Methods for determining convective heat transfer coefficients and boundary layer thickness

Abstract

The present disclosure relates to a boundary layer sensor (1) for determining the thickness of a boundary layer above a surface (65) of a body (6) around which a flow occurs, said sensor comprising a first temperature measuring device (31), a second temperature measuring device (32) and a third temperature measuring device (33), each located at a predetermined distance (X1, X2, X3) from the surface (65) of the body (6) around which a flow occurs, at least the second temperature measuring device (32) and the third temperature measuring device (33) including or consisting of at least one wire (21, 22, 23, 24), the wire (21, 22, 23, 24) extending from the surface (65) into a half-space adjacent to the surface and having a diameter of about 300 μm or less. The present disclosure also relates to a wind turbine, a vehicle, an aircraft, an indoor environment measuring device or a ship having such a boundary layer sensor, as well as a method for detecting the thickness of a boundary layer.

Description

[Technical field]

[0001] The present disclosure relates to a method for detecting a convective heat transfer coefficient on a surface of a body around which a flow occurs and / or is heated, in which a first temperature, a second temperature and a third temperature are measured at a predetermined distance from the surface of the body around which the flow occurs, and at least a first temperature measuring device, a second temperature measuring device and a third temperature measuring device are used for the temperature measurements. The present disclosure also relates to a method for detecting a boundary layer thickness on a surface of a body around which a flow occurs and / or is heated, in which the three temperatures are measured at a predetermined distance from the surface of the body around which the flow occurs. [Background technology]

[0002] A device for determining the convective heat transfer coefficient of a heated surface is known from DE 10 2016 107 212 A1. The known device measures the temperature difference between the surface temperature of the convective surface and the ambient temperature and a further temperature difference between the temperature in the vicinity of the convective surface in the boundary layer and the ambient temperature. The well-known sensor is based on the insight that the temperature profile in the boundary layer comprises an exponential curve with the convective heat transfer coefficient as a constant. By determining three support points, the exponential curve can thus be determined, from which the convective heat transfer coefficient can be determined. The known device may also be referred to below as a CHM sensor.

[0003] Alternatively, the exponential drop in air temperature on the convection surface can be measured optically using a laser differential interferometer. With this type of measurement setup, the temperature profile can be accurately detected and therefore the convection heat transfer coefficient h C However, the amount of technical equipment required makes this type of measurement unsuitable for routine use. Summary of the Invention [Problem to be solved by the invention]

[0004] It has been shown that the measured values ​​of the convective heat transfer coefficient determined optically by laser differential interferometry differ from the values ​​measured using a thermocouple design in the boundary layer, which is known from DE 10 2016 107 212 A1. Based on the prior art, it is therefore an object of the present disclosure to provide a method for detecting the convective heat transfer coefficient, which requires less technical equipment than the known optical measurements, but nevertheless provides equally accurate measurement results. [Means for solving the problem]

[0005] According to the present disclosure, this object is achieved by the method according to claim 1 and the method according to claim 2.

[0006] According to the present disclosure, the convective heat transfer coefficient h C In order to detect the temperature, it is proposed to measure at least three temperatures on the surface of the body around which the flow occurs and / or is heated. To measure the temperatures, at least a first temperature measuring device, a second temperature measuring device and a third temperature measuring device can be used, each of which is placed at a predetermined distance from the surface of the body around which the flow occurs and in each case at a different distance. In some embodiments of the present disclosure, the at least three temperature measuring devices can be resistance thermometers and / or thermocouples. In this specification, the distance from the surface of the body around which the flow occurs is defined as the length of the normal vector between each temperature measuring device and the surface.

[0007] In some embodiments of the present disclosure, a first temperature measuring device is placed directly on the surface of the body around which the flow occurs and / or is heated, a third temperature measuring device is placed a greater distance from the surface such that it constitutes the ambient temperature, and a second temperature measuring device is placed within the boundary layer, for example at a distance between about 1 mm and about 3 mm.

