CN104502402A - Method for measuring thermophysical property of columnar thermal insulation material - Google Patents

Abstract

The invention provides a method for measuring thermophysical property of a columnar thermal insulation material, which is used for determining radial heat conductivity, axial heat conductivity and volume heat capacity of the columnar orthotropic thermal insulation material by measuring temperature variation of one point of a tested sample. The method comprises the following steps: establishing a two-dimension cylindrical coordinate heat transfer model under effect of thermal interference of specific form in cylindrical coordinates; obtaining analytical solution of temperature variation of the orthotropic thermal insulation material in the time domain by adopting Laplace transformation, Hankel transformation and Laplace inverse transformation; analyzing correlation among sensitivity coefficients of the radial heat conductivity, the axial heat conductivity and the volume heat capacity and the influences of temperature variation caused by the parameters through calculation on the sensitivity; establishing a corresponding measurement system, and acquiring the transient response data of the temperature in real time; and meanwhile, determining the radial heat conductivity, the axial heat conductivity and the volume heat capacity of the tested orthotropic thermal insulation material by adopting an L-M parameter estimation method. The method provided by the invention is convenient to implement and adopts simple steps, and meanwhile can be used for measuring the radial heat conductivity, the axial heat conductivity and the volume heat capacity of the columnar thermal insulation material.

Description

A kind of method measuring the hot physical property of column heat-barrier material

Technical field

The invention belongs to material thermophysical property measurement technical field, in particular, provide a kind of new measuring method that simultaneously can be obtained multiple thermal physical property parameter by one-shot measurement, by measuring the temperature variation of a point in sample, determine the method for orthotropy heat-barrier material radial thermal conductivity, axial thermal conductivity and volumetric heat capacity.

Background technology

Material thermal physical property parameter is understanding, understand and one of evaluating material heat transfer property the most basic good and bad physical parameter, is key parameter particular thermal conductive process being carried out to fundamental research, analytical calculation and engineering design.Measurement accuracy thermal physical property parameter is significant to the development that energy utilization, building energy conservation, Aero-Space, new material exploitation, environmental protection and nuclear energy uses etc. are multi-field.Fibrous insulating material is all widely used in each field, and its thermal conductivity data is different with the difference of manufacturing process, material structure, fiber ply sequence and trend, additive level, presents typical anisotropic character.

In recent years, along with the active demand of scientific technological advance and commercial Application, there is conduction and the fibrous insulating material material of the plurality of advantages such as thermal conductivity is good, specific strength and specific modulus is high, chemical stability is excellent, toughness and thermal-shock resistance is high, good heat resistance, not only in the sophisticated industry such as Aero-Space, nuclear energy uses, and in automobile shipbuilding, build a bridge, electric mechanical manufacture, the every field such as therapeutic physical education be obtained for and apply widely.The Measurement accuracy of its thermal physical property data is not only the basic foundation of material property evaluation and fail-safe analysis, also to the design and manufaction level improving material, meet Chinese national economy and national defence the aspect such as normal data demand all significant.

Developed country pays much attention to the importance of material thermophysical property measurement, in succession establish thermophysical property measurement mechanism and the mechanism of sophisticated systems, as national measurement research institutes etc. such as the National Physical Laboratory (NPL) of the NIST of the U.S., Britain, the physical technique research institute (PTB) of Germany, the high temperature research institute of Russian Academy Of Sciences and ermal physics research institutes.In addition, more complete material thermal physical property measuring device is all had in the institution of higher learning such as Purdue Univ-West Lafayette USA, Japanese keio university, graceful Chester university of Britain, Munich, Germany polytechnical university and this university of Caro.These developed countries establish thermophysical property measurement national standard or the industry standard of this country in succession, as the ASTM of the U.S., German DIN, the JIS of Japan, the BS etc. of Britain, also have international standard ISO in addition.The thermophysical property measurement of China starts from the fifties in last century, mainly concentrates on scientific research institutions and Some Universities.Metal research institute of the Chinese Academy of Sciences, Shanghai Inst. of Silicate, Chinese Academy of Sciences, institute of the space flight First Academy 703, building materials institute, china institute of metrology and the unit such as Tsing-Hua University, University of Science & Technology, Beijing have carried out comparatively systematic study in the exploration of the hot physical property measurement method of material and the development of experimental provision.Shanghai Inst. of Silicate, Chinese Academy of Sciences just successfully developed laser flash method heat conductivity measuring device as far back as 1973, china institute of metrology is to steady heat conduction instrument, automatic heat insulation calorimeter studied in great detail, metal research institute of the Chinese Academy of Sciences utilizes laser flash to send out to carry out systematic study to the hot physical property of metal material, Tsing-Hua University is fruitful in the measurement of film thermal coefficient of diffusion in recent years, remarkable achievement is achieved in University of Science & Technology, Beijing is applied to more than the 1200 DEG C hot physical property of material recently measurement in plane heat source method, other colleges and universities in addition, R&D institution or enterprise or home-built equipment or purchase of equipment, also the thermophysical property measurement experimental provision being applicable to different materials is established.

