ViscoCorrectTM
A Recent Development
in Flow Linearisation
By Martin
Cuthbert MEng (Hons), Webtec Products Ltd.
This document is based
on research carried out at Sheffield University and has subsequently been named
ViscoCorrectTM. The author of
this document, Martin Cuthbert, has since been recognised by the BFPA with the
Young Engineerís Award 1997 for his dissertation 'Turbine flow meters: a design
tool and improved method of linearising flow'.
ViscoCorrectTM
is a registered trademark of Webtec Products Ltd.
Overview
ViscoCorrectTM
is a recent development in flow linearisation designed for use with the Webster
VT series of turbine flow meters. ViscoCorrectTM
allows VT type flow meters to be operated over a wide viscosity range whilst maintaining
consistently good accuracy. This is achieved by monitoring fluid temperature to
determine kinematic viscosity and using a custom dimensionless graph to calculate
the true flow rate.
Background
Information on Turbine Flow Meters
A turbine flow meter
typically consists of a rotor mounted on a shaft fitted longitudinally within
a housing. Fluid impacting on the turbine blades causes the turbine to rotate.
A magnetic transducer mounted perpendicular to the shaft measures the passing
of each blade. The relationship between flow and frequency is described by the
meter factor, or K factor where:
K factor = frequency
/ flow (pulses per litre)
A typical K factor
versus flow curve for a turbine flow meter is shown below.
Below approx. 20
lpm (dependent on flow meter size) a turbine flow meter is non-linear; this
is characterised by a rapid increase in K factor and a pronounced 'hump'. At
higher flows (above approx. 20 lpm) the curve becomes approximately linear,
this region is known as the 'linear range'. The initial 'hump' shape of the
curve is due to a combination of drag effects exerted on the turbine blade,
specifically bearing friction, magnetic detent, and viscosity effects. Bearing
friction is minimised by the use of precision ball-race bearings. Magnetic detent,
the effect of magnet drag due to the inductive transducer attracting the turbine
blade, is minimised by using a magneto-resistive type transducer and associated
electronics. The third source of drag is influenced by the viscosity properties
of the fluid being measured.
K factor Linearisation
At the simplest level,
K factor linearisation involves dividing the frequency signal from the flow meter
by a constant K factor to compute the volume flow rate. Whilst this method is
quite effective over the short linear range of the turbine it severely limits
the turndown ratio of the flow meter. In order to extend the flow range whilst
maintaining accuracy, K factor linearisation was improved to include a fifteen
point K factor versus flow curve, similar to the one shown on the previous page.
This method is very effective and provides accuracy of 1% of indicated reading
over a 100:1 turndown ratio, i.e.: one flow meter can measure from 4 to 400 lpm.
Limitations
A K factor versus flow
curve for a particular turbine flow meter is highly repeatable assuming it is
operated and calibrated using the same fluid at the same temperature. These limitations
are due to the effect of changes in viscosity on the performance of the turbine
flow meter, particularly at low flows as previously mentioned.
Kinematic viscosity
= absolute viscosity / density (cSt or mm2/s)
Kinematic viscosity
of a mineral oil is dependent on both temperature and pressure. A change in
pressure can lead to a small change in kinematic viscosity, typically though,
for working pressures under 100 bar the effect is minimal. A change in temperature
however, is more important as an increase in temperature results in a decrease
in kinematic viscosity. A typical mineral oil used in the fluid power industry
will have a kinematic viscosity of 32 cSt at 40ƒC but a viscosity of over 80
cSt at 20ƒC. Changes in viscosity effect both the shape and the vertical offset
of the K factor versus flow curve. The example below shows a turbine flow meter
tested on the same oil, ISO 32, at three different temperatures.
To obtain optimum
accuracy, turbine flow meters that use K factor linearisation must be used under
very strict fluid and temperature conditions dictated by the manufacturer.
