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Detailed HX Air Solid

Detailed heat exchanger between Air and Solid

  

 

Description

Equations

Variables

Connections

Parameters

See Also

Description

The Detailed HX Air Solid component models a heat exchanger between Fluid Air and Solid materials, which is for Laminar and Turbulent, for the lumped thermal fluid simulation of Air. This component calculates mainly pressure difference, mass flow rate and heat 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 and Geometrical coefficient for laminar flow, and the heat transfer coefficient calculation 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

Surface area for Heat exchange is defined with:

A__surface_act=A__surface

Geometrical coefficient for laminar flow is defined with:

Geo__act=geo__inExternal input of Geometrical coefficient=trueGeoothers

Heat transfer coefficient is calculated with:

h__act=kD__h_actC__generalRe__hm__generaloffset__generalPrn__general

Reynolds number for heat transfer coefficient is calculated with:

Re__h=maxρ__a+ρ__b2vD__hμ,0.1

Prandtl number is calculated with:

Pr=μc__pk

 

Type of pipe = Circular

Inner hydraulic diameter is defined with:

D__h_act=D__h

Flow area is defined with:

A__act=πD__h24

Surface area for Heat exchange is defined with:

A__surface_act=πD__hL

Geometrical coefficient for laminar flow is defined with:

Geo__act=1

Heat transfer coefficient is calculated with:

h__act=1κ__hh__lam+κ__hh__tur

h__lam=kD__h_act3.66

h__tur&equals;&lcub;kD__h_act0.023Re__h0.8Pr0.4`solid.T`<`port_a.T`&plus;`port_b.T`2kD__h_act0.023Re__h0.8Pr0.3others

&kappa;__h&equals;tanhIF__speedRe__hRe__CoT2&plus;12

Reynolds number for heat transfer coefficient is calculated with:

Re__h_target&equals;max&rho;__a&plus;&rho;__b2vD__h_act&mu;&comma;0.1

&DifferentialD;Re__h&DifferentialD;t&equals;Re__h_targetRe__hT__const

Prandtl number is calculated with:

Pr&equals;&mu;c__pk

 

Type of pipe = Rectangular

Inner hydraulic diameter is defined with:

D__h_act&equals;21a__rect&plus;1b__rect

Flow area is defined with:

A__act&equals;a__recb__rec

Surface area for Heat exchange is defined with:

A__surface_act&equals;a__rec&plus;b__rec2L

Geometrical coefficient for laminar flow is defined with:

Geo__act&equals;MapleSim.Interpolate1D`data&comma;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).

Heat transfer coefficient is calculated with:

h__act&equals;1&kappa;__hh__lam&plus;&kappa;__hh__tur

h__lam&equals;kD__h_act3.66

h__tur&equals;&lcub;kD__h_act0.023Re__h0.8Pr0.4`solid.T`<`port_a.T`&plus;`port_b.T`2kD__h_act0.023Re__h0.8Pr0.3others

&kappa;__h&equals;tanhIF__speedRe__hRe__CoT2&plus;12

Reynolds number for heat transfer coefficient is calculated with:

Re__h_target&equals;max&rho;__a&plus;&rho;__b2vD__h_act&mu;&comma;0.1

&DifferentialD;Re__h&DifferentialD;t&equals;Re__h_targetRe__hT__const

Prandtl number is calculated with:

Pr&equals;&mu;c__pk

 

Reynolds number for Friction factor calculation is defined with:

Re__target&equals;max&lcub;&rho;__adp0&rho;__bothersvD__h_act&lcub;&mu;__adp0&mu;__bothers&comma;0.1

&DifferentialD;Re&DifferentialD;t&equals;Re__targetReT__const

The friction factor of flow is calculated with:

&lambda;&equals;`HeatTransfer.Functions.lambda_Re`Re&comma;roughness&comma;D__h_act&comma;Re__CoT&comma;IF__speed&comma;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:

&lambda;__lam&equals;Geo__act64Re

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

&lambda;__tur&equals;0.25logroughnessD__h_act3.7&plus;5.74Re0.92

Intermittency is defined with:

&kappa;&equals;tanhIF__speedReRe__CoT2&plus;12

So, the friction factor is calculated with:

&lambda;&equals;1&kappa;&lambda;__lam&plus;&kappa;&lambda;__tur

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

 

The definition of Flow calculation is the following and:

Dynamics of mass = Static

Pressure difference is calculated with Darcy–Weisbach equation:

dp&equals;12&lambda;LD__h_actA__act2&lcub;&rho;__adp0&rho;__bothersmflow2signmflow

