Cv/Kv and xT Loss Model
AFT Arrow allows the user to enter valve loss coefficient data in terms of Kv or Cv. Conversions are handled seamlessly in the background. Kv is the metric equivalent to Cv.
The valve Cv loss model type is unique in that this loss model can be used as part of both the subsonic and sonic loss calculations across the valve.
Subsonic Loss
The relationship between valve Cv, xT, and flow is provided by ANSI/ISA-75.01.01-2012ANSI/ISA Standard 75.01.01-2012, Industrial-Process Control Valves - Part 2-1: Flow Capacity - Sizing equations for fluid flow under installed conditions, 2012, published by International Society of Automation, Research Triangle Park, North Carolina, USA standard as follows:
Where C is the flow coefficient (Cv or Kv) and N is a numerical constant found in Table 1 of the ANSI standard referenced above. The units for the flow, pressure and density will be based off of the numerical constant chosen. FP is a correction factor for piping geometry. This correction will be treated as 1 unless the Valve ID has been entered by the user.
The xsizing parameter is the ratio of the pressure drop across the valve to the inlet pressure of the valve for subsonic flow:
Y is the expansion factor, which accounts for the change in density as the gas passes through the vena contracta, and is calculated as follows:
where xT is the pressure ratio, x, when the valve has just begun to choke.
Sonic Loss
If choked flow occurs across the valve, then the mass flow equation above is still used. However, xsizing is now equivalent to xT, which is the pressure ratio when the valve first begins to choke.
Estimated Cv or Kv in Output
The Output window can display an estimated Cv or Kv when it was not explicitly defined by the user so long as the appropriate parameter is added in the Output Control. The estimated Cv or Kv value is calculated using the mass flow rate equation shown above, with xsizing estimated as follows:
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