METHOD FOR DETECTING THE CONVECTIVE HEAT TRANSFER COEFFICIENT AND THE THICKNESS OF AN INTERFACE

Abstract

An interfacial sensor and method for determining the thickness of an interface above a surface of a body around which flow occurs. The sensor has a first device for determining a first temperature, a second device for determining a second temperature and a third device for determining a third temperature. Each device is arranged at a predefinable distance (XI, X2, X3) from the surface of the body) around which flow occurs. At least the second device for determining the second temperature and the third device for determining the third temperature includes at least one wire which extends from the surface into a half-space adjoining the surface and which has a diameter of approximately 300 ?m or less. Such a sensor may find use in a wind turbine, a vehicle, an aircraft, a room climate measuring device or a ship.

Claims

1. A method for measuring a convective heat transfer coefficient h.sub.c on a surface (65) of a body (6) around which flow occurs and/or which is heated, comprising: with a first device (31), measuring a first temperature (T.sub.o) at a first distance X1 from the surface (65); with a second device (32), measuring a second temperature (T.sub.x) at a second distance X2 from the surface (65); with a third device (33), measuring a third temperature (T.sub.L) at a third distance X3 from the surface (65), where X1<X2<X3; and determining the convective heat transfer coefficient hc from the first, second and third temperatures (To, Tx, TL), the second distance X2 and the heat conduction coefficient ?M as follows: $h_c=\frac{{?}_M.Math.\left[\left(T_O-T_L\right)-\left(T_X-T_L\right)\right]}{X2.Math.\left(T_x-T_L\right)}$

2. The method according to claim 1, wherein the second distance X2 is 1 mm to 3 mm.

3. The method according to claim 1, wherein the first distance X1 is 0 mm so that the first temperature (T.sub.o) corresponds to the temperature of the surface (65).

4. The method according to claim 3, wherein the third distance X3 is sufficiently large so that the third temperature (T.sub.L) corresponds to a temperature of the surroundings of the body (6) around which flow occurs.

5. The method according to claim 3, wherein the third distance X3 is between 9 mm and 20 mm.

6. The method according to claim 5, wherein the third distance X3 is between 10 mm and 14 mm.

7. The method according to claim 5, wherein the third distance X3 is between 11 mm and 16 mm.

8. The method according to claim 1, wherein: the first device (31), the second device (32) and the third device (33) comprise thermocouples; a first thermoelectric voltage U.sub.1 is measured between the first device (31) and the third device (33); and a second thermoelectric voltage U.sub.2 IS measured between the second device (32) and the third device (33).

9. The method according to claim 1, wherein a parameter $?=\frac{{?}_M}{X2}$ is determined by a calibration measurement.

10. The method according to claim 9, wherein the calibration measurement is carried out by laser differential interferometry.

11. A method for measuring the thickness d of an interface above a surface (65) of a body (6) around which flow occurs and/or which is heated, comprising: with a first device (31), measuring a first temperature (T.sub.o) at a first distance X1 from the surface (65); with a second device (32), measuring a second temperature (T.sub.x) at a second distance X2 from the surface (65); with a third device (33), measuring a third temperature (T.sub.L) at a third distance X3 from the surface (65), where X1<X2<X3; and determining the thickness d of the interface is determined from the first, second and third temperatures (To, Tx, TL) and the distance X2 as follows: $d=\frac{{?}_L.Math.X2.Math.\left(T_x-T_L\right)}{{?}_M.Math.\left[\left(T_O-T_L\right)-\left(T_X-T_L\right)\right]}$ where: ?.sub.L denotes the heat conduction coefficient of a medium flowing around the surface (65); and ?.sub.M denotes the heat conduction coefficient of the first, second and third devices.

12. The method according to claim 11, wherein the second distance X2 is 1 mm to 3 mm.

13. The method according to claim 11, wherein the first distance X1 is 0 mm so that the first temperature (T.sub.o) corresponds to the temperature of the surface (65).

14. The method according to claim 13, wherein the third distance X3 is sufficiently large so that the third temperature (T.sub.L) corresponds to a temperature of the surroundings of the body (6) around which flow occurs.

