CN112485293B - Method for correcting hot surface temperature in large-temperature-difference heat flow meter method heat conduction instrument test - Google Patents
Method for correcting hot surface temperature in large-temperature-difference heat flow meter method heat conduction instrument test Download PDFInfo
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Abstract
The invention relates to a method for correcting the temperature of a hot surface in the test of a heat conduction instrument by a large temperature difference heat flow meter method, belongs to the technical field of the test of the heat conduction instrument, and solves the problem of low measurement precision of the heat conductivity caused by large nonuniformity of the temperature of the hot surface in the prior art. The method comprises the following steps: testing the standard sample by using a heat conduction instrument of a protection hot plate method under the condition of small temperature difference, and fitting to obtain a coefficient representing the functional relation between the temperature and the heat conductivity of the standard sample; testing a standard sample under a large temperature difference condition by using a large temperature difference heat flow meter method heat conduction instrument to obtain the weight coefficients of a plurality of temperature thermocouples in a central metering area of a hot surface of the sample; and testing the sample to be tested by using a large temperature difference heat flow meter method, and correcting the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample to be tested based on the weight coefficient to obtain the corrected hot surface temperature. The method can correct the temperature of the hot surface, and the corrected temperature of the hot surface is used for calculating the thermal conductivity, so that the accuracy of the thermal conductivity can be effectively improved.
Description
Technical Field
The invention relates to the technical field of testing of a large-temperature-difference heat flow meter method heat conduction instrument, in particular to a method for correcting the temperature of a hot surface in the testing of the large-temperature-difference heat flow meter method heat conduction instrument.
Background
In a large temperature difference heat flow meter method heat conduction instrument, in order to realize the temperature uniformity of a sample with the cross section size of 300mm multiplied by 300mm in a central metering area of 100mm multiplied by 100mm, a flat heater above the sample adopts a palace structure which is gradually encrypted from the center to the periphery so as to compensate the heat loss of a side wall surface of the sample. Although the temperature uniformity in the central metering area is effectively improved by the measure, the temperature uniformity cannot be completely realized, and the high-temperature test at 1000 ℃ shows that the temperature non-uniformity in the area is between 2 and 3 percent. Tests show that the temperature nonuniformity of the sample in the hot surface is large, and the temperature nonuniformity and the heat flow density nonuniformity of the cold surface are small. The non-uniformity of the hot face temperature is seen to be most pronounced. How to provide a correction algorithm for the non-uniformity to improve the measurement accuracy of the thermal conductivity is still lacking.
Disclosure of Invention
In view of the foregoing analysis, an embodiment of the present invention is directed to providing a method for correcting a temperature of a hot surface in a large-temperature-difference heat flow meter method heat conduction instrument test, so as to solve a problem in the prior art that a measurement accuracy of thermal conductivity is low due to large nonuniformity of the temperature of the hot surface.
The embodiment of the invention provides a method for correcting the temperature of a hot surface in a large-temperature-difference heat flow meter method heat conduction instrument test, which comprises the following steps:
step S1: testing the standard sample by using a heat conduction instrument of a protective hot plate method under the condition of small temperature difference, and fitting to obtain a coefficient representing the functional relation between the temperature and the heat conductivity of the standard sample;
step S2: testing a standard sample under a large temperature difference condition by using a large temperature difference heat flow meter method heat conduction instrument, and obtaining weight coefficients of a plurality of temperature thermocouples in a hot surface central metering area of the sample based on the obtained heat flow density of the standard sample in the thickness direction of the standard sample, the temperature measurement values of the plurality of temperature thermocouples in the hot surface central metering area, the temperature measurement values of the plurality of temperature thermocouples in a cold surface central metering area and the coefficients under different hot surface central point temperatures of the standard sample;
step S3: and testing the sample to be tested by using a large temperature difference heat flow meter method, and correcting the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample to be tested based on the weight coefficient to obtain the corrected hot surface temperature.
