Property Library For Propane FluidPRIME With LibPropan For .
Property Library forPropaneFluidPRIMEwith LibPropanfor Mathcad Prime Prof. Hans-Joachim KretzschmarMatthias KunickS. HerrmannM. Sünder
Property Library for the Calculation ofthe Properties of PropaneLibPropanFluidPRIME for Mathcad Prime Contents0 Package Contents1 Property Functions2 Application of FluidPRIME in Mathcad Prime 2.1 Installing FluidPRIME2.2 Licensing the LibPropan Property Library2.3 Example: Calculation of the Enthalpy h f(p,t,x) for Propane2.4 Removing FluidPRIME3 Program Documentation4 Property Libraries for Calculating Heat Cycles, Boilers, Turbines, and Refrigerators5 References6 Satisfied Customers KCE-ThermoFluidProperties UG & Co. KGProf. Dr. Hans-Joachim KretzschmarWallotstr. 3, 01307 Dresden, GermanyPhone: 49-351-27597860Mobile: 49-172-7914607Fax: 49-3222-4262250Email: info@thermofluidprop.comInternet: www.thermofluidprop.comKCE Kretzschmar Consulting Engineers
0/10. Package ContentsZip file "CD FluidPRIME LibPROP.zip" includes the following files:FluidPRIME LibPROP Docu.pdf- User’s GuideFunctions LibPROP.mcdx- Mathcad Prime worksheet with all functionsLibPROP.msi- MSI installersetup.exe- Setup installerLibPROP.dll- DLL with functions of the LibPROP libraryKCE Kretzschmar Consulting Engineers
1/11. Property FunctionsFunctionalDependencea f(p,t,x)cp f(p,t,x)Function Namea ptx PROPcp ptx PROPCall fromFortran programAPTXPROP(P,T,X)CPPTXPROP(P,T,X)Call in DLL LibPropanas parameterC APTXPROP(A,P,T,X)C CPPTXPROP(CP,P,T,X)Property orFunctionThermal diffusivitySpecific isobaric heat capacityUnitof the resultm2/skJ/(kg K)η f(p,t,x)eta ptx PROPETAPTXPROP(P,T,X)C ETAPTXPROP(ETA,P,T,X) Dynamic viscosityPa sh f(p,t,x)h ptx PROPHPTXPROP(P,T,X)C HPTXPROP(H,P,T,X)Specific enthalpykJ/kgκ f(p,t,x)λ f(p,t,x)kappa ptx PROPKAPTXPROP(P,T,X)C KAPTXPROP(KAP,P,T,X)Isentropic exponent-lambda ptx PROPLAMPTXPROP(P,T,X)C LAMPTXPROP(LAM,P,T,X) Thermal conductivityW/(m K)ν f(p,t,x)ny ptx PROPNYPTXPROP(P,T,X)C NYPTXPROP(NY,P,T,X)Kinematic viscositypmel f(t)pmel t PROPPMELPROP(T)C PMELPROP(PMEL,T)Melting pressure from temperaturem2/sbarps f(t)ps t PROPPSTPROP(T)C PSTPROP(PS,T)Vapor pressure from temperaturebarPr f(p,t,x)Pr ptx PROPPRPTXPROP(P,T,X)C PRPTXPROP(PR,P,T,X)Prandtl-Number-ρ f(p,t,x)rho ptx PROPROPTXPROP(P,T,X)C ROPTXPROP(RHO,P,T,X)Densitys f(p,t,x)s ptx PROPSPTXPROP(P,T,X)C SPTXPROP(S,P,T,X)Specific entropykg/m3kJ/(kg K)t f(p,h)t ph PROPTPHPROP(P,H)C TPHPROP(T,P,H) Ct f(p,s)t ps PROPTPSPROP(P,S)C TPSPROP(T,P,S)tmel f(p)tmel p PROPTMELPROP(P)C TMELPROP(TMEL,P)Backward function: Temperature frompressure and enthalpyBackward function: Temperature frompressure and entropyMelting temperature from pressurets f(p)ts p PROPTSPPROP(P)C TSPPROP(TS,P)Saturation temperature from pressure Cu f(p,t,x)u ptx PROPUPTXPROP(P,T,X)C UPTXPROP(U,P,T,X)Specific internal energykJ/kgv f(p,t,x)w f(p,t,x)v ptx PROPw ptx PROPVPTXPROP(P,T,X)WPTXPROP(P,T,X)C VPTXPROP(V,P,T,X)C WPTXPROP(W,P,T,X)Specific volumeIsentropic speed of soundm³/kgm/sx f(p,h)x ph PROPXPHPROP(P,H)C XPHPROP(X,P,H)kg/kgx f(p,s)x ps PROPXPSPROP(P,S)C XPSPROP(X,P,S)Backward function: Vapor fractionfrom pressure and enthalpyBackward function: Vapor fractionfrom pressure and entropy C Ckg/kgKCE Kretzschmar Consulting Engineers
1/2Units:t in Cp in barx in (kg of saturated steam)/(kg wet steam)Range of validityTemperature range:from tmel(p) to 326.85 CPressure range:from ps(tt) 1.7517 x 10-9 bar to 1000 barReference stateh 200 kJ/kg and s 1 kJ/(kg K) at t 0 C on the boiling curve (x 0)Details on the vapor fraction xThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixed details on the vapor fraction x are to be considered:Single-phase regionIf the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.Wet-steam regionIf the state point to be calculated is located in the wet steam region, a value for x between 0 and 1 (x 0 for saturated liquid, x 1 for saturated steam)must be