Lib Thermal Hydraulic

8/10/2019 Lib Thermal Hydraulic

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Thermal-Hydraulic library

Version 4.2 September 2004


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Copyright IMAGINE S.A. 1995-2004

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TABLE OF CONTENTS

1. Introduction...................................................... ............................................................. ... 1

2. Getting started with the Thermal-Hydraulic Library.................................................. 2

3. The thermal properties of the liquids.................................................... ......................... 9 3.1. Using the liquid thermal properties submodel ........................................................... 9

3.1.1. The "index of thermal hydraulic fluid" parameter............................................. 9 3.1.2. The "initial temperature" parameter ............................................................... 10 3.1.3. The "name of the fluid" parameter .................................................................. 10 3.1.4. The "filename for fluid characteristic data" parameter .................................. 11

3.2. Determining the thermal properties of the liquid.................................... ................. 11 3.2.1. Specific volume of a liquid......................................... ...................................... 11 3.2.2. Absolute viscosity of a liquid ...................................................................... ..... 12 3.2.3. Specific heat of a liquid ............................................................. ...................... 12 3.2.4. Thermal conductivity of a liquid........... ........................................................... 12

3.3. Generating your own thermal liquid properties ....................................................... 13

4. Running multi-liquid simulations......................................................................... ........ 18

5. Heat exchanger models based on effectiveness-NTU method .................................... 22 5.1. Effectiveness-NTU method ........................................................... .......................... 22 5.2. Liquid-liquid heat exchangers ................................................................ ................. 23 5.3. Liquid - gas heat exchangers .............................................................. ..................... 27

6. Modeling a system with thermal components: important rules................................. 28 6.1. Causality in the thermal-hydraulic library .............................................................. . 28 6.2. Other important rules.............................................................. ................................. 28

7. Formulation of equations and underlying assumptions ............................................. 30 7.1. Brief review of the theory: flow calculations .......................................................... 30

7.1.1. Basic equations..................................... ........................................................... 30 7.1.2. Further assumptions.................................................. ...................................... 31 7.1.3. About the Reynolds number............................................................... .............. 31 7.1.4. Resistive components: classification ............................................................... 32

7.1.4.1. Frictional drag category.................................. ......................................... 33 7.1.4.2. Local resistance category ........................................................... ............. 35 7.1.4.3. Frictional and local resistance category................................................ ... 35

7.2. Brief review of the theory: thermal calculations...................................................... 36 7.2.1. Basic equations..................................... ........................................................... 36

7.2.1.1. Capacitive Components................................ ........................................... 36 7.2.1.2. Resistive Components .......................................................... ................... 38 7.2.2. Further assumptions.................................................. ...................................... 39 7.2.3. About convection phenomena.......................................................... ................ 40

8. Advanced thermal-hydraulic properties...................................................................... 43

References............................................................................................ ............................... 47


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Using theThermal-Hydraulic Library

1. Introduction

Heat exchanges occur in most industrial processes either because they are wanted (ovens,heat exchangers) or because they are unavoidable (thermal shocks, thermal losses,friction). These exchanges are likely to occur through mobile fluids or between mobilefluids and the environment as soon as temperature differences are encountered.

The thermal-hydraulic library deals with liquids. It is based on a transient heat transferapproach and is used to model thermal phenomena in liquids (energy transport,convection) and to study the thermal evolution in these liquids when submitted todifferent kinds of heat sources. As a consequence, special thermal liquid properties areneeded.

In fact, the thermal-hydraulic library is separated in three categories, the thermal-

hydraulic, the thermal-hydraulic resistance and the thermal hydraulic valves categorieswhich are all treated in this manual as a unique library.

By using the thermal-hydraulic library it is also possible to model large thermal-hydraulicnetworks and evaluate pressure drops and mass flow rates through the components ofthese networks.

This library can be used alone or can be coupled with the other AMESim Thermal libraryand Cooling System library. These libraries contain some components having thermal

ports. Temperature and heat flow information can be exchanged between components ofthese three libraries through their thermal ports. Building systems with components

belonging to these three libraries permits the study of thermal interactions between solidsand liquids.

Before describing the thermal properties of the liquid, we will work through a smalltutorial example. Then a second example will be given followed by rules and advices.Finally, we will detail the theory and assumptions used in this library.

It is assumed that the reader is familiar with the use of AMESim . If this is not the case,we suggest that you do the tutorial exercises of the AMESim manual before attemptingthe examples below.


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2. Getting started with the Thermal-HydraulicLibrary

The thermal-hydraulic libraries comprises a set of basic components from which it is easyto model and observe the evolution of temperatures, pressures and mass flow rates in

hydraulic systems. By modeling the system shown in Figure 1, you will find that severalquestions are raised, they will be answered in this manual. Hence we recommend you dothis example as a first contact with the thermal library.

The system shown on Figure 1 is a part of a simplified injection system. It consists of a pump which is feeding the injectors, a pressure relief valve and a tank in which the flowrates coming from the pressure relief valve and the upstream part of the pump are mixed.The distribution of mass flow rates is imposed as shown on the sketch.

pump injector

pressurerelief valve

200 L/hr50 degC

100 L/hr 100 L/hr

75 L/hr

25 L/hr

Figure 1: simplified part of an injection system

In this example, the unit chosen for the volumetric flow rates is L/hr because it is one ofthe commonly used units in injection systems.

To model this system, select the thermal-hydraulic libraries category icons shown inFigure 2.

Figure 2: Thermal-hydraulic libraries category icons

This will produce the popups shown in Figure 3.


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Figure 3: components of the Thermal-hydraulic, Thermal-hydraulic Resistance andThermal-hydraulic Valves categories


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First look at the components available in this library. Display the titles of each component by moving the pointer over the icons. When this is done, build the model of the systemabove as shown in Figure 4.

Figure 4: model of a simplified injection circuit

This model comprises twenty elements from the thermal-hydraulic library and the signallibrary. Each is referenced in Figure 4 by a number. Fill in the parameters of thesecomponents as described in the table below leaving the other parameters at their defaultvalues. Finally, run a simulation with a final time of 50 seconds .

Submodel name and type Belongs to category Principal simulationparameters

0 TFFD1 thermal-

hydraulic properties

Thermal-Hydraulic filename to be used

$AME/libthh/data/ diesel.data1 CONS0 constant signal Signal, control andobservers

Constant value = 50

2, 5 CONS0 constant signal Signal, control andobservers

Constant value = 100

3, 6 GA00 submodel of again

Signal, control andobservers

Value of gain =0.0166667=1/60

(Convert L/hr into L/min)4, 7 TFQT0 signal into

volumetric flow rate(L/min)

Thermal-Hydraulic Default parameters

8 TFPC1 thermal-hydraulic adiabatic pipe

Thermal-Hydraulic Temperature at port 1 = 50 degCInternal diameter = 12 mm

Length = 0.4 m

9 TFND01 thermal-hydraulic junction Thermal-Hydraulic No parameters

10 TF223 thermal-hydraulic restriction

Thermal-Hydraulic Equivalent area = 0.018 mm 2

11, 20 TFTK0 thermal-hydraulic tank


12 TFPS0 pressure sensor Thermal-Hydraulic Default parameters13 FX00 output function of

an inputSignal, control and

observersExpression :

max(x-1000,0)


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14 LAG1 first order lag Signal, control andobservers

Default parameters

15 TFVR0 thermal-hydraulic variable

restriction

Thermal-Hydraulic Cross-sectional area = 0.042mm2

Maximum flow coefficient = 1.0 Critical flow number = 100

16, 19 TFPC3 thermal-hydraulic adiabatic pipe

Thermal-Hydraulic Temperature at port 1 = 50 degC

17 TFPC2 thermal-hydraulic adiabatic pipe

Thermal-Hydraulic Temperature at port 2 = 50 degC

18 TFND03 thermal-hydraulic node

Thermal-Hydraulic No parameters

The thermal-hydraulic library can be represented as shown below:

Thermal-Hydraulic Library

Resistive Components Capacitive Components

Flow calculations :mass flow rate

dm (kg/s)

Thermalcalculations :

enthalpy flow ratesdmh (W)

Flow calculations : pressure p (barA)

Thermalcalculations :temperature

T (degC)

The resistive submodels can be described as steady-state submodels . A more accuratedescription is they are instantaneous submodels. By this we mean that they are assumed toreact instantaneously to the temperatures and pressures applied to them so that they arealways in an equilibrium state.