On the basis of the scheme, the invention also makes the following improvements:
further, in the step S1,
the function relationship between the standard sample temperature and the thermal conductivity is as follows:
λ(T i )＝a 0 +a 1 T i +a 2 T i 2 +…+a M T i M (1)
wherein, T i The standard sample temperature at the ith test is shown, i is 1,2,3, …, P is shown, and P is the test times of the protective hot plate method heat conduction instrument; lambda (T) i ) Denotes the temperature of the standard sample as T i Thermal conductivity of (a) 0 、a 1 、a 2 、…、a M The method is characterized in that M coefficients representing a polynomial function relationship between the temperature and the thermal conductivity of a standard sample are provided, and M is less than or equal to P.
Further, based on the collected P times of standard sample temperature and thermal conductivity and formula (1), fitting to obtain the coefficient a 0 、a 1 、a 2 、…、a M 。
Further, the step S2 includes:
step S21: based on the obtained heat flux density of the standard sample in the thickness direction of the standard sample at different hot surface central point temperatures, the temperature measurement values of a plurality of temperature thermocouples in the hot surface central metering area, the temperature measurement values of a plurality of temperature thermocouples in the cold surface central metering area and the coefficient, obtaining the temperature average value of the hot surface of the sample at the corresponding hot surface central point temperature:
wherein, L represents the thickness of the sample to be measured; q. q of j The heat flow density in the thickness direction of the standard sample is represented in the j test, wherein j is 1,2,3, …, N and N represent the test times of the large-temperature-difference heat flow meter method heat conduction instrument; t is t j Represents the flat surface temperature of the standard sample at the j testMean value; t is a unit of j The average temperature value of the hot surface of the sample at the temperature of the central point of the hot surface in the j test is represented;
step S22: obtaining weight coefficients of a plurality of temperature thermocouples in the central measuring area of the hot surface of the sample based on the temperature measured values of the plurality of temperature thermocouples in the central measuring area of the hot surface of the standard sample at different central point temperatures of the hot surface and the temperature average value of the hot surface of the sample;
wherein, Y ═ T 1 ,T 2 ,…，T j ,…,T N ,1]′；
Further, the average value of the cold surface temperature of the standard sample is obtained by averaging the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the cold surface.
Further, when the central metering area is square, temperature thermocouples are respectively arranged at the following positions of the hot surface and the cold surface:
the center point of the sample, four vertexes of the central metering area and the midpoints of four edges of the central metering area.
Further, the cross-sectional dimension of the sample is 300mm × 300mm, and the central metering area is an area of 100mm × 100mm in the center of the sample.
Further, the small temperature difference means that the temperature difference between the hot surface and the cold surface of the standard sample is not more than 30 ℃.
Further, when the standard sample is tested under the condition of small temperature difference by using a heat conduction instrument adopting a protective hot plate method, the temperature of the standard sample is not more than 600 ℃.
Further, the large temperature difference means that the temperature difference between the hot surface and the cold surface of the standard sample exceeds 50 ℃, and the temperature of the central point of the cold surface of the standard sample is kept at 30 +/-10 ℃.
Compared with the prior art, the scheme of the invention has the following beneficial effects:
1. in a conventional thermal conductivity calculation method, if the temperature of the central point of the hot face is directly taken to participate in the thermal conductivity calculation, the influence of uneven temperature in the central metering area of the hot face is not considered; if a simple average value of the temperatures of different points in the central area is directly taken as the hot face temperature to participate in calculation, the influence of temperature nonuniformity is considered, but the influence degree of the temperature values at different positions on the calculation of the thermal conductivity is not considered. The correction method of the hot surface temperature in the test of the large-temperature-difference heat flow meter heat conduction instrument fully considers the weight coefficient of the temperature collected by the thermocouples distributed at different positions of the hot surface, provides a correction method of the hot surface temperature with higher reliability, can meet the actual test requirement, and is convenient for obtaining the heat conductivity with higher accuracy;
2. in the correction process, firstly, a standard sample is tested under the condition of small temperature difference through a protective hot plate method heat conduction instrument, and a coefficient representing the functional relation between the temperature and the heat conductivity of the standard sample is obtained through fitting; then, testing the same standard sample under a large temperature difference condition by using a large temperature difference heat flow meter method heat conduction instrument to obtain the weight coefficients of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample; and finally, testing the sample to be tested by using a large temperature difference heat flow meter method, and correcting the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample to be tested based on the weight coefficient to obtain the corrected hot surface temperature. The method has strong practicability and operability, and provides guidance for correcting the hot-face temperature for the personnel in the field.
