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HX Water Solid

Heat exchanger between Water and Solid

 

 

Description

Equations

Variables

Connections

Parameters

See Also

Description

The HX Water Solid component models a generic heat exchanger between Fluid Water and Solid materials for the lumped thermal fluid simulation of Water. 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 flow, and Dynamics of mass in the Water Settings component.

 

Type of flow = Linear and Dynamics of mass = Static

Pressure difference is calculated with:

dp=1Aα__linearmflow

Heat transfer coefficient is calculated with:

h__act=h

Reynolds number is calculated with:

Re__h=maxinStream`port_a.rho`+inStream`port_b.rho`2vD__hμ,0.1

Prandtl is calculated with:

Pr=visc__pk

 

Type of flow = Linear and Dynamics of mass = Dynamic

Mass flow rate is calculated with:

mflow=Aα__lineardp

Heat transfer coefficient is calculated with:

h__act=h

Reynolds number is calculated with:

Re__h=maxinStream`port_a.rho`+inStream`port_b.rho`2vD__hμ,0.1

Prandtl number is calculated with:

Pr=μc__pk

 

Type of flow = Square root and Dynamics of mass = Static

Pressure difference is calculated with:

dp=1Aα__sqrt2mflow2signmflow

Heat transfer coefficient is calculated with:

h__act=h

Reynolds number is calculated with:

Re__h=maxinStream`port_a.rho`+inStream`port_b.rho`2vD__hμ,0.1

Prandtl number is calculated with:

Pr=μc__pk

 

Type of flow = Square root and Dynamics of mass = Dynamic

In theory, Mass flow rate is calculated with:

mflow=Aα__sqrtdpsigndp

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

mflow=Aα__sqrt`HeatTransfer.Functions.regRoot`dp,sharpness

Heat transfer coefficient is calculated with:

h__act=h

Reynolds number is calculated with:

Re__h=maxinStream`port_a.rho`+inStream`port_b.rho`2vD__hμ,0.1

Prandtl number is calculated with:

Pr=μc__pk

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

 

Type of flow = Darcy-Weisbach and Dynamics of mass = Static

Pressure difference is calculated with Darcy–Weisbach equation:

dp=12λLD__hA2{inStream`port_a.rho`dp0inStream`port_b.rho`othersmflow2signmflow

Heat transfer coefficient is calculated with:

h__act=1κ__hh__lam+κ__hh__tur

h__lam=kD__h3.66

h__tur&equals;&lcub;kD__h0.023Re__h0.8Pr0.4`solid.T`<`port_a.T`&plus;`port_b.T`2kD__h0.023Re__h0.8Pr0.3others

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

Reynolds number is calculated with:

Re__h_target&equals;maxinStream`port_a.rho`&plus;inStream`port_b.rho`2vD__h&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 flow = Darcy-Weisbach and Dynamics of mass = Dynamic

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

mflow&equals;2D__hA2&lambda;L&lcub;inStream`port_a.rho`dp0inStream`port_b.rho`othersdpsigndp

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

mflow&equals;2D__hA2λL`HeatTransfer.Functions.regRoot2`dp&comma;dp_small&comma;inStream`port_a.rho`&comma;inStream`port_b.rho`&comma;true&comma;sharpness

Heat transfer coefficient is calculated with:

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

h__lam&equals;kD__h3.66

h__tur&equals;&lcub;kD__h0.023Re__h0.8Pr0.4`solid.T`<`port_a.T`&plus;`port_b.T`2kD__h0.023Re__h0.8Pr0.3others

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

Reynolds number is calculated with:

Re__h_target&equals;maxinStream`port_a.rho`&plus;inStream`port_b.rho`2vD__h&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

(*) `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;inStream`port_a.rho`dp0inStream`port_b.rho`othersA

`port_a.mflow`&equals;mflow

`port_b.mflow`&equals;mflow

Definitions related to Heat flow rate:

Q_flow&equals;h__actA__surface`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

If Fidelity of properties = Constant, properties &mu; and c__p and k are constants.

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

If Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97), properties are calculated with:

&mu;&equals;LUT__&mu;`port_a.p`&plus;`port_b.p`2&comma;`solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22

c__p&equals;LUT__c__p`port_a.p`&plus;`port_b.p`2&comma;`solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22

k&equals;LUT__k`port_a.p`&plus;`port_b.p`2&comma;`solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22

(*) The properties are defined with Liquid Water (Lookup table of IAPWS/IF97) and coefficients, see more in Water Settings.

If Fidelity of properties = IAPWS/IF97 standard, properties are calculated with:

&mu;&equals;Function__visinStream`port_a.rho`&plus;inStream`port_b.rho`2&comma;`solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22&comma;`port_a.p`&plus;`port_b.p`2&comma; 0

c__p&equals;Function__cp`port_a.p`&plus;`port_b.p`2&comma; `solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22&comma; 0

k&equals;Function__kinStream`port_a.rho`&plus;inStream`port_b.rho`2&comma; `solid.T`&plus;inStream`port_a.T`&plus;inStream`port_b.T`22&comma;`port_a.p`&plus;`port_b.p`2&comma; 0&comma; true

 

(*) The properties are defined with IAPWS/IF97 standard and coefficients, see more in Water 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`

 

Variables

Symbol

Units

Description

Modelica ID

dp

Pa

Pressure difference

p

mflow

kgs

Mass flow rate

mflow

v

ms

Velocity of flow

v

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 = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid.

Re_h_target

Pr

Prandtl number

Pr

&kappa;__h

Intermittency factor to calculate Transition zone, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid.

kappa_h

h__lam

Wm2K

Heat transfer coefficient for Laminar flow, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid.

h_lam

h__tur

Wm2K

Heat transfer coefficient for Turbulent flow, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid.

h_tur

Q_flow

W

Heat flow rate between solid materials and fluid Water.

 Q_flow

q_flow

Wkg

Specific energy between solid materials and fluid Water.

q_flow

&mu;

Pas

Dynamic viscosity

vis

c__p

JkgK

Specific heat capacity at the constant pressure

cp

k

WmK

Thermal conductivity

k

Connections

Name

Units

Condition

Description

Modelica ID

port__a

 

Water Port

port_a

port__b

 

Water Port

port_b

solid

 

Heat Port

solid

Parameters

Symbol

Default

Units

Description

Modelica ID

Watersimulationsettings 

WaterSettings1

Specify a component of Water simulation settings

Settings

Type offlow

Linear

Select Flow calculation type

 - Linear

 - Square root

 - Darcy-Weisbach

TypeOfFlow

&alpha;__linear

30

Flow coefficient for Linear type

alpha_lin

&alpha;__sqrt

3000

Flow coefficient for Square root type

alpha_sqrt

L

0.5

m

Pipe length (Only for Darcy-Weisbach)

L

D__h

0.01

m

Internal hydraulic diameter (Only for Darcy-Weisbach)

Dh

A

Pi40000

m2

Flow area

A

A__surface

Pi200

m2

Surface area for Heat exchange

A_surface

&lambda;

0.000015

Friction coefficient for Darcy-Weisbach equation

lambda

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

h

10

Coefficient of heat transfer

h

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

Water Overview

Water Basic Overview