Subcritical flow

The general equation to estimate the orifice area for subcritical flow depends on the type of PRV. 

Conventional and pilot-operated PRV The general equation of the orifice area is 

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Nozzle arrangements for various applications vary considerably. For subcritical flow measurement at the outlet end, where nozzle differential pressure p is less than the barometric pressure, flow should be measured with impact tubes and manometers as shown in Figure 20-3. 

Figure 20-3. Flow nozzle for subcritical flow. (Power Test Code 10, Compressors and Exhausters, American Society of Mechanical Engineers, 1965.)...

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 . 

For the exceptional cases of subcritical flow (e.g., where a PR valve is designed for a low set pressure and the total superimposed plus built-up back pressure exceeds the critical flow pressure), the following equation may be used applied ... 

For steam flow under subcritical flow conditions, the following equation... 

In subcritical flow the discharge coefficient is affected by the velocity of approach as well as the type of choke and the ratio of choke diameter to pipe diameter. Discharge coefficients for subcritical flow are given in Figure 2-24 as a function of the diameter ratio and the upstream Reynolds number. Since the flow rate is not initially known, it is expedient to assume C = 1, calculate Q, use this Q to calculate the Reynold s number, and then use the charts to find a better value of C. This cycle should be repeated until the value of C no longer changes. 

F2 = coefficient of subcritical flow, see Figure 7-29 T = relieving temperature of inlet gas or vapor, °R P = upstream relieving pressure, psia, = set pressure + allowable overpressure + atmospheric pressure, usually 14.7 psia), psia P2 = backpressure on valve, psia W = required flow through valve, lbs/hr V = vapor flow required through valve, standard cu fl/min at 14.7 psia and 60°F... 

Fig. D-5 shows an external compression air-intake designed for optimized use at Mach number 2.0. Fig. D-6 shows a set of computed airflows of an external compression air-intake designed for use at Mach number 2.0 (a) critical flow, (b) sub-critical flow, and (c) supercritical flow. The pressures at the bottom wall and the upper wall along the duct flow are also shown. Two oblique shock waves formed at two ramps are seen at the tip of the upper surface of the duct at the critical flow shown in Fig. D-6 (a). The reflected oblique shock wave forms a normal shock wave at the bottom wall of the throat of the internal duct. The pressure becomes 0.65 MPa, which is the designed pressure. In the case of the subcritical flow shown in Fig. D-6 (b), the shock-wave angle is increased and the pressure downstream of the duct becomes 0.54 MPa. However, some of the airflow behind the obhque shock wave is spilled over towards the external airflow. Thus, the total airflow rate becomes 68% of the designed airflow rate. In the case of the supercritical flow shown in Fig. D-6 (c), the shock-wave angle is decreased and the pressure downstream of the duct becomes 0.15 MPa, at which the flow velocity is stiU supersonic.

Figure D-6. Comparison of experimental and theoretical airflows under three types of operational conditions for the air-intake shown in Fig. D-5 (a) critical flow, (b) subcritical flow, and (c) supercritical flow.

Seeley (S21) discounted this mechanism on the basis of flow visualization studies. However, the experiments were at Re < Re given by Eq. (10-44), and thus appear to be in near-subcritical flow. 

Therefore, the following formula is used specifically for sizing valves for steam service at 3% overpressure. This formula is based on the empirical Napier formula for steam flow. API recommends some correction factors to account for the effects of superheat, backpressure and subcritical flow. In this particular calculation, an additional correction factor Kn is required by ASME when relieving pressure (Pi) is above 1500psia. 

P2 Ps => Subcritical flow (i.e. all liquid flow in this case) Pi Critical flow... 

This result may be obtained independently by differentiating Eq. (10.111) with respect toy and equating to zero. It may be observed that the depth, which may be plotted vertically to determine the curve, is also represented by the horizontal distance from the vertical axis to the 45° line. It is also seen that the upper limb of such a curve corresponds to subcritical flow, while the lower limb refers to the alternate condition of supercritical flow. 

The problem of determining where a hydraulic jump will occur is a combined application. In the case of supercritical flow on a mild slope, for instance, the tail water depth y2 is determined by the uniform flow depth jo for that slope. The rate of flow and the application of Eq. (10.133) then fix yu and the length of the M3 curve required to reach this depth from the upstream control may be computed from Eq. (10.123). Similarly, in the case of subcritical flow on a steep slope, the initial depth is equal to y0, the tail water depth is given by Eq. (10.133), and the length of the Si curve to the jump from the downstream control is computed from Eq. (10.123). For application of the hydraulic jump to design problems, and for analysis of the jump in circular and other nonrectangular sections, the reader is referred to more extensive treatises on the subject [42],... 

In the case of a real liquid in an open channel, it is necessary to differentiate between the behavior at subcritical and supercritical velocities. Subcritical flow in a rectangular channel has been investigated experimentally and has been found to conform fairly well to ideal conditions, especially within the first part of the bend [44], As the flow continues around the bend, the velocity distribution becomes complicated by the phenomenon of spiral flow, which for open channels is analogous to the secondary counterrotating currents found at bends in closed pipes. 

The relief valve selected should be one with equal or greater area than calculated using equation 13.105. Relief valve sizes are given in API Standard 526. Sizing equations for subcritical flow of vapors, liquids, steam, and two-phase mixtures are given in API RP 520. 

For compressible flows, two conditions exist critical and subcritical flow. Neglecting friction, subcritical flow occurs when ... 

Subcritical flow D/d = 2 (Control valve between pipe reducers) R 0.94 0.94 0.94 0.94... 

CALCULATE THE VALVE CAPACITY COEFFICIENT FOR SUBCRITICAL FLOW... 

CALCULATE THE CAPACITY COEFFICIENT FOR SUBCRITICAL FLOW CVS (W K)/3. SQRT(VALS)... 

C CHECK WHETHER FLOW IS CRITICAL OR SUBCRITICAL FLOW AND... 

Figure 1. Portrait of solutions induced by a saddle point S. 1 - Continuous solutions, subcritical flows 2 - Subcritical branch passing through saddle point 2 - Subcritical branch emerging from saddle point 2 - Supercritical branch emerging from saddle point 3 - Solution with turning point - States unattainable by continuous solutions Fj - States unattainable from stale R...

A transition from subcritical flow with A > 0 to supercritical flow with A < 0 through A = 0 can occur only in the presence of a singular point, in practice a saddle point. 

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