Demystifying Fluid Turbulence, Velocity and Flow Measurement | Automation.com

# Demystifying Fluid Turbulence, Velocity and Flow Measurement

October 262018

By Dan Cychosz, DP Flow Product Manager, Emerson Automation Solutions

One of the long-standing philosophical questions of life is whether the light goes off in a refrigerator when the door is closed. For process engineers, an even deeper question relates to knowing what happens inside pipes. Like the refrigerator, it is difficult to see inside and ascertain the answer. The behavior of fluids as they flow from place to place has caused much consternation and is still a mystery to many.

It’s easy to imagine liquid flowing through a pipe as a uniform column, but we know it is anything but. Piping characteristics or features cause a range of velocities across the pipe. The primary source is friction. While it may not look like there is much resistance to flow, it is a major consideration. Even in straight pipe with smooth interior, the liquid closest to the wall moves the slowest because it is rubbing against the pipe wall. The next layer in is slowed by the outermost, and so on. As a result, liquid at the center of the pipe moves the fastest (Figure 1). This is a description of laminar flow, where distinct layers are maintained. In turbulent flow conditions, which occur at higher velocities, vortices and eddies cause intermixing of these layers as the fluid moves down the pipe. If we talk about fluid velocity in a pipe, we are describing an average as if it is moving as a perfectly uniform column, but it isn’t.

Laminar flow is most efficient from a pure energy loss point of view; however, this is not a flow regime that can realistically be maintained in process piping since line sizes would have to be very large compared to flow. Turbulent flow is encountered in all but the most viscous fluid flows. Turbulent flow resulting from higher flow velocities should not be confused with flow disturbances that add a velocity gradient to the flow. These can be caused by piping configurations such as elbows and valves.

Figure 1: Laminar flow is actually a distribution of velocity, with the fastest moving fluid at the center.

### Taming Flow Disturbances

Flow disturbances are inherent in piping systems due to the need to change directions (elbows), control flow (valves) and take measurements (thermowells) among other things. Proper design and acknowledgement of these disturbances is critical in ensuring the overall process performs to expectations. Disturbances can have many sources in piping:

• Pipe fittings, such as elbows and tees.
• Pipe diameter changes.
• Valves.
• Obstructions, such as thermowells.
• Poor pipe alignment with welded joints.

There are many equations to calculate all sorts of values related to flow and piping, which are now used primarily to torture engineering students since instrumentation and modeling software tools now handle most of these tasks. In the real world, the objective is generally to minimize flow disturbances, which means avoiding creating sources of it wherever possible. Some devices are particularly sensitive to turbulence such as the inlet of a centrifugal pump, many types of spray nozzles and most types of flow meters. The remedy for all of these is requiring some length of straight pipe (often in conjunction with a flow straightener) ahead of and sometimes after the device. Let’s think about how this works.

Without getting too deeply into any math, two main variables affecting flow regimes are pipe diameter and fluid velocity. The pipe diameter aspect is not difficult to conceptualize. As the diameter of the liquid column increases, so does the complexity of the velocity profile, which is why straight pipe requirements are expressed in terms of pipe diameters.

Fluid velocity is also a factor, but it usually assumed to a large extent. The slower the liquid moves through a pipe, the more drastic the flow profile. Again, this is not hard to conceptualize: slow moving liquid creates less turbulence, allowing greater disparity between fluid velocity next to the pipe wall compared to the center of the pipe. Velocity tends to be skipped in these discussions because it normally falls within guidelines on pipe diameters required to handle flow volumes based on velocity. One rule of thumb for liquids calls for velocity less than 7 feet per second (fps) for medium-size pipe. Smaller diameters, such as less than 1-inch diameter, need a lower velocity.

Consequently, many of the straight pipe length recommendations assume a flow velocity within these guidelines. However, in recent years, plant designers have pushed these limits in an effort to reduce cost. For example, if sizing pipe to handle a flow of 200 gallons per minute (gpm), a 4-inch pipe would provide a velocity of about 5.0 fps and a pressure drop of barely 1 pound per square inch (psi) over a distance of 100 feet. The designer might try to save some cost by reducing the pipe to 3-inch, but velocity will go up significantly to about 8.7 fps, and pressure will drop by nearly 4 psi over 100 ft.

