Turbine

Turbine for boosted engines

• 

Libraries:
Powertrain Blockset / Propulsion / Combustion Engine Components / Boost

Description

The Turbine block uses the conservation of mass and energy to calculate mass and heat flow rates for turbines with either fixed or variable geometry. You can configure the block with a wastegate valve to bypass the turbine. The block uses two-way ports to connect to the inlet and outlet control volumes and the drive shaft. You can specify the lookup tables to calculate the mass flow rate and turbine efficiency. Typically, turbine manufacturers provide the mass flow rate and efficiency tables as a function of corrected speed and pressure ratio. The block does not support reverse mass flow.

If you have Model-Based Calibration Toolbox™, click Calibrate Performance Maps to virtually calibrate the mass flow rate and turbine efficiency lookup tables using measured data.

The mass flows from the inlet control volume to outlet control volume.

The Turbine block implements equations to model the performance, wastegate flow, and combined flow.

Virtual Calibration

If you have Model-Based Calibration Toolbox, click Calibrate Performance Maps to virtually calibrate the corrected mass flow rate and turbine efficiency lookup tables using measured data. The dialog box steps through these tasks.

Task	Description
Import turbine data	Import this turbine data from a file. For more information, see Using Data (Model-Based Calibration Toolbox). Turbine type Data Fixed geometry Speed, Spd, in rad/s Corrected mass flow rate, MassFlwRate, in kg/s Pressure ratio, PrsRatio, dimensionless Efficiency, Eff, dimensionless The speed, corrected mass flow rate, pressure ratio, and efficiency are in the 2nd-5th columns of the data file, respectively. The first and second rows of the data file provide the variable names and units. For example, use this format. Name: Spd MassFlwRate PrsRatio Eff Unit: rad/s kg/s     Data: 8373.3 0.02 1.21 0.44   ... ... ... ... Variable geometry Speed, Spd, in rad/s Corrected mass flow rate, MassFlwRate, kg/s Rack position, RackPos, dimensionless Pressure ratio, PrsRatio, dimensionless Efficiency, Eff, dimensionless Include data for several test points at each rack position operating point. The speed, corrected mass flow rate, rack position, pressure ratio, and efficiency are in the 2nd-6th columns of the data file, respectively. The first and second rows of the data file provide the variable names and units. For example, use this format. Name: Spd MassFlwRate RackPos PrsRatio Eff Unit: rad/s kg/s       Data: 8373.3 0.02 1 1.21 0.44   ... ...   ... ... Model-Based Calibration Toolbox limits the speed and pressure ratio breakpoint values to the maximum values in the file. To filter or edit the data, select Edit in Application. The Model-Based Calibration Toolbox Data Editor opens.
Generate response models	Model-Based Calibration Toolbox fits the imported data and generates response models. Turbine type Description Fixed geometry Data Response Model Corrected mass flow rate Square root turbine flow model described in Modeling and Control of Engines and Drivelines2 Efficiency Blade speed ratio (BSR) model described in Modeling and Control of Engines and Drivelines2 Variable geometry Model-Based Calibration Toolbox uses a point-by-point test plan to fit the data. For each rack position, the block uses these response models to fit the corrected mass flow rate and efficiency data. Data Response Model Corrected mass flow rate Square root turbine flow model described in Modeling and Control of Engines and Drivelines2 Efficiency Blade speed ratio (BSR) model described in Modeling and Control of Engines and Drivelines2 To assess or adjust the response model fit, select Edit in Application. The Model-Based Calibration Toolbox Model Browser opens. For more information, see Model Assessment (Model-Based Calibration Toolbox).
Generate calibration	Model-Based Calibration Toolbox calibrates the response model and generates calibrated tables. Turbine type Description Fixed geometry Model-Based Calibration Toolbox uses the response models for the corrected mass flow rate and efficiency tables. Variable geometry Model-Based Calibration Toolbox fills the corrected mass flow rate and efficiency tables for each rack position. Model-Based Calibration Toolbox then combines the rack position-dependent tables into 3D lookup tables for corrected mass flow rate and efficiency. To assess or adjust the calibration, select Edit in Application. The Model-Based Calibration Toolbox CAGE Browser opens. For more information, see Calibration Lookup Tables (Model-Based Calibration Toolbox).
Update block parameters	Update these corrected mass flow rate and efficiency parameters with the calibration. Turbine type Parameters Fixed geometry Corrected mass flow rate table, mdot_corrfx_tbl Efficiency table, eta_turbfx_tbl Corrected speed breakpoints, w_corrfx_bpts1 Pressure ratio breakpoints, Pr_fx_bpts2 Variable geometry Corrected mass flow rate table, mdot_corrvr_tbl Efficiency table, eta_turbvr_tbl Corrected speed breakpoints, w_corrvr_bpts2 Pressure ratio breakpoints, Pr_vr_bpts2 Rack breakpoints, L_rack_bpts3

