GB2518365A

GB2518365A - Apparatus and method for volumetric estimation of heated water

Info

Publication number: GB2518365A
Application number: GB1316554.3A
Authority: GB
Inventors: Suyeon Kim
Original assignee: EXERGY DEVICES Ltd
Current assignee: EXERGY DEVICES Ltd
Priority date: 2013-09-18
Filing date: 2013-09-18
Publication date: 2015-03-25
Anticipated expiration: 2033-09-18
Also published as: GB2518365B; GB201316554D0

Abstract

An apparatus for estimating heated water is adapted for use with a hot water tank 2 having a cold water inlet 8 at a bottom of the tank and a heated water outlet 6 at a top of the tank. An internal heat source 4 such as a heat exchange coil or immersion heater heats water in the tank. The apparatus includes a control unit 14 and first 10 and second 12 temperature sensors, measuring water temperature at the bottom of the tank or at the inlet and water temperature at a point between the top and bottom of the tank, ideally at the same height as the heat source, respectively. The control unit derives temperature profiles of the water within the tank using the measurements. Each profile has a section of constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank. The variation of temperature profiles over time are used to estimate the volume of heated water drawn off from the tank or the amount of heated water available.

Description

TITLE

Apparatus and method for volumetric estimation of heated water

DESCRIPTION

Technical Field

The present invention relates to the heating, storage and use of hot water for sanitary, space heating, or other purposes, and to an apparatus and method that can be used to estimate the volume of heated water within a tank.

Background to the Invention

It is commonly necessary for heated water to be stored in an insulated tank as part of the hcating system of a building. Typically the tank is provided with cold water from the mains supply and has some form of internal heat source that imparts energy to the cold water, heating it up to a working temperature. Examples of a heat source include an electric immersion heater or a heat exchanger coil through which a heating fluid from a separate boiler or other heat source is circulated. Heated water is then drawn off from the tank as required for sanitary use, space heating, or other purposes. The temperature of the water within the tank is regulated by a thermostat that engages heat input when the temperature of the water falls below the required level, and cuts off the heat input if the temperature reaches or exceeds the required level by more than a small margin determined by the thermostat hysteresis.

In general the purpose of the tank is to act as an energy store that allows heat input to be independent in time and quantity from heat consumption in the form of heated water. This works well as long as the water is at the required temperature when needed, implying the necessity either to predict when demand will occur, or to maintain the water at the required temperature continuously. The latter option is less efficient because keeping the contents of the tank at the required temperature continuously will cause eater heat loss to the environment than if the water is only reheated immediately prior to use. The more intermittent the use of heated water, the greater the inefficiency in continuous heating.

It is therefore useful to be able to predict the timing and volume of heated water use, so that losses can be minimised and energy savings achieved by reheating the tank iu'.u"ediately prior to use of the water. A prediction can be made by recording the times and amounts when heated water is drawn off and deducing from that data the routine behaviour and needs of the users of the heated water. For example, the occupants of a house might regularly get up and take showers at about 8 a.m. every day so a system for efficient production of heated water at the desired temperature would recognise this pattern and ensure the water was heated immediately prior to that time.

A disadvantage of such an arrangement arises when the users desire heated water outside their normal routine e.g., when one occupant has to get up at 6 a.m. This user will wish to know whether there is sufficient heated water available for their shower, so a useful adjunct to the prediction capability is the ability to display the status of the tank. Also, conventionally measurement of heated water drawn off would require installation of a flow meter in the tank outlet pipe. This is a costly item of equipment which is laborious to install so it is preferable to measure the volume of heated water used by a lower cost method. The present invention provides a low cost method.

Summary of the Invention

Because heated water has a lower density (i.e., it is lighter) than cooler water, the contents of any insulated tank storing heated water will stratify into layers from bottom to top where each layer is at a constant temperature that is hotter than the layer below it. Tf heating is taking place, convection currents will arise that circulate the heat input from the heat source and disrupt stratification, but when heating stops, convection ceases, and stratification is restored shortly afterwards. So when heating is not taking place the temperature of the contents of the tank can be described by a rising temperature profile from bottom to top.

The present invention uses a mathematical model of this temperature profile. From the variation over time of the temperature profiles, it is possible to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use. The mathematical model of the temperature profile estimates the temperature of the water at any level in the tank when stratified and not just at the points at which temperature measurements are taken, e.g., by temperature sensors. The comprehensive set of tank temperatures which are thereby available from the mathematical model of the temperature profile facilitate the presentation of the tank status to the user in the form of a simple graphical display or other means.

In particular, the present invention provides an apparatus for volumetric estimation of heated water comprising: a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank; an internal heat source (e.g., an immersion heater or a heat exchanger) for heating water within the tank; a control unit (e.g., an electronic controller); a first temperature sensor located to measure the temperature of the water at the bottom of the tank or the cold water inlet, the first temperature sensor providing first temperature measurements to the control unit; a second temperature sensor located to measure the temperature of the water at an intcrmcdiate point between thc bottom of the tank and the top of thc tank (typically at about the level of the heat source), the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles (e.g. by determining their variation over time) to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use.