In the invention, the technical schemes can be combined with each other to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.
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The drawings, in which like reference numerals refer to like parts throughout, are for the purpose of illustrating particular embodiments only and are not to be considered limiting of the invention.
Fig. 1 is a flowchart of a method for correcting the temperature of a hot surface in a large-temperature-difference heat flow meter method heat conduction instrument test in the embodiment of the invention.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The invention discloses a method for correcting the temperature of a hot surface in a large-temperature-difference heat flow meter method heat conduction instrument test, which is shown in a flow chart shown in figure 1 and comprises the following steps:
step S1: testing the standard sample by using a heat conduction instrument of a protective hot plate method under the condition of small temperature difference, and fitting to obtain a coefficient representing the functional relation between the temperature and the heat conductivity of the standard sample;
in step S1, based on the mathematical principle, the general functional relationship can be developed into the expression form of the sum of high-order polynomials by taylor series. In addition, a great deal of practical experience in thermal conductivity testing of insulation materials has also shown that the thermal conductivity versus temperature relationship can be well fitted with higher order polynomials over the temperature range being tested.
Therefore, in the present embodiment, it is assumed that the functional relationship between the standard sample temperature and the thermal conductivity is:
λ(T i )＝a 0 +a 1 T i +a 2 T i 2 +…+a M T i M (1)
wherein, T i The standard sample temperature at the ith test is shown, i is 1,2,3, …, P is shown, and P is the test times of the protective hot plate method heat conduction instrument; lambda (T) i ) Denotes the temperature of the standard sample as T i Thermal conductivity of (a) 0 、a 1 、a 2 、…、a M The method comprises the following steps of (1) representing M coefficients of a polynomial function relation between standard sample temperature and thermal conductivity, wherein M is less than or equal to P;
based on the collected P times of standard sample temperature and thermal conductivity and a formula (1), fitting to obtain the coefficient a 0 、a 1 、a 2 、…、a M (ii) a In the fitting process, the coefficients can be obtained by selecting the existing fitting mode, and the fitting mode is not limited in the embodiment.
Since the difference between the heat flow density and the temperature at different positions in the metering area of the cold surface of the standard sample is small, the measured values are directly averaged to be used as the average value of the heat flow density and the temperature of the cold surface. And the temperature difference at different positions in the hot-face measurement area of the sample is large, so the hot-face average temperature is obtained by adopting a weighted average algorithm, and step S2 introduces a specific process of obtaining the weight coefficient of the weighted average algorithm:
the step S2 specifically includes:
step S21: testing the same standard sample under a large temperature difference condition by using a large temperature difference heat flow meter method heat conduction instrument (the cold surface temperature of the standard sample is within 30 +/-10 ℃, and the hot surface temperature is set to be different, and can reach 1000 ℃);
based on the obtained heat flux density of the standard sample in the thickness direction of the standard sample at different hot surface central point temperatures, the temperature measurement values of a plurality of temperature thermocouples in the hot surface central metering area, the temperature measurement values of a plurality of temperature thermocouples in the cold surface central metering area and the coefficient, obtaining the temperature average value of the hot surface of the sample at the corresponding hot surface central point temperature:
wherein, L represents the thickness of the sample to be measured; q. q of j The heat flow density in the thickness direction of the standard sample is shown in the j test, j is 1,2,3, …, and N is the test times of the large temperature difference heat flow meter method heat conduction instrument; t is t j The average value of the cold surface temperature of the standard sample in the jth test is represented, and the average value is obtained by averaging the temperature measurement values of a plurality of temperature thermocouples in the cold surface central metering area; t is j The average temperature value of the hot surface of the sample at the temperature of the central point of the hot surface in the j test is shown;
due to a 0 ,a 1 ,a 2 ,…a M For the calculated quantity, the average values q of the heat flow density and the cold surface temperature are obtained by simple average calculation by utilizing the heat flow density and the temperature measured value of different positions in the central metering area of the cold surface of the sample at different temperatures j And t j Calculating the average temperature T in the hot surface metering area of the sample by the back-stepping calculation of the formula (2) j 。
