Air Detailed Flow - MapleSim Help
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Air Detailed Flow

Detailed flow calculation of Air

 

Description

Equations

Variables

Connections

Parameters

See Also

Description

The Air Detailed Flow component models a flow calculation which is for Laminar and Turbulent for the lumped thermal fluid simulation of Air. This component calculates mainly pressure difference and mass flow rate.

 

Equations

The calculation is changed based on parameter values of Type of pipe, and Dynamics of mass in the Air Settings component.

The definition of Inner hydraulic diameter and Flow area, Geometrical coefficient for laminar flow are explained in the following:

Type of pipe = General

Inner hydraulic diameter is defined with:

D__h_act=D__h

Flow area is defined with:

A__act=A

Geometrical coefficient for Laminar flow is defined with:

Geo__act=geo__inExternal input of Geometrical coefficient=trueGeoothers

Type of pipe = Circular

Inner hydraulic diameter is defined with:

D__h_act=D__h

Flow area is defined with:

A__act=πD__h24

Geometrical coefficient for laminar flow is defined with:

Geo__act=1

 

Type of pipe = Rectangular

Inner hydraulic diameter is defined with:

D__h_act=21a__rect+1b__rect

Flow area is defined with:

A__act=a__recb__rec

Geometrical coefficient for laminar flow is defined with:

Geo__act=MapleSim.Interpolate1D`data,b__recta__rect

(*) `MapleSim.Interpolate1D` is the function of Lookup table of 1D.

(*) data is specified with:

     - If data_source = inline, parameter table__rect.

     - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used

     - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).

 

Reynolds number is calculated with:

Re__target=max{ρ__adp0ρ__bothersvD__h_act{μ__adp0μ__bothers,0.1

ⅆReⅆt=Re__targetReT__const

The friction factor of flow is calculated with:

λ=`HeatTransfer.Functions.lambda_Re`Re,roughness,D__h_act,Re__CoT,IF__speed,Geo__act

(*) The above function `HeatTransfer.Functions.lambda_Re` is to calculated friction factor for Laminar and Turbulent flow.
The fundamental implementation is based on the following equations. Especially, the equation of Turbulent flow is Swamee and Jain's approximation[1] .

(Reference) Detailed implementation of Friction factor calculation

Friction factor of Laminar flow is calculated with:

λ__lam=Geo__act64Re

And, Turbulent flow's friction factor is defined with (Swamee and Jain's approximation):

λ__tur=0.25logroughnessD__h_act3.7+5.74Re0.92

Intermittency is defined with:

κ=tanhIF__speedReRe__CoT2+12

So, the friction factor is calculated with:

λ=1κλ__lam+κλ__tur

The following plot is Reynolds number vs Friction factor, and roughnessD__h_act=0.001, IF__speed=0.007, Re__CoT=3500, Geo__act=1.

 

The definition of Flow calculation is the following and :

Dynamics of mass = Static

Pressure difference is calculated with Darcy–Weisbach equation:

dp=12λLD__h_actA__act2{ρ__adp0ρ__bothersmflow2signmflow

Dynamics of mass = Dynamic

In theory, Mass flow rate is calculated with Darcy–Weisbach equation:

mflow=2D__h_actA__act2λL{ρ__adp0ρ__bothersdpsigndp

In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation:

mflow=2D__h_actA__act2λL`HeatTransfer.Functions.regRoot2`dp,dp_small,ρ__a,ρ__b,true,sharpness

(*) `HeatTransfer.Functions.regRoot2` is the same function as `Modelica.Fluid.Utilities.regRoot2`. To check the details of the package and view the original documentation, which includes author and copyright information, click here.

 

Definitions related to Mass flow rate and pressure :

dp=`port_a.p``port_b.p`

v=mflow{ρ__adp0ρ__bothersA__act

`port_a.mflow`=mflow

`port_b.mflow`=mflow

Density is calculated with:

ρ__a=inStream`port_a.rho`

ρ__b=inStream`port_b.rho`

If Fidelity of properties = Constant, properties are calculated with:

μ__a=μ

μ__b=μ

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

If Fidelity of properties = Ideal Gas (NASA Polynomial), properties are calculated with:

μ__a=Function__visinStream`port_a.T`

μ__b=Function__visinStream`port_b.T`

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

Port's variables are defined with:

`port_a.hflow`=inStream`port_b.hflow`

`port_b.hflow`=inStream`port_a.hflow`

`port_a.rho`=inStream`port_b.rho`

`port_b.rho`=inStream`port_a.rho`

`port_a.T`=inStream`port_b.T`

`port_b.T`=inStream`port_a.T`

References

[1] : Swamee P.K., Jain A.K. (1976): Explicit equations for pipe-flow problems. Proc. ASCE, J.Hydraul. Div., 102 (HY5), pp. 657-664.