In one arrangement, the apparatus can be fitted to existing equipment comprising a tank with an internal heat source. Such existing equipment might further comprise a control unit that can be modified to function as described herein. The existing equipment might also comprise a temperature sensor (e.g., a bimetallic strip sensor) which is used by a convdiltional boiler controller to coiltrol thc onioff operation of the boiler but which has no practical usc in the present invention. In such an arrangement, the apparatus to be fitted to the existing equipment would comprise the first temperature sensor, the second temperature sensor, and a replacement or modified contr& unit. In particular, the present invention provides an apparatus for volumetric estimation of heated water for use with existing equipment comprising a tank having a cold water inlet at a bottom of the tank and a heated water ouflet at a top of the tank, and an internal heat source (e.g., an immersion heater or a heat exchanger) for heating water within the tank; the apparatus comprising: a control unit (e.g., an electronic controller that can be replacement device or a modified version ofan existing device for controlling heat input); a first temperature sensor located to measure the temperature of the water at the bottom of the tank or thc cold water inlct, thc first tempcraturc scnsor providing first temperature measurements to the control unit; aM a second temperature sensor located to measure the temperature of the water at an intermediate point between the bottom of the tank and the top of the tank (typically at about the level of the heat source), the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, the temperature profile having a section of substantially constant tempcrature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles (e.g. by determining their variation over time) to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use.

The present invention provides a method for volumetric estimation of heated water within a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank, an internal heat source (e.g., an immersion heater or a heat exchanger) for heating water being located within the tank; the method comprising the steps of: measuring a first temperature of the water at the bottom of the tank or the cold water inlet; measuring a second temperature of the water at an intermediate point between the bottom of the tank and the top of the tank (typically at about the level of the heat source); using the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and using the temperature profiles (e.g. by determining their variation over time) to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use.

Each temperature profile can also have a second section of substantially constant temperature which approximates the substantially constant temperature within a bottom volume fraction of the tank.

The mathematical model used by the control unit to derive the temperature profiles requires the following key parameters: * The temperature of the hottest water at the top of tank, referred to herein as the top temperature T, and which approximates the substantially constant temperature within the top volume fraction of the tank.

* The temperature of the coldest water at the bottom of the tank, referred to herein as the bottom temperature 3,otom and which approximates the substantially constant temperature within the bottom volume fraction of the tank. The bottom temperature 77 is derived from the first temperature measurements provided by the first temperature sensor. For example, the bottom temperature oj1om can be the lowest temperature measurement provided by the first temperature sensor over a preceding time period or a preceding number of temperature measurements (or timesteps).

* The volume level 17L at which the first section of the temperature profile transitions to the section having a rising temperature gradient within the intermediate volume fraction.

* The slope of the rising temperature gradient within the intermediate volume fraction, referred to herein as the gradients of the temperature profile.

In other words, the tank volume can be divided into the top volume fraction at a substantially constant temperature (i.e., the top temperature the bottom volume fraction at a substantially constant temperature (i.e., the bottom temperature o,iom)' and the intermediate volume fraction, between the bottom volume fraction and the top volume fraction, having a rising temperature profile that forms the gradient joining the bottom and top temperatures.

The key parameters are determined from the first and second temperature measurements taken by the first and second temperature sensors, respectively. The first and second temperature sensors can be of any suitable type or construction, e.g., electronic sensors. The first temperature sensor must be located to measure the temperature of the incoming cold water so is located close to the bottom of the tank or may be conveniently attached to the cold water inlet pipe. If located close to the bottom of the tank, the first temperature sensor may be positioned within the tank or on the outside of the tank body. The second temperature sensor is located at the level of the internal heat source that supplies heat (typically at substantially the same level as the top of the heat source) such that it can measure the maximum temperature within the tank achieved by the heat source. The second temperature sensor may be positioned within the tank or on the outside of the tank body.

The first and second temperature measurements are taken frequently (e.g., every 5 minutes) and can be stored in a log file or memory of the control unit. The bottom temperature 1j0110m can then be derived from the first temperature measurements that are stored in the control unit. The control unit can also be used to control the onIoff operation of the intemal heat source (i.e., the control unit can provide commands for this purpose) and will typically store a preset or programmable maximum temperature nax against which the second temperature measurements are compared to determine when heating of the tank is considered complete so that heat input from the heat source can be terminated. For example, the maximum temperature I can be set at 60°C to ensure bacteria in the water are eliminated. When this temperature is measured by the second temperature sensor the control unit can turn the heat source off. The period of time during which the heat source is turned on to heat the water in the tank to the maximum temperature is referred to herein as a heating event.

The control unit can use the mathematical model to derive a temperature profile at periodic intervals (e.g., every 5 minutes) taking into account the following steps: * Step I -At the end of a heating event (i.e., when the heat source is turned oft) the top volume fraction can be assumed to comprise at least the entire volume of the tank at and above the level of the second temperature sensor -which is typically positioned at about the same level as the heat source -and will often comprise the entire volume of the tank at and above the level of the bottom of the heat source. The top volume fraction is defined as the volume of the tank above the volume level VL and, at the end of a heating event, the volume level is effectively set at a particular value that depends on the physical characteristics of the tank system, e.g., the location of the heat source within the tank, and can be a preset or programmable value that is stored in the control unit. The temperature of the top volume fraction can be assumed to be at the maximum temperature T (i.e., 2 = TmJ. The temperature profile of the intermediate volume fraction rises between the bottom temperature wttom provided by the first temperature scnsor (optionally the temperature measurement provided by the first temperature sensor immediately before the heating cvcnt startcd) and the top temperature 1,,,. Bccausc the control unit knows the top temperature l (which is assumed to be the maximum temperature ?), the bottom temperature T!ottc,m' and the preset or programmable value for the volume level VL, it can determine the gradient S of the rising temperature profile as the difference between the top and bottom temperatures J, divided by the volume level.

