RU2178166C2 - Method of complex determination of thermal and physical characteristics of solid and dispersive materials - Google Patents

Abstract

FIELD: thermal tests of solid and dispersive materials. SUBSTANCE: method of complex determination of thermal and physical characteristics of solid and dispersive materials consists in measurement of thickness of examined specimen and in bringing it into thermal contact along plane with standard specimen. Then examined and standard specimens are subjected to thermostatting at initial specified temperature. Temperatures on outer surfaces of examined and standard specimens are kept equal to specified initial temperature of thermos tatting, specific power of heat source is recorded and temperature of standard specimen in specified section is measured with constant time interval. Standard specimen comes in the form of package of two flat standard specimens with different thermophysical properties and thickness of each plate depends on relation of thermal diffusivity of materials of these specimens. Two sequential time moments when second derivative of temperature in time becomes equal to zero. Test is terminated with occurrence of second time moment. EFFECT: raised accuracy and high-speed measurement of thermal and physical characteristics of solid and dispersive materials. 2 dwg

Description

 The invention relates to the field of thermal testing of solid and dispersed materials, and in particular to the field of research of thermophysical characteristics of these materials.

 A known method for determining the thermal conductivity of materials in a wide temperature range [USSR Author's Certificate 1741036, class. G 01 N 25/18, 1992], which consists in the fact that in the thermostat are placed two test samples of a cylindrical shape, a flat central heater located between the samples, and also a differentially switched thermocouple, the hot junction of which is located in one of the test samples, and the cold on the border of this sample with a thermostat. Upon reaching a stationary state, the differential thermocouple signal and the power of a flat heater are recorded, these values are compared, and the thermal conductivity of the material under study is calculated from the result.

 The disadvantages of this method are the ability to determine only one thermophysical property of thermal conductivity, the long duration of the experiment due to the need to achieve a stationary state.

 A known method for determining the thermophysical characteristics of materials [USSR Copyright Certificate 1689825, class. G 01 N 25/18, 1991], namely, that the test sample is brought into thermal contact along the plane with the reference sample and the samples are thermostated at a given initial temperature, then heat is supplied to the plane inside the reference sample located at a known distance and parallel to the plane contact, and measure the temperature of the reference sample in a given section. The thickness of the test sample is measured, and the temperatures on the external surfaces of the reference and test samples are kept constant and equal to the set initial temperature of thermostating, the heat is supplied continuously and the values of the specific power of the heat source in time are recorded. The tests are stopped when the specified minimum rate of temperature change is reached, and the desired thermophysical characteristics of the material under study are calculated from the dependencies given in the claims.

, не для всех исследуемых материалов дает определенное минимальное значение погрешности. Поэтому у данного способа недостаточно высокая точность измерения теплофизических свойств, а также значительная длительность измерения, вызванная необходимостью достижения практически стационарного значения температуры, τ_к достигает 600. . . 900 с, а скорость изменения температуры должна быть S_min≈10^-4К/с.This method compared with [USSR Author's Certificate 1741036, cl. G 01 N 25/18, 1992] allows us to determine the complex of thermophysical characteristics measured up to time τ _to temperature T (l _e , τ) in the sample cross section x = l _e , but the set value of the integration parameter is p = -ln [10 ^-4 / T (τ _k )] / τ _k used in the integral temperature characteristics

, not for all the studied materials gives a certain minimum error value. Therefore, this method does not have a sufficiently high accuracy of measurement of thermophysical properties, as well as a significant measurement duration, due to the need to achieve a practically stationary temperature, τ _k reaches 600. . 900 s, and the rate of temperature change should be S _min ≈10 ^-4 K / s.

 The closest technical solution is a method for the comprehensive determination of the thermophysical characteristics of materials [Patent of the Russian Federation, cl. G 01 N 25/18, 1995], namely, that the thickness of the test sample is measured and brought into thermal contact along the plane with the reference sample, the test and reference samples are thermostated at the initial set temperature, then heat is continuously supplied to the section plane inside the reference a sample located at a given distance and parallel to the plane of contact, while the temperatures on the external surfaces of the test and reference samples are maintained equal to a given initial temperature of thermostating, They measure the specific power of the heat source and measure the temperature of the reference sample in a given section with a constant step in time, at each step determine the value of the dynamic parameter, which is the ratio of the temperature in a given section of the reference sample at the measurement step, whose number is a constant number less than the number of the last measurement step , to the temperature in the same section of the reference sample at the last measurement step, compare the value of the dynamic parameter with a given maximum value, m test terminated when exceeding a predetermined maximum dynamic parameter values and determine the required thermal characteristics of relationships given in the claims.

