SI Core Engine

Spark-ignition engine from intake to exhaust port

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Powertrain Blockset / Propulsion / Combustion Engine Components / Core Engine

Description

The SI Core Engine block implements a spark-ignition (SI) engine from intake to exhaust port. You can use the block in larger vehicle models, hardware-in-the-loop (HIL) engine control design, or vehicle-level fuel economy and performance simulations.

The SI Core Engine block calculates:

• Brake torque

• Fuel flow

• Port gas mass flow, including exhaust gas recirculation (EGR)

• Air-fuel ratio (AFR)

• Exhaust temperature and exhaust mass flow rate

• Engine-out (EO) exhaust emissions

  • Hydrocarbon (HC)

  • Carbon monoxide (CO)

  • Nitric oxide and nitrogen dioxide (NOx)

  • Carbon dioxide (CO₂)

  • Particulate matter (PM)

Air Mass Flow

To calculate engine air mass flow, configure the SI engine to use either of these air mass flow models.

Air Mass Flow Model	Description
SI Engine Speed-Density Air Mass Flow Model	Uses the speed-density equation to calculate the engine air mass flow, relating the engine air mass flow to the intake manifold pressure and engine speed. Consider using this air mass flow model in engines with fixed valvetrain designs.
SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	To calculate the engine air mass flow, the dual-independent cam phaser model uses: Empirical calibration parameters developed from engine mapping measurements Desktop calibration parameters derived from engine computer-aided design (CAD) data In contrast to typical embedded air mass flow calculations based on direct air mass flow measurement with an air mass flow (MAF) sensor, this air mass flow model offers: Elimination of MAF sensors in dual cam-phased valvetrain applications Reasonable accuracy with changes in altitude Semiphysical modeling approach Bounded behavior Suitable execution time for electronic control unit (ECU) implementation Systematic development of a relatively small number of calibration parameters

Brake Torque

To calculate the brake torque, configure the SI engine to use either of these torque models.

Brake Torque Model	Description
SI Engine Torque Structure Model	For the structured brake torque calculation, the SI engine uses tables for the inner torque, friction torque, optimal spark, spark efficiency, and lambda efficiency. If you select Crank angle pressure and torque on the block Torque tab, you can: Simulate advanced closed-loop engine controls in desktop simulations and on HIL bench, based on cylinder pressure recorded from a model or laboratory test as a function of crank angle. Simulate driveline vibrations downstream of the engine due to high-frequency crankshaft torsionals. Simulate engine misfires due to lean operation or spark plug fouling by using the injector pulse width input. Simulate cylinder deactivation effect (closed intake and exhaust valves, no injected fuel) on individual cylinder pressures, mean-value airflow, mean-value torque, and crank-angle-based torque. Simulate the fuel-cut effect on individual cylinder pressure, mean-value torque, and crank-angle-based torque.
SI Engine Simple Torque Model	For the simple brake torque calculation, the SI engine block uses a torque lookup table map that is a function of engine speed and load.

Fuel Flow

To calculate the fuel flow, the SI Core Engine block uses fuel injector characteristics and fuel injector pulse-width.

${\dot{m}}_{fuel}=\frac{N{S}_{inj}P{w}_{inj}{N}_{cyl}}{Cps\left(\frac{60s}{\min }\right)\left(\frac{1000mg}{g}\right)}$

To calculate the fuel economy for high-fidelity models, the block uses the volumetric fuel flow.

$$Q_{fuel}=\frac{{\dot{m}}_{fuel}}{\left(\frac{1000kg}{m^3}\right)S{g}_{fuel}}$$

The equation uses these variables.

${\dot{m}}_{fuel}$	Fuel mass flow, g/s
$\omega$	Engine rotational speed, rad/s
$$Cps$$	Crankshaft revolutions per power stroke, rev/stroke
$S_{inj}$	Fuel injector slope, mg/ms
$P{w}_{inj}$	Fuel injector pulse-width, ms
$N_{cyl}$	Number of engine cylinders
N	Engine speed, rpm
Sgfuel	Specific gravity of fuel
Qfuel	Volumetric fuel flow

The block uses the internal signal FlwDir to track the direction of the flow.

Air-Fuel Ratio

To calculate the air-fuel (AFR) ratio, the CI Core Engine and SI Core Engine blocks implement this equation.

$AFR=\frac{{\dot{m}}_{air}}{{\dot{m}}_{fuel}}$

The CI Core Engine uses this equation to calculate the relative AFR.

$\lambda =\frac{AFR}{AF{R}_s}$

To calculate the exhaust gas recirculation (EGR), the blocks implement this equation. The calculation expresses the EGR as a percent of the total intake port flow.

$$EG{R}_{pct}=100\frac{{\dot{m}}_{intk,b}}{{\dot{m}}_{intk}}=100y_{intk,b}$$

The equations use these variables.

$AFR$	Air-fuel ratio
AFRs	Stoichiometric air-fuel ratio
${\dot{m}}_{intk}$	Engine air mass flow
${\dot{m}}_{fuel}$	Fuel mass flow
λ	Relative AFR
yintk,b	Intake burned mass fraction
EGRpct	EGR percent
${\dot{m}}_{intk,b}$	Recirculated burned gas mass flow rate

Exhaust

The block calculates the:

• Exhaust gas temperature

• Exhaust gas-specific enthalpy

• Exhaust gas mass flow rate

• Engine-out (EO) exhaust emissions:

  • Hydrocarbon (HC)

  • Carbon monoxide (CO)

  • Nitric oxide and nitrogen dioxide (NOx)

  • Carbon dioxide (CO₂)

  • Particulate matter (PM)

The exhaust temperature determines the specific enthalpy.

