Spark Ignition Engine

R2026b

Spark ignition engine

Since R2022a

• 

Spark Ignition Engine block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simscape / Driveline / Engines & Motors

Description

The Spark Ignition Engine block represents a naturally aspirated, spark-ignited internal combustion engine. The engine can be an arbitrary configuration of one to four cylinders. This block is a composite block that uses a subcomponent implementation of these blocks:

• The SI Combustion Cylinder block represents an individual spark ignited combustion cylinder. The Spark Ignition Engine block controls how many SI Combustion Cylinder blocks it uses in the subcomponent implementation based on the value of the Number of cylinders parameter. You can adjust the valve timing to suit traditional gasoline engine applications as well as hybrid electric and plug-in hybrid electric vehicle applications.

• The Ignition Trigger block controls the igniter timing for the SI Combustion Cylinder blocks.

• The Air Intake block provides the intake manifold pressure to the SI Combustion Cylinder block. To enable the air intake implementation, select Compute air intake dynamics.

• The Crank Shaft block connects to each SI Combustion Cylinder block to report the crank-angle-resolved instantaneous torque.

• The Exhaust Manifold Thermal block abstracts the thermodynamics of the exhaust manifold and reports the temperature of the exhaust manifold. To compute the exhaust manifold thermal effects, select Compute exhaust manifold temperature.

Many of the Spark Ignition Engine parameters are identical to the parameters in the subcomponent blocks, and when the block implements subcomponent blocks, it uses the equations from those blocks. You can learn more about how the Spark Ignition Engine block uses each parameter by visiting the reference pages for the subcomponent blocks. You can use this block to learn how to create your own implementations of the subcomponent blocks by viewing the source code.

To visualize the engine performance properties for the block, click the View live script button in the Engine properties parameter.

Equations

The block derives performance information about the engine components using their respective relationship with the crank position, θ, where 0 degrees ≤ θ < 720 degrees. The block defines the crank starting position as the intake stroke at top dead center. For a four-stroke engine, each cylinder is uniquely affiliated with a crank position, where the crank position for a given cylinder i is θ_i. The block derives the angular velocity from θ as

$$\omega =\frac{d}{dx}\theta .$$

The block sets the first cylinder θ₁ = θ regardless of how many cylinders you simulate. When you set Number of cylinders to Two cylinders, the block calculates θ₂ as

$${\theta }_2={\theta }_1+\Delta ,$$

where Δ is the Spark angle difference parameter.

When you set Number of cylinders to Three cylinders, the block assumes that the cylinders are evenly phased such that

$$\begin{array}{l}{\theta }_2={\theta }_1+\left(1\cdot \frac{720°}{3}\right)\\ {\theta }_3={\theta }_1+\left(2\cdot \frac{720°}{3}\right)\end{array}$$

When you set Number of cylinders to Four cylinders, the block assumes that the spark angle difference is 180 degrees. You can select the firing order using the Firing order parameter.

Assumptions and Limitations

• The block ignores knocking and other combustion instabilities.

• The block ignores internal and external exhaust gas recirculation.

Examples

Single Cylinder Spark Ignition Engine

A crank-angle-resolved, naturally aspirated spark ignition engine. Control inputs such as throttle, intake VVT, air-to-fuel ratio, and spark advance vary during the simulation. You can simulate results from either an Otto cycle engine or an Atkinson cycle engine.

• Open Model

Ports

Inputs

IgSw — Ignitor switch, binary

physical signal

Physical signal output associated with the ignitor, where 0 turns off the ignitor and 1 turns on the ignitor.

Dependencies

To enable this port, set Spark input type to Fixed or Spark angle.

Programmatic Use

Port: IGSW

Pim — Intake manifold pressure input, kPa

physical signal

Physical signal input associated with the intake manifold, in kPa. When you clear Compute air intake dynamics, you supply the intake manifold pressure using this port. You can use this port as an alternative to providing the throttle command to port Thr.

Dependencies

To enable this port, clear Compute air intake dynamics.

Programmatic Use

Port: Pim_in

Thr — Throttle command input, unitless

physical signal

Physical signal input associated with the normalized throttle command, where 0 represents a fully closed throttle, and 1 represents a fully open throttle. The block maps this input to a throttle-open angle between 0 and 90 degrees.

