Nozzle Functions

Choking Nozzle Functions

In ES_StableIF97 AddIn choking nozzle functions are also included in addition to steam property functions.   Choking nozzle function is very useful in various engineering work, like steam turbine bypass valve analysis, safety valve analysis, etc.

Nozzle analysis equations for ideal gases are well established in various fluid mechanics text book.    In case of steam, however, application of ideal gas equations may cause considerable errors because steam properties of steam do not act as ideal gas.   Especially it is true for saturated wet steam and ideal gas equations are hardly used.

Process that nozzle reaches choking condition is like this.   As nozzle outlet pressure decreases from nozzle inlet pressure, in the beginning the mass flow rate per unit area increase because the rate of velocity change is bigger than the rate of specific volume change.   Then it reaches its maximum value at a nozzle output pressure and the state is called as choking.   If nozzle outlet pressure decreases below the choking pressure, the rate of specific volume change is bigger than the rate of velocity change and the mass flow rate per unit area decreases.

If the nozzle expansion behavior described above is considered in view of a constant mass flow rate instead of the mass flow rate per unit area, it is easily seen that nozzle area is inversely proportional to the mass flow rate per unit area.   Herein the area is nozzle cross sectional area.   This means that nozzle cross sectional area decreases till nozzle outlet pressure reaches choking pressure, and then it increases.   This is de-Laval nozzle.   In de-Laval nozzle expanding isentropically, the choking velocity equals to sonic velocity.

In case of superheated steam, the choking velocity equals to sonic velocity.   However, in case of wet steam, the choking velocity is quite different from sonic velocity.

The choking nozzle functions of ES_StableIF97 AddIn look up choking state by searching the state that have the maximum mass flow rate per unit area, instead of searching the state that enthalpy change by isentropical expansion equals to the energy of sonic velocity.   In order to increase accuracy of the functions for superheated steam, iteration of state looking up continues till choking velocity agrees with sonic velocity within 0.5 m/s range.   For this reason, the elapsed time of choking nozzle function for high pressure steam is longer than that of low pressure steam.

The choking nozzle functions of ES_StableIF97 AddIn do not calculate results and return the error string of "#ES/NZWErr!", if nozzle inlet state is compressed water under critical pressure(= 22.064 MPa) or entropy is less than critical entropy(= 4.412 kJ/kg/K) above critical pressure.   If the case, the expanding steam may pass through compressed water state.

If expanding steam pass through compressed water state and then enter into wet steam zone again, mass flow rate per unit area decreases abruptly for abrupt increase of specific volume.   This can not be considered as choking.

The choking nozzle functions of ES_StableIF97 AddIn assume that web steam expands in equilibrium state.   If dryness of wet steam is low, there is possibility that steam and water is isolated and flow separately.   Therefore, caution is paid to the results of the choking nozzle functions if nozzle inlet state is equal to 25 percent dryness or lower.

Please refer here for the list of choking nozzle functions of ES_StableIF97 AddIn.

 

Sub-critical Nozzle Functions

There are two kinds of nozzle functions in ES_StableIF97 AddIn.   One is choking nozzle functions described above, and the other is sub-critical nozzle functions with nozzle outlet pressure given.

If nozzle outlet pressure is equal to choking pressure or lower, the pressure at nozzle throat is same with choking pressure and analysis can be done only by choking nozzle functions.   However, if nozzle outlet pressure is higher than choking pressure, the pressure at nozzle throat is same with nozzle outlet pressure and the steam state at nozzle throat varies depending on nozzle outlet pressure.

Therefore, choking nozzle functions can not analyze all nozzle behaviors.    In order to analyze all nozzle behaviors, sub-critical nozzle functions are also required in addition to choking nozzle functions.

Please refer here for the list of sub-critical nozzle functions of ES_StableIF97 AddIn.


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