Heat-physical problems of cryogenic corpuscular targets
In order to solve heat-physical problems in producing cryogenic corpuscular targets, the special mathematical model is developed. In developing mathematical model the following physical processes and the phenomena were considered: capillary disintegration of jets from the liquid cryogen, convective...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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Bukharov, A.V. Ametistov, E.V. Ginevsky, A.F. Bukharova, M.A. 2017-01-17T14:41:35Z 2017-01-17T14:41:35Z 2013 Heat-physical problems of cryogenic corpuscular targets / A.V. Bukharov, E.V. Ametistov, A.F. Ginevsky, M.A. Bukharova // Вопросы атомной науки и техники. — 2013. — № 6. — С. 205-208. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.38.Kd, 44.05. + Е https://nasplib.isofts.kiev.ua/handle/123456789/112083 In order to solve heat-physical problems in producing cryogenic corpuscular targets, the special mathematical model is developed. In developing mathematical model the following physical processes and the phenomena were considered: capillary disintegration of jets from the liquid cryogen, convective heat exchange with environment, acceleration of drops in a gas stream, radiation heat exchange, cooling and freezing of drops. The model allows to define the general parameters of cryogenic corpuscular targets (temperature, speed, deviation from vertical) since the moment of reception of monodisperse drops of liquid cryogenic agent till the moment of reception of solid granules. Results of calculations on offered mathematical model were used at creation of a prototype of a cryogenic corpuscular target for spectrometer PANDA. Work was supported by grant RFBR 12-08-01170-а and grant MPEI. Для вирішення теплофізичних проблем отримання кріогенних корпускулярних мішеней розроблена спеціальна математична модель, у якій були враховані: капілярний розпад струменів рідкого кріоагента, конвективний теплообмін з довкіллям, прискорення крапель у газовому потоці, радіаційний теплообмін, охолодження і замерзання крапель. Модель дозволяє визначати основні параметри мішені (температуру, швидкість, відхилення від вертикалі) починаючи з моменту отримання монодисперсних крапель рідкого кріоагента до моменту отримання твердих гранул. Результати розрахунків з запропонованої математичної моделі були використані при створенні прототипу кріогенної корпускулярної мішені для спектрометра PANDA. Робота була підтримана грантом РФФД 12-08-01170-а і грантом МЕІ. Для решения теплофизических проблем получения криогенных корпускулярных мишеней разработана специальная математическая модель, в которой были учтены: капиллярный распад струй жидкого криоагента, конвективный теплообмен с окружающей средой, ускорение капель в газовом потоке, радиационный теплообмен, охлаждение и замерзание капель. Модель позволяет определять основные параметры мишени (температуру, скорость, отклонение от вертикали) начиная с момента получения монодисперсных капель жидкого криоагента до момента получения твёрдых гранул. Результаты расчётов по предлагаемой математической модели были использованы при создании прототипа криогенной корпускулярной мишени для спектрометра PANDA. Работа была поддержана грантом РФФИ 12-08-01170-а и грантом МЭИ. Work was supported by grant RFBR 12-08-01170-а and grant MPEI. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Применение ускоренных пучков. Детекторы и детектирование ядерных излучений Heat-physical problems of cryogenic corpuscular targets Теплофізичні проблеми кріогенних корпускулярних мішеней Теплофизические проблемы криогенных корпускулярных мишеней Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Heat-physical problems of cryogenic corpuscular targets |
| spellingShingle |
Heat-physical problems of cryogenic corpuscular targets Bukharov, A.V. Ametistov, E.V. Ginevsky, A.F. Bukharova, M.A. Применение ускоренных пучков. Детекторы и детектирование ядерных излучений |
| title_short |
Heat-physical problems of cryogenic corpuscular targets |
| title_full |
Heat-physical problems of cryogenic corpuscular targets |
| title_fullStr |
Heat-physical problems of cryogenic corpuscular targets |
| title_full_unstemmed |
Heat-physical problems of cryogenic corpuscular targets |
| title_sort |
heat-physical problems of cryogenic corpuscular targets |
| author |
Bukharov, A.V. Ametistov, E.V. Ginevsky, A.F. Bukharova, M.A. |