The question of whether or not to pursue this approach will come down to the expected higher pumping costs and possible increased pipe wear due to the higher velocity.

### Flow Disturbances and Flow Meters

For purposes of this discussion, we will limit the analysis to differential pressure (DP) flow meters, although this is not a major limitation since DP remains the most common technology. There are numerous variations on the concept, but in its most basic implementation, an orifice with a bore diameter smaller than the pipe diameter is inserted into a pipe between flanges. When the fluid flows through the restriction, it causes a pressure drop which can be measured by a DP transmitter (Figure 2).

Figure 2: A basic DP flow meter can take pressure measurements in a variety of locations.

Placement of the taps in relation to the vena contracta will determine the exact calculation used. The pressure taps can be located at different distances from the orifice plate (or other primary element), which affects the differential pressure sensed by the DP transmitter. In any case, the flow rate will be proportional to the square root of the differential pressure.

One of the reasons DP is so popular for measuring flow is its simplicity. Countless installations have been created by users with every imaginable configuration because they all work, and can be tailored to specific needs. The accuracy and precision of a DIY setup are in the eye of the builder, but so long as the users understand the quirks of a given installation, this is a good approach.

Such is not the case for a commercially-built DP flow meter. A user wanting a flow meter buys it with the expectation that it can deliver the kind of performance outlined in the catalog. If the specifications promise accuracy of ±1 percent with a turn-down ratio of 10-to-1, it has to be able to deliver that performance, provided the user complies with reasonable installation requirements.

Such requirements will likely call for a minimum length of straight, smooth pipe upstream and downstream from the primary element. The actual length will vary from design to design. Upstream requirements can be as low as zero, but are often 20 diameters and even higher. Downstream pipe length is usually one-third to one-half the upstream length.

A disturbed flow profile is a problem for the actual DP reading. The taps are placed in critical locations where the flow has known characteristics. It may be turbulent, but it is predictably turbulent. If the flow has characteristics the flow meter’s designers did not anticipate, such as putting a globe valve only a few pipe diameters from the primary element, the DP signal might be highly erratic or change the flow profile sufficiently to shift the reading well beyond the normal tolerance.

The range of velocity is implicit in the flow meter’s measuring range. For example, a flow meter designed for a 2-inch pipe won’t likely extend past 100 gpm and may top-out even lower given the velocities necessary to move that much liquid through a 2-inch pipe. At the other extreme, there will be a minimum flow required as well to create a high enough pressure drop across the primary element to generate a usable DP signal.

### Reducing Pipe Requirements

Sometimes finding the room necessary for a straight pipe length can be a problem. For example, Emerson’s Rosemount™ 3051SFP Integral Orifice Flow Meter (Figure 3) uses a conventional single orifice primary element and is built as a complete assembly. The unit sized for a 1-inch pipe includes straight pipe in both directions with an overall length of almost 30 inches, so the required straight pipe is built into the design. But what if the flow meter has to be installed in a location where that much straight pipe simply isn’t practical, say inside a skid unit where space is at a premium?

Figure 3: Some flow meters, such as a Rosemount 3051SFP, are built with the straight pipe sections as part of the design.

The installer might be tempted to saw off the pipe and see what happens. The likely effect will be difficult to predict exactly, but will probably involve some loss of precision, which might be tolerable depending on the application.

A better solution is to change the nature of the primary element to minimize the effect of a flow disturbance. Replacing one large orifice bore with four smaller ones (Figure 4), which are called conditioning orifices, can cause the same pressure drop and deliver the same measuring precision, but without the same need for straight pipe length. Naturally this comes at the cost of free passage which slightly increases the potential for clogging, but at least it offers another mechanism to solve a difficult application conundrum.

Figure 4: Using a conditioning orifice can reduce the need for straight pipe length.

The ability to solve specific application challenges depends on having the right tools capable of optimizing trade-offs when necessary. An accurate and effective flow meter requires a precision-built primary element combined with a precise and stable DP transmitter equipped high-performing electronics. This critical pairing is the heart of the measurement and is the place where accuracy and reliability begin.