$h_{exh}=C{p}_{exh}{T}_{exh}$

The exhaust mass flow rate is the sum of the intake port air mass flow and the fuel mass flow.

${\dot{m}}_{exh}={\dot{m}}_{intake}+{\dot{m}}_{fuel}$

To calculate the exhaust emissions, the block multiplies the emission mass fraction by the exhaust mass flow rate. To determine the emission mass fractions, the block uses lookup tables that are functions of the engine torque and speed.

$$\begin{array}{l}{y}_{exh,i}=f_{i\_frac}(T_{brake},N)\\ {\dot{m}}_{exh,i}={\dot{m}}_{exh}{y}_{exh,i}\end{array}$$

The fraction of air and fuel entering the intake port, injected fuel, and stoichiometric AFR determine the air mass fraction that exits the exhaust.

$$y_{exh,air}=\max \left[y_{in,air}-\frac{{\dot{m}}_{fuel}+y_{in,fuel}{\dot{m}}_{intake}}{{\dot{m}}_{fuel}+{\dot{m}}_{intake}}AF{R}_s\right]$$

If the engine is operating at the stoichiometric or fuel rich AFR, no air exits the exhaust. Unburned hydrocarbons and burned gas comprise the remainder of the exhaust gas. This equation determines the exhaust burned gas mass fraction.

$$y_{exh,b}=\max \left[(1-y_{exh,air}-y_{exh,HC}),0\right]$$

The equations use these variables.

$T_{exh}$	Engine exhaust temperature
$h_{exh}$	Exhaust manifold inlet-specific enthalpy
$C{p}_{exh}$	Exhaust gas specific heat
${\dot{m}}_{intk}$	Intake port air mass flow rate
${\dot{m}}_{fuel}$	Fuel mass flow rate
$${\dot{m}}_{exh}$$	Exhaust mass flow rate
$$y_{in,fuel}$$	Intake fuel mass fraction
yexh,i	Exhaust mass fraction for i = CO2, CO, HC, NOx, air, burned gas, and PM
$${\dot{m}}_{exh,i}$$	Exhaust mass flow rate for i = CO2, CO, HC, NOx, air, burned gas, and PM
Tbrake	Engine brake torque
N	Engine speed
yexh,air	Exhaust air mass fraction
yexh,b	Exhaust air burned mass fraction

Power Accounting

For the power accounting, the block implements equations that depend on Torque model.

When you set Torque model to Simple Torque Lookup, the block implements these equations.

Bus Signal			Description	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrIntkHeatFlw	Intake heat flow	${\dot{m}}_{intk}{h}_{intk}$
		PwrExhHeatFlw	Exhaust heat flow	$-{\dot{m}}_{exh}{h}_{exh}$
		PwrCrkshft	Crankshaft power	$-T_{brake}\omega$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrFuel	Fuel input power	${\dot{m}}_{fuel}LHV$
		PwrLoss	All losses	$T_{brake}\omega -{\dot{m}}_{fuel}LHV-{\dot{m}}_{intk}{h}_{intk}+{\dot{m}}_{exh}{h}_{exh}$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	Not used

When you set Torque model to Torque Structure, the block implements these equations.

Bus Signal			Description	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrIntkHeatFlw	Intake heat flow	${\dot{m}}_{intk}{h}_{intk}$
		PwrExhHeatFlw	Exhaust heat flow	$-{\dot{m}}_{exh}{h}_{exh}$
		PwrCrkshft	Crankshaft power	$-T_{brake}\omega$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrFuel	Fuel input power	${\dot{m}}_{fuel}LHV$
		PwrFricLoss	Friction loss	$-T_{fric}\omega$
		PwrPumpLoss	Pumping loss	$-T_{pump}\omega$
		PwrHeatTrnsfrLoss	Heat transfer loss	$T_{brake}\omega -{\dot{m}}_{fuel}LHV-{\dot{m}}_{intk}{h}_{intk}+{\dot{m}}_{exh}{h}_{exh}+T_{fric}\omega +T_{pump}\omega$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	Not used

hexh	Exhaust manifold inlet-specific enthalpy
hintk	Intake port specific enthalpy
${\dot{m}}_{intk}$	Intake port air mass flow rate
${\dot{m}}_{fuel}$	Fuel mass flow rate
$${\dot{m}}_{exh}$$	Exhaust mass flow rate
ω	Engine speed
Tbrake	Brake torque
Tpump	Engine pumping work offset to inner torque
Tfric	Engine friction torque
LHV	Fuel lower heating value

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Calibrate, Validate, and Optimize SI Engine with Dynamometer Test Harness

Simulate a spark-ignition (SI) engine and controller under a dynamometer test harness using the SI engine dynamometer reference application.

Ports

Input

InjPw — Fuel injector pulse-width

scalar

Fuel injector pulse-width, $P{w}_{inj}$, in ms.

SpkAdv — Spark advance

scalar

Spark advance, SA, in degrees crank angle before top dead center (degBTDC).

Dependencies

To create this port, for the Torque model parameter, select Torque Structure.

ICP — Intake cam phase angle command

scalar

Intake cam phase angle command, ${\phi }_{ICPCMD}$, in degCrkAdv, or crank degrees of advance relative to the intake phaser park position.

Dependencies

To create this port, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

ECP — Exhaust cam phase angle command

scalar

Exhaust cam phase angle command, ${\phi }_{ECPCMD}$, in degCrkRet, or crank degrees of retard relative to the exhaust phaser park position.

