Fanno flow

The pressure drop in (c), the vapour venting section, is by far the largest quantity and is limited by Fanno flow, when the velocity becomes sonic at the exit. This is because the volume flow of warm cryogen vapour is much greater than the volume flow in the 2-phase cooldown section, and is several hundred times greater than the liquid input volume flow. 

Fig. 8.4 Cooldown of pipeline showing liquid front, cooldown wave, Fanno flow of warm vapour,...

This flow, or Fanno flow, is well-known to blow-down wind-tunnel operators, in which the maximum mass flow is determined only by the local speed of sound S at ambient temperature, the exit pressure and the cross-sectional area of the exit (see, e.g. [4]). 

The velocity of the liquid front behind the cooldown wave is then determined entirely by the Fanno flow of the ambient temperature vapour flow ahead of the cooldown wave. 

The temperature or enthalpy of the gas may then be plotted to a base of entropy to give a Fanno line.iA This line shows the condition of the fluid as it flows along the pipe. If the velocity at entrance is subsonic (the normal condition), then the enthalpy will decrease along the pipe and the velocity will increase until sonic velocity is reached. If the flow is supersonic at the entrance, the velocity will decrease along the duct until it becomes sonic. The entropy has a maximum value corresponding to sonic velocity as shown in Figure 4.11. (Mach number Ma < 1 represents sub-sonic conditions Ma > 1 supersonic.)... 

Fanno lines are also useful in presenting conditions in nozzles, turbines, and other units where supersonic flow arises.(5)... 

Fanno Line Tables for Adiabatic Flow of Air in a Constant Area Duct... 

Table 1-1 Fanno Line—Adiabatic, Constant Area Flow (k = 1.400) ...

To understand the difference in stagnation pressure losses between subsonic and supersonic combustion one must consider sonic conditions in isoergic and isentropic flows that is, one must deal with, as is done in fluid mechanics, the Fanno and Rayleigh lines. Following an early NACA report for these conditions, since the mass flow rate (puA) must remain constant, then for a constant area duct the momentum equation takes the form... 

For adiabatic flow in a constant area duct, that is pu = constant, one has for the Fanno line... 

If flow restrictions are distributed throughout the system, other techniques, such as Fanno line analysis, must be used to estimate average gas flow rate. 

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