The capacitive submodels have 2 state variables: the temperature and the pressure whichare passed at ports. This means that each of these variables is defined by a differentialequation. These are very commonly used in thermal-hydraulic library systems and we willdescribe them as transient submodels.

In addition some components are both resistive and capacitive.

Thermal-hydraulic library components have thermal-hydraulic, thermal and signal ports.

Four variables are exchanged at thermal-hydraulic ports:Temperature T [degC]Enthalpy flow rate dmh [W]Pressure p [barA]Mass flow rate dm [kg/s]

Two variables are exchanged at thermal ports:Temperature T [degC]Heat flow rate dh [W]


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Next, we can compare the distribution of volumetric flow rates in the injector (flow incomponent 8 - flow in component 16) and in the pressure relief valve branch (flow incomponent 16) as shown in Figure 7. Finally, display the pressure drop in the pressurerelief valve (component 15: input pressure - output pressure) as shown in Figure 8. This

pressure drop is computed by subtracting the pressures computed at the pressure reliefvalve ports.

Figure 7: distribution of volumetric flow rates

Figure 8: pressure drop in the relief valve

In this model, the use of submodel TFFD1 associated with the icon below is veryimportant.

This submodel contains the thermal properties of the liquid used for the simulation. Moredetails on TFFD1 will be given in section 3.


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From this very basic example, the followingquestions are raised:

$ Flow computation considerations:

- How are the pressure drops computed in the thermal-hydraulic submodels?Some submodels in the thermal-hydraulic library compute pressure drops due to

frictional drag (distributed resistance) or to local changes in geometry (localresistance). In section 6, a brief review of the theory and the equations used tocompute the pressure drops is given.

$ Thermal considerations:

- What are the hypotheses used concerning heat transport in the liquids, heattransfers by convection and heat exchanges with the outside?

In section 6, a brief review of the theory and the equations concerning thesefeatures is given.

- How does the user have access to the thermal properties of the liquids and howare these properties dealt with in the thermal-hydraulic library?

The thermal-hydraulic library uses a special submodel TFFD1 to handle thethermal properties of the liquids. The use of this submodel will be fully describedin section 3.

- Is it possible for the user to use his own liquid thermal properties? Yes. To model the thermal properties of a liquid in the thermal-hydraulic library,the use of submodel TFFD1 is of great importance. This submodel requires afilename as parameter which contains all the data needed to have access to thethermal characteristic properties of the liquid. In what follows, we explain how thisfile can be generated using a special C utility delivered with the thermal-hydrauliclibrary.

- If the user has a system to model which contains several liquids, is it possible to

run multi-liquid simulations ? Yes. In some cases, systems comprise different liquids interacting with each other(heat exchanges). Use of more than one instance of submodel TFFD1 enables thehandling of multi-liquid systems.

- Which other libraries can be used in combination with the thermal-hydrauliclibrary?

It is very likely that some thermal systems will require solid materials togetherwith motionless or moving fluids. It is also possible that some users might like tostudy thermal losses due to friction in mechanical systems. A final section in thismanual will show how this can be achieved.


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3. The thermal properties of the liquids

3.1. Using the liquid thermal properties submodel

As we saw in the first tutorial example, the thermal-hydraulic library uses a specialsubmodel TFFD1 associated with the icon shown in Figure 9 to handle the thermal

properties of the liquid.

Figure 9: liquid thermal properties icon associated with submodel TFFD1

To understand how this submodel works, display its parameter popup as shown in Figure10.

Figure 10: parameters of liquid thermal properties submodel TFFD1

This submodel requires 4 parameters which are the index of thermal hydraulic fluid , theinitial temperature , the name of the fluid, and the filename for fluid characteristicdata .

3.1.1. The "index of thermal hydraulic fluid" parameter

This is an integer parameter used to reference a particular liquid. In the first tutorialexample, the liquid type index was equal to 1 and in this case referred to diesel fuel. This

index is used to make the link between the thermal properties of diesel for instance andthe submodels of the system which require the thermal properties of the diesel to computethe enthalpy flow rates, the mass flow rates, the pressures or the temperatures. Displaynow the parameter popup of submodel TF223 (representing the injector) of the firsttutorial example as shown in Figure 11.


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Figure 11: injector parameter popup

The default index of hydraulic fluid is 1. If you only have one liquid in your system, youcan leave the index of hydraulic fluid in TFFD1 and all other thermal-hydraulicsubmodels at their default value.

The important rule is: an icon associated with submodel TFFD1 inserted on the sketchof a system refers to one and only one liquid. If your system has more than one liquid,you must add the corresponding number of icons. An example of this is given in section 4.

3.1.2. The "initial temperature" parameter

This parameter is not used when working with thermal-hydraulic systems. It is used wheninserting the icon associated with submodel TFFD1 on the sketch of a hydraulic system

built with standard hydraulic submodels or with hydraulic resistance submodels.

If this icon is inserted on the sketch of such a system, it behaves like the "Robert BoschDiesel Properties" icon, in that it defines properties that replace the standard hydraulic

properties of AMESim.

When using the standard hydraulic properties of AMESim, there is no influence of thetemperature on the calculation of the fluid properties. By using the icon above andchanging the initial temperature parameter, it is possible to make the thermal properties ofthe liquid used vary as a function of not only pressure but also temperature. Thistemperature parameter will be considered as the average temperature of the fluid in thewhole system during the overall simulation.

3.1.3. The "name of the fluid" parameter

This is only there to remind the user the nature of the liquid used. It does not influence thecalculations in any way.


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3.2.2. Absolute viscosity of a liquid

In the thermal-hydraulic library, the absolute viscosity of a liquid referenced by an indexis calculated using a 2 nd order polynomial function of the temperature and the pressure asfollows:

, - 100(*

and

. /22 T bT b pb t t p &()&()&(*,

where - 0 is the reference absolute viscosity (given at reference temperature and pressure),b p is the absolute viscosity coefficient for the pressure, bt is the absolute viscositycoefficient for the temperature and bt2 is the absolute viscosity coefficient for the squaredtemperature. The absolute viscosity of the liquid is expressed in Ns/m2.

3.2.3. Specific heat of a liquid

In the thermal-hydraulic library, the specific heat of a liquid referenced by an index iscalculated using a 2 nd order polynomial function of the temperature as follows:

]T p)c( p)c()T()c(T)c([ pt ptt p p cc &&&&& ()()()()(* 220 1 where c p0 is the reference specific heat (given at a reference temperature), ct is the specificheat coefficient for the temperature, ct2 is the specific heat coefficient for the squaredtemperature, c p is the specific heat coefficient for the pressure and c pt is the specific heatcoefficient for the pressure*temperature term. The specific heat of the liquid is expressedin J/kg/degC .

