WO2002065079A1

WO2002065079A1 - Method and device for determining a coefficient of heat transfer from a sensor assembly to a fluid

Info

Publication number: WO2002065079A1
Application number: PCT/NL2002/000091
Authority: WO
Inventors: Frederik Van Der Graaf; Johannes Franciscus Maria Velthuis; Jozef Franciscus Catherina Smeets; Pieter Johannes Van Os; Ronald Zeelen; Alexander Willem Van Herwaarden; Frank Robert Riedijk
Original assignee: Nederlandse Organisatie Voor Toegepast-Natuurwetenschappelijk Onderzoek Tno
Priority date: 2001-02-12
Filing date: 2002-02-12
Publication date: 2002-08-22
Also published as: NL1017335C2

Abstract

Device and method for determining a heat flow to a fluid (15), comprising at least one thermodynamic sensor (1) and processing means connected to the at least one thermodynamic sensor (1). The processing means are equipped to calculate heat flows from and to the plurality of thermodynamic sensors (1) to the fluid (15) and to determine the coefficient of heat transfer from the heat flows associated with different ones of the plurality of thermodynamic sensors, the different thermodynamic sensors of the plurality of thermodynamic sensors being operated at different temperatures.

Description

Method and device for determining a coefficient of heat transfer from a sensor assembly to a fluid

The present invention relates to a method and device for determining a coefficient of heat transfer from a sensor assembly comprising a plurality of thermodynamic sensors to a fluid. This method and device can be used, inter alia, for deriving the flow rate and/or direction of flow in a fluid, such as a liquid or a gas.

Flow sensors are generally known and are used in many fields, such as the determination of air speed. Many flow sensors work on the basis of the thermodynamic principle. Sensors that work on the basis of this principle feed a known quantity of thermal energy to the fluid and determine the resulting rise in temperature. In another embodiment the sensor maintains a specific temperature difference between the sensor and the fluid and determines the quantity of thermal energy that has to be supplied in order to maintain this difference. In order to determine the temperature difference a separate temperature sensor is used to determine the absolute ambient temperature.

Disadvantages of these sensors are that a separate temperature sensor is required and that this has to be placed in the fluid in order to be able to measure a relevant ambient temperature. A further disadvantage is that the resulting structure of the sensor is not flat, which is disadvantageous for the accuracy of the measurement. The robustness of such sensors is also inadequate for some applications.

One aim of the present application is to provide a method and a device for determining a coefficient of heat transfer to a fluid which are robust and make compact construction possible.

In a first aspect this aim is achieved by a method of the type defined in the preamble, comprising the steps of calculating heat flows from and to the plurality of thermodynamic sensors to the fluid and determining the coefficient of heat transfer from the heat flows associated with different ones of the plurality of thermodynamic sensors, the different thermodynamic sensors of the plurality of thermodynamic sensors being operated at different temperatures. As a result of the use of two or more sensors it is not necessary to determine the temperature of the fluid individually and in principle the sensitivity to external influences (such as heating by solar radiation and heating/cooling of the sensor shell and its surroundings by other sources of heat) also decreases. Moreover, a higher degree of integration can be achieved, as a result of which a more compact device can be produced, partly because fewer external components are needed. A more robust and compact determination is thus possible under diverse conditions.

Sensors of the known type display a discernible reduced accuracy at higher flow rates and have a relatively slow dynamic reaction as a result of thermal capacities. In addition, the accuracy of the determination of the flow and the direction of flow can be disturbed by ambient influences such as heating by sunlight or spatially unequal heating and/or cooling of the sensor shell and its surroundings by other sources of heat.

In a further embodiment of the present invention the step for calculating heat flows from and to the plurality of thermodynamic sensors to the fluid comprises the steps of making a model of heat flows from and to each of the plurality of thermodynamic sensors with the aid of at least one thermal impedance, the at least one thermal impedance having specific thermal characteristics, and the model comprises at least one time-dependent temperature equation over the at least one thermal impedance, supplying heat to the plurality of thermodynamic sensors, measuring a first temperature on one side of the at least one thermal impedance and a second temperature on another side of the at least one thermal impedance and calculating the heat flow to the fluid by entering the first and second temperature of the at least one thermal impedance in the model. Preferably, the specific thermal characteristics of the at least one thermal impedance comprise the thermal capacity and thermal conductivity, expressed in joule/kgK and watt/mK, respectively, if necessary as a function of the temperature.