Dependencies

To create this port, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

AmbPrs — Ambient pressure

scalar

Ambient pressure, $P_{Amb}$, in Pa.

Dependencies

To create this port, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

EngSpd — Engine speed

scalar

Engine speed, N, in rpm.

Ect — Engine cooling temperature

scalar

Engine cooling temperature, T_coolant, in K.

Dependencies

To enable this parameter, for Torque model, select Torque Structure.

Intk — Intake port pressure, temperature, enthalpy, mass fractions

two-way connector port

Bus containing the upstream:

• Prs — Pressure, in Pa

• Temp — Temperature, in K

• Enth — Specific enthalpy, in J/kg

• MassFrac — Intake port mass fractions, dimensionless. EGR mass flow at the intake port is burned gas.

  Specifically, a bus with these mass fractions:

  • O2MassFrac — Oxygen

  • N2MassFrac — Nitrogen

  • UnbrndFuelMassFrac — Unburned fuel

  • CO2MassFrac — Carbon dioxide

  • H2OMassFrac — Water

  • COMassFrac — Carbon monoxide

  • NOMassFrac — Nitric oxide

  • NO2MassFrac — Nitrogen dioxide

  • NOxMassFrac — Nitric oxide and nitrogen dioxide

  • PmMassFrac — Particulate matter

  • AirMassFrac — Air

  • BrndGasMassFrac — Burned gas

Exh — Exhaust port pressure, temperature, enthalpy, mass fractions

two-way connector port

Bus containing the exhaust:

• Prs — Pressure, in Pa

• Temp — Temperature, in K

• Enth — Specific enthalpy, in J/kg

• MassFrac — Exhaust port mass fractions, dimensionless.

  Specifically, a bus with these mass fractions:

  • O2MassFrac — Oxygen

  • N2MassFrac — Nitrogen

  • UnbrndFuelMassFrac — Unburned fuel

  • CO2MassFrac — Carbon dioxide

  • H2OMassFrac — Water

  • COMassFrac — Carbon monoxide

  • NOMassFrac — Nitric oxide

  • NO2MassFrac — Nitrogen dioxide

  • NOxMassFrac — Nitric oxide and nitrogen dioxide

  • PmMassFrac — Particulate matter

  • AirMassFrac — Air

  • BrndGasMassFrac — Burned gas

Output

Info — Bus signal

bus

Bus signal that contains these block calculations.

Signal			Description	Variable	Units
IntkGasMassFlw			Engine intake air mass flow	${\dot{m}}_{air}$	kg/s
IntkAirMassFlw			Engine intake port mass flow	${\dot{m}}_{intk}$	kg/s
NrmlzdAirChrg			Engine load (that is, normalized cylinder air mass) corrected for final steady-state cam phase angles	$L$	N/A
Afr			Air-fuel ratio at engine exhaust port	$AFR$	N/A
FuelMassFlw			Fuel flow into engine	${\dot{m}}_{fuel}$	kg/s
FuelVolFlw			Volumetric fuel flow	Qfuel	m3/s
ExhManGasTemp			Exhaust gas temperature at exhaust manifold inlet	$T_{exh}$	K
EngTrq			Engine brake torque	$T_{brake}$	N·m
EngSpd			Engine speed	$N$	rpm
IntkCamPhase			Intake cam phaser angle	${\phi }_{ICP}$ i	crank degrees advance relative to park
ExhCamPhase			Exhaust cam phaser angle	${\phi }_{ECP}$	crank degrees retard relative to park
CrkAng			Engine crankshaft absolute angle	$${\displaystyle \underset{0}{\overset{(360)Cps}{\int }}EngSpd\frac{180}{30}d\theta }$$ where $$Cps$$ is crankshaft revolutions per power stroke	degrees crank angle
EgrPct			EGR percent	EGRpct	N/A
EoAir			EO air mass flow rate	$${\dot{m}}_{exh}$$	kg/s
EoBrndGas			EO burned gas mass flow rate	yexh,b	kg/s
EoHC			EO hydrocarbon emission mass flow rate	yexh,HC	kg/s
EoCO			EO carbon monoxide emission mass flow rate	yexh,CO	kg/s
EoNOx			EO nitric oxide and nitrogen dioxide emissions mass flow rate	yexh,NOx	kg/s
EoCO2			EO carbon dioxide emission mass flow rate	yexh,CO2	kg/s
EoPm			EO particulate matter emission mass flow rate	yexh,PM	kg/s
CylPrs			Cylinder pressure	N/A	Pa
EngTrqCrk			Crank-angle based engine torque	N/A	N·m
PwrInfo	PwrTrnsfrd	PwrIntkHeatFlw	Intake heat flow	${\dot{m}}_{intk}{h}_{intk}$	W
		PwrExhHeatFlw	Exhaust heat flow	$-{\dot{m}}_{exh}{h}_{exh}$	W
		PwrCrkshft	Crankshaft power	$-T_{brake}\omega$	W
	PwrNotTrnsfrd	PwrFuel	Fuel input power	${\dot{m}}_{fuel}LHV$	W
		PwrLoss	For Torque model set to Simple Torque Lookup: All losses	$T_{brake}\omega -{\dot{m}}_{fuel}LHV-{\dot{m}}_{intk}{h}_{intk}+{\dot{m}}_{exh}{h}_{exh}$	W
		PwrFricLoss	For Torque model set to Torque Structure: Friction loss	$-T_{fric}\omega$	W
		PwrPumpLoss	For Torque model set to Torque Structure: Pumping loss	$-T_{pump}\omega$	W
		PwrHeatTrnsfrLoss	For Torque model set to Torque Structure: Heat transfer loss	$T_{brake}\omega -{\dot{m}}_{fuel}LHV-{\dot{m}}_{intk}{h}_{intk}+{\dot{m}}_{exh}{h}_{exh}+T_{fric}\omega +T_{pump}\omega$	W
	PwrStored	Not used

EngTrq — Engine brake torque

scalar

Engine brake torque, $T_{brake}$, in N·m.