Dynamics of mass = Dynamic

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

mflow&equals;2D__h_actA__act2&lambda;L&lcub;&rho;__adp0&rho;__bothersdpsigndp

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

mflow&equals;2D__h_actA__act2λL`HeatTransfer.Functions.regRoot2`dp&comma;dp_small&comma;&rho;__a&comma;&rho;__b&comma;true&comma;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&equals;`port_a.p``port_b.p`

v&equals;mflow&lcub;&rho;__adp0&rho;__bothersA__act

`port_a.mflow`&equals;mflow

`port_b.mflow`&equals;mflow

Definitions related to Heat flow rate:

Q_flow&equals;h__actA__surface_act`solid.T`inStream`port_a.T`&plus;inStream`port_b.T`2

q_flow&equals;Q_flowmaxmflow&comma;0.00001

If Dynamics of mass is Static, specific enthalpy is defined with:

`port_a.hflow`&equals;inStream`port_b.hflow`mflow0inStream`port_b.hflow`&plus;q_flowothers

`port_b.hflow`&equals;inStream`port_a.hflow`&plus;q_flowmflow0inStream`port_a.hflow`others

If Dynamics of mass is Dynamic, specific enthalpy is defined with:

`port_a.hflow`&equals;inStream`port_b.hflow`dp0inStream`port_b.hflow`&plus;q_flowothers

`port_b.hflow`&equals;inStream`port_a.hflow`&plus;q_flowdp0inStream`port_a.hflow`others

Density is calculated with:

&rho;__a&equals;inStream`port_a.rho`

&rho;__b&equals;inStream`port_b.rho`

If Fidelity of properties = Constant, properties &mu; and c__p and k are constants and properties at each ports are:

&mu;__a&equals;&mu;

&mu;__b&equals;&mu;

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

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

&mu;__a&equals;Function__visinStream`port_a.T`

&mu;__b&equals;Function__visinStream`port_b.T`

μ&equals;Function__visinStream`port_a.T`&plus;inStream`port_b.T`2

c__p&equals;Function__cpinStream`port_a.T`&plus;inStream`port_b.T`2

k&equals;Function__kinStream`port_a.T`&plus;inStream`port_b.T`2

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

Port's variables are defined with:

`port_a.rho`&equals;inStream`port_b.rho`

`port_b.rho`&equals;inStream`port_a.rho`

`port_a.T`&equals;inStream`port_b.T`

`port_b.T`&equals;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

A__surface_act

m2

Surface area used for Heat exchange

A_surface_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

&lambda;

Friction factor

lambda

&lambda;__lam

Friction factor for Laminar flow

lambda_lam

&lambda;__tur

Friction factor for Turbulent flow

lambda_tur

&kappa;

Intermittency factor to calculate Transition zone

kappa

h__act

Wm2K

Heat transfer coefficient used for Fluid simulation

h_act

Re__h

Reynolds number for Heat transfer coefficient calculation

Re_h

Re__h_target

Targeted Reynolds number for Heat transfer coefficient calculation, if Fidelity of properties = Ideal Gas (NASA Polynomial) is valid.

Re_h_target

Pr

Prandtl number

Pr

&kappa;__h

Intermittency factor to calculate Transition zone, if Fidelity of properties = Ideal Gas (NASA Polynomial) is valid.

kappa_h

h__lam

Wm2K

Heat transfer coefficient for Laminar flow, if Fidelity of properties = Ideal Gas (NASA Polynomial) is valid.

h_lam

h__tur

Wm2K

Heat transfer coefficient for Turbulent flow, if Fidelity of properties = Ideal Gas (NASA Polynomial) is valid.

h_tur

Q_flow

W

Heat flow rate between solid materials and fluid Air

 Q_flow

q_flow

Wkg

Specific energy between solid materials and fluid Air

q_flow

&mu;

Pas

Dynamic viscosity

vis

c__p

JkgK

Specific heat capacity at the constant pressure

cp

k

WmK

Thermal conductivity

k

&rho;__a

kgm3

Density at port_a

rho_a

&rho;__b

kgm3

Density at port_b

rho_b

&mu;__a

Pas

Dynamic viscosity at port_a

vis_a

&mu;__b

Pas

Dynamic viscosity at port_b

vis_b

Connections

Name

Units

Condition

Description

Modelica ID

port__a

 

Air Port

port_a

port__b

 

Air Port

port_b

solid

 

Heat Port

solid

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

A__surface

PiD__hL

m2

Surface area for Heat exchange if Type of pipe = General.

A_surface

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

C__general

0.664

m

Gain parameter for Reynolds number in the generalized experimental equation of Internal flow convection generalized equation, only if Type of pipe = General.

C_forced

m__general

0.5

m

Exponent parameter for Reynolds number in the generalized experimental equation of Internal flow convection generalized equation, only if Type of pipe = General.

m_forced

offset__general

0

m

Offset parameter for Reynolds number in the generalized experimental equation of Internal flow convection generalized equation, only if Type of pipe = General.

offset_forced

n__general

13

m

Exponent parameter for Prandtl number in the generalized experimental equation of Internal flow convection generalized equation, only if Type of pipe = General.

n_forced

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