GB2559836A

GB2559836A - Determination of flow rate and fluid temperature

Info

Publication number: GB2559836A
Application number: GB1718195.9A
Authority: GB
Inventors: Parson Oliver; Maciol Ryszard
Original assignee: Centrica Connected Home Ltd
Current assignee: Centrica Connected Home Ltd
Priority date: 2017-11-02
Filing date: 2017-11-02
Publication date: 2018-08-22
Anticipated expiration: 2037-11-02
Also published as: WO2019086899A2; GB201718195D0; GB2559836B; WO2019086899A3

Abstract

A method for determining the flow rate in a pipe includes measuring a temperature difference between the pipe and the temperature of the surroundings of the pipe and dividing this difference by the difference between the temperature of the fluid entering the pipe and the temperature of the surroundings of the pipe. A non-linear conversion between the ratio derived in this way and the flow rate is used to estimate the flow rate. Also disclosed are methods for estimating the temperature of the fluid entering the pipe using either the temperature of the pipe or the local air temperature. The first method comprises: periodically receiving measurements of the temperature of the conduit; determining an extremal temperature of the conduit over a preceding time period of predetermined length; and using the determined extremal temperature as an estimate for the fluid temperature. The second method comprises: determining a rolling average of local air temperature over a preceding predetermined period; and using the determined rolling average of local air temperature as an estimate for the fluid temperature.

Description

(54) Title ofthe Invention: Determination of flow rate and fluid temperature

Abstract Title: Determining flow rate in a pipe from temperature difference between pipe and surroundings and between surroundings and fluid entering the pipe (57) A method for determining the flow rate in a pipe includes measuring a temperature difference between the pipe and the temperature of the surroundings of the pipe and dividing this difference by the difference between the temperature of the fluid entering the pipe and the temperature of the surroundings of the pipe. A non-linear conversion between the ratio derived in this way and the flow rate is used to estimate the flow rate. Also disclosed are methods for estimating the temperature of the fluid entering the pipe using either the temperature of the pipe or the local air temperature. The first method comprises: periodically receiving measurements ofthe temperature of the conduit; determining an extremal temperature ofthe conduit over a preceding time period of predetermined length; and using the determined extremal temperature as an estimate for the fluid temperature. The second method comprises: determining a rolling average of local air temperature over a preceding predetermined period; and using the determined rolling average of local air temperature as an estimate for the fluid temperature.

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Determination of flow rate and fluid temperature

The present invention relates to methods for determining a flow rate of a fluid through a pipe and for estimating the inlet temperature of the inlet fluid.

In domestic dwellings and commercial environments there is an increasing focus on environmental responsibility. One focus of this is water saving, and in particular unnecessary water wastage due to leaks for example from dripping taps or burst pipes. Not only is the detection of such things useful, but additional information which allows one to distinguish between these two different scenarios is beneficial.

The present invention aims to detect a flow rate through pipes, and further to estimate the flow rate.

As will be clear, the estimation method uses various temperatures in determining a flow rate. A further aim of the invention is therefore to provide a method for estimating the inlet flow temperature. As will be clear from the discussion below, these two aspects of the invention represent different aspects of a solution to a common problem, specifically, how to improve the detection and quantification of leaks in a fluid conduit system.

Disclosed herein is a method of determining rate of fluid flow through a conduit, the method comprising: determining a first quantity representative of a difference between a temperature of the conduit and a temperature of the surroundings of the conduit; determining a second quantity representative of a difference between a temperature of the fluid entering the conduit and a temperature of the surroundings of the conduit; calculating a third quantity by dividing the first quantity by the second quantity; and estimating the flow rate of the fluid through the conduit based on the third quantity, wherein estimating the flow rate from the third quantity includes performing a non-linear conversion between the third quantity and the flow rate, wherein the non-linear conversion has a higher rate of change of the third quantity with respect to flow rate at lower flow rates than at higher flow rates. The non-linearity of the conversion in this manner provides a high degree of sensitivity at low flow rates. This in turn allows the flow rate to be determined with higher accuracy at low flow rates, which are typical of the undetected situations often encountered in practice. For example, the very high flow rates encountered when a pipe (or conduit) bursts will usually be detected by other means because someone will likely notice flooding, water damage, etc. On the other hand, smaller leaks or dripping taps are less likely to come to a user’s attention, but when left for a long time can represent a significant total loss. The simple relationship set out above is easy to measure and consequently the method provides a convenient way of estimating the severity of a leak, as well as distinguishing between different types of leak, which may have characteristic flow rates. While a common example of a system in which this applies is a water supply system in a building, but the disclosure could apply equally to other fluids, e.g. a gas supply to a building. The determination of the flow rate may be performed only once, continuously, or periodically, depending on the circumstances.