15. The method according to claim 13, wherein the third distance X3 is between 9 mm and 20 mm.

16. The method according to claim 15, wherein the third distance X3 is between 10 mm and 14 mm.

17. The method according to claim 15, wherein the third distance X3 is between 11 mm and 16 mm.

18. The method according to claim 11, wherein: the first device (31), the second device (32) and the third device (33) comprise thermocouples; a first thermoelectric voltage U.sub.1 is measured between the first device (31) and the third device (33); and a second thermoelectric voltage U.sub.2 IS measured between the second device (32) and the third device (33).

19. The method according to claim 11, wherein a parameter $?=\frac{{?}_M}{X2}$ is determined by a calibration measurement.

20. The method according to claim 19, wherein the calibration measurement is carried out by laser differential interferometry

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The invention shall be explained in more detail below on the basis of drawings and an exemplary embodiment. In these drawings:

[0019] FIG. 1 shows a schematic representation of a known CHM sensor.

[0020] FIG. 2 shows an equivalent circuit diagram of the CHM sensor to illustrate the heat flows.

[0021] FIG. 3 shows a comparison of the convective heat transfer coefficient versus the flow velocity with the evaluation of the measurement signals according to the invention and the known evaluation of the measurement signals.

[0022] FIG. 4 shows the measured values of the second device for detecting a temperature against the distance X2 thereof from the surface for different convective heat transfer coefficients in the case of an evaluation of the measured values according to the invention and according to the prior art.

[0023] FIG. 5 shows the measured value of the second device for detecting a temperature at a constant heat transfer coefficient for different calibration values ?.

DETAILED DESCRIPTION

[0024] FIG. 1 shows a cross-section through a body 6 around which flow occurs and which has a surface 65. The body 6 can, for example, be part of a vehicle or aircraft or a ship. In other embodiments of the invention, the body 6 can be part of a wind turbine. In yet other embodiments of the invention, the body 6 can be part of a room climate measuring device which determines the convective heat transfer coefficient and/or the exchange of radiant heat with the environment. During the operation of the interface sensor 1, a forced flow or a convective flow flows around the body 6 so that a flow is formed in the half-space of the body 6 that is adjacent to the surface 65. The flow can run at least partially parallel to the body 6 or the surface 65. According to the invention, an interface sensor or CHM sensor 1 is used to detect the thickness of the interface and/or the convective heat transfer coefficient h.sub.c above the surface 65.

[0025] The interface sensor 1 is designed to detect three temperatures or two temperature differences. For this purpose, the interface sensor has a first device for detecting a first temperature 31, which is arranged at a first distance X1 from the surface 65. In the illustrated exemplary embodiment, the first device 31 for detecting a first temperature is located directly on the surface 65. The distance X1 is therefore 0 mm.

[0026] Furthermore, the interface sensor 1 has a second device 32 for detecting a second temperature, which is arranged at a distance X2 above the surface 65. The distance X2 can be between 1 mm and about 3 mm, for example. The distance X2 is selected in such a way that the second device 32 for detecting a second temperature is located within the interface forming above the surface 65.

[0027] Finally, the interface sensor 1 has a third device 33 for determining a third temperature, which is arranged at a distance X3 above the surface 65. The distance X3 can, for example, be between about 9 mm and about 20 mm or between about 10 mm and about 14 mm or between 11 mm and about 16 mm. The distance X3 is selected in such a way that the third device for determining a third temperature detects the ambient temperature of the medium flowing above the surface 65 outside the interface. Thus, the distance X3 above the surface 65 can be selected on the basis of the expected flow velocity in such a way that a longer distance is selected when the flow velocity is low and a shorter distance is selected when the flow velocity is high. Thus, from the foregoing, X1<X2<X3.

[0028] In the illustrated exemplary embodiment, the first, second and third devices 31, 32 and 33 for determining temperatures are designed as thermocouples. For this purpose, the interface sensor 1 has a first wire 21, which consists of a first material. One end of the first wire 21 is connected to one end of a second wire 22. The second wire 22 is made of a second material so that a thermoelectric voltage can be formed at the contact point, which voltage represents a measure of the first temperature T.sub.o of the surface 65.