3.2.4. Thermal conductivity of a liquid

In the thermal-hydraulic library, the thermal conductivity of a solid referenced by an indexis calculated using a 2 nd order polynomial function of the temperature as follows:

])T()d(T)d([ tt2

201 &&0 0 ()()(*

where 0 0 is the reference thermal conductivity (given at reference pressure andtemperature), d t is the thermal conductivity coefficient for the temperature and d t2 is thethermal conductivity coefficient for the squared temperature. The thermal conductivity ofthe liquid is expressed in W/m/degC .

These four properties described by polynomial functions are needed to define completelya thermal liquid. They give access to:

- the bulk modulus of the liquid:

dpd ' '

1 *


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- the volumetric expansion coefficient of the liquid:

'

'

2 dT d +

*

- the kinematic viscosity of the liquid:

'

- 3 *

- the thermal diffusivity of the liquid:

c p(*

' 0

2 2

The thermal properties of liquids are modeled in the thermal-hydraulic library from theseequations.

3.3. Generating your own thermal liquid properties

In order to get you started, the thermal-hydraulic library is provided with some predefinedthermal properties of liquids and associated parameter files which can be found in the$AME/libthh/data directory. These files can be used directly in the submodel TFFD1.The list of file names defining liquid properties is given in the APPENDIX section at theend of this manual. You are not limited to this list and you can create your own thermalliquid properties. To illustrate how you can generate files for TFFD1, we will use the datafor a coolant given in the following tables.

Special coolant

Properties at 293 K = 20 degC (Reference temperature)

' 0 (in kg/m3) - 0 (kg/m/s) c p0 (in J/kg/K) 00 (in W/m/K)

1049 0.0024 4189 0.46

Range of operating temperatures

0 to 110 degC

Range of operating pressures

0 to 500 bars

Reference pressure: p ref = 1 barA

Reference Bulk modulus = 13000 barA (at T ref and p ref )

Table 1: reference data and properties for a special coolant

Properties at various temperatures (in degC) and at reference pressure0 10 20 35 50 70 110

' (in kg/m 3) 1060 1055 1049 1040 1031 1019 995


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3 (in m 2/s) 499*10-08 314*10 -08 230*10 -08 154*10 -08 114*10 -08 82*10 -08 47*10 -08

cp (in J/kg/K) 4208 4197 4189 4181 4179 4185 4229

0 (in W/m/K) 0.456 0.46 0.463 0.468 0.473 0.479 0.493

Table 2: properties of the coolant at various temperatures

The pressure coefficient for specific volume is equal to:

105 p 10.7,710.13000

1)0 p,0T(

1a ++*+*1+*+ (PaA-1)

Determining the other coefficients involves a great deal of computation effort. A specialutility does this work for you. This utility requires the data in a special format.

Step1 : Supply the characteristic data of the liquid

You must supply in a file the characteristic data for the liquid. This characteristic dataconsists of:

- liquid name,- reference temperature,- minimum operating temperature,- maximum operating temperature,- reference pressure,- minimum operating pressure,- maximum operating pressure,- pressure coefficient for specific volume,- pressure * temperature coefficient fro specific volume,- squared pressure coefficient for specific volume,- pressure coefficient for absolute viscosity,- a set of temperatures,- corresponding values for density,

- corresponding values for specific heat,- corresponding values for thermal conductivity,- corresponding values for kinematic viscosity.

Here is a file for the coolant properties given above:

# fluid namespecial coolant# reference temperature (in degC)20.0# minimum temperature (in degC)0.0# maximum temperature (in degC)110.0# reference pressure (in PaA)1e5# minimum pressure (in PaA)0.0# maximum pressure (in PaA)500e5# pressure coefficient for specific volume-7.7e-10# pressure * temperature coefficient for specific volume0.0# squared pressure coefficient for specific volume0.0# pressure coefficient for absolute viscosity0.0


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# T(degC) rho(kg/m**3) cp(J/kg/degC) lam(W/m/degC) nu(m**2/s)0 1060 4208 0.456 499e-810 1055 4197 0.46 314e-820 1049 4189 0.463 230e-835 1040 4181 0.468 154e-850 1031 4179 0.473 114e-870 1019 4185 0.479 82e-8110 995 4229 0.493 47e-8

This file contains all the information needed by submodel TFFD1. You must strictly stickto the format of this file otherwise problems may occur when starting the simulation.

Therefore, to build your own characteristic data file, we recommend that you copy andedit the file $AME/libthh/data/coolant.

The editable lines of the file are those in bold characters. The following rules must befollowed:- do not edit the lines preceded by (#),- do not add blank lines.

Here, the properties are given for 7 temperature values. The user can choose to givemore values provided there is always the same number of values for each property.The minimum number is 3 values. It is advised to supply a great number of values soas to be very accurate. Generating this type of file requires a special attention.Therefore an erroneous value supplied for the density for example will affect the

computation of the bulk modulus and the volumetric expansion coefficient. Inaddition, the range of working temperatures and pressures for the fluid is specifiedin this file. You must ensure that the fluids used in the system work in the definedrange of temperature and pressure.

NOTA:

The pressure coefficient for density should NEVER be equal to zero. Thiscoefficient is calculated using the formula below:

),(a

T p p

00

1

1 *

Step2 : Generate the ASCII file for submodel TFFD1

When all the data are ready, give a name to the file, say coolant and run the utility calledliquidgen which is in the directory where coolant file is stored. The liquidgen utility can

be found in the directory $AME/libthh/data . It is advised to copy it in your localdirectory.

1- Type :

$AME/libthh/data/liquidgen

This will result in the following prompt:

"Enter the name of the file containing the data: "

2- Type the name of the file you have just generated:

coolantThis will result in a second prompt:


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"Enter the name of the file to be generated: "

3- Type now the name of the file which will be automatically generated and used insubmodel TFFD1:

coolant.data

Check that the coolant.data file has been correctly generated, it should be look like this :

Detail of the generated file coolant.data

21.000e+05 Reference pressure [PaA]2.000e+01 Reference temperature [degC]1.049e+03 Reference density [kg/m**3]2.413e-03 Reference absolute viscosity [kg/m/s]4.189e+03 Reference specific heat [J/kg/K]4.630e-01 Reference thermal conductivity [W/m/K]0.000e+00 Minimum pressure allowed [PaA]5.000e+07 Maximum pressure allowed [PaA]0.000e+00 Minimum temperature allowed [degC]1.100e+02 Maximum temperature allowed [degC]5.573e-04 Temperature coefficient for specific volume4.930e-07 Temperature squared coefficient for specific volume

-7.700e-10 Pressure coefficient for specific volume0.000e+00 Pressure * temperature coefficient for specific volume0.000e+00 Squared pressure coefficient for specific volume

-1.307e-02 Temperature coefficient for absolute viscosity5.585e-05 Temperature squared coefficient for absolute viscosity0.000e+00 Pressure coefficient for absolute viscosity

-1.701e-04 Temperature coefficient for specific heat3.074e-06 Temperature squared coefficient for specific heat

-2.244e-13 Pressure * temperature coefficient for specific heat-6.578e-11 Pressure coefficient for specific heat

7.096e-04 Temperature coefficient for thermal conductivity9.664e-08 Temperature squared coefficient for thermal conductivity

When all the data is ready, it is to wise to check that these properties are correct. This can be achieved by constructing the small system shown in Figure 12:

Figure 12: checking liquid thermal properties

Fill in the parameters as shown in the table below and run a simulation for 20 seconds :When the simulation is over, click on the icon associated with submodel TFFPR and plotthe density, the absolute viscosity, the specific heat and the thermal conductivity of thecoolant with respect to temperature as shown in Figure 13. You can then check if the fileyou generated is correct.