In some cases, the method further comprises a calibration step in which the relationship between the flow rate and the third quantity is determined for the conduit. The thermal response of typical systems can be quite complex and may depend on the size, wall thickness and material of the conduit; the specific fluid in the conduit and the fluid temperature and ambient temperature (i.e. temperature of the surroundings) of the conduit. While the exact response could be calculated, many of these quantities do not vary (or are relatively constant) during use of the system, so an in situ calibration can be performed. For example, the conduit (or pipe - the two terms will be used interchangeably herein) parameters are fixed, and the location of the pipe at the point at which temperatures are measured will often be sheltered so as not to vary much with time, particularly if it is located in a human-inhabited portion of a building where temperatures are typically held relatively constant at around 18-20°C, for comfort reasons. Consequently, the calibration in situ can be a valuable resource, which can be performed by an engineer when the monitoring system is installed, for example. A simple calibration would involve turning on a tap to cause fluid flow through the system. If the fluid flow rate from the tap is measured and the first, second and third quantities measured or calculated (as described herein), then a datum can be recorded for these values. Altering the flow rate for the tap can then be used to acquire further data points. In order to increase the flow rate beyond what is available from a single tap, multiple taps can be opened and the cumulative flow rate used in the recorded data points. Shutting off the entire flow through the system (e.g. using a stopcock) can be used to obtain a baseline, rather than the putative no-flow condition in which all taps and other known outlets are off, since there may be undetected leaks in the system. In some cases, the calibration may be periodically performed or updated. This may involve a manual calibration described above. Alternatively, depending on the context, automatic control of a tap or other outlet may be provided to allow an automatic calibration. Lastly, one or more taps or outlets may have flow meters attached to them, which allows an estimation of the flow rate in the system, and consequently allows data to be collected to improve the calibration.

The calibration may include fitting received data to a mathematical formula. Additionally or alternatively, the calibration may include populating a look-up table with received data. In either case, the estimating step may include referring to data received in the calibration step. This provides a convenient manner in which to provide a user with a quick estimation of the current flow rate. In the event that a user is not expecting any flow rate (or indeed a flow rate of the current estimated magnitude), the estimated flow rate may serve to alert the user to an abnormal condition. In some cases, the method can be configured to detect abnormal flow conditions and provide a targeted alert to a user, e.g. by an audible or visible alarm, sending a message to a mobile telephone, etc.

In the case where the received data are fit to a mathematical formula, the mathematical formula may include one or more of: a logarithmic term; an exponential term; a polynomial term; and/or a hyperbolic term. In other cases, a known function such as a sigmoid, an inverse reciprocal function, or an inverse tangent function may be used, for example.

The method may include allowing the conduit, fluid and/or surroundings temperatures to settle prior to the estimation step being performed. In some cases, the method includes waiting for the first, second or third quantity to settle prior to the estimate step being performed. This improves the stability of the system and therefore ensures that the estimated flow rate is as accurate as possible. Settling in this context may mean that the relevant quantity does not change by more than a particular threshold for at least a certain amount of time, e.g. 0.5°C for at least 1 minute. Additionally or alternatively, settling may mean that the rate of change of the relevant quantity is no larger than a threshold, e.g. no more than 0.5°C/minute. Optionally, the rate of change may be required to remain below the threshold for a minimum amount of time (e.g. 1 minute) before a determination is made that a given quantity has settled. In some cases, no settling is necessary. For example, where a pipe bursts and flow increases rapidly, the rate of change of a particular quantity (likely to be the first quantity) may change rapidly. When the rate of change of this quantity exceeds a particular threshold, e.g. 2°C/minute, the system may interpret this as a burst pipe and send an alert, regardless of the final values settled at. In this case, it is more important to alert a user quickly to the situation than it is to wait for a settled condition. Of course, the specific values given above are strongly dependent on the specific conditions in which the method is applied. Consequently they may vary significantly from these values.

The method may further comprise taking a measurement of a temperature of one or more of: the conduit; the surroundings of the conduit; and/or the fluid entering the conduit. Rather than relying on some other process or inferring the temperature of these quantities, the method may directly obtain some or all of them.

Alternatively or additionally, the system may estimate one or more of the temperature of: the conduit; the surroundings of the conduit; and/or the fluid entering the conduit. This allows the system to perform the calculations set out above irrespective of whether it has direct access to raw temperature data for one or more of the quantities.

Also described herein is a method of estimating the temperature of a fluid entering a conduit, the method comprising: periodically receiving measurements of the temperature of the conduit; determining an extremal temperature of the conduit over a preceding time period of predetermined length; and using the determined extremal temperature as an estimate for the fluid temperature. Using this method, installation of a monitoring system can be greatly simplified since it is not necessary to directly measure the inlet temperature of the fluid, so sensors need not be installed there. When there is no flow through the pipe, the pipe (and stationary fluid within the pipe) gradually settles at the ambient temperature of the pipe. As fluid flows through the pipe, the fluid cools or warms the pipe. Whether the pipe is cooled or warmed by the flow depends on whether the fluid is warmer or colder than the ambient temperature of the pipe. Under the assumption that measured changes in pipe temperature are due to fluid flow (although as set out above changes in pipe temperature due to ambient temperature changes can be controlled for by considering the difference between the pipe temperature and the ambient temperature of the pipe), the extremal pipe temperature (i.e. the highest or lowest) approaches the fluid temperature when the flow rate is large and/or the flow occurs for a long time. The pipe temperature comes closer to the fluid temperature under these conditions. The use of an extremal temperature over a preceding period allows changes in pipe temperature to be correlated with the fluid temperature. The use of a preceding time period allows the system to select an extremal temperature over a reasonable period, in which enough flow to bring the pipe close to the fluid temperature is likely to have occurred. This period should not be overly long, however, to allow the system to update the inlet temperature reasonably often. In practice, for example, the inlet temperature may change by around 0.5°C in a day. A good balance between these two considerations is to use the extremal temperature from the preceding 3 days as the estimated inlet fluid temperature.