Dependencies

To enable this port, select Compute air intake dynamics.

Programmatic Use

Port: thr_cmd

InVT — Intake Variable Valve Timing input, deg

physical signal

Physical signal input associated with the angle to shift the intake valve open and close timings, in degrees. Positive values advance the timing and negative values delay the timing.

Dependencies

To enable this port, select Intake Variable Valve Timing.

Programmatic Use

Port: dIV

ExVT — Exhaust Variable Valve Timing input, deg

physical signal

Physical signal input associated with angle to shift the exhaust valve open and close timings, in degrees. Negative values advance the timing and positive values delay the timing.

Dependencies

To enable this port, set Exhaust Variable Valve Timing.

Programmatic Use

Port: dEV

AfrCmd — Air-fuel ratio command input, unitless

physical signal

Physical signal input associated with the unitless air-fuel ratio command. Note that this is different from the stoichiometric air-fuel ratio for gasoline, which the block fixes at 14.6.

Dependencies

To enable this port, select Input air-fuel ratio and clear Input injector pulse width.

Programmatic Use

Port: afr_in

InjPw — Injector pulse width input, ms

physical signal

Physical signal input associated with the duration during which the injector is open to inject fuel, in ms. The block multiplies this signal by the value of the Injector slope parameter to calculate the amount of fuel that the injector releases during one pulse.

Dependencies

To enable this port, select Input air-fuel ratio and Input injector pulse width.

Programmatic Use

Port: InjPw_in

SA — Spark angle input, deg

physical signal

Physical signal input associated with the spark angle before top dead center, in deg.

Dependencies

To enable this port, set Spark input type to Spark angle.

Programmatic Use

Port: sa

IgTrig — Ignition trigger input, unitless

physical signal

Physical signal input associated with the ignition trigger. The block treats a rise from 0 to 1 as a trigger. The input must return to 0 before the block accepts another trigger.

Dependencies

To enable this port, set Spark input type to Spark trigger event.

Programmatic Use

Port: fire

Pback — Exhaust back pressure input, kPa

physical signal

Physical signal input associated with the exhaust back pressure, in kPa.

Dependencies

To enable this port, select Input back pressure.

Outputs

AvrTrq — Cycle-average net indicated torque output, N*m

physical signal

Physical signal output associated with the cycle-average net indicated torque in Nm.

Dependencies

To enable this port, select Cycle-average net indicated torque.

Programmatic Use

Port: trq_avr_out

AvrSpd — Cycle-average speed output, rad/s

physical signal

Physical signal output associated with the cycle-average speed output, in rad/s.

Dependencies

To enable this port, select Cycle-average speed.

Programmatic Use

Port: w_avr_out

Pim — Intake manifold pressure output, kPa

physical signal

Physical signal output associated with the intake manifold pressure, in kPa.

Dependencies

To enable this port, select Intake manifold pressure.

Programmatic Use

Port: Pim_out

crkpos — Crank position output, deg

physical signal

Physical signal output associated with the crank position, in degrees.

Dependencies

To enable this port, select Crank position.

Programmatic Use

Port: crkpos

AirMassFlow — Cylinder air mass flow output, g/s

physical signal

Physical signal output associated with the air mass flow, in g/s.

Dependencies

To enable this port, select Cylinder air mass flow .

Programmatic Use

Port: airMassFlow_out

FuelMassFlow — Cylinder fuel mass flow output, g/s

physical signal

Physical signal output associated with the fuel mass flow, in g/s.

Dependencies

To enable this port, select Cylinder fuel mass flow.

Programmatic Use

Port: fuelMassFlow_out

AFR — Air-fuel ratio output, unitless

physical signal

Physical signal output associated with the unitless air-fuel ratio response that the block attains during operation. Note that this is different from the stoichiometric air-fuel ratio for gasoline, which the block fixes at 14.6.

Dependencies

To enable this port, select Air-fuel ratio.

Programmatic Use

Port: afr_out

Vcyl — Cylinder volume output, cm^3

physical signal

Physical signal output associated with the cylinder volume, in cm³.

