DE102008020471B4 - Method for measuring a thermal transport size of a sample - Google Patents

Abstract

A method of measuring a thermal transport size of a sample (16), comprising the steps
(a) applying a constant heating power (q) to the sample (16) in a linear heat introduction point (18),
(b) detecting a time-dependent temperature difference (ΔT) between
(I) a first temperature measuring point (20) at a first distance (D1) to the heat introduction point (18) and
(ii) a second temperature measuring point (22) at a second distance (D2) to the heat introduction point (18) at a plurality of times (t _i ),
characterized in that
(c) the time-dependent temperature difference (ΔT) is detected at logarithmically equidistant time intervals, or the detection takes place at non-logarithmically equidistant time intervals, and the temperature differences are interpolated from the measured values thus obtained and
(d) the procedure the steps
Determining a maximum slope (ΔΔT _max ) of the time-dependent temperature difference (ΔT (Int)) as a function of a logarithmized time coordinate (In t) and
- Calculate the thermal conductivity (λ) from the maximum slope ((ΔΔT _max ).
and or
- Determining a ...

Description

The The invention relates to a method for measuring a thermal transport size of a Sample, comprising the steps of (a) applying time to the sample constant heat output in a linear heat input, (b) detection a time-dependent Temperature difference between a first temperature measuring point in a first distance to the heat introduction point and a second temperature measuring point at a second distance to the heat input point at several times.

According to one In the second aspect, the invention relates to a thermal transport size measuring device for measuring a thermal transport size of a sample, comprising (a) a Heating device for applying a constant time to the sample Heating power in a linear heat input point, (b) a first temperature gauge spaced at a first distance from Wärmeeinleitstelle is arranged, and (c) a second temperature gauge, which in a second distance to the heat introduction parts is arranged.

Around Transport sizes, for example the thermal conductivity or the thermal conductivity To measure, a variety of measuring methods is known. The known measuring methods are designed to determine only one of the thermal transport sizes. Should the thermal conductivity are measured, for example, the heating wire method is used. The disadvantage of this is that boundary conditions of the measuring device both inner and outer, one huge Affect the accuracy of measurement to be achieved. The boundary conditions However, they are difficult to control, so the measurement uncertainty can not be estimated. In the temperature conductivity measurement For example, the laser flash method is used in which the equipment costs considerably is. Another disadvantage is that the thermal load by the Laser pulse on the sample surface is too high.

From the DE 102 06 045 A1 a quasi-stationary method for measuring the thermal conductivity is known. Quasi-stationary methods have the disadvantage of a long measuring time.

From the EP 0 144 443 For example, a method for measuring the coagulation of milk is known. In this method, the heat input of a heating wire into the milk changes depending on whether the milk is coagulated or not. A disadvantage of this method is that it requires a phase transition of the material to be examined and thus is not suitable for the determination of the thermal conductivity or the thermal conductivity.

From the EP 1 698 890 A1 For example, a method for characterizing a hydrocarbon storage is known. In this method, the temporal change of the temperature in the deposit is measured and from this conclusions are made about the properties of the deposit. This method is not suitable for measuring small sample workpieces.

From the DE 2 363 122 For example, a method for measuring the heat transfer coefficient is known in which the thermal conductivity of the sample to be measured is calculated as a function of the thermal conductivity of the sensor. The disadvantage of this is that the thermal conductivity of the sensor itself is faulty, so that a systematic measurement error arises.

Of the Invention is based on the object, a method for measuring a indicate thermal transport size, the one increased Has accuracy.

The Invention solves the problem by a method according to claim 1.

With solves a second aspect the invention solves the problem by a generic thermal transport size detecting device, having an electrical control, which is adapted to Carry out a method according to the invention.

Of the Advantage of the method is that only low requirements the sample used consist. This is especially beneficial if a measurement of the thermal transport size on an existing object carried out that should not be destroyed shall be.

Another advantage is that simple measurement and evaluation can be used without the accuracy of the determined thermal transport size is adversely affected. In addition, the high measuring accuracy, the short measuring time and the low costs are advantageous. The time-dependent increase in temperature difference also has a characteristic course, be the marginal condition be low is influenced. Existing influences are easily recognizable. This contributes to a high measurement accuracy, which is achieved even with less accurate measuring instruments.

It Another advantage is that a small number of readings for example, less than 500, in particular less than 100, is sufficient to allow easy and fast evaluation. The Evaluation can also during the measurement of time-dependent Temperature difference can be performed without significant computational effort. The process is also quick to perform, so it too for applications suitable for which only a short measuring time is available. Thanks to the generic method Is it possible, performing the evaluation simply in real time during the measurement, taking little expensive Electronics needed becomes. The thermal transport size measuring device according to the invention is therefore inexpensive can be produced and used.

