# Flow Profile Theory & Practice

Sept. 26, 2010

Achieving Proper Velocity Distribution

Fluid flows at different velocities within a pipe’s cross-section. For well-developed, ideal flow, the fluid velocities will be highest near a pipe’s center, decreasing towards the pipe walls in symmetrical fashion. The shape that the fluid takes as it is flowing through the pipe is referred to as the velocity profile. In simple terms, a velocity profile is the distribution of velocities across a pipe.

You are probably aware that in an ideal installation, that is one with a great length of smooth straight pipe preceding the measurement point, the velocities are distributed in a regular and known way across the pipe. This is termed a “fully developed” condition. In almost all installations we encounter, the flow is turbulent, i.e., the Reynolds number is greater than 10,000. This condition is referred to as “fully developed turbulent flow.” Engineers have a good familiarity with the flow profile of a fully developed turbulent condition. They know the velocity distribution across the pipe cross-section. They can easily calculate the mean volumetric flow within the pipe from the point velocity obtained with an insertion probe.

However, if there is a disturbance in the flow upstream of the measuring point, such as a bend, or a valve, or a change in diameter, then the profile will not be fully developed. In this case, a calculation based on the insertion probe measurement will result in an incorrect value for volumetric flowrate. Flow profiling establishes the various fluid velocities across the diameter of a pipe at a cross-sectional location. By determining the pipe’s flow profile, and integrating the data to establish the mean flow velocity, instrument engineers can check on how accurately a flowmeter measures the true flowrate.

Defining terms:
• Mean velocity – Weighted average of all flow velocities across the pipe diameter.
• Sensed velocity – The velocity that is measured by the flowmeter.

Figure 1. To determine a flow profile, instrument engineers divide the pipe cross-section into several concentric annular areas.

To determine a flow profile, instrument engineers divide the pipe cross-section into several concentric annular areas, as indicated in Figure 1. They assume that the velocity within an annular area is constant, even though the velocities at the various points across the diameter differ. They weight each annular velocity depending on its influence on the mean velocity calculation. To get the mean velocity, they divide the weighted velocities by a mean velocity factor and sum the results.

Insertion Probes
Insertion probes serve as a convenient way to measure the different flow velocities across a pipe’s diameter. They measure fluid velocity only in the immediate area of the probe tip. While not extremely high-precision instruments, they can be used to give good accuracy in many difficult applications.

For example, the ABB AquaProbe, shown in Figure 2, is an insertion probe with an “inside out” electromagnetic flowmeter design. The coil sits on a shaped core at the tip, which has the effect of creating a spherical magnetic field in the flow. A conductive fluid that flows through the field generates a voltage potential in the same way as in a conventional electromagnetic flowmeter.

Figure 2. The ABB AquaProbe is an insertion probe with an “inside out” electromagnetic flowmeter design.

On the other hand, a full-bore electromagnetic meter looks across the full diameter of the pipe. It is influenced primarily by the velocity profile across the complete cross-sectional area of the pipe. Therefore the full-bore magmeter takes a reasonable average of flow velocities at its measurement location, as indicated in Figure 3.

Aside from determining flow profiles, insertion probes can be used to accurately measure fluid flowrates within a pipe, but only if the flow velocity profile at the probe location is well documented.

Measuring Flow Profiles
Several factors can influence measurement of a flow profile with an insertion probe.
• The flow velocities must fall below a value that would cause damage to the insertion probe taking a flow measurement.
• The internal diameter of the pipe at the measurement point must be accurately known.
• Sufficient measurements across the pipe diameter must be made to determine a meaningful profile.
• Measurement time at each point must be sufficiently long to determine a good flowrate average.
• Widely varying flowrates may make determination of the flow profile unworkable.
• The upstream pipe configuration will govern how many cross-sectional measurements will be necessary to accurately determine the flow profile.

Figure 3. A full-bore electromagnetic meter looks across the full diameter of the pipe. It is influenced primarily by the velocity profile across the complete cross-sectional area of the pipe.

Insertion probes of any type are subject to a specified maximum velocity because of vortex shedding. In a standard vortex flowmeter, for example, the bluff body in the meter causes vortices to be shed at a rate proportional to the velocity. Every such body, suspended at one end, has a fundamental frequency at which it vibrates in the flow. If the insertion probe, being a bluff body, experiences vibrations caused by vortex shedding that reaches its fundamental frequency, it will fail. Manufacturers offer charts of information with maximum fluid velocity plotted against insertion length.

