SU1762207A1 - Method of determination of thermal conductivity of materials - Google Patents

Abstract

The invention relates to a measurement technique and can be used to determine the magnitude of the thermal conductivity of soils, soils, bulk solids, etc. The purpose of the invention is to increase the productivity of the method by reducing the test time while maintaining the specified accuracy. A cylindrical probe of length L is introduced into the material under study and heated by a constant-power source of heat W. Five temperature values © 1 - €% of the probe are measured at times ti - ts, respectively, and the tl values are chosen from the condition ti ti k, where i is the sequence number of the moment in time, k t2 / ti. For the time ts - i - 5, form the parameter FI in the form FI - k 01- (2k + 2) in-1 + (4 + k + Ј) О | -2 - (2 + + 2) .Q +1 .Q A kk and repeat the measurement of temperature values 0j and times ti until the condition FI 0 is fulfilled, after which the value A is found in the form j. W L «-g-, D5PG (-2-k-Ј) -lnk« -k) e-H «+ k) -9-t - () e-i + {- e-) W E

Description

The invention relates to a measurement technique and can be used to determine the value of thermal conductivity of soil, soils, bulk solids and thermal insulation materials.

A known method for determining the thermal conductivity of materials, in which a cylindrical probe made in the form of metal wire, is immersed in a material, heated by an electric current, and the change in the electrical resistance of the wire between two points in time, ti and p. By changing the electrical resistance of the wire, (

which is proportional to the change in temperature of the probe, determine the value of I

In this method, it is necessary to take into account the thermophysical properties of the probe, the amount of thermal resistance of the electrical insulation itself and the thermal resistance of the contact of the insulation-material under study. The latter value depends on the conditions in which the measurement is made, the properties of the material being examined can vary considerably from one measurement to another. Thus, taking into account the thermal resistance of the contact, the insulation is studied material for practical use.

This method is difficult to implement, which reduces the accuracy of the determination.

The closest technical solution is a method for determining the magnitude A, in which a cylindrical probe is immersed in the material under study, is heated by a probe with a constant power source, the temperatures 0 | and © 2 probes at times ti and so on, respectively, where 12 ti and A value is determined by the formula

, Wln (t2 / tQ

Azh1 02-01

where W is the power of the heat source, W;

L is the probe length, m;

02, 0 | are the values of the excess probe temperature at the instants of time t2 and ti, respectively, С °. (2)

In method (2), the expression 0 (t) A Int + B is used to approximate the real 0 (t) dependence.

If the values of ti and d.2 are small, then approximation of the real dependence 0 (t) by this expression is incorrect, therefore the accuracy of determining the value of Ac using expression (1) decreases significantly with decreasing measurement time. Thus, method (2), which includes measuring the temperature at two points in time, does not allow an arbitrary reduction of the measurement time (without a significant increase in measurement error A), which determines its low productivity.

The purpose of the invention is to increase the productivity of the method by reducing the test time while maintaining the specified accuracy,

The drawing shows a block diagram of the device that implements the proposed method.

The device contains a heater power supply unit 1 connected in series, a cylindrical probe 2 and an amplifier 3. The device also contains a trunk 4, with which interface 5, a microcomputer 6, an analog-to-digital converter 7 (ADC) and a programmable timer 8 are connected. connected to the control input of the heater power supply unit 1, and the output of the amplifier 3 is connected to the input of the converter 7,

In one of the possible variants, the cylindrical probe 2 contains (not shown) a rod, a heater - a constant wire, wound on a rod, an RGtermopair. A rod with a heater and a thermocouple located on it

ten

15

20

The screen is protected. The power supply unit 1 is connected to the heater, and the signal from the thermocouple through the amplifier 3 is fed to the output of the ADC. The probe diameter d and its length L are selected from the condition L / d 30, and the thermocouple is located at a distance L / 2 from the end of the rod.

The method is carried out as follows.

A cylindrical probe, the initial temperature of which should be equal to the temperature of the material under study, is introduced into the material under study, after which the probe is heated by a constant-power heat source uniformly distributed along the length of the probe. Conditionally, we assume that at the time the probe starts heating, the time is t 0.

