Critical orifice

FIG. 6-55 Critical cavitation number vs. diameter ratio (3. Reprinted from Thotpe, Flow regime transitions due to cavitation in the flow through an orifice, " Int. J. Multiphase Flow, i6,1023-1045. Copyright 1990, with kindper-mission from Elsevier Science, Ltd., The Boulevard, Langford Lane, Kldlington 0X5 1GB, United Kingdom. )... 

Accuracy Square-edged orifices and venturi tubes have been so extensively studied and standardized that reproducibihties within 1 to 2 percent can be expected between standard meters when new and clean. This is therefore the order of reliabihty to be had, if one assumes (1) accurate measurement of meter differenfial, (2) selection of the coefficient of discharge from recommended published literature, (3) accurate knowledge of fluid density, (4) accurate measurement of critical meter dimensions, (5) smooth upstream face of orifice, and (6) proper location of the meter with respect to other flow-disturbing elements in the system. Care must also be taken to avoid even sh t corrosion or fouliug during use. 

When testing to estabhsh the thermodynamic performance of a steam turbine, the ASME Performance Test Code 6 should be followed as closely as possible. The effec t of deviations from code procedure should be carefully evaluated. The flow measurement is particularly critical, and Performance Test Code 19 gives details of flow nozzles and orifices. The test requirements should be carefully studied when the piping is designed to ensure that a meaningful test can be conducted. 

To determine the critical pressure ratio for gas sonic velocity across a nozzle or orifice use... 

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

The termination of the cone section is the apex orifice. The critical dimension is the inside diameter at the discharge point. The size of this orifice is determined by the application involved and must be large enough to permit the solids that have been classified to underflow to exit the cyclone without plugging. The normal minimum orifice size would be 10% of the cyclone diameter and can be as large as 35%. Below the apex is normally a splash skirt to help contain the underflow slurry in the case of a hydroclone. 

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. 

These conditions are similar to flow through orifices, nozzles, and venturi tubes. Flow through nozzles and venturi devices is limited by the critical pressure ratio, r,. = downstream pressure/upstream pressure at sonic conditions (see Figure 2-38C). 

Figure 2-38C. Critical Pressure Ratio, r, for compressible flow through nozzles and venturi tubes. By permission, Crane Co., Technical Paper 410, 1957. Also see 1976 edition. See note at Figure 2-18 explaining details of data source for chart. Note P = psia p= ratio of small-to-large diameter in orifices and nozzles, and contractions or enlargements in pipes.

Critical or sonic flow will usually exist for most (compressible) gases or vapors discharging through the nozzle orifice of a pressure relieving valve. The rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio P2/P1 (exit/inlet) until the linear velocity in the throat of the nozzle reaches the speed of sound in the gas at that location. Thus, the critical or sonic velocity or critical pressures are those conditions... 

At critical conditions, the maximum flow through the nozzle or orifice is [29]... 

Calculations of Orifice Flow Area for Conventional Pressure Relieving Valves, and Flow is Critical (sonic) Through Part of Relieving System, i.e., backpressure is less than 55% of the absolute relieving pressure (including set pressure plus accumulation). See Figure 7-7A, use... 

Calculations of Orifice Flow Area using Pressure Relieving Balanced Bellows Valves, with Variable or Constant Back Pressure. Must be used when backpressure variation exceeds 10% of the set pressure of the valve. Flow may be critical or non-critical for balanced valves. All orifice areas. A, in sq in. [68]. The sizing procedure is the same as for conventional valves listed above (Equations 7-10 ff), but uses equations given below incorporating the correction factors K, and K,, . With variable backpressure, use maximum value for P9 [33a, 68]. 

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... 

These distributors are fabricated of pipe lengths tied to a central distribution header (usually) %vith orifice holes drilled in the bottom of the various pipe laterals off the header. This style of distributor can be fed by pressure or gravity for clean fluids. The gravity feed is considered better for critical distillation application when uniformity of the flow of the drip points (or flow points) through out the cross-section of the tower is extremely important, and is excellent for low flow requirements such as below 10 gpm/ft2 [131]. 

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