By means of the model all heat flows from or to the thermodynamic sensor can be determined, modelled as thermal impedances. For each of the heat flows, the paths in the model are fixed in terms of thermal conductivity and thermal capacity. Preferably the thermal impedances are linked to actual structural components of a device that implements the method, such as a layer of known thermal characteristics between the thermodynamic sensor and a fixing body at a lower temperature or the thermal capacity of the thermodynamic sensor itself. The present invention makes it possible to determine the heat flow to the fluid with the aid of parameters that can be measured quickly, such as temperature, and calculations that are quick to carry out. As a result, determinations at a high frequency (for example 100 Hz) are possible and an improved dynamic range in a broad measurement range and improved dynamic characteristics are produced. The accuracy of the determination can be influenced by incorporating thermal impedances to possible heat sources and heat sinks in the model in greater or lesser detail.

With the aid of the present invention it is possible, for example, to calculate a shearing stress in the fluid from the coefficient of heat transfer, for example on the basis of an empirically determined relationship. Inter alia, the influence of the geometry of the device that contains the at least one thermodynamic sensor is incorporated in the empirically determined relationship.

In a further embodiment the flow rate and/or direction of flow of the fluid is determined from the coefficient of heat transfer. In this embodiment as well, this is preferably achieved using an empirically determined relationship in which the geometry of the device has been incorporated.

Yet a further embodiment of the present invention comprises the further step of detecting a transition point from a laminar flow to a turbulent flow in the fluid if the derivative of the coefficient of heat transfer as a function of time is above a specific threshold value. If the derivative of the coefficient of heat transfer, determined by means of the present method, as a function of time is above a specific threshold value this is an indication that a substantial change in the coefficient of heat transfer occurs within a short time, which is an indication of a transition from a laminar flow to a turbulent flow, or vice versa. The absolute value of the specific threshold value is greater than the derivative as a function of time in the case of a pure laminar flow or a pure turbulent flow.

In an alternative embodiment the method comprises the further step of detecting a transition point from a laminar flow to a turbulent flow in the fluid by analysing the energy content of the frequency spectrum of the coefficient of heat transfer. A transition from a laminar flow to a turbulent flow is characterised by a shift in the energy content of the frequency spectrum from low to high frequencies.

A further aspect of the present invention relates to a device for determining a coefficient of heat transfer to a fluid, comprising a sensor assembly containing a plurality of thermodynamic sensors and containing processing means connected to the plurality of thermodynamic sensors, the processing means being arranged to carry out the method according to the present invention. The abovementioned embodiments of the method can be implemented effectively using the device. Preferably, the processing means are further equipped to adjust the operating temperature of the plurality of thermodynamic sensors. These temperatures do not have to be constant during operation. As a result it is possible to allow the device to operate in a broad measurement range in diverse external conditions (temperature, pressure, etc.). In one embodiment the device also comprises a supporting body, the plurality of thermodynamic sensors being fixed to the supporting body with the aid of a fixing layer. Preferably, the fixing layer is a fixing layer having specific thermal properties. Because the thermodynamic sensors are fixed to the supporting body, for example with the aid of a thermally conducting adhesive layer, a much more robust device is produced.

In yet a further embodiment the device further comprises, for each of the plurality of thermodynamic sensors, a first temperature sensor for measuring a first temperature of the fixing layer on one side of the thermodynamic sensor, a second temperature sensor for measuring a second temperature of the fixing layer on the supporting body side and a heat sensor for measuring the heat supplied to the thermodynamic sensor.

