CN112683944B - Transient method heat insulation material heat conductivity testing method - Google Patents
Transient method heat insulation material heat conductivity testing method Download PDFInfo
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Abstract
The invention relates to a thermal conductivity testing method for a transient heat insulation material, belongs to the technical field of thermal conductivity testing, and solves the problem that the prior art cannot meet the thermal conductivity testing requirement of the heat insulation material above 1400 ℃. The method comprises the following steps: step S1: heating the upper and lower surfaces of the sample until the temperatures of the upper and lower surfaces of the sample are stable to the temperature set values, and obtaining the compensation temperature at the moment; step S2: after the temperatures of the upper surface and the lower surface of the sample are both stabilized at the temperature set value, controlling to heat the upper surface of the sample based on the difference between the temperature represented by the temperature control signal and the temperature of the upper surface of the sample acquired in real time, controlling to heat the lower surface of the sample based on the compensation temperature, and acquiring the temperatures of the upper surface and the lower surface of the sample in real time; step S3: and (3) obtaining the thermal conductivity of the sample based on the temperatures of the upper surface and the lower surface of the sample acquired in real time in the step (S2). The method can meet the thermal conductivity test requirement of the heat insulation material above 1400 ℃.
Description
Technical Field
The invention relates to the technical field of thermal conductivity testing, in particular to a thermal conductivity testing method for a transient heat insulation material.
Background
In the existing heat-insulating material heat conductivity testing equipment, a protection hot plate method testing device has a complex structure, and is difficult to realize the test at the temperature of over 700 ℃; the heat flow meter device has the advantages that the working temperature of the heat flow meter at one side of the cold surface of the sample is limited (cannot exceed 150 ℃), so when the temperature difference of the hot surface of the sample exceeds 1000 ℃ and the cold surface does not exceed 150 ℃, the temperature difference in the thickness direction of the sample is overlarge, a large heat flow density is required to be applied to reach the stability requirement, the maximum surface power load requirement of a heating wire in a flat plate heater at the hot surface of the sample is very high, the surface power load allowed by common materials is exceeded, and the heat conductivity test of the heat flow meter is difficult to realize under the conditions of the temperature difference of over 1400 ℃ and the large temperature difference under the condition of the heat flow meter; the heating plate in the quasi-steady-state planar heat source method equipment is not suitable for directly contacting the surface of the conductive material for high temperature conductivity test. In other existing heat conductivity testing methods, a laser pulse method heat conduction instrument can realize heat conductivity testing of metal and compact ceramic materials at a temperature above 1600 ℃, but when the method is used for testing heat insulation materials, the temperature response of the back surface of a sample is very low due to the small heating power of pulse laser, and an effective measuring signal cannot be obtained, so that the heat conductivity testing of the heat insulation materials at a temperature above 1400 ℃ cannot be met.
Thus, there is a need to develop test method research and test device development for thermal conductivity testing requirements above 1400 ℃ for carbon aerogel or TUFROC materials with electrical conductivity.
Disclosure of Invention
In view of the above analysis, the embodiment of the invention aims to provide a transient thermal conductivity testing method for a thermal insulation material, which is used for solving the problem that the prior art cannot meet the thermal conductivity testing requirement of the thermal insulation material above 1400 ℃.
The embodiment of the invention provides a method for testing the thermal conductivity of a transient heat insulation material, which comprises the following steps:
step S1: heating the upper and lower surfaces of the sample until the temperatures of the upper and lower surfaces of the sample are stable to the temperature set values, and obtaining the compensation temperature at the moment;
step S2: after the temperatures of the upper surface and the lower surface of the sample are both stabilized at the temperature set value, controlling to heat the upper surface of the sample based on the difference between the temperature represented by the temperature control signal and the temperature of the upper surface of the sample acquired in real time, controlling to heat the lower surface of the sample based on the compensation temperature, and acquiring the temperatures of the upper surface and the lower surface of the sample in real time;
step S3: and (3) obtaining the thermal conductivity of the sample based on the temperatures of the upper surface and the lower surface of the sample acquired in real time in the step (S2).
Based on the scheme, the invention also makes the following improvements:
further, the step S3 includes:
step S31: based on the temperature of the upper surface of the sample acquired in real time and the formula (1), obtaining the theoretical temperature of the lower surface of the sample at each sampling moment;
wherein x=l;m=0, 1,2,3 … …, L is the thickness of the sample, f (τ) is the temperature of the upper surface of the sample taken at the τ -th moment; alpha represents the thermal diffusivity of the sample;
step S32: obtaining a thermal diffusion coefficient alpha of the sample based on a temperature theoretical value of the lower surface of the sample at each sampling moment and a temperature value acquired in real time;
step S33: the thermal conductivity of the sample is obtained based on the thermal diffusivity, alpha, of the sample.
Further, in the step S33, the thermal conductivity λ of the sample is obtained according to formula (2):
λ＝αρC p (2)
wherein ρ is the density of the sample; c (C) p Is the specific heat capacity of the sample.