The method may include modifying the estimated fluid temperature based on a flow history of fluid through the conduit during the predetermined period. As set out above, the conduit will approach the fluid temperature and will settle at a value close to the fluid temperature.

Exactly how close the temperature of the pipe is to the temperature of the fluid when the system has settled depends in part on how large the flow is and how long it occurs for. In cases where there has been little flow (i.e. only low flow rates, only very short flows, a low total cumulative amount of fluid passing through the system, etc.), it may be beneficial to adjust the estimated temperature to take account of the incomplete settling. For example, since the pipe temperature will only ever approach the fluid temperature and never passes it, where the ambient pipe temperature (the temperature of the pipe’s surroundings) is warmer than the fluid temperature, then the estimated fluid temperature will always be higher than the true fluid temperature. Conversely when the ambient pipe temperature (the temperature of the pipe’s surroundings) is cooler than the fluid temperature, then the estimated fluid temperature will always be lower than the true fluid temperature. It is easy to see whether the fluid temperature is higher or lower than the ambient temperature, since the measured pipe temperature will start to increase or decrease respectively when flow starts.

Where flow has been low, the estimate will not be particularly accurate and it may be beneficial to apply a correction. Even where flow levels have been reasonably high and the estimate is reasonably good, a much smaller correction may be applied. Based on the foregoing discussion, this comprises an increase in the estimated temperature where the ambient pipe temperature is cooler than the fluid and a decrease in the estimated temperature where the ambient pipe temperature is warmer than the fluid. In order to gauge the magnitude of this correction term, the method for determining flow rate from the temperature measurements (described above) can be used to estimate the third quantity, i.e. how close to the fluid temperature the pipe has come based on information relating to the flow rate. By comparing the derived ratio of (the difference between pipe temperature and ambient temperature) to (the difference between the fluid temperature and the ambient temperature) to measurements of pipe and ambient temperatures at a given flow rate, the true fluid temperature can be estimated. In some cases, the estimated term may remain uncorrected when the total flow, maximal flow rate, and/or total time of flow exceed a respective threshold. In cases where one or all of these thresholds are not exceeded, the correction may be applied. Making the correction conditional upon the severity of the discrepancy conserves computational power unless it is important to do so. This may be beneficial where the sensors and processing equipment are battery powered, for example.

It should be noted that the non-linear conversion described above is particularly appropriate for making this correction. This is because the correction term is most important when the flow rate is (or has been) low, which causes a large discrepancy between the estimated and the actual fluid temperature, which in turn implies a large correction term. Since the non5 linear conversion is most sensitive at low flow rates, it is possible to distinguish between flow rates at the low end of the scale and correlate these with a wide range of temperature ratios.

The method may further comprise determining a no-flow condition during the preceding time period and using an alternative temperature in place of the extremal temperature during the preceding time period. In some cases the alternative temperature is the most recent extremal temperature determined after a respective predetermined period had occurred in which flow was detected through the conduit. In cases where the flow has been extremely low, an alternative to correcting the estimate may be to use a previously estimated value. This may be a value which has been determined following a predetermined preceding time period, i.e. by a previous iteration of the method described above in which the flow rate was high enough that the estimated temperature is deemed to be good enough. In effect, this means a value calculated after a period in which a no-flow determination was not made.

Alternatively the previous value which is reverted to could be a corrected estimate as set out above.

Another method of providing an alternative temperature estimate is to use a rolling average of local air temperature over a second predetermined period. The second predetermined period may be 10 days, for example, or it may be related to (e.g. the same as) the predetermined preceding time period. The temperature of stored water typically matches the ground temperature at a certain depth, which warms and cools as the air temperature changes. However, given that the ground has a significant thermal mass, the supply temperature can be considered as a smoothed version of the external temperature. Consequently, the rolling average external air temperature is a good proxy measure of inlet water temperature. Similar arguments apply in respect of other fluids being supplied, since they will be affected by external temperatures in a similar way. It may be beneficial to control for natural temperature variations by always taking the temperature measurement at the same time of day (since days are typically hotter than nights, for example). In addition, since the temperature of a day is strongly affected by factors such as how sunny it is that day, it may be beneficial to wait until the night time to ensure that the net heating effect is captured, but short-timescale variances are controlled for. For example, taking an external air measurement at midnight each day for use in the rolling average provides a good basis for this measurement.

Whichever value is used, it may be better to estimate the temperature in a different manner rather than rely on a poor estimate due to low or no flow in the preceding time period.