| author_facet |
Bukharov, A.V. Ametistov, E.V. Ginevsky, A.F. Bukharova, M.A. |
| topic |
Применение ускоренных пучков. Детекторы и детектирование ядерных излучений |
| topic_facet |
Применение ускоренных пучков. Детекторы и детектирование ядерных излучений |
| publishDate |
2013 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Теплофізичні проблеми кріогенних корпускулярних мішеней Теплофизические проблемы криогенных корпускулярных мишеней |
| description |
In order to solve heat-physical problems in producing cryogenic corpuscular targets, the special mathematical model is developed. In developing mathematical model the following physical processes and the phenomena were considered: capillary disintegration of jets from the liquid cryogen, convective heat exchange with environment, acceleration of drops in a gas stream, radiation heat exchange, cooling and freezing of drops. The model allows to define the general parameters of cryogenic corpuscular targets (temperature, speed, deviation from vertical) since the moment of reception of monodisperse drops of liquid cryogenic agent till the moment of reception of solid granules. Results of calculations on offered mathematical model were used at creation of a prototype of a cryogenic corpuscular target for spectrometer PANDA. Work was supported by grant RFBR 12-08-01170-а and grant MPEI.
Для вирішення теплофізичних проблем отримання кріогенних корпускулярних мішеней розроблена спеціальна математична модель, у якій були враховані: капілярний розпад струменів рідкого кріоагента, конвективний теплообмін з довкіллям, прискорення крапель у газовому потоці, радіаційний теплообмін, охолодження і замерзання крапель. Модель дозволяє визначати основні параметри мішені (температуру, швидкість, відхилення від вертикалі) починаючи з моменту отримання монодисперсних крапель рідкого кріоагента до моменту отримання твердих гранул. Результати розрахунків з запропонованої математичної моделі були використані при створенні прототипу кріогенної корпускулярної мішені для спектрометра PANDA. Робота була підтримана грантом РФФД 12-08-01170-а і грантом МЕІ.
Для решения теплофизических проблем получения криогенных корпускулярных мишеней разработана специальная математическая модель, в которой были учтены: капиллярный распад струй жидкого криоагента, конвективный теплообмен с окружающей средой, ускорение капель в газовом потоке, радиационный теплообмен, охлаждение и замерзание капель. Модель позволяет определять основные параметры мишени (температуру, скорость, отклонение от вертикали) начиная с момента получения монодисперсных капель жидкого криоагента до момента получения твёрдых гранул. Результаты расчётов по предлагаемой математической модели были использованы при создании прототипа криогенной корпускулярной мишени для спектрометра PANDA. Работа была поддержана грантом РФФИ 12-08-01170-а и грантом МЭИ.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112083 |
| citation_txt |
Heat-physical problems of cryogenic corpuscular targets / A.V. Bukharov, E.V. Ametistov, A.F. Ginevsky, M.A. Bukharova // Вопросы атомной науки и техники. — 2013. — № 6. — С. 205-208. — Бібліогр.: 6 назв. — англ. |
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2025-11-25T21:07:25Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №6(88) 205
HEAT-PHYSICAL PROBLEMS OF CRYOGENIC CORPUSCULAR
TARGETS
A.V. Bukharov, E.V. Ametistov, A.F. Ginevsky, M.A. Bukharova
Moscow Power and Engineering Institute (MPEI), Moscow, Russia
E-mail: boukharov@mail.ru
In order to solve heat-physical problems in producing cryogenic corpuscular targets, the special mathematical
model is developed. In developing mathematical model the following physical processes and the phenomena were
considered: capillary disintegration of jets from the liquid cryogen, convective heat exchange with environment,
acceleration of drops in a gas stream, radiation heat exchange, cooling and freezing of drops. The model allows to
define the general parameters of cryogenic corpuscular targets (temperature, speed, deviation from vertical) since
the moment of reception of monodisperse drops of liquid cryogenic agent till the moment of reception of solid gran-
ules. Results of calculations on offered mathematical model were used at creation of a prototype of a cryogenic cor-
puscular target for spectrometer PANDA. Work was supported by grant RFBR 12-08-01170-а and grant MPEI.