Thermodynamics

The block uses these equations to model the thermodynamics.

Calculation	Equations
Forward mass flow	${\dot{m}}_{turb}>0$ $p_{01}=p_{inlet}$ $p_{02}=p_{outlet}$ $T_{01}=T_{inlet}$ $h_{01}=h_{inlet}$
First law of thermodynamics	${\dot{W}}_{turb}={\dot{m}}_{turb}{c}_p\left(T_{01}-T_{02}\right)$
Isentropic efficiency	${\eta }_{turb}=\frac{h_{01}-h_{02}}{h_{01}-h_{02\text{s}}}=\frac{T_{01}-T_{02}}{T_{01}-T_{02\text{s}}}$
Isentropic outlet temperature, assuming ideal gas, and constant specific heats	$T_{02s}=T_{01}{\left(\frac{p_{02}}{p_{01}}\right)}^{\frac{\gamma -1}{\gamma }}$
Specific heat ratio	$\gamma =\frac{c_p}{c_p-R}$
Outlet temperature	$T_{02}=T_{01}+{\eta }_{turb}{T}_{01}\left\{1-{\left(\frac{p_{02}}{p_{01}}\right)}^{\frac{\gamma -1}{\gamma }}\right\}$
Heat flows	$q_{in,turb}={\dot{m}}_{turb}{c}_p{T}_{01}$ $q_{out,turb}={\dot{m}}_{turb}{c}_p{T}_{02}$
Drive shaft torque	${\tau }_{turb}=\frac{{\dot{W}}_{turb}}{\omega }$

The equations use these variables.

$p_{\text{inlet}}$,$p_{01}$	Inlet control volume total pressure
$T_{inlet}$, $T_{01}$	Inlet control volume total temperature
$h_{inlet}$, $h_{01}$	Inlet control volume total specific enthalpy
$p_{outlet}$, $p_{02}$	Outlet control volume total pressure
$T_{outlet}$	Outlet control volume total temperature
$h_{outlet}$	Outlet control volume total specific enthalpy
${\dot{W}}_{turb}$	Drive shaft power
$T_{02}$	Temperature exiting the turbine
$h_{02}$	Outlet total specific enthalpy
${\dot{m}}_{turb}$	Turbine mass flow rate
$q_{in,turb}$	Turbine inlet heat flow rate
$q_{out,turb}$	Turbine outlet heat flow rate
${\eta }_{turb}$	Turbine isentropic efficiency
$T_{02s}$	Isentropic outlet total temperature
$h_{02s}$	Isentropic outlet total specific enthalpy
$R$	Ideal gas constant
$c_p$	Specific heat at constant pressure
$\gamma$	Specific heat ratio
${\tau }_{turb}$	Drive shaft torque

Performance Lookup Tables

The block implements lookup tables based on these equations.

Calculation	Equation
Corrected mass flow rate	${\dot{m}}_{corr}={\dot{m}}_{turb}\frac{\sqrt{T_{01}/T_{ref}}}{p_{01}/p_{ref}}$
Corrected speed	${\omega }_{corr}=\frac{\omega }{\sqrt{T_{01}/T_{ref}}}$
Pressure expansion ratio	$p_r=\frac{p_{01}}{p_{02}}$
Efficiency lookup table	Fixed geometry (3-D table)	${\eta }_{turbfx,tbl}=f\left({\omega }_{corr},p_r\right)$
	Variable geometry (3-D table)	${\eta }_{turbvr,tbl}=f\left({\omega }_{corr},p_r,L_{rack}\right)$
Corrected mass flow lookup table	Fixed geometry (3-D table)	${\dot{m}}_{corrfx,tbl}=f\left({\omega }_{corr},p_r\right)$
	Variable geometry (3-D table)	${\dot{m}}_{corrvr,tbl}=f\left({\omega }_{corr},p_r,L_{rack}\right)$

The equations use these variables.