For large values of time, the dependence of temperature 0 on time t has the form

0 (t) A In t + B + - (with In t) + D), (2)

five

0

five

0

five

0

five

W

GD6 A 4LPA

B, C, D - coefficients, the values of which depend on the geometrical and thermophysical characteristics of the probe and material;

W - heat source power, W;

L is the probe length, M;

0- probe temperature, С °;

And - the coefficient of thermal conductivity of the material, W / M C °.

For small values of t, expression (2) is not valid, in particular, at t, the values of In t, (In t) / t increase indefinitely.

For small time values, the 0 (t) dependence is accurately described using complex expressions using Bessel functions, which does not allow obtaining an exact expression for finding the value of A in an explicit form for small values of t.

Thus, the entire time interval is t 0; + oo can be divided into three intervals.

In the first interval, t 0 -: d, the dependence 0 (t) is described by complex analytical expressions, which practically excludes the possibility of using this interval to determine the value A.

In the second time interval t td - tv, the dependence 0 (t) is described with the given accuracy by expression (2).

In the third time interval t tv, the dependence 0 (t) is described with a given accuracy by the expression given in (2).

In the proposed method, unlike the prototype, which uses the third

the time interval, to determine I, the second interval is used, which makes it possible to reduce the measurement time and, consequently, to improve the performance of the method. In order for the measured values of temperatures 0 to be obtained at the desired time interval, it is necessary to know in advance the limits of the intervals TA and te. The boundaries of intetoals (the applicability of an expression for approximating the actual dependence Q (t) depends on the value of I, on the value of the thermal diffusivity, on the value of thermal resistance, and other parameters whose values are not known in advance; therefore, in the general case, to know in advance exactly border spacing impossible.

At the same time, to obtain the maximum performance of the method, it is necessary to measure the values of 0 in the initial part of the second interval, i.e. as close as possible to IA, the value of which in each specific dimension of the self is unknown.

Therefore, in the described method, using the values of temperatures 0, calculate the perimeter FI, which would allow to determine whether the real dependence G (t) coincides with the dependence described by expression (2) (the second time interval) and only after the coincidence of these dependencies determine I value

The parameter FI is formed as follows. Measurements are made of five temperature values 1 1, 02, з h. © 4 and 0s probe at times ti, 12, Јz, t4 and ts, respectively, and the values ti, t2, t3, t4 and ts are chosen from the conditions

ti ti kM (3)

where k t2 / ti -,

i is the sequence number of the point in time.

The value of k is recommended to be chosen equal to k 1.05 - 1.3. If the instants of time ti - ts are in the second interval, i.e. expression (2) is valid, then, taking into account the identities ln (t / k) Int - In k, ln (k) I In k and equality (З), we have Gs Alnts + B + 1 / ts (clnts + D) (l nt5-lnk) + B + k / t5 (c (lnt5-lnk) + D) (In ts-21 nk) + B + k2 / ts (c (ln ts-2I nk) + D)

(lnts-3lnk) + B + kJ / t5 (c (nt5-3lnk} + D (lnt5-4lnk) + B + k4 / t5 (c (lnt5-4lnk) + D) Using (4), we find the values of Si ( 2Q2-Qi-Q3) / k; S2 2Q3-C 2-Q4 and 5z (204-0z-05) k:

(four)

Si

one

± r (2-k-Ј) (clnt5 + D) + (- 6-Mk + |) (cln k)

82-7- (2-k-Ј) (clnt5 + D) + H + 3k + -4 (cln k)

k21

 () (clnt5 + DM-2 + 2k) (cln k) (5) ts

If for the time t ts (l 5) the FI signal is generated in the form

Fs 2S2-Si-S3 2 (2 © з - © 2-05) - (202- © 1-0з) / Ц204 - © 3-05) © 5- {2k + 2) © 4 + (4-f | l + k) 03 (2+ |) 0

+

(6)

then F & 0, if the expression (2) correctly describes the real dependence 0 (t), since with the substitution of (5) into (6) all members of expression (6) are reduced (FS 0 is obtained), and expressions (5) are obtained , the outcome of the fairness of the expression (2).