The greater the number of velocity points measured across the pipe diameter, the greater the resolution of the flow profile. A high-profile resolution obviously improves confidence in the accuracy of the installed flowmeter. The industry’s rule of thumb calls for a minimum of seven points to determine a meaningful flow profile. Flow stability is also important when profiling. Otherwise, the velocity measured may be indicative of a new flowrate rather than the new position of the insertion probe. To check prior to starting the profile, place the probe at about the centerline of the pipe and log the measurement for five minutes.

Figure 4 shows a logged flowrate where the red line represents stable flow, and the black line represents erratic or unstable flow. Generally speaking, the flowrate should not change more than 2 percent over five minutes.

Figure 4. A logged flowrate where the red line represents stable flow, and the black line represents erratic or unstable flow.

Under most circumstances, carry out a full traverse of the pipe diameter when creating a profile. However, for large pipe diameters, where the insertion probe cannot reach across the full diameter, try a half profile. Nevertheless, remember that this is only valid when the flow profile is symmetrical about the pipe’s center.

Diagramming Flow Profiles
Diagrams can provide a helpful representation of flow velocity profiles in a two- or three-dimensional situation. A 2D diagram makes sense for flows that are symmetrical about the pipe’s axis. Otherwise, multiple profile diagrams must be made at various angles to provide a 3D representation across a pipe’s cross-section.

These representations are essentially vector diagrams. Steps to create a flow diagram include:
• Draw a line across the pipe at the point of interest.
• Divide the line into points — not too few, or the results will be poor; not too many, or the work will be too time consuming.
• At each point, draw a vector whose length represents the velocity at that point and whose direction reflects the flow direction.
• Join the vector ends with a line.
This resulting line has a shape that represents flow velocities within the pipe. The red and blue lines in Figure 5 show an ideal profile for fully developed turbulent and laminar flows, respectively. The dotted line indicates the mean flow velocity for the pipe, which represents the sensed value a flowmeter should measure.

Distorted Flow Profiles

Figure 5. The red and blue lines show an ideal profile for fully developed turbulent and laminar flows, respectively.

The fully developed flows described above result only after long runs of smooth, straight pipe. However, something like a bend, valve, or expansion upstream of the measuring point disturbs this ideal profile. The flow loses its fully developed condition. Figure 6 shows how well-developed flow profiles change after passing through various pipe configurations. Best practice is to take two profiles at 90 degrees, because in some cases one profile can look normal while the other can exhibit serious flow disturbance.

Figure 6. Shows how well-developed flow profiles change after passing through various pipe configurations.

Many kinds of flowmeters installed immediately after such piping conditions will lose accuracy. Obviously, it is best to have a fully developed profile at the measuring point. This can be achieved by installing the flowmeter after a straight pipe whose length depends on the nature of the disturbance upstream from the measurement point. These straight-pipe lengths were covered earlier in the article on flowmeter installation (“Flowmeter Piping Requirements,” Flow Control, May 2007, page 14).

Figure 7 shows the flow profiles calculated by software following a 90-degree elbow. While the disturbance is not large, a full-bore magmeter placed immediately after the bend would exhibit an error of about -1 percent FSD.

Figure 7. Shows the flow profiles calculated by software following a 90-degree elbow.

Figure 8 shows the complexity of flow profiles following a Tee, with lowest flow velocities represented in blue and highest in red. Even after 10 diameters the flow is not yet fully developed.

The major considerations in manually measuring a flow profile with an insertion flowmeter include:
• Insert the probe to the far wall.
• Take a flow velocity measurement.
• Move probe to next point.
• Measure at least seven points per profile.
• Continue until you have traversed the whole pipe diameter.
• Repeat the above at 90 degrees if you suspect flow profile is not symmetrical.

Figure 8. Shows the complexity of flow profiles following a Tee, with lowest flow velocities represented in blue and highest in red.

Log the point measurements, and take each long enough to assure a good average. Examine the logged data to establish the overall stability of the flow during the profile.

This is the third article in a five-part series on the history and operation of flowmeter technology. Part IV will appear in the July issue of Flow Control magazine.

Greg Livelli is a senior product manager for ABB Instrumentation, based in Warminster, Pa. He has more than 15 years experience in the design and marketing of flowmetering equipment. Mr. Livelli earned an MBA from Regis University and a bachelor’s degree in Mechanical Engineering from New Jersey Institute of Technology. Mr. Livelli can be reached at [email protected] or 215 674-6641.

www.abb.com

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