$p_{01}$	Inlet control volume total pressure
$p_r$	Pressure expansion ratio
$p_{02}$	Outlet control volume total pressure
$P_{ref}$	Lookup table reference pressure
$T_{01}$	Inlet control volume total temperature
$T_{ref}$	Lookup table reference temperature
${\dot{m}}_{turb}$	Turbine mass flow rate
$\omega$	Drive shaft speed
${\omega }_{corr}$	Corrected drive shaft speed
$L_{rack}$	Variable geometry turbine rack position
${\eta }_{turbfx,tbl}$	Efficiency 3-D lookup table for fixed geometry
${\dot{m}}_{corrfx,tbl}$	Corrected mass flow rate 3-D lookup table for fixed geometry
${\eta }_{turbvr,tbl}$	Efficiency 3-D lookup table for variable geometry
${\dot{m}}_{corrvr,tbl}$	Corrected mass flow rate 3-D lookup table for variable geometry

Wastegate

To calculate the wastegate heat and mass flow rates, the Turbine block uses a Flow Restriction block. The Flow Restriction block uses the wastegate flow area.

$A_{wg}=A_{wgpctcmd}\frac{A_{wgopen}}{100}$

The equation uses these variables.

$A_{wgpctcmd}$	Wastegate valve area percent command
$A_{wg}$	Wastegate valve area
$A_{wgopen}$	Wastegate valve area when fully open

Combined Flow

To represent flow through the wastegate valve and turbine, the block uses these equations.

Calculation	Equations
Blocks not configured with a wastegate valve	${\dot{m}}_{wg}=q_{wg}=0$
Total mass flow rate	${\dot{m}}_{total}={\dot{m}}_{turb}+{\dot{m}}_{wg}$
Total heat flow rate	$q_{inlet}=q_{in,turb}+q_{wg}$ $q_{outlet}=q_{out,turb}+q_{wg}$
Combined temperature exiting the wastegate valve and turbine	$T_{outflw}=\{\begin{array}{cc}\frac{q_{outlet}}{{\dot{m}}_{total}{c}_p}& {\dot{m}}_{total}>{\dot{m}}_{thresh}\\ \frac{T_{02}+T_{outflw,wg}}{2}& else\end{array}$

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

The equations use these variables.

${\dot{m}}_{total}$	Total mass flow rate through the wastegate valve and turbine
${\dot{m}}_{turb}$	Turbine mass flow rate
${\dot{m}}_{wg}$	Mass flow rate through the wastegate valve
$q_{inlet}$	Total inlet heat flow rate
$q_{outlet}$	Total outlet heat flow rate
$q_{in,turb}$	Turbine inlet heat flow rate
$q_{out,turb}$	Turbine outlet heat flow rate
$$q_{wg}$$	Wastegate valve heat flow rate
$T_{02}$	Temperature exiting the turbine
$T_{outflw}$	Total temperature exiting the block
$T_{outflw,wg}$	Temperature exiting the wastegate valve
${\dot{m}}_{thresh}$	Mass flow rate threshold to prevent dividing by zero
$c_p$	Specific heat at constant pressure

Power Accounting

For the power accounting, 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	PwrDriveshft	Power transmitted from the shaft	$-{\dot{W}}_{turb}$
		PwrHeatFlwIn	Heat flow rate at port A	$q_{outlet}$
		PwrHeatFlwOut	Heat flow rate at port B	$q_{outlet}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrLoss	Power loss	$-q_{inlet}-q_{outlet}+{\dot{W}}_{turb}$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	Not used

The equations use these variables.

${\dot{W}}_{turb}$	Drive shaft power
$q_{outlet}$	Total outlet heat flow rate
$q_{inlet}$	Total inlet heat flow rate

Examples

Build Conventional Vehicle Model

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

Ports

Input

Ds — Drive shaft speed

two-way connector port

ShaftSpd — Signal containing the drive shaft angular speed, $\omega$, in rad/s.

