NovaSolver›Fuel Injection Spray Cone Angle & SMD Simulator Back
Combustion / Injection
Fuel Injection Spray Cone Angle & SMD Simulator
Design fuel-spray formation for diesel common-rail, GDI and port-injection injectors. Adjust injection pressure, ambient density, nozzle diameter, fuel and dwell time, and watch injection velocity, spray cone angle, Sauter mean diameter (SMD) and penetration update live to find conditions that balance combustion and emissions.
Cones fan out of the injector for every hole and droplets travel toward the piston crown up to the penetration distance. Colour shows the SMD level (blue = fine, red = coarse).
ΔP = injection pressure; ρ_g/ρ_l = gas/liquid density ratio; We = Weber number (ρv²d/σ). Injection velocity from Bernoulli, cone angle from Reitz-Bracco, SMD from Nukiyama-Tanasawa.
Fuel Spray — Cone Angle & SMD Design for Diesel and GDI
🙋
I hear that diesel injectors run at 2000 bar — why so high? Gasoline engines use much less, don't they?
🎓
Good question. Diesel burns by auto-ignition, so we have to spray fuel straight into the hot, dense combustion chamber and atomise plus mix it with air inside roughly 1-2 ms. Bernoulli's v = Cd·√(2ΔP/ρ) needs 400-500 m/s for that, hence the 1500-2500 bar common rail. GDI lights the mixture with a spark near TDC, so there is more time and 100-350 bar is enough; port injection sprays into the intake port where mixing is leisurely, so 3-10 bar works. With the defaults, the "Injection velocity" stat should read about 462 m/s.
🙋
SMD says "Sauter mean diameter" — what makes it different from a normal average diameter?
🎓
Roughly speaking, SMD is the diameter you get by weighting with volume / surface area, and it is the most natural average when you care about evaporation and combustion. Evaporation rate scales with surface area, and the fuel mass you want to burn scales with volume. Smaller SMD means more specific surface, so droplets vaporise and mix with air faster. Diesel targets 5-20 μm, GDI 15-30 μm. The Nukiyama-Tanasawa correlation SMD ∝ d·We^(-0.32) tells you to cut SMD by using a smaller hole or raising injection pressure to push up the Weber number.
🙋
How do I set the cone angle? Wider feels like it should mix with more air.
🎓
That is the classic design tension. Reitz-Bracco tan(θ/2) = √(ρ_g/ρ_l)·4π·A/(3√3) shows the cone widens as in-cylinder gas density ρ_g rises — diesel high-compression gives 10-20°, GDI with swirl can reach 30-80°. But too wide and fuel impinges on the piston crown or chamber walls, dirtying the catalyst with HC and PM. Diesel aims for "fits inside the piston bowl", GDI for "reaches the spark plug", so the optimum changes with the application.
🙋
Penetration appears as a stat too. Is longer better?
🎓
Not always — too long or too short both hurt. The Hiroyasu-Arai correlation S ∝ (ΔP/ρ_g)^0.25·√(d·t) says penetration grows with pressure and time and shrinks with ambient density. Too short and the spray hangs near the injector, wasting chamber air; too long and it crashes into the piston, producing wall film and smoke. Diesel bore ≈ 80 mm typically wants 5-8 cm of penetration. With the defaults, the "Penetration" stat shows 8.2 cm. Raise pressure and it grows; raise ambient density and it shrinks.
🙋
One last thing — what is "multi-injection (Pre-Pilot-Main-After)" for?
🎓
It is what makes common rail so flexible. You can fire 5-9 events per cycle. A Pilot event pre-heats the chamber, cutting ignition delay, diesel knock and NOx. The Main event does the bulk of the burn, After extends combustion to re-burn soot, and Post injects extra fuel to regenerate the DPF. This simulator looks at a single event, but real engines combine these with EGR, SCR and DPF to meet Euro 7 or CARB ULEV — that is modern diesel development.
Frequently Asked Questions
Diesel ignites by auto-ignition, so fuel must be sprayed directly into the hot, dense (30-70 bar) combustion chamber and atomised plus mixed with air in roughly 1-2 ms. Common-rail systems run at 1500-2500 bar so that Bernoulli's v = Cd·√(2ΔP/ρ) gives 400-600 m/s injection velocity and the Weber number stays high enough to shatter the liquid column. GDI (gasoline direct injection) ignites with a spark near top dead centre, so it does not need instantaneous atomisation and 100-350 bar is enough; port injection sprays into the intake port where fuel has plenty of time to mix, so 3-10 bar is sufficient.
Mostly yes. SMD is the diameter weighted by volume / surface area, so it governs evaporation and combustion rate: smaller SMD means more specific surface, faster vaporisation, faster mixing and faster combustion. Diesel sprays target 5-20 μm and GDI 15-30 μm. Going extremely small has drawbacks though — the spray may evaporate before reaching the piston bowl, or penetration collapses so fuel cannot reach the far side of the chamber. The Nukiyama-Tanasawa correlation SMD ∝ d·We^(-0.32) says you cut SMD by using a smaller nozzle hole or by raising injection pressure (Weber number).
The Reitz-Bracco model gives tan(θ/2) = √(ρ_g/ρ_l)·4π·A/(3√3), so cone angle widens as ambient gas density ρ_g rises. Diesel under high compression (ρ_g ≈ 15-30 kg/m³) gives 10-20°; GDI with swirl can reach 30-80°. Wider cones improve air utilisation, but more fuel hits the piston crown and chamber walls, raising HC and PM. Diesel aims for 'fits inside the piston bowl', GDI for 'reaches the spark plug' — the optimum changes with the application.
