Click here to enlarge imageThe transit-time principle measures an average velocity across the pipe at a given chordal elevation. Figure 2 shows the velocity calculation based on the travel time of the sound pulse, the liquid sonic velocity, the acoustic path length, and the acoustic path angle. As shown, when the upstream and downstream travel times are combined to solve for the average velocity at a particular elevation the sonic velocity variable cancels. This is important to note because a multiple chordal-path transit-time flowmeter is not dependant on the liquid sonic velocity and can be applied to applications with drastic changes in the temperature.
As previously mentioned, there are a number of variables that determine a flowmeter’s overall system uncertainty (or accuracy). In a multiple chordal-path transit-time flowmeter system, these uncertainties are defined by four major components: the individual velocity measurements; cross-section area measurement; velocity integration (average velocity calculation); and random error. Typically the uncertainty of the velocity measurement and random error components are second order effects. The area measurement uncertainty is typically a fixed value and is based on the pipe diameter measurements taken during the installation. The largest contributor and most variable component to the overall uncertainty of a multiple chordal-path transit time flowmeter is the flow profile integration uncertainty.
In a four chordal-path elevation transit-time flowmeter, the acoustic chords are placed at ± 18 and 54 degrees with respect to the horizontal centerline of a pipe in full pipe applications. The integration technique is called the Jacobi-Gauss Integration Method (or Chebyshev Method). Computational fluid dynamics (CFD) analysis has been used to estimate the integration uncertainty of this method over a wide range of velocity profiles (from fully developed symmetrical profiles to highly disturbed velocity profiles). These analyses and previous field experience has shown that the uncertainty of the Jacobi-Gauss integration is in a range of ± 0.2% to 1.2%. As such, when a multiple chordal-path transit-time flowmeter is installed in a worst-case hydraulic location, its maximum overall uncertainty will be better than ± 1.5% for a four elevation chordal transit-time flowmeter. Therefore, even in the presence of highly disturbed velocity profiles, a multiple chordal-path transit-time flowmeter can perform accurately.
As the application of large UV disinfection systems continues to grow, the need for a viable flow measurement technology to address the challenges presented by these systems becomes more critical. The unique characteristics of the multiple chordal-path transit-time flow measurement technology enable a UV system to achieve the goal of assured continuous disinfection while maximizing the system’s throughput and efficiency. WW
About the Authors:
Guy Miller, P.E., is Engineering Manager at Accusonic Technologies. John Trofatter is General Manager for Accusonic Technologies