Оптимізація регулювання температури у рідинно-проточних кріостатах
З метою оптимiзацiї регулювання температури у крiосистемах на основi рiдинно-проточних крiостатiв враховано теплофiзичнi властивостi матерiалу, iз якого виготовлено елементи конструкцiї робочої камери крiостата. На прикладi результатiв експериментального використання розробленого пристрою для управл...
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Відділення фізики і астрономії НАН України
2010
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| Cite this: | Оптимізація регулювання температури у рідинно-проточних кріостатах / І.П. Жарков, О.М. Іващенко, С.В. Погребняк, В.В. Сафронов // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 351-356. — Бібліогр.: 12 назв. — укр. |
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| author | Жарков, І.П. Іващенко, О.М. Погребняк, С.В. Сафронов, В.В. |
| author_facet | Жарков, І.П. Іващенко, О.М. Погребняк, С.В. Сафронов, В.В. |
| citation_txt | Оптимізація регулювання температури у рідинно-проточних кріостатах / І.П. Жарков, О.М. Іващенко, С.В. Погребняк, В.В. Сафронов // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 351-356. — Бібліогр.: 12 назв. — укр. |
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| description | З метою оптимiзацiї регулювання температури у крiосистемах на основi рiдинно-проточних крiостатiв враховано теплофiзичнi властивостi матерiалу, iз якого виготовлено елементи конструкцiї робочої камери крiостата. На прикладi результатiв експериментального використання розробленого пристрою для управлiння крiостатом в температурному дiапазонi 4,2–350 К показано, що застосування цього методу пiдвищує точнiсть та економiчнiсть крiосистем.
В целях оптимизации регулирования температуры в криосистемах на основе жидкостно-проточных криостатов, учтены теплофизические свойства материала, из которого изготовлены элементы конструкции рабочей камеры криостата. На примере результатов экспериментального использования разработанного устройства для управления криостатом в температурном диапазоне 4,2–350 К показано, что применение этого метода позволяет повысить точность и экономичность криосистем.
In order to optimize the temperature control in cryosystems based on liquid flow cryostats, the thermal properties of the substance, of which the structural elements of the work chamber of cryostat are made, have been taken into account. The results of the experimental cryostat control in the temperature range 4.2–350 K are used to demonstrate that the developed device enhances the accuracy and the efficiency of cryosystems.
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PHYSICS EXPERIMENT TECHNIQUES
350 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
OPTIMIZATION OF TEMPERATURE CONTROL IN LIQUID
FLOW CRYOSTATS
I.P. ZHARKOV, A.N. IVASHCHENKO, S.V. POGREBNJAK, V.V. SAFRONOV
Institute of Physics, Nat. Acad. of Sci. of Ukraine
(46, Nauky Ave., Kyiv 03680, Ukraine; e-mail: zharkov@ iop. kiev. ua )
PACS 07.20.Mc
c©2010
In order to optimize the temperature control in cryosystems based
on liquid flow cryostats, the thermal properties of the substance,
of which the structural elements of the work chamber of cryostat
are made, have been taken into account. The results of the ex-
perimental cryostat control in the temperature range 4.2–350 K
are used to demonstrate that the developed device enhances the
accuracy and the efficiency of cryosystems.
1. Introduction
In modern cryosystems, the temperature of a specimen
under investigation, which is located in the work cham-
ber of a cryostat together with a temperature sensor, is
controlled by maintaining the “cold–heat” balance in it
[1]. There are a number of methods for thermostatting
which include, in particular, the radiant heat exchange
with the environment, heat exchange with a cooled sur-
face through a mechanical contact, heat-exchange gas,
and immediate heat transfer to a refrigerant. Conse-
quently, there are several methods of temperature con-
trol and stabilization in cryostats which affect their de-
sign. Namely, these are:
1. The Swenson method [2], in which the temperature
is varied in a wide range by changing the mass rate of
a refrigerant flow that moves in the work chamber. For
the temperature control of an investigated object to be
more exact, an electric heater which is located either on
the external wall of the chamber or immediately in the
refrigerant vapor flow is used.
2. The method of forced blow-off of an object with
a gas flow characterized by a given temperature. The
method was first developed by Knox and Cathbert [3]
and then elaborated by the authors [4]. Here, the tem-
perature of a cooled object changes owing to a variation
of the refrigerant temperature rather than the refriger-
ant mass flow.
There are also cryostats of other types, in which the
object to study is located immediately in the refrigerant
or in vacuum on a coldfinger that has a direct contact
with the refrigerant. Since the wide-range temperature
control is not effective in such cryostats, they are not
considered below.
