Turbine

Turbine for boosted engines

  • Library:
  • 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
  • Pressure ratio, dimensionless

  • Speed, rad/s

  • Efficiency, dimensionless

  • Corrected mass flow rate, kg/s

Variable geometry

  • Pressure ratio, dimensionless

  • Speed, rad/s

  • Rack position, dimensionless

  • Efficiency, dimensionless

  • Corrected mass flow rate, kg/s

Include data for several test points at each rack position operating point.

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 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.

CalculationEquations
Forward mass flow

m˙turb>0

p01=pinlet

p02=poutlet

T01=Tinlet

h01=hinlet

First law of thermodynamics

W˙turb=m˙turbcp(T01T02)

Isentropic efficiency

ηturb=h01h02h01h02s=T01T02T01T02s

Isentropic outlet temperature, assuming ideal gas, and constant specific heats

T02s=T01(p02p01)γ1γ

Specific heat ratio

γ=cpcpR

Outlet temperature

T02=T01+ηturbT01{1(p02p01)γ1γ}

Heat flows

qin,turb=m˙turbcpT01

qout,turb=m˙turbcpT02

Drive shaft torque

τturb=W˙turbω

The equations use these variables.

pinlet,p01

Inlet control volume total pressure

Tinlet, T01

Inlet control volume total temperature

hinlet, h01

Inlet control volume total specific enthalpy

poutlet, p02

Outlet control volume total pressure

Toutlet

Outlet control volume total temperature

houtlet

Outlet control volume total specific enthalpy

W˙turb

Drive shaft power

T02

Temperature exiting the turbine

h02

Outlet total specific enthalpy

m˙turb

Turbine mass flow rate

qin,turb

Turbine inlet heat flow rate

qout,turb

Turbine outlet heat flow rate

ηturb

Turbine isentropic efficiency

T02s

Isentropic outlet total temperature

h02s

Isentropic outlet total specific enthalpy

R

Ideal gas constant

cp

Specific heat at constant pressure

γ

Specific heat ratio

τturb

Drive shaft torque

Performance Lookup Tables

The block implements lookup tables based on these equations.

CalculationEquation

Corrected mass flow rate

m˙corr=m˙turbT01/Trefp01/pref

Corrected speed

ωcorr=ωT01/Tref

Pressure expansion ratio

pr=p01p02
Efficiency lookup tableFixed geometry (3-D table)ηturbfx,tbl=f(ωcorr,pr)
Variable geometry (3-D table)ηturbvr,tbl=f(ωcorr,pr,Lrack)
Corrected mass flow lookup tableFixed geometry (3-D table)m˙corrfx,tbl=f(ωcorr,pr)
Variable geometry (3-D table)m˙corrvr,tbl=f(ωcorr,pr,Lrack)

The equations use these variables.

p01

Inlet control volume total pressure

pr

Pressure expansion ratio

p02

Outlet control volume total pressure

Pref

Lookup table reference pressure

T01

Inlet control volume total temperature

Tref

Lookup table reference temperature

m˙turb

Turbine mass flow rate

ω

Drive shaft speed

ωcorr

Corrected drive shaft speed

Lrack

Variable geometry turbine rack position

ηturbfx,tbl

Efficiency 3-D lookup table for fixed geometry

m˙corrfx,tbl

Corrected mass flow rate 3-D lookup table for fixed geometry

ηturbvr,tbl

Efficiency 3-D lookup table for variable geometry

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.

Awg=AwgpctcmdAwgopen100

The equation uses these variables.

Awgpctcmd

Wastegate valve area percent command

Awg

Wastegate valve area

Awgopen

Wastegate valve area when fully open

Combined Flow

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

CalculationEquations

Blocks not configured with a wastegate valve

m˙wg=qwg=0

Total mass flow rate

m˙total=m˙turb+m˙wg

Total heat flow rate

qinlet=qin,turb+qwg

qoutlet=qout,turb+qwg

Combined temperature exiting the wastegate valve and turbine

Toutflw={qoutletm˙totalcpm˙total>m˙threshT02+Toutflw,wg2else

The equations use these variables.

m˙total

Total mass flow rate through the wastegate valve and turbine

m˙turb

Turbine mass flow rate

m˙wg

Mass flow rate through the wastegate valve

qinlet

Total inlet heat flow rate

qoutlet

Total outlet heat flow rate

qin,turb

Turbine inlet heat flow rate

qout,turb

Turbine outlet heat flow rate

qwg

Wastegate valve heat flow rate

T02

Temperature exiting the turbine

Toutflw

Total temperature exiting the block

Toutflw,wg

Temperature exiting the wastegate valve

m˙thresh

Mass flow rate threshold to prevent dividing by zero

cp

Specific heat at constant pressure

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionEquations

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

W˙turb

PwrHeatFlwIn

Heat flow rate at port A

qoutlet

PwrHeatFlwOut

Heat flow rate at port B

qoutlet

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrLoss

Power loss

qinletqoutlet+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.

