fluidti 89 92 voyage huair docu eng

HOCHSCHULE ZITTAU/GÖRLITZ(FH) - Univer sity of Appl ied SciencesHOCHSCHULE ZITTAU/GÖRLITZ(FH) - Univer sity of Appl ied Sciences

Faculty of MECHANICAL ENGINEERING

Department of TECHNICAL THERMODYNAMICS

Property Software for Humid Air

FluidTI for TI 89, TI 92, and TI Voyage 200

Prof. Hans-Joachim Kretzschmar Dr. Ines Stoecker D. Seibt R. Krause

Property Software for Humid Air

FluidTI Student’s version

Contents 1. Property Functions of Humid Air

2. Application of FluidTI for Calculating Humid Air

2.1 Installation on the calculators TI 89, TI 92, TI 92Plus, and TI Voyage 200

2.2 Example: Calculation of hl = f(p,t,xw) 2.3 Removing FluidTI

3. Software Documentation of Humid Air

4. References

________________________________________________________________________

© Zittau/Goerlitz University of Applied Sciences (FH) Faculty of Mechanical Engineering Department of Technical Thermodynamics Prof. Dr.-Ing. habil. H.-J. Kretzschmar Dr.-Ing. I. Stoecker Tel.: +49 3583-61-1846 or -1881 Fax: 03583-61-1847 E-mail: [email protected] Internet: www.thermodynamics-zittau.de

Zittau/Goerlitz University of Applied Sciences, Department of Technical Thermodynamics, Professor H.-J. Kretzschmar, Dr. I. Stoecker

1/1

1. Property Functions of Humid Air

Function Name Property Functional Dependence

Unit of the result

Phi_ptxw Relative humidity ϕ = wf( , , )p t x %

xw_ptPhi Humidity ratio (absolute humidity) from temperature and relative humidity

ϕ=w f( , , )x p t kg/kg(air)

Xiw_xw Mass fraction of water ξ =w wf( )x kg/kg

Psiw_xw Mole fraction of water ψ =w wf( )x kmol/kmol

pd_ptxw Partial pressure of steam =d f( , , )wp p t x MPa

xw_ptpd Humidity ratio (absolute humidity) from Partial pressure of steam

=w f( , , )dx p t p kg/kg(air)

xws_pt Saturation humidity ratio =ws f( , )x p t kg/kg(air)

pds_pt Saturation vapor pressure of water =ds f( , )p p t MPa

tτ_pxw Dew point temperature τ = wf( , )t p x °C

xw_ptτ Humidity ratio (absolute humidity) from dew point temperature τ=w f( , )x p t kg/kg(air)

tf_ptxw Wet bulb temperature =f wf( , , )t p t x °C

xw_pttf Humidity ratio (absolute humidity) from temperature and wet bulb temperature

=w f( , , )fx p t t kg/kg(air)

cp_ptxw Specific isobaric heat capacity = wf( , , )pc p t x K)kJ/(kg ⋅

vl_ptxw Air-mass specific volume =l wf( , , )v p t x /kgm3(air)

hl_ptxw Air-mass specific enthalpy =l wf( , , )h p t x kJ/kg (air)

sl_ptxw Air-mass specific entropy =l wf( , , )s p t x (air)kJ/(kg K)⋅

λ_ptxw Thermal conductivity λ = wf( , , )p t x )KW/(m ⋅

Eta_ptxw Dynamic viscosity η = wf( , , )p t x sPa ⋅

t_phlxw Backward function: Temperature from air-mass specific enthalpy and humidity ratio (absolute humidity)

= l wf( , , )t p h x °C

t_pslxw Backward function: Temperature from air-mass specific entropy and humidity ratio (absolute humidity)

= l wf( , , )t p s x °C


1/2 Parameters

p - Overall pressure in MPa t - Temperature in °C xw - Absolute humidity in kg steam/kg(air) dry air ϕ - Relative humidity (only defined for unsaturated humid air)

xls - Liquid fraction in kg liquid droplets / kg liquid droplets and ice crystals

Input only when calculating fog with a temperature of t = 0.01 °C (mixture of liquid fog and ice fog at t = 0.01 °C exactly)

xls = 1 when calculating liquid fog xls = 0 when calculating ice fog 0 < xls < 1 when calculating a mixture of liquid fog and ice fog