Opposite one Pulse method in which a short-term heat pulse is released into the sample is, it is advantageous that the sample of a lower maximum temperature is exposed, which protects the sample. There are also disturbing effects of contact layers and the heat capacity of the heating wire reduced.

Under the feature that capturing the time-dependent temperature difference in logarithmic equidistant intervals takes place, is to be understood in particular that the temperature differences in logarithmic equidistant intervals be measured. But it is also possible that the temperature differences not in logarithmic equidistant intervals be measured and in a subsequent step from the thus obtained Measured values the temperature differences are interpolated.

Under the feature that the times are in logarithmically equal time intervals, is to be understood in particular that a quotient of a first Time at which the temperature difference is measured, and a the second time following the first date, to which the Temperature difference is measured, constant, which is a geometric Order of the measuring times results.

The Applying the sample with a time-constant heating power For example, by a heating wire or a heating strip respectively. It is then a Heizdrahtverfahren, in his Full or half-space version.

According to one embodiment is the thermal transport size one thermal conductivity and the method comprises the steps of determining a maximum Slope of time-dependent Temperature difference depending from a logarithmized time coordinate and a calculation of the Thermal conductivity the maximum slope.

alternative or additively, the thermal transport size is a thermal conductivity and the method comprises the steps of determining a maximum slope time to which the maximum slope of the time-dependent temperature difference dependent on from the logarithmized time coordinate, and a calculation the thermal conductivity from the maximum slope time.

A particularly high accuracy in determining the thermal transport size is obtained when the slope curve of the time-dependent temperature difference an analytically writable fit curve is adjusted. The fit curve, the one solution the heat equation is preferably has only two adaptation parameters, namely the thermal conductivity to be measured and the thermal conductivity to be measured.

A Further improvement of the measuring accuracy is achieved when the second distance at most the half, in particular at most a third, a sample width of the sample and a length of the heat source is. In this way, outer edge effects suppressed.

One another advantage for the measuring method opposite the known Heizdrahtverfahren is the deciding necessity for foreknowledge the thermal conductivity the sample to set the correct measurement duration. This allows the Realization of the fully automatic measuring device, which saves personnel costs.

The measurement preferably lasts until the slope of the recorded temperature difference has sufficiently dropped after passing the maximum. For maximum determination, it is sufficient if the slope deviation is more than 2-3 times a measurement error variable. The measurement error variable is calculated from the measured values already measured. For the higher accuracy of the two measured values of the thermal conductivity and the thermal diffusivity in the evaluation by means of adaptation method is a longer measuring time necessary. It can be measured until external edge effects occur considerably.

Out practically realizable measuring device ratios of the sample size and heat source length for Distance D2 (twice to five times greater than D2 or higher), The measurement at the drop can be 0.8 times the maximum Slope of the measurement are interrupted. At a larger ratio of Sample size to the distance D2 is to be measured in particular until the slope up under 0.6 times or even dropped below 0.4 times is what improves the accuracy.

Prefers The method further comprises the steps of (a) calculating an Parameters that determine the deviation of the measured values from an analytical Solution, the heat conduction equation and (b) outputting one based on the parameter calculated measurement error value, which is the measurement error of the performed procedure characterized.

Prefers will be more than two time-dependent Temperature differences between three, four or more temperature measuring points detected, the temperature measuring points in pairs each Distances to Wärmeeinleitstelle to have. This multiple arrangement allows the measurements in inhomogeneous Substances.

in the The invention will be explained in more detail below with reference to the attached figures. there shows

1 a diagram of a thermal transport size measuring device according to the invention,

2 a flowchart of an embodiment of a method according to the invention and

3 a diagram in which the unitless slope of the time-dependent temperature difference as a function of the logarithmic unitless time coordinate is plotted.

1 shows a thermal transport size measuring device 10 with a heater 12 in the form of a heating wire, with a regulated power source 14 connected is. The power source 14 is designed to be connected to the heater 12 to apply such an electrical voltage that the heating device 12 gives a constant heating power q. For example, the power source indicates 14 a constant electric current I, provided that the electrical resistance of the wire is sufficiently constant with temperature change.

The heater 12 is in contact with a sample 16 from which a thermal transport quantity is to be measured, for example a thermal conductivity a or a thermal conductivity λ. There, where the sample 16 with the heater 12 Contact has, is a heat introduction site 18 , which in the present case is a line. The sample 16 has a sample width B, which is the distance from the heater 12 is measured. The heat introduction point is the length L.

In the sample 16 is a first temperature meter 20 arranged, which forms a first temperature measuring point and a first distance D1 from the heat introduction point 18 Has. In the sample 16 is also a second temperature meter 22 arranged, the second temperature measuring point forms a second distance D2 from the heat introduction point 18 has. The temperature meter 20 . 22 are via electrical cables with an electrical evaluation unit 24 connected. The temperature at these measuring points can also be optically captured with a pyrometer or infrared camera.

