CC BY
6
DOI: https://doi.Org/10.23670/IRJ.2022.120.6.004
ОЦЕНКА ВЛИЯНИЯ СОСТОЯНИЯ ТЕПЛООБМЕННОЙ ПОВЕРХНОСТИ НА ИНТЕНСИВНОСТЬ ТЕПЛООТДАЧИ ПРИ КАПЕЛЬНОМ КИПЕНИИ ЖИДКОСТИ
Научная статья
Васильев П.С.1' *, Рева Л.С.2, Шурак А.А.3
1 ORCID: 0000-0003-0262-686X;
1 2 3 Волгоградский государственный технический университет, Волгоград, Россия
* Корреспондирующий автор (nestorvv[at]mail.ru)
Аннотация
Обоснована актуальность разработки новых способов промышленной реализации процесса кипения как эффективного метода отвода теплоты. Показано, что капельное кипение - значительно более эффективный процесс, не сопровождающийся при этом нежелательными технологическими последствиями. Установлено, что на интенсивность теплоотдачи при капельном кипении жидкости значительно влияет состояние теплообменной поверхности, и поставлена задача количественной оценки этого влияния. Представлено подробное описание экспериментальной установки для исследования процесса капельного кипения, приведено уравнение для определения его коэффициента теплоотдачи и основные результаты корреляционного и регрессионного анализа полученных экспериментальных данных. Изложена основная идея и последовательность реализации метода количественной оценки физико-химических свойств теплообменной поверхности, приведены примеры и проанализированы полученные результаты. Предложены аналитические зависимости для определения относительной опорной длины профиля теплообменной поверхности. Сделаны выводы, подтверждающие научную и практическую значимость разработанного на основе положений математической статистики метода для инженерного проектирования высокоэффективных аппаратов, работающих по технологии капельного кипения.
Ключевые слова: капельное кипение, теплоотдача, теплообменная поверхность, шероховатость, степень смачивания, статистический анализ.
ASSESSING THE IMPACT OF THE STATE OF THE HEAT-EXCHANGE SURFACE ON THE HEAT TRANSFER INTENSITY DURING DROPLET BOILING
Research article
Vasilyev P.S.1' *, Reva L.S.2, Shurak A.A.3 1 ORCID: 0000-0003-0262-686X;
1 2 3 Volgograd State Technical University, Volgograd, Russia
* Corresponding author (nestorvv[at]mail.ru)
Abstract
This article justifies the relevance of the development of new methods for the industrial implementation of boiling as an effective heat removal method. The authors show that droplet boiling is a much more efficient process, which is not accompanied by undesirable technological consequences. It has been established that the heat transfer intensity during droplet boiling is significantly affected by the state of the heat-exchange surface, and the authors aim to quantify this effect. The article presents a detailed description of the experimental setup for the study of droplet boiling, as well as the equation for the determination of its heat transfer coefficient, and the main results of the correlation and regression analyses of the obtained experimental data. The authors outline the main idea and the implementation sequence of the quantitative assessment method for the physical and chemical properties of the heat-exchange surface, provide examples, and analyze the results. The article presents some analytical dependencies to determine the relative support length of the heat exchange surface profile. Conclusions are drawn confirming the scientific and practical significance of the method developed based on the mathematical statistics methods for the engineering design of high-efficiency devices operating based on the droplet boiling technology.
Keywords: droplet boiling, heat transfer, heat exchange surface, roughness, degree of wetting, statistical analysis.
Introduction
Boiling is a highly efficient heat removal method. The key advantage of using boiling is that it can remove greater heat currents from the heat-exchange surface without increasing its temperature and assuring a high power rating of the processing equipment. This process is used in many evaporation and rectification plants in the chemical, oil refining, heat and power, and other industries when generating steam in boilers at power plants and in many other modern devices.
For instance, volumetric water boiling features the following maximum values of the key process parameters: a 20-30 °С temperature drop, a 12-13 kW/(m2-°C) heat transfer coefficient, and a 0.7-0.8 MW/m2 heat current [1].