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Finally, rerun the first tutorial example using this time the coolant thermal properties. Plotthe evolution of the temperature at the pressure relief valve outlet and compare the resultswith those obtained using the diesel thermal properties as shown in Figure 14.

Submodel name and type Belongs to category Principal simulation parameters0 TFFD1 liquid thermal

propertiesThermal-hydraulic Filename :

coolant.data generated previously1 UD00 piecewise signal Signal, control and

observersStage1

From 0 to 110 for 5 sec

Stage2From 110 to 0 for 5 sec Stage3

From 0 to 110 for 5 sec Stage4

From 110 to 0 for 5 sec 2 UD00 piecewise signal Signal, control and

observersStage1

Constant value = 1 for 5 sec Stage2

Constant value = 150for 5 sec Stage3

Constant value = 300for 5 sec

Stage4Constant value = 400for 5 sec

3 TFPT0 conversion of asignal into a temperature

and a pressure

Thermal-hydraulic No parameters

4 TFFPR calculation ofthermal liquid properties

Thermal-hydraulic Default parameters

Figure 13: coolant thermal properties with respect to temperature and pressure

As you can see in Figure 13, the density and the specific heat are influenced bytemperature and pressure. This is due to the pressure coefficient for the density. The


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absolute viscosity could also behave like this, but with this data, it only varies withtemperature .

For the thermal conductivity of the liquids, it normally depends only on the temperature.

Figure 14: comparison between diesel and coolant properties

Note that the temperature at the pressure relief valve outlet reaches a higher level withdiesel because it has a specific heat and a density which are smaller than those for thecoolant.

4. Running multi-liquid simulations

The purpose of this section is to describe the facility available in the thermal-hydraulic

library to handle multi-liquid simulations . In some cases, several liquids are involved inthermal-hydraulic systems. This can occur when modeling heat exchangers. The rule thatmust be followed so as to run multi-liquid simulations is:

The user must put on the sketch one liquid thermal properties icon for each liquidinvolved in the system and set a different index for each icon. Finally, the index ofhydraulic fluids in each other submodels of the system must be updated. This rule isapplied in the following tutorial example.

Tutorial example:

In this new example, the following topics will be illustrated:- multi-liquid simulations- transient heat transfer approach- coupling thermal-hydraulic and thermal components


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A very simple heat exchanger diesel-coolant is shown in Figure 15. It is constituted of aninternal tube in which the coolant is flowing and an external tube. Diesel fuel is flowing

between the internal and the external tube in the opposite direction. The tubes are made ofaluminum. The wall of the external cylinder is considered to be insulated, there is no heatexchange with the environment.

Length = 1m

Diameter = 25 mm

Diesel, Td input= 100 degC, Q = 20 L/min

Coolant, Tc input = 20 degC, Q = 20 L/min

Figure 15: simple heat exchanger coolant-diesel

It is interesting to study the evolution of the outlet temperature of each liquid.We will first consider that the convective heat flow rate propagating is directly transmittedfrom the diesel to the coolant. We will not take into account the influence of thealuminum wall in the first part of this example.

To model this system, build the circuit shown in Figure 16:

Figure 16: heat exchanger modelThis model comprises 13 components belonging to the thermal-hydraulic and to the signallibraries. Fill in the parameters of this model as shown in the following table leaving theother parameters at their default values and run a simulation for 20 seconds.

Submodel name and type Belongs to category Principal simulation parameters0 TFFD1 thermal-hydraulic

propertiesThermal-Hydraulic filename generated previously

coolant.data


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1 CONS0 constant signal Signal, control andobservers

Constant value = 20

2, 12 CONS0 constant signal Signal, control andobservers

Constant value = 20

3 TFQT0 signal intovolumetric flow rate

(L/min)


4 TFPC5 thermal-hydraulic pipe with heat exchange

Thermal-Hydraulic Temperature at port 1 = 20 degCInternal diameter = 25 mm

Length = 1 mConvective exchange coefficient =

10000 W/m 2 /degC 5 TF223 thermal- hydraulic

restriction Thermal-Hydraulic Default parameters

6 TFTK1 thermal-hydraulictank


7 TFTK1 thermal-hydraulictank

Thermal-Hydraulic #tank temperature = 100 degC index of hydraulic fluid = 2

8 TF223 thermal- hydraulicrestriction

Thermal-Hydraulic Index of hydraulic fluid = 2

9 TFC00 Thermal-hydrauliccapacity

Thermal-Hydraulic Temperature at port 3 = 100 degCTotal volume = 0.5 L

Index of hydraulic fluid = 2 10 TFQT0 signal into

volumetric flow rate(L/min)

Thermal-Hydraulic Index of hydraulic fluid = 2

11 CONS0 constant signal Signal, control andobservers

Constant value = 100

13 TFFD1 thermal-hydraulic properties

Thermal-Hydraulic filename used previouslydiesel.data

Index of hydraulic fluid = 2When this is done, plot graphs of the temperatures in components TFPC5 and TFC00against time as shown in Figure 17.

Figure 17: evolution of diesel and coolant temperatures in the exchanger


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Diesel is cooled from 100 degC to 62 degC, which is the equilibrium temperature, after atransient behavior of approximately 3 seconds. The transient phenomenon is very fast

because the convective heat flow rate is directly transmitted from one liquid to another.To be more accurate, we should model the aluminum wall between diesel and coolantthrough which the heat is propagating. Modify the previous system as shown on Figure18, you will find how thermal and thermal-hydraulic components can be coupled.

Figure 18: simple heat exchanger model with aluminum wall

There are additive components in this model. Fill in the parameters of these newcomponents as shown in the table below and run a simulation for 20 seconds .

Submodel name and type Belongs to category Principal simulation parameters14 THSD0 thermal solid

propertiesThermal filename picked in $AME/dataTH/

aluminum.data15, 17 THHF0 Zero heat flow

sourceThermal No parameters

16 THC00 thermal capacity Thermal Default parameters18 TFPC5 thermal-hydraulic

pipe with heat exchangeThermal-Hydraulic Temperature at port 1 = 100 degC

Internal diameter = 25 mm Length = 1 m

Convective exchange coefficient =10000 W/m 2 /degC

Index of hydraulic fluid = 2

When this is done, display the evolutions of the temperatures in components 4, 16 and 18against time as shown in Figure 19.


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Figure 19: evolution of diesel, coolant and aluminum wall temperature

This time the diesel is cooled from 100 degC to 72 degC . This is because part of theconvective heat exchanged between both liquids is stored as energy in the aluminum wall.This last example is a very simple model of a heat exchanger. It is constructed from basiccomponents from the thermal and thermal-hydraulic library. This example shows how tocouple components from both libraries and gives a good outlook of what can be done withall these basic components. To be more accurate, we could have taken into accountconduction in the aluminum, heat exchanges with the environment for example.

5. Heat exchanger models based on effectiveness-

NTU method

5.1. Effectiveness-NTU method

The effectiveness-NTU (Number of Transfer Units) method is widely considered for heatexchanger analysis. It is used when only the inlet temperatures are known.

The heat exchanger is modeled considering three elements:$ the separated cold and hot fluids that exchange one another represented with two

similar parts,

$ the link between both parts with another intermediate element.Thus, gas-gas heat exchanger models with various flow arrangements can be built. In thesame way, gas-liquid heat exchangers can also be modeled coupling submodels TPEX01 or TPEX02 from the Thermal-pneumatic library to submodels TFEX01 or TFEX02 fromthe Thermal-hydraulic library. In every case, submodels TFPHI01 , TFPHI02 , TPPHI01 and TPPHI02 are used to connect both parts.


