fluidti 89 92 voyage idgas 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 Ideal Gases and Gas Mixtures

FluidTI for TI 89 and TI 92 TI Voyage 200

Prof. Hans-Joachim Kretzschmar Dr. Ines Stoecker Dipl.-Ing. (FH) L. Kleemann R. Krause

Property Functions for Ideal Gases and Gas Mixtures from the VDI-Guideline 4670

IDGAS FluidTI

Contents 1. Property Functions

1.1 Range of Validity and Structure of Program Library 1.2 Property Functions for Ideal Gases and Mixtures

2. Using "FluidTI - Ideal Gases and Mixtures" 2.1 Installation on the calculators TI 89, TI 92, TI 92Plus, and TI Voyage 200 2.2 Example: Calculation of the Enthalpy h = f(p,t) of a Gas

2.3 Example: Calculation of the Enthalpy h = f(t,ξ1... ξ10) of the Gas Mixture 2.4 Example: Calculation of the Mass Fraction ξi = f(i, ψ1...ψ10) of a Gas 2.5 Removing FluidTI

3. Software Documentation

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

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1. Property Functions 1.1 Range of Validity and Program Library Structure Calculation of thermodynamic properties of gases and mixtures of gases in ideal gas state is carried out with the algorithms of the

VDI-Guideline 4670 [1] while transport properties are calculated according to

Brandt [2] . Important properties were taken from the

Blanke [4] compendium.

It is possible to calculate mixtures of the following gases, which are in the following referred to as mixtures of gases:

Gas-No. Mixture gas

1 Argon Ar

2 Neon Ne

3 Nitrogen N2

4 Oxygen O2

5 Carbon monoxide CO

6 Carbon dioxide CO2

7 Steam H2O

8 Sulfur dioxide SO2

9 Air (dry)

10 Atmospheric Nitrogen

Calculation programs are valid in the temperature range:

from - 73.15 °C to 1,726.85 °C

Pressure range is restricted to the range in which the gas mixtures can be considered as ideal gases and thus ranges from

from above 0 MPa to 1 (3) MPa, maximum 5 MPa The assumption of “ideal gas” applies to a good approximation to 1 MPa, while above and to 5 MPa at temperatures below 500 °C you have to accept substantial inaccuracies of the properties calculated. These inaccuracies have only few effects on the calculation of the efficiency of gas turbines.

Available subprograms and functions in "FluidTI - Ideal Gases and Mixtures" are specified in the following subsection.


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1.2 Property Functions for Ideal Gases and Mixtures "Ideal Gases and Mixtures" Functional Dependence

Function Name

Property or Function

Unit of the Function Value

Source or Algorithm

Information on page

v = f(p, t,ξ1...ξ10 or ψ1...ψ10) v_pt_ig Specific volume of the mixture m³/kg ideal gas equation 3/13 h = f(t,ξ1...ξ10 or ψ1...ψ10 h_t_ig Specific enthalpy of the mixture kJ/kg [1] 3/4 s = f(p,t,ξ1...ξ10 or ψ1...ψ10) s_pt_ig Specific entropy of the mixture kJ/kg . K [1] 3/10 cp = f(t,ξ1...ξ10 or ψ1...ψ10) cp_t_ig Specific isobaric heat capacity of the

mixture kJ/kg . K [1] 3/2

κ = f(t,ξ1...ξ10 or ψ1...ψ10) Kappa_t_ig Isentropic exponent of the mixture - [1] 3/5

λ = f(t,ξ1...ξ10 or ψ1...ψ10) λ_t_ig Thermal conductivity of the mixture W/m . K [2], [3] 3/6

η = f(t,ξ1...ξ10 or ψ1...ψ10) Eta_t_ig Dynamic viscosity of the mixture Pa . s = kg/m . s [2], [3] 3/3

t = f(h,ξ1...ξ10 or ψ1...ψ10) t_h_ig Backward function: Temperature from the enthalpy of the mixture

K [1] 3/11

t = f(p,s,ξ1...ξ10 or ψ1...ψ10) t_ps_ig Backward function: Temperature from pressure and entropy of the mixture