The boiling of liquid in a volume restricted by the walls of the vessel is associated with such unwanted effects as the rapid drop of the heat transfer coefficient, heat-exchange surface overheating, and steam explosion [2].
Since the intensity of heat transfer during boiling determines the performance, dimensions, and price of processing equipment, the development of new and efficient implementation technologies for it is a relevant problem.
Droplet boiling stands for the evaporation during the boiling of a liquid fed on the heat-exchange surface regularly as droplets. It is one of the most efficient modern ways of increasing the intensity of heat transfer.
Even though this physical phenomenon has been under analysis for a long time [3], [4], [5] multiple research works by various authors [6], [10], [18], [23] practically do not cover the intensity of heat transfer during the droplet boiling of a liquid, the data on which are only provided in singular sources [9], [10], [11], [23].
The droplet boiling of water features the following maximum values of the key process parameters: a 140-160 °C temperature drop, a 90-100 kW/(m2-°C) heat transfer coefficient, and a 10-12 MW/m2 heat current [9], [10], [23].
This process lacks the unwanted effects typical of the volumetric boiling restricted by the walls of the vessel. Besides, droplet boiling almost completely lacks heat retention as boiling stops almost immediately when the feeding of the droplets of evaporated liquid to the processing apparatus stops due to the short evaporation times [11], [23].
Experimental research [21], [22], [23] produced equations to determine the droplet evaporation time on the heat-exchange surface, the contact patch diameter of the boiling droplet and the heat-exchange surface, the heat transfer coefficient, and the temperature at which the droplet begins to shift into the spheroidal state, which was used to integrate the erratic experimental data from different authors.
These situations allow us to view droplet boiling as an efficient processing technology.
However, to design the hardware for the industrial implementation of the droplet boiling technology, it is necessary to provide recommendations to account for the impact of the heat-exchange surface state on the heat transfer intensity.
In [7], [15], [19], [23] the authors demonstrate that the values of the key parameters of droplet boiling are determined by the heat-exchange surface material, its treatment grade, i.e. Roughness, and the degree of wetting with the liquid in question. The same is true for the nanostructured surfaces, where process parameters depend heavily on their state [16], [17].
In [18], the authors note that the use of porous heat-exchange surfaces allows increasing the temperature at which droplets shift to the spheroidal state by 1.5-2.5 times.
Thus, any heat-exchange surfaces feature uneven distribution (anisotropy) of their physical and chemical properties, namely roughness and degree of wetting, which has to be accounted for to assess the intensity of the heat transfer adequately when designing the hardware employing the droplet boiling technology.
Due to this, the development of the quantification method for the anisotropy of the physical and chemical properties of the heat-exchange surface is the goal of this work.
The experimental setup for the studying of droplet boiling
To study the heat transfer intensity during droplet boiling, we developed and manufactured an experimental setup comprised of the experimental device with a 550*82*8 mm carbon steel heat-exchange surface. This plate did not receive any extra treatment and had the same roughness as a rolled sheet.
The temperature of the plate was measured using the caulked-in chromel-copel thermocouples, the on the outer surface and one on the inner surface, whose EMF was measured accurate to a tenth of a millivolt with high-precision digital millivoltmeters. The plate temperature was also measured using an infrared thermometer/pyrometer for non-contact measurements. A set of metering devices including thermocouples, high-precision millivoltmeters, and a pyrometer allows for reliable monitoring of the heat-exchange surface temperature of the experimental device for various measurement ranges.
An electric-heater coil was installed inside the thermally insulated case of the experimental device. It was powered from the alternating current mains via the laboratory autotransformer. The amount of heat generated by the electric heater, i.e. its output, was monitored using a digital electronic voltmeter and amperemeter. To feed the liquid to the heat-exchange surface in the form of separate droplets, the experimental setup used a drip feeder with exchangeable calibrated nozzles.