[0008] It has now been discovered that heat flowing out through the leads and / or mechanical fastenings of a temperature measuring device can lead to erroneous measurements. In the prior art, this heat flow has not previously been taken into account, and so the convective heat transfer coefficient h C is the thermal conductivity of the fluid medium, λ L , the distance X2 of the second temperature measuring device, and the three measured temperatures T O , T X , T L It was determined from the following equation, which assumes a steady exponential curve of temperature in the boundary layer:

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[0009] However, according to the present disclosure, due to heat conduction through the individual components of the temperature measuring device, the temperature T X It has been found that the convection heat transfer coefficient h C is the measured temperature, the distance X2 of the second temperature measuring device, and the thermal conductivity λ of the device used in accordance with the present disclosure. M From this, it has been found that it should be correctly determined as follows:

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[0010] The convective heat transfer coefficient h measured in this way C corresponds substantially to the value measured by a laser differential interferometer, and the convective heat transfer coefficient h C can be obtained according to the present disclosure with significantly less technical equipment. Thus, according to the present disclosure, it is proposed to use a known device, which includes only three temperature measuring devices, for detecting the convective heat transfer coefficient, and to achieve a significant improvement in accuracy by a corrected evaluation of the detected measured values.

[0011] Similarly, in some embodiments of the present disclosure, it is also possible to determine the thickness d of the boundary layer above the surface of the body around which the flow occurs and / or is heated, where the thickness d of the boundary layer is determined by the maximum temperature difference e between the surface and the environment above the surface around which the flow occurs. -1 , i.e., the distance X=d at which the heat transfer coefficient decreases to about 36.788% (e is the Euler number). C is the thermal conductivity of the fluid medium, λ L and the boundary layer thickness d to h C = λ L d -1 Therefore, the boundary layer thickness d can be calculated by the measured temperature T O , T X and T L , the distance X2 of the second device for measuring the temperature on the surface, and the thermal conductivity λ of the flowing medium. L and the thermal conductivity of the sensor array, λ M It can be calculated as follows:

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[0012] In some embodiments of the present disclosure, the third temperature T L The distance X3 at which the temperature is measured may be between about 9 mm and about 20 mm. In other embodiments of the present disclosure, the distance X3 may be between about 10 mm and about 14 mm. In yet other embodiments of the present disclosure, the distance X3 may be selected to be between about 11 mm and about 16 mm. This allows the third temperature measurement device to be used to reliably measure the ambient temperature, which is largely unaffected by the surface temperature.

[0013] In some embodiments of the present disclosure, the first temperature measuring device, the second temperature measuring device, and the third temperature measuring device can be formed by a thermocouple, respectively, and a first thermoelectric voltage U1 is measured between the first temperature measuring device and the third temperature measuring device, and a second thermoelectric voltage U2 is measured between the second temperature measuring device and the third temperature measuring device. According to the present disclosure, the boundary layer thickness d or the convective heat transfer coefficient h CTo measure the thermal conductivity, it is proposed to correlate only the temperature differences of the first and third temperature measuring devices, or the second and third temperature measuring devices, so that these temperature differences can be directly represented by the measured thermoelectric power. This makes it easier to evaluate the measured values, since the electrical signal representing the convective heat transfer coefficient can be generated directly, with little technical equipment such as analog computing circuits. Analog computing circuits of this kind can be realized, for example, by means of operational amplifiers.

[0014] JPEG2024536401000005.jpg35169

[0015] In some embodiments of the present disclosure, the calibration measurements can be performed using laser differential interferometry, which provides a non-contact measurement and thus provides a means to measure the actual temperature T of the undisturbed boundary layer. X By comparing the measurements thus obtained with those of a second temperature measuring device, the sensor according to the present disclosure can be calibrated in a simple manner. [Brief description of the drawings]

[0016] [Figure 1] FIG. 1 is a schematic diagram of a known CHM sensor. [Diagram 2] FIG. 1 is an equivalent circuit diagram of a CHM sensor for explaining heat flow. [Diagram 3] 1 shows a comparison of convective heat transfer coefficient versus flow velocity from evaluation of a measurement signal according to the present disclosure and from evaluation of a known measurement signal. [Figure 4] 13 shows measurements of a second temperature measuring device versus distance X2 from a surface with different convective heat transfer coefficients to the second temperature measuring device when evaluating measurements according to the present disclosure and measurements according to the prior art. [Diagram 5] 4 shows measurements of a second temperature measuring device at a constant heat transfer coefficient for different calibration values ​​(λ). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] The present disclosure will now be described in more detail based on drawings and exemplary embodiments.

