Según Medway et al (1973) el Valor Absoluto se calcula, con la siguiente formula:

The calibration of a sensor is very important to ensure that the most accurate results can be obtained. In many cases calibration is required to be done for the specic scenario where measurements are to be made [14]. Because of the large numbers of parameters which aect the behaviour of domestic water installations, on-site calibration is likely required for a non-invasive ow meter for an EWH.

A simple calibration technique involves using an accurate sensor to give reference and to use these readings in the calibration of another sensor [14]. Osets and scaling factors can be considered to be simple calibration methods.

Some sensors can self calibrate using machine learning. An example of this is the system described in [16]. The system was designed to "solve a two phase linear programming and mixed linear geometric programming problem" to adaptively calibrate [16]. The calibration system proved to be successful, but a measured total ow rate was required to calibrate the multiple vibrations sensors used (which enabled appliance-level water consumption statistics) [16]. The presence of a trusted water ow rate value is not possible for a stand alone water ow rate meter (which is intended to provide the 'reference value'). Cross-correlation was used to identify which sensors received the highest weighting factor in [18].

Calibration of ultrasonic ow meters requires the compensation for the ow velocity prole which is dependant on the location of the sensors and the geometry of the ow path (both of which determine the ow prole) [12]. Thus if the sensors remain stationary and the ow conditions are within the range which the calibration was performed then recalibration should not be necessary. The installation procedure is important to ensure the correct operation of USFMs [12]. The location of the sensors must be such that fully developed ow is present for accurate results. If the ow prole is disturbed (not fully developed, e.g. asymmetric) then the ow calculations will be based on a cross section of ow that misrepresents the average ow rate in a way that Reynolds number calibrations cannot account for [12].

Accelerometers measure absolute g-force values but when used to detect vibration then additional calibration steps are required. Vibration propagation is complex and the any vibrations in a system can aect the measurement at all points in the system. Multiple tests are often required for relevant patterns to be distinguished which makes o-site ca- libration unlikely. In [20] the identication of frequency bands which were experimentally

found to correspond with ow rates was required for the specic scenario of a tap valve. In [17] a calibration process was required which diered for vibration sensors placed in dierent locations along the pipe (straight section or elbow).

Chapter 3

Thermal Modelling

Two thermal models of dierent complexity were developed with the intention of quanti- tatively estimating uid velocity using thermal data only.

The motivation for investigating thermal methods is given in Section 3.1. The most sim- plied steady-state thermal dierence model is discussed in Section 3.2. The preliminary thermal tests which were performed are mentioned in Secion 3.3. The expected relations- hip between measured temperature dierence and measured ow rate were not observed in preliminary thermal tests and a more complex thermal model was developed and simu- lated as discussed in Sections 3.5, 3.6 and 3.7. The diculties encountered in using the described thermal methods to attempt to measure EWH hot water ow rates is described in Section 3.8. Indications of the practicality and requirements of thermal methods for domestic EWH conditions is given in Section 3.9.

3.1 Thermal Method Motivation

Non-invasive thermal mass ow meters are often used to measure gas and low ow rate liquid ows [11, 27]. Thermal mass ow rate measurement traditionally requires the measurement of two or more temperatures along the longitudinal axis of a pipe and a heating element to provide a temperature increase which can be measured [27]. Liquid measurement of low ow rates (≤ 0.6 L min−1_{) was seen to be possible for the mass ow} measurement system used in [27] as described in Section 2.5.5.

For the EWH application it was roughly calculated that to use an external heating ele- ment to increase the temperature of the 22 mm copper piping and contained water volume would be impractical. The required power would be similar to the heating element contai- ned in the EWH. The requirement for non-invasive installation meant that invasive heat exchangers was not possible but were found to improve the performance of thermal mass measurement for liquids in [27].

For the EWH application it was noted that an existing heating device was already present in the form of the EWH element. The element heats the water within the EWH tank until it reaches the desired temperature (setpoint temperature). The water within the tank is assumed to at a uniform temperature, meaning that the water which ows in the outlet pipe should also be at a uniform temperature as well. An enclosed volume of water which is well mixed and at uniform temperature can be called a plug. The possibility of using the existing EWH element to act as a heating element for mass ow measurement purposes was investigated.

The energy input using the element can be measured using a SGC and if a relationship was found between longitudinal temperature drop during ow and measured ow rate then a thermal method similar to thermal mass ow meter could be created to estimate the ow rate of water owing out of the EWH unit. An empirical system which used a one or two node model of the EWH tank was used by Nel to estimate volumetric consumption in an EWH, but the success was limited to long duration ow events [28]. The alternative of modelling the outlet pipe behaviour is investigated in this chapter.