 Compared with [USSR Author's Certificate 1689825, cl. G 01 N 25/18, 1991] this method has a high speed, but the specified dynamic parameter for various materials to be studied will have different numerical values within (0.2.. 0.8), a fuzzy setting of which in advance may introduce an error into the result measurements, since a very informative section of the temperature change graph may not be taken into account. The disadvantage of this method is that to determine the thermophysical properties, temperature is used in only one section of the reference sample either above or below the heater, and for more accurate measurements, information is required on temperatures in two sections above and below the heater.

 The technical task of the invention is to improve the accuracy and speed of measuring the thermophysical characteristics of solid and dispersed materials.

g₁= pL₁ ²/a₁; (9)
g_э= pL_э ²/a_э; (10)
р₁, р₂ - параметры интегрирования Лапласа, определяемые из уравнений
p₁= p= T'(l, t₂)/T(l, t₂), (11)
p₂= kp= T'(l, t₁)/T(l, t₁); (12)
g_u - безразмерный параметр, определяемый из уравнения

k= p₂/p₁ - постоянный коэффициент (k≠1)

h - толщина исследуемого образца;
L_э - толщина верхнего эталонного образца;
L₁ - толщина нижнего эталонного образца;
l_э - расстояние от источника теплоты до плоскости измерения температуры внутри верхнего эталоннго образца;
l₁ - расстояние от источника теплоты до плоскости измерения температуры внутри нижнего эталонного образца;
m_э= (L_э-l_э)/L_э, m₁= (L₁-l₁)/L₁, η_э= l_э/L_э - геометрические параметры, вычисляемые до начала эксперимента;
a - температуропроводность исследуемого материала;
a_э - температуропроводность верхнего эталонного материала;
a₁ - температуропроводность нижнего эталонного материала;
λ - теплопроводность исследуемого материла;
λ_э - теплопроводность верхнего эталонного материала;
λ₁ - теплопроводность нижнего эталонного материала;
Q - удельная тепловая мощность источника теплоты;
T₁(l₁, t) - температура нижнего эталонного образца в сечении х= l₁;
T_э(l_э, t) - температура верхнего эталонного образца в сечении х= l_э;
t₁ - момент времени, когда вторая производная температуры становится равна нулю в первый раз: T"₁(l₁, t₁)= 0;
t₂ - момент времени, когда вторая производная температуры становится равна нулю во второй раз: T"₁(l₁, t₂) = 0, то есть время окончания эксперимента;
На фиг. 1 представлена графическая иллюстрация способа.The technical problem is achieved by the fact that in the method for the complex determination of the thermophysical characteristics of solid and dispersed materials, which consists in measuring the thickness of the test sample and bringing it into thermal contact along the plane with the reference sample, the test and reference samples are thermostated at the initial set temperature, then bring continuously heat to the section plane inside the reference sample, located at a given distance and parallel to the contact plane, while the temperatures at the external the surfaces of the test and reference samples are maintained equal to a given initial temperature of thermostating, the specific power of the heat source is recorded and the temperature of the reference sample in a given section is measured with a constant step in time, in contrast to the prototype, the reference sample is made in the form of a package of two flat reference samples with different thermophysical properties , and the thickness of each of them depends on the ratio of thermal diffusivity of the materials of these samples, to the contact plane of which the heat of a constant-in-time power is measured, the temperature is measured in predetermined sections of each reference sample, at each step of the temperature measurement, the first and second derivatives of the temperature are calculated over time in the indicated sections of the package of reference samples, two consecutive times are recorded when the second time derivative of the temperature becomes equal to zero, the tests are completed when the second of these time points occurs, and the required thermophysical characteristics are determined by the formulas
a = ph ² / g _u (1)

g ₁ = pL ₁ ² / a ₁ ; (9)
g _e = pL _e ² / a _e ; (10)
p ₁ , p ₂ - Laplace integration parameters determined from the equations
p ₁ = p = T '(l, t ₂ ) / T (l, t ₂ ), (11)
p ₂ = kp = T '(l, t ₁ ) / T (l, t ₁ ); (12)
g _u is the dimensionless parameter determined from the equation

k = p ₂ / p ₁ - constant coefficient (k ≠ 1)