Further, the step S32 includes:
an observation value matrix, a theoretical temperature matrix and an initial thermal diffusion coefficient alpha which are obtained according to the previous k times of sampling 0 k Iterative obtaining the thermal diffusion coefficient alpha of the previous k samples k The method comprises the steps of carrying out a first treatment on the surface of the The observation value matrix is composed of the temperature of the lower surface of the sample obtained by the previous k times of sampling, and the theoretical temperature matrix is composed of the theoretical temperature of the lower surface of the sample obtained by the previous k times of sampling;
sequentially increasing the sampling times, and obtaining the thermal diffusion coefficient of the current sampling times based on the thermal diffusion coefficient of the previous sampling times every time the sampling times are increased until the thermal diffusion coefficient converges; the converged thermal diffusivity was taken as the thermal diffusivity of the sample.
Further, the thermal diffusion coefficient alpha of the previous k samples is obtained through iteration k In the process, the thermal diffusivity is updated according to equation (3):
α j+1 l ＝α j l +(P l T (α j l )P l (α j l )) -1 ·P l T (α j l )(Y l -Ψ l (α j l )) (3)
wherein the observation matrix Y l ＝[y 1 ,y 2 ,···,y i ,···,y l ]，y i The temperature of the lower surface of the sample collected at the ith moment is represented; theoretical temperature matrix ψ l ＝[η 1 ,η 2 ,···,η i ,···,η l ]；η i ＝T 1 (L, i, alpha), alpha being the parameter to be solved; sensitivity coefficient matrix P l ＝[p 1 ,p 2 ,···,p i ,···,p l ]，j is the iteration number, l is the sampling number; alpha 0 l Representing the initial diffusion coefficient at the previous l samplings;
if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha of the previous k samples k 。
Further, each time the sampling frequency is increased, an initial thermal diffusion coefficient corresponding to the current sampling frequency is obtained according to the formula (4):
the thermal diffusivity is then updated according to equation (5):
if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha after increasing the sampling times every time l+1 。
Further, in the step S1, the lower surface of the specimen is heated by a lower heating assembly;
and taking the difference value between the temperature of the lower surface of the sample and the temperature of the interior of the lower heating assembly, which is acquired when the temperature of the upper surface and the temperature of the lower surface of the sample are both stable to the temperature set value, as the compensation temperature.
Further, the temperature control signal is a signal for controlling the upper surface of the sample to be linearly heated from a temperature set value to a temperature test set value and preserving heat for a set time.
Further, in the step S2, the heating the lower surface of the sample based on the compensated temperature control includes:
acquiring the temperature sum of the compensation temperature and the temperature of the lower surface of the sample in real time in the process of controlling the temperature rise and the heat preservation of the upper surface of the sample;
and controlling to heat the lower heating assembly based on the difference between the temperature and the temperature inside the lower heating assembly acquired in real time.
Further, measuring the temperature of the upper surface of the sample by using a first temperature thermocouple in contact with the upper surface of the sample;
measuring the temperature of the upper surface of the sample by using a second temperature thermocouple which is contacted with the lower surface of the sample;
the temperature inside the lower heating assembly is measured using a third temperature thermocouple in contact with the inside of the lower heating assembly.
Compared with the prior art, the invention has at least one of the following beneficial effects:
according to the transient heat insulation material heat conductivity testing method provided by the invention, the following two different process controls are realized by respectively controlling the temperature changes of the upper heating assembly and the lower heating assembly: 1. control of the preheating stage: the upper heating component and the lower heating component adopt the same temperature rising control program to heat the sample to a preset temperature and reach stability; 2. control of the test phase: the upper heating assembly heats the upper surface of the sample according to a new heating/insulating program, and the lower heating assembly is switched to a passive compensation heating control mode to realize the boundary condition that the lower surface of the sample approximates to the heat insulation wall surface. And in the test stage, the thermal conductivity of the sample is obtained by recording the curves of the temperature changes of the upper surface and the lower surface of the sample along with time in the processes of actively heating the upper surface and passively thermally compensating the lower surface of the sample.
According to the method for testing the thermal conductivity of the transient heat-insulating material, the back heat-insulating transient heat transfer model is analyzed in detail, a brand new method for obtaining the thermal diffusion coefficient is provided, and the method is used for testing the thermal conductivity of the transient heat-insulating material, so that the thermal conductivity of the transient heat-insulating material can be obtained quickly and conveniently; the thermal conductivity result obtained by the method has higher accuracy, and can meet the high-temperature thermal conductivity test requirement of the carbon aerogel or TUFROC material above 1400 ℃.
In the invention, the technical schemes can be mutually combined 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 may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
Fig. 1 is a schematic structural diagram of a device for testing thermal conductivity of a transient heat insulation material according to embodiment 1 of the present application;
fig. 2 is a schematic structural view of an upper heating plate and a lower heating plate provided in embodiment 1 of the present application;
fig. 3 is a schematic structural diagram of a heating and measurement control unit according to embodiment 2 of the present application;
fig. 4 is a flow chart of a method for testing the thermal conductivity of a transient thermal insulation material according to embodiment 3 of the present application.
Detailed Description
Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and together with the description serve to explain the principles of the invention, and are not intended to limit the scope of the invention.
