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CI Engine Speed-Density Air Mass Flow Model

To calculate the air mass flow in the compression-ignition (CI) engine, the CI Core Engine block uses a speed-density air mass flow model. The speed-density model uses the speed-density equation to calculate the engine air mass flow. The equation relates the engine air mass flow to the intake manifold gas pressure, intake manifold gas temperature, and engine speed. In the CI Core Engine block, the air mass flow and the cylinder air mass determine the engine load.

To determine the air mass flow, the speed-density air mass flow model uses this speed-density equation at the intake manifold and the volumetric efficiency. The model subtracts the exhaust gas recirculation (EGR) burned gas from the mass flow at the intake port.

m˙port=MAPVdN[1 min60s]CpsRairMATηvm˙air=m˙portm˙egr

The speed-density air mass flow model uses a volumetric efficiency lookup table to determine the volumetric efficiency.

The volumetric efficiency lookup table is a function of the intake manifold absolute pressure at intake valve closing (IVC) and engine speed



  • ηv is engine volumetric efficiency, dimensionless.

  • MAP is intake manifold absolute pressure, in KPa.

  • N is engine speed, in rpm.

To create the volumetric efficiency table, use the air mass flow rate from measured engine performance data and the speed-density equation.

ηv=CpsRairMATMAPVdN[1 min60s]m˙air

To calculate the engine load, the block divides the calculated unburned air mass by the nominal cylinder air mass. The nominal cylinder air mass is the mass of air (in kg) in a cylinder with the piston at bottom dead center (BDC), at standard air temperature and pressure.



The model implements equations that use these variables.


Engine air mass flow


Cycle average intake manifold pressure


Total engine air mass flow at intake ports, including EGR flow


Recirculated burned gas mass flow entering engine intake port


Displaced volume


Engine speed


Crankshaft revolutions per power stroke


Ideal gas constant for air and burned gas mixture


Cycle average intake manifold gas absolute temperature


Engine volumetric efficiency


Engine volumetric efficiency lookup table


Engine load (normalized cylinder air mass) at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles


Nominal engine cylinder air mass at standard temperature and pressure; piston at bottom dead center (BDC) maximum volume

PstdStandard pressure
TstdStandard temperature


[1] Heywood, John B. Internal Combustion Engine Fundamentals. New York: McGraw-Hill, 1988.

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