Intk — Intake port mass flow rate, heat flow rate, temperature, mass fraction

two-way connector port

Bus containing:

• MassFlwRate — Intake port mass flow rate, in kg/s

• HeatFlwRate — Intake port heat flow rate, in J/s

• Temp — Intake port temperature, in K

• MassFrac — Intake port mass fractions, dimensionless.

  Specifically, a bus with these mass fractions:

  • O2MassFrac — Oxygen

  • N2MassFrac — Nitrogen

  • UnbrndFuelMassFrac — Unburned fuel

  • CO2MassFrac — Carbon dioxide

  • H2OMassFrac — Water

  • COMassFrac — Carbon monoxide

  • NOMassFrac — Nitric oxide

  • NO2MassFrac — Nitrogen dioxide

  • NOxMassFrac — Nitric oxide and nitrogen dioxide

  • PmMassFrac — Particulate matter

  • AirMassFrac — Air

  • BrndGasMassFrac — Burned gas

Exh — Exhaust port mass flow rate, heat flow rate, temperature, mass fraction

two-way connector port

Bus containing:

• MassFlwRate — Exhaust port mass flow rate, in kg/s

• HeatFlwRate — Exhaust heat flow rate, in J/s

• Temp — Exhaust temperature, in K

• MassFrac — Exhaust port mass fractions, dimensionless.

  Specifically, a bus with these mass fractions:

  • O2MassFrac — Oxygen

  • N2MassFrac — Nitrogen

  • UnbrndFuelMassFrac — Unburned fuel

  • CO2MassFrac — Carbon dioxide

  • H2OMassFrac — Water

  • COMassFrac — Carbon monoxide

  • NOMassFrac — Nitric oxide

  • NO2MassFrac — Nitrogen dioxide

  • NOxMassFrac — Nitric oxide and nitrogen dioxide

  • PmMassFrac — Particulate matter

  • AirMassFrac — Air

  • BrndGasMassFrac — Burned gas

Parameters

Block Options

Air mass flow model — Select air mass flow model

Dual-Independent Variable Cam Phasing (default) | Simple Speed-Density

To calculate engine air mass flow, configure the SI engine to use either of these air mass flow models.

Air Mass Flow Model	Description
SI Engine Speed-Density Air Mass Flow Model	Uses the speed-density equation to calculate the engine air mass flow, relating the engine air mass flow to the intake manifold pressure and engine speed. Consider using this air mass flow model in engines with fixed valvetrain designs.
SI Engine Dual-Independent Cam Phaser Air Mass Flow Model	To calculate the engine air mass flow, the dual-independent cam phaser model uses: Empirical calibration parameters developed from engine mapping measurements Desktop calibration parameters derived from engine computer-aided design (CAD) data In contrast to typical embedded air mass flow calculations based on direct air mass flow measurement with an air mass flow (MAF) sensor, this air mass flow model offers: Elimination of MAF sensors in dual cam-phased valvetrain applications Reasonable accuracy with changes in altitude Semiphysical modeling approach Bounded behavior Suitable execution time for electronic control unit (ECU) implementation Systematic development of a relatively small number of calibration parameters

Dependencies

The table summarizes the parameter dependencies.

Air Mass Flow Model	Enables Parameters
Dual-Independent Variable Cam Phasing	Cylinder volume at intake valve close table, f_vivc Cylinder volume intake cam phase breakpoints, f_vivc_icp_bpt Cylinder trapped mass correction factor, f_tm_corr Normalized density breakpoints, f_tm_corr_nd_bpt Engine speed breakpoints, f_tm_corr_n_bpt Air mass flow, f_mdot_air Exhaust cam phase breakpoints, f_mdot_air_ecp_bpt Trapped mass flow breakpoints, f_mdot_trpd_bpt Air mass flow correction factor, f_mdot_air_corr Engine load breakpoints for air mass flow correction, f_mdot_air_corr_ld_bpt Engine speed breakpoints for air mass flow correction, f_mdot_air_n_bpt
Simple Speed Density	Speed-density volumetric efficiency, f_nv Speed-density intake manifold pressure breakpoints, f_nv_prs_bpt Speed-density engine speed breakpoints, f_nv_n_bpt

Torque model — Select torque model

Torque Structure (default) | Simple Torque Lookup

To calculate the brake torque, configure the SI engine to use either of these torque models.

Brake Torque Model	Description
SI Engine Torque Structure Model	For the structured brake torque calculation, the SI engine uses tables for the inner torque, friction torque, optimal spark, spark efficiency, and lambda efficiency. If you select Crank angle pressure and torque on the block Torque tab, you can: Simulate advanced closed-loop engine controls in desktop simulations and on HIL bench, based on cylinder pressure recorded from a model or laboratory test as a function of crank angle. Simulate driveline vibrations downstream of the engine due to high-frequency crankshaft torsionals. Simulate engine misfires due to lean operation or spark plug fouling by using the injector pulse width input. Simulate cylinder deactivation effect (closed intake and exhaust valves, no injected fuel) on individual cylinder pressures, mean-value airflow, mean-value torque, and crank-angle-based torque. Simulate the fuel-cut effect on individual cylinder pressure, mean-value torque, and crank-angle-based torque.
SI Engine Simple Torque Model	For the simple brake torque calculation, the SI engine block uses a torque lookup table map that is a function of engine speed and load.