Dependencies

To enable this port, select Cylinder volume.

Programmatic Use

Port: V_out

Pcyl — Cylinder pressure output, MPa

physical signal

Physical signal output associated with the cylinder pressure, in MPa.

Dependencies

To enable this port, select Cylinder pressure.

Programmatic Use

Port: P_out

Tcyl — Cylinder temperature output, K

physical signal

Physical signal output associated with the cylinder temperature, in K.

Dependencies

To enable this port, select Cylinder temperature.

Programmatic Use

Port: T_out

Conserving

F — Crank shaft driveline connection

mechanical rotational

Mechanical rotational conserving port associated with the crankshaft connection to the driveline. Include friction and inertia here to simulate engine load or directly connect other driveline elements.

Programmatic Use

Port: F

Parameters

Mechanical

Number of cylinders — Total cylinder count

Single Cylinder (default) | Two Cylinders | Three Cylinders | Four Cylinders

Number of spark ignition cylinders.

Programmatic Use

Parameter:	numCyls
Values:	"sdl.enum.engineNumCylinders.One" | "sdl.enum.engineNumCylinders.Two" | "sdl.enum.engineNumCylinders.Three" | "sdl.enum.engineNumCylinders.Four"

Spark angle difference — Two-cylinder engine spark angle phase

270 deg (default) | positive scalar

Spark angle difference for two-cylinder engines.

Dependencies

To enable this parameter, set Number of cylinders to Two Cylinders.

Programmatic Use

Parameter: twoCylSADiff

Firing order — Ignition order for four cylinder engines

1-3-4-2 (default) | 1-3-2-4

Firing order for four-cylinder engines. Firing order is engine specific, but your selection for this parameter will not affect the block performance. Controller development requires this information.

Dependencies

To enable this parameter, set Number of cylinders to Four Cylinders.

Programmatic Use

Parameter:	L4FiringOrder
Values:	"sdl.enum.engineFiringOrderFourCylinders.L4_1342" | "sdl.enum.engineFiringOrderFourCylinders.L4_1324"

Bore — Cylinder diameter

72.5 mm (default) | positive scalar

Diameter of the piston cylinder.

Programmatic Use

Parameter: bore

Stroke — Piston travel distance

80.5 mm (default) | positive scalar

Distance the piston head travels within the cylinder.

Programmatic Use

Parameter: stroke

Connecting-rod length — Length of connecting rod

141 mm (default) | positive scalar

Length of the piston connecting rod from hole center to hole center.

Programmatic Use

Parameter: conrod

Compression ratio — Static compression ratio

11.0 (default) | positive scalar

Ratio of the maximum to minimum cylinder volume.

Programmatic Use

Parameter: CR

Ambient

Ambient pressure — Reference air pressure

101.325 kPa (default) | positive scalar

Pressure of the air entering the intake.

Programmatic Use

Parameter: P_amb

Ambient temperature — Reference temperature

298.15 K (default) | positive scalar

Temperature of the air entering the intake.

Programmatic Use

Parameter: T_amb

Ambient air density — Reference density

1.225 mg/cm^3 (default) | positive scalar

Density of the air entering the intake.

Programmatic Use

Parameter: rho_air

Specific gas constant of dry air — Specific gas constant of dry air

288.1965 J/(K*kg) (default) | positive scalar

Specific gas constant of dry air.

Programmatic Use

Parameter: R_air

Air Intake

Compute air intake dynamics — Option to compute air intake dynamics

on (default) | off

Whether to compute the air intake dynamics. Selecting this parameter enables these parameters:

• Throttle response time constant

• Throttle rest angle

• Throttle plate diameter

• Throttle leakage area

• Intake manifold volume

Programmatic Use

Parameter:	UseAirIntake
Values:	"true" | "false"

Throttle response time constant — Throttle response time constant

0.1 s (default) | positive scalar

Time constant associated with the response rate of the engine to the throttle command.

Dependencies

To enable this parameter, select Compute air intake dynamics.

Programmatic Use

Parameter: c_thr

Throttle rest angle — Released throttle position

3 deg (default) | positive scalar

Radial distance from the resting throttle position to 0 degrees.