Thus, if the condition FS 0 is fulfilled for the values 0i 5, this means that ti, t2, t3, t4, ts are in the second time interval. For the 1 st time, the parameter FI (I 5) is similar to expression (6) in the following form:

 0- {2k + 2) 0-i + (4 + k + -;) 0i-2- {2 + Ј) 0-z +

QC

25

thirty

. + i 9-

(7)

five

0

five

0

five

If ti-4 ti-z, ti-2, ti-i. ti or at least tl-4 is in the first time interval, then FI 0, since for complex analytical expressions describing the 0 (t) relationship in the first interval, the identities valid only for logarithmic functions will not be valid: ln {t / l ) In t - In k, In (k) link. Practical testing of the method showed that dp of the first time interval is FI 0, and with increasing time t, with increasing I, the value of FI decreases, and at t tA FI 0, which allows using the value of the FI signal to determine the coincidence of the real dependence Q (t) and dependencies described by the expression (2). If the condition FS 0 is not fulfilled, then the sixth measurement of the superheat value 05 is made at time ts ti-kb ti k, the value of the parameter Fe is found and the condition Fe 0 is checked.

New measurements of the value of 0 at time points ti are made until the condition

FI 0. (8)

The more precisely equality (8) is fulfilled. the more accurately the real dependence 0 (t) is approximated by expression (2). After that. as

(9)

For the 1st moment of time, condition (8) was fulfilled, the value of A was found using the four last obtained values of temperatures 01, © And, (E | -2, 01-z of the probe, the values of which, taking into account the validity of expression (2) (FI 0) will be equal to Qi Alnti + B + 1 / ti (clnti + D) (lnti-nk) + B + k / ti (c (lnti-lnk) + D) (lnti-2tnk) + B + k2 / ti ( c (lnt -2lnk) + D) (lnti-3lnk) + B + k3 / ti (c (lnti-3lnk) + D

Using (9), we find the following values

one,

20i-2-k6M-0l-3 / k (Alnti + B) (2-k- -fi +

TO

fA (lnk) H + k + |), (10)

2e-i-k6 | -0l-2 / k (Alnti + B) (2-k- -) +

TO

+ A (lnk) (-2 + Ј). (11)

Subtracting (10) from (11) and taking into account that A

W3

---- y-, we get that the value of A can

g-k-) Ink

9-i - (2 jQ-j + jL Q,)

(12)

The value of n is recommended to be chosen in such a way that the condition tKtA is obviously fulfilled, which makes it possible to measure the value of A in the initial part of the second interval. Otherwise (ti IA), the value A will be found immediately after the first five measurements & i (Fs 0), however, the values ti, t2, t3, t and t5 will be large and will not be at the beginning of the second interval, which will reduce performance way.

The desired value of ti can also be found in a practical way without knowing the value of 1e. To do this, you need to spend a few

trial measurements of Au, changing the value of 11 to achieve, so that equality (8) is carried out at I 8-12.

The use of the invention allows

5 to improve the performance of the method and thereby reduce the cost of testing.

Claims (1)

The invention The method of determining thermal conductivity 10 of the material, including the introduction of a cylindrical probe into the material under study, heating the probe with a constant-power heat source and measuring the temperature of the probe 01 and 02 at two points in time ti and t2 15 by the subsequent calculation of the desired characteristic, characterized in that, in order to increase the productivity of the method by reducing the test time while maintaining the specified accuracy, the probe temperatures T, 04, and 05 are measured additionally at times ta, t4 and ts. which are chosen from the condition ti ti K1, where K t2 / ti, I is the sequence number of the time point of the temperature measurement, for the moment ts 25 calculates the value of the FI parameter of the form FI - k Gi- (2k + 2) Hey + (4 + k +1) - (2 + k zo + f) -Q-3 + {- a-4, the probe temperature is measured at subsequent time points selected from the condition ti ti K1 until the condition FI 0, 35 is fulfilled, and the desired characteristic is calculated using the last four values of the probe temperature f by the formula lo W (2-k-jL). | nk 40 ((k) in + + O-a- -c-fo- C-a-e) where W is the power of the probe heat source; L-length probe. / J five ZY eight 7 IF Tl