entered. In this case, the backward functions result in the appropriate value between 0 and 1 for x. When calculating wet steam either the givenvalue for t and p -1000 or the given value for p and t -1000 and in both cases the value for x between 0 and 1 must be entered.If p and t and x are entered as given values, the program considers p and t to be appropriate to represent the vapor pressure curve. If this is not the casethe calculation for the property of the chosen function results in –1000.Wet steam region: Temperature range from tt –187.625 C to tc 96.74 CPressure range from ps(tt) 1.7517 x 10-9 bar to pc 42.512 barNote.If the calculation results in –1000, the values entered represent a state point beyond the range of validity of LibPropan. For further information on each functionand its range of validity see Chapter 3. The same information may also be accessed via the online help pages.KCE Kretzschmar Consulting Engineers
2/12Application of FluidPRIME in Mathcad Prime FluidPRIME has been developed to calculate thermodynamic properties in Mathcad Prime more conveniently. Within Mathcad Prime, it enables the direct call of functions relating tohumid air from the LibProp property library.2.1Installing FluidPRIMEIn this section, the installation of FluidPRIME LibProp is described.After you have downloaded and extracted the zip-file "CD FluidPRIME LibProp.zip", you willsee the folderCD FluidPRIME LibPropin your Windows Explorer, Norton Commander etc.Now, open this folder by double-clicking on it.Within this folder you will see the following files and a folders:FluidPRIME LibProp Docu.pdfFunctions LibProp.mcdxLibProp.msisetup.exeLibProp.dllIn order to run the installation of FluidPRIME double-click the filesetup.exe.Note: If you get an error message during the installation, please try the LibProp.msi insteadof the setup.exe for the installation. The steps trough the install assistent are similiary onboth the .exe and the .msi file.After opening the installer-file you get the start window of the setup wizard (Figure 1.1).Please confirm with "Next".KCE Kretzschmar Consulting Engineers
2/2Figure 2.1: Setup WizardIn Figure 2.2 you can see a note window that will inform you additionally to the next steps.Figure 2.2: Note WindowClick on the "Next" button to get the "Select Installation Folder"-window (Figure 2.3).KCE Kretzschmar Consulting Engineers
2/3Figure 2.3: Select Installation FolderPlease click on "Browse6" to get another window where you can select the installation path.You will get the standard path:C:\Program Files\PTC\Now select your Mathcad Prime version folder. For exampleC:\Program Files\PTC\Mathcad Prime 5.0.0.0(Version 5.0.0.0).On the next step you have to choose the "Custom Functions" folder, so that your finalinstallation path looks likeC:\Program Files\PTC\Mathcad Prime 5.0.0.0\Custom Functions\that you can also see in Figure 2.4.KCE Kretzschmar Consulting Engineers
2/4Figure 2.4: "Browse for Folder"-window with the full installation pathPlease confirm with "OK" and continue in the further window (Figure 2.5) with "Next".Figure 2.5: "Select Installation Folder"-windowTo start the installation you have to click again on "Next".After a few moments, you gets a message that the installation was successful and you canexit the setup with "Close".The installation of FluidPRIME with the library LibProp is finished.Finally, please copy or overwrite the LibProp.dll-file in the installation folder that is describedbefore, with the file in the zip-file.KCE Kretzschmar Consulting Engineers
2/5During the installation process the following files will have been copied into the destinationfolder chosen, the standard being"C:\Program Files\PTC\Mathcad Prime 5.0.0.0\Custom Functions\":LC.dllLibProp.dllPRIME ote:The shown default installation path for Mathcad Prime may be different depending on theinstallation on your machine. In addition, the Mathcad Prime version can be another than5.0.0.0 that is used in this manual.The underscore after "Lib" in the figures before, is representative of the library name of thelibrary to be installed.2.2Licensing the LibProp Property LibraryWithin the installation that was shown in chapter 2.1 the licensing key will be registered onyour computer automatically.KCE Kretzschmar Consulting Engineers