It is worth noting that, when a cryostat construction
is being designed, the thermal characteristics of materi-
als the cryostat is to be made of are taken into account.
For instance, the most widespread material for manufac-
turing the work chamber of a cryostat is copper, because
its heat conductivity is among the highest in compari-
son with those for other metals. In flow systems with the
temperature control carried out by the Knox–Cathbert
method (leading western firms are mainly oriented to
fabricate temperature-control systems of this type), due
to the turbulence of the gas flow and the temperature
gradient at heating, the achieved temperature stability
amounts to ±0.1 K. Such cryosystems reveal a large
refrigerant consumption, as well as a temperature over-
control after the given value has been attained, which is
also a considerable drawback in the case where a preci-
sion cryostatting is needed, in particular, when studying
the phase transitions in substances.
Cryostats belonging to the Unified Thermoregulated
Cryogenic Systems (UTRECS) are based on the Swenson
method developed further by the authors [5–8]. They
include cryostats of the liquid flow type, the design of
which allows the laminar flow of a refrigerant through
the temperature-controlled chamber to be obtained. A
heat exchanger and a heater are placed on the exter-
nal side of the chamber, which provides the temperature
equalizing between refrigerant vapors and the chamber.
OPTIMIZATION OF TEMPERATURE CONTROL
In the chamber, there is a special frame with a speci-
men and a temperature sensor. In this geometry, the
refrigerant flows through the cryostat work chamber ow-
ing to an excess pressure which is created above the liq-
uid mirror in the tank with a liquid refrigerant. The
“cold–heat” balance, which is needed for maintaining a
given temperature, is provided making use of a temper-
ature regulator, by vanishing a mismatch between the
temperature sensor signal, which corresponds to an ac-
tual temperature of the studied specimen, and the given
temperature. However, since the thermal properties of
substances the cryostat work chamber is made of depend
on the temperature, the wide-range temperature control
is accompanied by the temperature overcontrol and tem-
perature oscillations. The control will be more effective,
if the amount of heat that is supplied into the thermo-
stat chamber is put in agreement with the temperature
dependence of the heat capacity of a work chamber ma-
terial. For a number of materials – including copper
which is widely applied for the fabrication of heat ex-
changing chambers – their temperature dependences of
heat capacity are known [9–12]. For today, we do not
know such cryosystem constructions, where this depen-
dence is taken into account.
This work aimed at developing a new approach in
cryostatting which would make allowance for the tem-
perature dependence of the heat capacity of a material
the work chamber of the cryostat is made of, in order to
increase the accuracy of the temperature fixation, avoid
the temperature overcontrol, and increase the cryostat
efficiency.
2. Theoretical Analysis
The constructional elements of a work chamber of the
UTRECS cryostat system are fabricated of copper. The
temperature dependence of its heat capacity CCu is ex-
hibited in Fig. 1 [6]. It is known [6] that CCu is pro-
portional to the squared temperature at low tempera-
tures (20 − 70 K) and weakly depends on it at high
temperatures (above 200 K). The temperature point
Tlim = 200 K can be selected as a threshold value which
separates the ranges with drastically different thermal
properties of copper.
In the stationary regime and when the refrigerant flow
is laminar, an equilibrium state is attained in the ther-
mostatting chamber of a cryostat. In this case, the
amount of heat brought into the chamber, Qc, is equal
to the difference between the heats that is obtained due
Fig. 1. Temperature dependence of the heat capacity of copper
to heating, Qh, and extracted at cooling, Qfr,
Qc = Qh −Qfr. (1)
The fulfillment of Eq. (1) is provided by controlling the
parameters of executive devices which include the volt-
age across the heater Uh and the magnitude of refriger-
ant vapor flow, the latter being governed by the cooling
control voltage Ufr.
If the chamber temperature Tc varies by dTc within
the time interval dt, the thermal balance equation (1)
can be rewritten as
CCumc
dTc
dt
= Ph − Pfr, (2)
where mc is the work chamber mass, and Ph and Pfr
are the heating and cooling powers, respectively.
3. Experimental Technique
Since the power supplied to the chamber is proportional
to the squared heating voltage Uh, it is necessary to de-
sign such a working mechanism for executive devices that
the control heating voltage should depend linearly on the
chamber temperature, in order to simulate the square-
law temperature dependence of the heat capacity. Let us
introduce the control parameter λ which approximately
corresponds to the temperature dependence of the cham-
ber material heat capacity: λ = Tc
Tlim
at Tc ≤ 200 K, and
λ = 1 at Tc > 200 K. Then, the maximal voltage across
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 351
I.P. ZHARKOV, A.N. IVASHCHENKO, S.V. POGREBNJAK et al.