[0018] FIG. 1 shows a cross-sectional view of a body 6 having a surface 65 around which flow occurs. The body 6 can be, for example, part of a vehicle or an aircraft or a watercraft. In another embodiment of the present disclosure, the body 6 can be part of a wind turbine. In yet another embodiment of the present disclosure, the body 6 can be part of an indoor environment measurement device that measures the convective heat transfer rate and / or the radiative heat exchange with the environment. During operation of the boundary layer sensor 1, a forced or convective current flows around the body 6, forming a flow in a half-space of the body 6 adjacent to the surface 65. This flow can flow at least partially parallel to the body 6 or the surface 65. According to the present disclosure, the boundary layer sensor or CHM sensor 1 measures the thickness of the boundary layer and / or the convective heat transfer rate h above the surface 65. C is used to detect

[0019] The boundary layer sensor 1 is designed to detect three temperatures or two temperature differences. For this purpose, it has a first temperature measuring device 31 arranged at a first distance X1 from the surface 65. In the illustrated exemplary embodiment, the first temperature measuring device 31 is arranged directly on the surface 65. The distance X1 is therefore 0 mm.

[0020] Furthermore, the boundary layer sensor 1 comprises a second temperature measuring device 32 arranged at a distance X2 above the surface 65. This distance X2 may be, for example, between 1 mm and about 3 mm. The distance X2 is selected such that the second temperature measuring device 32 is located within the boundary layer formed above the surface 65.

[0021] Finally, the boundary layer sensor 1 comprises a third temperature measuring device 33 arranged at a distance X3 above the surface 65. This distance X3 can be, for example, between about 9 mm and about 20 mm, or between about 10 mm and about 14 mm, or between about 11 mm and about 16 mm. The distance X3 is selected such that the third temperature measuring device measures the ambient temperature of the medium flowing above the surface 65 outside the boundary layer. The distance X3 above the surface 65 can therefore be selected based on the expected flow velocity, such that a larger distance is selected for a slower flow velocity and a smaller distance is selected for a faster flow velocity.

[0022] In the illustrated exemplary embodiment, the first, second and third temperature measuring devices 31, 32 and 33 are designed as thermocouples. For this purpose, the boundary layer sensor 1 has a first wire 21 made of a first material. One end of this first wire 21 is connected to one end of a second wire 22. This second wire 22 is made of a second material so as to be able to generate a thermoelectric voltage at the contact point, which voltage corresponds to the temperature T of the surface 65. O Represents the measured value of.

[0023] The first wire 21 also has a second end located a distance X3 from the surface 65. At this end, a third contact point is formed with the fourth wire 24. This contact point has a temperature T L Similarly, a further contact point with the third wire 23 is arranged along the longitudinal extension of the first wire 21. This contact point forms a third temperature measuring device 33 for measuring the temperature T X A second temperature measuring device 32 is formed for measuring the temperature.

[0024] In some embodiments of the present disclosure, two thermoelectric powers can be measured in this manner. The first thermoelectric power is measured by a first measuring device 41 between the second wire 22 and the fourth wire 24, and the second thermoelectric power is measured by a second measuring device 42 between the fourth wire 24 and the third wire 23. The first thermoelectric power is thus determined by a temperature difference T O -T LThe second thermoelectric voltage is the temperature difference T X -T L is the measured value.

[0025] The boundary layer sensor 1 can be attached to the surface 65 in a simple manner using an adhesive tape 7. This makes the boundary layer sensor 1 suitable for temporary or mobile use, e.g. for experiments in flow channels. Furthermore, the adhesive tape allows attachment without disturbing the topography of the surface.

[0026] In some embodiments, the boundary layer sensor 1 detects the temperature T O , T L , T X The devices 31, 32, 33 for measuring may also be provided with further elements, in particular mechanical fixing devices, which hold them in their intended position, thereby making it possible to prevent deformations or changes in the distances X2, X3 and / or to reduce the risk of mechanical damage to the boundary layer sensor 1.

[0027] The temperature profile in the boundary layer on the surface 65 follows an exponential function. Therefore, the known method for evaluating the measurements is essentially to O , T L , T X , which represent the boundary layer thickness and / or convective heat transfer coefficient. However, in accordance with the present disclosure, the first, third and fourth wires 21, 23, 24, and any optional mechanical support structures or mechanical fixation devices, are adapted to measure the distance T X It turns out that this can be used to derive the heat flow that distorts the convective heat transfer coefficient h determined by the boundary layer sensor 1. C is the convective heat transfer coefficient h measured non-contact by laser differential interferometry C Therefore, in this disclosure, the boundary layer thickness d and the convection heat transfer coefficient h C In order to detect more accurately, an alternative evaluation of the first and second thermoelectric powers is proposed. The derivation of the formula according to the present disclosure is explained based on FIG.

