Numerical Consistency of ES_StableIF97 Steam Table Functions

For each region, the numerical consistency is verified in three steps as below.

Step 1) shows IAPWS-IF97 test data.   IAPWS-IF97 documents provide the test data with the title of "Computer-program verification".   Step 1) is the image captured from IAPWS-IF97 documents.    For the abbreviated title of IAPWS-IF97 documents and region boundary, pleaser refer to IAPWS-IF97 (Basis of ES_StableIF97).

Step 2) shows ES_StableIF97 AddIn output data, which were calculated in a MS Excel sheet by ES_StableIF97 AddIn functions for verification of IAPWS-IF97 test data of Step 1).   Step 2) is the image captured from the MS Excel sheet.

Step 3) summarizes about consistency.    If ES_StableIF97 AddIn data are consistent with the IAPWS-IF97 test data in significant digits, just "OK" is written.

 

Region 1 Functions

How to make MS Excel sheet for Region 1 using ES_StableIF97 AddIn is presented in a separate page as linked below.   For numerical consistency for Region 1, the separate page is referred.

Please note that the Unit Legend for the ES_StableIF97 AddIn output data here was put into a separate sheet named as "Unit", in contrast to the Example 1 in which the Unit Legend was put into the same sheet and sp the cell addresses of unit arguments do not have the sheet identifier "Unit!".

1) IAPWS-IF97 Test Data : Table 5

Please refer to Example 1 : Numerical Consisency of ES_StableIF97 Steam Table Functions in Region 1, Table 5.

 2) ES_StableIF97 Output Data

Please refer to Example 1 : Numerical Consisency of ES_StableIF97 Steam Table Functions in Region 1, ES_StableIF97 data.

3) Consistency : OK

 

Region 2 Functions

1) IAPWS-IF97 Test Data : Table 15

2) ES_StableIF97 Output Data

3) Consistency : OK

 

Metastable Vapor Functions (Region 2)

1) IAPWS-IF97 Test Data : Table 18

2) ES_StableIF97 Output Data

3) Consistency : OK

 

Region 3 Functions

 1) IAPWS-IF97 Test Data : Table 33

2) ES_StableIF97 Output Data

3) Consistency :

IAPWS-IF97 provides the basic equations for Region 3 with temperature and density given, and the test data(Table 33) are also provided with temperature and density given, as shown in Step 1) above.

ES_StableIF97 uses IAPWS-IF97 basic equations for Region 3 calculation and the numerical consistency of the Region 3 basic equations was verified by ENGSoft internally.    

However, the functions of ES_StableIF97 should cover all regions with a given set of input arguments given by the user.   Region 3 should not be different from other regions in terms of input arguments.    Therefore, ES_StableIF97 takes iteration method for Region 3 functions, and so there is very small inconsistency in the final digit between IAPWS-IF97 test data(Step 1)) and ES_StableIF97 output data(Step 2)).   Therefore, it can be said that ES_StableIF97 functions in Region 2 are consistent with IAPWS-IF97 equations.

 

Region 4 Functions

 1) IAPWS-IF97 Test Data :

        Table 35 : Saturation Pressure Equation (Basic Equation)

        Table 36 : Saturation Temperature Equation (Backward Equation)

2) ES_StableIF97 Output Data

3) Consistency : OK

 

Region 5 Functions

 1) IAPWS-IF97 Test Data : Table 42

2) ES_StableIF97 Output Data

3) Consistency : OK


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