ABSTRACT
Curve fitting errors are reduced to <0.1% of reading (O.R.) from 1 to 3% of full scale by using Rosko/Strouhal Coefficient Equations for Paddlewheel Turbine Meters for viscosities from 0.2cSt to 150cSt. This finding was reproduced with several meters at two different flow laboratories. This technology behavior will be added to the Technical Report for ASME (The Flow Technology Cross Index as referred by Dr. M. J. Reader-Harris) that is in draft by Richard Fertell, in the Turbine Meter Section of the Flow Technology Application, Selection, and Use with Cross Index to Flow Technology Standards and Technical Report Documents (previously presented at FLOMEKO 2011 and CFM 2009).
INTRODUCTION
The paddlewheel turbine meter has been used for years in liquid cooling/heating systems for the Semiconductor Fabrication Equipment Industry, Super-Computers & Data Center Computers, Medical Equipment Industry, Security Scanning Industry, Military Power Generators and Welding Systems (Electric-contact type and some TIG), as well as Military Equipment Decontamination Systems, Fabric Chemical Batching (such as “stone washed fabrics”), and Batching, such as Vehicle Fluid (oils) Dispensing and Beverage Bottling/Dispensing (Wine and Beer and drinking water). Better control of these processes and energy used/recovered calculation is achieved through improved measurement uncertainty.
THEORY
Like other turbine meters, Paddlewheel Rotors generate data that is best characterized using Strouhal & Roshko Numbers, instead of curve fit collected data.
The results of such calculations on a paddlewheel sensor are <0.03% as listed in Table1 for room ambient water & 5cSt fluid versus curve fitting data in Graph.
The following two graphs show the error using Best Fit Straight Line for the performance of a unit at different viscosities. For the error at each point to be <1% O.R., the turndown ratio is restricted to 1.7:1; with a 2:1 turndown ratio, some points reach 3% O.R. error.
Note: The graph has reversed axes because the flow data was collected at particular unit output frequencies for comparison at different viscosities.
PRACTICE
The number of flow points collected and placement of the flow points along the unit performance curve determines the interpolation error between flow points. The more flow points collected in pronounced performance curve regions of the sensor, the smaller the interpolation error. As we see in the error graph, the lower end of the flow range requires more data collection than the upper ~40% of the flow range, like fan-blade turbine sensors.
Extra computing power can be is required to calculate the dimensionless Reynold’s Numbers, Strouhal and Roshko at both the calibration lab and the user application (or in the flow sensor).
CONCULSION
The non-linearity error of curve fitting data can be eliminated or greatly reduced in Paddlewheel rotor flow meters when using Roshko and Strouhal Numbers, just as with fan-blade turbine meters.
The useful turndown ratio can be extended from 2:1 to 7:1, and even 11:1 in some cases, for paddlewheel turbine meters because the curve fitting error is reduced from >35% to <0.1% O.R. error.
Future papers will address error reduction from: 1) interpolation calculation of Roshko and Strouhal Numbers between collected flow points, 2) interpolation calculation for flow points for viscosities between unit performance curves of different viscosities using Roshko and Strouhal Numbers.
REFERENCES
[1] Olivier, Paul, “Flow Technologies Workshop”, May 1997, Flow Dynamics, Scottsdale, AZ, USA
[2] “Assessment of uncertainty in calibration and use of flow measurement devices – Part 1: Linear calibration relationships”, International Standard, ISO 7066-1, 1st ed., (1997), pp. 1-28, ISO, Switzerland
Richard Fertell
Proteus Industries Inc.