This preferred embodiment makes it possible for the device to produce data relating to the flow rate at a high frequency (for example at a frequency of 100 Hz) because the device makes use of parameters that can be determined quickly and processing steps that are quick to carry out. In a further embodiment the plurality of thermodynamic sensors consists of a thin chip, for example a silicon chip. This embodiment has the advantage that the thermal capacity of the thermodynamic sensors is limited, as a result of which the dynamic characteristics of the device improve. The thermal capacity of the sensor can be incorporated in the calculations. In yet a further embodiment the sensor assembly is surrounded by an isothermal shell in order to ensure that the effect of a heat source outside the sensor is distributed over the entire sensor assembly. The isothermal shell leads to the temperature gradients outside the sensor assembly and asymmetric with respect to the sensor assembly at the location of the thermodynamic sensors being converted, as it were, into a minimum residual temperature gradient acceptable to the sensor assembly. As a result of the very good heat conduction by the isothermal shell, distribution of the heat takes place, whilst the temperature of the isothermal shell remains virtually homogeneous. The thermodynamic sensors consequently see this virtually homogeneous temperature. In this embodiment the device is even better able to withstand external influences.

Preferably, the supporting body consists of a thermally conducting body that is thermally connected to a cooling element, such as a Peltier element. Because the supporting element is kept at a specific temperature difference compared with the thermodynamic sensors, it is ensured that the supporting body is actually thermally stable in a broad temperature range, or in any event discharges heat with a certain thermal inertia. As a result the dynamic range of the device in question is ensured in a broad temperature range. In a further embodiment an upper side of each of the plurality of thermodynamic sensors is provided with a protective layer, the protective layer being in contact with the fluid during operation. This protective layer offers protection to the thermodynamic sensor against adverse influences from outside, such as against damage by rain, hail, aggressive substances and the like and against wear by, for example, sand. The present invention will now be explained in more detail with reference to a preferred embodiment and the appended drawings, in which

Fig. 1 shows a sectional view of a thermodynamic sensor that is used in a flow sensor according to one embodiment of the present invention;

Fig. 2 shows a sectional view of a flow sensor according to one embodiment of the present invention; and

Fig. 3 shows a partially exposed plan view of the flow sensor in Fig. 2.

Fig. 1 shows a sectional view of a thermodynamic sensor 1 that is used in a device according to the present invention. The device can be used to determine a flow rate and/or direction of flow in a fluid 15, such as a liquid or a gas (for example air) or to determine the shearing stress and/or direction of shear in the fluid. Fields of application of the present device and method are, inter alia, transport means (aircraft, trains, cars, ships), compressors or windmills. The thermodynamic sensor 1 can be a thermodynamic sensor known per se, for example a semiconductor chip that is provided with a measurement point at each edge or corner of the sensor in order also to be able to determine the direction of the flow. This is effected by determining the temperature difference between measurement points at opposite edges or corners.

The thermodynamic sensor 1 is (mechanically) connected to a supporting body 3, via a fixing layer 2, the thermal characteristics of which are preferably known. The supporting body 3 is preferably thermally stable or has a certain thermal inertia. The supporting body 3 can be, for example, a heat sink and the fixing layer 2 can be, for example, an adhesive layer. The fixing layer 2 acts, as it were, as a thermal impedance having a specific thermal capacity and thermal conductivity, which is inserted between the heat source on the thermodynamic sensor 1 and the supporting body 3. Because the thermodynamic sensor 1 is fixed to the supporting body 3 with the aid of the adhesive layer 2, a very robust construction of the flow sensor results. The thermodynamic sensor 1 is preferably constructed as a thin chip which, because of its dimensions, is not well able to withstand mechanical forces, which, for example, can be produced by shocks, raindrops or hail. By supporting the entire surface of the thermodynamic sensor 1, a mechanically strong construction is produced.

In the ideal case the thermodynamic sensor 1 would be completely thermally insulated on the underside, for example by a vacuum, as a result of which all heat generated in the thermodynamic sensor 1 would flow to the environment of the sensor 1. However, this would lead to a far less robust construction of the device.

By constructing the thermodynamic sensor 1 as a thin chip, for example in silicon technology, it is possible also to integrate processing means on the thermodynamic sensor 1 for carrying out signal handling and processing.

The thermodynamic sensor 1 is provided with at least one resistor 4 for measuring the dissipation from the thermodynamic sensor 1. This measurement can proceed very quickly. In addition the thermodynamic sensor 1 is provided with a temperature sensor 5 (one of which is shown in Fig. 1) for determining the (surface) temperature of the thermodynamic sensor 1. The heat-dissipating body is also provided with a temperature sensor 6 for determining the temperature of the heat-dissipating body 3. The resistor 4 can also be used for the controlled supply of heat to the thermodynamic sensor 1.