Dependencies

To enable this parameter, select Compute air intake dynamics.

Programmatic Use

Parameter: thr_rest

Throttle plate diameter — Throttle plate diameter

5 cm (default) | positive scalar

Diameter of the butterfly valve disc in the throttle body.

Dependencies

To enable this parameter, select Compute air intake dynamics.

Programmatic Use

Parameter: D_plate

Throttle leakage area — Throttle leakage area

1 cm^2 (default) | nonnegative scalar

Cumulative area of the throttle leakage.

Dependencies

To enable this parameter, select Compute air intake dynamics.

Programmatic Use

Parameter: S_leak

Intake manifold volume — Intake manifold volume

1000 cm^3 (default) | positive scalar

Volumetric capacity of the intake manifold.

Dependencies

To enable this parameter, select Compute air intake dynamics.

Programmatic Use

Parameter: V_im

Valves

Discharge coefficient for intake valve — Intake valve discharge coefficient

0.9 (default) | positive scalar

Ratio of actual discharge to ideal discharge for the intake valve.

Programmatic Use

Parameter: Cd_in

Intake valve open before TDC — IVO crank position

15 deg (default) | scalar in the range [-360,360]

Crank position before top dead center at which the intake valve opens. Measure from top dead center to the crank position in the opposite direction of the crank rotation.

Programmatic Use

Parameter: IVO_0

Intake valve close after BDC — IVC crank position

50 deg (default) | scalar in the range [-360,360]

Crank position after bottom dead center at which the intake valve closes. Measure from bottom dead center to the crank position in the same direction of the crank rotation.

Programmatic Use

Parameter: IVC_0

Exhaust valve open before BDC — EVO crank position

55 deg (default) | scalar in the range [-360,360]

Crank position before bottom dead center at which the exhaust valve opens. Measure from bottom dead center to the crank position in the opposite direction of the crank rotation.

Programmatic Use

Parameter: EVO_0

Exhaust valve close after TDC — EVC crank position

10 deg (default) | scalar in the range [-360,360]

Crank position after top dead center at which the exhaust valve closes. Measure from top dead center to the crank position in the same direction of the crank rotation.

Programmatic Use

Parameter: EVC_0

Intake Variable Valve Timing — Intake variable valve timing option

on (default) | off

Whether to control the intake valve timing. Selecting this parameter enables the InVT port.

Programmatic Use

Parameter:	UseInVVT
Values:	"true" | "false"

Exhaust Variable Valve Timing — Exhaust variable valve timing option

on (default) | off

Whether to control the exhaust valve timing. Selecting this port enables the ExVT port.

Programmatic Use

Parameter:	UseExVVT
Values:	"true" | "false"

Fuel

Lower heating value for gasoline — Fuel net calorific value

44.3 MJ/kg (default) | positive scalar

Lower heating value for gasoline. This value is also known as the fuel net calorific value.

Programmatic Use

Parameter: q_LHV

Input air-fuel ratio — Air-fuel ratio parameter option

on (default) | off

Whether to specify the air-fuel ratio by using the Air-fuel ratio parameter or the AfrCmd port.

Air-fuel ratio — Air-fuel ratio

14.6 (default) | positive scalar

Mixture ratio of air to fuel.

Dependencies

To enable this parameter, clear Input air-fuel ratio.

Input injector pulse width — Pulse width parameterization

on (default) | off

Whether to specify the injector pulse width.

Dependencies

To enable this parameter, select Input air-fuel ratio.

Programmatic Use

Parameter:	InputInjPw
Values:	"true" | "false"

Injector slope — Injector slope

6.5 mg/ms (default) | positive scalar

Slope of the fuel injector mass flow rate.

Dependencies

To enable this parameter, select Input air-fuel ratio and Input injector pulse width.

Programmatic Use

Parameter: Sinj

Combustion

Spark input type — Spark input type

Fixed (default) | Spark angle | Spark trigger event

Whether to parameterize the spark input using a fixed value, spark angle, or spark trigger events.