Example 1
The invention discloses a device for testing the thermal conductivity of a heat insulating material by a transient method, which is shown in a structural schematic diagram as shown in figure 1, and comprises an upper cold water plate, an upper heating component, a lower cold water plate and a heating and measuring control unit which are sequentially arranged from top to bottom; the upper heating component and the lower heating component are used for arranging a sample to be tested; and the heating and measuring control unit is used for controlling to heat the upper heating assembly based on the difference value between the temperature represented by the temperature control signal and the temperature of the upper surface of the sample acquired in real time after the temperatures of the upper surface and the lower surface of the sample are stabilized at the temperature set values, controlling to heat the lower heating assembly based on the compensation temperature of the lower heating assembly, and acquiring the heat conductivity of the sample based on the temperatures of the upper surface and the lower surface of the sample acquired in real time.
When the method is implemented, firstly, a sample to be tested is placed between an upper heating component and a lower heating component, then the upper heating component and the lower heating component are heated by a heating and measuring control unit at the same time until the temperatures of the upper surface and the lower surface of the sample are both stable to a set value, then the upper heating component is controlled to be heated based on the difference value between the temperature represented by a temperature control signal and the temperature of the upper surface of the sample acquired in real time, the lower heating component is controlled to be heated based on the compensation temperature of the lower heating component, and the thermal conductivity of the sample is obtained based on the temperatures of the upper surface and the lower surface of the sample acquired in real time.
Compared with the prior art, the transient method heat insulation material heat conductivity testing device provided by the embodiment realizes the following two different process control by respectively controlling the temperature changes of the upper heating component and the lower heating component: 1. control of the preheating stage: the upper heating component and the lower heating component adopt the same temperature rising control program to heat the sample to a preset temperature and reach stability; 2. control of the test phase: the upper heating assembly heats the upper surface of the sample according to a new heating/insulating program, and the lower heating assembly is switched to a passive compensation heating control mode to realize the boundary condition that the lower surface of the sample approximates to the heat insulation wall surface. And in the test stage, the thermal conductivity of the sample is obtained by recording the curves of the temperature changes of the upper surface and the lower surface of the sample along with time in the processes of actively heating the upper surface and passively thermally compensating the lower surface of the sample. The testing device can realize the high-temperature conductivity test of the carbon aerogel or TUFROC material at the temperature of 1400 ℃.
Preferably, in the preheating stage, after the temperatures of the upper and lower surfaces of the sample reach the set temperature values and stabilize, the upper and lower heating assemblies are considered to have a small temperature difference from the upper and lower surfaces of the sample, respectively, so that the heating assemblies can conduct heat to the upper and lower surfaces of the sample, thereby making the temperature of the sample constant, and a small difference exists between the temperatures of the lower surface of the sample and the inner portion of the lower heating assembly near the lower surface of the sample. When the sample enters the test stage, the upper surface of the sample is heated by the upper heating component actively, at this time, if the lower surface (i.e. the cold surface) of the sample is under the adiabatic boundary condition, since the heat at the hot surface (the upper surface of the sample in this embodiment) is continuously transferred to the cold surface (the lower surface of the sample in this embodiment), the temperature at the cold surface is gradually increased, if the lower heating component keeps the original heating power unchanged, the heat is reversely transferred to the lower heating component after the temperature of the cold surface of the sample is increased, and the adiabatic boundary assumption of the lower surface of the sample cannot be satisfied. Therefore, in the actual test process, as the temperature of the lower surface of the sample increases, the heating power of the lower heating assembly is gradually increased, so that the temperature of the lower heating assembly, which is close to the lower surface of the sample, and the temperature of the lower surface of the sample are ensured to be consistent as much as possible, and the approximate adiabatic boundary condition is realized. Based on the above, in the actual heating control process, the difference between the temperature of the upper and lower surfaces of the sample and the temperature of the inside of the lower heating assembly, which is acquired when the temperatures of the upper and lower surfaces of the sample are both stabilized at the temperature set value, is taken as the compensation temperature.
To achieve accurate determination of the temperature of the upper surface, lower surface, and interior of the lower heating assembly of the sample, the apparatus of this embodiment further comprises: the first temperature thermocouple T1, the second temperature thermocouple T2 and the third temperature thermocouple T3; a first through hole is formed in the center point of the upper cold water plate and the center point of the upper heating component along the thickness direction, the first through hole extends to the upper surface of the sample, and the end head of the first temperature thermocouple T1 passes through the first through hole to be in contact with the upper surface of the sample so as to obtain the temperature of the upper surface of the sample; a second through hole is formed in the center point of the lower cold water plate and the center point of the lower heating component along the thickness direction, the second through hole extends to the lower surface of the sample, and the end head of the second temperature thermocouple T2 passes through the second through hole to be in contact with the lower surface of the sample so as to obtain the temperature of the lower surface of the sample; and the end head of the third temperature thermocouple T3 passes through the second through hole and is in contact with the interior of the lower heating assembly, so as to obtain the temperature in the interior of the lower heating assembly. In order to ensure accuracy of measurement data, the tip of the second thermocouple T2 and the tip of the third thermocouple T3 are spaced apart by 2-3mm in the vertical direction. Illustratively, the first/second through-holes are preferably through-holes having a size of Φ8mm. Meanwhile, the first temperature thermocouple T1 can be a ceramic armored B-type thermocouple; the second temperature thermocouple T2 and the third temperature thermocouple T3 are B-type filament thermocouples, four leads of the two thermocouples are penetrated by ceramic tubes with four holes so as to ensure insulation between the two thermocouples, and the temperature measuring node of the T3 is slightly lower than the node of the T2.