Step 2 -After completion of the heating event, the water in the tank inevitably loses heat through the insulation to the surroundings. Tn other words, the top temperature 7, will not remain at the maximum temperature l but will start to gradually decrease. The control unit uses the second temperature measurements provided by the second temperature sensor to determine the rate at which the top temperature J is decreasing. This loss rate is referred to herein as the starting loss rate. Because the control unit knows the top temperature 7, (which is now gradually decreasing at the starting loss rate), the bottom temperature and the preset or programmable value for the volume level VL, it can determine the gradient S of the rising temperature profile as the difference between the top and bottom temperatures I,, divided by the volume level.

* Step 3 -When a user draws off some heated water from the tank through the heated water outlet, an equal volume of cold water is drawn in at the bottom of the tank through the cold water inlet. The period of time during which heated water is drawn off is referred to herein as a draw-off event. The cold water displaces the intermediate volume fraction upwards, resulting in a fall in the second temperature measurements provided by the second temperature sensor as it is now sensing a lower level of the rising temperature profile. Because the control unit knows the volume level VL and the gradient S (see Steps 1 and 2) and the fall in temperature measured by the second temperature sensor, it can determine thc proportion of thc tank volume that was drawn off as the fall in temperature divided by the gradient. The volume that was drawn off (which equals the volume of cold water drawn in) is used to determine a new volume level VL and hence the top volume fraction.

Step 4 -At the end of a draw-off event, heat conducts into the cold water at the bottom of the tank from the hotter layers above, with the effect of creating a new more shallow rising temperature profile in the intermediate volume fraction, i.e., the gradient S of the temperature profile is reduced. The control unit calculates the new gradient S of the temperature profile using the volume level VI. from Step 3, the bottom temperature ottom derived from the first temperature measurements provided by the first temperature sensor, and the top temperature I. To determine the top temperature I,, the control unit determines a loss rate that applies following the draw-off event. This loss rate will be greater than the starting loss rate mentioned in Step 2 because of the reduction in the top volume fraction so the starting body loss rate is increased proportionately to give a current loss rate, which is then used to determine an estimate of the current top temperature 1. Because the control unit knows the top temperature 7, (estimated using the current loss rate), the bottom temperature Tj0//0 and the volume level VL determined in Step 3, it can determine the gradient S of the rising temperature profile as the difference between the top and bottom temperatures divided by the volume level.

-10 -Steps 3 and 4 are repeated whenever a draw-off occurs.

In general terms, the mathematical model can apply a loss rate to the temperature of the hottest water at the top of tank. In one arrangement, the loss rate is determined using the second temperature measurements provided by the second temperature sensor. In one arrangement, the loss rate is determined using the second temperature measurements provided by the second temperature sensor immediately after a reheating event and is adjusted in accordance with a temperature differential between the water temperature and the ambient temperature outside the tank after a draw off event. This reflects the fact that there is a reduced volume of heated water within the tank.

It will be readily understood that the control unit maintains a current value for the top temperature T, (which can be equal to the maximum temperature Tmax at the completion of a heating event, or subsequently modified by an appropriate loss rate), the bottom temperature, the volume level TI, and the gradient S. In this way, it can determine at any time the complete temperature profile and the volume of heated water drawn off from the tank during a draw-off event.

The mathematical model is not an exact representation of the actual temperature profile and, in one arrangement of the present invention, a correction can be applied when the volume level VL exceeds a threshold volume level, typically about two thirds of the tank volume. This is because the temperature profile model can sometimes tend to over-estimate the top temperature 7, in this situation. If Steps 3 and 4 result in a volume level TI that is above the threshold volume level, the gradient S and the bottom temperature Tj,o,jom are used to independently calculate the water temperature at the threshold volume level. If the calculated water temperature is less than the value of the top temperature obtained from the cooling rate calculation in Step 4 above, it is taken as the new top temperature.

In one arrangement of the present invention, reheating of the water in the tank can be initiated by the control unit. Criteria that can be employed to decide when to initiate reheating include inter a/ia the time of day, a low value for the estimated top temperature, a low value for the second temperature measurement provided by the second temperature sensor, a high value for the volume level, or a combination thereof. The present invention allows this decision to be made on an efficient basis depending on the circumstances of the application. Once reheating takes place, the complction of the heating event brings the mathematical model back to Step 1.

Drawings Figure 1 is a schematic drawing showing an apparatus according to the present invention, the apparatus including a cylindrical water tank; Figure 2 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank; Figure 3 is a schematic drawing showing the temperature distribution within the water tank as a function of the volume fraction of the tank; Figure 4 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank immediately after reheating; Figure 5 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank immediately after a first draw-off event; Figure 6 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank settling down after a first draw-off event; Figure 7 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank immediately after a second draw-off event; Figure 8 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank settling dowil after a secoild draw-off event; Figure 9 is a graph showing the temperature distribution within the water tank as a function of the volume fraction of the tank when the top volume fraction falls below a threshold level; Figure 10 is a flow diagram for the determination of volume level within the water tank; -12 -Figure 11 is a flow diagram for the determination of a top temperature within the water tank; and Figure 12 is an example of a water tank temperature display.