A — Inlet pressure, temperature, enthalpy, mass fractions

two-way connector port

Bus containing the inlet control volume:

• InPrs — Pressure, $p_{\text{inlet}}$, in Pa

• InTemp — Temperature, $T_{inlet}$, in K

• InEnth — Specific enthalpy, $h_{inlet}$, in J/kg

B — Outlet pressure, temperature, enthalpy, mass fractions

two-way connector port

Bus containing the outlet control volume:

• OutPrs — Pressure, $p_{outlet}$, in Pa

• OutTemp — Temperature, $T_{outlet}$, in K

• OutEnth — Specific enthalpy, $h_{outlet}$, in J/kg

RackPos — Rack position

scalar

Variable geometry turbine rack position, $L_{rack}$.

Dependencies

To create this port, select Variable geometry for the Turbine type parameter.

WgAreaPct — Wastegate area percent

scalar

Wastegate valve area percent, $A_{wgpctcmd}$.

Dependencies

To create this port, select Include wastegate.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Units
TurbOutletTemp			Temperature exiting the turbine	K
DriveshftPwr			Drive shaft power	W
DriveshftTrq			Drive shaft torque	N·m
TurbMassFlw			Turbine mass flow rate	kg/s
PrsRatio			Pressure ratio	N/A
DriveshftCorrSpd			Corrected drive shaft speed	rad/s
TurbEff			Turbine isentropic efficiency	N/A
CorrMassFlw			Corrected mass flow rate	kg/s
WgArea			Wastegate valve area	m^2
WgMassFlw			Mass flow rate through the wastegate valve	kg/s
WgOutletTemp			Temperature exiting the wastegate valve	K
PwrInfo	PwrTrnsfrd	PwrDriveshft	Power transmitted from the shaft	W
		PwrHeatFlwIn	Heat flow rate at port A	W
		PwrHeatFlwOut	Heat flow rate at port B	W
	PwrNotTrnsfrd	PwrLoss	Power loss	W
	PwrStored		Not used

Ds — Drive shaft torque

two-way connector port

Trq — Signal containing the drive shaft torque, ${\tau }_{turb}$, in N·m.

A — Inlet mass flow rate, heat flow rate, temperature, mass fractions

two-way connector port

Bus containing:

• MassFlwRate — Total mass flow rate through wastegate valve and turbine, –${\dot{m}}_{total}$, in kg/s

• HeatFlwRate — Total inlet heat flow rate, –$q_{inlet}$, in J/s

• Temp — Total inlet temperature, $T_{inlet}$, in K

• MassFrac — 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

B — Outlet mass flow rate, heat flow rate, temperature, mass fractions

two-way connector port

Bus containing:

• MassFlwRate — Turbine mass flow rate through wastegate valve and turbine, ${\dot{m}}_{turb}$, in kg/s

• HeatFlwRate — Total outlet heat flow rate, $q_{outlet}$, in J/s

• Temp — Total outlet temperature, $T_{outflw}$, in K

• MassFrac — 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

Turbine type — Select turbine type

Fixed geometry (default) | Variable geometry

Turbine type.

Dependencies

The table summarizes the parameter and port dependencies.

Value	Enables Parameters	Creates Ports
Fixed geometry	Corrected mass flow rate table, mdot_corrfx_tbl Efficiency table, eta_turbfx_tbl Corrected speed breakpoints, w_corrfx_bpts1 Pressure ratio breakpoints, Pr_fx_bpts2	None
Variable geometry	Corrected mass flow rate table, mdot_corrvr_tbl Efficiency table, eta_turbvr_tbl Corrected speed breakpoints, w_corrvr_bpts2 Pressure ratio breakpoints, Pr_vr_bpts2 Rack breakpoints, L_rack_bpts3	RP

Include wastegate — Select

on (default) | off

Dependencies

Selecting the Include wastegate parameter enables:

• Wastegate flow area, A_wgopen

• Pressure ratio linearize limit, Plim_wg

Performance Tables

Calibrate Performance Maps — Calibrate tables with measured data

selection

If you have Model-Based Calibration Toolbox, click Calibrate Performance Maps to virtually calibrate the corrected mass flow rate and turbine efficiency lookup tables using measured data. The dialog box steps through these tasks.