PACS: 52.38.Kd, 44.05. + Е
INTRODUCTION
Cryogenic corpuscular targets are monodisperse
drops, or the solid monodisperse granules received at
condensation of inert gases. The sizes of targets lie in
the range of 10…1000 µm.
In high-energy physics the cryogenic corpuscular
targets are applied to interaction research with proton
beams of high luminosity [1]. Example of the physical
program would be the experimental investigations
within the FAIR project in Darmstadt, Germany. Ex-
periments are supposed to be made on an anti-proton
beam of an accumulative ring (HESR) with energy to
15 GeV.
The major element for realization of the physical
program is the internal target. The detector PANDA
placed in a ring HESR is a detector for registration of
interactions on an internal target. The single target cor-
responding to all requirements of the detector PANDA
is the cryogenic corpuscular target.
In laser technologies the cryogenic corpuscular tar-
gets are used for studying of laser acceleration of the
charged particles (electrons, protons and heavy ions)
[2]. Applications of laser acceleration will allow: to
create the compact sources of protons for a radiography;
will give the chance to make isotopes and to develop
new methods in nuclear medicine; will allow to make
experiments in nuclear physics on super-short periods.
Cryogenic corpuscular targets [3] have the follow-
ing properties that distinguish them from targets of other
types: high luminosity; renewability of a target; the
small sizes of particles (diameter of granules doesn't
exceed several tens microns); stability of sizes and
movement trajectories – the dispersion in diameters and
movement trajectories of granules doesn't exceed the
fraction of a millimeter.
The theoretical basic for installations on receiving
targets is Rayleigh's theory [4]. According to this theory
the jet breaks up to drops with the minimum dispersion
on the speed and the sizes (monodisperse drops) at a
certain relationship between a jet speed, jet diameter
and frequency of external excitation.
For monodisperse disintegration of cryogenic jets it
is necessary to satisfy the following conditions in addi-
tion: to eliminate external vibrations from the cooling
system; the liquid jet should be laminar; the temperature
gradient at liquefaction of gas and formation of a liquid
jet should be minimum [5, 6].
The operation of the installation on receiving cryo-
genic corpuscular targets is shown in Fig. 1. Construc-
tional target elements are: the cryostat; the generator of
spherical monodisperse drops; system of vacuum cham-
bers and sluices; a trap.
Fig. 1. Layout of the installation on receiving cryogenic
corpuscular targets
The installation operates as following. The cryo-
genic liquid jet follows from the drops generator to the
vacuum chamber. The jet breaks up to identical drops in
response to external excitation imposed on the fluid jet.
Due to intensive evaporation in the vacuum chamber
take place cooling of drops, drops freeze and become
solid granules.
Monodisperse solid granules through the system of
locks (sluices) arrive in the working chamber where there
is an interaction to a laser radiation. Sluices provide the
minimum leaking in the working chamber. For reduction
of leaking it is possible to use two and more vacuum
chambers separated among themselves by sluices.
The special mathematical model is developed for the
solution of heat-physical problems of producing cryo-
genic corpuscular targets.
ISSN 1562-6016. ВАНТ. 2013. №6(88) 206
1. MATHEMATICAL SIMULATION OF THE
PROCESSES IN PRODUCING CRYOGENIC
CORPUSCULAR TARGETS
By development of a mathematical model the fol-
lowing physical processes and the phenomena were
considered: the capillary disintegration of jets from the
liquid cryogen, the heat exchange with environment, the
interaction of drops with gas flow in the sluice.