All the high-speed experiments were recorded on a high-speed camera with the maximum framing rate of 5000 fps connected to a computer with special software installed to determine the key parameters of droplet boiling like the timing and required linear dimensions in seconds and millimeters respectively accurate to three decimal places.
To study this process on heat-exchange surfaces with different roughness and wetting parameters, we set exchangeable Petri dishes (flat discs of 62-64 mm in diameter with a bottom thickness of 2.5-3 mm and a 3 mm collar along the edge) on the experimental device plate. These dishes were made of lathed carbon steel, aluminum alloy, and brass and featured different roughness parameters. The surface temperature of exchangeable dishes at respective times was assumed equal to the temperature readings from the thermocouples in the experimental device. It was also monitored using a non-contact pyrometer. We must note that the readings of the pyrometer for aluminum and brass dishes corresponded with the thermocouple readings, while the readings for the steel dishes varied by up to 0.5 °C.
The roughness parameters of all the heat-exchange surfaces were measured separately using the profilograph/profilometer based on GOST 19300-86, and their degree of wetting was calculated using the water contact angle for liquid inleakage determined with the reading microscope. Table 1 shows the average numerical values of roughness and the degree of wetting for the heat-exchange surfaces used in experiments.
Table 1 - The average numerical values of roughness and the degree of wetting for heat-exchange surfaces
Heat-exchange surface material Roughness Degree of wetting
Ra, um Sm, um cos0, deg.
Carbon steel:
device plate 2,269 17,.4 0,6976
exchangeable dish 1 0,374 28,7 0,5064
exchangeable dish 2 8,964 255,5 0,1735
Aluminum alloy:
exchangeable dish 3 6,603 359,3 0,5832
exchangeable dish 4 16,943 551,5 0,5685
Brass:
exchangeable dish 5 6,312 409,5 0,2488
In the experiments, all the heat-exchange surfaces were positioned horizontally, and their temperatures ranged between 100 °C and 260-280 °C at an interval of 10-20 °C.
The experiments were carried out at atmospheric pressure using the droplets of distilled water whose geometry and weight parameters were determined as average: 2.333 mm, 2.567 mm, 2.800 mm, 3.783 mm, 4.234 mm, 4.840 mm, 5.692 mm.
The initial liquid temperature of the droplet was 20, 50, 80 and 95 °C. The drop height of the droplet changed at increments approximately equal to the droplet radius (so-called "soft" feed of droplets on the heat-exchange surface) until it reached 350400 mm.
The experimental procedures are detailed in our referenced sources [21], [22].
The equation to calculate the heat transfer coefficient of droplet boiling
Based on the results of the experimental research of droplet boiling, we obtained an equation to calculate the heat transfer coefficient, the parameter that determines the intensity of the process [23]:
Nu = 2,924 •Ю9 •Ra0906 •Oh36
■Re
0.073
h -1 _b_л
At
0.106
0.138
V Ra У
ГЖЛ
0.700
V W
V c у
(1)
a • dk
where Nu =--
1
is Nusselt similarity number;
a is the heat transfer coefficient, W/(m2-°Ç); dk is the droplet diameter, m;
Ra =
Oh =
Re =
g• p2 •Cn 4
jUl
At is Rayleigh similarity number;
U
dk w^dk • p
is Ohnesorge similarity number;
U
is Reynolds similarity number;
t, -1-
b n,
At
is the similarity simplex accounting for the impact of temperature factors;
S
is the similarity simplex accounting for the impact of heat-exchange surface roughness;
Ra
W
—a is the similarity simplex accounting for the impact of heat-exchange surface wetting degree;
W
w is the fall rate of the droplets of the liquid when they hit the heat-exchange surface, m/s;
tin is the initial temperature of the droplet liquid, °C;
At = ts - tb is thermal head, °C;
ts is the temperature of the heat-exchange surface, °C;
Ra is the average deviation of the heat-exchange surface profile, um;
Sm is the roughness pitch of the heat-exchange surface profile against the midline, um;
Wa =a- (1 + cos0) is the work of adhesion, J/m2;
wc = 2 • a is the work of cohesion, J/m2;
8 is the water contact angle of the heat-exchange surface during the liquid inleakage, deg.; the thermal and physical properties of the liquid measured at its boiling temperature tj: p is the density, kg/m3; y. is the dynamic viscosity coefficient, Pa-s; P is the volumetric expansion coefficient, °C-1 ; Cp is the specific mass heat capacity, J/(kg-°C); X is the thermal conductivity factor, W/(m-°C); a is the surface tension coefficient, J/m2.