Preferably, in this embodiment, the upper heating assembly sequentially includes, in a direction away from the upper surface of the sample: an upper soaking plate, an upper heating plate and refractory bricks which are used for being attached to the upper surface of the sample; the lower heating assembly includes in order along the direction of keeping away from sample lower surface: a lower soaking plate, a lower heating plate and refractory bricks which are used for being attached to the lower surface of the sample; and the end head of the third temperature thermocouple passes through the second through hole and is contacted with the inner part of the lower soaking plate.
Preferably, to achieve a more accurate thermal conductivity test of the insulation material, in this embodiment, the dimensions of the upper/lower soaking plate are adapted to the cross-sectional dimensions of the test specimen. Illustratively, when the cross-sectional dimension of the insulating material is 300mm×300mm, the cross-sectional dimension of the upper vapor chamber/lower vapor chamber is also 300mm×300mm. The upper soaking plate and the lower soaking plate are formed by two layers of structures, wherein one layer close to the upper heating plate and the lower heating plate (both made of tungsten-molybdenum alloy) is formed by boron nitride ceramics, so that the effects of high temperature resistance, electric insulation and heat conduction are achieved; the layer near the sample is composed of a molybdenum alloy plate and is used for providing a conduction heating plane which is high-temperature resistant, good in heat conduction and smooth in contact surface.
Preferably, the upper heating plate and the lower heating plate are both processed by tungsten-molybdenum alloy flat plates, and the sizes of the upper heating plate and the lower heating plate are also matched with the cross-sectional sizes of the test samples. Considering that the through holes for placing the thermocouples penetrate the upper and lower heating plates, the through holes should be kept away from the positions of the tungsten-molybdenum alloy strips in the upper and lower heating plates, i.e., the central points of the upper and lower heating plates may be hollow. Illustratively, considering that the conventional cross-sectional size requirement of the heat insulating material (i.e., the test specimen) is 300mm×300mm, the external dimensions of the tungsten-molybdenum alloy sheet are also 300mm×300mm, and the thickness may be set to 1mm. Meanwhile, an S-shaped groove was cut out on the flat plate by a water cutting method, the groove being 8mm wide and the width of the alloy strip being 7mm, to form an upper heating plate and a lower heating plate. Electrode binding posts are led out of two ends of the upper heating plate and the lower heating plate and are used for being connected with a heating and measuring control unit so as to realize temperature control of the upper heating plate and the lower heating plate. A schematic structure of the upper and lower heating plates is shown in fig. 2.
In addition, a layer of high-temperature refractory bricks with sufficient thickness is symmetrically arranged on the outer sides of the upper heating plate and the lower heating plate, a water cooling plate (namely the upper water cooling plate and the lower water cooling plate) which is made of stainless steel materials and internally provided with double-return channels is respectively arranged on the outer sides of the refractory bricks, cooling circulating water is introduced into the flat plate to forcedly refrigerate, and heat dissipated to the periphery of the heating plate is timely taken away. A fixing device is arranged at the central point of the outer side plane of the water cooling plate so as to fixedly install the thermocouple leading-out end at a determined position and prevent the thermocouple position from moving up and down. The periphery of the whole testing assembly (namely the periphery of the outer parts of the upper heating assembly, the upper cold water plate, the lower heating assembly and the lower cold water plate) is also made into a heat protection layer by using a layer of high-temperature refractory bricks so as to reduce the heat dissipation of the periphery facing the side wall of the whole assembly.
Preferably, the signal for controlling the upper surface of the sample to linearly rise from the temperature set value to the temperature test set value and preserving the temperature for a set time based on the temperature control signal described in the present embodiment;
preferably, heating the lower heating assembly based on the compensating temperature control includes:
acquiring the temperature sum of the compensation temperature and the temperature of the lower surface of the sample in real time in the process of controlling the temperature rise and the heat preservation of the upper surface of the sample;
and controlling to heat the lower heating assembly based on the difference between the temperature and the temperature inside the lower heating assembly acquired in real time.
Example 2
Embodiment 1 provides a more complete description of the functions of the heating and measuring control unit, and there are various implementation manners, embodiment 2 discloses a specific implementation manner of the heating and measuring control unit, and a schematic structural diagram thereof is shown in fig. 3, including: the system comprises a computer, a data acquisition meter, a first temperature controller, a second temperature controller, a first heating power supply, a second heating power supply and a change-over switch.
The first temperature control instrument controls the first heating power supply to control the temperature of the upper heating plate, the second temperature control instrument controls the second heating power supply to control the temperature of the lower heating plate, and when the device is used, the first heating power supply is correspondingly connected with the upper heating plate, and the second heating power supply is correspondingly connected with the lower heating plate.
