CN111610224B - Data processing method for transient measurement of thermophysical properties of material by hot-wire method - Google Patents
Data processing method for transient measurement of thermophysical properties of material by hot-wire method Download PDFInfo
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Abstract
The invention discloses a data processing method for transient measurement of thermophysical properties of a material by a hot wire method, which is characterized in that the objective rule of transient measurement of the thermophysical properties of the material is reflected by correcting a calculation formula of heat conductivity lambda and a heat diffusion coefficient a in the method, and the measured values of the heat conductivity, the heat diffusion coefficient, the specific heat capacity at constant pressure and the heat storage coefficient are accurately obtained.
Description
Technical Field
The invention belongs to the field of thermal science and heat transfer science, and relates to a method for measuring the thermophysical property of a material.
Background
The general principle of transient measurement of the thermophysical properties of the material by the hot wire method is that the temperature change rule of the contact interface between the surface of the hot wire and the medium in the heating and temperature rising process in the measuring device is as follows
In the formula, slope
Intercept of a beam
Areal density of heat flow
Where I represents the current passing in the hot wire, in units: ampere; r is the resistance of the hot wire, unit: ohm; r is a radical of hydrogen0Is the hot wire radius, in units: rice; l is the hot wire length, unit: and (4) rice.
Since equation (1) is a standard linear equation. Therefore, only one set of measuring device is developed, and a series of ln tau can be measured by adopting an experimental methodiAnd thetai(r0,τi) Linear fitting can be carried out by using a least square method, the slope k and the intercept D of a fitting straight line are calculated and substituted into the formulas (2) and (3), and the calculation formula of the thermal conductivity lambda of the material to be measured in the hot-wire method transient measurement can be immediately obtained as
Meanwhile, the calculation formula of the thermal diffusion coefficient a can be obtained as
Using the above formulas, transient measurements of the thermophysical properties of the materials appear to be achievable using the hot wire method.
However, this is far from the practical point that when a measuring device is developed for use in actual measurement, the applicant notes that: the measured value of the thermal conductivity obtained by measurement is far greater than the accepted value of the thermal conductivity of the material, and even the difference is of an order of magnitude. Why is this? This is the first difficulty encountered and needs to be treated carefully to be solved.
In addition, the applicant has also noted that: the measured thermal diffusivity is also an order of magnitude smaller, not in accordance with accepted values for the thermal diffusivity of materials.
Furthermore, when the measured values of the thermal conductivity and the thermal diffusivity obtained above are used to calculate the specific heat capacity at constant pressure of the material, the calculated value is an order of magnitude larger than the recognized value.
This series of problems shows the fact that: it seems that the general theory of the thermal-physical property of the material measured by the hot-wire method transient state established by directly applying the one-dimensional cylindrical surface heat transfer model and the derived calculation formula can not be directly used for the data calculation of the thermal-physical property of the material measured by the hot-wire method transient state.
Thus, the applicant is faced with two options, namely either abandoning the general theory of transient measurement of the thermophysical property of the material by the hot-wire method established according to the one-dimensional cylindrical surface heat transfer theory or modifying the calculation formula of the transient measurement of the thermophysical property of the material by the hot-wire method so as to enable the thermal conductivity and the thermal diffusivity of the material to be suitable for transient measurement. That is, if we want to continue to use the one-dimensional cylindrical surface heat transfer model to measure the thermophysical properties of the material in the hot-wire transient state, we have to modify equations (5) and (6) and explore new equations for transient measurement of thermal conductivity and thermal diffusivity calculation, so that we can more accurately measure the thermophysical properties of the material by reflecting the objective law of transient measurement of thermophysical properties of the material.
Disclosure of Invention
Aiming at the problems, through careful research and repeated verification, the inventor finds a new mathematical model for solving the thermal conductivity and the thermal diffusion coefficient, further perfects the theory and the method for transient measurement of the thermophysical properties of the material by a hot-wire method, and adopts the technical scheme that:
a data processing method for transient measurement of thermophysical properties of a material by a hot-wire method comprises the following steps:
first, preparation step
1) Manufacturing a standard sample of the material to be tested, wherein the sample is two homogeneous cube samples;
2) manufacturing a set of measuring instrument, wherein the measuring instrument comprises a probe, a current-stabilizing power supply, a data acquisition unit and a data processor;
3) establishing a physical mathematical model for solving the thermophysical parameters of the material, compiling a software program according to the physical mathematical model, writing out a code and storing the code into a measuring instrument;
second, measurement step
1) Clamping the probe between the two samples to make the hot wire stick to the central axis of the sample plane of the standard sample;
2) introducing constant current to the probe;
3) the probe sends the detected temperature signal to the data acquisition unit, and the data acquisition unit converts the temperature signal into a corresponding digital signal;
4) the data processor runs a software program to calculate and process the digital signal to obtain the value of the thermophysical parameter;
the method is characterized in that the physical mathematical model for solving the thermophysical parameters of the material is based on a primary integral expression of an accurate solution of a one-dimensional cylindrical surface heat transfer problem, and the temperature change rule at the contact interface of the hot wire surface and a medium is as follows in the heating and warming process:
in the formula, slope
Intercept of a beam
Areal density of heat flow
Where I represents the current passing in the hot wire, in units: ampere; r is the resistance of the hot wire, unit: ohm; r is0Is a hot wire halfDiameter, unit: rice; l is the hot wire length, unit: and (4) rice.