To carry out a method according to the invention, first an input device is used 26 For example, a keyboard or a touch screen, the selected heating power q and the distances D1 and D2 entered. In addition, the measured value number N is indicated, which indicates the number of measured values to be recorded in the course of carrying out a method according to the invention.

wobei t_mess eine voreingestellte oder erwartete Messdauer ist und dt ein Zeitinkrement ist, das einer Ansprechzeit entspricht, wenn ein analoges Messgerät verwendet wird, und einer Abtastrate entspricht, wenn ein analoges Messgerät verwendet wird.Then the measurement is started and both temperature meters 20 . 22 Take temperature readings T1 (t _i ) and T2 (t _i ) at short intervals. I is a run variable for which i = 1, 2, 3, ... N. The evaluation unit 24 calculates a factor from the number of measured values N to be recorded and the entered measuring time t _mess

where t _{meas is} a preset or expected measurement duration and dt is a time increment corresponding to a response time when an analog gauge is used and a sampling rate when using an analog gauge.

und es werden Messwerte zu den Zeitpunkten T0 = 1 s, T2 = 2 s, ..., T10 = 1024 s aufgenommen. Die Messwerte werden danach digitalisiert. Aus den so aufgenommenen Temperaturmesswerten berechnet die Auswerteeinheit 24 eine Temperaturdifferenz ΔT(ti) = T1(ti) – T2(ti) (2). The time increment dt determines a device-specific time variable. If, for example, N = 11 measured values are to be recorded in the measuring time t _mess = 1024 s and the time interval dt = 1 s, the result is

and measured values are recorded at the times T0 = 1 s, T2 = 2 s,..., T10 = 1024 s. The measured values are then digitized. The evaluation unit calculates from the thus recorded temperature measured values 24 a temperature difference .DELTA.T (t i ) = T1 (t i ) - T2 (t i ) (2).

The following describes, as seen from the temperature difference .DELTA.T (t _i), the thermal transport size is calculated. The exact solution of the heat equation for the temperature difference .DELTA.T (t) between the two points D1 and D2 is

there Egg is the integral sinus function.

folgt mit Gleichung (4)

For the logarithmic time In t follows

follows with equation (4)

und besitzt zu einem Maximalsteigungs-Zeitpunkt m_max, für das gilt:

The dimensionless part in parentheses describes the characteristic behavior of the temperature difference slope in logarithmic time, which is referred to in other than m

and has at a maximum slope time m _max , for which applies:

The thus calculated unitless maximum slope is only from the distances D1 and D2 dependent.

The measured values are recorded in logarithmically equidistant times t ₀ , t ₁ ,..., T _N , therefore it applies

wobei in der letzten Zeile Formel (8) eingesetzt wurde. Einsetzen der Definition von K_T nach Gleichung (3) und Auflösen nach λ liefert

In the maximum slope time t _max , approximately the difference quotient applies

where in the last line formula (8) was used. Substituting the definition of K _T according to equation (3) and solving for λ yields

The thermal diffusivity a can be calculated from the maximum slope time t _max by equating equation (8) for t _max with equation (6)

und ihren maximalen Wert

mit der entsprechenden Zeit t_max.The evaluation unit 24 detects the temperature difference .DELTA.T (t _i ) at the predetermined times t _i and determines therefrom, for example, numerically based on the difference quotient of the temperature difference slope

and their maximum value

with the appropriate time t _max .

und ihres fallenden Teils mit der Funktion nach (Gleichung 6) angepasst werden, die analytische Lösung für die gegebene Messvorrichtung darstellt und enthält als Anpassungsparameter die gemessenen Transportgrößen enthält.With the aid of equation (11), the thermal conductivity λ is then calculated and output on a display device not shown. Alternatively or additionally, by means of equation (12) the Tem permeability a calculated and output. The calculation of the measured heat transfer quantities λ and α can thereby be carried out with greater accuracy, that in an environment of maximum temperature difference gradient

and its falling part with the function according to (Equation 6), which represents the analytical solution for the given measuring device and contains as the adaptation parameter the measured transport quantities.

2 shows a flow chart of a method according to the invention, which can be realized with digital devices. In one step 1 the initial values are determined, where dt is the time increment (analog and analog digital sample rate response time). The time increment is usually between 1 ms and 1 s.

In one step 2 a calculation is made of the number of measurements ni for the ith temperature difference value for averaging in the form of a logarithmic signal smoothing.

