Control Volume System

Constant volume open thermodynamic system with heat transfer

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

Description

The Control Volume System block models a constant volume open thermodynamic system with heat transfer. The block uses the conservation of mass and energy, assuming an ideal gas, to determine the pressure and temperature. The block implements an automotive-specific Constant Volume Pneumatic Chamber block that includes thermal effects related to the under hood of passenger vehicles. You can specify heat transfer models:

  • Constant

  • External input

  • External wall convection

You can use the Control Volume System block to represent engine components that contain volume, including pipes and manifolds.

Thermodynamics

The Control Volume System block implements a constant volume chamber containing an ideal gas. To determine the rate changes in temperature and pressure, the block uses the continuity equation and the first law of thermodynamics.

dTvoldt=RTvolcvVchPvol((qiTvolcvm˙i)Qwall)dPvoldt=PvolTvoldTvoldt+RTvolVchm˙i

The block uses this equation for the volume-specific enthalpy.

hvol=cpTvol

The equations use these variables.

m˙i

Mass flow rate at port

qi

Heat flow rate at port

Vch

Chamber volume

Pvol

Absolute pressure in the chamber

R

Ideal gas constant

cv

Specific heat at constant volume

Tvol

Absolute gas temperature

Qwall

Wall heat transfer rate

hvol

Volume-specific enthalpy

cp

Specific heat capacity

Mass Fractions

The Control Volume Source block is part of a flow network. Blocks in the network determine the mass fractions that the block will track during simulation. The block can track these mass fractions:

  • O2 — Oxygen

  • N2 — Nitrogen

  • UnburnedFuel — Unburned fuel

  • CO2 — Carbon dioxide

  • H2O — Water

  • CO — Carbon monoxide

  • NO — Nitric oxide

  • NO2 — Nitrogen dioxide

  • PM — Particulate matter

  • Air — Air

  • BurnedGas — Burned gas

Using the conservation of mass for each gas constituent, this equation determines the rate change:

dyvol,jdt=RTvolPvolVch(m˙iyi,j+yvol,jm˙i)

The equations use these variables.

Vch

Chamber volume

Pvol

Absolute pressure in the chamber

R

Ideal gas constant

Tvol

Absolute gas temperature

yi,j

I-th port mass fraction for j = O2, N2, unburned fuel, CO2, H2O, CO, NO, NO2, PM, air, and burned gas

yvol,j

Control volume mass fraction for j = 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

External Wall Convection Heat Transfer Model

To calculate the heat transfer, you can configure the Control Volume Source block to calculate the heat transfer across the wall of the control volume.

The block implements these equations to calculate the heat transfer, Q1, from the internal control volume gas to the internal wall depth, Dint_cond.

Q1=Q1,conv=Q1,cond

Q1,conv=hint(xint)Aint_conv(Tint_gasTw_int)

Q1,cond=kintAint_condDint_cond(Tw_intTmass)

The block implements these equations to calculate the heat transfer, Q2, from the external wall depth, Dext_cond to the external gas.

Q2=Q2,conv=hext(xext)Aext_conv(Tw_extText_gas)

Q2,cond=kextAext_condDext_cond(TmassTw_ext)

This equation expresses the heat stored in the thermal mass.

dTmassdt=Q1Q2cpwallmwall

The block determines the interior convection heat transfer coefficient using a lookup table that is a function of the average mass flow rate.

m˙int_gas=12|m˙i|

The equations use these variables.

Q1

Heat flow from the internal gas to a specified wall depth

Q1,conv

Heat flow convection from the internal gas to the internal wall

Q1,cond

Conduction heat transfer rate

Q2

Heat transfer rate

Q2,conv

Convection heat transfer

Q2,cond

Heat flow conduction from the external middle portion of the wall to the external wall

Qmass

Heat stored in thermal mass

hint

Internal convection heat transfer coefficient

xint

Internal mass flow rate breakpoints

Aint_conv

Internal flow convection area

Tint_gas

Temperature of the gas inside the chamber

Tw_int

Temperature of the inside wall of the chamber

kint

Internal wall thermal conductivity

Aint_cond

Internal conduction area

Dint_cond

Internal wall thickness

hext

External convection heat transfer coefficient

xext

External velocity breakpoints

Aext_conv

External convection area

Text_gas

External gas temperature

Tw_ext

Temperature of the external wall of the chamber

kext

External wall thermal conductivity

Aext_cond

External conduction area

Dext_cond

External wall thickness

Tmass

Temperature of the thermal mass

cp_wall

Wall heat capacity

mwall

Thermal mass

Flwspd

External flow velocity

m˙int_gas

Average internal mass flow rate

Power Accounting

For the power accounting, the block implements these equation based on the number of inlet and outlet ports.