h is the thickness of the test sample;
L _e - the thickness of the upper reference sample;
L ₁ is the thickness of the lower reference sample;
l _e - the distance from the heat source to the plane of temperature measurement inside the upper reference sample;
l ₁ is the distance from the heat source to the plane of temperature measurement inside the lower reference sample;
m _e = (L _e -l _e ) / L _e , m ₁ = (L ₁ -l ₁ ) / L ₁ , η _e = l _e / L _e - geometric parameters calculated before the start of the experiment;
a - thermal diffusivity of the studied material;
a _e - thermal diffusivity of the upper reference material;
a ₁ - thermal diffusivity of the lower reference material;
λ is the thermal conductivity of the investigated material;
λ _e - thermal conductivity of the upper reference material;
λ ₁ - thermal conductivity of the lower reference material;
Q is the specific thermal power of the heat source;
T ₁ (l ₁ , t) is the temperature of the lower reference sample in the section x = l ₁ ;
T _e (l _e , t) is the temperature of the upper reference sample in the section x = l _e ;
t ₁ - the point in time when the second derivative of the temperature becomes zero for the first time: T " ₁ (l ₁ , t ₁ ) = 0;
t ₂ is the point in time when the second derivative of the temperature becomes zero a second time: T " ₁ (l ₁ , t ₂ ) = 0, that is, the time of the end of the experiment;
In FIG. 1 is a graphical illustration of the method.

The system consists of test sample 1 and two reference samples: upper 2 and lower 3. All samples are in the form of plates. A plane heat source 4 is placed in the contact plane of standards 2 and 3, generating it continuously with constant power. The test sample 1 is brought into thermal contact with the upper standard 2. In both reference samples temperature sensors are located: in the upper 5 - at a distance l _e , in the lower 6 - at a distance l ₁ from the heating plane. The external surfaces of the samples are brought into thermal contact with sinks of heat 7 with a constant temperature. Thermostatic wall 8 eliminates heat exchange with the environment. Constant heating power is provided by the stabilized power supply unit (BSP) 9. The temperature values measured by sensors 5 and 6 are converted by converters 10 and 11 into a signal convenient for transmission to the measuring and computing complex (IVC) 12, namely to the input unit 13 (for example , ADC). Computer 14 determines the temperature, the time of the experiment, calculates the first and second derivatives of the temperature, and when the specified value of the second (or first) derivative of the temperature is reached through the output unit 15 of the IVC (for example, the DAC), it disconnects (or changes) the signal from the BSP 9 through the switch 16 going to the flat heater 4. The CPM also includes a control unit and tasks 17 and a computer monitor 18.

 The method is implemented as follows.

Before the experiment, measure the thickness of the test sample h, the thickness of the upper reference L _e and the lower reference L ₁ samples are known in advance. Also known are the distances from the heating plane to the planes for measuring temperatures l _e and l ₁ .

 The test sample 1 is brought into thermal contact in a plane with the reference sample 2.

 The temperatures on the external surfaces of the test and reference samples are kept constant and equal to a given initial temperature of thermostating.

Heat is continuously supplied to the contact plane of reference samples 2 and 3. In the heat supply process, the temperature change in time t of the temperature values T ₁ (l ₁ , t) of the lower reference sample in the plane with the coordinate x = l ₁ and T _e (l _e , t) of the upper reference sample in the x = l _e plane is measured and recorded . At the same time, the first and second derivatives of the temperatures in both samples are calculated: T ₁ ^' (l ₁ , t), T " ₁ (l ₁ , t), T' _e (l _e , t), T" _e (l _e , t) . The value of the specific power of the heat source Q is known and constant throughout the test.

In the calculated dependences, the dimensionless parameter g = pL ² / a is used, where p is the Laplace integration parameter; L is a geometric parameter, in this case, the thickness of the test or reference sample; a - thermal diffusivity of the material of the sample in question. For two reference samples, dimensionless parameters are found by formulas (8) and (9), for the material under study, g _u = ph ² / a _u .

где T₁(l₁, t) и T_э(l_э, t) - измеряемые температуры в сечениях х= l₁ и х= l_э.The calculated dependences also use the integral characteristics of the temperatures T * ₁ (l ₁ , p) and T * _e (l _e , p) of the reference samples calculated by the well-known Laplace transform formula:

where T ₁ (l ₁ , t) and T _e (l _e , t) are the measured temperatures in the sections x = l ₁ and x = l _e .