Table 2 shows the key results of the correlation and regression analyses of the obtained experimental data. For Student's test, the least calculated value out of the seven obtained for each of the regression equation (1) coefficients is stated. The significance level for the calculation of statistical criteria was set at 0.05.
Table 2 - The values of the statistical parameters for equation (1)
Statistical parameter Value
Mean relative error ôme, % 11,29
Minimum relative error ômin, % - 33,19
Maximum relative error ômax, % + 31,64
Linear multiple correlation coefficient ry. 1-6 0,9789
End of the table 2 - The values of the statistical parameters for equation (1)
Statistical parameter Value
The calculated value of Cochran's test Qcai 0,0027
The critical value of Cochran's test Qcrtt 0,0238
The calculated value of Student's test tcai > 976
The critical value of Student's test tcrtt 1,9632
The calculated value of Fisher's test Fcai 1,0731
The critical value of Fisher's test Fcrtt 1,1581
The comparison of the calculated and critical values of the statistical criteria in Table 2 allows us to conclude that regression equation (1) is adequate and all of its coefficients are significant.
However, it is impossible to tell what proportion of random deviations from the forecast values of equation (1) is determined by the anisotropy of the physical and chemical properties of the heat-exchange surface, which presents a great academic and practical interest.
The quantification method for the anisotropy of the physical and chemical properties of the heat-exchange surface
The main idea of the suggested method is that the values of the minimum and maximum roughness deviations Ra and Sm at the basic distance from the average values of the heat-exchange values are, from the point of view of mathematical statistics, the minimum and maximum limits of the confidence interval of individual values of the relative profile bearing length [24], [25].
This method is implemented as follows.
We used the profilograph/profilometer to measure the roughness of the heat-exchange surface and plot the growth line of the bearing length of its profile. For each of the standard profile section levels (5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90 %), we determined the deviation (rest):
pi
(2)
where pt is the profile section level, %; ti is the relative profile bearing length, %.
The adequacy of the distribution of the obtained deviations ui is verified using the Shapiro-Wilk's test and the Epps-Pulley's test featuring the highest statistical power [26], [27] because the distribution of any roughness parameters has to be adequate at the outset [28].
We calculated the percent deviation of roughness (for the significance of 0.05) as follows [29]:
A = 1.96 • s,.
(3)
where s,, =
h
~yY-u) is the standard deviation for rest utbased on an unbiased dispersion estimate; u is the average rest ut.
Then we determined the numerical values of the anisotropy of the physical and chemical properties of the heat-exchange
surface: roughness parameters Ra
( A • 1 ±-I,
V 100.
1 ±- and the wetting degree cos 0 •
100 1
1 ±-
100
because the latter is
proportional to roughness [30].
By varying the obtained minimum and maximum roughness values Ra, Sm, as well as the wetting degree cos0, and inserting them in equation (1), we get:
Nu = 2,924 • 109 • K • K • Ra0 906 • Oh3 0™ • Re
-0.073
tb -1„ At
0.106 f ^-0.138
V Ra .
0.700
( W Л
a
, w
V c .
(4)
where K1 e
R
V a . max /
V Ra .
K e
W
V c . min /
V WC .
R
R
W
Л a .mini V a .
0.700
W
V c . max /
V WC .
0.138
is the roughness anisotropy coefficient;
is the wetting degree anisotropy coefficient.