Dependencies

The table summarizes the parameter dependencies.

Torque Model	Enables Parameters
Torque Structure	Inner torque table, f_tq_inr Friction torque table, f_tq_fric Engine temperature modifier on friction torque, f_fric_temp_mod Engine temperature modifier breakpoints, f_fric_temp_bpt Pumping work table, f_tq_pump Optimal spark table, f_sa_opt Inner torque load breakpoints, f_tq_inr_l_bpt Inner torque speed breakpoints, f_tq_inr_n_bpt Spark efficiency table, f_m_sa Spark retard from optimal, f_del_sa_bpt Lambda efficiency, f_m_lam Lambda breakpoints, f_m_lam_bpt
Simple Torque Lookup	Torque table, f_tq_nl Torque table load breakpoints, f_tq_nl_l_bpt Torque table speed breakpoints, f_tq_nl_n_bpt

Air

Number of cylinders, NCyl — Engine cylinders

4 (default) | scalar

Number of engine cylinders, $N_{cyl}$.

Crank revolutions per power stroke, Cps — Revolutions per stroke

2 (default) | scalar

Crankshaft revolutions per power stroke, $$Cps$$, in rev/stroke.

Total displaced volume, Vd — Volume

0.0015 (default) | scalar

Displaced volume, $V_d$, in m^3.

Ideal gas constant air, Rair — Constant

287 (default) | scalar

Ideal gas constant, $R_{air}$, in J/(kg·K).

Air standard pressure, Pstd — Pressure

101325 (default) | scalar

Standard air pressure, $P_{std}$, in Pa.

Air standard temperature, Tstd — Temperature

293.15 (default) | scalar

Standard air temperature, $T_{std}$, in K.

Speed-density volumetric efficiency, f_nv — Lookup table

array

The engine volumetric efficiency lookup table, $f_{{\eta }_v}$, is a function of intake manifold absolute pressure and engine speed

${\eta }_v=f_{{\eta }_v}(MAP,N)$

where:

• ${\eta }_v$ is engine volumetric efficiency, dimensionless.

• MAP is intake manifold absolute pressure, in KPa.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Simple Speed-Density.

Speed-density intake manifold pressure breakpoints, f_nv_prs_bpt — Breakpoints

[31 40.6428571428571 50.2857142857143 59.9285714285714 69.5714285714286 79.2142857142857 88.8571428571429 98.5 108.142857142857 117.785714285714 127.428571428571 137.071428571429 146.714285714286 156.357142857143 166] (default) | array

Intake manifold pressure breakpoints for speed-density volumetric efficiency lookup table, in KPa.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Simple Speed-Density.

Speed-density engine speed breakpoints, f_nv_n_bpt — Breakpoints

[750 1053.57142857143 1357.14285714286 1660.71428571429 1964.28571428571 2267.85714285714 2571.42857142857 2875 3178.57142857143 3482.14285714286 3785.71428571429 4089.28571428571 4392.85714285714 4696.42857142857 5000] (default) | array

Engine speed breakpoints for speed-density volumetric efficiency lookup table, in rpm.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Simple Speed-Density.

Cylinder volume at intake valve close table, f_vivc — 2-D lookup table

array

The cylinder volume at intake valve close table (IVC), $f_{Vivc}$ is a function of the intake cam phaser angle

$V_{IVC}=f_{Vivc}({\phi }_{ICP})$

where:

• $$V_{IVC}$$ is cylinder volume at IVC, in L.

• ${\phi }_{ICP}$ is intake cam phaser angle in crank degrees of advance relative to the intake phaser park position.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Cylinder volume intake cam phase breakpoints, f_vivc_icp_bpt — Breakpoints

[0 2.6316 5.2632 7.8947 10.5263 13.1579 15.7895 18.4211 21.0526 23.6842 26.3158 28.9474 31.5789 34.2105 36.8421 39.4737 42.1053 44.7368 47.3684 50] (default) | vector

Cylinder volume intake cam phase breakpoints, in L.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Cylinder trapped mass correction factor, f_tm_corr — Lookup table

array

The trapped mass correction factor table, $f_{TMcorr}$, is a function of the normalized density and engine speed

$T{M}_{corr}=f_{TMcorr}({\rho }_{norm}, N)$

where:

• $T{M}_{corr}$, is trapped mass correction multiplier, dimensionless.

• ${\rho }_{norm}$ is normalized density, dimensionless.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Normalized density breakpoints, f_tm_corr_nd_bpt — Breakpoints

[0.3 0.38947 0.47895 0.56842 0.65789 0.74737 0.83684 0.92632 1.0158 1.1053 1.1947 1.2842 1.3737 1.4632 1.5526 1.6421 1.7316 1.8211 1.9105 2] (default) | vector

Normalized density breakpoints, dimensionless.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Engine speed breakpoints, f_tm_corr_n_bpt — Breakpoints

[750 973.6842 1197.3684 1421.0526 1644.7368 1868.4211 2092.1053 2315.7895 2539.4737 2763.1579 2986.8421 3210.5263 3434.2105 3657.8947 3881.5789 4105.2632 4328.9474 4552.6316 4776.3158 5000] (default) | vector

Engine speed breakpoints, in rpm.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Intake mass flow, f_mdot_intk — Lookup table

array

The phaser intake mass flow model lookup table is a function of exhaust cam phaser angles and trapped air mass flow

${\dot{m}}_{intkideal}=f_{intkideal}({\phi }_{ECP},T{M}_{flow})$

where:

• ${\dot{m}}_{intkideal}$ is engine intake port mass flow at arbitrary cam phaser angles, in g/s.