The functioning of the flow sensor according to the present invention will now be explained. It is assumed that the thermodynamic sensor 1 loses heat to the fluid 15 and to the supporting body 3 (and possibly to other heat sinks). If other heat flows arise, this can be taken into account in an analogous manner.

In order to determine the flow rate of the fluid 15 at high frequency (for example 100 Hz) it is important to know how much heat flows to the fluid 15. This can be determined from the difference given by the heat dissipated in the thermodynamic sensor 1 less the heat flowing to the supporting body 3. The dissipated heat can be determined rapidly with the aid of, for example, resistor 4.

The amount of heat that dissipates to the supporting body 3 can be determined by measuring the temperature on either side of the fixing layer of known thermal characteristics 2. The temperature of the thermodynamic sensor 1 is measured with the aid of temperature sensor 5. If the thermodynamic sensor 1 is constructed as a semiconductor chip, the location of the temperature sensor 5 is not particularly important and the latter indicates the temperature at the transition between thermodynamic sensor 1 and fixing layer 2 with good accuracy. The temperature of the supporting body 3, that is measured with the aid of temperature sensor 6, lags substantially because the temperature distribution over the fixing layer 2 is not linear and varies as a function of time.

In order nevertheless to be able to determine at high frequency the amount of heat that flows via the fixing layer 2 to the supporting body 3, according to the present invention the time-dependent temperature equation over the fixing layer 2 is calculated, using the temperatures measured on either side of the fixing layer 2 as boundary conditions. Similar time-dependent temperature equations for other paths along which heat flows can also be incorporated in a model. To this end it is necessary that the thermal conductivity and thermal capacity of the fixing layer 2 (and, where appropriate, other thermal impedances) are accurately determined (optionally as a function of temperature). Because these are parameters that characterise the fixing layer 2, this can be carried out in advance. The quantity of heat that flows from the thermodynamic sensor 1 to the supporting body 3 can now be calculated from the calculated temperature distribution over the fixing layer 2 (which can be a rapid calculation). This is also carried out by a rapid calculation in the processing means.

The dynamic characteristics of the thermodynamic sensor 1 are known, which dynamic characteristics are characterised by the thermal capacity and conduction of the thermodynamic sensor 1. The dynamic characteristics of the thermodynamic sensor 1 can therefore be taken into account in order to calculate the heat flow from the thermodynamic sensor 1 to the fluid 15 at high frequency (for example 100 Hz).

Conversion of the heat flow to the fluid 15 into a flow rate and/or shearing stress is preferably carried out via calculation of the coefficient of heat transfer. This is a parameter known per se that is an unambiguous function of the flow rate for a specific configuration of the flow sensor and given that the flow in the fluid 15 is laminar or turbulent. In order to be able to take into account the characteristics of the fluid 15, this relationship has been specified in a dimensionless form, as a so-called Nusselt-

Reynold-Prandtl relationship. Parallel flow around a flat plate is taken as an example. The coefficient of heat transfer h_x, determined a distance x away from the front of the plate, can be converted to the air speed outside the boundary layer and then to the local wall shearing stress τ_x with the aid of the following generally known relationships:

Nu = h_xx/λ = 0.332 Re_x ^{0 5} Pr τ_x = 0.644 Re_x ^{"0 5} 0.5 pv² where

Nu is the dimensionless Nusselt number [-]; x is the distance from a point on the plate to the front edge [m]; h_x is the coefficient of heat transfer at distance x [W/mK]; λ is the coefficient of thermal conductivity in air [W/mK];

Re_x is the dimensionless Reynolds number, related to distance x;

Pr is the dimensionless Prandtl number; τ_x is the shearing stress at distance x [N/m²]; p is the density of air [kg/m³]; and v is the speed of air outside the boundary layer.

These relationships apply for a laminar boundary layer (Re_x < 3*10⁵). Other relationships can be established for other geometries and, for example, turbulent boundary layers in order to convert the coefficient of heat transfer to a wall shearing stress. The way in which this is carried out is analogous to what has been described above.

By monitoring the derivative of the calculated coefficient of heat transfer as a function of time it is possible (for identical external conditions) to detect a transition from laminar flow to turbulent flow. As soon as the derivative as a function of time rises above a certain threshold value, there is a substantial change in the coefficient of heat transfer within a short time, which is characteristic of such a transition.