The Figure shows the growth line of the bearing length for the carbon steel heat-exchange surface profile (exchangeable dish 1 in Table 1), for which the roughness deviation amounted to A = 36.02 %. At the same time, the calculated value of the Shapiro-Wilk's test is 0.893 and the critical value is 0.859; the calculated value of the Epps-Pulley's test is 0.270 and the critical value is 0.361, which confirms the adequacy of the distribution of ut deviations [26], [27].
0
10
20
30
40
e. 50 a.
60 70 80 90 100
Fig. 1 - The growth line of the bearing length for the carbon steel heat-exchange surface profile
(exchangeable dish 1 in Table 1).
Table 3 shows the value ranges for the anisotropy coefficients of the physical and chemical properties of all heat-exchange surfaces used in the experiments calculated using equation (4).
As we can see from Table 3, the anisotropy of the physical and chemical properties has the greatest impact on the carbon steel heat-exchange surface with minimum roughness (exchangeable dish 1 in Table 1). Its heat transfer intensity change during droplet boiling reaches ± 16.79 % on average, which exceeds the average relative error of equation (1) and makes the process the least controllable from the engineering viewpoint.
The anisotropy of the physical and chemical properties has the greatest impact on the aluminum alloy heat-exchange surface with maximum roughness (exchangeable dish 4 in Table 1). Its heat transfer intensity change during droplet boiling reaches ± 4.45 % on average, which assures the optimal implementation conditions from the engineering viewpoint.
Table 3 - The values of the anisotropy coefficients of the physical and chemical properties of the heat-exchange surfaces
Heat-exchange surface material Anisotropy coefficients for
roughness Ki degree of wetting K2
Carbon steel
device plate 0,942 - 1,062 0,938 - 1,061
exchangeable dish 1 0,912 - 1,096 0,923 - 1,074
exchangeable dish 2 0,953 - 1,049 0,982 - 1,018
Aluminum alloy
exchangeable dish 3 0,938 - 1,066 0.941 - 1,058
exchangeable dish 4 0,977 - 1,024 0,978 - 1,022
Brass
exchangeable dish 5 0,926 - 1,079 0,962 - 1,037
When using the suggested method in engineering design to determine the relative profile bearing length without metering the roughness of the heat-exchange surface in advance, we suggest using the following equations:
• for pi < tm = 31.63 %:
(
t . = t
pi m
Pi * Rmax
100 • R
^m * Rma.\
100 • R
\
• for Pi > tm = 31.63 %:
^100 • Rz - tm ■ Rmx Л
100 • R„
tpi= 100 - tm
100 - p, 50
(6)
where Rz is the height of heat-exchange surface profile roughness at 10 points, um; Rmax is the maximum height of the heat-exchange surface profile roughness, um.
Equations (5) and (6) were constructed by the authors of this work based on the common dependencies, and they feature the accuracy acceptable for engineering calculations. For these equations, parameters Rz and Rmax for various types and modes of mechanical processing of the heat-exchange surface are presented in reference sources, e.g. in [24], [25].
Conclusion
Based on the conducted research and using the methods of mathematical statistics, we developed an original quantification method for the impact of the anisotropy of the physical and chemical properties of the heat-exchange surface on the heat transfer intensity during the droplet boiling of a liquid.
The method is easy to implement and highly accurate, and it allows for the use of experimental and analytical methods to determine the values of anisotropy coefficients for roughness and wetting degree for any heat exchange surface. This, in its turn, helps provide a numerical assessment of the heat transfer intensity changes for the droplet boiling of a liquid on a specific heat-exchange surface.
The obtained results help us select the heat-exchange surface material, as well as the type and mode of its mechanical treatment, assuring the optimal conditions for this process, which can be interesting for the engineering design of high-efficiency devices employing the droplet boiling technology.
Фииаисироваиие Funding
Работа выполнена при финансовой поддержке This research was supported by the grant of the
гранта Президента Российской Федерации МК- President of the Russian Federation MK-1603.2022.4. 1603.2022.4.
Конфликт интересов Conflict of Interest
Не указан. None declared.
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