Bus Signal DescriptionEquations

PwrInfo

PwrTrnsfrd — Power transferred between blocks

  • Positive signals indicate flow into block

  • Negative signals indicate flow out of block

PwrHeatFlwi

Port i heat flow

qi

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrHeatTrnsfr

Heat transfer rate from wall to control volume

-Qwall

PwrStored — Stored energy rate of change

  • Positive signals indicate an increase

  • Negative signals indicate a decrease

PwrHeatStored

Rate of heat stored in the control volume

((qi)Qwall)

For example, if you configure your block with 3 input ports and 2 outlet ports, 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

PwrHeatFlw1

Inlet port 1 heat flow

q1

PwrHeatFlw2

Inlet port 2 heat flow

q2

PwrHeatFlw3

Inlet port 3 heat flow

q3

PwrHeatFlw4

Outlet port 4 heat flow

q4

PwrHeatFlw5

Outlet port 5 heat flow

q5

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrHeatTrnsfr

Heat transfer rate from wall to control volume

-Qwall

PwrStored — Stored energy rate of change

  • Positive signals indicate an increase

  • Negative signals indicate a decrease

PwrHeatStored

Rate of heat stored in the control volume

((qi)Qwall)

Ports

Input

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Bus containing:

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

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

  • 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

Dependencies

To create input ports, specify the Number of inlet ports parameter.

External heat transfer input to control volume, qhe, in Kg/s.

Dependencies

To create this port, select External input for the Heat transfer model parameter.

External flow velocity, Flwspd, in m/s.

Dependencies

To create this port, select External wall convection for the Heat transfer model parameter.

Dependencies

To create this port, select External wall convection for the Heat transfer model parameter.

Output

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Bus signal containing these block calculations.

SignalDescriptionUnits

Vol

Prs

Volume pressure

Pa

Temp

Volume temperature

K

Enth

Volume specific enthalpy

J/kg

Species

O2MassFrac

Oxygen mass fraction

NA

N2MassFrac

Nitrogen mass fraction

NA

UnbrndFuelMassFrac

Unburned gas mass fraction

NA

CO2MassFrac

Carbon dioxide mass fraction

NA

H2OMassFrac

Water mass fraction

NA

COMassFrac

Carbon monoxide mass fraction

NA

NOMassFrac

Nitric oxide mass fraction

NA

NO2MassFrac

Nitrogen dioxide mass fraction

NA

NOxMassFrac

Nitric oxide and nitrogen dioxide mass fraction

NA

PmMassFrac

Particulate matter mass fraction

NA

AirMassFrac

Air mass fraction

NA

BrndGasMassFrac

Burned gas mass fraction

NA

HeatTrnsfr

HeatTrnsfrRate

Wall heat transfer rate

J/s

MassFlw

Average internal mass flow rate

kg/s

IntrnTemp

Temperature of gas inside chamber

K

PwrInfo

PwrTrnsfrd

PwrHeatFlwi

Port i heat flow

W

PwrNotTrnsfrd

PwrHeatTrnsfr

Heat transfer rate from wall to control volume

W

PwrStored

PwrHeatStored

Rate of heat stored in the control volume

W

Bus containing the outlet control volume:

  • Prs — Chamber pressure, in Pa

  • Temp — Gas temperature, in K

  • Enth — Specific enthalpy, in J/kg

  • 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

Dependencies

To create outlet ports, specify the Number of outlet ports parameter.

Parameters

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Block Options

Number of inlet ports.

Dependencies

To create inlet ports, specify the number.

Number of outlet ports.

Dependencies

To create outlet ports, specify the number.

Dependencies

Selecting Constant or External wall convection enables the Heat Transfer parameters.

Select color for block icon:

  • Cold for blue

  • Hot for red

General

Chamber volume, Vch, in m^3.

Initial chamber pressure, Pvol, in Pa.

Initial chamber temperature, Tvol, in K.

Ideal gas constant, R, in J/(kg*K).

Specific heat capacity, cp, in J/(kg·K).

Heat Transfer

Constant heat transfer rate, qhe, in J/s.

Dependencies

To enable this parameter, select Constant for the Heat transfer model parameter.

External convection heat transfer coefficient, hext, in W/(m^2K).

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

External velocity breakpoints, xext, in m/s.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

External convection area, Aext_conv, in m^2.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Thermal mass, mwall, in kg.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Wall heat capacity, cp_wall, in J/(kg·K).

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Initial mass temperature, Tmass, in K.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

External wall thickness, Dext_cond, in m.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

External conduction area, Aext_cond, in m^2.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

External wall thermal conductivity, kext, in W/(m·K).

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal wall thickness, Dint_cond, in m.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal conduction area, Aint_cond, in m^2.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal wall thermal conductivity, kint, in W/(m·K).

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal convection heat transfer coefficient, hint, in W/(m^2K).

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal velocity breakpoints, xint, in kg/s.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer model parameter.

Internal convection area, Aint_conv, in m^2.

Dependencies

To enable this parameter, select External wall convection for the Heat transfer 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