(a) Show in the form of a table, how the increase in the following variables affects (increase or decrease) the ignition delay…

(a) Effect of variables on the ignition delay of a CI engine

Each variable is increased with all others held constant.

Self-ignition temperature of the fuel up: the delay increases, since the charge must reach a higher temperature before the fuel ignites. Cetane number up: the delay decreases, since a higher cetane fuel has a lower self-ignition temperature and breaks down faster. Compression ratio up: the delay decreases, as the air temperature and pressure at injection are higher. Intake pressure up: the delay decreases, since higher density speeds the pre-flame reactions. Intake temperature up: the delay decreases, as the end-of-compression temperature is higher. Air-fuel ratio up (leaner mixture): the delay increases slightly, as the cooler, less fuel-rich charge reacts more slowly. Exhaust gas recirculation up: the delay increases, since the charge has less oxygen and a lower temperature.

(b) Characteristics of an ideal working fluid for a vapour power cycle

The fluid should have a high latent heat of vaporisation and a high critical temperature, so that much energy is carried per kg and a high boiler temperature is possible without going supercritical. Its saturation pressure should be moderate at the boiler temperature, and not so low at the condenser temperature that deep vacuum and air leakage become problems. A low liquid specific volume keeps pump work small, a low liquid specific heat reduces the heat needed to reach boiling, and a low vapour specific volume keeps equipment compact. It should have good thermal conductivity and low viscosity for heat transfer, and a saturated-vapour line that gives dry or only slightly wet expansion in the turbine. Finally it should be chemically stable, non-corrosive, non-toxic, non-flammable, cheap and readily available. Water meets most of these, which is why it is used.

(c) Reheat factor of a steam turbine

Reheat factor = (sum of the isentropic enthalpy drops of the individual stages)/(isentropic enthalpy drop of the whole turbine, from the initial to the final pressure) = ΣH_i/H.

Proof that it exceeds 1. For an isentropic change, dh = v dp, so the isentropic drop between pressures p₁ and p₂ at entropy s is ∫v(p, s)dp from p₂ to p₁. The overall drop uses the initial entropy s₀: H = ∫v(p, s₀)dp. In a real multistage turbine, irreversibilities in each stage raise the entropy, so stage i begins at s_i ≥ s₀. Its isentropic drop is H_i = ∫v(p, s_i)dp over its own pressure interval. At constant pressure the specific volume of steam increases with entropy, (∂v/∂s)_p = (∂T/∂p)_s > 0. Hence v(p, s_i) > v(p, s₀) at every pressure in the stage, and so H_i exceeds the part of H lying in that pressure interval. Summing over all stages gives ΣH_i > H, so R.F. > 1.

On the h–s diagram this is because constant-pressure lines diverge towards higher entropy. Typical values are 1.02 to 1.06, and the excess drop is the heat reclaimed by the later stages from the friction losses of the earlier ones.

(d) Vapour compression versus vapour absorption refrigeration

Energy input: VCR uses mechanical work in a compressor; VAR uses heat in a generator, with only a small pump work. Refrigerant: VCR uses one pure refrigerant; VAR uses a refrigerant-absorbent pair such as NH₃-H₂O or LiBr-H₂O. Main parts: VCR has a compressor, condenser, expansion valve and evaporator; VAR replaces the compressor by absorber, pump, generator and often a rectifier. COP: VCR = Q_evap/W_comp, usually 3 to 5 or more; VAR = Q_evap/(Q_gen + W_pump), usually below 1. Moving parts and noise: VCR has a compressor, so more noise, vibration and maintenance; VAR has almost no moving parts and runs quietly. Size and cost: VCR is compact and cheap for small and medium units; VAR is bulky and costly to install but economic at large capacity when waste or solar heat is available. Temperature range: VCR reaches very low temperatures; LiBr-H₂O VAR cannot go below 0°C, and NH₃-H₂O VAR can but uses toxic ammonia. Uses: VCR in domestic refrigerators, air conditioners and cold stores; VAR in industrial plants, waste-heat recovery and solar cooling.

(e) Psychrometric properties from DBT and WBT by calculation

Given t = 35°C, t′ = 23°C, barometer 755 mm Hg: p = (755/760) × 1.01325 = 1.0066 bar. Vapour pressure at WBT, interpolating between 22°C and 24°C: p′_v = 0.026431 + 0.5 × (0.029832 − 0.026431) = 0.028132 bar. Apjohn equation: p_v = p′_v − 1.8p(t − t′)/2700 = 0.028132 − 1.8 × 1.0066 × 12/2700 = 0.028132 − 0.008053 = 0.020079 bar.

(i) Relative humidity. The saturation pressure at 35°C is (0.053201 + 0.059423)/2 = 0.056312 bar, so φ = 0.020079/0.056312 = 35.7%. (ii) Humidity ratio: ω = 0.622p_v/(p − p_v) = 0.622 × 0.020079/0.98650 = 0.01266 kg/kg dry air. (iii) Dew point: the saturation temperature at 0.020079 bar lies between 16°C (0.018173) and 18°C (0.020630), so t_dp = 16 + 2 × (0.020079 − 0.018173)/(0.020630 − 0.018173) = 17.55°C. (iv) Enthalpy: h = 1.005t + ω(2501 + 1.86t) = 35.18 + 0.01266 × 2566.1 = 67.7 kJ/kg dry air.