The no-flow condition may comprise the difference between the temperature of the conduit and the temperature of the surroundings of the conduit being less than a threshold for the duration of the predetermined period. An example of a suitable threshold is 0.5°C. In some cases, depending on the circumstances, a no flow condition may take other values, e.g. 0.2°C or even 0.1 °C.

Additionally or alternatively, a no-flow condition may comprise the rate of change of the temperature of the conduit being less than a threshold for the duration of the predetermined period. An example of a suitable threshold is 1°C/minute.

Indeed, also disclosed herein is a method of estimating the temperature of a fluid entering a conduit, the method comprising: determining a rolling average of local air temperature over a preceding predetermined period; and using the determined rolling average of local air temperature as an estimate for the fluid temperature. As set out above, this provides a good proxy measurement of the inlet fluid temperature because the temperature of stored water typically matches the ground temperature at a certain depth, which warms and cools as the air temperature changes. However, given that the ground has a significant thermal mass, the supply temperature can be considered as a smoothed version of the external temperature. Consequently, the rolling average external air temperature is a good proxy measure of inlet water temperature. Similar arguments apply in respect of other fluids being supplied, since they will be affected by external temperatures in a similar way. It may be beneficial to control for natural temperature variations by always taking the temperature measurement at the same time of day (since days are typically hotter than nights, for example). In addition, since the temperature of a day is strongly affected by factors such as how sunny it is that day, it may be beneficial to wait until the night time to ensure that the net heating effect is captured, but short-timescale variances are controlled for. For example, taking an external air measurement at midnight each day for use in the rolling average provides a good basis for this measurement. The predetermined period in this case may be 10 days, for example.

In some cases, both the rolling average air temperature and the extremal pipe temperature methods may be used together, e.g. to verify one another, or to provide correction terms to improve the estimate. The system may include a learning algorithm to automatically improve the estimate based on historical data, for example.

In some cases the estimated fluid temperature is modified using a different temperature. For example if the rolling average air temperature was used to provide the estimate, it may be modified with extremal pipe temperature data. Similarly, if the extremal pipe temperature was used to provide the estimate, then the rolling average air temperature method may be used to modify the estimate. In any case, of course, the ratiometric method set out above may be used to improve the estimate.

The method may further include making the temperature measurements to calculate the rolling average air temperature or the extremal pipe temperature. This means that the method can be self-contained and not rely on externally sourced data.

The methods of estimating the inlet fluid temperature set out above may be used to provide the inlet fluid temperature for the flow rate estimation method set out above.

Also disclosed herein is a flow measuring device for attaching to a conduit configured to carry out any or all of the methods described above. The device may include, where appropriate, one or more temperature sensors; one or more flow rate detectors; one or more detectors for attaching to taps and/or outlets; one or more processors for receiving raw data and performing the calculations set out above; and/or one or more communications interfaces for communicating with remote devices (including sensors, servers, networks, etc.).

Specific examples will now be disclosed with reference to the Figures, in which:

Figure 1 shows a flow monitoring system installed on a conduit;

Figure 2 shows an example of various temperatures changing over time in response to a flow condition;

Figure 3 shows an example of a non-linear conversion between the flow rate and a temperature ratio;

Figure 4 shows data on rolling extremal temperatures;

Figure 5 shows data on rolling average external air temperatures;

Figure 6 is a flow chart illustrating a method disclosed herein;

Figure 7 is a flow chart illustrating another method disclosed herein; and Figure 8 is a flow chart illustrating a further method disclosed herein.

Consider Figure 1, which schematically shows a fresh water plumbing network 100 for a domestic dwelling. In this embodiment, a single supply pipe 102 enters the dwelling and branches into multiple branches 104, 106. Herein, we refer generically to the pipe 102, 104,

106 as 108, the pipe being a form of fluid conduit carrying clean water 110, a fluid, which flows into the property in the direction of the arrow labelled 112.

In order to make a flow determination - typically to determine whether there is a leak from the plumbing network - a flow determination apparatus is used. In this example, a single housing 114, but examples with multiple housings at different locations on the plumbing network are possible. Similarly, there may be an on-board processing unit inside the housing to locally perform the calculations discussed herein, or the sensor may be configured to communicate with a remote processor.

Each housing 114 may house first 116 and second 118 temperature sensors. The first temperature sensor 116 is to measure the temperature of pipe 108, whereas the second temperature sensor 118 measures the local ambient temperature (i.e. the temperature of the surroundings of the pipe). The exact design of the housing 114 is not critical to the method or system, so long as the first sensor is in good thermal contact with the pipe 108, and the second sensor is able to accurately measure the ambient temperature. Other desirable features include the attachment of the housing 114 to the pipe 108 not constituting too great a thermal load and ease of installation.

Each housing may also be provided with a transmitter - such as a Bluetooth (RTM) Low Energy transmitter - which can carry out some processing and/or transmits data elsewhere. Each housing may also be provided with a power source (not shown), such as a battery, to power the transmitter and the temperature sensors.