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The heat exchanger effectiveness 4 is defined as:

maxqq*4

where q is the actual heat transfer rate and qmax is the maximum heat transferrate.

The number of transfer units NTU is a dimensionless parameter and is defined as:

min*

C AU

NTU *

where U is the overall heat transfer coefficient, A is the total area and Cmin is theminimum heat capacity rate.

There are many relations given for the heat exchanger effectiveness 4 as a function of the NTU and Cr=Cmin/Cmax numbers. These are based on analytical calculations availablefor various types of heat exchangers. Examples of functions commonly used aresummarized in the APPENDIX 1 section of this manual.

5.2. Liquid-liquid heat exchangers

The purpose of this section is to describe the way of modeling liquid-liquid heatexchangers considering various flow arrangements with:

! the effectiveness directly fixed by a signal source," some cross flow considerations,# some parallel flow considerations,$ some counter flow considerations.

For the last three cases, the flow arrangement expressions are set in the submodelsTPPHI01 and are used to compute the heat flow rate through the heat exchangers as wellas their effectiveness.

The interesting point here is to compare the difference in the heat exchanger performancesdue to the flow arrangements.


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Figure 20: heat exchangers based on the NTU-effectiveness method

The interesting point here is to compare the difference in the heat exchanger performancesdue to flow arrangement.

This is highlighted with the proposed model in Figure 20. It consists in a 1.889 kg/s 300degC hot coolant fluid flow which is refreshed with a 1 Kg/s 35 degC fresh coolant fluidflow. We consider a cross flow heat exchanger, a parallel flow heat exchanger and acounter flow heat exchanger.

Fill in the parameters of these components as described in the table below leaving theothers at their default values. Finally, run a simulation with a final time of 10 seconds witha communication interval of 0.01 second .

Submodel name and type Belongs tocategory

Main simulation parameters

1 TFFD1thermal- hydraulic

properties

Thermal-Hydraulic file name: coolant

2 TFFD1thermal- hydraulic

properties

Thermal-Hydraulic file name: coolantindex of thermal hydraulic fluid = 2

3 TFMTSsignal into thermal-hydraulic mass flow

rate

Thermal-Hydraulic # mass flow rate port 1 = 1 Kg/ssource temperature = 35 degC

4 TFMTSsignal into thermal-hydraulic mass flow

rate

Thermal-Hydraulic # mass flow rate port 1 = 1 Kg/sindex of thermal hydraulic fluid = 2

source temperature = 300 degC


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5 TFPC1thermal- hydraulic

adiabatic pipe

Thermal-Hydraulic # temperature at port 1 = 35 degC

5 bis TFPC1thermal- hydraulic

adiabatic pipe

Thermal-Hydraulic # temperature at port 1 = 300 degCindex of thermal hydraulic fluid = 2

6 TFEX01thermal- hydraulic

half heat exchanger

Thermal-Hydraulic # heat exchanger outlet temperature =35 degC

6 bis TFEX01thermal- hydraulic

half heat exchanger

Thermal-Hydraulic ## heat exchanger outlet temperature =300 degC

index of thermal hydraulic fluid = 2

7 TF223thermal- hydraulic

restriction

Thermal-Hydraulic index of thermal hydraulic fluid = 2

8 TFTK0thermal- hydraulic

tank

Thermal-Hydraulic index of thermal hydraulic fluid = 2

9 CONS0constant signal


constant value = 0.5

10 CONS0

constant signal

Signal, control and

observers

constant value = 2.1

11 TFPHI01thermal-pneumatic

heat flow ratecalculation

Thermal-Hydraulic filename or expression forepsilon=f(x,cr): x



Thermal-Hydraulic filename or expression forepsilon=f(x,cr):

1-exp((1/(cr+1e-6))*(x^0.22)*(exp(-cr*(x^0.78))-1))




(1-exp(-x*(1+cr)))/(1+cr)




(1-exp(-x*(1+cr)))/(1-cr*exp(-x*(1-cr)))

When this is done, plot a graph of the outlet temperatures in components TFEX01 againsttime as shown in Figure 21, Figure 22 and Figure 23.


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Figure 23: outlet liquid temperatures (hot liquid). 1. cross flow; 2. parallel flow;3. counter flow

One can easily see that every arrangement leads to different outlet temperatures for hotand cold liquids. The most efficient arrangement is the counter flow heat exchanger sincethe hot liquid temperature is the lowest and the cold liquid temperature the highest.

5.3. Liquid - gas heat exchangers

By using elements from the thermal-hydraulic and the thermal-pneumatic a liquid gasheat exchanger can be modeled as shown below:

Figure 24: liquid - gas heat exchanger


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6. Modeling a system with thermal components:important rules

This section will detail the important rules that should be followed to model correctly asystem with the thermal-hydraulic library components.

6.1. Causality in the thermal-hydraulic libraryAs previously stated, , it is necessary to distinguish two types of components in thethermal-hydraulic library.- The capacitive components are the volumes in which the temperature and the

pressure are computed. These temperature and pressure are computed from theenthalpy and mass flow rates inputs at ports of these components.

- The resistive components are the components in which the enthalpy and mass flowrates are evaluated from the temperatures and pressures inputs at ports of thesecomponents.

This implies that a thermal-hydraulic model is always built with resistive componentsconnected by capacitive components as shown in Figure 25.

Figure 25: connection rule

6.2. Other important rules

$ The thermal-hydraulic library deals with liquids.

$ It is better if the user builds the system slowly and run a simulation after each portion ofcircuit is added. This normally leads to a better understanding of the system and theresults. It is also less likely that the setting of parameters will be forgotten. The user willhave to be very careful when running multi-liquid simulations: the liquid type indicesmust be adjusted in the corresponding submodels.

$ Files of thermal liquid properties are available in the $AME/libthh/data directory. Fulllist of these files is given in the APPENDIX section. This list contains filenames of some


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7. Formulation of equations and underlyingassumptions

7.1. Brief review of the theory: flow calculations

7.1.1. Basic equations

The evaluation of pressure drops and friction factors in every resistive component of thethermal-hydraulic library is based on Idel'cik's [5] formulation and assumptions.

In a network, part of the total energy is expended overcoming the resistance forces created by real viscous fluids. Therefore, the term fluid resistance or hydraulic loss represents theirreversible loss of total energy over a given system length. The fundamental relation used

to evaluate the total pressure drop p& in a resistive component is based on Bernoulli'swell known equation (1):2

2tot 1tot tot w2 p p p ! max

' 5 *+* (1)

with

fr loc 5 5 5 )* (2)where

& p tot total pressure drop;5 total friction factor;5 loc local friction factor (local change in geometry);

5 fr frictional drag factor (pressure drops due to equivalent straight pipesegments of length l , diameter D); ' density of the fluid computed at mean pressure and upstream temperature;wmax maximum stream velocity.

From equation (1) we can express the total pressure drop as a function of the volumetricflow rate:

2min

2

A2Q

p ! ' 5 * (3)

where

Q volumetric flow rate;

Amin smallest cross-sectional area of the element considered.

Every resistive component in the thermal-hydraulic library uses equation (3). Thisequation is manipulated so as to compute the volumetric flow rate from the pressure drop.


