Orifice critical flow

For comparison, the outlet temperature for gas at critical flow accross an orifice is given by... 

As normally designed, vapor flow through a typical high-lift safety reliefs valve is characterized by limiting sonic velocity and critical flow pressure conditions at the orifice (nozzle throat), and for a given orifice size and gas composition, mass flow is directly proportional to the absolute upstream pressure. 

Back pressure reduces the pressure drop across the orifice of any type of PR valve. This results in reduced discharge rates in the case of vapors, if the back pressure exceeds the critical flow pressure. For liquids, any back pressure reduces the pressure drop and results in a lower discharge rate. 

Critical and Subcritical Flow - The maximum vapor flow through a restriction, such as the nozzle or orifice of a pressure relief valve, will occur when conditions are such that the velocity through the smallest cross-sectional flow area equals the speed of sound in that vapor. This condition is referred to as "critical flow" or "choked flow . 

We shall first consider the case of non-flashing liquids. In this situation, there is no critical flow pressure limiting the flow of liquid through a PR valve orifice, as opposed to the case of vapor flow. The discharge rate is a function of the pressure drop across the valve and can be estimated by the following expression ... 

Calculate individually the orifice area required to pass the flashed vapor component, using Equation (5a), (3b), (4), (5), or (6), as appropriate, according to service, type of valve and whether the back pressure is greater or less than the critical flow pressure. 

Calculate individually the orifice area required to pass the unflashed hquid component, using Equation (8). The pressure drop term Pj should be made equal to the set pressure minus the total back pressure developed by the vapor portion at critical flow pressure, except when the critical flow pressure is less than the calculated total back pressure (superimposed plus built-up), considering the combined liquid and vapor flow. In the latter case, P should be made equal to set pressure minus the calculated total back pressure. 

Heni, R. E. and H. K. Fauske, 1971, The Two-Phase Critical Flow of One-Component Mistuies in Nozzles, Orifices, and Short Tubes, J. Heat Transfer, pp 179-187, May. 

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... 

Figure 4.7. Maximum overpressure in vapor cloud explosions after critical-flow propane jet release dependent on orifice diameter (a) undisturbed jet (b) jet into obstacles and confinement.

In general, the sonic or critical velocity is attained for an outlet or downstream pressure equal to or less than one half the upstream or inlet absolute pressure condition of a system. The discharge through an orifice or nozzle is usually a limiting condition for the flow through the end of a pipe. The usual pressure drop equations do not hold at the sonic velocity, as in an orifice. Conditions or systems exhausting to atmosphere (or vacuum) from medium to high pressures should be examined for critical flow, otherwise the calculated pressure drop may be in error. 

Calculate relieving area by applicable equation for critical or non-critical flow, using tlie flow rate determined in (3) above. (See Equation 7-10 and following). The area actually selected for orifice of safety type valve must have orifice equal to or greater than calculated requirements. For a rupture disk application, the full free open cross-sectional area of pipe connections in inlet and exit sides must be equal to or be greater than the calculated area. 

For rupture disk sizing the downstream pressure is assumed to reach the critical flow pressure although the dowm stream pressure initially may be much low er. Under these conditions the flow through the orifice that the disk produces on rupture is considered to be at critical flow. The assumptions of critical pressure do not apply... 

Critical Flow in Short Pipes, Nozzles, and Orifices... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The metal orifices we use were purchased from Mlllipore and drilled out to obtain desired flow rates. Plastic or nylon orifices, however, are available from General Metal Works. The flow rates of metal orifices are dependent on pump vacuum until the pressure drop reaches 17" of mercury. At this point the flow becomes critical and is Independent of pressure drop as long as the vacuum is equal to or greater than 17" of mercury. The plastic orifice has a different design, and reaches critical flow with only 10" of mercury pump vacuum (Figure 8). 

For the case of critical flow through a square- or sharp-edged concentric circnlar orifice (where r < r, as discussed earlier in this subsection), use Eqs. (10-31), (10-32), and (10-33) as given for critical-flow nozzles. However, nnhke nozzles, the flow through a sharp-edged orifice continues to increase as the downstream pressure drops below that... 

Dilution—A cylinder of the compressed gas is fitted with a metering apparatus (regulator and/or critical flow orifice) and the effluent stream is injected directly into the dilution system. The flow rates of the analyte can be calibrated and the concentration of each test atmosphere can be calculated from the known dilution air flows. 

Dirt and moisture are the worst enemies of the performance of all PD gas meters, so inlet filtering should be used when indicated. Pressure and temperature should either be controlled or compensated. The testing (or proving, as it is called in the gas utility industry) of gas meters is usually done by an accurately calibrated "bell" of cylindrical shape that is sealed in a tank by a suitable liquid. The lowering of the bell discharges a known volume of air through the meter under test. Other standards used to calibrate gas meters are calibrated orifices and critical flow nozzles. These devices compare rates of flow rather than fixed volumes. 

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