Fig. 2. Block diagram of the control device
a heater Uhmax = λUref , where Uref is the reference volt-
age for a heater, and the maximal capacity produced by
it is
Ph max =
U2
h max
Rh
= λ2U
2
ref
Rh
, (3)
where Rh is the heater resistance.
To provide the maximal heat exchange between re-
frigerant vapors and the work chamber, the former pass
through a capillary–heat exchanger system which is a
component of the chamber. As a result, the gas gets a
temperature that is practically equal to that of the cham-
ber, and the cooling power can be expressed in terms of
the heat which is extracted by the gas blown through
the chamber within a time unit. Taking the Clapeyron–
Mendeleev equation into account at Tc > T0, where T0
is the initial gas temperature (T0 = 4.2 K for helium),
we obtain
Pfr =
CHeµp
R
dV
dt
, (4)
where p, CHe, and µ are, respectively, the pressure, heat
capacity, and molar mass of the refrigerant; dV
dt is the
rate of refrigerant vapor blowing through the cryostat
chimney, and R is the gas constant.
To provide the relation Pfr ∼ T 2
c , we must realize the
dependence dV
dt ∼ T 2
c . The quadratic dependence of the
cryostat column-in blowing rate is ensured by the square-
law dependence of the relative pulse duration for pulses,
which are used to control the gas flow by means of an
electrodynamic valve, on the voltage Ufr which is used to
control a pulse-width modulator. If the maximal cooling
voltage Ufr max = λUref , then the maximal cooling pulse
ratio is determined from the expression
τ
τ0
=
U2
fr
U2
ref
= λ2, (5)
where τ and τ0 are the duration and the repetition period
of cooling pulses, respectively. At the pulse ratio (5), the
rate of column-in blowing with refrigerant vapors is
dV
dt
=
dV0
dt
τ
τ0
=
dV0
dt
λ2, (6)
where dV0
dt is the maximal rate of column-in blowing at
a completely open valve.
4. Experimental Part
To implement the thermostatting by means of the
method described above, we developed a device for
the temperature control, the block diagram of which is
shown in Fig. 2.
A required temperature Tset can be set by means of
either a control keyboard or an external computer. The
microprocessor provides a control over the process of
temperature setting in the chamber, Tc, at the level Tset.
The duration of every program cycle is Δt = 100 ms, and
it includes the following operations which are executed
in sequence:
– an analog-to-digital converter is used to measure the
voltage across the temperature sensor, U (Tci
) (the sub-
script i corresponds to the measurement time moment
ti);
352 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
OPTIMIZATION OF TEMPERATURE CONTROL
Fig. 3. Relative heating and cooling powers and their sum
– the measured voltage U (Tci) is recalculated into the
actual temperature code, Tci
, in accordance with the
data obtained at the temperature sensor calibration and
stored in the nonvolatile memory of the processor;
– the difference ΔTi = Tset−Tci
between the codes of the
setted, Tset, and actual, Tc, temperatures is calculated;
– the rate of actual temperature change is calculated,
dTi
dt ≈
ΔTi−1−ΔTi
Δt , where the subscript i− 1 corresponds
to the previous measurement;
– the values obtained for ΔTi and dTi
dt are used to cal-
culate the control code ni which is used to form the Uh-
and Ufr-signals.
The control code is calculated by the expression
ni = ni−1 +K1ΔTi +K2
dTi
dt
, (7)
where K1 and K2 are the weight coefficients for the pro-
portional and differential components, respectively; and
ni−1 is the previous value of control code at the moment
ti−1.
To form the signal Uh, the code of λni is written into
the registers of a digital-to-analog converter (DAC). In
this case, the heating voltage is
Uh = Urefλ
ni
n0
, (8)
where n0 is the maximal value of control code which
is defined by the register capacity of DAC. Then, the
Fig. 4. Time diagrams for the final stage of reaching the the preset
value of temperature in the old (1 ) and new (2 ) cryostat systems.
The initial temperature of the chamber is 300 K, the final one is
5 K
heating power is
Ph =
λ2
(
Uref
ni
n0
)2
Rh
. (9)
To form Ufr, the code of λ (n0 − ni) is written into
the DAC registers. Then, we have
Ufr = Urefλ
n0 − ni
n0
. (10)
After the squaring by means of an amplifier-multiplier,
the signal Ufr is applied to a pulse-width modulator,
and the cooling power is
Pfr =
CHeµp
RΔt
λ2
(
Uref
n0 − ni
n0
)2
. (11)
5. Results and Their Discussion
The described approach to thermostatting was put into
the basis of a new device developed by us for the temper-
ature control in the range from 4.2 to 350 K. In Fig. 3,
the dependences of the relative heating and cooling pow-
ers, as well as their sum, on the relative value of control
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 353
I.P. ZHARKOV, A.N. IVASHCHENKO, S.V. POGREBNJAK et al.