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7.1.2. Further assumptions

In each resistive component, the following assumptions are made:

$ the flow is one-dimensional,$ the gravitational effects are significant in the hydraulic pipe submodels only,$ the pressures displayed are total pressures ,$ cavitation phenomena are not dealt with,

All submodels use the following units :

Total pressure Bar Absolute (barA)Volumetric flow rate Liter per minute(L/min)Mass flow rate Kilogram per second (kg/s)Friction factor Dimensionless (null)Reynolds number Dimensionless (null)Geometrical dimensions Millimeter (mm)Relative roughness Dimensionless (null)Angles Degree (degree)

7.1.3. About the Reynolds number

The flow regimes can either be laminar or turbulent. Laminar flow is stable, the streamlayers move without mixing with each other. The turbulent regime is characterized by arandom displacement of finite masses mixing strongly with each other. In classic fluid

power hydraulic applications flow is predominately laminar or transitional. In applicationsusing the thermal-hydraulic library, turbulent flow is also common.

It is known that the flow regime depends on the relationship between the inertia andviscosity forces (internal friction) in the stream, which can be expressed by adimensionless number, the Reynolds number given by:

3 3 ...min

max

h

hh

A DQ Dw Re ** (4)

where

wmax maximum stream velocity; Dh hydraulic diameter;3 kinematic viscosity of the fluid used computed at working pressure and

temperature; Ahmin hydraulic cross-sectional area.

In the rest of this document the Reynolds number at which the transition between laminarand turbulent flow occurs will be called the critical Reynolds number . This is not an

absolute constant but its value in a component can vary considerably with the geometry.

In thermal-hydraulic submodels where friction is modeled, laminar and turbulent regimesare taken into account and the following assumptions are used:

- when the flow is laminar, the total pressure drop is proportional to the flow velocity.- when the flow is turbulent, the total pressure drop is proportional to the square of the

velocity.


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Figure 27 shows the way laminar and turbulent regime are taken into account in resistivesubmodels.

There are two types of submodels which differ in the way they deal with the criticalReynolds number:

- Type 1: Submodels using Idel'cik [5] friction factors tables so that the criticalReynolds number is not used explicitly because it is already taken into account in thetables.

- Type 2: Submodels with fixed friction factors supplied by the user and using thecritical Reynolds number. A suitable value must be given to the critical Reynoldsnumber depending on the nature of the fitting.

Total pressure drop

& p = k.QVolumetric flow rate

Laminar Turbulent

& p = k.Q 2

Figure 27: laminar to turbulent flow transition

7.1.4. Resistive components: classification

A more detailed classification of resistive submodels in the thermal-hydraulic library isgiven below:

Resistive Components

Components whichcompute frictional drag Components whichcompute localresistance

Components whichcompute frictional drag+ local resistance

The following paragraphs describe these submodel categories.


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7.1.4.1. Frictional drag category

Submodels belonging to this category are used to model resistance to flow in straighttubes and conduits. The pressure losses along a straight tube of constant cross-sectionalarea are calculated from the Darcy-Weisbach equation (5):

2

2

h A2Q

Dl

p !

min

. '

0 * (5)

where0 friction coefficient of the segment of relative unit length l/D h =1;

Dh hydraulic or equivalent diameter;l length of flow segment.

For this type of submodel, in order to make an analogy with equation (2), the total frictionfactor 5 is given by:

h Dl

0 5 * (6)

In straight tubes, the resistance to the motion of a liquid or a gas under conditions oflaminar flow is due to the force of internal friction. This happens when one layer of the

liquid (or gas) has a relative motion compared to the others. These viscosity forces are proportional to the flow velocity. We then have:

)( Re0 0 6 (7)

As the Reynolds number increases, the inertia forces, which are proportional to thevelocity squared, begin to dominate. As flow becomes turbulent , there is a significantincrease in the resistance to the motion. Part of this increase is due to the roughness of thewall surface. Therefore we have:

),( rr Re0 0 6 (8)

where rr is the relative roughness.

The relative roughness is calculated as the ratio of the average height of asperities to thetube diameter. See details in Figure 28:

l

Dh

&

Figure 28: relative roughness definition


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The submodels in the thermal-hydraulic library found in this category are:

TFPC0, TFPC2, TFPC3TFPC4

Thermal-hydraulic pipes withCompressibility + frictional effects

TF234Thermal-Hydraulic annular pipe (relative roughness

does not have any influence because in this submodel, theflow is supposed to be always laminar).

7.1.4.2. Local resistance category

Submodels belonging to this category do not have a friction factor which takes intoaccount a special length. These components evaluate the local total pressure drop due totheir local geometry. This local geometry induces a sudden change in the stream velocityor direction and the total pressure drop is given as:

2

2maxw p loc

' 5 *& (10)

The submodels in the hydraulic resistance library found in this category are:

TF220TF221TF222TF223

Thermal-hydraulic restrictions (local change of cross-sectional area).

TF230 Sudden expansion/contraction (abrupt local change ofcross-sectional area).

TF208TF22B

ToTF22D

Thermal-hydraulic intersecting holes(local change ofstream direction).

TF22ETo

TF22I

Thermal-hydraulic volumes connected to pipes (localgeometry variation of the connection fitting).

TF206TF20BTF20C

Thermal-hydraulic T-junctions(local change of streamdirection).

The friction factors computed for these components can depend on the Reynolds number,on a parameter related to the change in geometry, but not on the length (as it is local) oron the relative roughness.

7.1.4.3. Frictional and local resistance category

This is the last category and it concerns components which create a progressive resistanceto flow. This is due to a variation of their geometry and the length in which this change in

geometry occurs. Good examples are diffusers and bends.

For this type of submodels, the total pressure drop is computed as follows :

2)(

2maxw p loc fr

' 5 5 )*& (11)

The submodels found in this category are:


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TF232TF23B

ToTF23E

Thermal-hydraulic bends (progressive variation ofstream direction).

TF236Thermal-hydraulic diffuser for progressive

expansion/contraction (progressive variation ofstream velocity).

In these submodels it is necessary to compute a local friction factor and a frictional dragfactor.

7.2. Brief review of the theory: thermal calculations

As previously said, there are two types of components in the thermal-hydraulic library:

- Resistive components,- Capacitive components.

7.2.1. Basic equations

7.2.1.1. Capacitive Components

In these components, the pressure and the temperature are computed from theirderivatives with respect to time. These components can be considered as control volumes .The pressure is a state variable and is computed from the mass conservation assumption.In addition, we must consider the following assumption: in the control volume, the liquid

properties are homogeneous .

The mass of liquid in the volume is given by:

V m 7* ' (12)

The continuity equation for the one-dimensional flow gives:

oi dmdmdt dm +* (13)

where dmi is the incoming mass flow rate in the volume and dmo is the outgoing massflow rate.

Control volumedm i dmo

It is possible, from equations (12) and (13), to formulate the continuity equation in termsof the density derivative as follows:

V dt dV

dt dm

dt d ' '

+* (14)


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The density being a thermodynamic property of the liquid, it is a function of pressure andtemperature:

. /T , p ' ' * (15)By differentiating with respect to temperature and pressure, equation (15) leads to:

dT

T

dp

p

d 78

8)78

8* ' ' ' (16)

From this equation, it is now possible to write the continuity equation in terms of the pressure derivative as follows:

9:;

7

88+

88* dT T

d

p

dp '

' ' 1

(17)

Using the definition of the liquid properties and more particularly the bulk modulus andthe volumetric expansion coefficient, the pressure derivative with respect to time is given

by:

9:;

7)7*

dt dT

dt d

dt dp

2 '

' 1 .

1 (18)

where:

. /

p

T , p

88* ' '

1 is the isothermal fluid bulk modulus,

. /T

T , p

8

87+* '

' 2

1 is the volumetric expansion coefficient.