• ${\phi }_{ECP}$ is exhaust cam phaser angle in crank degrees of retard relative to the exhaust phaser park position.

• $T{M}_{flow}$ is flow rate equivalent to corrected trapped mass at the current engine speed, in g/s.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Exhaust cam phase breakpoints, f_mdot_air_ecp_bpt — Breakpoints

[0 2.6316 5.2632 7.8947 10.5263 13.1579 15.7895 18.4211 21.0526 23.6842 26.3158 28.9474 31.5789 34.2105 36.8421 39.4737 42.1053 44.7368 47.3684 50] (default) | vector

Exhaust cam phaser breakpoints for air mass flow lookup table, in crank degrees of retard relative to park.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Trapped mass flow breakpoints, f_mdot_trpd_bpt — Breakpoints

[0 5.7895 11.5789 17.3684 23.1579 28.9474 34.7368 40.5263 46.3158 52.1053 57.8947 63.6842 69.4737 75.2632 81.0526 86.8421 92.6316 98.4211 104.2105 110] (default) | vector

Trapped mass flow breakpoints for air mass flow lookup table, in g/s.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Air mass flow correction factor, f_mdot_air_corr — Lookup table

array

The intake air mass flow correction lookup table, $f_{aircorr}$, is a function of ideal load and engine speed

${\dot{m}}_{air}={\dot{m}}_{intkideal}{f}_{aircorr}(L_{ideal},N)$

where:

• $L_{ideal}$ is engine load (normalized cylinder air mass) at arbitrary cam phaser angles, uncorrected for final steady-state cam phaser angles, dimensionless.

• N is engine speed, in rpm.

• ${\dot{m}}_{air}$ is engine intake air mass flow final correction at steady-state cam phaser angles, in g/s.

• ${\dot{m}}_{intkideal}$ is engine intake port mass flow at arbitrary cam phaser angles, in g/s.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Engine load breakpoints for air mass flow correction, f_mdot_air_corr_ld_bpt — Breakpoints

vector

Engine load breakpoints for air mass flow final correction, dimensionless.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Engine speed breakpoints for air mass flow correction, f_mdot_air_n_bpt — Breakpoints

vector

Engine speed breakpoints for air mass flow final correction, in rpm.

Dependencies

To enable this parameter, for the Air mass flow model parameter, select Dual-Independent Variable Cam Phasing.

Torque

Torque table, f_tq_nl — Lookup table

[L x N] array

For the simple torque lookup table model, the SI engine uses a lookup table map that is a function of engine speed and load, $T_{brake}=f_{TnL}(L,N)$, where:

• $T_{brake}$ is engine brake torque after accounting for spark advance, AFR, and friction effects, in N·m.

• L is engine load, as a normalized cylinder air mass, dimensionless.

• N is engine speed, in rpm.

The simple torque lookup model assumes that the calibration has negative torque values to indicate the non-firing engine load (L) versus speed (N) condition. The calibrated table (L-by-N) contains the non-firing data in the first table row (1-by-N). When the fuel delivered to the engine is zero, the model uses the data in the first table row (1-by-N) at or above 100 AFR. 100 AFR results from fuel cutoff or very lean operation where combustion cannot occur.

Dependencies

To enable this parameter, for the Torque model parameter, select Simple Torque Lookup.

Torque table load breakpoints, f_tq_nl_l_bpt — Breakpoints

[0.2 0.275 0.35 0.425 0.5 0.575 0.65 0.725 0.8 0.875 0.95 1.025 1.1 1.175 1.25] (default) | vector | [1 x L] vector

Engine load breakpoints, L, dimensionless.

Dependencies

To enable this parameter, for the Torque model parameter, select Simple Torque Lookup.

Torque table speed breakpoints, f_tq_nl_n_bpt — Breakpoints

[750 1053.57142857143 1357.14285714286 1660.71428571429 1964.28571428571 2267.85714285714 2571.42857142857 2875 3178.57142857143 3482.14285714286 3785.71428571429 4089.28571428571 4392.85714285714 4696.42857142857 5000] (default) | vector | [1 x N] vector

Engine speed breakpoints, N, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Simple Torque Lookup.

Crank angle pressure and torque — Enable Crank angle signals

off (default) | on

If you select Crank angle pressure and torque on the block Torque tab, you can:

• Simulate advanced closed-loop engine controls in desktop simulations and on HIL bench, based on cylinder pressure recorded from a model or laboratory test as a function of crank angle.

• Simulate driveline vibrations downstream of the engine due to high-frequency crankshaft torsionals.

• Simulate engine misfires due to lean operation or spark plug fouling by using the injector pulse width input.

• Simulate cylinder deactivation effect (closed intake and exhaust valves, no injected fuel) on individual cylinder pressures, mean-value airflow, mean-value torque, and crank-angle-based torque.

• Simulate the fuel-cut effect on individual cylinder pressure, mean-value torque, and crank-angle-based torque.

Dependencies

To enable this parameter, set Torque model to Torque Structure.

