Flow Restriction

Isentropic ideal gas flow through an orifice

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  • Powertrain Blockset / Propulsion / Combustion Engine Components / Fundamental Flow

Description

The Flow Restriction block models isentropic ideal gas flow through an orifice. The block uses the conservation of mass and energy to determine the mass flow rate. The flow velocity is limited by choked flow.

You can specify these orifice area models:

  • Constant

  • External input

  • Throttle body geometry

Equations

The Flow Restriction block implements these equations.

CalculationEquations

Standard orifice

m˙orf=ΓΨ(Pratio)

Pratio=PdownstrPupstr

Γ=AeffPupstrRTupstr

Pcr=(2γ+1)γγ1

Ψ={γ(2γ+1)γ+1γ1Pratio<Pcr2γγ1(Pratio2γPratioγ+1γ)PcrPratioPlimPratio1Plim12γγ1(Plim2γPlimγ+1γ)Plim<Pratio

Constituent mass flow rates

m˙i=m˙orfyupstr,i

Constant orifice area

Aeff=Aorf_cnstCdcnst

External input orifice area

Aeff=Aorf_extCdext

Throttle body geometry

θthr=Pctthr90100

Aeff_thr=π4Dthr2Cd_thr(θthr)

Heat flow rate

qorf=m˙orfhupstr

The equations use these variables.

Aeff, Aeff_thr

Effective orifice cross-sectional area

Aorf_cnst, Aorf_ext

Orifice area

Cdcnst, Cdext

Discharge coefficient

R

Ideal gas constant

Pcr

Critical pressure at which choked flow occurs

γ

Ratio of specific heats

Γ

Flow function based on pressure ratio

Pratio

Pressure ratio

Pupstr

Upstream orifice pressure

Pdownstr

Downstream orifice pressure

Plim

Pressure ratio limit to avoid singularities as the pressure ratio approaches 1

yupstr,i

Upstream species mass fraction for i = O2, N2, unburned fuel, CO2, H2O, CO, NO, NO2, PM, air, and burned gas

m˙i

Mass flow rate for i = O2, N2, unburned fuel, CO2, H2O, CO, NO, NO2, PM, air, and burned gas

θthr

Throttle angle

Pctthr

Percentage of throttle body that is open

Cd_thr

Throttle discharge coefficient

Dthr

Throttle body diameter at opening

m˙orf

Orifice mass flow

hupstr

Upstream specific enthalpy

qorf

Heat flow rate

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

PwrHeatFlwIn

Heat flow rate at port A

qorf

PwrHeatFlwOut

Heat flow rate at port B

-qorf

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

Not used

PwrStored — Stored energy rate of change

  • Positive signals indicate an increase

  • Negative signals indicate a decrease

Not used

Ports

Input

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Bus containing orifice:

  • Prs — Pressure, in Pa

  • Temp — Temperature, in K

  • Enth — Specific enthalpy, in J/kg

  • MassFrac — Inlet 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 orifice:

  • Prs — Pressure, in Pa

  • Temp — Temperature, in K

  • Enth — Specific enthalpy, in J/kg

  • MassFrac — Outlet 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

External area input for orifice area, Aorf_ext, in m^2.

Dependencies

To create this port, select External input for the Orifice area model parameter.

Percentage of throttle body that is open, Pctthr.

Dependencies

To create this port, select Throttle body geometry for the Orifice area model parameter.

Output

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Bus containing:

  • MassFlw — Mass flow rate through inlet, in kg/s

  • HeatFlw — Inlet heat flow rate, in J/s

  • Temp — Inlet temperature, in K

  • MassFrac — Inlet 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:

  • MassFlw — Outlet mass flow rate, in kg/s

  • HeatFlw — Outlet heat flow rate, in J/s

  • Temp — Outlet temperature, in K

  • MassFrac — Outlet 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 signal containing these block calculations.

SignalDescriptionUnits

Flw

PrsAdj

DwnstrmPrs

Downstream pressure

Pa

UpstrmPrs

Upstream pressure

Pa

PrsRatio

Pressure ratio

NA

DwnstrmTemp

Downstream temperature

K

UpstrmTemp

Upstream temperature

K

OrfMassFlw

Mass flow rate through orifice

kg/s

Species

O2MassFlw

Oxygen mass flow rate

kg/s

N2MassFlw

Nitrogen mass flow rate

kg/s

UnbrndFuelMassFlw

Unburned gas mass flow rate

kg/s

CO2MassFlw

Carbon dioxide mass flow rate

kg/s

H2OMassFlw

Water mass flow rate

kg/s

COMassFlw

Carbon monoxide mass flow rate

kg/s

NOMassFlw

Nitric oxide mass flow rate

kg/s

NO2MassFlw

Nitrogen dioxide mass flow rate

kg/s

NOxMassFlw

Nitric oxide and nitrogen dioxide mass flow rate

kg/s

PmMassFlw

Particulate matter mass flow rate

kg/s

AirMassFlw

Air mass flow rate

kg/s

BrnedGasMassFlw

Burned gas mass flow rate

kg/s

PwrInfo

PwrTrnsfrd

PwrHeatFlwIn

Heat flow rate at port A

W

PwrHeatFlwOut

Heat flow rate at port B

W

PwrNotTrnsfrd

Not used

PwrStored

Not used

Area

FlwArea

Cross-sectional flow area

m^2

EffctArea

Effective orifice cross-sectional area

m^2

ThrAng

Throttle area, if applicable

deg

Parameters

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Block Options

Orifice area model.

Dependencies

The orifice area model enables the parameters on the Area Parameters tab.

Block icon color:

  • Cold for blue.

  • Hot for red.

General

Ratio of specific heats, γ.

Ideal gas constant, R, in J/(kg·K).

Pressure ratio limit to avoid singularities as the pressure ratio approaches 1, Plim.

Area

Constant area value, Aorf_cnst, in m^2.

Dependencies

To enable this parameter, select Constant for the Orifice area model parameter.

Discharge coefficient for constant area, Cdcnst.

Dependencies

To enable this parameter, select Constant for the Orifice area model parameter.

Discharge coefficient for external area input, Cdext.

Dependencies

To enable this parameter, select External input for the Orifice area model parameter.

Throttle body diameter at opening, Dthr, in mm.

Dependencies

To enable this parameter, select Throttle body geometry for the Orifice area model parameter.

Discharge coefficient table, Cd_thr.

Dependencies

To enable this parameter, select Throttle body geometry for the Orifice area model parameter.

Angle breakpoints, Thrang_bpts, in deg.

Dependencies

To enable this parameter, select Throttle body geometry for the Orifice area model parameter.

References

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

Extended Capabilities

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

Introduced in R2017a