[0029] The first wire 21 also has a second end which is arranged at a distance X3 from the surface 65. A third contact point with a fourth wire 24 is formed at this end. This contact point forms the third device 33 for determining the third temperature T.sub.L. Similarly, a further contact point with a third wire 23 is located along the longitudinal extension of the first wire 21. This contact point forms the second device 32 for determining the second temperature T.sub.x.

[0030] In some embodiments of the invention, two thermoelectric voltages can thus be determined. A first thermoelectric voltage is determined by means of a first measuring device 41 between the second wire 22 and the fourth wire 24, and a second thermoelectric voltage is determined by means of a second measuring device 42 between the fourth wire 24 and the third wire 23. The first thermoelectric voltage is thus a measure of the first temperature difference T.sub.o?T.sub.L. The second thermoelectric voltage is a measure of the second temperature difference T.sub.x? T.sub.L.

[0031] The interface sensor 1 can be attached to the surface 65 in a simple manner by means of an adhesive tape 7. Due to this, the interface sensor 1 is also suitable for a temporary or mobile use, for example for experiments in a flow channel. In addition, the adhesive tape renders possible a mounting without disturbing the geometry of the surface.

[0032] In some embodiments, the interface sensor 1 can contain further elements, in particular mechanical fastening apparatuses which hold the device 31, 32 and 33 for determining the temperatures T.sub.o, T.sub.L and T.sub.x in the intended positions thereof. This can prevent deformation or a change in the distances X2 and X3 and/or reduce the risk of mechanical damage to the interface sensor 1.

[0033] The temperature profile within the interface above the surface 65 follows an exponential function, which is why known methods for evaluating the measured values are essentially based on deriving the coefficients of an exponential function from the measured values T.sub.o, T.sub.x and T.sub.L, which coefficients represent the interface thickness and/or the convective heat transfer coefficient. According to the invention, however, it was realized that the first, third and fourth wires 21, 23 and 24 and optional mechanical support structures or fastening apparatuses are used to derive a heat flow which distorts the measured value T.sub.x at the distance X2. As a result, the convective heat transfer coefficients h.sub.c determined by means of the interface sensor 1 differ from the convective heat transfer coefficients h.sub.c measured without contact by means of laser differential interferometry. Therefore, the invention proposes an alternative evaluation of the first and second thermoelectric voltages in order to obtain a more accurate detection of the interface thickness d and the convective heat transfer coefficient h.sub.c. The derivation of the formula according to the invention is explained on the basis of FIG. 2.

[0034] FIG. 2 shows a thermal equivalent circuit diagram of the sensor shown in FIG. 1. The first device 31, the second device 32 and the third device 33 for determining the first, second and third temperatures, respectively, are here each designated by the temperature level T.sub.o, T.sub.x and T.sub.L measured by these devices. The amount of heat q2+q4 flows along the sensor 1 due to the convective heat transfer from the surface 65 having the temperature T.sub.o into the surrounding half-space having the temperature T.sub.L. In this respect, the following applies:

[00005]$q2=h_c.Math.\left(T_O-T_x\right)$$q4=h_c.Math.\left(T_x-T_L\right)$

[0035] Furthermore, the amount of heat q1+q3 flows from the surface 65 due to the heat transfer along the first wire 21, the third wire 23 and the fourth wire 24 as well as along possibly existing mechanical support structures, which are not shown in FIG. 1. In this respect, the following applies:

[00006]$q1=\frac{{?}_M}{X2}.Math.\left(T_O-T_x\right)$$q3=\frac{{?}_1}{X3-X2}.Math.\left(T_X-T_L\right)$

[0036] As explained in FIG. 2, the heat flows along the sensor can be represented in an electrical equivalent circuit diagram, which is subject to the well-known Kirchhoff's laws of electrical engineering, the respective temperature level corresponding to the electrical voltage and the heat flow density corresponding to the electrical current. Thus, the equivalent circuit diagram shown in FIG. 2 is subject to the first Kirchhoff's law:

[00007]$\text{?}=q_1+q_2=q_3+q_4.$$\text{?}\text{indicates text missing or illegible when filed}$

[0037] Furthermore, the second Kirchhoff's law applies

[00008]$T_O-T_L=\left(T_O-T_X\right)+\left(T_X-T_L\right).$

[0038] The total convective heat flow emanating from the surface 65 (neglecting the radiant heat) corresponds to the temperature difference between the surface 65 and the medium surrounding the surface 65. The following therefore applies:

[00009]$q_{\mathrm{GES}}=\left(T_O-T_L\right).Math.h_C=\left[\left(T_O-T_X\right)+\left(T_X-T_L\right)\right].Math.h_C.$

[0039] It follows that q.sub.GES=q.sub.2+q.sub.4=q.sub.1+q.sub.2.

[0040] Thus, the following applies

[00010]$q_4=q_1.$

[0041] It follows therefrom that

[00011]$\left(T_X-T_L\right).Math.h_C=\left(T_O-T_X\right).Math.\frac{{?}_M}{X2}.$

Here, ?.sub.M denotes the heat conduction coefficient of the sensor arrangement 1, which results from the geometry and the respectively employed materials. Since X2 is also a constant resulting from the geometry of sensor 1, the convective heat transfer coefficient h.sub.c only depends on the constant

[00012]$?=\frac{{?}_M}{X2}$

and the measured temperature differences. Constant ? here denotes the heat transmission coefficient of the sensor. Since the temperature differences, as described above, are given directly by the thermoelectric voltages U.sub.1 and U.sub.2, the convective heat transfer coefficient h.sub.c and the interface thickness values derived therefrom can be determined simply by forming a difference, multiplication and division. Constant ? can here be advantageously determined by a calibration measurement. On the one hand, this avoids a time-consuming calculation and, on the other hand, sample scattering from different but nominally identical sensors 1 can be taken into account in a simple manner.

[0042] The present relationships shall be explained in more detail below by means of an exemplary embodiment. A surface 65 is considered, which has a surface temperature T.sub.o of 20? C. The surface 65 is located in an environment having an air temperature T.sub.L=0? C. In addition to the first device 31 for determining a first temperature T.sub.o and a third device 33 for determining a third temperature T.sub.L, the sensor 1 also has a second device 32 for determining a second temperature T.sub.x, which is at a distance X2=2 mm from the surface 65. In the illustrated exemplary embodiment, the measured second temperature T.sub.x=17.1? C.

[0043] The sensor used according to the invention has a calibration factor ?=30 W.Math.m.sup.?2.Math.K.sup.?1. When evaluating the measured values T.sub.o?T.sub.L and T.sub.x?T.sub.L obtained according to the invention, the convective heat transfer coefficient h.sub.c results from the equation

[00013]$\text{?}=\frac{{?}_M\text{?}\left[\left(T_O-T_L\right)-\left(\text{?}-T_L\right)\right]}{X2.Math.\left(T_x-T_L\right)}.$$\text{?}\text{indicates text missing or illegible when filed}$

[0044] According to the invention, the convective heat transfer coefficient is thus h.sub.c=5 W.Math.m.sup.?2.Math.K.sup.?1.

[0045] This results in a total heat flux density of 100 W.Math.m.sup.?2. The partial heat flux densities shown in FIG. 2 then amount to

[00014]$q_1=85.5W.Math.m^{-2}$$q_2=14.5W.Math.m^{-2}$$q_3=14.5W.Math.m^{-2}$$q_4=85.5W.Math.m^{-2}$

[0046] When evaluating the measured values T.sub.o?T.sub.L and T.sub.x?T.sub.L obtained according to the prior art, the convective heat transfer coefficient h.sub.c results from the equation

[00015]$h_C=\frac{{?}_L.Math.\left[\ln \left(T_O-T_L\right)-\ln \left(T_x-T_L\right)\right]}{X2}.$

[0047] The value of the convective heat transfer coefficient calculated in this way is h.sub.c=2.17 W.Math.m.sup.?2.Math.K.sup.?1. The total heat flow is calculated therefrom as 43.4 W.Math.m.sup.?2. Since the heat flow via the material of the sensor is not taken into account according to the prior art, the amount of the measured value T.sub.x of the second device 32 for determining a temperature is systematically overestimated, resulting in a measurement error of approximately 56% in the illustrated exemplary embodiment.

