Flow Restriction

Isentropic ideal gas flow through an orifice

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Libraries:
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.

Calculation	Equations
Standard orifice	${\dot{m}}_{orf}=\Gamma \cdot \Psi \left(P_{ratio}\right)$ $P_{ratio}=\frac{P_{downstr}}{P_{upstr}}$ $\Gamma =\frac{A_{eff}\cdot P_{upstr}}{\sqrt{R\cdot T_{upstr}}}$ $$P_{cr}={\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma }{\gamma -1}}$$ $$\Psi =\{\begin{array}{cc}\sqrt{\gamma {\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{\gamma -1}}}& P_{ratio}<P_{cr}\\ \sqrt{\frac{2\gamma }{\gamma -1}\left(P_{ratio}{}^{\frac{2}{\gamma }}-P_{ratio}{}^{\frac{\gamma +1}{\gamma }}\right)}& P_{cr}\le P_{ratio}\le P_{lim}\\ \frac{P_{ratio}-1}{P_{lim}-1}\sqrt{\frac{2\gamma }{\gamma -1}\left(P_{lim}{}^{\frac{2}{\gamma }}-P_{lim}{}^{\frac{\gamma +1}{\gamma }}\right)}& P_{lim}<P_{ratio}\end{array}$$
Constituent mass flow rates	$${\dot{m}}_i={\dot{m}}_{orf}{y}_{upstr,i}$$
Constant orifice area	$A_{eff}=A_{orf\_cnst}\cdot C{d}_{cnst}$
External input orifice area	$A_{eff}=A_{orf\_ext}\cdot C{d}_{ext}$
Throttle body geometry	${\theta }_{thr}=Pc{t}_{thr}\cdot \frac{90}{100}$ $A_{eff\_thr}=\frac{\pi }{4}{D}_{thr}{}^2{C}_{d\_thr}\left({\theta }_{thr}\right)$
Heat flow rate	$q_{orf}={\dot{m}}_{orf}{h}_{upstr}$

The equations use these variables.

$A_{eff}$, $A_{eff\_thr}$	Effective orifice cross-sectional area
$A_{orf\_cnst}$, $A_{orf\_ext}$	Orifice area
$C{d}_{cnst}$, $C{d}_{ext}$	Discharge coefficient
$R$	Ideal gas constant
$P_{cr}$	Critical pressure at which choked flow occurs
γ	Ratio of specific heats
$\Gamma$	Flow function based on pressure ratio
$P_{ratio}$	Pressure ratio
$P_{upstr}$	Upstream orifice pressure
$P_{downstr}$	Downstream orifice pressure
$P_{lim}$	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
$${\dot{m}}_i$$	Mass flow rate for i = O2, N2, unburned fuel, CO2, H2O, CO, NO, NO2, PM, air, and burned gas
${\theta }_{thr}$	Throttle angle
$Pc{t}_{thr}$	Percentage of throttle body that is open
Cd_thr	Throttle discharge coefficient
$D_{thr}$	Throttle body diameter at opening
${\dot{m}}_{orf}$	Orifice mass flow
hupstr	Upstream specific enthalpy
qorf	Heat flow rate

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

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	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

Examples

Build Conventional Vehicle Model

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

Ports

Input

A — Inlet orifice pressure, temperature, enthalpy, mass fractions

two-way connector port

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

B — Outlet orifice pressure, temperature, enthalpy, mass fractions

two-way connector port

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

Area — Orifice area

scalar

External area input for orifice area, $A_{orf\_ext}$, in m^2.

Dependencies

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

ThrPct — Throttle body percent open

scalar

Percentage of throttle body that is open, $Pc{t}_{thr}$.

Dependencies

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

Output

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

two-way connector port

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

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

two-way connector port

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

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal				Description	Units
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

Block Options

Orifice area model — Select model

Constant (default) | External input | Throttle body geometry

Orifice area model.

Dependencies

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

Image type — Icon color

Cold (default) | Hot

Block icon color:

• Cold for blue.

• Hot for red.

General

Ratio of specific heats, gamma — Ratio

1.3998 (default) | scalar

Ratio of specific heats, γ.

Ideal gas constant, R — Constant

287.05 (default) | scalar

Ideal gas constant, $R$, in J/(kg·K).

Pressure ratio linearize limit, Plim — Limit

0.95 (default) | scalar

Pressure ratio limit to avoid singularities as the pressure ratio approaches 1, $P_{lim}$.

Area

Constant area value, Aorf_cnst — Area

.1 (default) | scalar

Constant area value, $A_{orf\_cnst}$, in m^2.

Dependencies

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

Discharge coefficient, Cd_cnst — Coefficient

1 (default) | scalar

Discharge coefficient for constant area, $C{d}_{cnst}$.

Dependencies

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

Discharge coefficient, Cd_ext — Coefficient

1 (default) | scalar

Discharge coefficient for external area input, $C{d}_{ext}$.

Dependencies

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

Throttle diameter, Dthr — Diameter

50 (default) | scalar

Throttle body diameter at opening, $D_{thr}$, in mm.

Dependencies

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

Discharge coefficient table, ThrCd — Coefficient

[0.001; 0.735] (default) | vector

Discharge coefficient table, C_{d_thr}.

Dependencies

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

Angle breakpoints, ThrAngBpts — Angle

[0; 90] (default) | vector

Angle breakpoints, $Th{r}_{ang\_bpts}$, 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™.

Version History

Introduced in R2017a