Up to now, although carried out a large amount of fruitful research both at home and abroad in thermophysical property measurement, establish and there is material proving installation formulated corresponding measurement standard targetedly.But the thermal conductivity measurements of current existing maturation is as Hot-strip Method, heat-pole method, hot-disk etc., and all based on the principle model of isotropic material, the thermal conductivity being unsuitable for fibrous material is measured.And protect hot plate method, plane heat source method etc., then need repeatedly to convert the thermal conductivity that direction of measurement could determine material different directions, add complicacy and the error of experiment.Therefore, in the urgent need to developing a kind of measuring method just being determined anisotropic material different directions thermal conductivity by one-shot measurement accurately and efficiently.

Summary of the invention

The object of the invention is to: provide can obtain orthogonal each method to anisotropic fiber heat-barrier material radial thermal conductivity, axial thermal conductivity and volumetric heat capacity by a kind of by one-shot measurement simultaneously.

To achieve these goals, provide and a kind ofly determine the orthogonal respectively to thermal conductivity and volumetric heat capacity of material by some temperature measured in sample.

The technical scheme of this law invention is: a kind of method measuring the hot physical property of column heat-barrier material, and concrete steps are as follows:

Step 1: to highly respectively establishing the two-dimensional columns coordinate heat transfer model under the hot interference effect of particular form in cylindrical coordinates to anisotropy heat-barrier material for 0.01m ~ 0.05m, radius are that the column of 0.01m ~ 0.10m is orthogonal, its governing equation as shown in Equation 1:

$\mathrm{\ρ}{c}_p\frac{\∂T(r,z,\mathrm{\τ})}{\∂\mathrm{\τ}}={\mathrm{\λ}}_r\frac{\∂T^2(r,z,\mathrm{\τ})}{\∂r^2}+{\mathrm{\λ}}_r\frac{1}{r}\frac{\∂T(r,z,\mathrm{\τ})}{\∂r}+{\mathrm{\λ}}_z\frac{\∂T^2(r,z,\mathrm{\τ})}{\∂z^2}$ (formula 1)

Its starting condition and boundary condition be as shown in Equation 2:

T (r, z, τ) | _τ=0=T ₀(formula 2a),

$-{\mathrm{\λ}}_z\frac{\∂T(r,z,\mathrm{\τ})}{\∂z}{|}_{z=0}=\left\{\begin{array}{cc}q& 0\≤r\≤R_1\\ 0& R_1\≤r\≤R_2\end{array}\right.$ (formula 2b),

T (r, z, τ) | _{z → ∞}=T ₀(formula 2c),

$\frac{\∂T(r,z,\mathrm{\τ})}{\∂r}{|}_{r=0}=0$ (formula 2d),

$-{\mathrm{\λ}}_r\frac{\∂T(r,z,\mathrm{\τ})}{\∂r}{|}_{r=R}=h[T(r,z,\mathrm{\τ})-T_0]$ (formula 2e),

In formula, T is temperature; T ₀for environment temperature; τ is the time; λ _rfor sample radial coefficient of heat conductivity, λ _zfor the density that sample axial thermal conductivity, ρ are tested sample, C _pbe respectively sample specific heat at constant pressure; Q is flat heat source heat flow density; R ₁for heating radius; R ₂for radius of specimen, r is radial coordinate, and z is axial coordinate; H is the complex heat transfer coefficient between sample and environment;

In described heat transfer model, the heat interference of described particular form is step hot-fluid.Each characterisitic parameter scope of measured column orthotropy heat-barrier material is as shown in table 1.