 

Variables

Symbol

Units

Description

Modelica ID

dp

Pa

Pressure difference

p

mflow

kgs

Mass flow rate

mflow

v

ms

Velocity of flow

v

D__h_act

m

Inner hydraulic diameter used for Fluid simulation

Dh_act

A__act

m2

Flow area used for Fluid simulation

A_act

Geo__act

Geometrical coefficient used for Fluid simulation

Geo_act

Re

Reynolds number for Friction factor calculation

Re

Re__target

Targeted Reynolds number for Friction factor calculation

Re_target

λ

Friction factor

lambda

λ__lam

Friction factor for Laminar flow

lambda_lam

λ__tur

Friction factor for Turbulent flow

lambda_tur

κ

Intermittency factor to calculate Transition zone

kappa

ρ__a

kgm3

Density at port_a

rho_a

ρ__b

kgm3

Density at port_b

rho_b

μ__a

Pas

Dynamic viscosity at port_a

vis_a

μ__b

Pas

Dynamic viscosity at port_b

vis_b

Connections

Name

Condition

Description

Modelica ID

port__a

 

Air Port

port_a

port__b

 

Air Port

port_b

geo_in

if External input of Geometrical coefficient = false

Geometrical coefficient input

geo_in

Parameters

Symbol

Default

Units

Description

Modelica ID

Airsimulationsettings 

AirSettings1

Specify a component of Air simulation settings

Settings

Type ofpipe

Circular

Select pipe type

 - General

 - Circular pipe

 - Rectangular pipe

TypeOfPipe

L

0.1

m

Pipe length

L

D__h

0.1

m

Internal hydraulic diameter if Type of pipe is General or Circular.

Dh

a__rect

0.1

m

Horizontal length only if Type of pipe = Rectangular.

a_rec

b__rect

0.2

m

Vertical length only if Type of pipe = Rectangular.

b_rec

A

14Pi__D__h2

m2

Flow area only if Type of pipe = General.

A

roughness

0.000025

m

Absolute roughness of pipe, with a default for a smooth steel pipe

roughness

External input ofGeometricalcoefficient

false

If true, Geometrical coefficient is defined by the input. And, if Type of pipe = Rectangular, this parameter is valid.

Geo_ext

Geo

1

Geometrical coefficient for Laminar flow only if Type of pipe = General and External input of Geometrical coefficient = false.

Geo

data source__rect

inline

-

See Data Source Options section above.

DSM_geo_rec

table__rect

01.50.11.3230.21.1920.31.0940.41.0230.50.97160.60.93600.70.91200.80.89830.90.89091.00.8887

Geometrical coefficient for Rectangular pipe, if data source__rect = inline.

[1] :Volume flow rate

[2] :Pressure difference

table_geo_rec

data__rect

2

-

Geometrical coefficient for Rectangular pipe, if data source__rect =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx)

data_geo_rec

columns__rect

2

-

Determines which columns of the data table will be used to interpolate.

For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on.

columns_geo_rec

skip rows__rect

0

-

Number of rows that are skipped from the top of the data table.

skiprows_geo_rec

smoothness__rect

Table points are linearly interpolated

-

Determines whether the data points will be interpolated linearly or with a cubic spline.

smoothness_geo_rec

dp__small

0.1

Pa

Approximation of function for |dp| <= dp_small

dp_small

sharpness

1.0

Sharpness of approximation for sqrt(dp) and sqrt(rho * dp)

sharpness

T__const

0.001

s

Time constant for Reynolds number calculation

T_const

Re__CoT

3500

Reynolds number of the center of Transition zone

Re_CoT

Spread ofIntermittencyfactor

0.007

Changing rate of Intermittency factor

IF_spread

See Also

Heat Transfer Library Overview

Air Overview

Air Shapes Overview