Step S22: obtaining weight coefficients of a plurality of temperature thermocouples in the central measuring area of the hot surface of the sample based on the temperature measured values of the plurality of temperature thermocouples in the central measuring area of the hot surface of the standard sample at different central point temperatures of the hot surface and the temperature average value of the hot surface of the sample;
assuming that R thermocouples (R is less than or equal to N) are arranged in the central metering area of the hot surface of the sample, the temperature measurement values in the jth thermal conductivity test are respectively T j1 ,T j2 ,…,T jk ,…T jR . Suppose the weight values of R thermocouples are respectively b 1 ,b 2 ,…，b k ,…b R Then there is
b 1 +b 2 +…+b k +…+b R ＝1
T 11 b 1 +T 12 b 2 +…+T 1k b k +…+T 1R b R ＝T 1
……
T j1 b 1 +T j2 b 2 +…+T jk b k +…+T iR b R ＝T j
……
T N1 b 1 +T N2 b 2 +…+T Nk b k +…+T NR b R ＝T N
The above series of equations is written as a matrix situation as follows:
Y (N+1)×1 ＝T (N+1)×R ·B R×1 (3)
wherein
Y＝[T 1 ,T 2 ,…，T j ,…,T N ,1]′
B＝[b 1 ,b 2 ,…,b k ,…,b R ]′
b k The weight coefficient of the kth temperature thermocouple in the central metering area of the sample hot surface is represented, wherein k is 1,2, R and R represent the number of the temperature thermocouples in the central metering area of the sample hot surface, and R is less than or equal to N;
T j,k and (4) representing the temperature measurement value of the kth temperature thermocouple in the central metering area of the hot surface of the sample at the j test.
Y and T are known amounts and B is a quantity to be determined.
Define the sum of squared residuals S as:
S＝(Y-T·B)′·(Y-T·B)
when S takes an extreme value, the optimal solution of B can be obtained
Namely, it is
Wherein T is k Is the kth column vector of the matrix T.
Thus, the following formula:
by solving the above equation, the
Step S3: and testing the sample to be tested by using a large temperature difference heat flow meter method, and correcting the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample to be tested based on the weight coefficient to obtain the corrected hot surface temperature.
Obtaining the weighted value of the temperature of R points in the hot surface central metering area through the calculation
The method is used as a set of built-in parameters of a large temperature difference heat flow meter method heat conduction instrument.
When testing the thermal conductivity of a sample, the temperature at different points in the hot-face metrology area is measured as T ═ T 1 ，T 2 ，T 3 ，…，T R ]', then adopt
The effective average temperature of the hot face of the sample was taken into account in the calculation of the thermal conductivity.
It should be noted that, since the protection hot plate method heat conduction instrument and the large temperature difference heat flow meter method heat conduction instrument are both in the prior art, this embodiment is not described again.
In a conventional thermal conductivity calculation method, if the temperature of the central point of the hot face is directly taken to participate in the thermal conductivity calculation, the influence of uneven temperature in the central metering area of the hot face is not considered; if a simple average value of the temperatures of different points in the central area is directly taken as the hot face temperature to participate in calculation, the influence of temperature nonuniformity is considered, but the influence degree of the temperature values at different positions on the calculation of the thermal conductivity is not considered.
The correction method of the hot surface temperature in the test of the large-temperature-difference heat flow meter method heat conduction instrument provided by the invention fully considers the weight coefficient of the temperature collected by the thermocouples distributed at different positions of the hot surface, provides a correction method of the hot surface temperature with higher reliability, can meet the actual test requirement, and is convenient for obtaining higher-precision heat conductivity.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (10)
1. A method for correcting the temperature of a hot surface in the test of a large-temperature-difference heat flow meter method heat conduction instrument is characterized by comprising the following steps:
step S1: testing the standard sample by using a heat conduction instrument of a protection hot plate method under the condition of small temperature difference, and fitting to obtain a coefficient representing the functional relation between the temperature and the heat conductivity of the standard sample;
step S2: testing a standard sample under a large temperature difference condition by using a large temperature difference heat flow meter method heat conduction instrument, and obtaining weight coefficients of a plurality of temperature thermocouples in a hot surface central metering area of the sample based on the obtained heat flow density of the standard sample in the thickness direction of the standard sample, the temperature measurement values of the plurality of temperature thermocouples in the hot surface central metering area, the temperature measurement values of the plurality of temperature thermocouples in a cold surface central metering area and the coefficients under different hot surface central point temperatures of the standard sample;
step S3: and testing the sample to be tested by using a large temperature difference heat flow meter method, and correcting the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the hot surface of the sample to be tested based on the weight coefficient to obtain the corrected hot surface temperature.
