Diesel fuel injection: pumps, injectors and common rail

Why it matters

In a CI engine the fuel system does the job that the throttle and spark plug do in a petrol engine: it decides how much fuel burns, when it starts burning and how fast. Injection pressure, timing and spray quality set the engine's power, smoke, NOx, noise and fuel economy, which is why the move from mechanical pumps to electronically controlled common rail was the single biggest step in modern diesel development.

Key ideas

What an injection system must do. Every diesel injection system has to:

• Meter the correct quantity of fuel per cycle per cylinder, equal in every cylinder, and vary it with load (diesel engines are quality-governed: load is changed by fuel quantity, not by throttling air).
• Time the start of injection correctly (a few degrees before TDC, advanced with speed) and control the rate of injection during the event.
• Atomise the fuel into fine droplets, give the spray enough penetration to reach the air across the chamber, and distribute it through the air charge.
• Cut off sharply at the end of injection, with no dribbling (dribble gives smoke and HC).

Atomisation and penetration pull against each other: smaller holes and higher pressure give finer droplets, but very fine droplets lose momentum quickly and penetrate less. Chamber design (next topics) and nozzle choice are matched to each other.

Air injection versus solid injection. Early diesels blew fuel in with compressed air (air injection); all modern engines use solid (airless) injection, where the liquid fuel itself is pressurised and forced through a nozzle.

Types of solid injection system.

• Individual pump (jerk pump) system – an in-line pump with one plunger-and-barrel element per cylinder, driven by a camshaft at half engine speed (four-stroke). The plunger has a helical groove; rotating it through the control rack changes the point at which the spill port is uncovered, so the effective stroke and therefore the quantity delivered change, while the plunger's total stroke stays fixed. A delivery valve with a retraction collar lets the pipe pressure drop quickly at cut-off, preventing secondary injection and dribble. A governor moves the rack.
• Distributor (rotary) pump – one pumping element that serves all cylinders in turn through a rotating distributor; compact, used on smaller engines.
• Unit injector – pump and injector combined in one body at each cylinder, driven by an overhead cam; no high-pressure pipe, so very high pressures are possible.
• Common rail (CRDI) – a high-pressure pump keeps a shared accumulator (the rail) at a controlled pressure; electronically controlled solenoid or piezo injectors open on command from the ECU.

The injector and nozzle. In a conventional injector a spring holds the needle on its seat. Fuel from the pump acts on the needle's pressure shoulder; when the hydraulic force exceeds the spring force (the nozzle opening pressure, set by spring preload) the needle lifts and fuel sprays out; when pump delivery stops, pressure falls and the spring snaps the needle shut. Nozzle types:

• Single-hole and multi-hole nozzles – used in direct-injection (open chamber) engines, where the spray itself must reach the air; multi-hole nozzles with very small holes (around 0.1–0.2 mm) are standard.
• Pintle nozzle – the needle has an extension (pintle) projecting through a single orifice, giving a hollow cone spray and a self-cleaning action; used in indirect-injection (pre-chamber/swirl chamber) engines where air motion does the mixing.
• Pintaux nozzle – a pintle nozzle with an auxiliary hole that sprays first, to help cold starting.

Common rail in more detail. The defining feature is that injection pressure is decoupled from engine speed and load. In a jerk pump the pressure depends on plunger speed, so it is low at low engine speed; in a common rail the rail pressure (typically up to about 1600–2500 bar in current engines; take the exact figure from the manufacturer's data) is held by a pressure sensor and a pressure-control valve. Because the injector is opened electrically, the ECU can split each cycle into pilot, main and post injections:

• a small pilot shortens the delay period of the main injection, reducing the pressure-rise rate, combustion noise and NOx;
• the main injection at high pressure gives fine atomisation and low smoke;
• post injections raise exhaust temperature to help regenerate a particulate filter or light off the catalyst.

The penalties are cost, the need for very clean, water-free fuel with adequate lubricity (clearances are a few micrometres), and complex electronic diagnosis.

Connection to neighbouring topics. Injection timing and rate drive the delay period and knock behaviour in CI combustion; spray pattern must match the combustion chamber; injection strategy is a main lever for NOx and PM control.

Formulas

ṁ_f = bsfc × P_b

• ṁ_f = fuel mass flow (kg/h or kg/s); bsfc = brake specific fuel consumption (kg/kWh); P_b = brake power (kW).

n_inj = K × N / (60 × n_s)

• n_inj = injections per second for the whole engine (1/s); K = number of cylinders; N = engine speed (rev/min); n_s = 2 for a four-stroke, 1 for a two-stroke engine.

m_inj = ṁ_f / n_inj and V_inj = m_inj / ρ_f

• m_inj = mass injected per cycle per cylinder (kg); V_inj = its volume (m³); ρ_f = fuel density (kg/m³, about 830–850 for diesel; take from data).

t_inj = θ / (6 × N)

• t_inj = injection duration (s); θ = injection duration in crank angle degrees; N in rev/min (one revolution per minute = 6 degrees per second).

v_f = C_v × √(2 × (p_inj − p_cyl) / ρ_f)

• v_f = jet velocity at the nozzle exit (m/s); p_inj = injection (rail) pressure (Pa); p_cyl = cylinder pressure during injection (Pa); C_v = velocity coefficient (dimensionless). Valid for steady incompressible flow through the orifice.

