9.129.

An important characteristic of gaseous coolants, particularly from the safety viewpoint, is that the maximum flow rate is limited by the velocity of sound in the gas. This flow limitation applies to all compressible fluids, e. g., steam that may have been vaporized during the course of a coolant blowdown (§12.79) of a water-cooled reactor. The velocity of sound c in an ideal gas, equal to the limiting flow rate, can be expressed as

where у = cjcv, the ratio of the specific heats, R is the ideal molar gas constant, T is the absolute temperature, and M is the molecular weight.[12]

9.130.

In the flow of gas through a channel, the temperature changes as the pressure is reduced since adiabatic conditions can normally be as­sumed. Therefore, other, more complex relations must be used when con­sidering limiting flow in terms of the upstream conditions or when friction must be allowed for. However, as a rough guide, the critical (or limiting) flow conditions can generally be expressed in terms of the pressure; thus,

where 7 for helium, a monatomic gas, is 1.66 (§9.130), and the molecular weight is 4.0 x 10 “3 kg.

where Pc is the pressure at the critical flow condition and P0 is the upstream pressure. For monatomic gases at all temperatures (7 = 1.66) and for diatomic gases up to about 500°C (7 = 1.40), Pc/P0 is roughly 0.5. This means that when the downstream pressure of the gas is less than about half the upstream pressure, a limiting flow condition is likely to occur. In the case of compressible flow through a pipe, frictional effects reduce the limiting velocity, as to be expected.

9.131. Critical or “choked” flow also occurs in two-phase systems, but the analysis picture is complicated by the need for writing sets of defining conservation equations for each phase and expressing interfacial transport of mass, momentum, and energy. For example, in steam-water flow through a pipe, flashing of the water occurs toward the exit as the fluid encounters a decrease in pressure. Therefore, experimental measurements have an important role in developing predictive models useful for design. As in single-phase compressible flow, frictional effects reduce the maximum velocity.