The measuring signal input end M of the first temperature controller is connected with the lead wire of the thermocouple T1, the setting signal input end S is connected to the control computer, and the temperature setting value signal sent by the computer is received. The leads of thermocouple T2 are split into two pairs in parallel. The data acquisition table is connected with the computer and converts the voltage signals transmitted by the leads into temperature signals and sends the temperature signals to the computer for recording and processing. The other pair of leads is connected to the measurement signal input terminal M of the second temperature controller through a change-over switch. Similarly, the lead wires of the thermocouple T3 are also divided into two pairs in parallel, one pair is connected with the data acquisition meter, and the other pair is connected with the second temperature control instrument through the change-over switch. With the change-over switch, the second temperature controller receives the signal of T2 as a real-time measurement signal input value when in the warm-up mode, and receives the signal of T3 as a real-time measurement signal input value when in the test mode, the change-over switch being controlled by the computer.
Preferably, in the heating and measuring control unit, the heating process may be divided into a preheating type and a test mode. Wherein, preheat mode: the heating at 1400℃is taken as an example for illustration. The computer sends the temperature set value 1400 ℃ to two temperature controllers through a set signal input end S, a measurement signal input end M of the first temperature controller receives signals of a thermocouple T1, and a measurement signal input end M of the second temperature controller receives signals of a thermocouple T2 through a change-over switch. The power supply is started to start heating. When the temperatures of the upper and lower surfaces of the sample reached 1400 c and were stabilized, the preheating mode was ended. The term "stable" as used herein means that the temperature of the upper and lower surfaces of the sample does not deviate from the set temperature value within a predetermined time range, for example, if the temperature of the upper and lower surfaces of the sample does not deviate from the set temperature value within 10 seconds during a test+0.1℃indicates that stabilization is achieved. The computer acquires and records the temperature difference delta T0 (=T3-T2) of the lower surfaces T2 and T3 of the sample at the moment according to the temperatures of the upper surface and the lower surface of the sample acquired at the end moment of the preheating mode, and enters the testing mode. In the test mode stage, the computer converts the change-over switch of the second temperature controller into a receiving T3 signal and sends 1400 to the slave computer via the set signal input terminal SThe temperature rising signal of 1800s from the temperature of 1450 ℃ and then 1800s of heat preservation is sent to the first temperature controller, and the first heating power supply is started to start heating. At this time, the data acquisition meter starts to continuously acquire signals of thermocouples T1, T2 and T3 and convert the signals into temperature values to be sent to the computer, the computer records the three groups of data, processes the actually measured temperature T2 (T) of the thermocouple T2 into (T2 (T) +Δt0), and sends the (T2 (T) +Δt0) as a set value to the setting signal input end S of the second temperature controller in real time as a set value, the actually measured temperature T3 (T) value of the thermocouple T3 is input to the measurement input end M of the second temperature controller, and the real-time set value (T2 (T) +Δt0) and the real-time measured value T3 (T) are compared to generate a control signal to be sent to the second heating power supply to control the temperature state of the lower surface of the sample. The control process is to actively heat the upper surface of the sample and passively compensate the boundary condition of the heated approximate heat insulation wall surface of the lower surface. In test mode, the computer continuously records data of T1 and T2 temperatures over time and uses them as measurement data for calculating the thermal conductivity of the test sample. The temperature data of T3 is not related to the calculation of thermal conductivity, and is only used as reference temperature data in the experimental process. It should be noted that, in the above process, the manner in which the temperature controller generates the control signal based on the signals of the two input ends may be implemented by using an existing PID algorithm, and the algorithm is the prior art, which is not described herein.
Based on the measurement data, the computer performs the following operations to obtain the thermal conductivity of the sample:
after obtaining data of temperature changes of the upper surface and the lower surface of the sample with time in the process of active heating of the upper surface and passive thermal compensation of the lower surface of the sample, the following operations can be performed to obtain the thermal conductivity of the sample:
step (1): based on the temperature of the upper surface of the sample acquired in real time and the following formula, obtaining the theoretical temperature of the lower surface of the sample at each sampling moment;
wherein x=l;m=0, 1,2,3 … …, L is the thickness of the sample, f (τ) is the temperature of the upper surface of the sample taken at the τ -th moment; alpha represents the thermal diffusivity of the sample;
step (2): based on the temperature theoretical value of the lower surface of the sample at each sampling moment and the temperature value acquired in real time, obtaining the thermal diffusion coefficient of the sample through a nonlinear parameter evaluation algorithm;
step (3): based on the thermal diffusivity α of the sample, obtaining the thermal conductivity λ of the sample:
λ＝αρC p
wherein ρ is the density of the sample; c (C) p Is the specific heat capacity of the sample.