Previous work showed that the capillary disintegra-
tion of jets from the liquid cryogen differs from disinte-
gration of normal liquids a little. Therefore for simula-
tion of capillary disintegration were used the results of
the linear Rayleigh`s theory.
There are the heat exchange connected to evaporation,
convective and radiation in simulating processes of heat
exchange of drops with environment. For cooling as the
result of the evaporation in case of a free-molecular
mode, i.e. Kn>>1 (Knudsen number), the mass flow from
a drop surface was defined by the use of Hertz-Knudsen
formula. And for cooling as the result of the evaporation
in case of a continuous mode, i.e. Kn<<1, the mass flow
from a drop surface is define by the use of Labuntsov-
Kryukov formula for intensive evaporation.
The model of the sluice with an exponential profile
was used in simulating of the drops interaction with gas
flow. Such sluice allows to receive a gas current with
the smallest pressure gradient along the sluice.
Using a mathematical model the program for calcu-
lation of drops parameters in different chambers was
created. The program consists of one head program and
nine subprograms.
From head part of the program takes place the re-
course to different subprograms. The block-diagram of
the program is shown in Fig. 2.
Calculation of heat-physical parameters of drops and
granules happens as follows:
1. At first it is necessary to select gas from which we
receive cryogenic corpuscular targets. Having addressed
to the appropriate table of properties, it is possible to
calculate the change of parameters of the drops received
from any gases, for example, deuterium, argon, krypton
or xenon.
2. After that, File 1 opens where the initial parame-
ters of drops (for appropriate gas) and systems are read.
3. File 2 and File 3 open in turn, where necessary
properties of solid, liquid and gaseous nitrogen or hy-
drogen are read.
4. The File res.dat and File res.xls open, in which re-
sults will be output afterwards.
5. It is determined the ordinal number of the cham-
ber, which the drop moves, by:
a) If it is the first chamber, the subprogram Subrou-
tine.8 calculates the length of not broken up part of the
jet Lj at the chamber entrance, and then Subroutine 1
considers the temperature change dT/dx and radius
change dR/dx of a drop when it is passing chamber.
b) If the chamber is not the first, the check proceeds:
- if it is the second chamber, it means that the drop
moves in the vacuum sluice; thus there is an appeal to
subprograms of Subroutine 6 and Subroutine 7 which
calculate the sluice geometry and drop parameters in the
sluice respectively;
- if is the chamber is not the first and not the second,
it means that the drop moves in the subsequent cham-
bers, and temperature change dT/dx and change radius
on length dR/dx is calculated according to subprogram
Subroutine1.
Fig. 2. Block-diagram of the program
6. Referring to the subprogram Subroutine 2, it is re-
porting to the user about errors if they exist.
7. The program is complete. After its completion in
the files res.dat and res.xls all necessary results will be
output. By these results the dependences diagrams of
required parameters from coordinate in each chamber
are plotted further.
Thus, having set on an input by initial parameters of
drops and geometry of constructional elements of instal-
lation it is possible to define: T temperature, radius R,
evaporation percent, and mass flow from a target sur-
face in any chamber of the installation.
2. THE RESULTS OF CALCULATIONS
OF HEAT-PHYSICAL TARGETS
CHARACTERISTICS
The program was used for determination of heat-
physical characteristics of targets from hydrogen and
nitrogen in different chambers of installation on receiving
targets for the detector PANDA. It is supposed that
installation will consist of four chambers and one sluice
located between the first and second chambers. Main
geometrical characteristics of chambers: the first chamber
(the chamber of triple point) has 5 cm length; the sluice
between the first and second chambers has length of
10 cm and average diameter 300 µm; the second and
third chambers have length of 30 cm.
Following are some results of calculations of heat-
physical characteristics of cryogenic corpuscular targets
from hydrogen for each chamber of the installation.
