The positive error means the flowmeter is overreading, in this instance, for every 100 kg of steam passing through, the flowmeter registers 106.96 kg.
Equation 4.4.2 may be used to generate a chart showing the expected error in flow for an error in pressure, as shown in Figure 4.4.7.
When comparing Figure 4.4.6 with Figure 4.4.7, it can be seen that the % error due to lack of density compensation for the vortex flowmeter is approximately double the % error for the orifice plate flowmeter. Therefore, density compensation is essential if steam flow is to be measured accurately. If the steam flowmeter does not include an inbuilt density compensation feature then extra pressure and/or temperature sensors must be provided, linked back to the instrumentation system.
Dryness fraction variation
The density of a cubic metre of wet steam is higher than that of a cubic metre of dry steam. If the quality of steam is not taken into account as the steam passes through the flowmeter, then the indicated flowrate will be lower than the actual value.
Dryness fraction (
) has already been discussed in Module 2.2, but to reiterate; dryness fraction is an expression of the proportions of saturated steam and saturated water. For example, a kilogram of steam with a dryness fraction of 0.95, contains 0.95 kilogram of steam and 0.05 kilogram of water.
Example 4.4.4
As a basis for the following examples, determine the density (
) of dry saturated steam at 10 bar g with dryness fractions of 1.0 and 0.95.
The effect of dryness fraction on flowmeters that measure differential pressure
To reiterate earlier comments regarding differential pressure flowmeter errors, mass flowrate (q
_{m}_{}_{}_{}) will be proportional to the square root of the density (
), and density is related to the dryness fraction. Changes in dryness fraction will have an effect on the flow indicated by the flowmeter.
Equation 4.4.4 can be used to determine the relationship between actual flow and indicated flow:
All steam flowmeters will be calibrated to read at a pre-determined dryness fraction (
), the typically value is 1. Some steam flowmeters can be recalibrated to suit actual conditions.
Example 4.4.5
Using the data from Example 4.4.4, determine the percentage error if the actual dryness fraction is 0.95 rather than the calibrated value of 1.0, and the steam flowmeter was indicating a flowrate of 1 kg/s.
Therefore, the negative sign indicates that the flowmeter under-reads by 2.46%. Equation 4.4.4 is used to compile the graph shown in Figure 4.4.8.
The effect of dryness fraction on vortex flowmeters
It can be argued that dryness fraction, within sensible limitations, is of no importance because:
• Vortex flowmeters measure velocity.
• The volume of water in steam with a dryness fraction of, for example, 0.95, in proportion to the steam is very small.
• It is the condensation of dry steam that needs to be measured.
However, independent research has shown that the water droplets impacting the bluff body will cause errors and as vortex flowmeters tend to be used at higher velocities, erosion by the water droplets is also to be expected. Unfortunately, it is not possible to quantify these errors.
Conclusion
Accurate steam flowmetering depends on:
• Taking pressure variations into account - Pressure will vary in any steam system, and it is clearly futile to specify a flowmeter with an accuracy of ±2% if pressure variations alone can give errors of ±10%. The steam flowmetering package must include density compensation.
• Predictable dryness fraction - Measurement of dryness fraction is very complex; a much easier and better option is to install a steam separator prior to any steam flowmeter. This will ensure that the dryness fraction is always close to 1.0, irrespective of the condition of the steam supplied.
Superheated steam
With saturated steam there is a fixed relationship between steam pressure and steam temperature. Steam tables provide detailed information on this relationship. To apply density compensation on saturated steam, it is only necessary to sense either steam temperature or steam pressure to determine the density (
). This signal can then be fed, along with the flow signal, to the flow computer, where, assuming the computer contains a steam table algorithm, it will then do the calculations of mass flowrate.
However, superheated steam is close to being a gas and no obvious relationship exists between temperature and pressure. When measuring superheated steam flowrates, both steam pressure and steam temperature must be sensed and signalled simultaneously. The flowmeter instrumentation must also include the necessary steam table software to enable it to compute superheated steam conditions and to indicate correct values.
If a differential pressure type steam flowmeter is installed which does not have this instrumentation, a flow measurement error will always be displayed if superheat is present.
This is best shown as an example.
Example 4.4.6
Consider a differential pressure flowmeter fitted with pressure reading equipment, but no temperature reading equipment. The flowmeter thinks that it is reading saturated steam at 10 bar g with its corresponding temperature of 184°C. Unfortunately the steam being measured is superheated with a temperature of 220°C.
Using equation 4.4.2 the error in reading can be calculated based on the lower than anticipated density for superheated steam.
In this case the meter would over read by 5%
Using the same parameters as example 4.4.6, determine the actual flowrate if the flowmeter displays a flowrate of 250 kg/h.
Equation 4.4.5 can be used to calculate the actual value from the displayed menu.