Flow Limiting Nozzle

Welker Flow Limiting Nozzles will allow turbine meters to flow at designed capacities while at the same time providing them with the over-range protection required without significant pressure loss to the flowing system.

Many devices have been developed to assist the gas industry with the challenges of flow measurement and control. Some are very complex and are most innovative, while others are just as important but very simple.

Two examples of such devices are the somewhat complex turbine meter and the seemingly simple orifice plate. These two instruments are not similar in any way, but ironically both are used to measure the flow of fluid through a pipeline. The orifice plate can also be placed in line a short distance from the turbine meter to be used as a critical flow orifice to protect the turbine meter’s measuring mechanism (over-range protection).

The turbine meter is a fluid velocity-measuring device. It depends upon the flow of gas to cause the turbine rotor to turn at a speed proportional to the gas flow rate. The complete measuring mechanism of a turbine meter includes the aforementioned rotor along with the turbine rotor shafting, bearings, flow passage area, and the necessary support housing structure.

Turbine meters are generally designed for a maximum line flow rate so as not to exceed a certain turbine rotor speed in rpm. In February 1976 the A.G.A. Transmission Measurement Committee established a Turbine Meter Task Group. This group was to recommend among other things the correct methods of installing turbine meters for measuring gas. This group noted that over-range protection, if practiced, could prevent severe damage from being done to a turbine meter measuring mechanism in cases of sudden turbine over-speeding caused by extreme gas velocities. Extreme gas velocities can occur when pressurizing, blowing down, or purging the associated meter run (see Appendix A for more turbine meter information).

A critical orifice may be sized to limit the flow through a turbine meter to 120% of its maximum rated capacity, as most turbine meters can be used at 120% capacity with no damaging effects as long as the lubrication schedule is “stepped up” (turbine meter manufacturer should be consulted). Using an orifice plate in such an application does come at a price. Critical (sonic) flow, as a rule of thumb, is only reached when the pressure downstream of a restricting element is half that of the upstream pressure. This means that half of the internal energy (available working pressure) of the flowing fluid upstream of the orifice plate is converted to kinetic energy as the velocity of the flowing fluid reaches the speed of sound of said fluid and passes through the orifice plate. A permanent pressure loss will occur even at sub-critical (sub-sonic) flow rates when an orifice plate (Figure 1) is used, and using an orifice plate as a critical flow device can result in up to an undesirable 50% permanent pressure loss. This pressure loss becomes important when large volumes of fluid are being pumped at high velocities, in which case power savings would quickly offset the investment in a Welker Flow Limiting Nozzle.

The same undesired results hold true when using a standard flow nozzle (Figure 2). This “pressure loss phenomena” occurs in both instances because of the sudden expansion incurred by the gas as it exits both the orifice plate and the noted nozzle. The pressure loss through the nozzle is somewhat lessened because of the long radius (circular arc) nozzle inlet. The standard nozzle will not be mentioned anymore in this paper, but it should be understood that the terms “standard nozzle” and “orifice plate” are interchangeable for the paper’s duration.
To better understand just what is happening downstream of the orifice plate that causes the permanent pressure loss and how the Welker Flow Limiting Nozzle will prevent such an unnecessary problem, one must have an understanding of how and why an orifice plate is able to limit capacity. A closer look at fluid mechanics associated with a one dimensional high-velocity gas flow is necessary.

As pressure upstream of an orifice plate increases, the flow rate through the plate also increases. If the upstream pressure remains the same and the downstream pressure drops, the flow rate through the orifice plate again increases. This increase in flow rate with increasing upstream pressure and decreasing downstream pressure holds true until the downstream pressure reaches .5457% of the upstream pressure for a gas with a ratio of specific heats (k) equal to 1.3. At this point the gas is flowing at its speed of sound and the flow rate will not be increased if the downstream pressure is reduced further. This state of flow is known as any of the following:

Sonic Flow (sonic velocity)
Critical Flow (critical velocity)
Choked Flow
Local Speed of Sound

Information about small disturbances in fluid flows propagates through fluids at the local speed of sound. When the fluid is moving at the local speed of sound, certain kinds of information, such as a pressure drop downstream of the orifice plate, will be unable to travel upstream against the flow. When the pressure downstream of the orifice plate is greater than .5457% of the upstream pressure, the gas velocity is sub-critical (sub-sonic). The information of a decrease in downstream pressure will propagate upstream at the local speed of sound, thus increasing the gas flow rate through the orifice plate. This increase in gas flow rate (ft³/hour) will continue to its maximum capacity for the particular sized orifice plate until the downstream pressure is once again .5457% of the upstream pressure.

It’s important to understand that an increase in upstream pressure will always increase the flow rate through an orifice plate until the downstream pressure is approximately half of the upstream pressure. At choked flow, at the orifice plate throat, the gas mass flow rate through the orifice is only a function of upstream conditions, and critical flow exists when the mass flow rate through the orifice plate is the maximum possible rate for the existing upstream conditions.

For working purposes we will define high velocity as gas flows in excess of 200 ft/sec. Most pipeline companies will establish velocity limits that will be somewhat lower than the aforementioned rate. 50 to 70 ft/sec max. is probably closer to what gas pipelines are allowing for gas transmission velocities.

As gas moves through and out of the orifice plate, it starts expanding. In an expanding high-velocity gas flow, the gas can convert significant amounts of internal energy into kinetic energy. This results in large decreases in gas temperature as well as in velocities much higher than might be expected. The density of the gas decreases dramatically as the gas velocity increases until the velocity reaches the local speed of sound (the speed of sound for the fluid at its temperature).