ISSN 1562-6016. ВАНТ. 2013. №6(88) 207
2.1. THE FIRST CHAMBER
(CHAMBER OF TRIPLE POINT)
In the first chamber the process of formation of the
identical hydrogen drops is carried out. There is
suggested to support the jet parameters near triple point
in order to avoid the premature freezing of a jet before
disintegration it on the drops. For the jet with the
diameter of 30 µm (drops diameter D ≈ 50 µm) and the
initial jet speed of vj = 11 m/s the length of not broken
up part of the jet Lj ≈ 2,8 mm.
Fig. 3. Dependence of drop temperature on coordinate
in first chamber
With the initial temperature of Tн = 14 K and
chamber pressure of P ≈ 70…100 µbar the drop
temperature decreases in case of movement a little, and
drop radius practically doesn't change, the drop remains
liquid. Dependence of temperature on longitudinal
coordinate has been plotted in Fig. 3. Cooling of drops
is carried out on very small section.
2.2. VACUUM SLUICE
From results of calculations follows that gas pressure
in the sluice falls approximately twice, temperature
decreases slightly (ΔT~2 К), and the Reynolds number
increases from Re=3521 to Re=16970. Therefore, the
mode of a current can be turbulent.
The estimates show that such gas flow can't destroy
a hydrogen drop with diameter to smaller D ≈ 120 µm,
the capillary pressure exceeds pressure connected to
external forces approximately on the order much.
However such flow strongly accelerates a drop.
Results of calculation of change of drops speed on
longitudinal coordinate in the sluice are shown in Fig. 4.
For drops with a diameter of 50 µm the final drop
speed after passing of the sluice can be from 30 m/s (for
sluices length of 5 cm) to 60 m/s (for sluices length of
20 cm). And only for drops with a diameter of 20 µm the
final speed can reach 120 m/s with a length of the sluice
of 20 cm. With a length of the sluice 10 cm the drops will
have the speed of 90 m/s on an output from the sluice.
Fig. 4. Dependence of drops speed on coordinate
in the sluice
Results of calculation of change of drops diameter
and temperature on longitudinal coordinate in the sluice
are shown in Fig. 5 and 6. In calculations the length of
the sluice was of 10 cm. Such length provides input
speed of microtargets in the accelerator necessary for
the detector PANDA.
It will be noted that the freezing of drops take place
with the motion in the sluice. The drops with the
diameter of 120 µm freeze on a section from 1.3 cm to
2.6 cm from the sluice beginning. Drops of the smaller
size freeze even quicker. Drops temperature is reduced
to T ≈ 10 K, and the drops radius decreases by 5%.
Fig. 5. Dependence of drops temperature on coordinate
in the sluice
Fig. 6. Dependence of drops diameter on coordinate
in the sluice
2.3. SECOND AND THIRD CHAMBERS
In the second and third chambers the drops which
became solid granules, move in the vacuum conditions.
There is some distinction between chambers. In the
second chamber the walls cool, and in the third chamber
the walls are hot. Last it is caused by features of
spectrometer construction PANDA.
Fig. 7. Dependence of drops temperature on coordinate
in the second chamber
Results of calculation of change of granules
temperature on longitudinal coordinate in the second
chamber are shown in Fig. 7. Input parameters are the
parameters calculated for the previous chamber. From the
given results it is visible that there is a sharp reduction of
granules temperature due by evaporation in the second
chamber on an initial section, however only small part of
granules (~0.5% from radius) have time to evaporate. The
change of radius and temperature of granules terminates
at distance about 20 cm from an input in the chamber.
The outlet temperature of the chamber is T ≈ 4.85 K.
Results of calculation of change of granules
temperature on longitudinal coordinate for the third
chamber are shown in Fig. 8. There is radiation heating
of drops from warm walls in the third chamber.
