Sonic Limit

The vapor flow in the heat pipe vapor case is quite similar to the flow characteristics encountered in a converging-diverging nozzle. Very high velocity, choked flow, and pressure recovery are evident in the operation of heat pipes, which are functions of the heat input and rejection rates. 

Curve A It demonstrates a subsonic condition with slight temperature recovery in the condenser. The temperature decreases along the evaporator section as the vapor stream is accelerated due to mass addition caused by evaporation. 

Curve B When the condenser temperature is lowered by increasing the heat rejection rate, the evaporator temperature is also lowered. The vapor velocity at the exit becomes sonic and critical, and choked flow condition exists. 

Curves C and D Further increasing the heat rejection rate only lowers the condenser temperature because the rate of heat transfer could not be increased due to the existence of choked flow. The change in condenser temperature has no effect upon the evaporation 

In a heat pipe of constant vapor core diameter, the vapor stream accelerates and decelerates because of the vapor addition in the evaporator and vapor removal in the condenser. Velocity variations in a converging-diverging nozzle result from a constant mass flow through a variable area, whereas in a heat pipe velocity, variations result from a variable mass flow through a constant area. 

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Somogyi method, in sugar analysis, 23 475 Sonication, 16 410-411 Sonic limit, heat pipe, 13 230 Sonogashira coupling... 

IMeasured value based on reaching the sonic limit of mercury in the heat pipe ... 

Estimating the efficiency of a nozzle depends ultimately on the results of tests on similar systems, and the manufacturer will supply a figure at the design point, either explicitly or from the thermodynamic data that accompany the turbine flowsheet. However, the control engineer will need to consider off-design conditions, including particularly the sonic limitations that may occur if the pressure drop falls below a critical value. 

A Viscous limit B Sonic limit C Capillary limit D Entrainment limit E Boiling limit (low T fluids)... 

Figure 13.11 Temperature-axial location plot of a typical sodium heat pipe to explain the sonic limit...

The sonic limit occurs when the Mach number at the evaporator exit is unity. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

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. 

Since the pressure drop is quite high, there is a possibility of approaching sonic velocity in the line. This will result in a potential noise problem. Hence, it is a good practice to limit the velocity to 60 percent of the sonic velocity or a 0.6 Mach number. 

Instrumentation level instrumentation for MLO (standpipe level and ultrasonic) has limited use in a shutdown accident. Standpipe level is correct in the absence pressure m the system Ulirti sonic is correct only when the level is within the reactor coolant loops. 

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... 

When the relieving scenarios are defined, assume line sizes, and calculate pressure drop from the vent tip back to each relief valve to assure that the back-pressure is less than or equal to allowable for each scenario. The velocities in the relief piping should be limited to 500 ft/sec, on the high pressure system and 200 ft/sec on the low pressure system. Avoid sonic flow in the relief header because small calculation errors can lead to large pressure drop errors. Velocity at the vent or flare outlet should be between 500 ft/sec and MACH 1 to ensure good dispersion. Sonic velocity is acceptable at the vent tip and may be chosen to impose back-pressure on (he vent scrubber. 

Sonic Conditions Limiting Flow of Gases and Vapors... 

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. 

For example, for a line discharging a compressible fluid to atmosphere, the AP is the inlet gauge pressure or the difference between the absolute inlet pressure and atmospheric pressure absolute. When AP/Pi falls outside the limits of the K curves on the charts, sonic velocity occurs at the point of discharge or at some restriction within the pipe, and the limiting value for Y and AP must be determined from the tables on Figure 2-38A, and used in the velocity equation, Vj, above [3]. 

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). 

Determine sonic velocity at oudet conditions and check against a calculated velocity using flow rate. If sonic is the lower, it must be used as limiting, and capacity is limited to that corresponding to this velocity. 

If the pressure drop across the valve is to be more than 42 per cent of the inlet absolute pressure the valve selection is the same as if the pressure drop were only 42 per cent. With this pressure ratio the steam flow through the valve reaches a critical limit, with the steam flowing at sonic velocity, and lowering the downstream pressure below 58 per cent of the inlet absolute pressure gives no increase in flow rate. When the heater needs a higher pressure, or when the pressure required in the heater is not known, it is safer to allow a smaller pressure drop across the control valve. If the necessary heater pressure is not known, a pressure drop across the control valve of 10-25 per cent of the absolute inlet pressure usually ensures sufficient pressure within the heater. Of course, in the case of pressure-reducing valves the downstream pressure will be specified. 

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