An apparatus according to the present invention is shown in Figure 1.

An insulated cylindrical water tank 2 is equipped with an internal coil heat source 4 that can bc supplied with hot water (or othcr hcat carrying fluid) from a boiler (not shown). The water within the body of the tank is then heated by conduction from the heat source and may be drawn off at the top of the tank 2 through a heated water outlet 6. Water drawn off is replaced by cold water supplied via the cold water inlet 8 at the bottom of the tank 2. First and second temperature sensors 10, 12 respectively measure the temperature of the cold water inlet pipe at the point where it enters the tank 2 and the temperature of the water at a height level corresponding generally to the top of the heat source 4.

An electronic control unit 14 reads the temperature measurements provided by the first and second temperature sensors 10, 12 at frequent intervals (at least every 5 minutes) and stores the temperature values in a log file or memory. An interval between temperature measurements is referred to herein as a timestep. The first temperature sensor 10 provides first temperature measurements 1 and the second temperature sensor 12 provides second temperature measurements T2 which are used by the electronic control unit 14 to derive the temperature profiles.

The electronic control unit 14 has a display 16 which uses coloured or shaded bars (e.g., darker shading or redder colour indicates hotter water) to indicate the temperature of the water at certain levels within the tank 2. The user can then see at a glance the volume of hot water within the tank and its temperature.

The electronic control unit 14 stores two temperature values and Tmjn which can be preset or programmable. Tmjn is the temperature that is considered to be the -13 -minimum acceptable temperature for the water in the tank and when the temperature measurements indicate it has been reached, the electronic control unit 14 initiates a request to the boiler for reheating to commence. Tma is the temperature at which the electronic control unit 14 considers the tank 2 to be frilly heated (e.g., 60°C). When the temperature measurements indicate that this maximum temperature has been reached, the electronic control unit 14 requests the boiler to cease heating. The interpretation of the first and second temperature measurements provided by the temperature sensors 10, 12 is part of the operation of the mathematical model which will now be described.

Mathematical model of temperature profile A summary of the mathematical notation used by the mathematical model is given in

Table 1.

A typical temperature profile within a tank of the type shown in Figure 1 is given by the dashed line in Figure 2. This plots the temperature of a horizontal level within the tank against the volume of the tank up to that level expressed as a fraction of the normalised volume of the tank (i.e., the bottom of the tank = 0 and the top of the tank = 1). This horizontal level is referred to herein as the volume level. Because of the cylindrical shape of the tank, the volume level also conesponds approximately to the fractional height of the tank.

The mathematical model used by the electronic control unit 14 represents the typical temperature profile as a set of three straight lines -the solid lines in Figure 2. Such a temperature profile comprises three distinct sections. The first section (section EF) represents the cold water layers at the bottom of the tank (the bottom volume fraction) which have a substantially constant temperature. The second section (section FG) represents the water layers in the middle of the tank (the intermediate volume fraction) which has a rising temperature gradient. The third section (section GH) represents the heated water layers at the top of the tank (the top volume fraction) which have a substantially constant temperature. These volume fractions within the tank 2 are also shown in Figure 3.

-14 -The electronic control unit 14 uses the first and second temperature measurements 11, T from the temperature sensors 10, 12 to determine the temperature profile as an approximation to the typical tcmperature profile shown in dashed linc in Figure 2 and to maintain the temperature profile as it changes during normal use, e.g., in response to heat loss from the tank 2 and when heated water is drawn off by the user.

To illustrate how the temperature profiles are determined and maintained by the electronic control unit 14, the following description relates to a cycle of normal use starting with the heating of the water in the tank (a heating event), followed by a succession of draw-off events and tank cooling, and ending with re-heating. At each stage the key parameters of the mathematical model that are determined are: * -the temperature of the hottest water in the tank 2, i.e., the temperature of the third section of the temperature profile which is the horizontal line GH in Figure 1 * -the lowest temperature in the tank, i.e., the temperature of the first section of the temperature profile which is the horizontal line EF in Figure 2..

* VL -the volume level at which the third section of the temperature profile transitions to a second section with a rising temperature gradient, i.e., point G in Figure 2.

* S -the slope or gradient of the second section of the temperature profile, i.e. the slope or gradient of the straight line FO in Figure 2.

The first temperature measurements] provided by the first temperature sensor 10 provide information on both cold water inlet temperature (e.g., when a draw-off event causes cold water to be drawn into the tank 2 through the cold water inlet) and the temperature of the water at a volume level of about 0.12 when the water is stratified, i.e., when there is no draw-off or heating in progress. The first temperature measurements] can be used to determine the bottom temperature I,,,&,m which can be lowest recent temperature measured by the first temperature sensor 10. In other -15 -words, the first temperature measurements J provided over a preceding time period (e.g., 30 minutes) or a preceding number of timesteps can be analysed and the lowest value used as the bottom temperature wflorn Thc second temperature sensor 12 is typically located at a volume level of about 0.33.

The bottom of the heat source 4 is typically located at a volume level of about 0.15.