Cylinder pressure, f_crk_prs — Cylinder pressure table

L x M x N array

Cylinder pressure table Prs, as a function of speed N, load L, and crank angle M, in Pa.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

Brake torque, f_crk_btq — Brake torque table

L x M x N array

Brake torque table T_brake, as a function of speed N, load L, and crank angle M, in N·m.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

Speed breakpoints, f_crk_n_bpt — Speed breakpoints

[750 5000] (default) | 1 x N vector

Speed breakpoints, N, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

Load breakpoints, f_crk_l_bpt — Load breakpoints

[0.2 1.4] (default) | 1 x L vector

Load breakpoints, L. No dimension.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

Crank angle breakpoints, f_crk_ang_bpt — Crank angle breakpoints

[60 660] (default) | 1 x M vector

Crank angle breakpoints, M, in deg.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

TDC compression angles by cylinder, f_crk_tdc_ang — TDC compression angles by cylinder

[0 540 180 360] (default) | vector

Top dead center (TDC) compression angles by cylinder, in deg.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure. Select Crank angle pressure and torque.

Inner torque table, f_tq_inr — Lookup table

array

The inner torque lookup table, $f_{Tqinr}$, is a function of engine speed and engine load, $T{q}_{inr}=f_{Tqinr}(L,N)$, where:

• $T{q}_{inr}$ is inner torque based on gross indicated mean effective pressure, in N·m.

• L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Friction torque table, f_tq_fric — Lookup table

array

The friction torque lookup table, $f_{Tfric}$, is a function of engine speed and engine load, $$T_{fric}=f_{Tfric}\left(L,N\right)$$, where:

• $T_{fric}$ is friction torque offset to inner torque, in N·m.

• L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Engine temperature modifier on friction torque, f_fric_temp_mod — Lookup table

[3.96 3.22 2.56 2.26 2.11 2 1.9 1.83 1.76 1.7 1.65 1.6 1.55 1.49 1.44 1.41 1.38 1.35 1.32 1.3 1.27 1.25 1.24 1.21 1.2 1.18 1.16 1.15 1.13 1.12 1.11 1.1 1.09 1.08 1.07 1.06 1.05 1.05 1.04 1.03 1.02 1.02 1.01 1.01 1 1 1 0.999 0.997 0.995 0.993 0.991 0.989 0.987] (default) | vector | vector

Engine temperature modifier on friction torque, ƒ_fric,temp, dimensionless.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Engine temperature modifier breakpoints, f_fric_temp_bpt — Breakpoints

[274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380] (default) | vector | vector

Engine temperature modifier breakpoints, in K.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Pumping torque table, f_tq_pump — Lookup table

array

The pumping torque lookup table, ƒ_Tpump, is a function of engine load and engine speed, Tpump=ƒTpump(L,N), where:

• T_pump is pumping torque, in N·m.

• L is engine load, as a normalized cylinder air mass, dimensionless.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Optimal spark table, f_sa_opt — Lookup table

array

The optimal spark lookup table, $f_{SAopt}$, is a function of engine speed and engine load, $S{A}_{opt}=f_{SAopt}(L,N)$, where:

• SA_opt is optimal spark advance timing for maximum inner torque at stoichiometric air-fuel ratio (AFR), in deg.

• L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless.

• N is engine speed, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Inner torque load breakpoints, f_tq_inr_l_bpt — Breakpoints

[0.2 0.28571 0.37143 0.45714 0.54286 0.62857 0.71429 0.8 0.88571 0.97143 1.0571 1.1429 1.2286 1.3143 1.4] (default) | vector

Inner torque load breakpoints, dimensionless.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Inner torque speed breakpoints, f_tq_inr_n_bpt — Breakpoints

[750 1053.5714 1357.1429 1660.7143 1964.2857 2267.8571 2571.4286 2875 3178.5714 3482.1429 3785.7143 4089.2857 4392.8571 4696.4286 5000] (default) | vector

Inner torque speed breakpoints, in rpm.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Spark efficiency table, f_m_sa — Lookup table

array

The spark efficiency lookup table, $f_{Msa}$, is a function of the spark retard from optimal

$\begin{array}{l}{M}_{sa}=f_{Msa}(\Delta SA)\\ \Delta SA=S{A}_{opt}-SA\end{array}$

where:

• $M_{sa}$ is the spark retard efficiency multiplier, dimensionless.

• $\Delta SA$is the spark retard timing distance from optimal spark advance, in deg.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Spark retard from optimal, f_del_sa_bpt — Breakpoints

[0 0.75 1.5 2.25 3 3.75 4.5 5.25 6 6.75 7.5 8.25 9 9.75 10.5 11.25 12 12.75 13.5 14.25 15 15.75 16.5 17.25 18 18.75 19.5 20.25 21 21.75 22.5 23.25 24 24.75 25.5 26.25 27 27.75 28.5 29.25 30 30.75 31.5 32.25 33 33.75 34.5 35.25 36 36.75 37.5 38.25 39 39.75 40.5 41.25 42 42.75 43.5 44.25 45 45.75 46.5 47.25 48] (default) | vector

Spark retard from optimal inner torque timing breakpoints, in deg.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Lambda efficiency, f_m_lam — Lookup table

array

The lambda efficiency lookup table, $f_{M\lambda }$, is a function of lambda, $M_{\lambda }=f_{M\lambda }(\lambda )$, where:

• $M_{\lambda }$ is the lambda multiplier on inner torque to account for the air-fuel ratio (AFR) effect, dimensionless.