In one step 3 deliver the temperature gauge 20 . 22 temporally equidistant measured values, for example at intervals of 5 ms. From this, the logarithmically equidistant temperature difference measured values ΔT are determined by forming a moving average over ni measured values.

In one step 4 will be out of the step 3 determined temperature difference .DELTA.T _i the slope ΔΔT (t _i ) calculated at the time t _i . In step 5 the time t _{i is} calculated as a geometric mean from the start and end times of the current logarithmic time interval.

In step 6 the maximum slope m _max and the maximum slope time t _{max is} determined. If a termination condition 7 is satisfied, there is an output of the results, namely he thermal conductivity λ and the thermal diffusivity a.

In step 7 two alternative termination conditions are shown. The measurement is ended when either the preset measuring time has been reached. Alternatively, the measurement may be terminated when the last measured value for the slope m is less than 0.8 of the previous maximum value.

aufgetragen.In 3 is the unitless slope m (unitless) for different quotients D2 / D1 against the logarithmic unitless time coordinate

applied.

10

Thermotransport sizer

12

heater

14

power source

16

sample

18

Wärmeeinleitstelle

20

temperature measuring

22

temperature measuring

24

evaluation

26

input device

N

number the measured values

D1

first distance

D2

second distance

B

sample width

L

Length of Wärmeeinleitstelle

q

heating capacity

a

thermal diffusivity

λ

thermal conductivity

t

Time

t _mess

measuring time

dt

response time or tasting

i

counting index 1, 2 ...

T1

temperature

T2

temperature

.DELTA.T

temperature difference

ΔΔT

pitch the temperature difference

f

factor

Claims (9)

Method for measuring a thermal transport size of a sample ( 16 ), with the steps (a) applying the sample ( 16 ) with a time-constant heating power (q) in a linear heat introduction point ( 18 ), (b) detecting a time-dependent temperature difference (ΔT) between (i) a first temperature measuring point ( 20 ) at a first distance (D1) to the heat introduction point ( 18 ) and (ii) a second temperature measuring point ( 22 ) at a second distance (D2) to the heat introduction point ( 18 ) at a plurality of points in time (t _i ), characterized in that (c) the time-dependent temperature difference (ΔT) is recorded at logarithmically equidistant time intervals or the detection takes place at non-logarithmically equidistant time intervals and the temperature differences are interpolated from the measured values obtained in this way and ( d) the method comprises the steps - determining a maximum slope (ΔΔT _max ) of the time-dependent temperature difference (ΔT (Int)) as a function of a logarithmic time coordinate (In t) and - calculating the thermal conductivity (λ) from the maximum slope ((ΔΔT _max ) and / or - determining a maximum slope time (t _max ) at which the maximum slope ((ΔΔT _max ) of the time-dependent temperature difference (ΔT (In t)) is dependent on the logarithmic time coordinate (In t), and Calculating the thermal conductivity (a) from the maximum slope time (t _max ). Method according to claim 1, characterized by steps - To adjust a time-dependent Slope function of time-dependent Temperature difference (ΔT (In t)) with a compensation function, in particular one of the thermal conductivity and the thermal conductivity as a parameter-containing analytical solution for the time-dependent slope function, and - Determine thereby the thermal conductivity and / or thermal conductivity using the compensation function. Method according to one of the preceding claims, characterized characterized in that one of the second distance (D2) at most the half, in particular at most a third, a sample width (B) and a heat source length L is. Method according to one of the preceding claims, characterized in that the application of the sample ( 16 ) with the temporally constant heating power (q) by means of a heating wire ( 12 ), a heating strip or a radiation source. Method according to one of the preceding claims, characterized in that the time-dependent temperature difference (ΔT) is measured until the slope (ΔΔT) of the measured temperature differences after passing the maximum slope ((ΔΔT _max ) below 0.8, in particular below 0 , 6, in particular, falls below 0.4 of the maximum level. Method according to one of the preceding claims, characterized characterized in that the temperature differences with a digital gauge recorded and a digital signal smoothing is performed. Method according to one of the preceding claims, characterized characterized in that the signal smoothing by means of averaging is carried out by running at a constant rate measured values such that the number of calculated values with a constant factor during the Measurement increases. Thermotransport size measuring device for measuring a thermal transport size of a sample ( 16 ), with (a) a heating device for charging the sample ( 16 ) with a time-constant heating power (q) in a linear heat introduction point ( 18 ), (b) a first temperature meter ( 20 ), which at a first distance (D1) to the heat introduction point ( 18 ), and (c) a second temperature meter ( 22 ), which at a second distance (D2) to the heat introduction parts ( 18 ), characterized by (d) an evaluation unit ( 24 ) arranged to perform a method according to any one of the preceding claims. Thermotransportgrößenmessvorrichtung according to claim 8, characterized in that the heating device ( 12 ) is a heating wire.