При соблюдении условия (18) можно контролировать ход эксперимента по температурным кривым T₁(l₁, t) и T_э(l_э, t). Вычислять первую и вторую производные можно для любого эталона как для верхнего T_э ^'(l_э, t), T_э ^"(l_э, t), так и для нижнего T'₁(l₁, t), T₁ ^''(l₁, t).Obviously, for the two integral characteristics T * ₁ (l ₁ , p) and T _e ^* (l _e , p), the parameter p is the same number. In order to fulfill this condition, during the tests it is necessary to observe the following ratio of the parameters of the reference samples obtained from dependences (8) and (9):

Subject to condition (18), the experiment can be monitored by the temperature curves T ₁ (l ₁ , t) and T _e (l _e , t). The first and second derivatives can be calculated for any standard, both for the upper T _e ^' (l _e , t), T _e ^" (l _e , t), and for the lower T' ₁ (l ₁ , t), T ₁ ^'' (l ₁ , t).

In FIG. 2 shows graphs of the functions 1-T (l, t) (where l - l ₁ or l _e ), 2 -e- ^kpt T (l, t), 3 - e ^-pt T (l, t). The temperature curve T (l, t) has two special consecutive time instants t ₁ and t ₂ in which the first time derivative of the temperature becomes constant T ^' (l, t) = const, T ^' (l, t ₂ ) = const , and the second time derivative of the temperature becomes equal to zero, i.e., T "(l, t ₁ ) = 0, T ^'' (1, t ₂ ) = 0. When the moment t ₂ arrives, the test ends.

From the analysis of the integrand e ^-pt T (1, t) in formulas (16) and (17), we can find the values of the integration parameters p ₁ and p ₂ :
p ₁ = p = T '(l, t ₂ ) / T (l, t ₂ ), (19)
p ₂ = kp = T '(l, t ₁ ) / T (l, t ₁ ). (20)
The coefficient k is found from the relation
k = p ₂ / p ₁ . (21)
The required thermophysical characteristics of the studied sample 1 are determined by formulas (1), (2) obtained from the solution of the boundary-value heat transfer problem in the region of Laplace integral transforms.

 An example of a specific implementation of the method.

 Several materials were tested: polymethylmethacrylate, caprolon-B, glass-8, polytetrafluoroethylene, etc. Let us show specific measurements using an example of a sample of polymethylmethacrylate.

The thickness h = 2.75 • 10 ^-3 m of the test sample of polymethylmethacrylate was previously measured with a micrometer. Then, the test sample was brought into thermal contact along the plane with a reference sample made in the form of a package of two reference samples with different thermophysical properties. The upper sample is made of quartz, its thermal diffusivity a _e = 3.45 • 10 ^-6 m ² / s, thermal conductivity λ _e = 7.21 W / (m • K), thickness L _e = 4.5 • 10 ^-3 m. The lower sample is made of polymethylmethacrylate, its thermal diffusivity a ₁ = 1.1 • 10 ^-7 m ² / s, thermal conductivity λ ₁ = 0.19 W / (m • K), thickness L ₁ = 0.8 • 10 ^-3 m , In both reference samples, temperature sensors are located in the planes l _e = 2.25 • 10 ^-3 m and l ₁ = 0.4 • 10 ^-3 m. On the external surfaces of the reference and studied samples were placed sinks 7 of constant-temperature heat made in in the form of flow heat exchangers. Reference 2, 3 and test 1 samples were placed in an air thermostat. After stabilization of the temperature of the samples, a heat source 4 was turned on, made in the form of a flat electric heater. After the heat source 4 was turned on, heat was supplied to it with a constant time power of Q = 320 W / m ² continuously until the end of the experiment. The moment of switching on the heat source was taken as the start of the experiment time t = 0. At equal time intervals Δt = 0.1 s, the values of temperatures in both reference samples T ₁ (l ₁ , t) and T _e (l _e , t) were recorded. Since in the experiment the ratio of the parameters of the reference samples is observed (18), the first and second derivatives of the temperature were calculated only for one lower sample: T ' ₁ (l ₁ , t), T " ₁ (l ₁ , t). Two points in time were recorded when the second derivative of the temperature of the lower sample vanishes: t ₁ = 15 s, t ₂ = 72 s (studies have shown that for most solid and dispersed materials t ₁ = 12.. 17 s, t ₂ = 70.. 90 s ). At time t _{2, the} experiment was completed.