• $\lambda$ is lambda, AFR normalized to stoichiometric fuel AFR, dimensionless.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Lambda breakpoints, f_m_lam_bpt — Breakpoints

[0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1] (default) | vector

Lambda effect on inner torque lambda breakpoints, dimensionless.

Dependencies

To enable this parameter, for the Torque model parameter, select Torque Structure.

Exhaust

Exhaust temperature table, f_t_exh — Lookup table

array

The exhaust temperature lookup table, $f_{Texh}$, is a function of engine load and engine speed

$T_{exh}=f_{Texh}(L,N)$

where:

• T_exh is engine exhaust temperature, in K.

• L is normalized cylinder air mass or engine load, dimensionless.

• N is engine speed, in rpm.

Load breakpoints, f_t_exh_l_bpt — Breakpoints

[0.2 0.275 0.35 0.425 0.5 0.575 0.65 0.725 0.8 0.875 0.95 1.025 1.1 1.175 1.25] (default) | vector

Engine load breakpoints used for exhaust temperature lookup table, dimensionless.

Speed breakpoints, f_t_exh_n_bpt — Breakpoints

[750 1053.57142857143 1357.14285714286 1660.71428571429 1964.28571428571 2267.85714285714 2571.42857142857 2875 3178.57142857143 3482.14285714286 3785.71428571429 4089.28571428571 4392.85714285714 4696.42857142857 5000] (default) | vector

Engine speed breakpoints used for exhaust temperature lookup table, in rpm.

Exhaust gas specific heat at constant pressure, cp_exh — Specific heat

1005 (default) | scalar

Exhaust gas-specific heat, $C{p}_{exh}$, in J/(kg·K).

CO2 mass fraction table, f_CO2_frac — Carbon dioxide (CO₂) emission lookup table

array

The SI Core Engine CO₂ emission mass fraction lookup table is a function of engine torque and engine speed, CO2 Mass Fraction = ƒ(Speed, Torque), where:

• CO2 Mass Fraction is the CO₂ emission mass fraction, dimensionless.

• Speed is engine speed, in rpm.

• Torque is engine torque, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select CO2.

CO mass fraction table, f_CO_frac — Carbon monoxide (CO) emission lookup table

array

The SI Core Engine CO emission mass fraction lookup table is a function of engine torque and engine speed, CO Mass Fraction = ƒ(Speed, Torque), where:

• CO Mass Fraction is the CO emission mass fraction, dimensionless.

• Speed is engine speed, in rpm.

• Torque is engine torque, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select CO.

HC mass fraction table, f_HC_frac — Hydrocarbon (HC) emission lookup table

array

The SI Core Engine HC emission mass fraction lookup table is a function of engine torque and engine speed, HC Mass Fraction = ƒ(Speed, Torque), where:

• HC Mass Fraction is the HC emission mass fraction, dimensionless.

• Speed is engine speed, in rpm.

• Torque is engine torque, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select HC.

NOx mass fraction table, f_NOx_frac — Nitric oxide and nitrogen dioxide (NOx) emission lookup table

array

The SI Core Engine NOx emission mass fraction lookup table is a function of engine torque and engine speed, NOx Mass Fraction = ƒ(Speed, Torque), where:

• NOx Mass Fraction is the NOx emission mass fraction, dimensionless.

• Speed is engine speed, in rpm.

• Torque is engine torque, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select NOx.

PM mass fraction table, f_PM_frac — Particulate matter (PM) emission lookup table

array

The SI Core Engine PM emission mass fraction lookup table is a function of engine torque and engine speed where:

• PM is the PM emission mass fraction, dimensionless.

• Speed is engine speed, in rpm.

• Torque is engine torque, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select PM.

Engine speed breakpoints, f_exhfrac_n_bpt — Breakpoints

[750 1053.57142857143 1357.14285714286 1660.71428571429 1964.28571428571 2267.85714285714 2571.42857142857 2875 3178.57142857143 3482.14285714286 3785.71428571429 4089.28571428571 4392.85714285714 4696.42857142857 5000] (default) | vector

Engine speed breakpoints used for the emission mass fractions lookup tables, in rpm.

Dependencies

To enable this parameter, on the Exhaust tab, select CO2, CO, NOx, HC, or PM.

Engine torque breakpoints, f_exhfrac_trq_bpt — Breakpoints

[0 15 26.4285714285714 37.8571428571429 49.2857142857143 60.7142857142857 72.1428571428571 83.5714285714286 95 106.428571428571 117.857142857143 129.285714285714 140.714285714286 152.142857142857 163.571428571429 175] (default) | vector

Engine torque breakpoints used for the emission mass fractions lookup tables, in N·m.

Dependencies

To enable this parameter, on the Exhaust tab, select CO2, CO, NOx, HC, or PM.

Fuel

Injector slope, Sinj — Slope

6.45161290322581 (default) | scalar

Fuel injector slope, $S_{inj}$, mg/ms.

Stoichiometric air-fuel ratio, afr_stoich — Air-fuel ratio

14.6 (default) | scalar

Air-fuel ratio, $AFR$.

Fuel lower heating value, fuel_lhv — Heating value

46e6 (default) | scalar

Fuel lower heating value, LHV, in J/kg.

Fuel specific gravity, fuel_sg — Specific gravity

0.745 (default) | scalar

Specific gravity of fuel, Sg_fuel, dimensionless.

References

[1] Gerhardt, J., Hönninger, H., and Bischof, H., A New Approach to Functional and Software Structure for Engine Management Systems — BOSCH ME7. SAE Technical Paper 980801, 1998.

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

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Version History

Introduced in R2017a