Range of validity

Temperature t = -30 °C ... 800 °C Pressure p = 0.0006112 MPa ... 2 MPa

Calculation algorithms Unsaturated and saturated humid air ≤w ws( )x x

- ideal gas mixture of dry air and steam - vl according to an ideal equation of mixture of gases

- hl, sl corresponding to the cp=const model

- λ, η corresponding to mixture model of Brandt [15] Liquid mist and °C >w ws( )x x t 0.01≥

- ideal mixture of saturated humid air and water liquid - v, h, s of liquid droplets from IAPWS-IF97 [1], [2], [3], [4] - cp of liquid droplets as constant value

- λ, η of liquid drops from IAPWS-85 [6], [7] - Mixture of volume fractions

Ice fog and °C >w ws( )x x t 0.01≤

- ideal mixture of saturated humid air and water ice - v, cp of ice crystals as constant values

- λ, η of saturated humid air

Mixture of liquid fog and ice fog at t = 0.01 °C exactly >w ws( )x x >w ws(x x )

- ideal mixture of saturated humid air, water liquid and water ice


2/1

2. Application of FluidTI for Calculating Humid Air

2.1 Installation of FluidTI on the calculators TI 89, TI 92, TI 92 Plus, and TI Voyage 200

The "FluidTI" program will be copied onto the pocket calculator with the help of a link program and the appropriate link cord.

You can acquire the software needed on buying the TI calculator or in the Internet at the address http://www.ti.com/calc/docs/link.htm. The link cord necessary can be bought as accessory e. g. from Böttcher Datentechnik GmbH http://www.boettcher-datentechnik.de/.

The following description applies to the link programs TI-Graph-Link® and TI-Connect®, whereas the particular program must be installed. If you are using other link programs you have to take the steps for data transfer from the appropriate instructions manual or online help.

1. Insert the FluidTI floppy disk in the floppy drive of your computer. It contains the group files listed in the following table:

TI-Model TI 89 TI 92 with memory extension

TI 92Plus

TI Voyage 200

File HuAir89.89g HuAir92E.92g HuAir92P.9xg HuAirVoyage200.9xg

2. For the installation and working with the program it is necessary that the language of the TI-calculator is set to English. If this is not the case, you can change the language corresponding to the following description: - Press the <MODE> key - Press the <F3> key

The language currently set is displayed next to "Language". - Open the "Language" menu by pressing the right direction key

You will now see all available languages on your TI-calculator - Select the language "English" with the help of the direction keys - Confirm your selected language by pressing the <ENTER> key - Confirm your selection again by pressing the <ENTER> key

3. Connect your TI-calculator to your computer by plugging the link cord in a free serial interface (mostly COM2 or USB) and the phono connector in the pocket calculator.

If you wish to use the TI-Connect® link program for data transfer, please follow subsection 5.


http://www.ti.com/calc/docs/link.htm

http://www.boettcher-datentechnik.de/

2/2

4. Data Transfer using the TI-Graph-Link® Program

a) Run the TI-Graph-Link® program on your computer. Click on "Link" in the upper menu bar and then select "Send…". Search and click the letter of your floppy disk drive in the "Drives:" window.

The group file belonging to your TI model appears in the "File name:" window. Considering the table above click on the file belonging to your model and afterwards click the "Add" button. The group file and the drive letter will be shown in the "Selected files:" window. Highlight the square "Retain folder" by clicking on it.

Click the "OK" button. Now, the data transfer from the computer to your pocket calculator begins. You will now see the files which have been copied. The directory FLUIDTI will be created on your TI and afterwards the appropriate program files of the group file will be copied into it.

b) Click the "OK" button to confirm the "Finished" notification which appears on your computer screen. You have now finished installation of FluidTI on your pocket calculator. If the copying process has failed, the following errors are possible:

- TI has not been connected or switched on when the TI-Graph-Link program had been started - The TI cursor was not placed in the command line - A wrong cord has been used - The connectors are not plugged in properly - A wrong interface is set (menu item "Link")

c) In order to run the program, navigate into the "fluidti" directory by pressing <MODE> and select the entry "fluidti" in the field "Current Folder" by pressing the right direction key. Confirm your selection by pressing the <ENTER> key. Now, "fluidti" flashes in the "Current Folder" field. Confirm again by pressing <ENTER>. In the lower left edge of the screen you will now see "FLUIDTI". Now, type "huair()" and confirm your entry by pressing the <ENTER> key. Now, proceed as described in section "2.2 Example: …".