Fig. 5. Temperature dependences of the overcontrol for the old
(1 ) and new (2 ) cryostat systems
Fig. 6. Temperature dependences of the stability for the old (1 )
and new (2 ) cryostat systems
code are depicted. One can see that, at the quadratic
character of control influences, the sum of the relative
heating and cooling powers is linear in the relative value
of control code.
In Fig. 4, the typical experimental plots showing how
the temperature approaches a given value are shown:
when a temperature control device is used, but the ther-
mal properties of a substance the chamber was fabricated
of are not taken into consideration, and when the new
approach was applied. It is evident that the new control
device allows the temperature to reach a preset value
Fig. 7. Temperature dependences of the refrigerant consumption
for the old (1 ) and new (2 ) cryostat systems
without overcontrol and faster in comparison with the
old method.
For the experimental testing of the efficiency of the
proposed improvements for cryostat systems, we com-
pared the metrological (the overcontrol level and the sta-
bility) and economic (the refrigerant consumption) pa-
rameters of the new and old cryostat systems. In so
doing, the overcontrol level was defined as the maximal
deviation of the temperature Tc from Tset after the time
moment teq, when they became equal. The stability was
defined as the maximal deviation of Tc from Tset within
30 min after the time teq + 2 min. The temperature de-
pendences of the overcontrol, stability of the established
temperature, and refrigerant consumption are shown in
Figs. 5 to 7, in that order.
It follows from Fig. 5 that the restrictions of the max-
imal heater power and the cooling level leads to a sub-
stantial reduction of the overcontrol in the whole tem-
perature range under consideration. The minimal level
of the overcontrol (of 0.02 K) is observed in the range
20–200 K which is characterized by a fast change of the
temperature dependence of the copper heat capacity (see
Fig. 1).
From Fig. 6, it follows that the consideration of the
heat capacity of a thermostatting chamber material al-
lowed us to make the stability of established tempera-
tures as much as 1.5 to 2 times higher. In the examined
temperature interval, the largest instability was observed
at a temperature of 10 K and did not exceed 0.04 K.
354 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
OPTIMIZATION OF TEMPERATURE CONTROL
Figure 7 demonstrates that the refrigerant consump-
tion in the new cryosystem decreased by 15% on the
average in comparison with the old one.
6. Conclusion
Hence, taking the thermal properties of the substance
of a work chamber of cryostatting systems into account
has allowed us to substantially increase their precision
characteristics, avoid the overcontrol, and reduce the re-
frigerant consumption, which opens new opportunities
for carrying out a precision physical experiment. As a
result of the practical use of the control device devel-
oped by us, the cryosystem tuning became simpler, and
its reliability is enhanced.
1. A.I. Belyaeva, V.I. Silaev, and Yu.E. Stetsenko, Flow-
ing Cryostats for Laboratory Researches (Kyiv, Naukova
Dumka, 1987) (in Russian).
2. C.A. Swenson and R.H. Staht, Rev. Sci. Instrum. 25, 608
(1954).
3. W.P. Knox and J.D. Cathbert, Rev. Sci. Instrum. 39,
1181 (1968).
4. A.I. Belyaeva, V.I. Silaev, Yu.N. Stelmakhov, and
Yu.E. Stetsenko, Cryogenics 23, 303 (1983).
5. V.S. Medvedev, V.M. Ermakov, P.V. Vodolazskii et al.,
Authors’ Certificate USSR N 436334, MKI G05d 23/30,
G05d 16/06; Byull. Izobret. SSSR N 26, 126 (July 15,
1974) (in Russian).
6. I.P. Zharkov, V.M. Ermakov, V.V. Safronov, and
A.G. Tchmul, Visn. Khark. Derzh. Univ., Ser. Biofiz. N 3,
125 (1999).
7. I.P. Zharkov, V.M. Ermakov, V.V. Safronov, and
A.G. Tchmul, Proceedings of the 1-st Ukrainian Scientific
Conference on Semiconductor Physics UNKN-1 (Asrto-
print, Odesa, 2002), Vol. 2, p. 279 (in Russian).
8. I.P. Zharkov, V.V. Safronov, and A.G. Tchmul,
Ukrainian Patent N 18778, MPK (2006) G05D23/30 (in
Russian); Byul. N 11, 1 (November 15, 2006).