The formula and fitting iterative process used in the above steps are described as follows:
backside adiabatic transient heat transfer model: setting the thickness of the flat sample to L and the initial temperature to T 0 (refer to the temperature at all locations within the sample). When time t>At 0, the boundary surface of x=0 has a time-varying temperature t=f (T), and the back surface of the sample, i.e., the x=l, is not in heat exchange with the outside, and an adiabatic boundary condition is adopted. Wherein x represents the distance from any point in the sample to the hot surface by taking the position of the plane where the hot surface of the sample is located as 0 point and the direction pointing to the other surface along the thickness direction as positive. The hot face of the sample is located above and the cold face is located below, and is therefore forward downwards in the thickness direction. In this embodiment, therefore, x=0, i.e., the upper surface of the sample, since the sample hot face is below the upper cold face. Accordingly, the cold side, i.e., the lower side, of the sample is at x=l.
The upper and lower surface temperatures of the sample described in the preheating stage in this example 1 were both stabilized at the temperature set point in order to satisfy the initial condition T (x, 0) =t 0 The method comprises the steps of carrying out a first treatment on the surface of the The test stage actively heats the upper surface of the sample to meet the boundary condition T (0, T) =f (T), and the lower heating plate is switched to a special adiabatic boundary condition control mode to meetIs a condition of (2).
When time T >0, the derivation of the expression of the temperature distribution T (x, T) at any position in the sample is:
the mathematical description of the heat transfer equation is shown below:
in formula (3), T (0, T) means a temperature T at which x=0 is at time T, and the following expressions are the same. T (0, T) =f (T) means that the temperature at time T x=0 is f (T), and f (T) is a value that varies with temperature. This expression gives the boundary condition at x=0.
The solving process of the equation is as follows:
1) Order the
T＝T 1 (x，t)+T 0 (4)
Bringing equation (4) into equation (3) yields:
thus, for the initial condition T (x, 0) =t 0 Directly deducting T from the state of (2) 0 And simplifying the process. Equation (5) is solved as follows.
2) Equation:
the solution of (c) is t=f (τ).
3) Equation:
the solution of (2) is:
wherein cos beta m L=0, i.e
4) From 2) and 3) above, equations can be obtained
The solution of (2) is:
5) According to the Du Hamei rule, the solution of equation (5) can be expressed by the solution of equation (8) (i.e., expression (9)) in the following form:
wherein x represents the distance from any point inside the sample to the upper surface of the sample, and x=l when calculating the theoretical temperature of the lower surface of the sample;m=0, 1,2,3 … …, L is the thickness of the sample, f (τ) is the temperature of the upper surface of the sample taken at the τ -th moment; α represents the thermal diffusivity of the sample, which is an unknown quantity;
in the above formula, the thermal diffusivity alpha is the heat conduction parameter to be evaluated, and the temperature T 1 The differentiation of (x, t, α) by α can be obtained:
wherein cos beta m L=0, i.em=0, 1,2,3, … …, when calculatedAt the theoretical temperature of the lower surface of the sample, x=l; l is the thickness of the sample, and f (tau) is the temperature of the upper surface of the sample collected at the tau th moment; α represents the thermal diffusivity of the sample, which is an unknown quantity;
from the analytical solution of one surface heating, backside adiabatic model of semi-infinite large plate and (10), it can be seen that the temperature distribution function of the model is a nonlinear function of the thermal diffusivity, alpha. Thus, if the thermal diffusivity is solved in the reverse direction using the temperature response curve, a nonlinear parameter estimation algorithm is required. The derivation process of the algorithm is as follows:
first, the following matrix is defined:
observation value matrix: y is Y l ＝[y 1 ,y 2 ,···,y i ,···,y l ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein y is i The temperature of the lower surface of the sample collected at the ith moment is represented; l represents the number of samplings;
theoretical temperature matrix: psi l ＝[η 1 ,η 2 ,···,η i ,···,η l ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein eta i ＝T 1 (L, i, α), wherein α is a parameter to be solved;
sensitivity coefficient matrix P l ＝[p 1 ,p 2 ,···,p i ,···,p l ]Wherein, the method comprises the steps of, wherein,
the value of α is evaluated using the least squares method:
S＝(Y-Ψ) T ·(Y-Ψ) (13)
so that
P T Ψ＝P T Y (15)
Since matrices P and ψ are nonlinear functions of α, the above equation cannot be solved directly to α, requiring that ψ be at α=α 0 Linear expansion of the positionPerforming first order approximation:
Ψ(α)＝Ψ(α 0 )+P(α 0 )·(α-α 0 ) (16)
carrying (16) into (15)
P T (α 0 )Y≈P T (α 0 )Ψ(α 0 )+P T (α 0 )P(α 0 )(α-α 0 ) (17)
And (3) finishing to obtain a Gaussian iteration formula:
α j+1 l ＝α j l +(P l T (α j l )P l (α j l )) -1 ·P l T (α j l )(Y l -Ψ l (α j l )) (18)
wherein j is the iteration number, and l is the sampling number; alpha 0 l Representing the initial diffusion coefficient at the previous l samplings;
thus, when calculating the thermal diffusivity, alpha, for the first k samples (i.e., t=k) k In this case, it is possible to assume a alpha 0 k Repeating Gaussian iteration according to formula (18) until alpha converges, taking the converged alpha as the thermal diffusion coefficient alpha of the previous k samples k ；
Wherein alpha is k Satisfies the following formula:
wherein alpha is v k Representation to give alpha k The result of the previous gaussian iteration; delta is generally 10 -4 ，δ 1 Generally take 10 -100 。
When the sample is added once (i.e. l=k+1), the observation matrix can be expressed as:namely, a block matrix form formed by combining an observation value matrix of the previous k times of sampling and an observation value of the (k+1) th times of sampling; accordingly, it isThe theoretical temperature matrix ψ and the sensitivity coefficient matrix P can be processed identically, so that the following results are obtained:
more generally, in calculating the thermal diffusivity corresponding to the first l+1 (l. Gtoreq.k) samples, the Gaussian iteration can be described as follows:
in the process of iteration using equation (19), the start value of the iteration may be determined according to equation (20).