Task	Description
Import turbine data	Import this turbine data from a file. For more information, see Using Data (Model-Based Calibration Toolbox). Turbine type Data Fixed geometry Speed, Spd, in rad/s Corrected mass flow rate, MassFlwRate, in kg/s Pressure ratio, PrsRatio, dimensionless Efficiency, Eff, dimensionless The speed, corrected mass flow rate, pressure ratio, and efficiency are in the 2nd-5th columns of the data file, respectively. The first and second rows of the data file provide the variable names and units. For example, use this format. Name: Spd MassFlwRate PrsRatio Eff Unit: rad/s kg/s     Data: 8373.3 0.02 1.21 0.44   ... ... ... ... Variable geometry Speed, Spd, in rad/s Corrected mass flow rate, MassFlwRate, kg/s Rack position, RackPos, dimensionless Pressure ratio, PrsRatio, dimensionless Efficiency, Eff, dimensionless Include data for several test points at each rack position operating point. The speed, corrected mass flow rate, rack position, pressure ratio, and efficiency are in the 2nd-6th columns of the data file, respectively. The first and second rows of the data file provide the variable names and units. For example, use this format. Name: Spd MassFlwRate RackPos PrsRatio Eff Unit: rad/s kg/s       Data: 8373.3 0.02 1 1.21 0.44   ... ...   ... ... Model-Based Calibration Toolbox limits the speed and pressure ratio breakpoint values to the maximum values in the file. To filter or edit the data, select Edit in Application. The Model-Based Calibration Toolbox Data Editor opens.
Generate response models	Model-Based Calibration Toolbox fits the imported data and generates response models. Turbine type Description Fixed geometry Data Response Model Corrected mass flow rate Square root turbine flow model described in Modeling and Control of Engines and Drivelines2 Efficiency Blade speed ratio (BSR) model described in Modeling and Control of Engines and Drivelines2 Variable geometry Model-Based Calibration Toolbox uses a point-by-point test plan to fit the data. For each rack position, the block uses these response models to fit the corrected mass flow rate and efficiency data. Data Response Model Corrected mass flow rate Square root turbine flow model described in Modeling and Control of Engines and Drivelines2 Efficiency Blade speed ratio (BSR) model described in Modeling and Control of Engines and Drivelines2 To assess or adjust the response model fit, select Edit in Application. The Model-Based Calibration Toolbox Model Browser opens. For more information, see Model Assessment (Model-Based Calibration Toolbox).
Generate calibration	Model-Based Calibration Toolbox calibrates the response model and generates calibrated tables. Turbine type Description Fixed geometry Model-Based Calibration Toolbox uses the response models for the corrected mass flow rate and efficiency tables. Variable geometry Model-Based Calibration Toolbox fills the corrected mass flow rate and efficiency tables for each rack position. Model-Based Calibration Toolbox then combines the rack position-dependent tables into 3D lookup tables for corrected mass flow rate and efficiency. To assess or adjust the calibration, select Edit in Application. The Model-Based Calibration Toolbox CAGE Browser opens. For more information, see Calibration Lookup Tables (Model-Based Calibration Toolbox).
Update block parameters	Update these corrected mass flow rate and efficiency parameters with the calibration. Turbine type Parameters Fixed geometry Corrected mass flow rate table, mdot_corrfx_tbl Efficiency table, eta_turbfx_tbl Corrected speed breakpoints, w_corrfx_bpts1 Pressure ratio breakpoints, Pr_fx_bpts2 Variable geometry Corrected mass flow rate table, mdot_corrvr_tbl Efficiency table, eta_turbvr_tbl Corrected speed breakpoints, w_corrvr_bpts2 Pressure ratio breakpoints, Pr_vr_bpts2 Rack breakpoints, L_rack_bpts3

Corrected mass flow rate table, mdot_corrfx_tbl — Lookup table

array

Corrected mass flow rate lookup table for fixed geometry, ${\dot{m}}_{corrfx,tbl}$, as a function of corrected driveshaft speed, ω_corr, and pressure ratio, p_r, in kg/s.

Dependencies

To enable this parameter, select Fixed geometry for the Turbine type parameter.

