Compressible fluids choked flow

Critical (or choked) Maxinriim flow condition for compressible fluids... 

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at... 

The flow coefficient Cv is determined by calibration with water, and it is not entirely satisfactory for predicting the flow rate of compressible fluids under choked flow conditions. This has to do with the fact that different valves exhibit different pressure recovery characteristics with gases and hence will choke at different pressure ratios, which does not apply to liquids. For this reason, another flow coefficient, Cg, is often used for gases. Cg is determined by calibration with air under critical flow conditions (Fisher Controls, 1977). The corresponding flow equation for gas flow is... 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

The maximum flow rate of a compressible fluid (gas or two-phase) for a given upstream pressure. Choking is described in 9.2. 

Figure 6.1 shows the layout of the system being modelled. The compressible fluid is being carried from an upstream vessel at pressure pi to a downstream vessel at pressure p. The pressure just inside the entrance to the pipe is pi, where in general P2 p - The pressure just inside the outlet of the pipe is py. For many cases, py = P4, but this does not hold for the case of choked flow, where py > p. ... 

Choked flow also called critical flow is defined in single-phase flow as the flow when the fluid Mach number which is the ratio between the local fluid velocity and the local sound speed in the fluid approaches unity. For compressible single-phase flow or for gas-liquid two-phase flow when Mach number equal to one, the pressure gradient asymptotically... 

The method of calculating system vent flow is illustrated in Figure 10. The fluid flow model chosen consisted of a transfer line having a distributed impedance due to valves, line friction, etc, with an orifice at the downstream end. During pressurized cooldown, the downstream orifice operates at, or near, choked flow, and compressible fluid flow theory was used to calculate vent flow. 

Compressible fluid, when stored in a vessel at high pressure, can escape at very high velocity to a relatively low downstream pressure. If the pressure difference between the vessel and downstream equipment is high, the fluid will escape at sonic velocity, and the situation is called choked flow. 

There are several instances where choked flow rates are required to be estimated. Typical examples are overpressuring drain lines due to gas breakthrough, overpressuring flare lines during blowdown, etc. The general equation of compressible fluid flow [6] is... 

---