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Air Volume

Control volume element of Air

 

Description

Equations

Variables

Connections

Parameters

See Also

Description

The Air Volume component models a generic control volume for the lumped thermal fluid simulation of Air. This component calculates mainly the mass and energy conservation.

 

Equations

The calculation is changed based on parameter values of Fidelity of properties and Dynamics of mass in the Air Settings component.

 

Fidelity of properties = Constant and Dynamics of mass = Static

If Type of Branch is ab+c+d (Branching), Mass conservation is calculated with:

NumOfRoute=x=b,c,d{1.0port__x on=true0.0port__x on=false

`port_x.mflow`=1NumOfRoute`port_a.mflow`  if port__x on=true x=b,c,d

`port_a.p`=p

`port_x.p`=p if port__x on=true x=b,c,d

If Type of Branch is a+c+db (Confluence), Mass conservation is calculated with:

NumOfRoute=1.0+x=c,d{1.0port__x on=true0.0port__x on=false

`port_b.mflow`=(`port_a.mflow`+x=c,d{`port_x.mflow`port__x on=true0.0port__x on=false) 

`port_a.p`=p

p=1NumOfRoutex=a,c,d{`port_x.p`port__x on=true0.0port__x on=false

`port_b.p`=p

Energy conservation is calculated with:

c__pMⅆTⅆ t=`port_a.mflow`ActualStream`port_a.hflow` +x=b,c,d{`port_x.mflow`ActualStream`port_x.hflow`port__x on=true0.0port__x on=false+{`heat.Q_flow`useHeatPort=true0.0useHeatPort=false

State equation:

p=ρR__gasT

Relationship of mass:

u=UM

M=ρV

Definition of Enthalpy:

hflow=Function__hflowT

u=hflowpρ

Port definitions:

`port_a.hflow`=hflow

`port_x.hflow`=hflow if port__x on=true x=b,c,d

`port_a.rho`=ρ

`port_x.rho`=ρ if port__x on=true x=b,c,d

`port_a.T`=T

`port_x.T`=T if port__x on=true x=b,c,d

v1=`port_a.mflow`ActualStream`port_a.rho`A1

vi=`port_x.mflow`ActualStream`port_x.rho`Ai if port__x on=true x=b,c,d,the order of vector is b=2,c=3,d=4

`heat.T`=T

(*) Regarding the value of properties, see more details in Air Settings.

Fidelity of properties = Constant and Dynamics of mass = Dynamic

Mass conservation is calculated with:

ⅆρⅆ t=`port_a.mflow`+x=b,c,d{`port_x.mflow`port__x on=true0.0port__x on=falseV

`port_a.p`=p

`port_x.p`=p if port__x on=true x=b,c,d

Energy conservation is calculated with:

ⅆUⅆ t=`port_a.mflow`ActualStream`port_a.hflow` +x=b,c,d{`port_x.mflow`ActualStream`port_x.hflow`port__x on=true0.0port__x on=false+{`heat.Q_flow`useHeatPort=true0.0useHeatPort=false

State equation:

p=ρR__gasT

Relationship of mass:

u=UM

M=ρV

Definition of Enthalpy:

hflow=Function__hflowT

c__pR__gasⅆTⅆ t=ⅆUⅆ tρVUρ2V

Port definitions:

`port_a.hflow`=hflow

`port_x.hflow`=hflow if port__x on=true x=b,c,d

`port_a.rho`=ρ

`port_x.rho`=ρ if port__x on=true x=b,c,d

`port_a.T`=T

`port_x.T`=T if port__x on=true x=b,c,d

v1=`port_a.mflow`ActualStream`port_a.rho`A1

vi=`port_x.mflow`ActualStream`port_x.rho`Ai if port__x on=true x=b,c,d,the order of vector is b=2,c=3,d=4

`heat.T`=T

(*) Regarding the values and equations of properties, see more details in Air Settings.

 

Fidelity of properties: Ideal Gas (NASA Polynomial) and Dynamics of mass = Static

If Type of Branch is ab+c+d (Branching), Mass conservation is calculated with:

NumOfRoute=x=b,c,d{1.0port__x on=true0.0port__x on=false

`port_x.mflow`=1NumOfRoute`port_a.mflow`  if port__x on=true x=b,c,d

`port_a.p`=p

`port_x.p`=p if port__x on=true x=b,c,d

If Type of Branch is a+c+db (Confluence), Mass conservation is calculated with:

NumOfRoute=1.0+x=c,d{1.0port__x on=true0.0port__x on=false

`port_b.mflow`=(`port_a.mflow`+x=c,d{`port_x.mflow`port__x on=true0.0port__x on=false) 

`port_a.p`=p

p=1NumOfRoutex=a,c,d{`port_x.p`port__x on=true0.0port__x on=false

`port_b.p`=p

Energy conservation is calculated with:

Function__cpTMⅆTⅆ t=`port_a.mflow`ActualStream`port_a.hflow` +x=b,c,d{`port_x.mflow`ActualStream`port_x.hflow`port__x on=true0.0port__x on=false+{`heat.Q_flow`useHeatPort=true0.0useHeatPort=false

