SI Combustion Cylinder

Spark-ignited, four-stroke internal combustion cylinder

Since R2022a

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Libraries:
Simscape / Driveline / Engines & Motors / Engine Subcomponents

Description

The SI Combustion Cylinder block represents the crank-angle-resolved, instantaneous pressure production dynamics of a spark-ignited, four-stroke internal combustion engine cylinder. You can use this block as a subcomponent in a composite internal combustion engine block, such as the Spark Ignition Engine block. The block computes the instantaneous cylinder pressure and also provides optional outputs to collect additional information. To obtain the instantaneous torque, connect one or more of these blocks with the Crankshaft block. This page uses these common industry abbreviations:

• TDC — Top dead center

• BDC — Bottom dead center

• IVO — Intake valve open

• IVC — Intake valve close

• EVO — Exhaust valve open

• EVC — Exhaust valve close

• VVT — Variable valve timing

Equations

The block depends on the angular position of the crank, θ, where TDC is 0°, and the crank position can range from 0° to 720°. Using this definition, 0° is the intake TDC, and 360° is the combustion TDC. The block calculates the instantaneous cylinder volume as a function of the crank position such that

$$V\left(\theta \right)=V_{cl}+V_{displ}\cdot \frac{1}{2}\left(\frac{l}{a}+1-\cos \theta -\sqrt{{\left(\frac{l}{a}\right)}^2-{\sin }^2\theta }\right),$$

where:

• V_cl is the clearance volume.

• V_displ is the displacement volume, which the block finds from the Bore and Stroke parameters.

• l is the Connecting-rod length parameter.

• a is the crank radius.

The block calculates V_cl as

$$V_{cl}=\frac{V_{displ}}{r_c-1},$$

where r_c is the Compression ratio parameter. The time derivative of V(θ) scales the instantaneous power that the cylinder generates, Q(θ), such that

$$Q_{cyl}(\theta )=\left(P_{cyl}\left(\theta \right)-P_{amb}\right)\cdot \frac{d}{dt}V\left(\theta \right),$$

where P_cyl(θ) is the cylinder pressure as a function of the crank position, and P_amb is the Ambient pressure parameter. The block formulation to compute P_cyl(θ) depends on which part of the stroke cycle is active in the cylinder.

Valve Timing and Stroke Cycle

These plots show the stroke status with respect to the crank position. The spiral line represents the crank rotation. The spiral begins at IVO and ends at EVC. Depending on timing, there may be overlapping times where both the intake and exhaust valves have the same condition. Positive overlap happens when IVO occurs before EVC. Negative overlap happens when EVC occurs before IVO. Using this definition, there can be six unique modes depending on whether the overlap occurs before, during, or after TDC. The block approximates these modes.

This plot shows a typical valve timing scenario where IVO occurs 15 degrees before TDC, and IVC occurs 50 degrees after BDC. EVO occurs at 55 degrees before BDC, and EVC occurs at 10 degrees after TDC. Note the 25 degrees of positive overlap where the intake valves open before the exhaust valves close. The table demonstrates the six valve overlap modes.

	Before TDC	During TDC	After TDC
Positive Overlap
Negative Overlap

You adjust the parameters in the Valves section to represent either an Otto cycle or an Atkinson cycle. Gasoline engines typically use the Otto cycle due to its balance of power and efficiency. Hybrid engines and some modern gasoline engines use the Atkinson cycle to enhance fuel efficiency by sacrificing power output. Using Atkinson cycle timings for either the Spark Ignition Engine or SI Combustion Cylinder blocks results in:

• A smaller effective compression ratio and larger expansion ratio

• Improved fuel efficiency

• Reduced torque and power for a given displacement

The figure shows a comparison of typical timings for the Otto cycle and the Atkinson cycle :

Cylinder Modes

During normal operation, the engine cylinders require a minimum engine speed to maintain stable combustion. However, during transient operations, such as using the starter motor to turn the crank, the cylinder completes stroke cycles without attaining stable combustion. The block takes these slow engine speed interactions into account such that the block considers 18 possible modes. These are the slow engine operation modes:

1. Slow Intake

2. Slow Compression-Expansion

3. Slow Exhaust

4. Slow Positive Overlap Before TDC

5. Slow Positive Overlap During TDC

6. Slow Positive Overlap After TDC

7. Slow Negative Overlap Before TDC

8. Slow Negative Overlap During TDC

9. Slow Negative Overlap After TDC

These are the regular engine operation modes:

10. Intake

11. Compression-Expansion

12. Exhaust

13. Positive Overlap Before TDC

14. Positive Overlap During TDC

15. Positive Overlap After TDC

16. Negative Overlap Before TDC

17. Negative Overlap During TDC

18. Negative Overlap After TDC

The block gives each discrete mode a transition constraint by using the mode chart feature. The table shows which transitions the block allows.

Mode Transition	Allowed Modes
Slow ↣ Slow	1 ↣ 2 2 ↣ 3 3 ↣ 4, 5, 6, 7, 8, 9 4, 5, 6, 7, 8, 9 ↣ 1
Slow ↣ Regular	4, 5, 6, 7, 8, 9 ↣ 10
Regular ↣ Regular	10 ↣ 11 11 ↣ 12 12 ↣ 13, 14, 15, 16, 17, 18 13, 14, 15, 16, 17, 18 ↣ 10
Regular ↣ Slow	10 ↣ 2 11 ↣ 3 12 ↣ 4, 5, 6, 7, 8, 9 13, 14, 15, 16, 17, 18 ↣ 1

The flow chart in the figure visually depicts how the block steps through the modes.