Experimentally, a series of ln τ and θ (r) were measured0Tau), linear fitting is carried out by using a least square rule, the slope k and the intercept D of a fitting straight line are calculated and substituted into the formulas (2) and (3), and then the formula (4) is substituted, so that the calculation formula for obtaining the thermal conductivity lambda of the material to be measured by the hot-wire method transient measurement is shown as
The thermal diffusion coefficient a is calculated by the formula
As can be seen from the above equation (5), the main factor causing the thermal conductivity λ to become larger in magnitude is the heat ray radius too small, generally 10-4Magnitude. If remove 2 π r0This factor, equation (5) will be reduced to
Changing from equation (5) to equation (7) by removing a constant factor of 2 π r0The concept of the heat flux density is changed from the heat flux surface density to the heat flux linear density, and the change does not change the physical meaning of the formula; but the magnitude relation of the calculation formula is adjusted, so that the magnitude of the transient measurement thermal conductivity of the hot wire method is not increased, and the physical meaning of the calculation formula is kept unchanged; just as such, it is reasonable and reliable that formula (5) becomes formula (7); therefore, when the thermophysical property of the material is measured in a hot-wire transient manner by using the one-dimensional cylindrical surface heat transfer model, the formula (7) can be used as a calculation formula of the thermal conductivity without any ambiguity.
Since the calculation formula of the thermal conductivity lambda adopts the concept of linear energy flow density, the calculation formula of the thermal diffusivity a needs to be changed correspondingly in order to keep the consistency of the thermal conductivity lambda. The definition of the intercept from the linear fit can be derived as follows: by
The above formula can be rewritten as
Then there are
Solving a from the above formula to obtain a calculation formula of the thermal diffusion coefficient a
In the above formula, when the heat ray radius is small, r is considered to be0→ 0. Then it must haveThus is provided with
This is an approximate expression; generally, the value of the hot wire radius ranges from 0.05 mm to 1.0 mm. The error of this approximation, calculated by taking the hot line radius to be 0.1 mm, can be estimated as follows: when the radius of the heat-extracting line is r0When the grain size is 0.0001 m, the grain size is
e0.0001=2.718280.0001=1.0001 (13)
It can be seen that the deviation from 1 is only one ten thousandth. Therefore, it is considered that there should be no observable effect in the actual measurement of the thermal diffusivity.
From this analysis, it is considered that when the thermal physical properties of the material are measured transiently by the hot-wire method, the formula for calculating the thermal diffusivity can be used
Coefficient of formula
Thus, the final formula for measuring the thermal diffusivity in a transient manner by the hot-wire method is obtained as
Where k is the slope of the fitted line and D is the intercept of the fitted line.
The method has the beneficial effects that:
by correcting the calculation formula of the thermal conductivity lambda and the thermal diffusion coefficient a in the method, the objective rule of transient measurement of the thermophysical property of the material can be reflected, the measurement precision is improved, and the related parameter values of the thermophysical property of the material, such as the thermal conductivity, the thermal diffusion coefficient, the constant pressure specific heat capacity and the heat storage coefficient, can be measured more accurately.
Detailed Description
A data processing (calculating) method for transient measurement of thermophysical properties of a material by a hot-wire method comprises the following steps:
first, preparation step
1) Manufacturing a standard sample of the material to be tested, wherein the sample is two homogeneous cube samples;
2) manufacturing a set of measuring instrument, wherein the measuring instrument comprises a probe, a current-stabilizing power supply, a data acquisition unit and a data processor;
3) establishing a physical mathematical model for solving the thermophysical parameters of the material, compiling a software program according to the physical mathematical model, writing out codes and storing the codes into a measuring instrument;
second, measurement step
1) Clamping the probe between the two samples to make the hot wire stick to the central axis of the sample plane of the standard sample;
2) introducing constant current to the probe;
3) the probe sends the detected temperature signal to the data acquisition unit, and the data acquisition unit converts the temperature signal into a corresponding digital signal;
4) the data processor runs a software program to calculate and process the digital signal to obtain the value of the thermophysical parameter;
the physical mathematical model for solving the thermophysical parameters of the material is based on a primary integral expression of an accurate solution of a one-dimensional cylindrical surface heat transfer problem, and in the heating and warming process, the temperature change rule at the contact interface of the hot wire surface and the medium is as follows:
in the formula, slope
Intercept of a beam
Areal density of heat flow
Where I represents the current passing in the hot wire, in units: ampere; r is the resistance of the hot wire, unit: ohm; r is0Is the hot wire radius, in units: rice; l is the hot wire length, unit: and (4) rice.