In the parameter value table that table 1 measuring system adopts:

Table 1The parameter values used in the measuring system

Step 2: adopt Laplace conversion and Hankel transfer pair governing equation, starting condition and boundary condition to change, then by the method for Analytical Solution, obtain the analytic solution of sample internal temperature field distribution in frequency domain.On this basis, carry out Laplace inverse transformation, finally solve the temperature variation analytic solution in the time domain obtained in orthotropy heat-barrier material.

Step 3: carry out sensitivity analysis to thermal characteristic parameter to be measured respectively, to determine each parameter beta _jto measured value T (t during generation subtle change _j, β) influence degree.For the ease of comparative analysis mutual between different parameters, have employed the sensitivity coefficient of " zero dimension ", it is defined as shown in Equation 3:

${X_{\mathrm{ij}}}^{*}={\mathrm{\β}}_j{X}_j(t_i,\mathrm{\β})={\mathrm{\β}}_j\frac{\∂T(t_i,\mathrm{\β})}{\∂{\mathrm{\β}}_j}$ (formula 3)

In formula, X is sensitivity coefficient, and β is measured parameter, and T is absolute temperature, the i:i moment, j: a jth parameter;

" zero dimension " sensitivity coefficient represents the rate of change that measuring-signal changes relatively to parameter, has the dimension identical with measuring-signal.Calculate according to the sensitivity coefficient of formula 3 to each thermal characteristic parameter, the correlativity between the sensitivity coefficient analyzing each parameter and thermal parameter on the impact of temperature variation, thus determine the possibility being obtained three solve for parameters by one-shot measurement.

Step 4: the measuring system setting up column orthotropy heat-barrier material temperature, the electric heating sheets of sheet is placed between the tested column sample of identical two of shape, for producing on each tested sample surface and set identical hot undesired signal in theory calculate.Applying hot-fluid on column orthotropy heat-barrier material surface is 0.1W/m ²~ 1000W/m ²the undesired signal of step constant heat flux, when the heat time is 5min ~ 20min, adopt multi-path data collecting device after temperature compensation and filtering, the transient temperature response data of central shaft upwards measurement point in the tested sample under the hot interference effect of Real-time Obtaining.

Step 5: the temperature-responsive data obtained when the temperature-responsive data calculated based on analytic solution and actual measurement, application L-M method for parameter estimation, can obtain the axial thermal conductivity of columnar orthotropy heat-barrier material, radial thermal conductivity and volumetric heat capacity amount three parameters simultaneously.

The invention has the advantages that: owing to adopting technique scheme, the invention provides one and implement convenient, the simple measuring method of step, the axial thermal conductivity of columnar orthotropy heat-barrier material, radial thermal conductivity and volumetric heat capacity amount three important parameters can be measured simultaneously.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of measurement of the present invention.

In figure:

1. sample 2.. heating plate 3. point for measuring temperature

Embodiment

Below with reference to accompanying drawings the specific embodiment of the present invention is described.In the following description, do not have to describe generally acknowledged function or structure in detail, obscure the present invention to avoid occurring unnecessary details.