At the end of a heating event During a heating event, energy is input to the tank 2 via the heat source until the second temperature measurements T2 provided by the second temperature sensor 10 reach Tnaax when the electronic control unit 14 turns the heat source off At the end of the heating event, the top volume fraction is assumed to comprise the entire volume of the tank at and above a level near the bottom of the heat source. In other words, the top volume fraction starts at a volume level of about 0.20 and continues to a volume level of 1.0 as shown in Figure 4. This means that the volume level VL at which the third section of the temperature profile transitions to a second section is about 0.20 and the top volume fraction corresponds to about 80% of the tank volume. The value of the volume level TI at the end of a heating event will be a preset or programmable value that is used by the electronic control unit 14 and will depend on the particular tank and heat source combination.

The temperature of the top volume fraction can be assumed to be at the maximum temperature Trnax at which the heat input stops. Immediately following a. heating event the bottom volume fraction is assumed to be zero, i.e., the temperature profile does not include the first section represented in Figure 2 by the horizontal line EF.

Since the second temperature sensor 12 determines the temperature at which heating ceases the second temperature measurements T provided to the electronic control unit 14 can also be assumed to be at the maximum temperature T hence: -16 -(1) The slope or wadient S of the second section of the temperature profile is given by: = -OttO (2)

VL

The temperature profile shown in Figure 4 can therefore be determined by the mathematical model on the basis of the key parameters.

It will be readily appreciated that, after completion of the heating event, the contents of the tank will lose heat through the insulation to the surroundings. At cach timestep after the end of the heating event: = T -ooI (3) where Tcoc, is the estimated loss in temperature due to cooling computed at each timestep from the known loss rate of the tank 2 immediately after reheating (when the cooling rate is the starting loss rate and is given by the small difference in temperature between successive measurements of T by the second temperature sensor 12). Once a draw-off takes place this measured cooling rate must be adjusted to give the current cooling rate using an algorithm which increases the cooling rate with increasing volume level I'lL (and hence a corresponding reduction in the top volume fraction and increase in the ratio of surface area to volume) An example of a method for calculating J, is described below. But other methods can be used where appropriate.

At the end of a draw-off event During a draw-off event, cold water is drawn in at the bottom of the tank 2 through the cold water inlet S to replace heated water that is drawn off at the top of the tank -17 -through the heated water outlet 6. This causes the temperature gradient shown in Figure 4 to be displaced upwards. Figure 5 shows the straight line that represents the second section of the temperature profile shifted from AB to A'B' whilst the gradient or slope S stays the same. The second temperature measurements iT. provided by the second temperature sensor 12 will decrease to iT'2 and the electronic control unit 14 uses the difference between the measurements before and after the draw-off event to calculate the change in the volume fraction level VL using the slope or gradient from equation (2) as follows: (4) AVL= ( (7 1ottom)/VL Thc same calculation can be carried out using the first temperature measurements 1 and 27 (provided before and after the draw-off event) as follows: AVL= (6) (? Iottom)/VL By taking the larger value from these two calculations of Vt a more accurate result is obtained since it is possible that one of the first and second temperature sensors 10, 12 may be located where the actual temperature profile is curved as shown by the dashed line in Figure 2 and so a smaller temperature change occurs leading to an underestimate of the volume level.

Thc top volume fraction (i.e., the amount of heated water that is available in the tank) can be taken to include the contents of the tank above the volume level Vt. The change in the volume level Vt can therefore be used to determine the change in the top volume fraction, i.e., how much heated water remains in the tank 2. For example, -18-Figure 5 shows that the volume level VL changes from about 0.2 to about 0.39. This means that before the draw-off event the top volume fraction is about 80% of the tank volume. But after the draw-off event the top volume fraction is oniy about 61% of the tank volume.

As time passes following a draw-off event, the temperature at the bottom of the tank (as measured by the first temperature sensor 10) rises as heat is conducted downwards from the intermediate volume fraction immediately above it. The temperature profile therefore settles down over time to a new gradient or slope of A'B instead of AB as shown in Figure 6.

This cycle repeats for each draw-off event. A second draw-off event is shown in Figures 7 and 8. It can be seen that, after each draw-off event, the volume level VL will increase and the top volume fraction will decrease. The volume level VL following the end of each draw-off event can be determined using equations (4) to (6) taking into account the current slope or gradient S. However the temperature profile will typically alter when the volume level VL reaches (or falls below) a certain threshold volume level VL, . In particular, a sharp temperature drop can occur. The threshold volume level VL, can be preset or programmable and is stored in the electronic control unit 14. In practice, the threshold volume level VL, can be between about 0.65 and about 0.75 which is equivalent to a top volume fraction of between about 25% and about 35% of the tank volume.

With reference to Figure 9, if is the temperature of the top volume fraction arising from the natural cooling loss if the sharp temperature drop did not occur then: old = -T0301 (7) -19 -Recalling that the second temperature sensor 12 is typically located at a volume level of about 0.33, if an assumption is made that the temperature at the threshold volume level VL is the same as the present top temperature J, then it is possible to calculate 1 using the gradient between T,, I,, and 1op old as follows: op' op oid' (8) VL-0.33 VL'-0.33 and whcrc: = * + -0.33 (VL' -0.33) (9) op old -T, This takes the hot water tank 2 from reheating to reaching a low level of heated water (top volume fraction). In the apparatus shown in Figure 1, re-heating is initiated by thc control unit 14 whcn falls below a threshold tcmpcrature I, which is likely to occur soon after the volume threshold J/L has been reached. As indicated herein, the decision to reheat may be made on a variety of criteria, or be initiated manually.

The cycle is completed when I reaches flax and the control unit 14 causes heating to cease.