2/62.3Example: Calculation of the Enthalpy h f(p,t,x) for Waterand SteamNow we will calculate, step by step, the specific enthalpy h as a function of pressure p,temperature t and vapor fraction x for water and steam from the Industrial FormulationIAPWS-Propan, using FluidPRIME.- Start Mathcad Prime.- Type "p:" and enter the value for the pressure p in bar.(Range of validity of propane:from pt 1.7517 x 10-9 bar to 1000 bar)e. g.: Enter "p:100" for the first operand- Type "t:" and enter the value for the temperature t in C.(Range of validity of propane:t tmel(p) 6 326.85 C)e. g.: Enter "t:50" for the second operand- Type "x:" and enter the value for the vapor fraction x in kgsat. steam / kgwet steam.Since the wet steam region is calculated automatically by the subprograms, the followingfixed details on the vapor fraction x are to be considered when the value for x is entered:Single-phase regionIf the state point to be calculated is located in the single-phase region (liquid orsuperheated steam) x –1 must be entered as a pro-forma value.Wet-steam regionIf the state point to be calculated is located in the wet steam region, a value for xbetween 0 and 1 (x 0 for saturated liquid, x 1 for saturated steam) must be entered.When calculating wet steam either the given value for t and p -1 or the given value forp and t -1 and in both cases the value for x between 0 and 1 must be entered.If p and t and x are entered as given values, the program considers p and t to beappropriate to represent the vapor pressure curve. If it is not the case the calculation forthe property of the chosen function to be calculated results in –1.Vapor pressure curve of Propane:tt –187.625 C . tc 96.74 Cps(tt) 1.7517 x 10-9 bar 6 pc 42.512 bare. g.: Enter "x:-1" for the third operand- Confirm your entry by pressing the "ENTER" key.- Your Mathcad Prime calculation window should look like Figure 2.3:Figure 2.3: Example Mathcad Prime sheet after input of the given parameters- Now, type open the file Functions LibPROP.mcdx. In this Mathcad Prime worksheet youcan find all the functions of the libraryKCE Kretzschmar Consulting Engineers
2/7- Search the function h ptx Propan( , , ) and mark it by drag a selection rectangle aroundit.- Copy the marked function and paste it into your example worksheet- Click it the function and type "h:" in front of it.- Your Mathcad Prime calculation window should look like Figure 2.4:Figure 2.4: Example Mathcad Prime sheet- Now click in the first operand in the brackets of the function. . You can now enter thevalue for p either by entering the value directly or by entering the name of the variablewhere the value was saved. e.g.: Enter "p".- Situate the cursor on the next placeholder and set all the variables we set above.- Close the input formula by pressing the "Enter"-Key.- You can now go on working with the variable h which we have just calculated.- If you wish to see the result, you have to type the following command on the next line inthe Mathcad Prime window:"h ".You will now see the result h 649.196. The corresponding unit is kJ/kg (see table of theproperty functions in Chapter 1).In the next figure you can see the calculated value.Figure 2.5: Example Mathcad Prime sheet with finished calculationKCE Kretzschmar Consulting Engineers