Using experimental methods, measure oneSeries ln τ and θ (r)0Tau), linear fitting by least square rule, calculating slope k and intercept D of fitting straight line, substituting into (2) and (3), and substituting into (4), to obtain heat conductivity lambda of material to be measured by hot-wire method
The thermal diffusion coefficient a is calculated by the formula
However, when the two formulas (5) and (6) are used for experimental measurement, the measured experimental values are far from the recognized values of the thermal conductivity and the thermal diffusion coefficient of the sample to be measured, and even the difference of the order of magnitude occurs; obviously, the two formulas (5) and (6) cannot be directly used for measuring the thermal conductivity and the thermal diffusivity, and need to be corrected.
As can be seen from the above equation (5), the main factor causing the thermal conductivity λ to become larger in magnitude is the heat ray radius too small, generally 10-4Magnitude. If remove 2 π r0This factor, equation (5) will be reduced to
Changing from equation (5) to equation (7) by removing a constant factor of 2 π r0The concept of the heat flux density is changed from the heat flux surface density to the heat flux linear density, and the change does not change the physical meaning of the formula; but the magnitude relation of the calculation formula is adjusted, so that the magnitude of the transient measurement thermal conductivity of the hot wire method is not increased, and the physical meaning of the calculation formula is kept unchanged; just as such, it is reasonable and reliable that formula (5) becomes formula (7); therefore, when the thermophysical property of the material is measured in a hot-wire transient mode by using a one-dimensional cylindrical surface heat transfer model, the formula (7) can be used as a calculation formula of the heat conductivity, and no ambiguity is caused.
Since the calculation formula of the thermal conductivity lambda adopts the concept of linear energy flow density, the calculation formula of the thermal diffusivity a needs to be changed correspondingly in order to keep the consistency of the thermal conductivity lambda. From the linear fit, a definition of the intercept is obtained, which can be derived as follows: by
The above formula can be rewritten as
Then there are
Solving a from the above formula to obtain a calculation formula of the thermal diffusion coefficient a
In the above formula, when the heat ray radius is small, r can be considered to be0→ 0. Then there must be er0 → 1; thus is provided with
This is an approximate expression. Generally, the value of the hot wire radius ranges from 0.05 mm to 1.0 mm. The error of this approximation, calculated by taking the hot line radius to be 0.1 mm, can be estimated as follows: when the radius of the heat-extracting line is r0When the grain size is 0.0001 m, the grain size is
e0.0001=2.718280.0001=1.0001 (13)
It can be seen that the deviation from 1 is only one ten thousandth. Therefore, it is considered that there should be no observable effect in the actual measurement of the thermal diffusivity.
From this analysis, it is considered that when the thermal physical properties of the material are measured transiently by the hot-wire method, the formula for calculating the thermal diffusivity can be used
Coefficient of formula
Thus, the applicant obtained the final formula for measuring the thermal diffusivity using the hot-wire method transient as
Where k is the slope of the fitted line and D is the intercept of the fitted line.
It should be noted that, in the above analysis, the formula (11) has a general meaning. (16) Formula (iii) is just a specific example. Only if the specific conditions are met.
Through the demonstration, the conclusion can be drawn that the established general theory of transient measurement of the thermophysical properties of the material by the hot wire method is accurate according to the one-dimensional cylindrical surface heat transfer theory. However, if this theory is used to practice the measurement, the concept of the heat flux density must be applied. And the calculation formula of the thermal conductivity is changed into the formula (7); meanwhile, the calculation formula of the thermal diffusivity must be changed to the formula (11).
When a specific condition is satisfied, the calculation may be performed by expression (16). The data processing method is firstly proposed by the inventor of the present application in the research process, and can be called as Chen's algorithm. When the method is used for processing the measured data, the measured values of the thermal conductivity and the thermal diffusion coefficient of the material can be ensured to be correct, and the coordination and consistency of transient measured values of the specific heat capacity at constant pressure and the thermal storage coefficient can also be ensured to be correct.
