CN107966472A - A kind of lossless method for fast measuring of high temperature contact thermal resistance - Google Patents

A kind of lossless method for fast measuring of high temperature contact thermal resistance Download PDF

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CN107966472A
CN107966472A CN201711264412.6A CN201711264412A CN107966472A CN 107966472 A CN107966472 A CN 107966472A CN 201711264412 A CN201711264412 A CN 201711264412A CN 107966472 A CN107966472 A CN 107966472A
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mrow
msub
mtd
mfrac
test specimen
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CN107966472B (en
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魏东
胡斌
石友安
杨肖峰
肖光明
刘磊
杜雁霞
桂业伟
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00Investigating or analyzing materials by the use of thermal means
    • G01N25/20Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity

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Abstract

The invention discloses a kind of lossless method for fast measuring of high temperature contact thermal resistance, according to medium temperature transonic characteristic, using ultrasonic pulse-echo method, ultrasound propagation time under the conditions of acquisition Transient Heat Transfer, Optimization Solution heat conduction inverse problem, can it is quick, lossless, non-contactly measure the interface contact heat resistance parameter varied with temperature.Measuring device is simple needed for the method for the present invention, measurement period is short, and is not required sensor to be contacted with test specimen, avoids interference that sensor contacts with test specimen and measurement range is limited be subject to sensor resistance to elevated temperatures.

Description

A kind of lossless method for fast measuring of high temperature contact thermal resistance
Technical field
The present invention relates to the lossless quick measurement side in ultrasound detection field, in particular to a kind of high temperature contact thermal resistance Method.
Background technology
In structural thermal specificity analysis and anti-thermal design, thermal contact resistance is one of important parameter, its value accurately whether It is directly related to the quality of thermal control design.Thermal resistance between too high or too low estimation contact interface all can produce shadow to structural thermal Ring, can cause structure service efficiency low when serious or trigger security risk.Therefore, the thermal contact resistance of interface is measured in aviation The fields such as space flight, machine-building, microelectronics, biomedicine, instrument and meter have important application value.Thermal contact resistance is one By temperature, load, medium, the hot physical property of material, surface roughness, material mechanical feature, material surface property, environment etc. it is numerous because The nonlinear problem of plain coupling influence.Existing theoretical model is difficult to use in practice, and the experimental study of thermal contact resistance has become The main method of engineer application.
Make a thorough investigation of whether experiment hot-fluid is stablized, thermal contact resistance measuring method is generally divided into steady state measurement method and instantaneous measurement Two kinds of method.Stable state subtraction unit is simple, method is ripe, but time of measuring is grown.Transient Method includes photothermal laser mensuration, thermal imaging Method, flash flicker methods etc., its advantage are in response to fast, non-contact, measurement exemplar size and may diminish to nanometer scale, but its Measurement process is easily affected by various factors, and the derivation of equation is relative complex, and measurement accuracy is also difficult to ensure that.The present invention passes through ultrasound Characteristic carries out the Optimization Solution of the equation of heat conduction during sound of echo, obtains the thermal contact resistance of two test specimen interfaces, substantially It is that steady state method and Transient Method are combined, i.e., transient prediction is employed on mode of heating, and is then employed in the calculating of thermal contact resistance The measuring principle of steady state method, therefore the advantages of with two methods and avoid its shortcoming.
The content of the invention
The object of the present invention is to provide a kind of lossless method for fast measuring of high temperature contact thermal resistance, using ultrasonic pulse-echo method, Ultrasound propagation time under the conditions of acquisition Transient Heat Transfer, contact heat quick, lossless, that non-contactly measure interface varies with temperature Resistance.
To achieve the above object, the present invention adopts the following technical scheme that:
Step 1:Two test specimens are taken, are respectively designated as the first test specimen and the second test specimen, two tested Part contacts with each other.
Step 2:By calibration experiment, the second test specimen internal ultrasonic velocity of wave propagation V passes corresponding with temperature T are obtained System.
Step 3:First test specimen is heated, by common ultrasound method, it is tested to obtain second Part tiThe ultrasonic propagation time t at momenti,exp
Step 4:Establish the Optimized model of high temperature contact thermal resistance measurement.The object function of optimization is:
Wherein:R is two test specimen interfaces thermal contact resistance to be measured;ti,calThe t obtained for numerical computationsiMoment Ultrasonic propagation time, the time of measuring ordinal number that subscript i is represented, n represent total time of measuring points;L2For the second test specimen The length in tested direction.
Constraints is:
Wherein:T1(x,t),T2(x, t) is the temperature field in two test specimens, and k, C and ρ are respectively test specimen material Thermal conductivity factor, specific heat capacity and density;T(t)X=0To heat border, heated by heater;For contact interface side Boundary, T2For the temperature at the second test specimen contact interface.
Step 5:The methods of by infrared or contact thermocouple, obtainThe temperature change on surface.
Step 6:Heat conduction inverse problem is solved using common Sequential Quadratic Programming method or Descended simplex method, obtains the The thermal contact resistance R of one test specimen and the second test specimen contact surface.
In conclusion by adopting the above-described technical solution, the beneficial effects of the invention are as follows:
The present invention is based on ultrasonic method, and required measuring device is simple, measurement period is short, and sensor and test specimen is not required Contact, avoids interference that sensor contacts with test specimen and measurement range is limited be subject to sensor resistance to elevated temperatures.
1st, this method only measures once, and test specimen heating surface carries out being warming up to such as 500 DEG C of predetermined temperature value, you can obtains Interface contact heat resistance parameter under room temperature to 500 DEG C of different temperatures, has the advantages such as measuring speed is fast, cost is low;
When the 2nd, carrying out non-cpntact measurement based on electromagnetism or laser-ultrasound, material at high temperature thermophysical property measurement is hardly by sensor The influence of heat resistance, has the big advantage of measurement range.
Brief description of the drawings
Examples of the present invention will be described by way of reference to the accompanying drawings, wherein:
The flow of Fig. 1 interface contact heat resistance measuring methods;
The interface contact heat resistance measurement result that Fig. 2 is varied with temperature.
Embodiment
All features disclosed in this specification, or disclosed all methods or during the step of, except mutually exclusive Feature and/or step beyond, can combine in any way.
Technique according to the invention scheme and step carry out the implementation of concrete case, as follows:
M1Test specimen one end is subject to T=550 DEG C of panel heater, and remaining surface is all adiabatic face, and ultrasonic probe is placed in M2 Test specimen upper surface, using vertical incidence mode excitation pulse ultrasonic wave, based on measurement M2The echo propagation time in test specimen Change, indirect problem, inverting M are coupled by solving thermal acoustic1Test specimen and M2The thermal contact resistance at test specimen interface.
Case1M1Test specimen and M2The thermal contact resistance R at test specimen interface is not varied with temperature, true value 5.952e-5m2℃W-1.Ginseng Number recognition result 5.952e-5m2℃W-1, error 0.006%.
Case1M1Test specimen and M2The thermal contact resistance R at test specimen interface is varied with temperature, and true value is
R=1.47e-15 × T4-2.01e-12×T3+9.65e-10×T2-2.12e-07×T+3.88e-05(m2℃W-1), wherein T is temperature.Above-mentioned material parameter is fitted acquisition by experimental data in advance, in engineering in practice usually in advance to contact Thermal resistance does not have any priori, therefore thermal contact resistance is expressed as to the segmentation letter with position and time change in heat transfer model Number, and the function is provided by parameter identification, specific calculation process is as shown in Figure 1.
Fig. 2 gives the thermal contact resistance measurement result varied with temperature.Characterized with 6 piecewise functions, mean error is less than 0.146%.
The invention is not limited in foregoing embodiment.The present invention, which expands to, any in the present specification to be disclosed New feature or any new combination, and disclose any new method or process the step of or any new combination.