The thermophysical properties of the studied material were determined and calculated using IVK 12 (Fig. 1), built on the basis of a personal computer with a Pentium processor according to formulas (1) - (15). Moreover, according to experimental data, first of all, the values of the integration parameters p ₁ and p _{2 were} calculated according to formulas (19), (20). The following values were obtained: p ₁ = 0.09 s ^-1 , p ₂ = 0.74 s ^-1 , k = 8.2. Then we found the integral temperature characteristics T * ₁ (l ₁ , p), T * _e (l _e , p) from dependences (5), (6) and heat fluxes q * _e (p), q * _u (p) , q * _e (kp), q _u ^* (kp) according to formulas (3), (4), (12), (13). The values of the dimensionless parameters g _e and g _{1 were} calculated from dependences (8), (9), and from equation (10) the value g _u = 6.3 was found. After that, the thermal diffusivity and thermal conductivity of the material under study were calculated using formulas (1) and (2).

As a result of the test, the following values of the thermophysical characteristics of the test sample were obtained: thermal conductivity λ _u = 0.185 W / (m • K), thermal diffusivity a _u = 1.08 • 10 ^-7 m ² / s. The relative error in determining thermal diffusivity and thermal conductivity was 3.6% and 2.6%, respectively.

 Compared with the prototype method, the accuracy and speed of measuring the thermophysical characteristics of solid and dispersed materials are increased due to the fact that the reference sample is made in the form of a package of two flat reference samples with different thermophysical properties, and the temperature is controlled in both standards in predetermined planes, as well as the test duration is reduced, since the experiment ends at the moment when the second time derivative of the temperature becomes zero for the second time.

Claims (1)

A method for the complex determination of the thermophysical characteristics of solid and dispersed materials, which consists in measuring the thickness of the test sample and bringing it into thermal contact along the plane with the reference sample, the test and reference samples are thermostated at the initial set temperature, then heat is continuously supplied to the section plane inside the reference a sample located at a given distance and parallel to the plane of contact, while the temperatures on the outer surfaces of the investigated and reference vol samples are maintained equal to a given initial temperature of thermostating, the specific power of the heat source is recorded and the temperature of the reference sample in a given section is measured with a constant step in time, characterized in that the reference sample is made in the form of a package of two flat reference samples with different thermophysical properties, and the thickness of each of them depends on the thermal diffusivity ratio of the materials of these samples, to the contact plane of which heat is supplied with a constant-time power, the temperature is measured in predetermined sections of each reference sample, at each temperature measurement step, the first and second time derivatives of the temperature are calculated in the indicated sections of the package of reference samples, two consecutive time instants are recorded when the second time derivative of the temperature becomes zero, the tests are completed when the second of these points in time, and the desired thermophysical characteristics are determined by the formulas
a = ph ² / g _u ;

g ₁ = pL ₁ ² / a ₁ ;
g _e = pL _e ² / a _e ;
m _e = (L _e - l _e ) / L _e ;
m ₁ = (L ₁ - l ₁ ) / L ₁ ;
η _e = l _e / L _e ;

Laplace integration parameters;
g _u is the dimensionless parameter determined from the equation

k = p ₂ / p ₁ - constant coefficient (k ≠ 1);

h is the thickness of the test sample;
L _e - the thickness of the upper reference sample;
L ₁ is the thickness of the lower reference sample;
l _e - the distance from the heat source to the plane of temperature measurement inside the upper reference sample;
l ₁ is the distance from the heat source to the plane of temperature measurement inside the lower reference sample;
a - thermal diffusivity of the studied material;
a _e - thermal diffusivity of the upper reference material;
a ₁ - thermal diffusivity of the lower reference material;
λ is the thermal conductivity of the investigated material;
λ _e - thermal conductivity of the upper reference material;
λ ₁ - thermal conductivity of the lower reference material;
Q is the specific thermal power of the heat source;
T ₁ (l ₁ , t) is the temperature of the lower reference sample in sections x = l ₁ ;
T _e (l _e , t) is the temperature of the upper reference sample in the cross section x = l _e ;
t ₁ is the point in time when the second derivative of the temperature becomes zero for the first time: T ₁ '' (l ₁ , t ₁ ) = 0;
t ₂ is the point in time when the second derivative of the temperature becomes zero a second time: T ₁ '' (l ₁ , t ₂ ) = 0, that is, the time of the end of the experiment.

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