Calculation of loss rate The objective is to take a loss rate (e.g., the starting loss rate mentioned in Step 2 above) and adjust it to reflect the decrease in the volume of the top volume fraction as heated water is drawn off, which causes the loss rate to increase. The top volume fraction can be approximated as a cylinder of diameter ci and height 1, where 1 = (1-VL) as shown in Figure 3.

Then the volume and surface area (sa) of the top volume fraction are given by: -20 -volume = (10) sa=-c12,r+dl,r (11) Loss rate from the temperature difference between the inside and outside of the tank 2 varies in proportion to the surface over volume. The loss rate R can be derived by dividing equation (11) by equation (10) as follows: 41+ 2d Rx (12) dl It is therefore possible to define the loss rate R using a constant k which will be specific to a particular example of the apparatus depending on the quality of the tank insulation: (13) dl Assuming that the height of tank 2 is twice that of the diameter we can replace dwith its normalised value consistent with the volume scale shown in Figure 3, i.e. d = 0.5. Then: (14)

I

A typical figure for starting loss rate measured at Step 2 just after reheating might be 0.05°C per timestep (i.e., T,°01 = 0.05°C) when the top volume fraction 1 is 0.8. Then equation (14) can be used by the control unit 14 to determine the constant k as follows: 0.05 = 2k(3.2 + 1) ,hence k = 0.00476 (15) 0.8 A value for T001 to be used at other values for / can then be obtained as follows: Ioo1 = 20.00476(41+I)ooo95419 (16) However, equation (16) does not take into account the dependency of loss rate on the difference between the temperature of the water in the top volume fraction (J) and the temperature of the room in which the tank is located. As the tank cools, the temperature differential will tend to reduce (assuming the room temperature stays constant) so this effect slows down the cooling rate. If room temperature were to fall, this would tend to increase the cooling rate.

For example, assuming that the temperature of the water was T11 when k was estimated in equation (15) and given that the surrounding room temperature is constant atT0, equation (16) can be modified as follows: 0.009514 + 1(T -T) = T -T (17) max mom Equation (17) is used by control unit 14 to calculate I,,,. If the control unit 14 is part of a heating control system it may have a measured value for T,002, otherwise it can use a default or preset value such as 19°C which will provide adequate accuracy for many purposes.

Practical operation of the example control unit -22 -When the control unit 14 is switched on for the first time, it assumes that is equal tothetemperature measurcdbythc secondtemperature sensor 12, i.e., 1.

If the value of is less than the minimum temperature T11, the control unit 14 can initiatc heating as described herein. Otherwise, the control unit 14 assumes that the bottom temperature TbQ,/011 is equal to the temperature measured by the first temperature sensor 10, i.e., 1ottorn = 1, and the volume level is equal to the level of the second temperature sensor 12, i.e., VL = 0.33 for the particular example shown in Figure 1.

Thc control unit 14 calculatcs the slopc or gradient S using cquation (2) and has enough information to proceed with the determination of a temperature profile.

The control unit 14 calculates a value for the fall in temperature due to cooling at each timestep (7) using a default cooling rate which is replaced by the measured starting loss ratc whcn hcating takcs place for thc first timc.

Following this initialisation, at each timestep the control unit 14 executes the following steps: 1. Check whether reheating is in progress. If no' proceed to the next step. If yes' and T2 is eater than T stop heating and proceed to the next step. If yes' and T, is less than Tmax continue heating.

2. Determine the volume level VL in accordance with the flowchart of Figure 10.

3. Determine the top temperature 1 in accordance with the flowchart of Figure 11. If is less than T11 initiate reheating.

4. Determine the bottom temperature Tjjom as the lowest value of temperature measurements l provided by the first temperature sensor in the last 30 minutes.

-23 - 5. If reheating has taken place, or if 30 minutes have elapsed since a draw-ofL calculate a new value of S using equation (2). Otherwise retain the current value of S. 6. Derive a complete temperature profile from bottom to top of the tank using the key parameters of i VL, and S. Following each timestep, the control unit 14 holds a temperature profile similar to those shown in Figures 4 to 9. It can therefore evaluate the temperature at any level of the tank and use these temperatures for a graphical display. For example, the display could take the form of 4 bars as shown in Figure 12. The bars from top to bottom indicate the temperature at various volume levels such as VL = 0.8, Vt = 0.6, VL = 0.4, and VL = 0.2, respectively. A temperature above the maximum temperature nax is indicated by a black bar, while a temperature below the minimum temperature 1ll is indicated by a white bar. Intermediate temperatures are indicated by shading whose density is proportional to the temperature. it will be readily appreciated that other forms of presentation are possible which make use of colours or temperatures at fewer or more levels.