K [1] 3/12

M = f(ξ1...ξ10 or ψ1...ψ10) M_ig Molar mass of the mixture kg/kmol [4] 3/7 R = f(ξ1...ξ10 or ψ1...ψ10) R_ig Specific gas constant of the mixture kJ/kg . K [4] 3/9 ξi = f(i,ψ1...ψ10) Xsi_igas_Psi_ig Mass fraction of the gas mixture i from

mole fractions of all gas mixtures kg/kg Conversion with the

rule of mixture 3/14

ψi = f(i,ξ1...ξ10) Psi_igas_Xsi_ig Mole fraction of the gas mixture i from mass fractions of all gas mixtures

kmol/kmol Conversion with the rule of mixture

3/8

Hochschule Zittau/Görlitz (FH), Fachgebiet Technische Thermodynamik, Prof. Dr.-Ing. habil. H.-J. Kretzschmar, Dr.-Ing. I. Stöcker

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Mixture gases

Gas-No. Mixture gas 1 Argon Ar 2 Neon Ne 3 Nitrogen N2

4 Oxygen O2

5 Carbon monoxide

CO

6 Carbon dioxide CO2

7 Steam H2O

8 Sulfur dioxide SO2

9 Air (dry) from VDI4670 [1]

Composition in mole fractions: 78.1109 % N2 20.9548 % O2 0.9343 % Ar

Composition in mass fractions: 75.5577 % N2 23.1535 % O2, 1.2888 % Ar

10 Atmospheric Nitrogen corresponding to Brandt [2]

Composition in mole fractions: 98.7750 % N2, 0.0400 % CO2, 1.1820 % Ar, 0.0030 % Ne Composition in mass fractions: 98.2586 % N2, 0.0625 % CO2, 1.6768 % Ar 0.0021 % Ne


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Units

Formula Symbol Description Unit

t Temperature °C

p Pressure MPa

ξ1 ... ξ10 Mass fractions of gas mixtures kg/kg

ψ1... ψ10 Mole fractions or volume fractions of gas mixtures kmol/kmol

art Input parameters: art = 1 for input of composition in mass fractions ξ1, ... ξ10

art = 0 for input of composition in mole fractions ψ1, ... ψ10

zu1 ... zu10 for art =1 Composition as mass fractions ξ1, ... ξ10 kg/kg

zu1 ... zu10 for art =0 Composition as mole fractions ψ1, ... ψ10 kmol/kmol

Range of validity: Reference states: Temperature range: t = -73.15 °C to 1726.85 °C Thermodyn. Factor for single component

Pressure: p = 1 kPa ... 5 MPa Pressure 1.01325 bar

Specific volume: v = 5.1 m3/kg ... 2,9 109 m3/kg Temperature 273.15 K

Specific enthalpy: h = -136 kJ/kg ... 4100 kJ/kg Enthalpy 0 kJ/kg

Specific entropy: s = 2.8 KJ/kg K ... 9.7 KJ/kg K Entropy 0 kJ/kg

Note: If the calculation results in -1 or -1000, this indicates that the values entered are located outside the range of validity or the sum of the values entered ξ1,… ξ10 or. ψ1, ... ψ10 entered does not result in 1.


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2. Using "FluidTI - Ideal Gases and Mixtures"

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

The "FluidTI - Ideal Gases and Mixtures" 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 TI 92Plus,

TI Voyage 200

File IdGas89.89g IdGas92E.92g IdGas92P.9xg IdGasVoyage200.9xg

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/

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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".

Type "idgas()" and confirm your entry by pressing the <ENTER> key.

Now, proceed as described in section 2.3.

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.


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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-Connect® 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

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 "idgas()" and confirm your entry by pressing the <ENTER> key.

Now, proceed as described in section 2.2.


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2.2 Calculation of the Entropy s = f(p, t) of a Gas

We will now calculate, step by step, the specific entropy s as a function of temperature t = 250 °C, and pressure p = 1 MPa. The result of the specific entropy calculated is to be saved within the variable "s1".

Please carry out the following instructions:

1. Run the "FluidTI - Ideal Gases and Mixtures" program as described in section 2.1.

2. After leaving the start screen by pressing <ENTER>, you will see the menu with which you can choose to calculate either individual gases or gas mixtures.

Select "individual gas" and confirm by pressing <ENTER> twice.

