Venturi
The Venturi junction type requires two connecting pipes. This junction type allows you to model the irrecoverable loss that occurs through a venturi area change, which is frequently used in conjunction with pressure taps in flow measurement devices. It also allows you to specify loss factors as a function of a flow parameter.
The Venturi Properties window follows the first of the two basic Properties window formats, displaying the connecting pipes in a fixed format. The Venturi junction does not have an explicit flow direction, but adopts a flow direction from the connecting pipes.
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Cd (Perry's) - Described in more detail below.
For convenience, you can specify constant loss characteristics of a venturi as a discharge coefficient (Cd) or as a loss factor (K).
If you would like to model the pressure loss through the Venturi as varying with the flow rate, select the radio button next to Resistance Curve under the Loss Model tab of the Venturi Properties window. Once Resistance Curve is selected, additional features appear that allow you to input pressure drops versus flow data. To enter this data, you can specify polynomial constants, fit a curve to available data, or use interpolated x-y data.
Discharge Coefficient Loss Model
Subsonic losses are defined for the Venturi Cd (Perry's) loss model using the discharge coefficient, Cd. This model is appropriate for both venturis and nozzles and includes the effect of dynamic pressure recovery that occurs in the downstream pipe. The mass flow through the junction is calculated via the following equation: (Perry, 10-14 (1997)Perry, R. H., Green, D. W., Perry's Chemical Engineers' Handbook, 7th Edition, McGraw-Hill, New York, NY, 1997.)
Where ṁ is the mass flow rate, Y is the expansibility factor, A is the throat area of the venturi or nozzle, P1 is the inlet pressure, P2 is essentially the pressure at the vena contracta, gc is the unit conversion constant, ρ1 is the inlet density, and β is the diameter ratio of the throat relative to the upstream pipe. While this is equivalent to the flow calculation in ASME MFC-3M-2004, the two approaches differ in calculation of expansibility factors and in the conversion from the differential pressure, P1 - P2, to the irreversible pressure loss.
Note: The differential pressure loss P1 - P2 is not equivalent to the change in static pressure across the junction. The static pressure at the throat, P2, is not equal to the static pressure into the downstream pipe, which assumes fully developed flow and depends on the pipe area.
The expansibility factor, which can be viewed as a junction Output Parameter, is calculated in terms of the pressure ratio r and specific heat ratio γ.
As previously noted, the differential pressure is the pressure difference between the upstream pressure and the vena contracta, and does not account for the recovery of the dynamic pressure that occurs in the downstream pipe. Because the flow is assumed to be fully developed at the inlet of the downstream pipe, this recovery must be incorporated at the junction itself by converting the differential pressure loss to the irreversible pressure loss, which is treated as the stagnation pressure loss.
For information on the discharge coefficient loss model see the Discharge Coefficient Loss Model topic.
CdA for Sonic Choking
An optional input in the Venturi Properties window is the CdA for sonic choking. This parameter describes the effective area restriction in the venturi for the purpose of calculating sonic choking. In most cases, information on the CdA must be obtained from test or manufacturer data.
A sonic CdA value will be assumed from the subsonic Cd and throat area when using the Cd (Inline) loss model if no sonic CdA value is specified. This is to avoid issues with expansibility factor convergence. For that loss model, the sonic CdA and subsonic CdA should generally be equal.
Note: The CdA for sonic choking may be different from the subsonic CdA loss model option in xStream. The discharge coefficient can vary at different pressure ratios due to the vena contracta moving closer to or farther from the orifice restriction. For the highest accuracy the CdA used for subsonic and sonic losses should be tested and entered separately. See the "Modeling Choked Flow Through an Orifice" white paper on AFT's website for more information.