Claims (1)

1. a kind of lossless method for fast measuring of high temperature contact thermal resistance, it is characterised in that comprise the following steps:
Step 1:Two test specimens are taken, are respectively designated as the first test specimen and the second test specimen, two test specimen phases Mutually contact;
Step 2:By calibration experiment, the correspondence of the second test specimen internal ultrasonic velocity of wave propagation V of acquisition and temperature T;
Step 3:First test specimen is heated, by common ultrasound method, obtains the second test specimen ti The ultrasonic propagation time t at momenti,exp
Step 4:Establish the Optimized model of high temperature contact thermal resistance measurement.The object function of optimization is:
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>{</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>c</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>e</mi> <mi>x</mi> <mi>p</mi> </mrow> </msub> <mo>}</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>{</mo> <mn>2</mn> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <msub> <mi>L</mi> <mn>2</mn> </msub> </msubsup> <mfrac> <mn>1</mn> <mrow> <mi>V</mi> <mo>&amp;lsqb;</mo> <mi>T</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mfrac> <mi>d</mi> <mi>x</mi> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>exp</mi> </mrow> </msub> <mo>}</mo> </mrow> <mn>2</mn> </msup> </mrow>
Wherein:R is two test specimen interfaces thermal contact resistance to be measured;ti,calThe t obtained for numerical computationsiThe ultrasound at moment Wave propagation time, the time of measuring ordinal number that subscript i is represented, n represent total time of measuring points;L2It is tested for the second test specimen The length in direction;
Constraints is:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mi>c</mi> <mo>)</mo> </mrow> <mn>1</mn> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>x</mi> <mo>&lt;</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>t</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>R</mi> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> </mrow> </mtd> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mi>c</mi> <mo>)</mo> </mrow> <mn>2</mn> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>&lt;</mo> <mi>x</mi> <mo>&lt;</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>t</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>R</mi> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> </mrow> </mtd> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein:T1(x,t),T2(x, t) is the temperature field in two test specimens, and k, C and ρ are respectively the heat conduction of test specimen material Coefficient, specific heat capacity and density;T(t)|X=0To heat border, heated by heater;For contact interface border, T2 For the temperature at the second test specimen contact interface;
Step 5:The methods of by infrared or contact thermocouple, obtainThe temperature change on surface;
Step 6:Heat conduction inverse problem is solved using common Sequential Quadratic Programming method or Descended simplex method, obtains the first quilt The thermal contact resistance R of test block and the second test specimen contact surface.
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