As an alternative, the frequency spectrum of the coefficient of heat transfer can be analysed. A transition from laminar to turbulent flow is characterised by a shift in the frequency spectrum from low to high frequencies. If the aim is for a flow sensor of flat construction it is not possible to use a protruding temperature sensor for the fluid 15. Fig. 2 shows an embodiment of the flow sensor with two thermodynamic sensors la, lb. If the two thermodynamic sensors la, lb are operated at different temperatures, the coefficient of heat transfer (and thus the flow rate of the fluid 15) can be determined from the two heat flows determined. After all, in this case the (unknown) temperature of the fluid 15 will drop out of the equations. This is possible only if the coefficients of heat transfer of the two thermodynamic sensors la, lb are identical, which can be achieved by keeping the dimensions of the thermodynamic sensors la, lb small and placing them close to one another. Preferably, the two thermodynamic sensors la, lb are then not placed too close to one another or downstream of one another in order to prevent them influencing one another as a result of the thermal boundary layer.

In yet a further embodiment of the flow sensor according to the present invention the flow sensor is provided with two or more thermodynamic sensors la, lb. Depending on the conditions (orientation of flow with respect to the thermodynamic sensors), two sensors which do not influence one another can then be switched on.

Combination of the signals from two or more thermodynamic sensors la, lb also has the advantage that environmental influences that have the same effect on both thermodynamic sensors la, lb drop out in the final result. This applies, for example, to the influence of (reflected) sunlight on the flow sensor or other external conditions.

By setting the operating temperature of the two thermodynamic sensors la, lb in the absolute sense and with respect to one another and controlling the dissipated energy in each of the thermodynamic sensors la, lb, the flow sensor can be kept in an optimum working range in diverse environmental conditions and rapid and accurate measurements over a wide range are possible.

In order to calculate the coefficient of heat transfer a number of characteristic properties of the fluid 15 must be known, such as the temperature, pressure, density, viscosity, composition and/or the moisture content. However, it can be demonstrated that these properties do not have to be determined with very high accuracy, so that it is also possible to determine these in a more advantageous location (that is to say not just above the thermodynamic sensor la, lb).

Preferably, the flow sensor according to the present invention is provided with processing means that are equipped to carry out the abovementioned calculations. Preferably, the processing means are integrated on the thermodynamic sensor 1, so that signal processing can take place locally, for example in silicon technology. As an alternative, the measured signals (from the resistor 4 and the temperature sensors 5, 6) are fed to the outside via conductors, in order to be processed remotely by processing means in accordance with the abovementioned calculations.

Fig. 2 shows a cross-section of a flow sensor according to the present invention. Fig. 3 shows the same flow sensor in a partially exposed plan view. The flow sensor has a housing 12 within which a supporting body 3 is placed. The temperature of the supporting body 3 is kept at a specific, low value at the bottom, as a result of which a temperature difference is produced compared with the thermodynamic sensor 1 and the supporting body 3 will act as a heat sink. This can be achieved, for example, with the aid of a cooling element 13, such as a Peltier element.

The housing 12 is provided at the top (over which the fluid 15 flows) with an opening in which a mask 10 is fitted. The mask 10 is provided with two openings for the two thermodynamic sensors la, lb. In the preferred embodiment shown in Fig. 2 a protective layer 9a, 9b has been placed above the thermodynamic sensors la, lb, which protective layers protect the thermodynamic sensors la, lb against outside influences (such as scratches or wear).

The thermodynamic sensors la, lb are fixed to the supporting body 3 with the aid of adhesive layers 2a, 2b. For reasons of clarity further details, such as the location of temperature sensors 5, 6 and wiring of the thermodynamic sensors la, lb, have been omitted from Fig. 2. Connection of the chip containing the thermodynamic sensors la, lb to the outside world can, for example, take place via the flexible printed-circuit board indicated by reference numeral 11. For the sake of clarity a possible location of temperature sensor 6 for measuring the temperature of the supporting body 3 is shown in Fig. 3, close to the transition from heat-dissipating body 3 to the fixing layer 2b.