That is, when calculating the thermal diffusivity at the previous sampling time of l+1 (l.gtoreq.k), the thermal diffusivity determined at the previous time is substituted into the formula (10) and the formula (11) to calculate P l ，P l T ，Ψ l ，η l+1 And p l+1 Then carrying out calculation in a formula (20) to obtain alpha 0 l+1 Then, the iteration is carried out by using the formula (19) to obtain… until convergence, the thermal diffusivity alpha at the previous k+1 time is obtained k+1 。
The thermal diffusivity at a subsequent time is obtained according to formulas (10), (11), (19), and (20).
The nonlinear evaluation algorithm of the parameters to be evaluated is given above. After the temperature f (t) of the upper surface of the sample and the temperature response of the inside or the back surface of the sample are measured, the thermal diffusivity can be calculated reversely by using the formula (10), the formula (11) and the formula (19).
Example 3
The invention discloses a method for testing the thermal conductivity of a heat insulating material by a transient method, which is shown in a flow chart of FIG. 4 and comprises the following steps:
step S1: heating the upper and lower surfaces of the sample until the temperatures of the upper and lower surfaces of the sample are stable to the temperature set values, and obtaining the compensation temperature at the moment;
step S2: after the temperatures of the upper surface and the lower surface of the sample are both stabilized at the temperature set value, controlling to heat the upper surface of the sample based on the difference between the temperature represented by the temperature control signal and the temperature of the upper surface of the sample acquired in real time, controlling to heat the lower surface of the sample based on the compensation temperature, and acquiring the temperatures of the upper surface and the lower surface of the sample in real time;
step S3: and (3) obtaining the thermal conductivity of the sample based on the temperatures of the upper surface and the lower surface of the sample acquired in real time in the step (S2).
Step S31: obtaining the theoretical temperature of the lower surface of the sample at the corresponding sampling moment based on the temperature of the upper surface of the sample acquired in real time and a formula (10);
step S32: obtaining a thermal diffusion coefficient alpha of the sample based on a temperature theoretical value of the lower surface of the sample at each sampling moment and a temperature value acquired in real time;
step S33: based on the thermal diffusivity α of the sample and equation (21), the thermal conductivity λ of the sample is obtained:
λ＝αρC p (21)
wherein ρ is the density of the sample; c (C) p Is the specific heat capacity of the sample.
Preferably, step S32 includes:
an observation value matrix, a theoretical temperature matrix and an initial thermal diffusion coefficient alpha which are obtained according to the previous k times of sampling 0 k Iterative obtaining the thermal diffusion coefficient alpha of the previous k samples k The method comprises the steps of carrying out a first treatment on the surface of the Wherein the observation value matrix consists of the temperature of the lower surface of the sample obtained by sampling for the previous k times, and the theoretical temperature matrix consists of the temperature of the lower surface of the sample obtained by sampling for the previous k timesThe theoretical temperature of the lower surface of the sample obtained by k times of sampling is formed; the thermal diffusion coefficient alpha of the previous k samples is obtained through iteration k In the process, updating the thermal diffusivity according to formula (18); if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha of the previous k samples k 。
Sequentially increasing the sampling times, and obtaining the thermal diffusion coefficient of the current sampling times based on the thermal diffusion coefficient of the previous sampling times every time the sampling times are increased until the thermal diffusion coefficient converges; the converged thermal diffusivity was taken as the thermal diffusivity of the sample. In the process, each time the sampling frequency is increased, an initial thermal diffusion coefficient corresponding to the current sampling frequency is obtained according to a formula (20): the thermal diffusivity is then updated according to equation (19): if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha after increasing the sampling times every time l+1 。
In addition, it should be further noted that, the data used in the embodiment of the present method may be collected by the apparatus in embodiment 1 or embodiment 2, so the specific implementation process of the embodiment of the present invention may be referred to the above apparatus embodiment, and this embodiment is not repeated herein. Since the principle of the embodiment is the same as that of the embodiment of the device, the method also has the corresponding technical effects of the embodiment of the device.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (5)
1. The method for testing the thermal conductivity of the heat insulation material by the transient method is characterized by comprising the following steps of:
step S1: heating the upper and lower surfaces of the sample until the temperatures of the upper and lower surfaces of the sample are stable to the temperature set values, and obtaining the compensation temperature at the moment;
step S2: after the temperatures of the upper surface and the lower surface of the sample are both stabilized at the temperature set value, controlling to heat the upper surface of the sample based on the difference between the temperature represented by the temperature control signal and the temperature of the upper surface of the sample acquired in real time, controlling to heat the lower surface of the sample based on the compensation temperature, and acquiring the temperatures of the upper surface and the lower surface of the sample in real time;