Example:
The speed of sound in air at 70 °F is 1,128 ft/sec. and can be calculated using equation 1

where:
C=speed of sound of air
g=acceleration of gravity
k=ratio of specific heats
M=molecular weight of air
P=pressure of system
R=individual gas constant for air
T=temperature of system
Vₛ=specific volume of air
Ρ=density of air

The same equation can be used for more complex gases after substituting in the correct values for the constants and variables noted above.

In high-velocity gas flows, the mass flow rate is considered constant or steady state. This means that the mass flow rate at the entrance, the throat, and the outlet of the restricting device are equal to each other and we can therefore apply the steady-flow mass balance equation (equation 2).

where:
mE =mass flow rate at restricting device entrance,lbₘ/sec
mᴛ=mass flow rate at restricting device throat,lbₘ/sec
mO=mass flow rate at restricting device outlet,lbₘsec

For an ideal gas the mass flow rate can be calculated (equation 3).

where:
Ρ = density of gas, lbm/ft²
A =cross-sectional flow area,ft²
V=velocity of gas ft⁄sec

By combining equations 2 and 3, we can derive equation 4.

Equation four presents somewhat of a problem when using an orifice plate as a choking device. As noted previously, the gas starts to expand as it moves through and out of the orifice plate. In an expanding high-velocity gas flow, the gas converts large amounts of internal energy (available working pressure) into kinetic energy (large decreases in gas temperature and extremely high gas velocities). The density of the gas “drops off” dramatically as the gas velocity increases to equal the local speed of sound. The orifice provides no means of controlling the expanding flow because it only has one cross-sectional area for a very short distance. The velocity of the gas downstream of the orifice plate starts to quickly slow down, but the density of the gas does not increase near as fast and internal energy (available working pressure) is lost.

Welker Flow Limiting Nozzles are designed with a converging section inlet, a short throat, and a diverging section outlet, much like that of a Venturi tube (Figure 3).

Often times because a full-length Venturi tube can be so expensive, the tube is shortened considerably. Since most of the pressure is recovered in the region of high velocity, this process is acceptable. A large part of the possible pressure recovery can be obtained by using a truncated recovery cone having an outlet diameter somewhat smaller than the inlet diameter.

The Welker Flow Limiting Nozzle (Figure 4) has been designed to have the gas velocity be of some small value at the inlet and increase linearly with distance through the convergent section to the throat. Because this is an expanding flow, the density (as noted earlier) decreases with distance. In the sub-sonic range, velocity goes up faster than density goes down; so the flow area decreases to keep PEAEVE constant. However, as the gas goes faster and faster, density drops more and more rapidly, until at the local speed of sound it is decreasing just as rapidly as velocity is increasing. Since the decrease in density equals the increase in velocity at the local speed of sound, the area of the throat remains the same for a short distance. Downstream of the nozzle throat, the cross-sectional area diverges gradually to prevent pressure loss brought about by turbulence due to separation. In effect, the expanding flow associated with an orifice plate is contained and controlled within the walls of the Welker Flow Limiting Nozzle’s diverging section. The density of the gas does not recover (increase) as fast as the velocity decreases downstream of the throat, so the cross-sectional area is increased gradually to keep PₒAₒVₒ constant (see Appendix B for more Welker Flow Limiting Nozzle information).

Turbine meters need over-range protection to prevent turbine rotor over-speeding caused by extreme gas velocities. Orifice plates can be used as over-range protection devices, but the permanent pressure losses associated with such practices are questionable. By incorporating knowledge of Venturi tube type flow devices into the manufacturing of Welker Flow Limiting Nozzles, Welker is able to provide a cost-effective way to allow turbine meters to flow at designed capacities, while at the same time providing them with the over-range protection required without causing a substantial pressure loss to the flowing system.

Typical performance data for a turbine meter rated at 10,000 ACFH would read as follows:

where:
Base Pressure (Pb)=14.73 psia
Base Temperature (Tb)=60 ℉
Ave. Atmospheric Pressure (Pa)= 14.48 psia
Super-compressibility Factor (Fpv) based on .6 specific gravity gas and 0% CO2 and N2 per A.G.A. Report No. 8.
The first question one might ask after looking at the above information might be: How can a meter rated for 10,000 ACFH have a maximum flowrate of 379,415 SCFH at 500 psig?
To find out the answer to the preceding question, one must only substitute actual values in place of the nomenclature noted in equation 1.
SCFH=(Fpv)²(Fᵀ)(Fᴘ)ACFH Equation 1
where:
(Fpv)²=compressibility ratio for working pressure
FT=Temperature Factor=((520 ℉)/(460 ℉)+working temp.)
FP=Pressure Factor=(working press.+(14.48 psia)/(14.73 psia))
(Value SCFH)=(1.0863)(520/460+60)(500+14.48/14.73)(Value ACFH)
(Value SCFH)=(1.0863)(520/460+60)(500+14.48/14.73)(10,000 ACFH)
(Value SCFH)=(1.0863)(1.0)(34.93)(10,000 ACFH)=379,415 SCFH
This exercise helps to enable an individual to better understand how a turbine meter rated for 10,000 ACFH capacity can flow at rates that at first glance seem much too high.

Flow Profile for 12” Sonic Nozzle
180 MMscfd @ 614.7 ps