2. The method for correcting the hot face temperature in the test of the large temperature difference heat flow meter method heat conduction instrument according to claim 1, wherein in the step S1,
the function relationship between the standard sample temperature and the thermal conductivity is as follows:
λ(T i )＝a 0 +a 1 T i +a 2 T i 2 +…+a M T i M (1)
wherein, T i The standard sample temperature at the ith test is shown, i is 1,2,3, …, P is shown, and P is the test times of the protective hot plate method heat conduction instrument; lambda (T) i ) Denotes the temperature of the standard sample as T i Thermal conductivity of (a) 0 、a 1 、a 2 、…、a M The method is characterized in that M coefficients representing a polynomial function relationship between the temperature and the thermal conductivity of a standard sample are provided, and M is less than or equal to P.
3. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to claim 2,
based on the collected P times of standard sample temperature and thermal conductivity and a formula (1), fitting to obtain the coefficient a 0 、a 1 、a 2 、…、a M 。
4. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter type heat conduction instrument according to claim 3, wherein the step S2 comprises the following steps:
step S21: based on the obtained heat flux density of the standard sample in the thickness direction of the standard sample at different hot surface central point temperatures, the temperature measurement values of a plurality of temperature thermocouples in the hot surface central metering area, the temperature measurement values of a plurality of temperature thermocouples in the cold surface central metering area and the coefficient, obtaining the temperature average value of the hot surface of the sample at the corresponding hot surface central point temperature:
wherein, L represents the thickness of the sample to be measured; q. q.s j The heat flow density in the thickness direction of the standard sample is represented in the j test, wherein j is 1,2,3, …, N and N represent the test times of the large-temperature-difference heat flow meter method heat conduction instrument; t is t j The average value of the cold surface temperature of the standard sample in the j test is shown; t is a unit of j The average temperature value of the hot surface of the sample at the temperature of the central point of the hot surface in the j test is represented;
step S22: obtaining weight coefficients of a plurality of temperature thermocouples in the central measuring area of the hot surface of the sample based on the temperature measured values of the plurality of temperature thermocouples in the central measuring area of the hot surface of the standard sample at different central point temperatures of the hot surface and the temperature average value of the hot surface of the sample;
wherein, Y ═ T 1 ,T 2 ,…，T j ,…,T N ,1]′；
5. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to claim 4,
the average value of the cold surface temperature of the standard sample is obtained by averaging the temperature measurement values of a plurality of temperature thermocouples in the central metering area of the cold surface.
6. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to any one of claims 1 to 5,
when the central metering area is square, temperature thermocouples are respectively arranged at the following positions of the hot surface and the cold surface:
the center point of the sample, four vertexes of the central metering area and the midpoints of four edges of the central metering area.
7. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to any one of claims 1 to 5,
the cross-sectional dimensions of the sample were 300mm by 300mm and the central metering area was the area of the sample at the centre of 100mm by 100 mm.
8. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to any one of claims 1 to 5,
the small temperature difference means that the temperature difference between the hot surface and the cold surface of the standard sample is not more than 30 ℃.
9. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to any one of claims 1 to 5,
when the standard sample is tested by using a heat conduction instrument of a protection hot plate method under the condition of small temperature difference, the temperature of the standard sample does not exceed 600 ℃.
10. The method for correcting the temperature of the hot surface in the test of the large-temperature-difference heat flow meter method heat conduction instrument according to any one of claims 1 to 5,
the large temperature difference means that the temperature difference between the hot surface and the cold surface of the standard sample exceeds 50 ℃, and the temperature of the central point of the cold surface of the standard sample is kept at 30 +/-10 ℃.
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