The data collected by the sensors can be used to demonstrate how a flow determination can be made with this apparatus. The apparatus relies on the fact that, if there is no flow in the pipe 108, then the temperature of the pipe - sensed by the first temperature sensor will converge with the ambient temperature - sensed by the second temperature sensor.

When there is a substantial flow, the temperature of the pipe 108 will diverge from the ambient temperature. This is most notable in domestic plumbing networks the closer to the point of entry of the supply pipe 102 into the premises. This is because the temperature of the fluid flowing through the pipe 108 - here, water - is likely to be different to the ambient temperature. In the domestic plumbing context, this is because pipes external to the dwelling are buried in the ground. In temperate climates such as the United Kingdom, it is likely that the water flowing into a dwelling will be significantly lower than ambient temperature and this explanation will be based on that assumption, although this embodiment will function well also with water significantly above ambient (for example, in an air-conditioned home in a hot climate).

This means that, in the example of a temperate climate, a substantial flow will lead to a sudden drop in temperature of the fluid flowing through the pipe 108 and so a drop in the temperature of the pipe 108 itself. Where there is a low flow, the temperature of the fluid in the pipe 108 and so the pipe 108 itself will still move towards ambient temperature. We have appreciated that the ratio of the difference between pipe ambient temperatures to the difference between pipe and fluid temperatures can be used to determine whether there is any flow and to estimate the level of that flow. Additionally, this effect can be used to estimate the inlet fluid temperature, since the pipe tends towards that temperature, with larger flows resulting in the pipe temperature settling closer to the inlet fluid temperature than smaller flows do. This allows the flow rate to be estimated whenever a constant flow is detected. In addition to the ambient and pipe sensor data, the algorithm takes as an input the water supply temperature, which can also be estimated.

The sensing unit may be a battery-powered device with Wi-Fi connectivity. Since powering up Wi-Fi modules consumes a significant amount of battery, the device may connect to the leak platform only every 6 hours, unless a leak has started or ended in which case it may send an alert at that time, classifying the leak as small or large using the methods set out herein.

A schematic example 200 of temperature measurements taken by the exemplary sensing apparatus of Figure 1 is shown in Figure 2. Specifically, the temperature of the pipe 220, its surroundings 222 and of the inlet temperature of the fluid 224 are plotted with respect to time. The plot 200 encompasses a transition from a low- or no-flow situation to a (high) flow condition. The times at which flow is occurring are indicated by arrow 226. Although the time and temperature scales are arbitrary, the time scale is on a small enough scale that the ambient 222 and fluid 224 temperatures do not change significantly. Indeed, since this is a schematic, the plot is simplified to show no change in these quantities in order to clarify the desired effect.

It can be seen from plot 200 that the effect of flow stating is for the pipe temperature 220 to drift away from the ambient temperature 222 and come closer to the fluid temperature 224.

The plot 200 also shows two derived quantities, a first quantity 228 obtained by subtracting the pipe temperature 220 from the ambient temperature 222 and a second quantity 230 io obtained by subtracting the fluid temperature 224 from the ambient temperature 224. A third quantity it obtainable by dividing the first quantity by the second quantity. It can be readily seen that the third quantity will be small (indeed, approaches zero) as the pipe 220 and the ambient 222 temperatures come close to one another (or even become equal). As described above, this occurs when the flow rate is low. Similarly, it is clear that the third quantity approaches the value of one when the pipe 220 and fluid 224 temperatures come close to one another. As set out above, this corresponds to a high flow condition.

Note that the preceding discussion holds even if the ambient 222 and fluid 224 temperatures vary with time. This is because the method considers difference between ambient 222 and pipe 220 temperatures and between ambient 222 and fluid 224 temperatures. In this way variance in the temperatures shown as constant in the plot 200 are taking into account by the method, and are thereby controlled for.

It can be seen from Figure 2 that the ratio is clearly defined at all times (since it is a simple subtraction). In some cases it may be preferable to wait for the various temperatures to settle to a roughly constant value before determining the first 228, second 230, and third quantities, to improve the accuracy of the determination.

A sample plot 300 comparing the flow rate to the third quantity (i.e. the ratio of [the difference between the ambient 222 and pipe 220 temperatures] to [the difference between the ambient 222 and fluid 224 temperatures]) is shown in Figure 3. Note the logarithmic scale for the flow rate. It is clear that the relationship in this case is a non-linear one in which the rate of change of the ratio with respect to flow rate is much larger at low flow rates than it is at high flow rates. Note that only 3% of the scale of the flow rate causes around 80% of the ratio change to occur. In other words, the governing equation linking the two variables is much more sensitive at low flow rates, and consequently can be used to accurately distinguish between different situations with a higher accuracy when the flow rate is low than when the flow rate is high.

As such, it is possible to accurately discriminate between low flow rates such as a drip and a trickle (e.g. 1 L/h produces a ratio of 0.4 while 5 L/h produces a ratio of 0.8). However it is not possible to accurately discriminate between flow rates when the flow rate is high (e.g. 20 L/h produces a ratio of 0.92 and 25 L/h produces a ratio of 0.93).

