ENGR217 2021 Q1Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2021 Q1[VALID] official answers

Answer ALL parts (a) - (d).

A Formula 1 car uses a 2.4 litre, 4-stroke, 8-cylinder petrol engine with a total mass of 95 kg. At 19,000 rpm, the engine produces 550 kW of power. The overall engine efficiency is 33% and the breathing and mechanical efficiencies can be assumed to be 85% and 90% respectively. We will model this engine as an Otto cycle operating on an ideal gas and you may assume that Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K} and γ=1.4\gamma = 1.4, where γ\gamma is the adiabatic index.

Formulas you may need
  • Otto cycle efficiency: ηth=1−T1T2=1−1rγ−1\eta_{th} = 1 - \dfrac{T_1}{T_2} = 1 - \dfrac{1}{r^{\gamma-1}} (on the formula sheet)
  • Overall efficiency: ηo=ηth ηb ηm\eta_o = \eta_{th}\,\eta_b\,\eta_m (learn this)
  • Power: P=Wnet N ηb ηmP = W_{net}\,N\,\eta_b\,\eta_m with N=rpm120N = \dfrac{\mathrm{rpm}}{120} power strokes per second per cylinder for a 4-stroke (learn this)
  • Brake work: Wb=ηmWnetW_b = \eta_m W_{net} (learn this)
  • Ideal gas: pV=mRgTpV = mR_gT; cv=Rgγ−1c_v = \dfrac{R_g}{\gamma-1} (on the formula sheet)
  • Adiabatic process: TVγ−1=constantTV^{\gamma-1} = \text{constant} (on the formula sheet)
  • Isochoric heat addition: ΔQ=mcv(T3−T2)\Delta Q = m c_v (T_3 - T_2); ηth=Wnet/Qin\eta_{th} = W_{net}/Q_{in} (on the formula sheet)
  • Adiabatic work: ΔW=−ΔU=mcvΔT\Delta W = -\Delta U = m c_v \Delta T (on the formula sheet)
  • Isentropic efficiencies: ηc=Wc,sWc,a\eta_c = \dfrac{W_{c,s}}{W_{c,a}}, ηe=We,aWe,s\eta_e = \dfrac{W_{e,a}}{W_{e,s}} (learn this)
  • Back work ratio: rbw=Win/Woutr_{bw} = W_{in}/W_{out} (given in the question)
  1. (a)
    Determine the compression ratio, brake work and net work output per cylinder, per cycle.
    [10]2:2
  2. (b)
    Given that at the intake, the air pressure and temperature are p1=101 kPap_1 = 101\ \mathrm{kPa} and T1=303 KT_1 = 303\ \mathrm{K}. Determine the temperature at each stage in the process, the work done during compression and expansion and the required heat addition per cylinder per cycle.
    [8]2:2
  3. (c)
    Let's now assume that the isentropic efficiency of the compression and expansion strokes are 70% and 85% respectively. Determine the back work ratio of the engine for the adiabatic assumption and with the isentropic efficiencies stated. You may assume the heat addition and compression ratio remains the same. Recall that the back work ratio is given as: rbw=WinWoutr_{bw} = \dfrac{W_{in}}{W_{out}}
    [4]
  4. (d)
    Discuss the advantages and disadvantages of using a turbocharger on this engine.
    [3]Third