In concrete enforcement, suppose in the temperature range measured, the anisotropy of column orthotropy heat-barrier material, its axial thermal conductivity, radial thermal conductivity and volumetric heat capacity amount are unknown solve for parameter, and other dimensional parameters and physical parameter are constant.Under the cylindrical coordinates set up, height Z=0.05m, radius R ₂in the Two-Dimensional Heat model of the column orthotropy heat-barrier material of=0.05m, governing equation and boundary condition are respectively such as formula shown in 4 and formula 5:

$\mathrm{\ρ}{c}_p\frac{\∂T(r,z,\mathrm{\τ})}{\∂\mathrm{\τ}}={\mathrm{\λ}}_r\frac{\∂T^2(r,z,\mathrm{\τ})}{\∂r^2}+{\mathrm{\λ}}_r\frac{1}{r}\frac{\∂T(r,z,\mathrm{\τ})}{\∂r}+{\mathrm{\λ}}_z\frac{\∂T^2(r,z,\mathrm{\τ})}{\∂z^2}$ (formula 4)

Starting condition and boundary condition be as shown in Equation 5:

T (r, z, τ) | _τ=0=T ₀(formula 5a)

$-{\mathrm{\λ}}_z\frac{\∂T(r,z,\mathrm{\τ})}{\∂z}{|}_{z=0}=\left\{\begin{array}{cc}q& 0\≤r\≤R_1\\ 0& R_1\≤r\≤R_2\end{array}\right.$ (formula 5b)

T (r, z, τ) | _{z → ∞}=T ₀(formula 5c)

$\frac{\∂T(r,z,\mathrm{\τ})}{\∂r}{|}_{r=0}=0$ (formula 5d)

Wherein, the factor of environmental baseline these two aspects when considering orthotropy heat-barrier material thermophysical property and simulated experiment, the parameter value adopted in calculating is as shown in table 2.

The parameter value that table 2 embodiment adopts

Table 2The parameter values used in the specific example

For formula 4 and 5, adopt Laplace conversion and Hankel transfer pair governing equation, starting condition and boundary condition to change, then adopt the method for Analytical Solution, obtain the analytic solution of sample internal temperature field distribution in frequency domain.On this basis, by Laplace inverse transformation, finally solve the temperature variation analytic solution in the time domain obtained in orthotropy heat-barrier material.During calculating, initial temperature field is set to room temperature, and other parameters are arranged by table 2.

In order to verify the correctness of analytic solution, the diabatic process of CFD software Fluent 6.3 pairs of samples under identical operating mode is adopted to carry out numerical simulation.The numerical solution of control sample internal point temperature rise and analytic solution, result shows under identical operating mode, orthogonal respectively to the numerical solution of anisotropy sample temperature field and the result of analytic solution completely the same, the sufficient proof correctness of analytic solution.

Based on the result of carried out theoretical analysis, sensitivity analysis is carried out to the orthotropy heat-barrier material thermal physical property parameter to be estimated related to, in numerical solution, calculates " zero dimension " sensitivity coefficient of each parameter based on formula 6:

$X_{\mathrm{ij}}=\frac{T(t_i,{\mathrm{\β}}_1,\·\·\·,{\mathrm{\β}}_j+\mathrm{\Δ}{\mathrm{\β}}_j,\·\·\·,{\mathrm{\β}}_p)-T(t_i,{\mathrm{\β}}_1,\·\·\·,{\mathrm{\β}}_j-\mathrm{\Δ}{\mathrm{\β}}_j,\·\·\·,{\mathrm{\β}}_p)}{2\mathrm{\Δ}{\mathrm{\β}}_j}$ (formula 6)

The result of sensitivity analysis shows, the absolute value of the space relative sensitivity of radial thermal conductivity, axial thermal conductivity and volumetric heat capacity is larger the closer to thermal source, more less close to sample outer boundary, and is in the same order of magnitude with sample space temperature rise response.Can analyze further and show, longitudinal center line is measured on warm spot apart from heating plate z distance and position, trend is different over time for the sensitivity coefficient of radial thermal conductivity, axial thermal conductivity and volumetric heat capacity, mutual ratio is non-constant, show that these three parameters to be measured are linear independences, therefore, this three parameters can be estimated by once testing simultaneously.

