Experimental and Analytical Solution for Rayleigh Bernard Convection · 2017-10-13 · Natural...
Transcript of Experimental and Analytical Solution for Rayleigh Bernard Convection · 2017-10-13 · Natural...
International Journal of Computation and Applied Sciences IJOCAAS, Volume 3, Issue 2, October 2017, ISSN: 2399-4509
224
Abstract— Natural convection has an undeniable effect
on the thermal-flow processes in engineering practice. The tanks
used in most mobile engineering systems are approximately of
parallelepiped shape. Such tanks may contain all kinds of
hydraulic fluids, so that the research done has chosen water and
air that represent the majority of fluids that can be found in the
given tanks. The paper will show the influence of external effects,
most of all, of temperature changes upon thermal-flow processes
taking place in the given tanks. The obtained results should more
closely show the real flow regimes taking place in the given tanks
as well as their influence upon the deposition of solid particles
that can be found in the given tanks.
Index Terms— Rayleigh-Bernard Convection, laminar
convection, turbulent convection, heat, humidity.
I. INTRODUCTION
he first and the simplest case of the fluid flow which is
described in fluid mechanics is a laminar flow. Such flow
takes place until the flow parameters, such as the
Reynolds number, do not reach a critical value [1]. After that,
the laminar flow becomes unstable under the influence of
small disturbances so that it cannot be maintained as such; so,
it turns into a turbulent one. This flow is extremely unstable
while its mathematical modelling most often extremely
complicated [2].
The most obvious example of the above-mentioned is a
lighted cigarette lying in an ashtray. If we look at the plume of
smoke that arises from the top of the cigarette, one can notice
that in the initial stage it looks relatively smooth and has a
straight flow path. Once it reaches a certain height, the path
suddenly shatters into a spatially and temporally disordered
form. It means that, due to the instability, the laminar flow
switched to the turbulent one [3, 4].
The criterion that determines when the fluid flow
changes or retains its status is called the stability criterion. The
stability criterion plays a central role in fluid mechanics, when
it comes to the fluids that are exposed to disturbance, given
that the instability can cause their transition from the laminar
to the turbulent state [5]. The theory of linear stability in fluid
mechanics implies predicting the critical Reynolds number at
which the fluid flow instability appears [6].
Sadoon K. Ayad is currently a lecturer in the Mechanical Eng. Dept.,
University of Technology, Baghdad, Iraq. E. mail: [email protected]
Predrag Živković is currently an assistant Prof. University of Nis/ Faculty of
Mechanical Engineering, Nis, Serbia. E. mail: [email protected]
Mladen Tomić is currently an assistant Prof. University of Nis/ Faculty of
Mechanical Engineering, Nis, Serbia. E. mail: [email protected]
Natural convection in enclosed spaces has been the
subject of study in energetics for a long time. It appears in a
wide range from the smallest scale (in pipelines, channels,
tanks) to the largest ones (atmosphere, the molten planet core).
The occurring processes depend on geometry and temperature
of respective surfaces, which defines the type of flow that
would occur [7].
A special group of these flows occur when the flow is
performed between the parallel plates of different
temperatures, usually when the temperature of the lower plate
is higher than the upper temperature - well known Rayleigh -
Bénard convection [8, 9]. The flow was experimentally
explained by the French scientist Henri Bénard (Henri Claude
Bénard (1874-1939)) in 1900. Nobel Prize winner for physics,
Lord Rayleigh (John William Strutt, 3rd Baron Rayleigh
(1842-1919)) in 1918 was the first to lay the theoretical
foundations based on the temperature gradient [10]. In this
approach, the boundary conditions at the top and bottom of the
observed domain imply the disappearance of the vertical
velocity component, which is not in accordance with the
Bénard experiment. References [11, 12] have made changes to
the model based on surface tension, which brought the model
into agreement with the experiment, i.e. physical reality.
The given examples of natural convection are still
based on the generalization of the plates between which the
flow takes place being unlimited. In engineering practice, this
is not the case, so that this research will define the influence of
the side walls to the flow, without idealization and within the
real three-dimensional domain [13].
The main objective of the current research is to
determine the real flow parameters in the real tanks exposed to
external influences. As the temperature gradient is the main
cause of a given flow, temperature measurements were
obtained in a real temperature range occurring at the location
where the experiment was be performed, i.e. in the laboratory
of the Faculty of Mechanical Engineering, Niš. The
temperature gradient source is insolation; since it is clear that
the convection intensity, or the occurring velocities, are in
direct proportion to the given temperature difference, what is
to be taken into account are the greatest temperature
differences occurring at respective surfaces.
