# SI Combustion Cylinder

Spark-ignited, four-stroke internal combustion cylinder

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• 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

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

where:

• Vcl is the clearance volume.

• Vdispl 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 Vcl as

`${V}_{cl}=\frac{{V}_{displ}}{{r}_{c}-1},$`

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

`${Q}_{cyl}\left(\theta \right)=\left({P}_{cyl}\left(\theta \right)-{P}_{amb}\right)\cdot \frac{d}{dt}V\left(\theta \right),$`

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

Valve Timing and Stroke Cycle

You can visualize the stroke status with respect to the crank position by using these plots. The plots show a spiral line that 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 TDCDuring TDCAfter TDC
Positive Overlap

Negative Overlap

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:

1. Intake

2. Compression-Expansion

3. Exhaust

4. Positive Overlap Before TDC

5. Positive Overlap During TDC

6. Positive Overlap After TDC

7. Negative Overlap Before TDC

8. Negative Overlap During TDC

9. 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 TransitionAllowed 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.

## Ports

### Input

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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.

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`.

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`.

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.

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`.

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`.

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

#### Dependencies

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

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

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

### Output

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

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`.

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

#### Dependencies

To enable this port, set Cylinder volume to `On`.

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

#### Dependencies

To enable this port, set Cylinder pressure to `On`.

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

#### Dependencies

To enable this port, set Cylinder temperature to `On`.

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`.

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

#### Dependencies

To enable this port, set Air mass flow to `On`.

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

#### Dependencies

To enable this port, set Fuel mass flow to `On`.

## Parameters

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### Mechanical

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.

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

Diameter of the piston cylinder.

Distance the piston head travels within the cylinder.

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

Ratio of the maximum to minimum cylinder volume.

### Ambient

Pressure of the air entering the intake.

Temperature of the air entering the intake.

Density of the air entering the intake.

Specific gas constant of dry air.

### Valves

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

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.

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.

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.

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.

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

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

### Combustion

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

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

Slope of the fuel injector mass flow rate.

#### Dependencies

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

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

Time constant for the cylinder pressure slow decay.

Time constant for the cylinder temperature slow decay.

### Exhaust

Time constant to specify the exhaust gas temperature decay.

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.

#### Dependencies

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

Back-pressure speed constant.

#### Dependencies

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

### Simulation

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

Crank position at the start of the simulation.

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

### Output

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

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

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

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

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

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

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

## Version History

Introduced in R2022a