ISSN 1562-6016. ВАНТ. 2013. №6(88) 208
Granules temperature quickly increases and reaches a
stationary value already at distance of 10 cm from an
input in the chamber. Under the influence of radiation
the granule begins to evaporate. The granule with the
diameter of 50 µm decreases by only 0.5% at distance
of 50 cm from an input in the chamber. Granule speed
in the chamber is 44 m/s.
Fig. 8. Dependence of drops temperature onl coordinate
in the third chamber
CONCLUSIONS
The analysis of the received results allows to draw
the conclusion on existence of the problems requiring
additional researches.
It is the problem of determination of drops
parameters during the passing of the vacuum sluice and
extracting drops into vacuum. The calculations indicates
that the Reynolds number can significantly exceed
critical Re =2300 value for some sluices, and, therefore,
the gas flow can be highly turbulent. It may happen that
a path of drops deviate from an installation axis.
Besides, according to results of calculations,it is
possible situation in case of supercritical differential
pressures near the output section of a nozzle when the
drop passes a compression discontinuty. By our
estimates, the strength of solid hydrogen and nitrogen
sufficient to avoid adiabatic explosion when the drop
passes a compression discontinuty. However the liquid
or not completely frozen granule can desintegrates in
these conditions.
In calculations in determining the freezing moment
of drops the possible overcooling of drops isn't consid-
ered. Thus, it is possible that the drop overcools in the
vacuum sluice and doesn`t freeze, and the probability of
adiabatic explosion increases.
Results of calculations on offered mathematical
model were used at creation of a prototype of a cryo-
genic corpuscular target for spectrometer PANDA.
Work was supported by grant RFBR 12-08-01170-а
and grant MPEI.
REFERENCES
1. W. Erni, I. Keshelashvili, A. Aab, et al. Technical
design report for the PANDA (Anti Proton Annihila-
tions at Darmstadt) Straw Tube Tracker Strong in-
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ТЕПЛОФИЗИЧЕСКИЕ ПРОБЛЕМЫ КРИОГЕННЫХ КОРПУСКУЛЯРНЫХ МИШЕНЕЙ
А.В. Бухаров, Е.В. Аметистов, А.Ф. Гиневский, М.А. Бухарова
Для решения теплофизических проблем получения криогенных корпускулярных мишеней разработана
специальная математическая модель, в которой были учтены: капиллярный распад струй жидкого криоаген-
та, конвективный теплообмен с окружающей средой, ускорение капель в газовом потоке, радиационный
теплообмен, охлаждение и замерзание капель. Модель позволяет определять основные параметры мишени
(температуру, скорость, отклонение от вертикали) начиная с момента получения монодисперсных капель
жидкого криоагента до момента получения твёрдых гранул. Результаты расчётов по предлагаемой матема-
тической модели были использованы при создании прототипа криогенной корпускулярной мишени для
спектрометра PANDA. Работа была поддержана грантом РФФИ 12-08-01170-а и грантом МЭИ.
ТЕПЛОФІЗИЧНІ ПРОБЛЕМИ КРІОГЕННИХ КОРПУСКУЛЯРНИХ МІШЕНЕЙ
А.В. Бухаров, Є.В. Аметістов, А.Ф. Гіневський, М.А. Бухарова
Для вирішення теплофізичних проблем отримання кріогенних корпускулярних мішеней розроблена спе-
ціальна математична модель, у якій були враховані: капілярний розпад струменів рідкого кріоагента, конве-
ктивний теплообмін з довкіллям, прискорення крапель у газовому потоці, радіаційний теплообмін, охоло-
дження і замерзання крапель. Модель дозволяє визначати основні параметри мішені (температуру, швид-
кість, відхилення від вертикалі) починаючи з моменту отримання монодисперсних крапель рідкого кріоаге-
нта до моменту отримання твердих гранул. Результати розрахунків з запропонованої математичної моделі
були використані при створенні прототипу кріогенної корпускулярної мішені для спектрометра PANDA.
Робота була підтримана грантом РФФД 12-08-01170-а і грантом МЕІ.
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