II. MATHEMATICAL MODEL
Despite the complex mathematical model, under certain
conditions, we can predict how the instability is affecting the
structure of the turbulent flow. A typical example is the
Rayleigh - Bénard convection in which a thin layer of fluid,
limited by two parallel plates is heated from below. Due to the
temperature differences in the fluid layers, the flow under the
impact of the buoyancy forces occurs in the fluid. Depending
Experimental and Analytical Solution for
Rayleigh-Bernard Convection
Sadoon K. Ayed, Predrag Živković, Mladen Tomić
T
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on the flow parameters, different cell structures are formed in
the temperature, velocity and vorticity fields. In the case of 3D
flow, so-called rolls are formed [14].
Therefore, the Rayleigh-Bénard's problem in its
simplest form and in the way it was treated in its earliest
study, is the case of the so-called infinite layer. In such a case,
the fluid layer is limited by two infinite horizontal plates. The
surface is heated from below, i.e. it is at a higher temperature
than the upper plate [15]. The upward heating has a negative
temperature gradient since the fluid is denser on the top than
on the bottom; such a formation, with the denser fluid at the
top, is potentially unstable. When the temperature gradient is
below a certain value, the natural tendency of a fluid to be
moving due to the buoyancy forces will be disrupted due to
the viscosity of the fluid, and heat dissipation. Thermal
instability occurs when the negative temperature gradient
exceeds a certain critical value [16].
The thermal convection phenomenon caused by the
negative thermal gradient is known as the Rayleigh-Bénard
convection. As for the physicality of the phenomenon,
however, combining both names into a single expression adds
confusion in understanding of the convection mechanism,
which is still not fully resolved: Bénard observed phenomenon
in which instability due to the temperature dependence on the
surface tension coefficient played an important part, while
Rayleigh studied the convection caused by other types of
instability, namely by non-uniformity of temperature (and
density) of the fluid layer. The term Rayleigh-Bénard
convection is usually attributed to the convection resulting
from the Rayleigh mechanism, while the term Bénard-
Marangoni convection refers to thermo-capillar convection
[17, 18].
There are numerous examples of the Rayleigh-Bénard
convection such as electro-convection (where the fluid is a
liquid crystal and there is a time-varying potential along the
cell), the binary fluids (with two different fluids within a cell)
and the Bénard-Marangoni convection (where the top plate
does not exist so that the surface tension acts as an additional
driving force). This case plays a major role in the development
of stability theory in hydrodynamics [19].
Other systems showing the properties of model forming
are the Taylor-Couette flow (between concentric rotating
cylinders), the Faraday waves (which occur in the fluid cell
with vertical disorders) and reaction-diffusion systems
(oscillating chemical reactions) [20].
Cell formation is a characteristic of the systems which
are far from equilibrium. They can be thrown out of balance
by different physical mechanisms. Some of them are:
temperature difference in the fluid, electrical potential
difference or chemical reactions. For each of the driving
forces there is a dissipation mechanism, such as viscosity,
which opposes the unbalancing of the system. The balance
between the driving force and the dissipation mechanism
results in the cell formation that can have different shapes
(circular, square, hexagonal, spiral, stripes...) [21, 22].
Mass conservation equation
𝜕𝜌
𝜕𝑡+𝜕(𝜌𝑢𝑖)
𝜕𝑥𝑖= 0,
(1)
Momentum conservation equations – Navier-Stokes
equations
𝜕(𝜌𝑢𝑖)
𝜕𝑡+𝜕(𝜌𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗
=𝜕(𝜏𝑖𝑗)
𝜕𝑥𝑗−𝜕𝑝
𝜕𝑥𝑖
+ 𝑓𝑖 ,
(2)
Energy conservation equation
𝜕(𝜌ℎ)
𝜕𝑡+𝜕(𝜌𝑢𝑖ℎ)
𝜕𝑥𝑖
=𝜕(𝑗𝑖ℎ)
𝜕𝑥𝑖+ 𝜇𝛷 + 𝑆ℎ ,
(3)
where are: ρ density, ui velocity components, p pressure, fi
source terms of the equations of conservation of momentum
(volume, Coriolis, buoyancy forces, etc.) that can be ignored,
h entalphy, Sh production/destruction of energy, jih fluxes of
diffusive energy transport. In all the equations, we can notice,
on the left hand side, unsteady and convective terms, while
those that are diffuse and source can be noticed on the right
hand side [23].
In Newtonian fluid viscous stresses are proportional to
the deformation so that tensor τij has the following form
𝜏𝑖𝑗 = 𝜇 (
𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
)−𝜇2
3
𝜕𝑢𝑘𝜕𝑥𝑘
𝛿𝑖𝑗 , (4)
where are: μ dynamic viscosity of the fluid, δij Kronecker delta
operator (δij=1 for i=j and δij=0 for i≠j).