2/82.4 Removing FluidPRIMETo remove FluidPRIME with the library LibPROP from your hard drive, carry out the followingsteps:- Click "Start" in the lower task bar of your desktop, then "Settings" and then "ControlPanel".- Now, double click on "Add or Remove Programs".- In the list box of the "Add or Remove Programs" window that appears select "FluidPRIME- LibPROP" by clicking on it and click the "Add/Remove6" button.- In the following dialog box click "Yes" and wait until the windows is closing.- Finally, close the "Add or Remove Programs" and "Control Panel" windows.Now FluidPRIME with the library LibPROP has been removed.KCE Kretzschmar Consulting Engineers
3/13. Program DocumentationThermal Diffusivity a f(p,t,x)Function Name:a ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION APTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C APTXPROP(A,P,T,X)REAL*8 A,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultAPTXPROP, A or a ptx PROP – Thermal diffusivity a λ *vcpin m2 / sRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult APTXPOP -1000, A -1000 or a ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelat p 1000 and t tc 96.74 C or t t t 187.625 CSaturation lines:at t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25], [30]KCE Kretzschmar Consulting Engineers
3/2Specific Isobaric Heat Capacity cp f ( p, t , x )Function Name:cp ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION CPPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C CPPTXPROP(CP,P,T,X)REAL*8 CP,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultCPPTXPROP, CP or cp ptx PROP Specific isobaric heat capacity c p in kJ / (kg K )Range of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult CPPTXPROP -1000, CP -1000 or cp ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelSaturation lines:at p 1000 and t tc 96.74 C or t t t 187.625 Cat t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25]KCE Kretzschmar Consulting Engineers
3/3Dynamic Viscosity η f ( p,t , x )Function Name:eta ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION ETAPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C ETAPTXPROP(ETA,P,T,X)REAL*8 ETA,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultETAPTXPROP, ETA or eta ptx PROP Dynamic viscosity η in Pa sRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult ETAPTXPROP -1000, ETA -1000 or eta ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelat p 1000 and t tc 96.74 C or t t t 187.625 CSaturation lines:at t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25], [29]KCE Kretzschmar Consulting Engineers
3/4Specific Enthalpy h f(p,t,x)Function Name:h ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION HPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C HPTXPROP(H,P,T,X)REAL*8 H,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultHPTXPROP, H or h ptx PROP - Specific enthalpy h in kJ/kgRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of wet steamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located in the wet steam region, a value for x between 0 and 1(x 0 for saturated liquid, x 1 for saturated steam) must be entered.When calculating wet steam either the given value for t and p -1000 or the given value for p andt -1000 and in both cases the value for x between 0 and 1 must be entered.If p and t and x are entered as given values, the program considers p and t to be appropriate torepresent the vapor pressure curve.Wet steam region :Temperature ranges from t t 187.625 C C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult HPTXPROP -1000, H -1000 or h ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelWet steam region:at p 1000 and t tc 96.74 C or t t t 187.625 Cat t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25]KCE Kretzschmar Consulting Engineers
3/5Isentropic Exponent κ f ( p,t , x )Function Name:kappa ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION KAPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C KAPTXPROP(KAP,P,T,X)REAL*8 KAP,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultKAPTXPROP, KAP or kappa ptx PROP Isentropic exponent κ w2p vRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult KAPTXPROP, KAP -1000 or kappa ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelat p 1000 and t tc 96.74 C or t t t 187.625 CSaturation lines:at t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25]KCE Kretzschmar Consulting Engineers