State equation:

p=ρR__gasT

Relationship of mass:

u=UM

M=ρV

Definition of Enthalpy:

hflow=Function__hflowT

u=hflowpρ

Port definitions:

`port_a.hflow`=hflow

`port_x.hflow`=hflow if port__x on=true x=b,c,d

`port_a.rho`=ρ

`port_x.rho`=ρ if port__x on=true x=b,c,d

`port_a.T`=T

`port_x.T`=T if port__x on=true x=b,c,d

v1=`port_a.mflow`ActualStream`port_a.rho`A1

vi=`port_x.mflow`ActualStream`port_x.rho`Ai if port__x on=true x=b,c,d,the order of vector is b=2,c=3,d=4

`heat.T`=T

(*) The properties are defined with NASA polynomials and coefficients. For details, see Air Settings.

Fidelity of properties: Ideal Gas (NASA Polynomial) and Dynamics of mass = Dynamic

Mass conservation is calculated with:

ⅆρⅆ t=`port_a.mflow`+x=b,c,d{`port_x.mflow`port__x on=true0.0port__x on=falseV

`port_a.p`=p

`port_x.p`=p if port__x on=true x=b,c,d

Energy conservation is calculated with:

ⅆUⅆ t=`port_a.mflow`ActualStream`port_a.hflow` +x=b,c,d{`port_x.mflow`ActualStream`port_x.hflow`port__x on=true0.0port__x on=false+{`heat.Q_flow`useHeatPort=true0.0useHeatPort=false

State equation:

p=ρR__gasT

Relationship of mass:

u=UM

M=ρV

Definition of Enthalpy:

hflow=Function__hflowT

Function__cpTR__gasⅆTⅆ t=ⅆUⅆ tρVUρ2V

Port definitions:

`port_a.hflow`=hflow

`port_x.hflow`=hflow if port__x on=true x=b,c,d

`port_a.rho`=ρ

`port_x.rho`=ρ if port__x on=true x=b,c,d

`port_a.T`=T

`port_x.T`=T if port__x on=true x=b,c,d

v1=`port_a.mflow`ActualStream`port_a.rho`A1

vi=`port_x.mflow`ActualStream`port_x.rho`Ai if port__x on=true x=b,c,d,the order of vector is b=2,c=3,d=4

`heat.T`=T

(*) The properties are defined with NASA polynomials and coefficients. For details, see Air Settings.

 

 

Variables

Symbol

Units

Description

Modelica ID

p

Pa

Pressure

p

T

K

Temperature

T

ρ

kgm3

Density

rho

hflow

Jkg

Specific enthalpy

hflow

u

Jkg

Specific energy

u

U

J

Energy

u

M

kg

Mass

M

mflow

kgs

Mass flow rate

mflow

NumOfRoute

Number of valid routes

NumOfRoute

v

ms

Velocity of flow

v

Connections

Name

Units

Condition

Description

Modelica ID

port__a

 

Air Port

port_a

port__b

if port_c on is true.

Air Port

port_b

port__c

if port_d on is true.

Air Port

port_c

port__d

if port_b on is true.

Air Port

port_d

states

if Internal states output is true.

Internal states output. The breakdown list of output variables in states are the followings:

 [1] : Pressure     [2] : Temperature

 [3] : Density       [4] : Specific enthalpy

 [5] : Velocity of port_a

 [6] : Velocity of port_b

 [7] : Velocity of port_c

 [8] : Velocity of port_d

states

heat

if Heat port is true.

Heat Port

heat

Parameters

Symbol

Default

Units

Description

Modelica ID

Airsimulationsettings 

AirSettings1

Specify a component of Air simulation settings

Settings

V

0.001

m3

Volume of the node

V

A

Pi400,Pi400,Pi400,Pi400

m2

Flow area of each port

 1 : port_a,    2 : port_b

 3 : port_c,    4 : port_d

A

port__b on

false

If true, port_b is valid

sw_b

port__c on

false

If true, port_c is valid

sw_c

port__d on

false

If true, port_d is valid

sw_d

p__start

101325

Pa

Initial condition of Pressure

p_start

T__start

293.15

K

Initial condition of temperature

T_start

Internalstatesoutput

false

If true, the output of the internal states is valid. The breakdown list of output variables in states are the followings:

 [1] : Pressure                [2] : Temperature

 [3] : Density                  [4] : Specific enthalpy

 [5] : Velocity of port_a  [6] : Velocity of port_b

 [7] : Velocity of port_c  [8] : Velocity of port_d

useStates

Heat port

false

If true, Heat port is valid

useHeatPort

Type ofBranch

ab+c+d

Branch type setting only for Static mass flow simulation, when Dynamics of mass option of Air Setting is Static.

 ab+c+d : 

   The input flow is split into 3 ports

 a+c+db 

   The input flows from 3 ports is confluent

TypeOfBranch

See Also

Heat Transfer Library Overview

Air Overview

Air Basic Overview