W˙turb

Drive shaft power

qoutlet

Total outlet heat flow rate

qinlet

Total inlet heat flow rate

Ports

Input

expand all

ShaftSpd — Signal containing the drive shaft angular speed, ω, in rad/s.

Bus containing the inlet control volume:

  • InPrs — Pressure, pinlet, in Pa

  • InTemp — Temperature, Tinlet, in K

  • InEnth — Specific enthalpy, hinlet, in J/kg

Bus containing the outlet control volume:

  • OutPrs — Pressure, poutlet, in Pa

  • OutTemp — Temperature, Toutlet, in K

  • OutEnth — Specific enthalpy, houtlet, in J/kg

Variable geometry turbine rack position, Lrack.

Dependencies

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

Wastegate valve area percent, Awgpctcmd.

Dependencies

To create this port, select Include wastegate.

Output

expand all

Bus signal containing these block calculations.

SignalDescriptionUnits

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

PwrTrnsfrdPwrDriveshft

Power transmitted from the shaft

W

PwrHeatFlwIn

Heat flow rate at port A

W
PwrHeatFlwOut

Heat flow rate at port B

W
PwrNotTrnsfrdPwrLoss

Power loss

W
PwrStored

Not used

Trq — Signal containing the drive shaft torque, τturb, in N·m.

Bus containing:

  • MassFlwRate — Total mass flow rate through wastegate valve and turbine, –m˙total, in kg/s

  • HeatFlwRate — Total inlet heat flow rate, –qinlet, in J/s

  • Temp — Total inlet temperature, Tinlet, 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

Bus containing:

  • MassFlwRate — Turbine mass flow rate through wastegate valve and turbine, m˙turb, in kg/s

  • HeatFlwRate — Total outlet heat flow rate, qoutlet, in J/s

  • Temp — Total outlet temperature, Toutflw, 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

expand all

Block Options

Turbine type.

Dependencies

The table summarizes the parameter and port dependencies.

ValueEnables ParametersCreates 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

Dependencies

Selecting the Include wastegate parameter enables:

  • Wastegate flow area, A_wgopen

  • Pressure ratio linearize limit, Plim_wg

Performance Tables

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
  • Pressure ratio, dimensionless

  • Speed, rad/s

  • Efficiency, dimensionless

  • Corrected mass flow rate, kg/s

Variable geometry

  • Pressure ratio, dimensionless

  • Speed, rad/s

  • Rack position, dimensionless

  • Efficiency, dimensionless

  • Corrected mass flow rate, kg/s

Include data for several test points at each rack position operating point.

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 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 lookup table for fixed geometry, m˙corrfx,tbl, as a function of corrected driveshaft speed, ωcorr, and pressure ratio, pr, in kg/s.

Dependencies

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

Efficiency lookup table for fixed geometry, ηturbfx,tbl, as a function of corrected driveshaft speed, ωcorr, and pressure ratio, pr, dimensionless.

Dependencies

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

Corrected drive shaft speed breakpoints for fixed geometry, ωcorrfx,bpts1, in rad/s.

Dependencies

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

Pressure ratio breakpoints for fixed geometry, prfx,bpts2.

Dependencies

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

Corrected mass flow rate lookup table for variable geometry, m˙corrvr,tbl, as a function of corrected driveshaft speed, ωcorr, and pressure ratio, pr, in kg/s.

Dependencies

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

Efficiency lookup table for variable geometry, ηturbvr,tbl, as a function of corrected driveshaft speed, ωcorr, and pressure ratio, pr, dimensionless.

Dependencies

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

Corrected drive shaft speed breakpoints for variable geometry, ωcorrvr,bpts1, in rad/s.

Dependencies

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

Pressure ratio breakpoints for variable geometry.

Dependencies

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

Rack position breakpoints for variable geometry, Lrack,bpts3.

Dependencies

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

Performance map reference temperature, Tref, in K.

Performance map reference pressure, Pref, in Pa.

Wastegate

Area of fully opened wastegate valve, Awgopen, in m^2.

Dependencies

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

Dependencies

Flow restriction linearization limit, plim,wg.

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

Properties

Ideal gas constant R, in J/(kg·K).

Specific heat at constant pressure, cp, 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.

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