ViscoCorrectTM
ViscoCorrectTM
is a refined method of K factor linearisation that allows you to accurately measure
flow over a wide range of viscosities. This means one turbine flow meter can be
used on a variety of different fluids and over a range of temperatures, allowing
you to choose your own test criteria.The linearisation curve is created from a
series of tests carried out over a range of different viscosities and flows. The
resulting data is plotted against custom axes, the y-axis uses Stm, a dimensionless
form of the K factor, whilst the x-axis uses Rem, a modification of the Reynolds
number. Because Rem includes both frequency and kinematic viscosity, the tests
carried out at different viscosities can be plotted together in one smooth curve.
Since the axes are dimensionless, linearisation curves for different sizes of
turbine flow meter can be combined together. Once calibrated, a VT type turbine
flow meter measures the fluid temperature and sends this signal along with the
turbine frequency to the C1000
data acquisition system. Using a look-up table for the fluid under
test, the kinematic viscosity is quickly obtained from the temperature. Frequency,
kinematic viscosity and constants defining the flow meter characteristics are
combined to calculate Rem. A mathematical model of the linearisation curve (shown
below), stored within the C1000 evaluates the corresponding Stm value. The frequency
and Stm value are then used to calculate the true volume flow rate.
ViscoCorrectTM
is extremely effective at lower viscosities, typically providing accuracy better
than 1% of indicated flow for viscosities between 1 and 40 cSt (highlighted
in grey in the table below). For viscosities between 40 and 60 cSt ViscoCorrectTM
still provides considerable improvements in accuracy over K factor linearisation,
this is demonstrated in the picture above, where the displayed error has been
reduced from approx. 12 % to approx. 2% for a test at 60 cSt.
Look-up
table to calculate kinematic viscosity (cSt) of mineral oils at specific temperatures
Viscosities highlighted in grey indicate turbine flow meter accuracy of better
than 1% of indicated reading (VT Range).
Fluid
type
Temp. °C |
ISO
15 |
ISO
22 |
ISO
32 |
ISO
47 |
ISO
56 |
ISO
68 |
Kerosene |
| 0 |
85.9 |
165.6 |
309.3 |
449.9 |
527.6 |
894.3 |
3.5 |
| 10 |
49.0 |
87.0 |
150.8 |
204.7 |
244.9 |
393.3 |
2.8 |
| 20 |
30.4 |
50.5 |
82.2 |
105.5 |
127.9 |
196.1 |
2.3 |
| 30 |
20.1 |
31.6 |
48.8 |
59.8 |
73.1 |
107.7 |
2.0 |
| 40 |
14.0 |
21.0 |
31.0 |
36.6 |
44.9 |
63.9 |
1.7 |
| 50 |
10.2 |
14.7 |
20.8 |
23.9 |
29.4 |
40.5 |
1.4 |
| 60 |
7.7 |
10.7 |
14.7 |
16.5 |
20.2 |
27.2 |
1.3 |
| 70 |
6.0 |
8.1 |
10.9 |
12.0 |
14.6 |
19.2 |
1.1 |
| 80 |
4.8 |
6.4 |
8.4 |
9.1 |
11.1 |
14.3 |
1.0 |
| 90 |
4.0 |
5.2 |
6.6 |
7.2 |
8.7 |
11.1 |
|
| 100 |
3.3 |
4.3 |
5.5 |
6.0 |
7.1 |
8.9 |
|
| 110 |
2.9 |
3.6 |
4.6 |
5.1 |
5.9 |
7.5 |
|
| 120 |
2.5 |
3.2 |
4.0 |
4.4 |
5.1 |
6.4 |
|
ISO 15, 22, 32, 46 and 68 based on typical figures for the Esso Nuto range
of HM oils. ISO 37 based on Shell Tellus HM oil. Typical figures used
for Kerosene. |
A unit of flow,
like lpm, is an inferred standard, as no standard for flow exists. Flow is a
calculated measurement based on fluid volume and time. Tests have been carried
out by measuring the mass of oil to flow through a turbine flow meter over a
period of time. A hydrometer is used to ascertain density. True volume is computed
from mass and density. Time is measured using a Droitwich frequency standard.
The measurement of mass, density, and time are all traceable to national standards.
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Webtec Products Ltd (March 2004)