In equation (4) diffusive flux of energy transport jih
includes energy transport by conduction and viscous
dissipation. This can be expressed in the form:
𝑗𝑖ℎ = 𝛤𝑇
𝜕𝑇
𝜕𝑥𝑖, (5)
where
𝛷 =
1
2(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
)
2
−2
3
𝜕𝑢𝑘𝜕𝑥𝑘
𝜕𝑢𝑙𝜕𝑥𝑙
, (6)
and
ℎ = 𝑐𝑝𝑇 (7)
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where ΓT = λ is diffusion coefficient of enthalpy, or in this case
thermal conductivity [24].
The change of density as a function of temperature for
incompressible fluids can be assumed in the linear form
𝜌 = 𝜌0(1 − 𝛽(𝑇 − 𝑇0)) (8)
where β is compressibility factor of dimension K-1.
For the Navier-Stokes equations, where ρ is constant, we
obtain
𝜌𝜕𝑢𝑖𝜕𝑡
+ 𝜌𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗
= 𝜇𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
) −𝜕𝑝
𝜕𝑥𝑖+ 𝜌𝑔𝑖 ,
(9)
respectively
𝜌 (
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗)
= 𝜇𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
)
−𝜕𝑝
𝜕𝑥𝑖+ 𝜌𝑔𝑖,
(10)
where body forces fi are replaced by ρgi.
(𝜌0 + 𝜌′) (𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗) = 𝜇
𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
)
−𝜕𝑝0𝜕𝑥𝑖
−𝜕𝑝′
𝜕𝑥𝑖+ 𝜌0gi + 𝜌′gi,
and noting that in the hydrostatics
𝜕𝑝0𝜕𝑥𝑖
= 𝜌0gi (11)
we finally obtain
(𝜌0 + 𝜌′) (
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗)
= μ𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
) − 𝜌0𝑔𝑖
−𝜕𝑝′
𝜕𝑥𝑖+ 𝜌gi.
(12)
Dividing the whole expression with ρ0, we obtain
(1 +
𝜌′
𝜌0)(
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗)
= ν𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
) −1
𝜌0
𝜕𝑝′
𝜕𝑥𝑖
+𝜌′
𝜌0gi.
(13)
For small values of density variation the following is obtained
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗= ν
𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
)
−1
𝜌0
𝜕𝑝′
𝜕𝑥𝑖+𝜌′
𝜌0gi.
(14)
A member of the right-hand side with ρ' remains in the
expression, because the size of gi is large enough to affect the
expression. Finally, taking into account density dependence on
temperature, we obtain
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗= 𝜈
𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
) −1
𝜌0
𝜕𝑝′
𝜕𝑥𝑖− gi𝛽𝛥𝑇.
(15)
If p=p0+p', then dp=dp', followed by
𝜕𝑢𝑖𝜕𝑡
+𝜕(𝑢𝑖𝑢𝑗)
𝜕𝑥𝑗= ν
𝜕
𝜕𝑥𝑗(𝜕𝑢𝑖𝜕𝑥𝑗
+𝜕𝑢𝑗𝜕𝑥𝑖
) −1
ρ0
𝜕𝑝
𝜕𝑥𝑖− gi𝛽Δ𝑇,
(16)
By introducing the dimensionless quantities for
velocity U, time τ, pressure and temperature �̅� and �̅�, and
length �̅� we obtain equation in the following form:
1
𝑃𝑟(𝜕𝑈𝑖
𝜕𝜏+𝜕(𝑈𝑖𝑈𝑗)
𝜕�̅�𝑗) =
𝜕2𝑈𝑖
𝜕�̅�𝑗2 −
𝜕�̅�
𝜕�̅�𝑖+ 𝑅𝑎�̅�,
(17))
In this expression, Pr represents the Prandtl number,
while the Rayleigh number Ra, analogously to the Reynolds
number, is the ratio of the buoyancy and the viscous forces,
that is
𝑅𝑎 =
g𝛽𝛥𝑇𝐿3
𝜈𝑎.
(18))
Further interest is to determine the stability limit of the
Rayleigh-Bénard convection, and the effect of the disturbance,
or perturbation on the fluid state.
In practice, there are three types of the tank - spherical,
cylindrical and prismatic. The first two types are mainly
storage tanks of large volume, and therefore stationary. As
most of the reservoirs in mobile systems are approximately of
parallelepiped shape (for vehicles, in the airplanes wings and
fuselage...), this research will focus on this type [25].