Programmatic Use

Parameter:	SparkInputType
Values:	"sdl.enum.engineSparkInputType.Const" | "sdl.enum.engineSparkInputType.Angle" | "sdl.enum.engineSparkInputType.Trigger"

Spark advance BTDC — Spark advance before top dead center

20 deg (default) | positive scalar

Spark advance before top dead center.

Programmatic Use

Parameter: SA_const

Combustion duration — Combustion duration

50 deg (default) | positive scalar

Duration of combustion as a portion of the crank shaft rotation.

Programmatic Use

Parameter: comb_bd

Cylinder pressure slow decay time constant — Cylinder pressure slow decay rate

60 s (default) | positive scalar

Time constant for the cylinder pressure slow decay.

Programmatic Use

Parameter: dt_Pcyl_slow_decay

Cylinder temperature slow decay time constant — Cylinder temperature slow decay rate

600 s (default) | positive scalar

Time constant for the cylinder temperature slow decay.

Programmatic Use

Parameter: dt_Tcyl_slow_decay

Exhaust

Exhaust gas temperature decay time constant — Exhaust temperature decay rate

5 ms (default) | positive scalar

Time constant for the exhaust gas temperature decay.

Programmatic Use

Parameter: dt_exh_decay

Input back pressure — Back pressure input option

on (default) | off

Option to input the back-pressure pressure constant and speed constant.

Programmatic Use

Parameter:	InputBackPressure
Values:	"true" | "false"

Back-pressure pressure constant — Pressure constant for back pressure

50 kPa (default) | positive scalar

Back-pressure pressure constant.

Dependencies

To enable this parameter, clear Input back pressure.

Programmatic Use

Parameter: dP_exh

Back-pressure speed constant — Speed constant for back-pressure

6000 rpm (default) | positive scalar

Back-pressure speed constant.

Dependencies

To enable this parameter, clear Input back pressure.

Programmatic Use

Parameter: dw_exh

Exhaust manifold thermal effects — Enable exhaust manifold thermal model

on (default) | off

Whether to model thermal effects in the exhaust manifold. Selecting this parameter enables the exhaust manifold thermal model and the thermal port.

Programmatic Use

Parameter:	UseExhaustThermal
Values:	"true" | "false"

Compute exhaust manifold temperature — Option to compute exhaust manifold temperature

on (default) | off

Whether the block computes the exhaust manifold temperature. Selecting this parameter enables these parameters:

• Surface area of exhaust wall

• Mass of exhaust wall

• Heat capacity of exhaust wall

• Time constant of exhaust heat flow

• Convective heat transfer coefficient for the outer side of exhaust

• Radiation constant

• Stefan-Boltzmann constant

Programmatic Use

Parameter:	OutputTexh
Values:	"true" | "false"

Surface area of exhaust wall — Exhaust wall surface area

1 m^2 (default) | positive scalar

Surface area of the exhaust wall. This wall is only the surface area of the internal wall that makes contact with the exhaust.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: S_exh

Mass of exhaust wall — Exhaust wall total mass

5 kg (default)

Mass of the exhaust wall.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: M_exh

Heat capacity of exhaust wall — Exhaust wall heat capacity

100 J/(K*kg) (default) | positive scalar

Heat capacity of the exhaust wall.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: C_exh

Time constant of exhaust heat flow — Exhaust heat flow time constant

10 s (default) | positive scalar

Time constant for the rate of exhaust heat flow.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: k_gas

Convective heat transfer coefficient for the outer side of exhaust — Exhaust external convective heat transfer coefficient

100 W/(K*m^2) (default) | positive scalar

Convective heat transfer coefficient for the outer side of the exhaust.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: h_convection

Radiation constant — Exhaust radiation constant

0.3 (default) | positive scalar

Radiation constant of the exhaust.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: k_radiation

Stefan-Boltzmann constant — Stefan-Boltzmann constant of exhaust

5.7e-8 W/(K^4*m^2) (default) | positive scalar

Stefan-Boltzmann constant for the total exhaust.

Dependencies

To enable this parameter, select Compute exhaust manifold temperature.

Programmatic Use

Parameter: SB

Simulation

Initial intake manifold pressure — Initial pressure inside intake manifold

101.325 kPa (default) | positive scalar

Intake manifold pressure at the start of the simulation.

