Compressible flows choked flow

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... 

To analyze compressible flow through chokes it is assumed that the entropy of the fluid remains constant. The equation of isentropic flow is... 

Typical manufacturer s values of Cv to be used with Eq. (10-29) require the variables to be expressed in the above units, with hv in ft. [For liquids, the value of 0.658 includes the value of the density of water, pw = 62.3 lbm/ft3, the ratio g/gc (which has a magnitude of 1), and 144 (in./ft)2]. For each valve design, tables for the values of the flow coefficients as a function of valve size and percent of valve opening are provided by the manufacturer (see Table 10-3, pages 318-319). In Table 10-3, Km applies to cavitating and flashing liquids and C applies to critical (choked) compressible flow, as discussed later. 

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.,... 

Choking is a phenomenon that occurs in high speed compressible flow (e.g. in relief systems). It occurs because, as the pressure falls along a pipe or through a nozzle, the fluid density decreases. This, means that the volumetric flow rate and, hence, the velocity increases (because the mass flow is constant). Choking occurs when the downstream pressure is reduced to the point where the velocity cannot increase any more. This effectively limits the maximum velocity and, hence, flow rate of the fluid. 

Re), and the isentropic index or ratio of specific heats (7). The dependent group relates the mass of discharge to the valve size and to the reservoir conditions. It is suitable for assessing dynamical similarity under conditions of choked compressible flow. Substitution of PJRTq for Po in the dependent group produces a more conventional representation ... 

A graph of discharge coefficient ( m) plotted against dimensionless lift L/D) is known as a flow characteristic. Fig. 9 shows an example of flow characteristics plotted for various pressure ratios relieving from an air receiver, where Pb is the total backpressure at the valve exit port and Pq the reservoir total pressure.According to ideal one-dimensional compressible flow theory, choked flow should occur at pressure ratios below 0.528. In practice, choked flow will occur at lower pressure ratios because of friction losses upstream of the curtain area. Nevertheless, the curves in Fig. 9 are close-together at pressure ratios below 0.333, and have collapsed to almost a single curve for ratios less than 0.25. Other work shows a similar effect. 

Typical flow coefficient values are shown in Table 5.14, in which K , applies to cavitating and flashing liquids and Ci applies to critical (choked) compressible flow, as discussed below. 

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... 

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