[0028] FIG. 2 shows a thermal equivalent circuit diagram of the sensor shown in FIG. 1. A first temperature measuring device 31, a second temperature measuring device 32 and a third temperature measuring device 33 are now connected to each other to measure the temperature level T O , T X and T L The temperature T O From surface 65 having temperature T L Due to convective heat transfer to the surrounding half-space having a mass of 0.01 mm, a quantity of heat q2+q4 flows along the sensor 1. In this regard, the following equation applies:

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[0029] Additionally, a quantity of heat q1+q3 flows from surface 65 due to heat transfer along first wire 21, third wire 23 and fourth wire 24, as well as possible mechanical support structures not shown in Figure 1. In this regard, the following formula applies:

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[0030] As explained in Figure 2, the heat flow along the sensor can be represented by an electrical equivalent circuit diagram according to Kirchhoff's laws, well known in electrical engineering, where each temperature level corresponds to a voltage and the heat flow density corresponds to a current. Therefore, the following Kirchhoff's first law applies to the equivalent circuit diagram shown in Figure 2:

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[0031] Additionally, Kirchhoff's second law applies.

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[0032] The total amount of convective heat emanating from surface 65 (neglecting radiative heat) is equivalent to the temperature difference between surface 65 and the medium surrounding surface 65. Therefore, the following formula applies:

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[0033] This is expressed as follows:

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[0034] This relationship will be explained in more detail below with reference to an exemplary embodiment. O Consider a surface 65 with an air temperature T L = 0°C. O and a first device 31 for measuring the temperature T L In addition to the third device 33 for measuring the temperature T X In the illustrated exemplary embodiment, a second device 32 for measuring the measured temperature T X =17.1℃.

[0035] The sensor used in accordance with the present disclosure has a calibration factor Λ=30 W m -2 ·K -1 The measured value T obtained according to the present disclosure O -T L and T X -T L When evaluating the convection heat transfer coefficient h C is obtained from the following equation:

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[0036] As a result, the total heat flux density is 100 W m -2 The partial heat flux density shown in Figure 2 is as follows: q1=85.5W m -2 q2=14.5W m -2 q3=14.5W m -2 q4=85.5W m -2

[0037] The measured value T obtained according to the prior art O -T L and T X -T L When evaluating the convection heat transfer coefficient h C is obtained from the following equation:

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[0038] The above-mentioned situation in the exemplary embodiment will be explained again below with reference to Figs. 3-4. In Fig. 3, the vertical axis is the convection heat transfer coefficient h C The horizontal axis is the flow velocity v (unit: m s -1 ) is shown in Fig. 1. This figure shows the convection heat transfer coefficient h CThe values ​​of h are plotted against the flow velocity, showing the results evaluated according to known methods (x) and according to the method proposed in this disclosure (◯). Figure 3 shows that the measurements of the convective heat transfer coefficient according to the prior art are systematically underestimated, with the measurement error increasing strongly as the flow velocity v increases. According to the present disclosure, it is possible to obtain a convective heat transfer coefficient h using a thermal sensor known per se, even at high flow velocities. C For the first time, it is now possible to detect measurement values ​​with high accuracy.

[0039] Figure 4 shows that the heat flow into or out of the material of sensor 1 is proportional to the measured value T X The effect of the distance X2 on the temperature is shown on the vertical axis as a function of the measurement T in Kelvin. X -T L is plotted on a logarithmic scale, with the temperature T X The distance X2 of the second device 32 for measuring the heat transfer coefficient is plotted. A total of six curves are shown, two for each of three different convective heat transfer coefficients, where the curves are as follows: [Table 1]

[0040] FIG. 4 shows that the method according to the present disclosure provides significant accuracy improvements, especially when the convective heat transfer coefficient is large and the sensor geometry is relatively large, i.e., when the distance X2 is large.