In general, the relationship between flow rate and ratio has the following form:

1. At no flow rate, the ratio is zero ll

2. The ratio converges towards an asymptote of 1 as the flow rate increases towards infinity; and

3. The gradient decreases with increasing flow rate.

In order to model the relationship, any function obeying the above rules is a suitable candidate. For example, the relationship between the temperature difference ratio (R) and flow rate (f) may follow any of the following equations:

Inverse reciprocal functions

Functions of the form:

may be used in this context. The variable a can be used to uniformly scale the gradient of the function. Experimentally values of a at or close to 0.5 are seen to be reasonable in typical systems.

Sigmoid functions

Logistic function

These functions take the form:

⁼ (1 + e~^b-r> ~ ¹ and once more varying the value of b changes the steepness of the curve. Values of b at or close to 1 are seen to be reasonable in typical systems.

Inverse-tangent function

These functions take the form:

_R ^tan¹^ /) π and once more varying the value of c changes the steepness of the curve. Values of c at or close to 1 are seen to be reasonable in typical systems.

As will be appreciated linear combinations (appropriately scaled to retain features 1 and 2) of these different equations may also be used to model the relationship.

The ratio is used rather than absolute temperatures as it is more robust to varying differences between the ambient and supply temperature. For example, a flow rate of 1 L/h might achieve a pipe temperature of 16 degrees under an ambient temperature of 20 degrees and a water temperature of 10 degrees, while the same flow might achieve a pipe temperature of 18 degrees given the same ambient temperature but a water temperature of 15 degrees. As such, the difference between the pipe and the ambient temperature is 4 degrees in the first case and 2 degrees in the second case, but the ratio is 0.4 in both cases. Therefore, it is not necessary to adjust absolute temperature thresholds individually for each case, and instead can use the same ratio threshold in all situations.

The curve shown in Figure 3 will depend in general on the exact parameters of the system under consideration. It may be desirable in some cases to calibrate the apparatus during installation, periodically, when a change is made to the system (a new tap is fitted, for example), etc. This calibration effectively means performing measurements and/or calculations to obtain a plot such as that shown in Figure 3, so that the two variables can be linked to one another.

In some cases it is possible to directly measure the inlet fluid temperature in addition to directly measuring the pipe and ambient temperatures. However, it is often impractical to do this, and instead the fluid temperature is estimated. Figure 4 shows a plot 400 of the ambient temperature 422 (shown in dark grey) and the pipe temperature 420 the (shown in light grey) over a period of a few months. The data points are close together and show as a solid mass in parts. Nonetheless, it is clear that the pipe temperature 420 drops below the ambient temperature 422 for large portions of the period being investigated. This is interpreted as being due to flow events, which cause inlet fluid to cool the pipe (as the inlet temperature is in this case cooler than the ambient temperature 422). This shows a convenient method of estimating the fluid temperature - simply consider the extremal temperature reached over a preceding predetermined time period. This line is shown in the plot as a thick black line 432, which considers the extremal temperature (lowest, in this case since the fluid is cooler than the ambient temperature 422) over the preceding three days. This extremal temperature 432 can be used as an estimated inlet temperature. Clearly when large flow events happen typically at least once in a three day period, then the estimate derived in this way will be reasonably accurate. In any case, it may be possible to improve the estimated value in the various ways discussed above.

In most cases, the supply temperature is estimated by taking a rolling 3 day minimum of the pipe temperature, although the exact period used can be changed according to circumstances. The 3 day rolling window was chosen since it provides a good trade-off between assuring that the such a flow event has occurred in that window, and also the estimate stays up to date since the water temperature changes as the outside air temperature changes. The minimum temperature is used since the pipe is assumed to reach the water supply temperature under a high flow rate water usage event (> 100 L/h) lasting a reasonable amount of time (> 5 minutes). Of course, in cases where the inlet water is warmer than the ambient temperature, it will be a maximum temperature which is reached in this way. It is important that the usage event lasts a reasonable amount of time, since the pipe has a certain thermal mass that will take a few minutes to cool down, even under a high waterflow. In practice, changes have been observed of up to 1 degree in 48 hours.

area in which the method fails is when there is no flow for a long period (see e.g. the period between 9 November and 23 November 2016 in Figure 4). Clearly it is necessary to rule-out estimates when there have been no high flow events over the 3 day window (e.g. a house is unoccupied during a holiday). To do so, flow events within the 3 day period are assumed when a minimum temperature is seen such that the pipe temperature is at least 1.5 degrees lower than the ambient temperature at the time of that minimum temperature. If no such event has occurred, an older estimate of the water supply temperature is used, since an older estimate under a high water flow is preferable to a more recent estimate under a small or non-existent water flow. Other methods of improving or replacing the estimate obtained in a no-flow period are described above.

Figure 5 illustrates an alternative method of estimating the fluid temperature. The temperature of stored water typically matches the ground temperature at a certain depth, which warms and cools as the air temperature changes. However, given that the ground has a significant thermal mass, the supply temperature can be considered as a smoothed version of the external temperature.