The temperature is a state variable and is computed from the energy conservationassumption. The first equation describes the relationship between the specific internalenergy and the specific enthalpy of the liquid:

' p

hu +* (19)

where u is the specific internal energy, h is the specific enthalpy, p is the pressure and ' is the density of the liquid. The energy in the control volume is given by:

mgz 2

mV um E

2

))7* (20)

The three terms in equation (20) represent respectively the internal energy, the kineticenergy and the potential energy.


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We modify equation (20) introducing the second assumption: the kinetic and potentialenergies in the control volume are neglected. This leads to:

mu E * (21)

The derivative of the specific enthalpy can be written as follows:

dt

dpT

dt

dT

cdt

dh p '

2 )1( +)* (22)

Differentiating and combining equations (19), (21) and (22) leads to the followingrelation:

hdmdt dpT m

Qdmhdmhdt dT

cm oi p (+))+* ' 2 ..

.. ! (23)

where m is the mass of liquid in the volume, c p is the specific heat of the liquid at constant pressure, dmh i is the incoming enthalpy flow rate, dmho is the outgoing enthalpy flow rate,

Q! is the heat flow rate exchanged with the outside, V is the volume, dm is the mass flowrate through the volume, 2 is the volumetric expansion coefficient, ' is the fluid densityand h is the specific enthalpy.

Finally, the temperature derivative with respect to time is given by:

dt dp

cT

cmQhdmdmhdmh

dt dT

p p

oi ... ' 2 ))(++*

! (24)

Equation (24) is the complete energy equation represented by the temperature derivativewith respect to time. The pressure derivative term in this equation shows the cross-coupling effect with the continuity equation (18) represented by the pressure derivative

with respect to time.

7.2.1.2. Resistive Components

In these components, the mass flow rate and the enthalpy flow rates are computed.

The mass flow rate is calculated from Bernoulli's equation written in the previous sectionof this manual. It is computed as follows:

'

' p.

A.c.dm q&* 2 (25)

The enthalpy flow rate is computed as follows:

hdmdmh (* (26)

where dm is the mass flow rate through the resistive component and h is the specificenthalpy of the fluid.


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7.2.2. Further assumptions

Concerning the thermal aspects in the components of the thermal-hydraulic library, thefollowing assumptions are made :

$ the flow is one dimensional,$ the properties of the liquid are homogeneous in the volumes,$ aeration and cavitation phenomena are not taken into account,

$ in the liquids, heat transfers by radiation or conduction are neglected with respect toconvection phenomena,$ the displayed temperatures are total temperatures .

Heat transfer by convection

The key feature of this kind of heat exchange is the movement of a fluid. This phenomenon can be seen in Figure 31 below:

solid

Tsolid

Moving fluid (Tfluid)

? convection

Tsolid > Tfluid

Figure 31: convection phenomenon between a solid and a fluid

$ the thermal properties of the liquids are functions of pressure and temperature only(see next section).

All submodels use the following units :

Temperature Degree Celsius ( degC )Heat and enthalpy flow rate Watt ( W )Geometrical dimensions Millimeter ( mm)Exchange area Millimeter squared ( mm2)Exchange coefficients Watt per degree Celsius ( W/degC )Radiation exchange coefficient Watt per Kelvin^4 (W/K 4)Density Kilogram per meter cube (kg/m 3)Thermal conductivity Watt per meter per degree Celsius (W/m/degC)Specific heat Joule per kilogram per degree Celsius (J/kg/degC)Prandtl number Dimensionless ( null )Reynolds number Dimensionless ( null )Nusselt number Dimensionless ( null )Grashof number Dimensionless ( null )


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7.2.3. About convection phenomena

As previously stated, convection takes place as soon as a fluid is moving along the wall ofa solid. Convection phenomenon is the combination of two heat transfer modes:- conduction in the thickness of the laminar film of fluid in contact with the wall. In

this film, it is considered that there is no mixing.- outside this laminar layer, heat is transferred due to a mixing of the fluid particles in a

flow supposed to be turbulent. We then talk about a mixing temperature Tm.

The general form of the equation expressing the convection heat flow rate is given by:

)( Ah T T wmconvection +((*? (27)where h is the convective exchange coefficient, A is the exchange area, T m is the mixingtemperature of the fluid and T w is the wall temperature.

There are two kinds of convective exchange and we now give a brief review of theassumptions and equations governing these phenomena.

Forced convection

We talk about forced convection as soon as a fluid moves under the action of amechanical external source and flows along a solid wall. Basically, the forced convectionheat flow rate is computed using the following equation:

)( Ah T T wm forced forced +((*? (28)where h forced is the forced convective exchange coefficient, A is the exchange area, T m andT w are respectively the mixing temperature of the fluid and the temperature of the solidwall.

The major problem is to determine h forced . We express it as:

. /c dim

forced Pr , Re Nu

h 0 (*

(29)

where Nu is a dimensionless number called the Nusselt number, 0 is the thermalconductivity of the fluid and cdim is a characteristic geometrical dimension of theexchange.

The Nusselt number can be interpreted as a dimensionless temperature gradient at thesurface. It characterizes the thermal exchange between the fluid and the solid wall. It isusually taken to be a function of two dimensionless numbers which are the Prandtlnumber and the Reynolds number.

The Prandtl number is given by the following relation:

0 c p Pr

(*

(30)


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where - is the absolute viscosity of the fluid, c p is the specific heat of the fluid and 0 is thethermal conductivity of the fluid. These thermal properties depend on pressure andtemperature. The Prandtl number characterizes the thermal properties of the fluid.

The Reynolds number is given as follows:

3 DV

Re (*

(31)

where V is the velocity of the fluid, D is the hydraulic diameter of the flow and 3 is thekinematic viscosity of the fluid. The Reynolds number can be interpreted as the ratio ofthe inertia and viscous forces. It characterizes the flow regime of the fluid.There are a lot of relations available for the Nusselt number as a function of the Prandtland the Reynolds number. These are based on experiment available either for externalflow or internal flow conditions. Examples of functions commonly used are summarizedin the APPENDIX section of this manual.

Free convection

Free convection occurs when the movement of the fluid is due to variations of its densityinduced by heat exchanges between the fluid and the solid wall. The free convection heatflow rate is computed using the following equation:

)( Ah T T wm free free +((*? (32)where h free is the free convective exchange coefficient, A is the exchange area, T m and T w are respectively the mixing temperature of the fluid and the temperature of the solid wall.The major problem is to determine h free . We express it as:

. /

cdim

free Pr ,Gr Nu

h 0 (*

(33)

where Nu is a dimensionless number called the Nusselt number, 0 is the thermalconductivity of the fluid and cdim is a characteristic geometrical dimension of theexchange. The Nusselt number can be interpreted as a dimensionless temperature gradientat the surface. It characterizes the thermal exchange between the fluid and the solid wall.It is usually taken to be a function of two dimensionless numbers which are the Grashofnumber and the Prandtl number.

The Grashof number is given by the following relation:

2

23

-

2 ' )( g Gr

T T c w f dim +((((* (34)

where - is the absolute viscosity of the fluid, cdim is a characteristic geometrical dimensionof the exchange, ' is the density of the fluid, g is the gravity acceleration, 2 is thevolumetric expansion coefficient of the fluid, T f is the fluid temperature and T w is the solidwall temperature.