[0041] JPEG2024536401000017.jpg31169

[0042] Figure 5 shows the relationship between the measured value T X In addition, Fig. 5 shows that, especially for mechanically robust sensors, the thermal conductivity λ increases almost logarithmically due to the large amount of material used. M is large, indicating that there is a substantial error in the measurements, which can be more than a factor of two.

[0043] Of course, the present disclosure is not limited to the illustrated embodiments. The above description should therefore be considered as illustrative rather than limiting. The following claims should be understood as meaning that the indicated features are present in at least one embodiment of the present disclosure. This does not exclude the presence of further features. To the extent that the description or claims define a "first" feature and a "second" feature, this designation is used to distinguish between similar features without establishing priority. Research leading to these results has been funded by the European Union.

Claims

1. The convective heat transfer coefficient h on the surface (65) of the body (6) around which the flow occurs and / or is heated. Ｃ A method for measuring measuring a first temperature (T O ) at a first distance X1 from said surface (65) by a first temperature measuring device (31); measuring a second temperature (T x ) at a second distance X2 from the surface (65) with a second temperature measuring device (32); measuring a third temperature (T L ) at a third distance X3 from the surface (65) with a third temperature measuring device (33); Here, X1<X2<X3, The convective heat transfer coefficient h Ｃ the first temperature, the second temperature, the third temperature (T Ｏ , T Ｘ , T Ｌ ), the second distance X2 and the thermal conductivity λ Ｍ and determining the value of the Convective heat transfer coefficient h Ｃ Measurement method. [Equation 1]

2. The second distance X2 is 1 mm to 3 mm. The method of claim 1.

3. The first temperature (T Ｏ ) corresponds to the temperature of the surface (65), and the first distance X1 is 0 mm. The method of claim 1.

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

5. the third distance X3 is between 9 mm and 20 mm; The method of claim 3.

6. the third distance X3 is between 10 mm and 14 mm; The method of claim 5.

7. the third distance X3 is between 11 mm and 16 mm; The method of claim 5.

8. the first temperature measuring device (31), the second temperature measuring device (32), and the third temperature measuring device (33) include thermocouples; First thermoelectric voltage U １ is measured between the first temperature measuring device (31) and the third temperature measuring device (33), and Second thermoelectric power U ２ is measured between the second temperature measuring device (32) and the third temperature measuring device (33), The method of claim 1.

9. The following parameter Λ is determined by calibration measurements: The method of claim 1. [Equation 2]

10. the calibration measurement is performed by laser differential interferometry; 10. The method of claim 9.

11. 1. A method for measuring the thickness d of a boundary layer above a surface (65) of a body (6) around which a flow occurs and / or is heated, comprising the steps of: measuring a first temperature (T O ) at a first distance X1 from said surface (65) by a first temperature measuring device (31); measuring a second temperature (T x ) at a second distance X2 from the surface (65) with a second temperature measuring device (32); measuring a third temperature (T L ) at a third distance X3 from the surface (65) with a third temperature measuring device (33); Here, X1<X2<X3, The thickness d of the boundary layer is calculated by dividing the first temperature, the second temperature, and the third temperature (T Ｏ , T Ｘ , T Ｌ ) and the second distance X2, as follows: [Equation 3] where λ Ｌ denotes the thermal conductivity of the flowing medium around said surface (65), and λ Ｍ represents the thermal conductivities of the first, second, and third temperature measuring devices; A method for measuring the boundary layer thickness d.

12. The second distance X2 is 1 mm to 3 mm. The method of claim 11.

13. The first temperature (T Ｏ ) corresponds to the temperature of the surface (65), and the first distance X1 is 0 mm. The method of claim 11.

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

15. the third distance X3 is between 9 mm and 20 mm; The method of claim 13.

16. the third distance X3 is between 10 mm and 14 mm; 16. The method of claim 15.

17. the third distance X3 is between 11 mm and 16 mm; 16. The method of claim 15.

18. the first temperature measuring device (31), the second temperature measuring device (32), and the third temperature measuring device (33) include thermocouples; First thermoelectric voltage U １ is measured between the first temperature measuring device (31) and the third temperature measuring device (33), and Second thermoelectric power U ２ is measured between the second temperature measuring device (32) and the third temperature measuring device (33), The method of claim 11.

19. The following parameter Λ is determined by calibration measurements: The method of claim 11. [Equation 4]

20. the calibration measurement is performed by laser differential interferometry; 20. The method of claim 19.

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