Critical flow rate

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-... 

Instead of using just energy conservation, Moody (1975) derived a revised model that takes into account all the conservation laws. He found that critical flow rate is given by a determinantal equation that gives G as a function of p, X, and S. 

Vessel blowdown. The previously mentioned relationships for the critical flow rate of a steam-water mixture can be employed with the conservation of mass and energy for a vessel of fixed volume to determine its time-dependent blowdown properties. The range of problems associated with coolant decompression in water-cooled reactors is quite broad. The types of hypothetical (some are even incredible) reactor accidents may be... 

Edwards, A. R., 1968, Conduction Controlled Flashing of a Fluid and the Production of Critical Flow Rate in One-Dimensional System, AHSB (S)R 147, UK Atomic Energy Authority, Risley, England. (3)... 

Hsu, Y. Y., 1972, Review of Critical Flow Rate, Propagation of Pressure Pulse, and Sonic Velocity in Two-Phase Media, NASA TN D-6814, NASA Lewis Res. Ctr, Cleveland, OH. (3)... 

The release of non-Brownian particles (diameter s 5 pm) from surfaces has been studied. The influence of several variables such as flow rate, particle size and material, surface roughness, electrolyte composition, and particle surface charge has been considered. Experiments have been performed in a physically and chemically well-characterized system in which it has been observed that for certain particle sizes there exists a critical flow rate at which the particles are released from surfaces. This critical flow rate has been found to be a function of the particle size and composition. In addition, it has been determined that the solution pH and ionic strength has an effect on the release velocity. 

A critical flow rate or velocity for release of particles has been observed. 

Step 2—acquisition of mass flow rate data some experimental precautions must be taken in order to obtain the proper data since the objective is to determine the two-phase critical flow rate by measuring the emptying time ATe, and... 

The subscript s denotes an isentropic path for ideal nozzle flow. For ideal gas with Pok = constant, substitution of this isentropic expansion law into Eq. (23-98) yields the following critical pressure ratio PJP and critical flow rate Gc ... 

Effect of Initial Concentration and Column Length on the Critical Flow Rate, Lc... 

Fig. 6. Effect of initial concentration on breakdown time and critical flow rate.

The relations between escaping concentration and time, column length and breakdown time, and flow rate and breakdown time, as predicted by the theory, were found to be valid for the solid-gas reaction between activated silver permanganate and carbon monoxide. However, the predicted linear relation between critical column length and the logarithm of the initial concentration was not confirmed. Similarly, the reciprocal of the critical flow rate did not vary linearly with log Co. The critical column length increased with increasing flow rate but was unaffected by the initial concentration. 

Figure 15.18. Droplet size as a function of the flow rate of oil through the micro-channel. At lower flow rates, the droplet size is independent of the flow rate (regime 1), while from a certain critical flow rate, the droplets become larger (regime 2) (Dekkers 2003).

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... 

Steady fiow will occur with fine powders if the target flow rate (feed rate through the system) is below the critical flow rate that occurs when the solids stress is balanced by the air pressure at the outlet. The target flow rate is often controlled by a feeder, such as at the inlet to a compression machine (press feed frame). The critical flow rate, and the flow properties tests used to determine it, is described in more later in this chapter. At target flow rates exceeding the critical flow rate, unsteady flow can occur by two different modes described below. 

Permeability A review of the permeability test method and application of the results (critical flow rate). 

Higher flow rates than the calculated critical flow rate may occur, but can result in non-steady or erratic feed and the resulting adverse effects. Permeability values can also be used to calculate the time required for fine powders to settle or deaerate in equipment. 

Reduce the target feed rate If possible, reducing the target feed rate (tableting rate) to be less than the critical flow rate will be beneficial, but is often impractical since it will result in a decreased production rate. 

Consider gas pressure differentials A gas pressure differential can have a beneficial or adverse effect upon two-phase flow effects. A positive gas pre.ssure differential at the outlet (i.e., bin/press hopper/etc. at a higher gas pressure than the equipment downstream) may be beneficial in overcoming a feed rate limitation, as the air pressure is forcing the material in the direction of flow. Conversely, a negative gas pressure differential at the outlet can further reduce the critical flow rate, since the negative gas pressure acts to further retard the flow rate. 

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