3/6Thermal Conductivity λ f ( p,t , x )Function Name:lambda ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION LAMPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C LAMPTXPROP(LAM,P,T,X)REAL*8 LAM,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultLAMPTXPROP, LAM or lambda ptx PROP Thermal conductivity λ in W / m KRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult LAMPTXPROP -1000, LAM -1000 or lambda ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelSaturation lines:at p 1000 and t tc 96.74 C or t t t 187.625 Cat t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25], [30]KCE Kretzschmar Consulting Engineers
3/7Kinematic Viscosity ν f ( p, t , x )Function Name:ny ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION NYPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C NYPTXPROP(NY,P,T,X)REAL*8 NY,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultNYPTXPROP, NY or ny ptx PROP Kinematic viscosity ν η v in m² / sRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid or saturated steam, it is adequate to enter either the given value for tand p -1000, or the given value for p and t -1000, plus the value for x (x 0 or x 1). If p and t andx are entered as given values, the program will consider p and t to be appropriate to represent thevapor pressure curve.Saturated liquid and saturated vapor line :Temperature ranges from t t 187.625 C to tc 96.74 CPressure ranges from ps (t t ) 1.7517 10 9 bar to pc 42.512 barResults for wrong input valuesResult NYPTXPROP -1000, NY -1000 or ny ptx PROP -1000 for input values:Single phase region:p 1000 bar or p ps (t t ) 1.7517 10 9 bar or(x -1)t 326.85 C or t tmelat p 1000 and t tc 96.74 C or t t t 187.625 CSaturation lines:at t 1000 and p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar orat p pc 42.512 bar or p ps (t t ) 1.7517 10 9 bar andt tc 96.74 C or t t t 187.625 CReferences: [22], [25], [29]KCE Kretzschmar Consulting Engineers
3/8Melting Pressure pmel f ( t )Function Name:pmel t PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION PMELPROP(T)REAL*8 TSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C PMELPROP(PMEL,T)REAL*8 PMEL,P,T,XInput Values:T - Temperature t in CResultPMELTPROP, PMEL or pmel t PROP Melting pressure pmel in barRange of validityTemperature range:from t t 187.625 C to -178.537 CResults for wrong input valuesResult PMELTPROP -1000, PMEL -1000 or pmel t PROP -1000 for input values:t t t 187.625 C or t -178.537 CReferences: [28], [25]KCE Kretzschmar Consulting Engineers
3/9Prandtl-Number Pr f(p,t,x)Function Name:Pr ptx PROPSubroutine with function value:for call from FortranREAL*8 FUNCTION PRPTXPROP(P,T,X)REAL*8 P,T,XSubroutine with parameter:for call from DLLINTEGER*4 FUNCTION C PRPTXPROP(PR,P,T,X)REAL*8 PR,P,T,XInput Values:P - Pressure p in barT - Temperature t in CX - Vapor fraction x (kg of saturated steam)/(kg wet steam)ResultPRPTXPROP, PR or Pr ptx PROP Pr andtl Number Pr η * cpλRange of validityTemperature range:from tmel to 326.85 CPressure range:from ps (t t ) 1.7517 10 9 bar to 1000 barDetails on the vapor fraction x and on the calculation of saturated liquid and saturatedsteamThe wet steam region is calculated automatically by the subprograms. For this purpose the following fixeddetails on the vapor fraction x are to be considered:If the state point to be calculated is located in the single-phase region (liquid or superheated steam) x –1 must be entered as a pro-forma value.If the state point to be calculated is located on the saturated liquid line, x 0 must be entered. Whencalculating saturated steam (saturated vapor line) x 1 must be entered.The calculation for x-values between 0 and 1 is not possible.When calculating saturated liquid
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