In this way, it can be concluded that: one set of final calculation formulas for transient measurement of the thermophysical properties of the material by the hot-wire method is as follows:
calculation formula of thermal conductivity
Calculation formula of thermal diffusion coefficient
When a specific condition is satisfied, the calculation may be performed by the expression (16)
According to the definition formula of the thermal diffusion coefficient, after the thermal conductivity and the thermal diffusion coefficient are measured, if the density of the material to be measured is known (or measured), the constant pressure specific heat capacity of the material to be measured can be measured
After measuring the thermal conductivity and the thermal diffusivity, if the thermal action period T is knownhThe heat storage coefficient of the material to be measured can be measured (unit in seconds)
Therefore, the measurement of thermophysical parameters of the material to be measured, such as thermal conductivity, thermal diffusion coefficient, constant-pressure specific heat capacity, heat storage coefficient and the like, by adopting hot wire transient measurement is realized.
The above algorithm, having obtained a verification of the practical measurements, is reliable.
Claims (3)
1. A data processing method for transient measurement of thermophysical properties of a material by a hot-wire method comprises the following steps:
first, preparation step
1) Manufacturing a sample of a material to be detected, wherein the sample is two cuboid samples;
2) manufacturing a set of measuring instrument, wherein the measuring instrument comprises a probe, a current-stabilizing power supply, a data acquisition unit and a data processor;
3) establishing a physical mathematical model for solving the thermophysical parameters of the material, compiling a software program according to the physical mathematical model, writing out codes and storing the codes into a measuring instrument;
second, measurement step
1) Clamping the probe between the two samples to make the hot line joint with the central axis of the sample plane;
2) introducing constant current to the probe;
3) the probe sends the detected temperature signal to the data acquisition unit, and the data acquisition unit converts the temperature signal into a corresponding digital signal;
4) the data processor runs a software program to calculate and process the digital signal to obtain the value of the thermophysical parameter;
the method is characterized in that the physical mathematical model for solving the thermophysical parameters of the material is based on a primary integral expression of an accurate solution of a one-dimensional cylindrical surface heat transfer problem, and the temperature change rule at the contact interface of the hot wire surface and a medium is as follows in the heating and warming process:
in the formula, slope
Intercept of a beam
Heat flux areal density of hot wire surface
Where I represents the current passing in the hot wire, in units: ampere; r is the resistance of the hot wire, unit: ohm; r is0Is the hot wire radius, in units: rice; l is the hot wire length, unit: rice;
experimentally, a series of ln τ and θ (r) were measured0Tau), linear fitting is carried out by using a least square rule, the slope k and the intercept D of a fitting straight line are calculated and substituted into the formulas (2) and (3), and then the formula (4) is substituted, so that the calculation formula for obtaining the thermal conductivity lambda of the material to be measured by the hot-wire method transient measurement is shown as
The thermal diffusion coefficient a is calculated by the formula
As can be seen from the observation of equation (5), the main factor that causes the magnitude of the thermal conductivity λ measurement to become large is that the hot wire radius is too small, typically at 10-4Magnitude; if remove 2 π r0This factor, equation (5) will be reduced to
Changing from equation (5) to equation (7) by removing a constant factor of 2 π r0The concept of heat flux density of the electric heating is changed from heat flux surface density to heat fluxLinear density, this change does not change the physical meaning of the formula; but the magnitude relation of the calculation formula is adjusted, so that the magnitude of the transient measurement thermal conductivity of the hot wire method is not increased, and the physical meaning of the calculation formula is kept unchanged; just as such, it is reasonable and reliable that formula (5) becomes formula (7); therefore, when the thermophysical property of the material is measured in a hot-wire method transient state by using the one-dimensional cylindrical surface heat transfer model, the formula (7) is used as a calculation formula of the heat conductivity, and no ambiguity occurs;
because the calculation formula of the thermal conductivity lambda adopts the concept of linear energy flow density, the calculation formula of the thermal diffusion coefficient a needs to be changed correspondingly in order to keep the consistency of the thermal conductivity lambda; the definition of the intercept from the linear fit can be derived as follows: by
The above formula is rewritten as
Then there are
Solving a from the above formula to obtain a calculation formula of the thermal diffusion coefficient a
3. The method for processing data of thermophysical property of a material measured in a transient state by a hot-wire method according to claim 2, wherein the method comprises measuring the thermophysical property of the material by a hot-wire method
Is an approximate expression; generally, the value range of the hot wire radius is between 0.05 and 1.0 millimeter; the error of this approximation, calculated by taking the hot line radius to be 0.1 mm, can be estimated as follows: when the radius of the heat-extracting line is r0When the grain size is 0.0001 m, then
e0.0001=2.718280.0001=1.0001 (13)
It can be seen that the deviation from 1 is only one ten thousandth; therefore, it is considered that, in the actual measurement of the thermal diffusivity, there should be no observable effect;
from this analysis, it is considered that when the thermal physical properties of the material are measured transiently by the hot-wire method, the formula for calculating the thermal diffusivity can be used
Coefficient of formula
Thus, the final formula for measuring the thermal diffusivity in a transient manner by the hot-wire method is obtained as
Where k is the slope of the fitted line and D is the intercept of the fitted line.
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