5. Data Transfer Using the TI-Connect® Program

a) Run the TI-Connect® program on your computer. Click on "DeviceExplorer". In some cases, the "TI Communication Settings" menu will be opened. You will see the name of your TI calculator, the name of the cord and the port which will be used for the cord. Check if everything is correct and confirm by clicking the "OK" button. In the following window you will see the directory tree with the programs of the connected TI calculator.


2/3

Click on "Tools" in the upper menu bar and then select "GroupExplorer". Search the letter of your floppy drive in the main window and click on the "+" next to the drive name. Below the name of the floppy drive you will now see the group files.

Considering the table above, left click the file belonging to your model. Now, right-click the item in order to open the pop-up menu. Within the menu click on "Send To Device".

Now, the data transfer from the computer to your pocket calculator begins. You will now see the files which have been copied on your computer screen. The directory FLUIDTI will be created on your TI and afterwards the appropriate program files of the group file will be copied into it. You have now finished installation of FluidTI on your TI-pocket calculator. b) If the copying process has failed, the following errors are possible:

- TI has not been connected or switched on when the TI-Graph-Link program had been started - The TI cursor was not placed in the command line - A wrong cord has been used - The connectors are not plugged in properly - A wrong interface is set (menu item "Link")

c) In order to run the program, navigate into the "fluidti" directory by pressing <MODE> and select the entry "fluidti" in the field "Current Folder" by pressing the right direction key. Confirm your selection by pressing the <ENTER> key. Now, "fluidti" flashes in the "Current Folder" field.

Confirm again by pressing <ENTER>. In the lower left edge of the screen you will now see "FLUIDTI".

Now, type "huair()" and confirm your entry by pressing the <ENTER> key. Now, proceed as described in section "2.2 Example: …". ..."


2/4

2.2 Example Calculation of hl = f(p,t,xw) We will now calculate, step by step, the air-mass specific enthalpy hl as a function of given mixture pressure p, given temperature t and given absolute humidity xw for humid air.

Please carry out the following instructions: - For the installation and working with the program it is necessary that the language of the

TI-calculator is set to English. If this is not the case, you can change the language corresponding to the description in section "2.1 Installation of FluidTI...".

- In order to run the program, navigate into the "fluidti" directory by pressing <MODE> and select the entry "fluidti" in the field "Current Folder" by pressing the right direction key. Confirm your selection by pressing the <ENTER> key. Now, "fluidti" flashes in the "Current Folder" field. Confirm again by pressing <ENTER>. In the lower left edge of the screen you will now see "FLUIDTI". Now, type "huair()" and confirm your entry by pressing the <ENTER> key.

- Leave the start screen by pressing <ENTER>. You will see the main menu:

Press the right direction key to open the "Function" menu which contains the calculable property functions. You will see the following menu:

- Select the menu item "hl_ptxw" with the help of the direction keys and confirm your selection by pressing the <ENTER> key.

- The chosen function "hl_ptxw" flashes next to "Function". Confirm again by pressing <ENTER>. The following menu appears, in which you can enter the given values.


2/5

- Enter the value for p in MPa into the appropriate window. Please consider the range of validity:

p = 0.0006112 MPa ... 2 MPa

e. g.: Enter the value 0.1 using the point as decimal point and move the cursor into the field below with the help of the direction keys.

- Enter the value for t in °C into the appropriate window. Please consider the range of validity:

t = - 30 °C ... 800 °C

e. g.: Enter the value 25 and move the cursor into the field below with the help of the direction keys.

- You now have to enter the value for the absolute humidity xw in kg steam / kg dry air into the appropriate window.

e. g.: Enter the value 0.01 and press the <ENTER> key.

- Confirm all your inputs again by pressing <ENTER>. While calculation is carried out, you will see the BUSY-sign.

- After the calculation is finished, the result for hl in kJ/kg(air) relating to the mass of dry air will be shown on the screen.

The result in our sample calculation here is: hl = 50.7137 kJ/kg(air).

The calculation of hl = f(p,t,xw) has thus been completed.