-24 -d Tank diameter I Height of the top volume fraction k Tank cooling constant R Loss rate of the top volume fraction S Slope of the temperature gradient T Tank bottom temperature bn/.jom Past tank top temperature 27 Present tank top temperature 271,_old Tank top temperature expected from cooling loss T1 Fafl in temperature due to cooling at each timestcp Past temperature measured by the first temperature sensor 10 Present temperature measured by the first temperature sensor 10 Past temperature measured by the second temperature sensor 12 Present temperature measured by the second temperature sensor 12 T Maximum heated water temperature flux Minimum heated water temperature T Room temperature P1)0 VL Past volume level at which the transition from gradient to level temperature takes place VT] Present volume level at which the transition from gradient to level temperature takes place 11 Threshold volume level where the top temperature drops sharply

Table 1

Claims

-25 -CLAIMS1. An apparatus for volumetric estimation of heated water comprising: a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank; an internal heat source for heating water within the tank; a control unit; a first temperature sensor located to measure the temperature of the water at the bottom of the tank or the cold water inlet, the first temperature sensor providing first temperature measurements to the control unit; a second temperature sensor located to measure the temperature of the water at an intermediate point between the bottom of the tank and the top of the tank, the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantiafly constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use.
2. An apparatus for volumetric estimation of heated water for use with existing equipment comprising a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank, and an internal heat source for heating water within the tank; the apparatus comprising: a control unit; -26 -a first temperature sensor located to measure the temperature of the water at the bottom of the tank or the cold water inlet, the first temperature sensor providing first temperature measurements to the control unit; and a second temperature sensor located to measure the temperature of the water at an intermediate point between the bottom of the tank and the top of the tank, the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive tempcraturc proflics of the watcr within thc tank from thc bottom to the top, each temperature profile having a section of substantially collstant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of hcatcd water within the tank that is available for use.
3. An apparatus according to claim 1 or claim 2, wherein the heat source is an immcrsion hcater or a hcat exchanger.
4. An apparatus according to any preceding claim, wherein the control unit is an electronic controller.
5. An apparatus accordillg to any precedillg claim, whereill the intermediate point is about the level of the heat source.
6. An apparatus according to any preceding claim, wherein cach tcmpcraturc profile has a second section of substantially constant temperature which approximates the substantially constant temperature within a bottom volume fraction of the tank. -27 -
7. An apparatus according to any prcccding claim, whcrcin thc control unit derives each temperature profile using a mathematical model that uses the following key parameters: (i) the temperature of the hottest water at the top of tank, (ii) the tcmpcrature of thc coldest watcr at thc bottom of thc tank which is dcrivcd from thc first temperature measurements provided by the first temperature sensor, (iii) the volume level at which the first section of the temperature profile transitions to the section having a rising temperature gradient within the intermediate volume fraction, and (iv) the slope of the rising temperature gradient within the intermediate volume fraction.
8. An apparatus according to claim 7, wherein the mathematical model applies a loss rate to the temperature of the hottest water at the top of tank.
9. An apparatus according to claim 8, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor.
10. An apparatus according to claim 8 or claim 9, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor immediately after a reheating event and is adjusted in accordance with a temperature differential between the water temperature and the ambient temperature outside the tank after a draw off event.
11. An apparatus according to any preceding claim, wherein the control unit includes a log file or memory for storing the first and second temperature measurements.
12. An apparatus according to any preceding claim, wherein the control unit provides commands to control the onioff operation of the heat source.
13. An apparatus according to any preceding claim, wherein the control unit compares the second temperature measurements against a preset or programmable maximum temperature. -28 -
14. An apparatus according to any preceding claim, wherein the control unit derives the temperature profiles at periodic intervals.
15. An apparatus according to any preceding claim, further comprising means for displaying information indicative of the amount and/or temperature of the heated water within the tank.
16. A method for volumetric estimation of heated water within a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank, an internal heat source for heating water being located within the tank; the method comprising thc steps of: measuring a first temperature of the water at the bottom of the tank or the cold water inlet; measuring a second temperature of the water at an intermediate point between the bottom of the tank and the top of the tank (typically at about the level of the heat source); using the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profllc having a section of substantially constant tcmpcraturc gradicnt which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and using the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use
17. A method according to claim 16, wherein each temperature profile has a second section of substantially constant temperature which approximates the substantially constant temperature within a bottom volume fraction of the tank.-29 -
18. A method according to claim 16 or claim 17, wherein each temperature profile is derived using a mathematical model that uses the following key parameters: (i) the temperature of the hottest water at the top of tank, (ii) the temperature of the coldest water at the bottom of the tank which is derived from the first temperature measurements provided by the first temperature sensor, (iii) the volume level at which the first section of the temperature profile transitions to the section having a rising temperature gradient within the intermediate volume fraction, and (iv) the slope of the rising tempcraturc gradicnt within thc intcrmcdiatc volume fraction.
19. A method according to claim iS, wherein the mathematical model applies a loss rate to the temperature of the hottest water at the top of tank.
20. A method according to claim 19, wherein the loss rate is determined using the second temperature measurements.
21. A method according to claim 19 or claim 20, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor immediately after a reheating event and is adjusted in accordance with a temperature differential between the water temperature and the ambient temperature outside the tank after a draw off event.
22. A method according to any of claims 16 to 2i, wherein the first and second temperature measurements are stored.
23. A method according to any of claims 16 to 22, further comprising the step of using the temperature profiles to control the onloff operation of the heat source.