Here a plot 500 compares the external air temperature 534, a rolling 10-day average of the external air temperature 536 and the measured water from a tap 538 (having waited for the temperature to settle). It is clear that while the air temperature 534 (measured at midnight each night to minimise variability due to day/night and amount of sunlight) varies quite a lot from day to day, the rolling average of this quantity 536 smooths much of the detail out. Moreover, the rolling average 536 correlates well with the measured water temperature 538, albeit with an offset. Once more calibration could be used to bring these two values into closer alignment.

This alternative estimation can be used as well as or instead of the extremal temperature method. In some examples, both methods may be used in conjunction with one another to improve the accuracy.

Turning now to Figure 6, a flow chart 600 is shown illustrating the method of estimating flow rate. The method starts at step 640, in which a first quantity representative of a difference between a temperature of the conduit and a temperature of the surroundings of the conduit is determined.

Next, in step 642 a second quantity representative of a difference between a temperature of the fluid entering the conduit and a temperature of the surroundings of the conduit is determined.

A third quantity is then determined in step 644 by dividing the first quantity by the second quantity.

Finally, in step 646, the flow rate of the fluid through the conduit is estimated based on the third quantity, wherein estimating the flow rate from the third quantity includes performing a non-linear conversion between the third quantity and the flow rate, wherein the non-linear conversion has a higher rate of change of the third quantity with respect to flow rate at lower flow rates than at higher flow rates. This method allows for a simple estimation of the flow rate from some readily obtained or estimated temperature information.

Figure 7 shows a flow chart 700 illustrating a method of estimating the temperature of the fluid entering the system. Starting at step 748, periodically measurements of the temperature of the conduit are received.

Next, at step 750, an extremal temperature of the conduit over a preceding time period of predetermined length is determined. This period may be three days, for example, as described above.

Finally, at step 752, the determined extremal temperature is used as an estimate for the fluid temperature. This provides a simple method of estimating a quantity which is often difficult to measure directly.

Consider now Figure 8. This shows a flow chart 800 illustrating an alternative method of estimating the inlet temperature. Starting at step 854, the method determines a rolling average of local air temperature over a preceding predetermined period, this may be a ten day period, for example. Such information is readily obtained from e.g. weather services.

The rolling average is then used as an estimate for the fluid temperature in step 856. Once more the method provides a readily accessible method of estimating the fluid inlet temperature, without needing to got to the expense and difficulty of installing a temperature sensor.

Claims

1. A method of determining rate of fluid flow through a conduit, the method comprising:

determining a first quantity representative of a difference between a temperature of the conduit and a temperature of the surroundings of the conduit;

determining a second quantity representative of a difference between a temperature of the fluid entering the conduit and a temperature of the surroundings of the conduit;

calculating a third quantity by dividing the first quantity by the second quantity; and estimating the flow rate of the fluid through the conduit based on the third quantity, wherein estimating the flow rate from the third quantity includes performing a non-linear conversion between the third quantity and the flow rate, wherein the non-linear conversion has a higher rate of change of the third quantity with respect to flow rate at lower flow rates than at higher flow rates.

2. A method according to claim 1, further comprising a calibration step in which the relationship between the flow rate and the third quantity is determined for the conduit.

3. A method according to claim 2, wherein the calibration step is performed on installation.

4. A method according to claim 2 or 3, wherein the calibration step is performed periodically.

5. A method according to any one of claims 2 to 4, wherein the calibration step includes fitting received data to a mathematical formula.

6. A method according to claim 5, wherein the mathematical formula includes one or more of:

a logarithmic term; an exponential term; a polynomial term; and/or a hyperbolic term.

7. A method according to any one of claims 2 to 6, wherein the calibration step includes populating a look-up table with received data.

8. A method according to any one of claims 2 to 7, wherein the estimating step includes referring to data received in the calibration step.

9. A method according to any preceding claim wherein the conduit, fluid and/or surroundings temperatures are allowed to settle prior to the estimation step being performed.

10. A method according to any preceding claim, further comprising taking a measurement of a temperature of one or more of:

the conduit;

the surroundings of the conduit; and/or the fluid entering the conduit.

11. A method according to any preceding claim, further comprising estimating one or more of the temperature of:

the conduit;

the surroundings of the conduit; and/or the fluid entering the conduit.

12. A method of estimating the temperature of a fluid entering a conduit, the method comprising:

periodically receiving measurements of the temperature of the conduit; determining an extremal temperature of the conduit over a preceding time period of predetermined length; and using the determined extremal temperature as an estimate for the fluid temperature.

13. The method of claim 12, wherein the predetermined length is 3 days.

14. The method of claim 12 or 13, wherein the estimated fluid temperature is modified based on a flow history of fluid through the conduit during the preceding time period.

15. The method of any one of claims 12 to 14, further comprising determining a no-flow condition during the preceding time period and using an alternative temperature in place of the extremal temperature during the preceding time period.

16. The method of claim 15, wherein the no-flow condition comprises the difference between the temperature of the conduit and the temperature of the surroundings of the conduit being less than a threshold for the duration of the predetermined period.