On this basis, carry out test to measure.Heating plate applies q=1000W/m ²step hot-fluid, heat time is 200s, according to schematic diagram, heating plate is placed between sample, use multi-channel data acquisition device, the transient temperature response of the measurement point on measurement sample longitudinal center line, on distance heating plate z distance and position, the data of Real-time Obtaining temperature variation, and by communicating with host computer, transfer data to host computer, and the process such as temperature compensation and filtering is carried out to temperature signal.Meanwhile, adopting formula 4 and 5, by calculating, the Temperature Distribution calculated value under special parameter value condition can be obtained.

Finally, the temperature variation obtained based on analytical Calculation and the temperature variation data obtained by actual measurement, adopted L-M method for parameter estimation, determine the radial thermal conductivity of tested orthotropy heat-barrier material, axial thermal conductivity and volumetric heat capacity simultaneously.

Although the present invention describes with reference to its specific embodiment, it should be appreciated by those skilled in the art, when not departing from the scope of the present invention be defined by the following claims, the various amendments of form and details can be carried out to it.

Claims (5)

1. measure the method for the hot physical property of column heat-barrier material for one kind, the method is used for the temperature variation by measuring a point in sample, determine the method for orthotropy heat-barrier material radial thermal conductivity, axial thermal conductivity and volumetric heat capacity, it is characterized in that: to being highly the column orthotropy heat-barrier material that 0.01m ~ 0.05m, radius are 0.01m ~ 0.10m, establish the Two-Dimensional Heat model under the hot interference effect of particular form; Concrete steps are as follows:

Step 1: under setting up the hot interference effect of particular form, the governing equation formula 1 of the Two-Dimensional Heat model of orthotropy heat-barrier material under cylindrical coordinates, as follows:

(formula 1);

Its starting condition and boundary condition, as follows:

T (r, z, τ) | _τ=0=T ₀(formula 2a),

(formula 2b),

T (r, z, τ) | _{z → ∞}=T ₀(formula 2c),

(formula 2d),

(formula 2e),

In formula, T is temperature; T ₀for environment temperature; τ is the time; λ _rfor sample radial coefficient of heat conductivity, λ _zfor the density that sample axial thermal conductivity, ρ are tested sample, C _pbe respectively sample specific heat at constant pressure; Q is flat heat source heat flow density; R ₁for heating radius; R ₂for radius of specimen, r is radial coordinate, and z is axial coordinate; H is the complex heat transfer coefficient between sample and environment;

Step 2: adopt the temperature variation in analytical method solving column orthotropic heat-barrier material;

Step 3: the sensitivity coefficient of calculating parameter, carries out sensitivity analysis;

Step 4: the transient response data of Real-time Collection temperature;

Step 5: application parameter method of estimation, determines the axial thermal conductivity of column orthotropic heat-barrier material, radial thermal conductivity and volumetric heat capacity amount.

2. the method for claim 1, is characterized in that, the heat transfer model of described step 1, implies and thinks two-dimensional axial symmetric model, and the heat interference of described particular form is step hot-fluid.

3. the method for claim 1, it is characterized in that, in Analytical Solution method in described step 2, Laplace conversion and Hankel transfer pair governing equation, starting condition and boundary condition is adopted to change, then by the method for Analytical Solution, the analytic solution of sample internal temperature field distribution in frequency domain are obtained, on this basis, carry out Laplace inverse transformation, finally solve the temperature variation analytic solution in the time domain obtained in orthotropy heat-barrier material.

4. the method for claim 1, is characterized in that, the thermal parameter β in described step 3 _jsensitivity coefficient be the sensitivity coefficient of " zero dimension ":

In formula: X ^*for sensitivity coefficient, β is solve for parameter, and T is absolute temperature, and i is i-th sampling instant within the scope of the whole test duration, and j is a jth solve for parameter;

Sensitivity analysis comprises the following steps:

A, calculate the sensitivity coefficient of each thermal characteristic parameter;

B, determine solve for parameter sensitivity coefficient between correlativity.

5. the method for claim 1, it is characterized in that, method for parameter estimation in described step 5 adopts L-M method to carry out parameter estimation, adopt the temperature variation data of a point in sample to estimate multiple thermal physical property parameters, finally determine the radial thermal conductivity of orthotropy heat-barrier material, axial thermal conductivity and volumetric heat capacity simultaneously.