Control Volume System

Constant volume open thermodynamic system with heat transfer

• 

×

Libraries:
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.

$$\begin{array}{l}\frac{d{T}_{vol}}{dt}=\frac{R{T}_{vol}}{c_v{V}_{ch}{P}_{vol}}\left({\displaystyle \sum \left(q_i-T_{vol}{c}_v{\dot{m}}_i\right)-Q_{wall}}\right)\\ \frac{d{P}_{vol}}{dt}=\frac{P_{vol}}{T_{vol}}\frac{d{T}_{vol}}{dt}+\frac{R{T}_{vol}}{V_{ch}}{\displaystyle \sum {\dot{m}}_i}\end{array}$$

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

$$h_{vol}=c_p{T}_{vol}$$

The equations use these variables.

${\dot{m}}_i$	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:

$$\frac{d{y}_{vol,j}}{dt}=\frac{R{T}_{vol}}{P_{vol}{V}_{ch}}\left({\displaystyle \sum {\dot{m}}_i{y}_{i,j}}+y_{vol,j}{\displaystyle \sum {\dot{m}}_i}\right)$$

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
$${\dot{m}}_i$$	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, D_{int_cond}.

$Q_1=Q_{1,conv}=Q_{1,cond}$

$Q_{1,conv}=h_{int}\left(x_{int}\right)•A_{int\_conv}•\left(T_{int\_gas}-T_{w\_int}\right)$

$Q_{1,cond}=k_{int}•\frac{A_{int\_cond}}{D_{int\_cond}}•\left(T_{w\_int}-T_{mass}\right)$

The block implements these equations to calculate the heat transfer, Q₂, from the external wall depth, D_{ext_cond} to the external gas.

$Q_2=Q_{2,conv}=h_{ext}\left(x_{ext}\right)•A_{ext\_conv}•\left(T_{w\_ext}-T_{ext\_gas}\right)$

$Q_{2,cond}=k_{ext}•\frac{A_{ext\_cond}}{D_{ext\_cond}}•\left(T_{mass}-T_{w\_ext}\right)$

This equation expresses the heat stored in the thermal mass.

$\frac{d{T}_{mass}}{dt}=\frac{Q_1-Q_2}{c_{p_{wall}}{m}_{wall}}$

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

$${\dot{m}}_{int\_gas}=\frac{1}{2}{\displaystyle \sum \left|{\dot{m}}_i\right|}$$

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
$${\dot{m}}_{int\_gas}$$	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			Description	Equations
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	$\left({{\displaystyle \sum }}^{\text{}}\left(q_i\right)-Q_{wall}\right)$

For example, if you configure your block with 3 input ports and 2 outlet ports, 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	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	$\left({{\displaystyle \sum }}^{\text{}}\left(q_i\right)-Q_{wall}\right)$

Examples

Build Conventional Vehicle Model

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

Ports

Input

C — Inlet mass flow rate, heat flow rate, mass fractions

two-way connector port

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.

HeatTrnsfrRate — Heat transfer

scalar

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

Dependencies

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

ExtnlFlwVel — External flow velocity

scalar

External flow velocity, Flw_spd, in m/s.

Dependencies

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

ExtnlTemp — Ambient temperature, K

scalar

Dependencies

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

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Units
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

C — Outlet pressure, temperature, enthalpy, mass fractions

two-way connector port

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

Block Options

Number of inlet ports — Number of ports

1 (default) | 0 | 2 | 3 | 4

Number of inlet ports.

Dependencies

To create inlet ports, specify the number.

Number of outlet ports — Number of ports

1 (default) | 0 | 2 | 3 | 4

Number of outlet ports.

Dependencies

To create outlet ports, specify the number.

Heat transfer model — Select model

Constant (default) | External input | External wall convection

Dependencies

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

Image type — Icon color

Cold (default) | Hot

Select color for block icon:

• Cold for blue

• Hot for red

General

Chamber volume, Vch — Volume

0.0029 (default) | scalar

Chamber volume, V_ch, in m^3.

Initial chamber pressure, Pinit — Pressure

101325 (default) | scalar

Initial chamber pressure, P_vol, in Pa.

Initial chamber temperature, Tinit — Temperature

298 (default) | scalar

Initial chamber temperature, T_vol, in K.

Ideal gas constant, R — Ideal gas constant

287 (default) | scalar

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

Specific heat capacity, cp — Specific heat

1005 (default) | scalar

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

Heat Transfer

Heat transfer rate, q_he — Rate

0 (default) | scalar

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

Dependencies

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

External convection heat transfer coefficient, ext_tbl — Manifold external air

[40 160 740 2000] (default) | vector

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

Dependencies

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

External velocity breakpoints, ext_bpts — Manifold external air

linspace(0,180,4) (default) | vector

External velocity breakpoints, x_ext, in m/s.

Dependencies

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

External convection area, Aext_conv — Manifold external air

0.125 (default) | scalar

External convection area, A_{ext_conv}, in m^2.

Dependencies

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

Thermal mass, m_wall — Manifold wall general

7 (default) | scalar

Thermal mass, m_wall, in kg.

Dependencies

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

Wall heat capacity, cp_wall — Manifold wall general

900 (default) | scalar

Wall heat capacity, c_{p_wall}, in J/(kg·K).

Dependencies

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

Initial mass temperature, Tmass — Manifold wall general

293.15 (default) | scalar

Initial mass temperature, T_mass, in K.

Dependencies

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

External wall thickness, Dext_cond — Manifold wall external

0.004 (default) | scalar

External wall thickness, D_{ext_cond}, in m.

Dependencies

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

External conduction area, Aext_cond — Manifold wall external

0.003 (default) | scalar

External conduction area, A_{ext_cond}, in m^2.

Dependencies

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

External wall thermal conductivity, kext — Manifold wall external

25 (default) | scalar

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

Dependencies

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

Internal wall thickness, Dint_cond — Manifold wall internal

0.004 (default) | scalar

Internal wall thickness, D_{int_cond}, in m.

Dependencies

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

Internal conduction area, Aint_cond — Manifold wall internal

0.003 (default) | scalar

Internal conduction area, A_{int_cond}, in m^2.

Dependencies

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

Internal wall thermal conductivity, kint — Manifold wall internal

25 (default) | scalar

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

Dependencies

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

Internal convection heat transfer coefficient, int_tbl — Manifold internal air

[40 160 740 2000] (default) | vector

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

Dependencies

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

Internal mass flow rate breakpoints, int_bpts — Manifold internal air

linspace(0.0020,0.1100,4) (default) | vector

Internal velocity breakpoints, x_int, in kg/s.

Dependencies

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

Internal flow convection area, Aint_conv — Manifold internal air

0.125 (default) | scalar

Internal convection area, A_{int_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™.

Version History

Introduced in R2017a