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The Prandtl number is given by the following relation:

0 c p Pr

(*

(35)

where - is the absolute viscosity of the fluid, c p is the specific heat of the fluid and 0 is thethermal conductivity of the fluid. These thermal properties depend on pressure and

temperature. The Prandtl number characterizes the thermal properties of the fluid.There are a lot of relations available for the Nusselt number as a function of the Prandtland the Grashof number. These are based on experiment available either for external flowor internal flow conditions. Examples of functions commonly used are summarized in theAPPENDIX section of this manual.


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8. Advanced thermal-hydraulic properties

For most industrial applications where both pressure and temperature variations areimportant, we recommend that you use TFFD2 submodel. This submodel uses polynomialfunctions to evaluate the thermal-hydraulic properties of the liquid used for thesimulation. The fluid properties concerned are the density, the viscosity, the specific heat

at constant pressure, the thermal conductivity, the bulk modulus, the volumetric expansioncoefficient and the specific enthalpy. In this submodel, the order of the polynomial formshas been increased so that it enables to reproduce very accurately the evolution of thefluid properties as a function of pressure and temperature. In addition, this submodelaccounts for cavitation phenomena.

To test this advanced properties submodel, build the system shown in Figure 26. Itcomprises 5 elements from the Thermal-Hydraulic and the Signal libraries. Each elementis referenced in Figure 26 by a number. Fill in the parameters of these components asdescribed in the table below, leaving the other parameters at their default values.

Figure 26: Checking advanced thermal-hydraulic properties

Submodel name and type Belongs to category Principal simulation parameters0 TFFD2

thermal-hydraulic

advanced propertieswith cavitation

Thermal-hydraulicfilename :

$AME/libthh/data_advanced/

diesel80_rme20.data

1 UD00

piecewise linearsignal


stage1

output at start of stage 1 : 20output at end of stage 1 : 20duration of stage 1 : 1 sec

2 UD00

piecewise linearsignal


stage1

output at start of stage 1 : 1output at end of stage 1 : 2000

duration of stage 1 : 1 sec

3 TFPT0conversion of asignal into a

temperature and a pressure

Thermal-hydraulic no parameters

4 TFFPRcalculation of thermal

liquid propertiesThermal-hydraulic default parameters


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Use the batch facility (in Tools menu, Batch setup option) to define four temperaturevalues at which the fluid properties will be calculated (20, 37, 80 and 120 [degC]) and

perform a simulation over 1 second with a communication interval equal to 0.01 second .When this is done, plot the density and the bulk modulus of the fluid versus pressure forthese four temperatures as shown in figure 10.

Figure 27: Thermal properties of the liquid

From these results, it is easy to understand that variations in pressure and in temperaturein a thermal-hydraulic system have a great importance on the thermal-hydraulic propertiesof a fluid. Indeed, if we consider a temperature variation from 20 to 120 degC at constant

pressure (say 1000 barA ), the density variation is almost equal to 60 kg/m 3 (that is to say a7% decrease of the value of the density).

Similarly, if we consider a pressure variation from 1 to 2000 barA at constant temperature(say 20 degC), the density variation is almost equal to 70 kg/m 3 (that is to say an increaseof 8% of the value of the density).

It follows that the cross-coupling effects between temperature and pressure have a strongimpact on the properties of the fluid. To observe this, display the evolution of all the

properties available for plotting in submodel TFFPR as shown in figure 28. To do this, usethe batch facility to define five pressure values at which the fluid properties will becalculated (1, 500, 1000, 1500 and 2000 [barA]) and for each run, vary the temperaturefrom 0 to 120 degC.


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Figure 28: Thermal-hydraulic properties of a special diesel fuel with respect topressure and temperature

In addition, the submodel TFFD2 takes into account cavitation phenomena. To show this,change the parameters of component number 2 so as to vary the pressure from 0 to 1barA. Run the simulation using the same final time and communication interval as

previously and display the density and the bulk modulus of the fluid as a function of

pressure for the four temperatures defined above as shown in figure 29.

Figure 29: Density and bulk modulus evolution in aeration and cavitation conditions


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References

[Ref. 1] Franck P. Incropera, David P. DeWitt, Fundamentals of Heat and MassTransfer, Fourth Edition, John Wiley & Sons, 1996.

[Ref. 2] Franck P. Incropera, David P. DeWitt, Fundamentos de Transferencia

de Calor e de Massa, Terceira ediao, Guanabara Koogan, 1992.

[Ref. 3] J. P. Holman, Heat Transfer, S I Metric Edition, McGraw-Hill BookCompany, 1989.

[Ref. 4] Bernard Eyglunent, Thermique thorique et pratique l'usage del'ingnieur, Editions Herms, 1994.

[Ref. 5] I.E. Idel'cik, Handbook of Hydraulic Resistance, 3 rd Edition, BegellHouse Inc., 1996.

[Ref. 6] D.S. Miller, Internal Flow systems, 2 nd Edition, Amazon Technology,1989.

[Ref. 7] Jacques Faisandier, Mcanismes olo-hydrauliques, Editions Dunod,1987.


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S S ee p pt t eemmbbeer r 22000044 A A p p p peenn d d i i x x 11 / / 44

APPENDIX

Values for friction factors given in the literature for special fitting configuration

All these values are extracted from data provided by J. Faisandier [7].

1 Sudden expansion/contraction:

d1

d2

5exp 0.81 0.64 0.49 0.36 0.25 0.16 0.09 0.04 0.01d2/d1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.95cont 0.4 0.38 0.34 0.30 0.24 0.18 0.1 0.05 0.015

Ljdflsdflsdjfljsdlkfjsdlfjlsqflksdflsdjflsdjfmlksdjfmklsdjflksjdfljsdlfjsldkjfsdjflksdlfjsdlfjs

2 Volumes connected to pipes:

Sharp entry

5 = 0.5 to 1.0

Extended entry

5 = 0.68 to 2.5

Conical entry90 degrees

5 = 0.25

Conical entry60 degrees5 = 0.1 to 0.18

Rounded entry

5 = 0.04 to 0.1

3 Junctions:

T-junction90 degrees

5 = 1.2


5 = 0.1


5 = 0.5


5 = 2.5 to 3


5 = 0.06


5 = 0.15

90 60


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4 Intersecting holes:

5 = 0.6 to 0.9 5 = 0.15 5 = 0.6 5 = 0.5 5 = 1.1

All the following values are extracted from data provided by Incropera and DeWitt [1].

Summary of most common Nusselt correlation for external flow forced convection heattransfer:

Correlation Geometry Conditions Nu = 0.332Re 0.5Pr 0.33 Flat plate Laminar, local, 0.6 @Pr< 50 Nu = 0.664Re 0.5Pr 0.33 Flat plate Laminar, average,

0.6 @Pr< 50 Nu = 0.0296Re 0.8Pr 0.33 Flat plate Turbulent, local, Re


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where Gr is the Grashof number and Pr is the Prandtl number. It is explained in the theoreticalsection of this manual how to compute these 2 numbers. Here are the values of C and n constant for different geometrical configuration of the free convection heat transfer:

For laminar flow, n = 0.25 For turbulent flow, n = 0.33

C coefficientGeometry andorientation of the wall

Characteristicdimension of the

exchangeLaminar convection

n = 0.25Turbulent convection

n = 0.33Vertical plate or cylinder Height 0.59

(104


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One shell pass(2, 4,tube passes)

n shell pass(2n, 4n,tube passes)

1

21

2

21

2

21

21

)1(exp1

)1(exp1

)1(12

+

CCD

CCE

F

9:;

)++

9:;

)+)

(

CCG

CCH

I

)))7*r

r

r r

C NTU

C NTU

C C 4

1

1

1

1

1

111

11

+

99:;

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