9. H. Jones, Proc. Roy. Soc. A 240, 321 (1957).
10. D.L. Martin, Can. J. Phys. 38, 17 (1960).
11. K.K. Kelley, J. Chem. Phys. 11, 16 (1943).
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A. Wexler, Phys. Rev. 98, 1699 (1955).
Received 14.04.09.
Translated from Ukrainian by O.I. Voitenko
ОПТИМIЗАЦIЯ РЕГУЛЮВАННЯ ТЕМПЕРАТУРИ
У РIДИННО-ПРОТОЧНИХ КРIОСТАТАХ
I.П. Жарков, О.М. Iващенко, С.В. Погребняк, В.В. Сафронов
Р е з ю м е
З метою оптимiзацiї регулювання температури у крiосистемах
на основi рiдинно-проточних крiостатiв враховано теплофiзи-
чнi властивостi матерiалу, iз якого виготовлено елементи кон-
струкцiї робочої камери крiостата. На прикладi результатiв
експериментального використання розробленого пристрою для
управлiння крiостатом в температурному дiапазонi 4,2–350 К
показано, що застосування цього методу пiдвищує точнiсть та
економiчнiсть крiосистем.
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 355
|
| id | nasplib_isofts_kiev_ua-123456789-13409 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2071-0194 |
| language | Ukrainian |
| last_indexed | 2025-11-30T21:59:13Z |
| publishDate | 2010 |
| publisher | Відділення фізики і астрономії НАН України |
| record_format | dspace |
| spelling | Жарков, І.П. Іващенко, О.М. Погребняк, С.В. Сафронов, В.В. 2010-11-08T15:07:54Z 2010-11-08T15:07:54Z 2010 Оптимізація регулювання температури у рідинно-проточних кріостатах / І.П. Жарков, О.М. Іващенко, С.В. Погребняк, В.В. Сафронов // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 351-356. — Бібліогр.: 12 назв. — укр. 2071-0194 PACS 07.20.Mc https://nasplib.isofts.kiev.ua/handle/123456789/13409 53.082.1; 531.76+53.08:621.38 З метою оптимiзацiї регулювання температури у крiосистемах на основi рiдинно-проточних крiостатiв враховано теплофiзичнi властивостi матерiалу, iз якого виготовлено елементи конструкцiї робочої камери крiостата. На прикладi результатiв експериментального використання розробленого пристрою для управлiння крiостатом в температурному дiапазонi 4,2–350 К показано, що застосування цього методу пiдвищує точнiсть та економiчнiсть крiосистем. В целях оптимизации регулирования температуры в криосистемах на основе жидкостно-проточных криостатов, учтены теплофизические свойства материала, из которого изготовлены элементы конструкции рабочей камеры криостата. На примере результатов экспериментального использования разработанного устройства для управления криостатом в температурном диапазоне 4,2–350 К показано, что применение этого метода позволяет повысить точность и экономичность криосистем. In order to optimize the temperature control in cryosystems based on liquid flow cryostats, the thermal properties of the substance, of which the structural elements of the work chamber of cryostat are made, have been taken into account. The results of the experimental cryostat control in the temperature range 4.2–350 K are used to demonstrate that the developed device enhances the accuracy and the efficiency of cryosystems. uk Відділення фізики і астрономії НАН України Методика фізичного експерименту Оптимізація регулювання температури у рідинно-проточних кріостатах Оптимизация регулирования температуры в жидкостно-проточных криостатах Optimization of Temperature Control in Liquid Flow Cryostats Article published earlier |
| spellingShingle | Оптимізація регулювання температури у рідинно-проточних кріостатах Жарков, І.П. Іващенко, О.М. Погребняк, С.В. Сафронов, В.В. Методика фізичного експерименту |
| title | Оптимізація регулювання температури у рідинно-проточних кріостатах |
| title_alt | Оптимизация регулирования температуры в жидкостно-проточных криостатах Optimization of Temperature Control in Liquid Flow Cryostats |
| title_full | Оптимізація регулювання температури у рідинно-проточних кріостатах |
| title_fullStr | Оптимізація регулювання температури у рідинно-проточних кріостатах |
| title_full_unstemmed | Оптимізація регулювання температури у рідинно-проточних кріостатах |
| title_short | Оптимізація регулювання температури у рідинно-проточних кріостатах |
| title_sort | оптимізація регулювання температури у рідинно-проточних кріостатах |
| topic | Методика фізичного експерименту |
| topic_facet | Методика фізичного експерименту |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/13409 |
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