24. A method according to any of claims 16 to 23, wherein the temperature profiles are derived at periodic intervals. -30 -25. A method according to any of claims 16 to 24, flurther comprising the step of displaying infbrmation indicative of the amount and/or temperature of the heated water within the tank.26. An apparatus lbr volumetric estimation of heated water substantially as described herein and with reference to Figure 1.Amendments to the daims have been filed as follows.CLAIMS1. An apparatus for volumetric estimation of heated water comprising: a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank; an internal heat source for heating water within the tank; a control unit; a first temperature sensor located to measure the temperature of the water at the bottom of the tank or the cold water inlet, the first temperature sensor providing first temperature measurements to the control unit; a second temperature sensor located to measure the temperature of the water at an intermediate point between the bottom of the tank and the top of the tank, the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for eee use. *0*. *2. An apparatus for volumetric estimation of heated water, the apparatus being specifically adapted for use with existing equipment comprising a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank, and SO..0 * an internal heat source for heating water within the tank; the apparatus comprising: a control unit; a first temperature sensor located to measure the temperature of the water at the bottom of the tank or the cold water inlet, the first temperature sensor providing first temperature measurements to the control unit; and a second temperature sensor located to measure the temperature of the water at an intermediate point between the bottom of the tank and the top of the tank, the second temperature sensor providing second temperature measurements to the control unit; wherein the control unit uses the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and wherein the control unit uses the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the amount of heated water within the tank that is available for use.3. An apparatus according to claim 1 or claim 2, wherein the heat source is an immersion heater or a heat exchanger.4. An apparatus according to any preceding claim, wherein the control unit is an electronic controller. * *o.. . . . . . 5. An apparatus according to any preceding claim, wherein the intermediate point is at the level of the heat source.* 6. An apparatus according to any preceding claim, wherein each temperature * : ": profile has a second section of substantially constant temperature which approximates the substantially constant temperature within a bottom volume fraction of the tank.7. An apparatus according to any prcccding claim, whcrcin thc control unit derives each temperature profile using a mathematical model that uses the following key parameters: (i) the temperature of the hottest water at the top of tank, (ii) the tcmpcrature of thc coldest watcr at thc bottom of thc tank which is dcrivcd from thc first temperature measurements provided by the first temperature sensor, (iii) the volume level at which the first section of the temperature profile transitions to the section having a rising temperature gradient within the intermediate volume fraction, and (iv) the slope of the rising temperature gradient within the intermediate volume fraction.8. An apparatus according to claim 7, wherein the mathematical model applies a loss rate to the temperature of the hottest water at the top of tank.9. An apparatus according to claim 8, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor.10. An apparatus according to claim 8 or claim 9, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor immediately after a reheating event and is adjusted in accordance with a temperature differential between the water temperature and the ambient temperature outside the tank after a draw off event.11. An apparatus according to any preceding claim, wherein the control unit includes a log file or memory for storing the first and second temperature measurements.12. An apparatus according to any preceding claim, wherein the control unit provides commands to control the onioff operation of the heat source.13. An apparatus according to any preceding claim, wherein the control unit compares the second temperature measurements against a preset or programmable maximum temperature.14. An apparatus according to any preceding claim, wherein the control unit derives the temperature profiles at periodic intervals.15. An apparatus according to any preceding claim, further comprising means for displaying information indicative of the amount and/or temperature of the heated water within the tank.16. A method for volumetric estimation of heated water within a tank having a cold water inlet at a bottom of the tank and a heated water outlet at a top of the tank, an internal heat source for heating water being located within the tank; the method comprising the steps of: measuring a first temperature of the water at the bottom of the tank or the cold water inlet; measuring a second temperature of the water at an intermediate point between the bottom of the tank and the top of the tank; using the first and second temperature measurements to derive temperature profiles of the water within the tank from the bottom to the top, each temperature profile having a section of substantially constant temperature gradient which approximates the temperature gradient within an intermediate volume fraction of the tank, and a first section of substantially constant temperature which approximates the substantially constant temperature within a top volume fraction of the tank; and using the temperature profiles to estimate one or more of the volume of heated water drawn off from the tank, the temperature of the water within the tank, and the * * amount of heated water within the tank that is available for use * 17. A method according to claim 16, wherein each temperature profile has a second section of substantially constant temperature which approximates the * substantially constant temperature within a bottom volume fraction of the tank.* ..,** * * 18. A method according to claim 16 or claim 17, wherein each temperature profile is derived using a mathematical model that uses the following key parameters: (i) the 18. A method according to claim 16 or claim 17, wherein each temperature profile is derived using a mathematical model that uses the following key parameters: (i) the temperature of the hottest water at the top of tank, (ii) the temperature of the coldest water at the bottom of the tank which is derived from the first temperature measurements provided by the first temperature sensor, (iii) the volume level at which the first section of the temperature profile transitions to the section having a rising temperature gradient within the intermediate volume fraction, and (iv) the slope of the rising tempcraturc gradicnt within thc intcrmcdiatc volume fraction.19. A method according to claim iS, wherein the mathematical model applies a loss rate to the temperature of the hottest water at the top of tank.20. A method according to claim 19, wherein the loss rate is determined using the second temperature measurements.21. A method according to claim 19 or claim 20, wherein the loss rate is determined using the second temperature measurements provided by the second temperature sensor immediately after a reheating event and is adjusted in accordance with a temperature differential between the water temperature and the ambient temperature outside the tank after a draw off event.22. A method according to any of claims 16 to 2i, wherein the first and second temperature measurements are stored.23. A method according to any of claims 16 to 22, further comprising the step of using the temperature profiles to control the onloff operation of the heat source.24. A method according to any of claims 16 to 23, wherein the temperature profiles are derived at periodic intervals.
25. A method according to any of claims 16 to 24, flurther comprising the step of displaying infbrmation indicative of the amount and/or temperature of the heated water within the tank.
26. An apparatus lbr volumetric estimation of heated water substantially as described herein and with reference to Figure 1.