step S3: acquiring the thermal conductivity of the sample based on the temperatures of the upper surface and the lower surface of the sample acquired in real time in the step S2;
in the step S1, heating the lower surface of the sample by a lower heating assembly;
taking the difference value between the temperature of the lower surface of the sample and the temperature of the interior of the lower heating component, which is acquired when the temperature of the upper surface and the temperature of the lower surface of the sample are both stable to a temperature set value, as the compensation temperature;
the temperature control signal is a signal for controlling the upper surface of the sample to be linearly heated from a temperature set value to a temperature test set value and preserving heat for a set time;
in the step S2, the heating the lower surface of the sample based on the compensated temperature control includes:
acquiring the temperature sum of the compensation temperature and the temperature of the lower surface of the sample in real time in the process of controlling the temperature rise and the heat preservation of the upper surface of the sample;
controlling heating of the lower heating assembly based on the temperature and a difference between the temperature and the temperature inside the lower heating assembly acquired in real time;
the step S3 includes:
step S31: based on the temperature of the upper surface of the sample acquired in real time and the formula (1), obtaining the theoretical temperature of the lower surface of the sample at each sampling moment;
wherein x=l;l is the thickness of the sample, and f (tau) is the temperature of the upper surface of the sample collected at the tau th moment; alpha represents the thermal diffusivity of the sample; x represents the distance from any point in the sample to the hot surface, and t represents the moment, wherein the position of the plane where the hot surface of the sample is located is 0 point, the direction pointing to the other surface along the thickness direction is positive;
step S32: obtaining a thermal diffusion coefficient alpha of the sample based on a temperature theoretical value of the lower surface of the sample at each sampling moment and a temperature value acquired in real time;
step S33: acquiring the thermal conductivity of the sample based on the thermal diffusivity alpha of the sample;
the step S32 includes:
an observation value matrix, a theoretical temperature matrix and an initial thermal diffusion coefficient alpha which are obtained according to the previous k times of sampling 0 k Iterative obtaining the thermal diffusion coefficient alpha of the previous k samples k The method comprises the steps of carrying out a first treatment on the surface of the The observation value matrix is composed of the temperature of the lower surface of the sample obtained by the previous k times of sampling, and the theoretical temperature matrix is composed of the theoretical temperature of the lower surface of the sample obtained by the previous k times of sampling;
sequentially increasing the sampling times, and obtaining the thermal diffusion coefficient of the current sampling times based on the thermal diffusion coefficient of the previous sampling times every time the sampling times are increased until the thermal diffusion coefficient converges; the converged thermal diffusivity was taken as the thermal diffusivity of the sample.
2. The method according to claim 1, wherein in the step S33, the thermal conductivity λ of the sample is obtained according to formula (2):
λ＝αρC p (2)
wherein ρ is the density of the sample; c (C) p Is the specific heat capacity of the sample.
3. The method for testing the thermal conductivity of the transient heat insulation material according to claim 1, wherein the thermal diffusion coefficient alpha of the previous k samples is obtained through iteration k In the process, the thermal diffusivity is updated according to equation (3):
α j+1 l ＝α j l +(P l T (α j l )P l (α j l )) -1 ·P l T (α j l )(Y l -Ψ l (α j l )) (3)
wherein the observation matrix Y l ＝[y 1 ,y 2 ,···,y i ,···,y l ]，y i The temperature of the lower surface of the sample collected at the ith moment is represented; theoretical temperature matrix ψ l ＝[η 1 ,η 2 ,···,η i ,···,η l ]；η i ＝T 1 (L, i, alpha), alpha being the parameter to be solved; sensitivity coefficient matrix P l ＝[p 1 ,p 2 ,···,p i ,···,p l ]，j is the iteration number, l is the sampling number; alpha 0 l Representing the initial diffusion coefficient at the previous l samplings;
if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha of the previous k samples k 。
4. The method for testing the thermal conductivity of a transient heat insulating material according to claim 3, wherein each time the number of sampling is increased, an initial thermal diffusion coefficient corresponding to the current number of sampling is obtained according to formula (4):
the thermal diffusivity is then updated according to equation (5):
if the updated thermal diffusion coefficient converges, ending the iteration, and taking the updated thermal diffusion coefficient as the thermal diffusion coefficient alpha after increasing the sampling times every time l+1 。
5. The method for testing the thermal conductivity of a transient heat insulating material according to any one of claim 1 to 4,
measuring the temperature of the upper surface of the sample by using a first temperature thermocouple which is contacted with the upper surface of the sample;
measuring the temperature of the upper surface of the sample by using a second temperature thermocouple which is contacted with the lower surface of the sample;
the temperature inside the lower heating assembly is measured using a third temperature thermocouple in contact with the inside of the lower heating assembly.
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