Mode Transition Flowchart

The block captures the effect of the valve timings on the effective compression ratio and considers the effect of IVC much later than BDC which can reduce the amount of air charged in the combustion cylinder. However, the block ignores internal exhaust gas recirculation.

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

Input

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.

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 milliseconds. 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, set Input injector pulse width to On.

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, set Input injector pulse width to Off.

Pim — Intake manifold pressure input, kPa

physical signal

Physical signal input associated with the intake manifold, in kPa. When you set Compute air intake dynamics to Off, 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.

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, set Intake Variable Valve Timing to On.

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 to On.

Pback — Exhaust back pressure input, kPa

physical signal

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

Dependencies

To enable this port, set Input back pressure to On.

CrkPos — Crank position, deg

physical signal

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

Spd — Engine rotational speed, rad/s

physical signal

Physical signal input associated with the engine rotational speed, in rad/s.

Output

CylPwr — Cylinder power, W

physical signal

Physical signal output associated with the cylinder power, in W.

Weo — Engine outlet gas energy flow, W

physical signal

Physical signal output associated with the engine outlet gas energy flow, in W.

Dependencies

To enable this port, set Engine outlet gas energy flow to On.

Vcyl — Cylinder volume output, cm^3

physical signal

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

Dependencies

To enable this port, set Cylinder volume to On.

Pcyl — Cylinder pressure output, MPa

physical signal

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

Dependencies

To enable this port, set Cylinder pressure to On.

Tcyl — Cylinder temperature output, K

physical signal

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

Dependencies

To enable this port, set Cylinder temperature to On.

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, set Air-fuel ratio to On.

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, set Air mass flow to On.

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, set Fuel mass flow to On.

Parameters

Mechanical

Number of cylinders as a system — Total combustion cylinder count in series

1 (default) | positive scalar

Total number of combustion cylinders connected to a single Crank Shaft block. The value of this parameter should be the same as the number of SI Combustion Cylinder blocks in the system.

Cylinder number — Cylinder number in series

1 (default) | positive scalar

Assignment number for this SI Combustion Cylinder block. Each SI Combustion Cylinder block must use a unique value for Cylinder number.

Bore — Cylinder diameter

75.0 mm (default) | positive scalar

Diameter of the piston cylinder.

Stroke — Piston travel distance

84.7 mm (default) | positive scalar

Distance the piston head travels within the cylinder.

Connecting-rod length — Length of connecting rod

141 mm (default) | positive scalar

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

Compression ratio — Static compression ratio

11.0 (default) | positive scalar

Ratio of the maximum to minimum cylinder volume.

Ambient

Ambient pressure — Reference air pressure

101.325 kPa (default) | positive scalar

Pressure of the air entering the intake.

Ambient temperature — Reference temperature

(273.15 + 25) K (default) | positive scalar

Temperature of the air entering the intake.

Ambient air density — Reference density

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

Density of the air entering the intake.

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.

Valves

Discharge coefficient for intake valve — Intake valve discharge coefficient

0.5 (default) | positive scalar

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

Intake valve open before TDC — IVO crank position before TDC

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

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

Intake valve close after BDC — IVC crank position after BDC

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

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

Exhaust valve open before BDC — EVO crank position before BDC

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

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

Exhaust valve close after TDC — EVC crank position after TDC

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

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

Intake Variable Valve Timing — Option to control intake VVT

On (default) | Off

Option to control the intake valve timing. Set this parameter to On to enable the InVT port.

Exhaust Variable Valve Timing — Option to control exhaust VVT

On (default) | Off

Option to control the exhaust valve timing. Set this parameter to On to enable the ExVT port.

Combustion

Lower heating value for gasoline — Fuel net calorific value

44.3e+6 J/kg (default)

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

Input injector pulse width — Option to input injector pulse width

On (default) | Off

Option to specify the injector pulse width. Set this parameter to On to enable the InjPw port.

Injector slope — Injector slope

6.5 mg/ms (default) | positive scalar

Slope of the fuel injector mass flow rate.

Dependencies

To enable this parameter, set Input injector pulse width to On.

Combustion duration — Combustion duration

50 deg (default) | positive scalar

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

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

60 s (default) | positive scalar

Time constant for the cylinder pressure 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.

Exhaust

Exhaust gas temperature decay time constant — Exhaust temperature decay rate

5 ms (default) | positive scalar

Time constant to specify the exhaust gas temperature decay.

Input back pressure — Back pressure input option

On (default) | Off

Option to input the back-pressure pressure constant and speed constant. Set this parameter to On to enable the Pback port.

Back-pressure pressure constant — Pressure constant for back-pressure

50 kPa (default) | positive scalar

Back-pressure pressure constant.

Dependencies

To enable this parameter, set Input back pressure to Off.

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

6000 rpm (default) | positive scalar

Back-pressure speed constant.

Dependencies

To enable this parameter, set Input back pressure to Off.

Simulation

Engine speed simulation limit — Maximum engine speed

8500 rpm (default) | positive scalar

Maximum engine speed allowed during the simulation. If the engine speed exceeds this value, the block prevents combustion.

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

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

Crank position at the start of the simulation.

Initial engine speed — Initial engine speed

0 rpm (default) | nonnegative scalar

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

Output

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.

Cylinder pressure — Option to output cylinder pressure

On (default) | Off

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

Cylinder temperature — Option to output cylinder temperature

On (default) | Off

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

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.

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.

Fuel mass flow — Option to output fuel mass flow

On (default) | Off

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

Version History

Introduced in R2022a

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.