17. The method of claim 15 or 16, wherein the no-flow condition comprises the rate of change of the temperature of the conduit being less than a threshold for the duration of the predetermined period.

18. The method of any one of claims 15 to 17, wherein the alternative temperature is the most recent extremal temperature determined after a respective predetermined period had occurred in which flow was detected through the conduit.

19. The method of claim 18, wherein the alternative temperature is a rolling average of local air temperature over a second predetermined period.

20. The method of claim 19, wherein the second predetermined period is 10 days.

21. A method of estimating the temperature of a fluid entering a conduit, the method comprising:

determining a rolling average of local air temperature over a preceding predetermined period; and using the determined rolling average of local air temperature as an estimate for the fluid temperature.

22. The method of claim 21, wherein the predetermined period is 10 days.

23. A flow measuring device for attaching to a conduit, comprising:

a housing a temperature sensor mounted in the housing, the housing configured for holding the temperature sensor in good thermal contact with a conduit; and a processor configured to carry out the method of any preceding claim.

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Intellectual

Property

Office

Application No: GB1718195.9 Examiner: Ms Danielle Jones

23. The method of any one of claims 12 to 22, wherein the estimated fluid temperature is modified using a different temperature.

24. The method of claim 24, wherein the different temperature is one or more of: the temperature of the surroundings of the conduit; and the local air temperature.

25. The method of any one of claims 1 to 11, wherein the temperature of the fluid entering the conduit is estimated by the method of any one of claims 12 to

24.

26. A flow measuring device for attaching to a conduit configured to carry out the method of any one of claims: 1 to 11; 12 to 20; 21 or 22; 23 or 24; or

25.

AMENDMENTS TO CLAIMS HAVE BEEN FILED AS FOLLOWS

Claims

1607 18

calculating a third quantity by dividing the first quantity by the second quantity; and estimating the flow rate of the fluid through the conduit based on the third quantity, wherein estimating the flow rate from the third quantity includes performing a non-linear conversion between the third quantity and the flow rate, wherein the non-linear conversion has a higher rate of change of the third quantity with respect to flow rate at lower flow rates than at higher flow rates;

the method further comprising taking a measurement of a temperature of one or more of:

the conduit;

the surroundings of the conduit; and/or the fluid entering the conduit;

wherein the measurement of one or more temperatures is used in determining the first and/or second quantity.

3. A method according to claim 2, wherein the calibration step is performed periodically.

4. A method according to any one of claims 2 or 3, wherein the calibration step includes fitting the estimated flow rate and the calculated third quantity to a mathematical formula.

5. A method according to claim 4, wherein the mathematical formula includes one or more of:

a logarithmic term; an exponential term; a polynomial term; and/or a hyperbolic term. 6. A method according to any one of claims 2 to 5, wherein the calibration step includes populating a look-up table with received data. 7. A method according to any one of claims 2 to 6, wherein the estimating step includes referring to data received in the calibration step. 8. A method according to any preceding claim wherein the conduit, fluid and/or surroundings temperatures are allowed to settle prior to the estimation step being performed. 9. 00 A method according to any preceding claim, further comprising estimating one or more of the temperature of: the conduit; ο the surroundings of the conduit; and/or the fluid entering the conduit. co Ί— 10. The method of claim 9, wherein estimating the temperature of a fluid entering the conduit comprises: periodically receiving measurements of the temperature of the conduit; determining an extremal temperature of the conduit over a preceding time period of predetermined length; and using the determined extremal temperature as an estimate for the fluid temperature. 11. The method of claim 10, wherein the predetermined length is 3 days. 12. The method of claim 10 or 11, wherein the estimated fluid temperature is modified based on a flow history of fluid through the conduit during the preceding time period.

13. The method of any one of claims 10 to 12, further comprising determining a no-flow condition during the preceding time period and using an alternative temperature in place of the extremal temperature during the preceding time period.

14. The method of claim 13, wherein the no-flow condition comprises the difference between the temperature of the conduit and the temperature of the surroundings of the conduit being less than a threshold for the duration of the predetermined period.

15. The method of claim 13 or 14, wherein the no-flow condition comprises the rate of change of the temperature of the conduit being less than a threshold for the duration of the predetermined period.

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16. The method of any one of claims 13 to 15, wherein the alternative temperature is the most recent extremal temperature determined after a respective predetermined period had occurred in which flow was detected through the conduit.

17. The method of claim 16, wherein the alternative temperature is a rolling average of local air temperature over a second predetermined period.

18. The method of claim 17, wherein the second predetermined period is 10 days.

19. The method of claim 9, wherein estimating the temperature of a fluid entering the conduit comprises:

20. The method of claim 19, wherein the predetermined period is 10 days.

21. The method of any one of claims 10 to 20, wherein the estimated fluid temperature is modified using a different temperature.

22. The method of claim 21, wherein the different temperature is one or more of:

the extremal temperature of the conduit in the case where the estimated fluid temperature is derived from the rolling average air temperature; and the rolling average local air temperature in the case where the estimated fluid temperature is derived from the extremal temperature of the conduit.