Programmatic Use

Parameter: Pim_0

Initial crank position (0-720 CAdeg) — Initial crank position

0 deg (default) | scalar in the range [0,720]

Crank position at the start of the simulation.

Programmatic Use

Parameter: ca0

Initial engine speed — Initial engine speed

0 rpm (default) | nonnegative scalar

Rotational speed of the engine at the start of the simulation.

Programmatic Use

Parameter: w0

Engine speed simulation limit — Maximum engine speed

8500 rpm (default) | positive scalar

Maximum engine speed allowed during the simulation. If the block exceeds this value, it will generate an error and stop the simulation.

Programmatic Use

Parameter: EngSpdSimLimit

Output

Cycle-average net indicated torque — Option to output cycle-average net indicated torque

off (default) | on

Whether to output the cycle-average net indicated torque from physical signal port AvrTrq.

Programmatic Use

Parameter:	OutputTorqueAvr
Values:	"true" | "false"

Cycle-average speed — Option to output cycle-average speed

off (default) | on

Whether to output the cycle-average speed from physical signal port AvrSpd.

Programmatic Use

Parameter:	OutputSpeedAvr
Values:	"true" | "false"

Crank position — Option to output crank position

off (default) | on

Whether to output the crank position from physical signal port crkpos.

Programmatic Use

Parameter:	OutputCrkpos
Values:	"true" | "false"

Air/fuel ratio — Option to output air/fuel ratio

off (default) | on

Whether to output the air/fuel ratio from physical signal port AFR.

Programmatic Use

Parameter: AFR_const

Parameter: OutputAFR

Engine outlet gas energy flow — Option to output engine outlet gas energy flow

off (default) | on

Whether to output engine outlet gas energy flow from physical signal port Weo.

Cylinder volume — Option to output the cylinder volume

on (default) | off

Whether to output the cylinder volume from physical signal port Vcyl.

Programmatic Use

Parameter:	OutputVcyl
Values:	"true" | "false"

Cylinder pressure — Option to output cylinder pressure

on (default) | off

Whether to output the cylinder pressure from physical signal port Pcyl.

Programmatic Use

Parameter:	OutputPcyl
Values:	"true" | "false"

Cylinder temperature — Option to output cylinder temperature

on (default) | off

Whether to output the cylinder temperature from physical signal port Tcyl.

Programmatic Use

Parameter:	OutputTcyl
Values:	"true" | "false"

Input air/fuel ratio — Option to output the air-to-fuel ratio

on (default) | off

Whether to output the air-to-fuel ratio from physical signal port AFR.

Programmatic Use

Parameter:	InputAFR
Values:	"true" | "false"

Air mass flow — Option to output cylinder air mass flow

on (default) | off

Whether to output the intake manifold pressure from physical signal port AirMassFlow.

Programmatic Use

Parameter:	OutputAirMassFlow
Values:	"true" | "false"

Fuel mass flow — Option to output fuel mass flow

on (default) | off

Whether to output the fuel mass flow from physical signal port FuelMassFlow.

Programmatic Use

Parameter:	OutputFuelMassFlow
Values:	"true" | "false"

Utilities

Engine properites — Visualize engine performance

button

Use the Open live script button to visualize engine performance properties.

Version History

Introduced in R2022a

R2025a: Enumeration Updates

These parameters now use a checkbox.

• Air-fuel ratio

• Air mass flow

• Compute air intake dynamics

• Compute exhaust manifold temperature

• Crank position

• Cycle-average net indicated torque

• Cycle-average speed

• Cylinder air mass flow

• Cylinder fuel mass flow

• Cylinder pressure

• Cylinder temperature

• Cylinder volume

• Engine outlet gas energy flow

• Exhaust Variable Valve Timing

• Fuel mass flow

• Input air/fuel ratio

• Input back pressure

• Input injector pulse width

• Intake manifold pressure

• Intake Variable Valve Timing

These parameters used drop downs in previous releases.

R2024b: Simulate an Atkinson cycle

When you adjust the intake and exhaust valve timings to align with the Atkinson cycle, the block demonstrates the expected engine behavior.