Vapor - critical flow

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. 

If the superimposed back pressure is less than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is unaffected and back pressure is not a factor. However, builtup back pressure on a conventional pressure relief valve will affect its flow capacity and operating characteristics, and should not exceed 100% of its set pressure. If total back pressure (superimposed plus built-up) is greater than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is affected, and total back pressure is incorporated into the sizing procedure. Any back pressure reduces the capacity of a conventional PR valve in liquid service, and... 

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 . 

If the pressure Pj downstream of the restriction is less than the critical flow pressure, then the maximum obtainable flow which occurs at critical velocity is a function of P, and P but is unaffected by Pj. If Pj is greater than P , however, then the flow is termed "subcritical," and the rate is a function of P, and Pj. There are thus two equations for sizing PR valves in vapor service, depending on whether the flow is critical or subcritical. 

The first step in sizing a PR valve for vapor flow is to determine the critical flow pressure P from the following equation ... 

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 ... 

By trial and error procedure, determine the amount of liquid which flashes by an isoenthalpic (constant enthalpy) expansion to the critical flow pressure (or actual pressure if greater than critical) for the flashed vapor. 

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. 

Note The curves above represent a compromise of the values recommended by a number of relief valve manufacturers and may be used when the make of the valve or the actual critical f ow pressure point for the vapor or gas is unknown. When the make is known, the manufacturer should be consulted tor the correction factor. These curves are for set pressures of 50 pounds per square inch gauge and above. They are limited to back-pressure below critical flow pressure for a given set pressure. For subcntical flow back-pressures below 50 pounds per square inch gauge, the rnanufacturer must be consulted tor values of Kk. 

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.

The lower velocity in the throat does not affect the jet s performance, as long as the velocity remains above the speed of sound. If the velocity in the throat falls below the speed of sound, we say that the jet has been forced out of critical flow. The sonic pressure boost is lost. As soon as the sonic boost is lost, the pressure in the vacuum tower suddenly increases. This partly suppresses vapor flow from the vacuum tower. The reduced vapor flow slightly unloads condenser 1 and jet 2 shown in Fig. 16.2. This briefly draws down the discharge pressure from jet 1. The pressure in the diffuser throat declines. The diffuser throat velocity increases back to, or above, sonic velocity. Critical flow is restored, and so is the sonic boost. The compression ratio of the jet is restored, and the vacuum tower pressure is pulled down. This sucks more vapor out of the vacuum tower, and increases the loads on condenser 1 and... 

When the fluid flowing through the valve is a compressible gas or a vapor, then the design must consider whether critical flow is achieved in the nozzle of the valve. The critical flow rate is the maximum flow rate that can be achieved and corresponds to a sonic velocity at the nozzle. If critical flow occurs, then the pressure at the nozzle exit cannot fall below the critical flow pressure Pcf, even if a lower pressure exists downstream. The critical flow pressure can be estimated from the upstream pressure for an ideal gas using the equation... 

Equation 5-29 is valid for liquid flowing below its saturation temperature in the turbulent zone with a viscosity value that is close to that of water and size of pipe. Also, the control valve must be the same. Equation 5-29 can also be applied, if the vapor pressure of the liquid at the flowing temperature is equal to or less than one-half the upstream pressure. Eor this case, the vapor pressure of the liquid is substituted for downstream pressure, P2 and the valve coefficient is calculated. The calculated must be corrected by a critical flow factor, Cj, where C corr is defined by... 

The expression used to determine the relief area for vapor discharge when the back pressure is less than the critical flow pressure is ... 

The discharge reactive force is based on the assumption that critical flow of the gas or vapor is obtained at the outlet of the relief device and the discharge is horizontal to the atmosphere. For any gas or vapor, the reactive force can be expressed as ... 

Tuning can be troublesome with the vapor inlet scheme if flow across the valve changes from noncritical to critical upon reboiler turndown (67, 68, 362). As boilup falls, so does the absolute pressure downstream of the valve. When the ratio of upstream to downstream pressure exceeds a critical value, critical flow is established through the valve, and the downstream pressure ceases to affect the vapor flow rate. The controller dynamics differ under critical and noncritical flow. A loop tuned for noncritical flow tends to be unstable when flow becomes critical, while a loop tuned for critical flow tends to be sluggish when flow becomes noncritical (67, 68). 

There are numerous studies of the heterogeneous nucleation, considering bubble density and vapor generation rate [2], the critical flow rates for nucleation [3], thermal mechanic condition for the inception of flashing [4], and bubble size, velocity and concentration in flashing flow behind a sudden constriction in vertical flow in a pipe [5]. 

Cavitation can also lead to local destruction of protective layers. In rapidly flowing liquid and on solid surfaces that oscillate in the liquids, gas or steam bubbles are produced at sites at which the pressure in the liquid is briefly lowered to vapor pressure due to flow in excess of the critical flow rate threshold. When the pressure is raised again, these bubbles collapse suddenly (implosion) and a jet of liquid hits the material surface at a high rate of speed. This sudden stress load pattern is continuously exposing or creating active surfaces on which increased corrosion (cavitation corrosion) takes place in an aggressive medium. 

Critical flow occurs when a compressible fluid velocity approaches the speed of sound about 1000 ft/s. Process piping handling vapor is typically designed to work at a velocity of 100 ft/s. 

Critical flow Vapor flowing at the speed of sound. 

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