In Figs 2 and 3 it is furthermore shown that the flow sensor has a housing 12 that surrounds the heat-dissipating body 3 as an isothermal shell. Openings are made in the isothermal shell 12 only at the location of the thermodynamic sensors la, lb. The isothermal shell 12 provides a further reduction in the sensitivity of the flow sensor to external influences by evenly distributing the heat that enters the sensor from a specific point outside the sensor over the entire sensor. It will be clear to those skilled in the art that the examples shown are merely embodiments of the present invention and that variants of these examples are also considered to be incorporated in the present invention.

Claims

1. Method for determining a coefficient of heat transfer from a sensor assembly comprising a plurality of thermodynamic sensors (1) to a fluid (15), comprising the steps of: calculating heat flows from and to the plurality of thermodynamic sensors (1) to the fluid (15); determining the coefficient of heat transfer from the heat flows associated with different ones of the plurality of thermodynamic sensors, the different thermodynamic sensors of the plurality of thermodynamic sensors being operated at different temperatures.

2. Method according to Claim 1, wherein the step for calculating heat flows from and to the plurality of thermodynamic sensors to the fluid comprises the steps of: making a model of heat flows from and to each of the plurality of thermodynamic sensors (1) with the aid of at least one thermal impedance, the at least one thermal impedance having specific thermal characteristics, and the model comprises at least one time-dependent temperature equation over the at least one thermal impedance, supplying heat to the plurality of thermodynamic sensors (1), measuring a first temperature on one side of the at least one thermal impedance and a second temperature on another side of the at least one thermal impedance and calculating the heat flow to the fluid (15) by entering the first and second temperature of the at least one thermal impedance in the model.

3. Method according to Claim 2, wherein the specific thermal characteristics of the at least one thermal impedance comprise a heat capacity and a thermal conductivity.

4. Method according to Claim 1, 2 or 3, comprising the further step of calculating a shearing stress and/or direction of shear in the fluid (15) from the coefficient of heat transfer.

5. Method according to Claim 1, 2 or 3, comprising the further step of calculating the flow rate and/or direction of flow of the fluid (15) from the coefficient of heat transfer.

6. Method according to Claim 5, comprising the further step of detecting a transition point from a laminar flow to a turbulent flow in the fluid (15) if the derivative of the coefficient of heat transfer as a function of time is above a specific threshold value.

7. Method according to Claim 5, comprising the further step of detecting a transition point from a laminar flow to a turbulent flow in the fluid (15) by analysing the energy content of the frequency spectrum of the coefficient of heat transfer.

8. Device for determining a coefficient of heat transfer to a fluid (15), comprising a sensor assembly containing a plurality of thermodynamic sensors (1) and containing processing means connected to the plurality of thermodynamic sensors (1), the processing means being arranged to carry out the method according to one of Claims 1 to 1.

9. Device according to Claim 8, wherein the processing means are further arranged to adjust the operating temperature of the plurality of thermodynamic sensors

(1) to different values.

10. Device according to Claim 8 or 9, further comprising a supporting body (3), the plurality of thermodynamic sensors (1) being fixed to the supporting body (3) with the aid of a fixing layer (2).

11. Device according to Claim 10, wherein the fixing layer (2) has specific thermal properties.

12. Device according to one of Claims 8 to 11, wherein the device further comprises, for each of the plurality of thermodynamic sensors (1), a first temperature sensor (5) for measuring a first temperature of the fixing layer

(2) on one side of the thermodynamic sensor (1), a second temperature sensor (6) for measuring a second temperature of the fixing layer (2) on the supporting body (3) side, a heat sensor (4) for measuring the heat supplied to the thermodynamic sensor

(1).

13. Device according to one of Claims 8 to 12, wherein the plurality of thermodynamic sensors (1) consists of a thin chip.

14. Device according to one of Claims 8 to 13, wherein the sensor assembly con- taining the plurality of thermodynamic sensors (1) is surrounded by an isothermal shell

(12).

15. Device according to one of Claims 10 to 14, wherein the supporting body (3) consists of a thermally conducting body that is thermally connected to a cooling element (13).

16. Device according to one of Claims 8 to 15, wherein an upper side of each of the plurality of thermodynamic sensors (1) is provided with a protective layer, the protective layer (9a, 9b) being in contact with the fluid (15) during operation.