V_inj = C_d × A_n × √(2 × Δp / ρ_f) × t_inj

• A_n = total nozzle orifice area (m²); C_d = discharge coefficient of the nozzle (typically 0.6–0.8, take from data); Δp = p_inj − p_cyl (Pa). Assumes constant pressure difference through the injection period.

A_n = z × π × d_n² / 4

• z = number of holes; d_n = hole diameter (m).

Worked examples

Example 1 (standard): fuel per injection. A four-cylinder, four-stroke diesel develops 60 kW brake power at 2400 rev/min with bsfc = 0.22 kg/kWh. Diesel density is 830 kg/m³. Find the fuel injected per cycle per cylinder in mg and mm³.

1. Fuel flow: ṁ_f = bsfc × P_b = 0.22 × 60 = 13.2 kg/h = 13.2 / 3600 = 3.667 × 10⁻³ kg/s.
2. Injections per second: n_inj = K × N / (60 × n_s) = 4 × 2400 / (60 × 2) = 80 1/s.
3. Mass per injection: m_inj = ṁ_f / n_inj = 3.667 × 10⁻³ / 80 = 4.583 × 10⁻⁵ kg = 45.8 mg.
4. Volume: V_inj = m_inj / ρ_f = 4.583 × 10⁻⁵ / 830 = 5.52 × 10⁻⁸ m³ = 55.2 mm³.

Answer: 45.8 mg (about 55.2 mm³) per cycle per cylinder.

Example 2 (GATE level): sizing nozzle holes. A common-rail injector must deliver 30 mg of diesel (ρ_f = 830 kg/m³) per injection in 20° of crank rotation at 2000 rev/min. Rail pressure is 1200 bar and mean cylinder pressure during injection is 50 bar. The nozzle has 6 holes with C_d = 0.7. Find the hole diameter.

1. Injection time: t_inj = θ / (6 × N) = 20 / (6 × 2000) = 1.667 × 10⁻³ s.
2. Pressure difference: Δp = (1200 − 50) × 10⁵ = 1.15 × 10⁸ Pa.
3. Ideal jet velocity: √(2Δp/ρ_f) = √(2 × 1.15 × 10⁸ / 830) = √(2.771 × 10⁵) = 526.4 m/s.
4. Volume per injection: V_inj = 30 × 10⁻⁶ / 830 = 3.614 × 10⁻⁸ m³.
5. Total orifice area: A_n = V_inj / (C_d × √(2Δp/ρ_f) × t_inj) = 3.614 × 10⁻⁸ / (0.7 × 526.4 × 1.667 × 10⁻³) = 5.885 × 10⁻⁸ m² = 0.0589 mm².
6. Area per hole = 0.0589 / 6 = 9.81 × 10⁻³ mm²; d_n = √(4 × a / π) = √(4 × 9.81 × 10⁻³ / π) = 0.112 mm.

Answer: d_n ≈ 0.112 mm per hole, a realistic value for a modern multi-hole DI nozzle.

Common mistakes

• Using engine speed directly as injections per second for a four-stroke engine; each cylinder injects once every two revolutions.
• Forgetting to subtract cylinder pressure from injection pressure in the orifice equation, or leaving pressure in bar instead of pascals.
• Converting crank angle to time with 360 × N instead of 360 × N / 60 (that is, 6N degrees per second).
• Saying the jerk-pump helix changes the plunger stroke: the geometric stroke is fixed by the cam; the helix changes the effective (delivery) stroke.
• Assuming higher injection pressure only helps: it reduces smoke but, by speeding up premixed burning, can raise NOx and noise unless timing and pilot injection are adjusted.
• Mixing up pintle (IDI, single orifice with projecting pintle) and multi-hole (DI) nozzles.

For GATE ME

Expect short numericals on fuel quantity per cycle per cylinder from bsfc and power, injection duration from crank angle and speed, jet velocity from pressure difference, and nozzle orifice area or hole diameter. Conceptual questions test the quantity-control method of a jerk pump, the role of the delivery valve, nozzle types against chamber types, and why common rail allows pressure independent of speed and multiple injections. Practise unit conversions (bar to Pa, mg to kg, degrees to seconds) until they are automatic.

Quick check

1. How does rotating the plunger of a jerk pump change the quantity delivered?
2. Which nozzle type suits an indirect-injection (swirl chamber) engine?
3. A four-stroke, 6-cylinder engine runs at 1800 rev/min. How many injections per second occur in total?
4. What is the purpose of a pilot injection?
5. How long (in ms) does a 15° injection last at 3000 rev/min?

Answers: 1. The helical groove uncovers the spill port earlier or later, changing the effective stroke; 2. Pintle (or pintaux) nozzle; 3. 6 × 1800 / 120 = 90 per second; 4. To shorten the delay of the main injection, reducing pressure-rise rate, noise and NOx; 5. 15 / (6 × 3000) s = 0.833 ms.