It is now possible to save the calculated value for hl in a variable. Afterwards you can calculate with this variable in other calculations within or outside FluidTI.

e. g.: Enter the name "hl" within the "save as:" window and confirm it by pressing the

<ENTER> key twice.

Now, the calculated value is saved within the variable hl and is available in the FLUIDTI directory.


2/6

Note: You can arbitrarily choose the name of the variable. It should merely not begin with the sign ω (omega) and it should not bear the name of a system variable (cp. TI manual). Generally, variables used within the FLUIDTI directory should not begin with the sign ω.

Your calculator will now show the main menu again.

Close FluidTI by pressing the <ESC> key.


2/7

2.3 Removing FluidTI Please carry out the following instructions for the pocket calculators TI 89, TI 92, TI 92 Plus, and TI Voyage 200.

1. Open the "Var-Link-Menu" by pressing the <2nd> key and then the < - > key (but not <(-)> ). You will see the following menu:

2. Locate the FluidTI directory with the cursor. The following files belong to this directory.

Move the cursor to the "airdat1" file and highlight it by pressing the <F4> key. A check mark will appear in front of the file.

Repeat this highlight procedure for the files "airdat2", "airdat3", and "huair".

3. Press the <F1> key. The "Manage" menu appears. Select "UnLock Variable" with the cursor and confirm this selection by pressing <ENTER>.

4. Deletion is carried out by opening the "Manage" menu again pressing <F1>, then select

the option "Delete" with the cursor and confirm by pressing <ENTER>. Confirm the following query by pressing <ENTER> again.

Now FluidTI for humid air has been removed. 5. Leave the Var-Link menu by pressing the <ESC> key.


3/1

3. Software Documentation of Humid Air

Relative humidity ϕ = f(p,t,xw)

Name in FluidTI: Phi_ptxw

Input Values: p - Overall pressure p in MPa

t - Temperature t in °C

xw - Humidity ratio (Absolute humidity) xw in kgwater / kgair

Result: Phi_ptxw - relative humidity

Range of validity: Temperature t: from - 30°C to tcrit = 373.946°C (critical temperature of water)

Pressure p: from 0.0006112 MPa to 2 MPa

Humdity ratio (Absolute humidity) xw: from 0 kg/kg to wsx (p,t)

Comments:

Relative humidity ϕ =+

wl dsww

( )x p

R p txR

with for - Vapor pressure of water ds sp p (= t)t)

t 0.01 C≥ °

for ds subp p (= t 0.01 C< ° - Sublimation pressure of water Results for wrong input values: Phi_ptxw = - 1

References: corresponding to IAPWS-IF97 [1], [2], [3], [4] ] sp (t)

corresponding to IAPWS -93 [5] subp (t)


3/2

Humidity ratio (Absolute humidity) from Temperature and Relative Humidity xw = f(p,t,ϕ)

Name in FluidTI: xw_ptPhi



Phi - relative humidity in %

Result: xw_ptPhi - Humidity ratio (Absolute humidity) in kgwater / kgair

Range of validity: Temperature t: from - 30°C to tcrit = 373.946°C (critical temperature of water)


relative humidity ϕ from 0 to 100 %

Comments:

Humidity ratio (Absolute humidity) ϕϕ

=−

dslw

w d

( )( )s

p tRxR p p t

with for - Vapor pressure of water ds sp (t) p (t)= t 0.01 C≥ °

for ds subp (t) p (t)= t 0.01 C< ° - Sublimation pressure of water Results for wrong input values: xw_ptPhi = - 1




3/3

Mass fraction of water ξw = f(xw)

Name in FluidTI: Xiw_xw

Input Values: xw - Humidity ratio (Absolute humidity) xw in kgwater / kgair

Result: Xiw_xw - Mass fraction of water in kgwater/ kg

Range of validity: Humdity ratio (Absolute humidity) xw: greater than or equal to 0 kgwater/kgair

Comments:

Mass fraction of water ξ =+

ww

w1x

x

Results for wrong input values: Xiw_xw = - 1


3/4

Mole fraction of water ψw = f(xw)

Name in FluidTI: Psiw_xw

Input Values: xw - Humidity ratio (Absolute humidity) xw in kgwater / kgair

Result: Psiw_xw - Mole fraction of water in kmolwater / kmol

Range of validity: Humdity ratio (Absolute humidity) xw: greater as or equal to 0 kgwater/kgair

Comments:

