Air Detailed Flow
Detailed flow calculation of Air
Description
Equations
Variables
Connections
Parameters
See Also
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.
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
A__act=π⋅D__h24
Geometrical coefficient for laminar flow is defined with:
Geo__act=1
Type of pipe = Rectangular
D__h_act=21a__rect+1b__rect
A__act=a__rec⋅b__rec
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__adp≥0ρ__bothers⋅v⋅D__h_act{μ__adp≥0μ__bothers,0.1
ⅆReⅆt=Re__target−ReT__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__act⋅64Re
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__speed⋅Re−Re__CoT2+12
So, the friction factor is calculated with:
λ=1−κ⋅λ__lam+κ⋅λ__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=12⋅λ⋅LD__h_act⋅A__act2⋅{ρ__adp≥0ρ__bothers⋅mflow2⋅signmflow
Dynamics of mass = Dynamic
In theory, Mass flow rate is calculated with Darcy–Weisbach equation:
mflow=2⋅D__h_act⋅A__act2λ⋅L⋅{ρ__adp≥0ρ__bothers⋅dp⋅signdp
In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation:
mflow=2⋅D__h_act⋅A__act2λ⋅L⋅`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__adp≥0ρ__bothers⋅A__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.
Symbol
Units
Modelica ID
dp
Pa
Pressure difference
p
mflow
kgs
Mass flow rate
v
ms
Velocity of flow
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__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
Density at port_b
rho_b
μ__a
Pa⋅s
Dynamic viscosity at port_a
vis_a
μ__b
Dynamic viscosity at port_b
vis_b
Name
Condition
port__a
Air Port
port_a
port__b
port_b
geo_in
if External input of Geometrical coefficient = false
Geometrical coefficient input
Default
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
Pipe length
D__h
Internal hydraulic diameter if Type of pipe is General or Circular.
Dh
a__rect
Horizontal length only if Type of pipe = Rectangular.
a_rec
b__rect
0.2
Vertical length only if Type of pipe = Rectangular.
b_rec
A
14⋅Pi__⋅D__h2
Flow area only if Type of pipe = General.
roughness
0.000025
Absolute roughness of pipe, with a default for a smooth steel pipe
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.
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
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
Approximation of function for |dp| <= dp_small
dp_small
sharpness
1.0
Sharpness of approximation for sqrt(dp) and sqrt(rho * dp)
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
Heat Transfer Library Overview
Air Overview
Air Shapes Overview
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