Common-rail systems can split up to 5-9 events per cycle, each with a job. Pre / Pilot pre-heats the chamber, cutting ignition delay, diesel knock and NOx. Main does the bulk of combustion, After extends the burn to re-oxidise soot, and Post adds fuel for DPF regeneration. This simulator looks at a single event, but real engines combine these with EGR, SCR and DPF to meet Euro 7 and CARB ULEV emissions limits.
Real-world applications
Common-rail diesel passenger cars and trucks: 1500-2500 bar, 7-10 hole piezo injectors with Pre-Pilot-Main-After multi-injection is the modern standard. The SMD of 5-10 μm, cone of 6-10° and penetration of 5-10 cm that this tool predicts are tailored to the piston-bowl diameter and combustion-chamber volume, and the CO₂-NOx-PM trade-off is closed out by combining EGR, SCR and DPF to meet Euro 7 or the Japanese Post New Long-Term standard.
GDI (gasoline direct injection) engines: 100-350 bar, 6-8 hole side-feed multi-hole or spray-guided architectures. They use stratified combustion for fuel economy at part load and switch to homogeneous combustion at full load, so cone angle 30-80° and SMD 15-25 μm are tuned across the load map. Poor atomisation drives up particle number (PN); to clear Euro 6d-Temp's PN limit of 6×10¹¹ #/km a gasoline particulate filter (GPF) is often added.
Marine 2-stroke and stationary diesels: bore 500-900 mm, injection pressure 800-1500 bar, nozzle 400-700 μm running on heavy fuel. The simulator's parameter range used at the upper end gives SMD 30-60 μm — coarser droplets — but the chamber is huge, so penetration over 30 cm and long burn times still produce complete combustion. IMO Tier III is reached by combining SCR and EGR.
Lagrangian spray models in CAE (KIVA, CONVERGE, OpenFOAM): production CFD tracks discrete particles with Reitz's WAVE / KH-RT breakup, coupled with collision, evaporation and turbulent dispersion submodels. The 0-D correlations in this tool are useful for setting CFD inlet boundary conditions or as a sanity check on the resulting SMD, cone angle and penetration — orders of magnitude apart usually signal a setup error.
Common misconceptions and pitfalls
The first big pitfall is treating Bernoulli velocity as the real injection velocity. This tool uses v = Cd·√(2ΔP/ρ) with Cd = 0.7, but real discharge coefficients move between 0.6 and 0.85 depending on nozzle shape (VCO, SAC, k-factor), needle lift transients and cavitation. Just before end-of-injection the needle is barely lifted, Cd drops, the cone is disturbed and SMD worsens — the well-known "end-of-injection coarsening". Cd = 0.7 is fine for early-stage 0-D sizing, but downstream you need CFD with cavitation and turbulent gas-liquid coupling.
Second, do not treat the Nukiyama-Tanasawa constants as gospel. SMD = 4.12·d·We^(-0.32)·Re^(-0.07)·(ρ_g/ρ_l)^(-0.18) was fitted to axisymmetric sprays in the original work, and modern diesel or GDI nozzles routinely scatter by ±50% around it. Biodiesel (FAME) with its higher viscosity and surface tension breaks up later and produces larger SMD than the correlation predicts. Calibrate with PDPA (phase Doppler) or Mie-scattering measurements rather than trusting a correlation.
Finally, "wider cone = better combustion" is too simple. Reitz-Bracco predicts the initial liquid-core cone; the vapor-phase cone observed in real sprays is 1.5-2× wider due to gas entrainment. Over-widen the cone in GDI and droplets wet the spark plug, causing misfires; in diesel they hit the piston crown and produce smoke. Cone angle has to be designed together with bore diameter, bowl diameter and swirl ratio, never on its own.
How to Use
Enter injection pressure (MPa) for your injector type: 1600–2200 MPa for common-rail diesel, 5–12 MPa for port-injection, 200–350 MPa for GDI.
Set ambient density (kg/m³)—typically 1.2 for atmospheric air or 3.5–8.5 for high-pressure chamber conditions.
Input nozzle hole diameter (μm): 50–150 μm for diesel, 200–300 μm for port-injection.
Specify injection duration (ms): 0.5–5 ms for transient events or continuous spray analysis.
Read six outputs: velocity, mass flow, mass per cycle, cone angle, SMD, and penetration depth.
Worked Example
Common-rail diesel injector: 1800 MPa pressure, 1.2 kg/m³ ambient (sea level), 90 μm nozzle hole, 2.0 ms pulse. Solver yields: injection velocity 565 m/s, total mass flow 0.048 kg/s, mass per cycle 96 mg, spray cone angle 22.5°, SMD 18.4 μm, spray penetration 8.2 cm at 1 ms. These values match experimental PIV and laser-diffraction measurement ranges for modern Bosch CRi3 and Delphi ECD injectors.
Practical Notes
Higher injection pressure (>2000 MPa) reduces SMD and widens cone angle, improving fuel atomization and combustion efficiency in heavy-duty diesel engines.
Nozzle erosion increases hole diameter 5–10% over 500 million cycles; simulate aged holes to predict emission drift.
Ambient density dominates penetration length; in turbocharged boosted chambers (8 kg/m³), penetration drops 60% versus naturally aspirated conditions.
GDI injectors show non-uniform spray patterns; use average SMD cautiously and validate with high-speed imaging.