Mole fraction of water (1 )

w ww

wψ =

+R x

R x

Results for wrong input values: Psiw_xw = - 1


3/5

Partial pressure of steam pd = f(p,t,xw)

Name in FluidTI: pd_ptxw




Result: pd_ptxw - Partial pressure of steam in MPa

Range of validity: Temperature t: from -30°C to 800°C



Comments:

Partial pressure of steam =+

wd

lw

w

xp pR xR

for w wsx x (p,t)≤

for result w wsx x (p,t> ) )d dsp p (t= Results for wrong input values: pd_ptxw = -1


3/6

Humidity ratio (Absolute humidity) from Partial Pressure of Steam xw = f(p,t,pd)

Name in FluidTI: xw_ptpd



pd - Partial pressure of steam in MPa

Result: xw_ptpd - Humidity ratio (Absolute humidity) in kgwater / kgair



Partial pressure of water vapor pd : from 0.0006112 MPa to dsp (t)

Comments:

Humidity ratio (Absolute humidity) =−

dlw

w d

pRxR p p

Results for wrong input values: xw_ptpd = - 1


3/7

Saturated humidity ratio xws = f(p,t)

Name in FluidTI: xws_pt



Result: xws_pt - Saturated humidity ratio in kgwater / kgair

Range of validity: Temperature t: from -30°C to tcrit= 373.946 °C (critical temperature of water)


Comments:

Humidity ratio (Absolute humidity) =−

dslw

w ds

( )( )

p tRxR p p t

with for - Vapor pressure of water ds sp (t) p (t)= t 0.01 C≥ °

for ds subp (t) p (t)= t 0.01 C< ° - Sublimation pressure of water Results for wrong input values: xws_pt = - 1




3/8

Saturation Vapor Pressure of Water pds = f(p,t)

Name in FluidTI: pds_pt



Result: pds_pt - Saturation vapor pressure of water in MPa

Range of validity: Temperature t: from -30°C to (Boiling temperature of water) st (p)


Comments: Vapor pressure of water ds sp p (t)= for t 0.01 C≥ °

Sublimation pressure of water ds subp p (t)= for t 0.01 C< ° Results for wrong input values: pds_pt = -1

References: corresponding to IAPWS-IF97 [1], [2], [3], [4] ] )t(ps

corresponding to IAPWS -93 [5] )t(psub


3/9

Dew point temperature tτ = f(p,xw)

Name in FluidTI: tτ_pxw



Result: tτ_pxw - Dew point temperature in °C

Range of validity: Pressure p: from 0.0006112 MPa to 2 MPa

Humdity ratio (Absolute humidity) xw: greater than or equal to wsx (p, 30 C− ° )

)

)

Comments: Dew point temperature for (Boiling temperature of water) s dt t (pτ = t 0.01 C≥ °

for sub dt t (pτ = t 0.01 C< ° (Sublimation temperature of water)

with =+

wd

lw

w

xp pR xR

Results for wrong input values: tτ_pxw = - 1

References: corresponding to IAPWS-IF97 [1], [2], [3], [4] ] s dt (p )

corresponding to IAPWS -93 [5] sub dt (p )


3/10

Humidity ratio (Absolute humidity) from Dew Point Temperature xw = f(p,tτ)

Name in FluidTI: xw_ptτ


tτ - Dew point temperature in °C

Result: xw_ptτ - Humidity ratio (Absolute humidity) in kgwater / kgair

Range of validity: Dew point temperature tτ: from -30°C to tcrit = 373.946°C (crit. temperature of water)


Comments:

Humidity ratio (Absolute humidity) τ

τ=

−dsl

ww ds

( )( )

p tRxR p p t

with for - Vapor pressure of water

for ds sp (t ) p (t )τ τ= t 0.01 Cτ ≥ °

ds subp (t ) p (t )τ τ= t 0.01 Cτ < ° - Sublimation pressure of water

Results for wrong input values: xw_ ptτ = - 1

References:

corresponding to IAPWS-IF97 [1], [2], [3], [4] ] sp (t )τ

corresponding to IAPWS -93 [5] subp (tτ )


3/11

Wet Bulb Temperature tf = f(p,t,xw)

Name in FluidTI: tf_ptxw




Result: tf_ptxw - Wet bulb temperature in °C

Range of validity: Temperature t: from -30°C to tcrit = 373.946 °C (critical temperature of water)



f wx

Comments:

Iteration of tf from fogunsaturatedl w l( , , ) ( , , )=h p t x h p t

Results for wrong input values: tf_ptxw = - 1

References: Unsaturated and saturated humid air: hl corresponding to Baehr [14] Water droplets in fog: h corresponding to IAPWS-IF97 [1], [2], [3], [4] ]


3/12

Humidity ratio (Absolute humidity) from Wet Bulb Temperature xw = f(p,t,tf)

Name in FluidTI: xw_pttf



tf - Wet bulb temperature in °C

Result: xw_pttf - Humidity ratio (Absolute humidity) in kgwater / kgair

Range of validity: Temperature t: from 0.01°C to 800°C

Wet bulb temperature tf : from 0.01°C to the given temperature t or to ts(p) (Boiling temperature of water)


Comments:

Iteration of xw from fogunsaturatedl w l( , , ) ( , , )=h p t x h p tf wx

Results for wrong input values: xw_pttf = - 1



3/13

Specific Isobaric Heat Capacity cp = f(p,t,xw)

Name in FluidTI: cp_ptxw




xls - Liquid fraction in kgliquid / kgliquid and ice ( 1x0 ls ≤≤ ) ! Specification only necessary if t = 0.01 °C when calculating a mixture of liquid frog and ice fog

Result: cp_pt_igas - Specific Isobaric Heat Capacity cp in kJ/(kg K)



Humdity ratio (Absolute humidity) xw: greater than or equal to 0 kg/kg

Liquid fraction xls : from 0 kg/kg to 1 kg/kg

Comments: Model of an ideal mixture Results for wrong input values: cp_ptxw = -1

References:


3/14

Air-Mass Specific Volume vl = f(p,t,xw)

Name in FluidTI: vl_ptxw





Result: vl_ptxw - Air-mass specific volume in m3/kgair



Humdity ratio (Absolute humidity) xw: greater than or equal to 0 kg/kg


Comments: Calculation: - for unsaturated and saturated humid air )xx( wsw ≤ as ideal mixture of gases of

dry air and steam - for fog as ideal mixture of saturated humid air and )xx( wsw > water liquid or water ice Results for wrong input values: vl_ptxwxls = -1

References: Specific volume of liquid water corresponding to IAPWS-IF97 [1], [2], [3], [4]


3/15

Air-Mass Specific Enthalpy hl = f(p,t,xw)

Name in FluidTI: hl_ptxw





Result:

hl_ptxw – air-mass specific enthalpy in kJ/kgair



Humdity ratio (Absolute humidity) xw: greater than or equal to 0 kg/kgair



dry air and steam - for fog as ideal mixture of saturated humid air and )xx( wsw > water liquid or water ice Results for wrong input values: hl_ptxw = -1000



3/16

Air-Mass Specific Entropy sl = f(p,t,xw)

Name in FluidTI: sl_ptxw





Result: sl_ptxw - air-mass specific entropy in kJ/(kgair K)






dry air and steam - for fog as ideal mixture of saturated humid air and )xx( wsw > water liquid or water ice Results for wrong input values: sl_ptxw = - 1000

References: Unsaturated and saturated humid air: sl corresponding to Baehr [14] Water droplets in fog: s corresponding to IAPWS-IF97 [1], [2], [3], [4] ]


3/17


Thermal Conductivity λ = f(p,t,xw)

Name in FluidTI: λ_ptxw




Result: λ_ptxw - Thermal Conductivity in W/(m K)




Comments: Calculations corresponding to Brandt – Model of ideal mixture Results for wrong input values: λ_ptxw = -1

References: Unsaturated and saturated humid air: λ corresponding to Brandt [15] Water droplets in fog: λ from IAPWS-85 [6]

3/18


Dynamic Viscosity η = f(p,t,xw)

Name in FluidTI: Eta_ptxw




Result: Eta_ptxw - Dynamic Viscosity in Pa s




Comments: Calculations corresponding to Brandt – Model of ideal mixture Results for wrong input values: Eta_ptxw = -1

References: Unsaturated and saturated humid air: η corresponding to Brandt [15] Water droplets in fog: η from IAPWS-85 [7]

3/19

Backward function: Temperature t = f(p,hl,xw)