Efficiency table, eta_turbfx_tb — Lookup table

array

Efficiency lookup table for fixed geometry, ${\eta }_{turbfx,tbl}$, as a function of corrected driveshaft speed, ω_corr, and pressure ratio, p_r, dimensionless.

Dependencies

To enable this parameter, select Fixed geometry for the Turbine type parameter.

Corrected speed breakpoints, w_corrfx_bpts1 — Fixed geometry

[0 1552 3104 4657 6209 7761 9313 1.087e+04 1.242e+04 1.397e+04] (default) | vector

Corrected drive shaft speed breakpoints for fixed geometry, ${\omega }_{corrfx,bpts1}$, in rad/s.

Dependencies

To enable this parameter, select Fixed geometry for the Turbine type parameter.

Pressure ratio breakpoints, Pr_fx_bpts2 — Fixed geometry

[1 1.333 1.667 2 2.333 2.667 3 3.333 3.667 4] (default) | vector

Pressure ratio breakpoints for fixed geometry, $p_{rfx,bpts2}$.

Dependencies

To enable this parameter, select Fixed geometry for the Turbine type parameter.

Corrected mass flow rate table, mdot_corrvr_tbl — Lookup table

array

Corrected mass flow rate lookup table for variable geometry, ${\dot{m}}_{corrvr,tbl}$, as a function of corrected driveshaft speed, ω_corr, and pressure ratio, p_r, in kg/s.

Dependencies

To enable this parameter, select Variable geometry for the Turbine type parameter.

Efficiency table, eta_turbvr_tbl — Lookup table

array

Efficiency lookup table for variable geometry, ${\eta }_{turbvr,tbl}$, as a function of corrected driveshaft speed, ω_corr, and pressure ratio, p_r, dimensionless.

Dependencies

To enable this parameter, select Variable geometry for the Turbine type parameter.

Corrected speed breakpoints, w_corrvr_bpts2 — Variable geometry

[0 1752 3504 5257 7009 8761 1.051e+04 1.227e+04 1.402e+04 1.577e+04] (default) | vector

Corrected drive shaft speed breakpoints for variable geometry, ${\omega }_{corrvr,bpts1}$, in rad/s.

Dependencies

To enable this parameter, select Variable geometry for the Turbine type parameter.

Pressure ratio breakpoints, Pr_vr_bpts2 — Variable geometry

[1 1.306 1.611 1.917 2.222 2.528 2.833 3.139 3.444 3.75] (default) | vector

Pressure ratio breakpoints for variable geometry.

Dependencies

To enable this parameter, select Variable geometry for the Turbine type parameter.

Rack breakpoints, L_rack_bpts3 — Variable geometry

[0 0.2 0.3 0.5 0.7 1] (default) | vector

Rack position breakpoints for variable geometry, $L_{rack,bpts3}$.

Dependencies

To enable this parameter, select Variable geometry for the Turbine type parameter.

Reference temperature, T_ref — Temperature

293.15 (default) | scalar

Performance map reference temperature, $T_{ref}$, in K.

Reference pressure, P_ref — Pressure

101325 (default) | scalar

Performance map reference pressure, $P_{ref}$, in Pa.

Wastegate

Wastegate flow area, A_wgopen — Area

0.0003 (default) | scalar

Area of fully opened wastegate valve, $A_{wgopen}$, in m^2.

Dependencies

To enable Wastegate flow area, A_wgopen, select the Include wastegate parameter.

Pressure ratio linearize limit, Plim_wg — Area, m^2

0.95 (default) | scalar

Dependencies

Flow restriction linearization limit, $p_{lim,wg}$.

To enable Pressure ratio linearize limit, Plim_wg, select the Include wastegate parameter.

Properties

Ideal gas constant, R — Constant

287 (default) | scalar

Ideal gas constant $R$, in J/(kg·K).

Specific heat at constant pressure, cp — Specific heat

1005 (default) | scalar

Specific heat at constant pressure, $c_p$, in J/(kg·K).

References

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

[2] Eriksson, Lars and Lars Nielsen. Modeling and Control of Engines and Drivelines. Chichester, West Sussex, United Kingdom: John Wiley & Sons Ltd, 2014.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a