Heat engines

Name the four strokes of a petrol engine and describe what happens in each one: position of the piston, state of the valves, and what happens to the fuel-air mixture.

The figure schematically shows the four strokes of an internal combustion engine, but one is covered. State which stroke is missing, what occurs during it, and how you deduce it from the position of the piston and the valves of the adjacent strokes.

Explain the basic differences between a two-stroke engine and a four-stroke engine: how many revolutions of the crankshaft each cycle requires, how gases enter and leave, and why two-stroke engines are usually lighter but more polluting.

Define the cylinder bore and the piston stroke, and write the formula for unit displacement in terms of both. Why can two engines with the same displacement behave very differently if one is 'long-stroke' (stroke greater than bore) and the other is 'oversquare'?

The figure shows a cylinder with its bore and stroke dimensioned. Calculate the unit displacement $V_u = \pi \cdot \frac{D^2}{4} \cdot c$ using the data from the figure, express it in $\text{cm}^3$, and calculate the total displacement if the engine has three cylinders.

An engine has four cylinders of unit displacement $500\ \text{cm}^3$. a) Calculate the total engine displacement. b) If the volume of the combustion chamber of each cylinder (with the piston at top dead centre) is $50\ \text{cm}^3$, calculate the compression ratio $r = \frac{V_u + V_c}{V_c}$. c) Explain what improvement and what risk a high compression ratio involves.

Compare the Otto cycle (petrol) with the Diesel cycle: how fuel is introduced, how ignition occurs, and what compression ratio each uses. Reason why Diesel engines are usually more efficient at partial load.

Explain why a Diesel engine does not need spark plugs: what happens to the air temperature when it is highly compressed, when the Diesel fuel is injected, and how auto-ignition occurs. Relate this to its higher compression ratio.

Many internal combustion engines in hybrid vehicles use the Atkinson/Miller cycle instead of the conventional Otto cycle. a) Sketch and explain on a schematic $p\text{-}V$ diagram how the expansion stroke is made larger than the effective compression stroke by delaying the closure of the intake valves (variable valve timing VVT). What impact does this phase shift have on the utilization of gas energy and on the exhaust temperature? b) If the Atkinson cycle offers superior thermal efficiency, justify why it is not widely used in conventional passenger cars without hybridization or supercharging, paying attention to specific power and cylinder filling at low engine speeds. c) Justify how the hybrid system synergistically solves and compensates for this intrinsic limitation of the Atkinson engine.

An engine delivers a torque of $180\ \text{N}\cdot\text{m}$ at $3\,000\ \text{rpm}$. a) Express the angular velocity in $\text{rad/s}$ ($\omega = \frac{2 \pi n}{60}$). b) Calculate the power output $P = M \cdot \omega$ and express it in $\text{kW}$. c) Calculate the work produced by each cylinder explosion if the engine is a four-cylinder, four-stroke engine.

The specific fuel consumption of an engine is $240\ \text{g/kWh}$. a) Calculate how much petrol it consumes in one hour operating at $50\ \text{kW}$. b) Using the calorific value of petrol ($\approx 12\ \text{kWh/kg}$), calculate the thermal efficiency of the engine. c) Comment on the result in light of the typical loss balance.

On the test bench, the following data are obtained for a four-cylinder, four-stroke engine ($1\,600\ \text{cm}^3$ total displacement): at $2\,500\ \text{rpm}$ it delivers a torque of $145\ \text{N}\cdot\text{m}$ while consuming $6,8\ \text{kg/h}$ of gasoline ($P_c = 44\ \text{MJ/kg}$); at $6\,000\ \text{rpm}$ its torque drops to $110\ \text{N}\cdot\text{m}$ while consuming $19,2\ \text{kg/h}$. a) Determine the effective power at both engine speeds and calculate the engine's brake thermal efficiency at each of them. b) A mechanic states: "At $6\,000\ \text{rpm}$, the engine draws in more air per second, so cylinder filling and combustion are better, and engine torque should be at its maximum." Refute this statement technically and thermodynamically, justifying the torque drop at high engine speeds based on volumetric efficiency (throttling at the valves) and mechanical friction losses.