(a) The air-fuel ratio of an SI engine varies under different operating conditions. Write the air-fuel ratio requirement for an…

(a) Air-fuel ratio requirement of an SI engine (10 marks)

The chemically correct (stoichiometric) air-fuel ratio for petrol is about 14.7:1. The engine needs a different mixture strength in each regime.

• Idling or no-load: a rich mixture of about 11:1 to 13:1. With the throttle almost closed, the manifold pressure is low, so the fresh charge is small and is diluted by a large fraction of residual exhaust gas. Fuel also vaporises and mixes poorly at low air speed. A rich mixture gives a flammable, easily ignited charge, a stable idle, and no misfire.
• Cruising or part-load: a lean mixture of about 15:1 to 17:1 (about 16:1). Here the aim is economy, not maximum power. Excess air ensures that all the fuel burns completely, giving the highest thermal efficiency and lowest specific fuel consumption, with low CO. (An engine with a three-way catalyst is instead held at 14.7:1 by closed-loop control, to keep CO, HC and NOₓ low.)
• Maximum power or full-load: a rich mixture of about 12:1 to 13:1 (10–20% rich). Maximum power occurs at this strength, because the flame speed is highest and all the oxygen in the air is used. The extra fuel also cools the charge as it vaporises, which lowers the tendency to knock and the exhaust valve temperature, at the cost of higher fuel consumption.

(b) Functions and properties of engine lubricating oil (10 marks)

Functions.

• Lubrication: it forms a film between moving surfaces, so friction and wear fall, and less power is lost.
• Cooling: it carries heat away from the piston, bearings and cylinder walls, to the sump.
• Sealing: it fills the gap between piston rings and liner, so it reduces gas leakage (blow-by) and keeps compression.
• Cleaning: it carries wear particles, soot and carbon to the filter, and its detergent and dispersant additives keep them suspended, preventing sludge and deposits.
• Corrosion protection: it forms a protective film and neutralises the acids from combustion (alkaline reserve).
• Cushioning: it damps shock loads on bearings and gears.

Essential properties.

• Suitable viscosity, and a high viscosity index, so it changes little with temperature.
• Oiliness (film strength) and anti-wear character under boundary lubrication.
• Low pour point for cold starting, and high flash and fire points for safety.
• Thermal and oxidation stability, so it does not thicken, form sludge or varnish at high temperature.
• Low volatility and low carbon-residue tendency.
• Detergency and dispersancy, an alkaline reserve (TBN), and corrosion and rust inhibition.
• Anti-foaming, water-separating ability, and compatibility with seals and metals.

(c) Steam flow in a convergent nozzle at different pressure ratios (10 marks)

Let the pressure ratio be back pressure to inlet pressure, p_b/p₁. The critical pressure ratio at the throat is p*/p₁ = (2/(n + 1))^(n/(n−1)), that is 0.546 for superheated steam (n = 1.3) and 0.577 for dry saturated steam (n = 1.135). For a convergent nozzle, the design condition is p_b/p₁ equal to this critical ratio.

• (i) At the design (critical) ratio: the steam expands from p₁ to p* exactly at the exit, so the exit pressure equals the back pressure. The exit velocity is sonic (M = 1), and the mass flow rate is at its maximum value (the nozzle is just choked). The expansion is complete inside the nozzle.
• (ii) At a pressure ratio higher than design (back pressure above the critical value): the flow is subsonic throughout. The exit pressure equals the back pressure, exit M < 1, the exit velocity is lower than sonic, and the mass flow rate is less than the maximum. It rises as the back pressure is lowered towards the critical value.
• (iii) At a pressure ratio lower than design (back pressure below the critical value): the flow is choked. The steam expands only to the critical pressure p* at the exit, where M = 1, and the exit pressure stays above the back pressure. The remaining expansion (p* to p_b) takes place outside the nozzle, in the jet, and it is uncontrolled and gives no extra velocity in the nozzle. The velocity and mass flow rate remain at their maximum values and do not change with further lowering of the back pressure.

A convergent nozzle can never give supersonic exit flow, since M = 1 is reached at the throat at most. A convergent–divergent nozzle is needed to expand to a lower pressure with supersonic velocity.

(d) Deviations in the compression process of an actual vapour-compression cycle (10 marks)

The simple saturated cycle assumes that the vapour enters the compressor as dry saturated vapour at the evaporator pressure, and is compressed isentropically to the condenser pressure. In an actual cycle:

• Superheated suction vapour. The refrigerant enters the compressor with some superheat, since it picks up heat in the evaporator outlet and suction line. This is deliberate, to ensure that no liquid enters the compressor (liquid slugging), and it also raises the discharge temperature.
• Suction pressure drop. The pressure at the compressor inlet is lower than the evaporator pressure, because of frictional pressure drop in the suction line and suction valves, which lowers the density and mass flow.
• Non-isentropic compression. The path is polytropic, with rising entropy, due to friction, heat exchange with the cylinder walls and internal irreversibilities, so the work input is larger than the isentropic work and the discharge temperature is higher for the same pressure ratio (isentropic efficiency below 1).
• Higher discharge pressure. The pressure at the compressor discharge is above the condenser pressure, to overcome the pressure drop in the discharge valves, line and condenser.
• Heat loss. Some heat is lost from the compressor and discharge line to the surroundings, so the discharge enthalpy is a little lower than in adiabatic compression.
• Volumetric and mechanical losses. Clearance volume, and leakage past piston rings and valves, reduce the mass delivered, and mechanical friction in the compressor adds to the power input.

(e) Room ADP and coil ADP (10 marks)

Coil ADP (apparatus dew point). On the psychrometric chart, the coil process line is the line joining the state of the air entering the cooling coil (usually a mixture of fresh and return air) with the state of the air leaving it, and this line is extended to the saturation curve. Its intersection with the saturation curve is the coil ADP. It represents the effective mean surface temperature of the cooling coil, which the air would reach if the coil were of infinite size and the air fully contacted it. Its slope corresponds to the grand sensible heat factor (GSHF), which includes the ventilation load.

Room ADP. It is found by drawing the room sensible heat factor (RSHF) line through the room state, and extending it to the saturation curve. It represents the lowest effective surface temperature that would just meet the room's sensible and latent load, that is the ADP needed if the air passed over the coil were the room air alone.

Condition for equality. The two are the same when the RSHF line and the coil process line coincide, that is when GSHF = RSHF. That happens when the coil handles only the room load: 100% recirculated air with no fresh (outside) air load entering the coil and no other loads such as duct gain or reheat. The state entering the coil is then the room state itself. Any ventilation air makes the coil line steeper (GSHF < RSHF), and the coil ADP then lies below the room ADP.