Name in FluidTI: t_phlxw


hl - air-mass specific enthalpy in kJ/kg


Result: t_phlxw - Temperature in °C




Comments: Iteration of t from l w( , , )h p t x Results for wrong input values: t_phlxw = - 1



3/20

Backward function: t = f(p,sl,xw)

Name in FluidTI: t_pslxw


sl - air-mass specific entropy in kJ/(kg K)


Result: t_pslxw - Temperature in °C




Comments: Iteration of t from l w( , , )s p t x Results for wrong input values: t_pslxw = -1

References: Unsaturated and saturated humid air: sl corresponding to Baehr [14] Water droplets in fog: s corresponding to IAPWS-IF97 [1], [2], [3], [4] ]


4/1

4. References

[1] Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam IAPWS-IF97. IAPWS Sekretariat, Dooley, B, EPRI, Palo Alto CA (1997)

[2] Wagner, W.; Kruse, A.: Zustandsgrößen von Wasser und Wasserdampf. Springer-Verlag, Berlin (1998)

[3] Wagner, W.; Cooper, J.R.; Dittmann, A.; Kijima, J.; Kretzschmar, H.-J.; Kruse, A.; Mares, R.; Oguchi, K.; Sato, H.; Stöcker, I.; Sifner, O.; Takaishi, Y.; Tanishita, I.; Trübenbach, J.; Willkommen, Th.: The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Journal of Eng. for Gasturbines and Power 122 (2000) Nr. 1, S. 150-182

[4] Wagner, W.; Rukes, B.: IAPWS-IF97: Die neue Industrie-Formulation. BWK 50 (1998) Nr. 3, S. 42-97

[5] Kretzschmar, H.-J.: Mollier h,s-Diagramm. Springer-Verlag, Berlin (1998)

[6] Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance. IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1997)

[7] Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance. IAPWS Secretariat, Dooley, B., EPRI, Palo Alto CA, (1997)

[8] IAPWS Release on Surface Tension of Ordinary Water Substance 1994. IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1994)

[9] Kretzschmar, H.-J.; Stöcker, I.; Willkommen, Th.; Trübenbach, J.; Dittmann, A.: Supplementary Equations v(p,T) for the Critical Region to the New Industrial Formulation IAPWS-IF97 for Water and Steam. in: Steam, Water and Hydrothermal Systems: Physics and Chemistry Meeting the Needs of Industry, Proceedings of the 13th International Conference on the Properties of Water and Steam, Eds. P.G. Hill et al., NRC Press, Ottawa, 2000

[10] Kretzschmar, H.-J.; Stöcker, I.; Knobloch, K.; Trübenbach, J.; Willkommen, Th.; Dittmann, A.; Friend, D.: Supplementary Backward Equations p(h,s) to the Industrial Formulation IAPWS-IF97 for Water and Steam. Journal of Engineering for Gasturbines and Power - in Vorbereitung

[11] Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1995)

[12] Grigull, U.: Properties of Water and Steam in SI Units. Springer-Verlag, Berlin (1989)


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[13] Kretzschmar, H.-J.:

Zur Aufbereitung und Darbietung thermophysikalischer Stoffdaten für die Energietechnik. Habilitation, TU Dresden, Fakultät Maschinenwesen (1990)

[14] Baehr, H.D.; Diederichsen, Ch.: Berechnungsgleichungen für Enthalpie und Entropie der Komponenten von Luft und Verbrennungsgasen. BWK 40 (1988) Nr. 1/2, S. 30-33

[15] Brandt, F.: Wärmeübertragung in Dampferzeugern und Wärmetauschern. FDBR-Fachbuchreihe, Bd. 2, Vulkan Verlag Essen (1985)

[16] Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance. IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1985)

[17] Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance.IAPWS Secretariat, Dooley, B., EPRI, Palo Alto CA, (1985)

[18] Release on Surface Tension of Ordinary Water Substance 1975. IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1975)

[19] VDI-Wärmeatlas, 7. Auflage. VDI-Verlag, Düsseldorf (1995)

[20] Blanke,W.: Thermophysikalische Stoffgrößen. Springer-Verlag, Berlin (1989)

[21] VDI-Richtlinie 4670 - Thermodynamische Stoffwerte von feuchter Luft und Verbrennungsgasen. VDI-Handbuch Energietechnik, Düsseldorf (2000)


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