3. In the main menu, select the gas "oxygen" next to "Choose a gas" and confirm by pressing <ENTER> twice.

4. In the next menu "Function input" choose the function "s_pt_ig" and confirm by pressing <ENTER> twice.


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5. In the "Input" menu, you now have to enter the values of the given state variables. According to our example, type the values "1" for p in MPa and the value "250" for t in °C. Confirm your input by pressing the <ENTER> key twice. Now, the calculation will be carried out.

Note:

Please make sure that the input values are located within the range of validity of the chosen function (cp. section 1.2).

While the calculation is carried out, you will see the "Busy" symbol in the lower right edge of your screen.

6. After the calculation has been carried out successfully the "Output" menu appears.

Next to "save as :" enter the name "s1" for the variable in which the result is going to be saved. You can now use the result in further calculations within or outside "FluidTI - Ideal Gases and Mixtures". An example would be the input of the entropy calculated before when calculating the function "t_ps_ig". Go back to the main menu by pressing the <ENTER> key.

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.


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2.3 Calculation of the Enthalpy h = f(t,ξ1... ξ10) of a Gas Mixture We will now calculate, step by step, the specific enthalpy h of a flue gas as a function of temperature t = 100 °C, and a mixture consisting of the following mass fractions:

13 % carbon monoxide, 11 % steam, and 76 % air nitrogen. Please carry out the following instructions: 1. Run the "FluidTI - Ideal Gas and Mixture" program as described in section 2.1. 2. After leaving the start screen by pressing <ENTER>, you will see the menu with which you

can choose to calculate either individual gases or gas mixtures. Select "gas mixture" and confirm by pressing <ENTER> twice.

3. In the main menu, select the entry "mass fraction ξi" next to "Input in" because we need to enter the gas fractions in mass fractions in our sample calculation. You must confirm your input by pressing the <ENTER> key.

4. The input of the gas fractions will be carried out within two separate screens. It is not necessary to enter a value for the gases whose percentage of the mixture is 0. You may also enter the value "0" for these gases. In the first screen you have to enter the fractions of argon, neon, nitrogen, oxygen, and carbon monoxide. Corresponding to our example you have enter the value "0.13" for carbon monoxide. Confirm by pressing <ENTER>.

Note:

Use the point on your keypad as decimal point. The sum of the fractions of the individual gases must result in 1.


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In the second screen you have to enter the fractions of carbon dioxide, steam, sulfur dioxide, air (dry), and air nitrogen. Enter the value "0.11" for steam and "0.76" for air nitrogen. Confirm your input by pressing the <ENTER> key.

Note:

Use the point on your keypad as decimal point. The sum of the fractions of the individual gases must result in 1.

5. Chose the function "h_t_ig" in the function input menu and confirm by pressing <ENTER>.

6. Now the parameter input window pops up. Here you have to enter the appropriate state variables of the function such as temperature, pressure, enthalpy, and entropy. The function "h_t_ig" only depends on the temperature. Now, type "100" for t in °C and confirm your entry by pressing the <ENTER> key. Now, the calculation will be carried out automatically.

Note:

Please make sure that the input values are located within the range of validity of the chosen function (see section 1.2).

7. While the calculation is carried out, you will see the "Busy" symbol in the lower right edge of your screen. After the calculation of the chosen function has been carried out successfully the "Output" menu appears. It is now possible to save the calculated result in a variable and to use it in another calculation. Go back to the main menu by pressing the <ENTER> key.


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2.4 Calculation of the Mass Fraction ξi = f(i, ψ1...ψ10) of a Gas

We will now calculate, step by step, the mass fraction ξi of argon as a function of the given mixture consisting of the following mole fractions: 20 % argon and 80 % carbon monoxide Please carry out the following instructions: 1. Run the "FluidTI - Ideal Gas and Mixture" program as described in section 2.1. 2. After leaving the start screen by pressing <ENTER>, you will see the menu with which you

can choose to calculate either individual gases or gas mixtures. Select "gas mixture" and confirm by pressing <ENTER> twice.

3. In the main menu, select the entry "mol fraction ψi" next to "Input in" because we need to

enter the gas fractions in mole fractions in our sample calculation. You must confirm your input by pressing the <ENTER> key.

4. Enter the values "0.2" for argon and "0.8" for carbon monoxide. It is not necessary to enter a value for the gases whose percentage of the mixture is 0. You may also enter the value "0" for these gases. Confirm by pressing <ENTER>.