[0048] The situation described above in the exemplary embodiment is explained again below on the basis of FIGS. 3 to 4. FIG. 3 here shows the convective heat transfer coefficient h.sub.c on the ordinate and the flow velocity v in m.Math.s.sup.?1 on the abscissa. The drawing shows the value for the convective heat transfer coefficient h.sub.c against the velocity, which is determined in a wind tunnel with a sensor shown in FIG. 1, once when evaluating the measured values according to the known method (x) and once according to the method proposed according to the invention (o). FIG. 3 shows that the amount of the measured value of the convective heat transfer coefficient according to the prior art is systematically underestimated, the measurement error increasing strongly as the flow velocity v increases. According to the invention, it has been possible for the first time to detect the measured value for the convective heat transfer coefficient h.sub.c with good accuracy, even for high flow velocities, using a thermal sensor known per se.

[0049] FIG. 4 illustrates the influence of the heat flow flowing off or entering via the materials of the sensor 1 on the measured value T.sub.x on the basis of the distance X2. Here, the measured value T.sub.x?T.sub.L in Kelvin is plotted on the ordinate on a logarithmic scale and the distance X2 of the second device 32 for determining the second temperature T.sub.x is plotted on the abscissa. A total of six curves are shown, two curves each for three different convective heat transfer coefficients. Here,

TABLE-US-00001 curve A shows the expected measured value T.sub.x according to the prior art for h.sub.c = 4.83 W .Math. m.sup.?2 .Math. K.sup.?1 curve A.sub.n shows the expected measured value T.sub.x according to the invention for h.sub.c = 4.83 W .Math. m.sup.?2 .Math. K.sup.?1 curve B shows the expected measured value T.sub.x according to the prior art for h.sub.c = 10.0 W .Math. m.sup.?2 .Math. K.sup.?1 curve B.sub.n shows the expected measured value T.sub.x according to the invention for h.sub.c = 10.0 W .Math. m.sup.?2 .Math. K.sup.?1 curve C shows the expected measured value T.sub.x according to the prior art for h.sub.c = 20.0 W .Math. m.sup.?2 .Math. K.sup.?1 curve C.sub.n shows the expected measured value T.sub.x according to the invention for h.sub.c = 20.0 W .Math. m.sup.?2 .Math. K.sup.?1

[0050] FIG. 4 shows that, in particular in the case of large convective heat transfer coefficients and relatively large sensor geometries, i.e. increasing distance X2, the method according to the invention results in a considerable increase in accuracy.

[0051] FIG. 5 shows the dependence of the measured value T.sub.x on the basis of the sensor geometry and the materials used for the sensor. The measured value T.sub.x?T.sub.L in Kelvin is here plotted linearly on the ordinate. The abscissa shows the constant

[00016]$?=\frac{{?}_M}{X2}.$

The value indicated on the abscissa is thus a measure of the thermal conductivity of the materials of the sensor or the cross-section thereof and of the distance of the second device 32 for determining a temperature T.sub.x from the surface 65.

[0052] FIG. 5 shows an approximately logarithmic increase in the measured value T.sub.x with increasing parameter ?. In addition, FIG. 5 shows that in particular mechanically robust sensors which have a large heat conduction coefficient ?.sub.M due to the large amount of material employed, cause a considerable error in the measurement, which can amount to a factor of 2 or more.

[0053] Of course, the invention is not limited to the illustrated embodiments. Therefore, the above description should not be regarded as limiting but as explanatory. The following claims should be understood as meaning that an indicated feature is present in at least one embodiment of the invention. This does not exclude the presence of further features. Insofar as the description or the claims define first and second features, this designation is used to distinguish between similar features without establishing an order of priority. The research work having led to these results has been funded by the European Union.