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5. Chose the function "ξ_igas_ψ_ig" in the function input menu and confirm by pressing <ENTER>.

6. Now the input window for selecting the gases pops up. Chose the gas "argon" in the input menu and confirm by pressing <ENTER>.

7. While the calculation is carried out, you will see the "Busy" symbol in the lower right edge of your screen. After the calculation of the chosen function has been carried out successfully the "Output" menu appears. It is now possible to save the calculated result in a variable and to use it in another calculation. Go back to the main menu by pressing the <ENTER> key.


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2.5 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. Search the FLUIDTI directory with the cursor and highlight it by pressing the <F4> key. In

front of the FluidTI directory and the appropriate files appears a checkmark.

If you have other FluidTI programs installed on your TI (e. g. Water and Steam from IAPWS-IF97 or Humid Air (cp=const)), you will find them in the FLUIDTI directory as well. If you do not wish to remove them, please make sure that they are not checkmarked. If necessary you have to move the cursor on these files and remove the checkmark by pressing the <F4> key. Checkmark only those files which should really be deleted. The program package "FluidTI - Ideal Gas and Mixture" contains the following files: igasdat1, igasdat2, igasdat3, igasdat4, and idgas.

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 has been removed.


3/1


3. Software Documentation

Specific Isobaric Heat Capacity cp = f(t, ξ1...ξ10 or ψ1...ψ10)

Name in "FluidTI - Ideal Gas and Mixture"

cp_t_ig

Input Values:

t - Temperature t in °C art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ zu1...zu10 - composition in mass fractions ξ1...ξ10 in kg/kg - composition in mole fractions ψ1... ψ10 in kmol/kmol

Result:

cp_t_ig or cp - specific isobaric heat capacity in kJ/(kg K)

Range of validity: Temperature t: from -73.15 °C to 1,726.85 °C

Comments:

Model of an ideal mixture Results for wrong input values:

cp_t_ig or cp = -1

References:

cp from VDI 4670 [1]

3/2


Dynamic Viscosity η = f(t, ξ1...ξ10 or ψ1...ψ10)


Eta_t_ig

Input Values:

t - Temperature t in °C art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ

zu1...zu10 - composition in mass fractions ξ1...ξ10 in kg/kg - composition in mole fractions ψ1... ψ10 in kmol/kmol

Result:

Eta_t_ig or eta - dynamic viscosity in Pa s


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

References:

Unsaturated and saturated humid air: η corresponding to Brandt [2]

3/3


Specific Enthalpy h = f(t, ξ1...ξ10 or ψ1...ψ10)

Name in FluidTI- Ideal Gas and Mixture:

h_t_ig

Input Values:

t - Temperature t in °C

art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ zu1...zu10 - composition in mass fractions ξ1...ξ10 in kg/kg - composition in mole fractions ψ1... ψ10 in kmol/kmol

Result:

h_t_ig or h - specific enthalpy in kJ/kg


Comments:

Model of an ideal mixture

Results for wrong input values:

h_t_ig or h = -1000

References:

h from VDI 4670 [1]

3/4

Isentropic Exponent κ = f(t, ξ1...ξ10 or ψ1...ψ10)


Kappa_t_ig

Input Values:



Result:

Kappa _t_ig or Kappa – Isentropic exponent


Comments:

Kappa p

p

cc R

κ =−


Kappa _t_ig or Kappa = -1

References:

Unsaturated and saturated humid air: cp from VDI 4670 [1]


3/5


Thermal Conductivity λ = f(t, ξ1...ξ10 or ψ1...ψ10)


λ_t_ig

Input Values:



Result:

λ_t_ig or λ - Thermal conductivity in W/(m K)

Range of validity: Temperature T: Temperature t: from -73.15 °C to 1,726.85 °C

Comments:

Calculations corresponding to Brandt – Model of ideal mixture


λ_t_ig or Lambda = -1

References:

Unsaturated and saturated humid air: λ corresponding to Brandt [2]

3/6


Molar Mass M = f(t, ξ1...ξ10 or ψ1...ψ10)


M_ig

Input Values: art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ


Result:

M_ig or M - Molar mass in kg/kmol

Comments:

Calculations according to Blanke


M_ig or M = -1

References:

M corresponding to Blanke [4]

3/7

Mole Fraction ψi = f(i, ξ1...ξ10)


Psi_igas_Xsi_ig

Input Values:

i - Description of the gas

zu1...zu10 - composition in mass fractions ξ1...ξ10 in kg/kg

Result:

Psi_igas_Xsi_ig or Psi - Mole fraction in kmol/kmol

Comments:

Mole fraction: i

i ii i( )

RR

ψ ξξ

= ⋅⋅∑


Psi_igas_Xsi_ig or Psi = -1


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Specific Gas Constant R = f(ξ1...ξ10 or ψ1...ψ10)


R_ig

Input Values: art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ zu1...zu10 - composition in mass fractions ξ1...ξ10 in kg/kg - composition in mole fractions ψ1... ψ10 in kmol/kmol

Result:

R_ig or R - Specific gas constant in kJ/(kg K)

Comments:

Specific gas constant: i i

i( )RR ξ ⋅= ∑

or: i

ii

1

( )R

Rψ=

∑


R_ig or R = -1


3/9


Specific Entropy s = f(p,t,ξ1...ξ10 or ψ1...ψ10)


s_pt_ig

Input Values:

p - Overall pressure p in MPa



Result:

s_pt_ig or s - Entropy in kJ/(kg K)

Range of validity: Pressure p: from 1 Pa to 5 MPa

Temperature t: from -73.15 °C to 1,726.85 °C

Comments:

Model of an ideal mixture


s_pt_ig or s = -1000

References:

s from VDI 4670 [1]

3/10


Backward Function t = f(h, ξ1...ξ10 or ψ1...ψ10)


t_h_ig

Input Values:

h - Enthalpy h in kJ/kg art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ


Result:

t_h_ig or t - Temperature in °C

Range of validity: Enthalpy h: from -135.6 kJ/kg to 4100 kJ/kg

Comments:

Iteration of t from h = f(t, zu1...zu10)


t_h_ig or t = -1

References:

h from VDI 4670 [1]

3/11


Backward function t = f(p, s, ξ1...ξ10 or ψ1...ψ10)


t_ps_ig

Input Values:


s - Entropy s in kJ/(kg K) art - Type of composition: art=1 for composition in mass fractions ξ art=0 for composition in mole fractions ψ


Result:

t_ps_ig or t - Temperature in °C


Enthalpy s: from -2.377 kJ/(kg K) to 9.706 kJ/(kg K)

Comments:

Iteration of T from s (p, t, zu1...zu10)


t_ps_ig or t = -1

References:

s from VDI 4670 [1]

3/12

Specific Volume v = f(p, t, ξ1...ξ10 or ψ1...ψ10)


v_pt_ig

Input Values:




Result:

v_pt_ig or v - Specific volume in m3/kg


Temperature t: from -73.15 °C to 1,726.85 °C

Comments:

Specific volume v from: pTRv ⋅

= m


v_pt_ig or v = -1


3/13

Mass Fraction ξi = f(i, ψ1... ψ10)


Xsi_igas_Psi_ig

Input Values:

i - Description of the gas

zu1...zu10 - composition in mole fractions ψ1... ψ10 in kmol/kmol

Result:

Xsi_igas_Psi_ig or Xsi - Mass fraction in kg/kg

Comments:

Mass fraction: i

i ii i( )

MM

ξ ψψ

= ⋅⋅∑


Xsi_igas_Psi_ig or Xsi = -1


4/1

4. References

[1] VDI Richtlinie 4670 u. Thermodynamische Stoffwerte von feuchter Luft und Verbrennungsgasen

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

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

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

[5] 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)

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

[7] 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.

ASME Journal of Eng. for Gasturbines and Power 122 (2000) Nr. 1, S. 150-182

[8] Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance.

IAPWS Sekretariat, Dooley, B., EPRI, Palo Alto CA, (1997)

[9] Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance.

IAPWS Secretariat, Dooley, B., EPRI, Palo Alto CA, (1997)

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

[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)

[13] Kretzschmar, H.-J.: Zur Aufbereitung und Darbietung thermophysikalischer Stoffdaten für die

Energietechnik. Habilitation, TU Dresden, Fakultät Maschinenwesen (1990)


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