Since it is known that the intensities of the velocities
that occur at such convection are quite low, the study is based
on the numerical experiment. For the purpose of validation of
the numerical experiment, an experimental installation is
formed with respective dimensions H×W×L of 1×2×4
(500×250×125mm, in x, y and z directions, respectively) [26].
The experiment comprised the measurement of the
temperature profiles in several sections, both vertical and
horizontal.
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III. EXPERIMENTAL SETUP
As there are many types of hydraulic fluids we can find
in real tanks, the real as well as the practical experiments were
carried out with five different working fluids - water, diesel
fuel, motor oil, alcohol and air (the case of an "empty" tank).
One can, with sufficient accuracy, assume that the chosen
fluids faithfully represent the majority of fluids that can be
found in the real tanks.
Since the impacts of the Rayleigh-Bénard convection
on real tanks are not extensively explored in the available
literature, the aim of this study is to show the real thermal-
flow processes in the case of the aforementioned
parallelepiped tank. Better knowledge of these processes can
increase the safety and reliability of the whole systems of
which they are component parts, which is of exceptional
importance, especially for tanks in various hydraulic systems
of an aircraft.
Fig. 1: Scheme of experimental installation
In order to confirm the results of the experiment, in the
premises of the Laboratory for Thermal Engineering, the
experimental installation was formed in which the temperature
was measured at 16 points in the chamber, in several sections,
both vertical and horizontal, using a special construction of
PT100 temperature sensors that enabled chamber sealing in
respective positions. The chamber is insulated on the sides by
sponge and Styrofoam. Additional check-up of the results is
done by thermal imaging camera.
As can be seen in the diagram of Fig. 2, above the
chamber there is a water area, 50mm high, in which there is a
heater, which is through the variable resistor (Variac) can
accurately heat the water. In this chamber there is a mixer, for
equalization of the temperature of the water, and thus the hot
plate, which is located on the opposite side of the heater. The
chamber is equipped with the trestles which enable its turning
so that the hot plate can be either at the top or the bottom of
the chamber. External influences are simulated by heating the
upper plate (insolation). The following Fig. shows the
temperature field at the appropriate layers of insulation,
obtained by thermal imaging camera Flir E30.
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Fig. 2 Checking the temperature field by thermal imaging camera for the
gradual removal of insulation in case of air as the working medium
Fig. 3 Structure and parameters of temperature probes TS-05 with PT100
temperature sensor
A. Measuring system
The measurement system was developed in cooperation with
firm Nigos, Nis [27]. It consists of two eight-channel data
loggers for collecting data on temperatures in respective
chamber locations. This approach gives temperature profiles
in three vertical sections, on either side of the chamber, in
order to determine the temperature deviation from the "front"
(sunny) and "rear" side of the chamber. In order to determine
the uniformity of temperature distribution of hot plate, close to
it a set of 5 temperature sensors was located at one lateral side
and two on the other.
The temperature measurement and acquisition were
done by 2 eight-channel loggers VT08 and 16 PT100 probes
type TS05, 0.1ºC accuracy, enabling the necessary chamber
sealing (Fig. 5). Calibration of PT100 probes using a reference
thermocouple (TP) is shown in the following Fig.
Microprocessor logger VT08, in addition to
temperature measurement is comparing the measured values
with the set limit values. If some measured value of the
measuring point exceeds the permitted limit, one of the relay
outputs, serving as alarms, is activated. The limit values are
widely adjustable. There is a possibility of adjusting the
temperature offset for each input. The upper display shows the
measured current value of the temperature measuring points,
and the bottom shows the number of the measuring point.
Changing the display can be automatic or manual. In
automatic change, the display for a limited time alternates
measured points for which the measured temperature values
are displayed. In the case of manual changes, permanent
display of the desired measuring point can be set.
B. System for data acquisition – NIGOS Manager Acquisition
Software
NIGOS Manager is a PC application that enables
monitoring and management of all the measuring and control
devices that have embedded communication interface [28].
The application allows communication with devices over a
serial or USB port and the appropriate adapter. It is possible to
work and in a LAN network using a communication server to
remote computers.
The user with administrator access rights defines the
network of devices the application communicates with. He has
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the ability to choose the parameters of the device monitored
(diagram with current values is generated) and archive them in
a database. Based on the data collected, reports can be
generated afterwards in a graphical or table form, or the data
can be exported to a file for processing in other applications
for table calculations such as Excel, Calc, etc.
There is also the possibility of entry of data from the
report to a file. Data is written to the .csv (comma-separated
values) format. This file can be opened in any text editor, as in
Microsoft Office Excel. Report generation can be a time-
consuming operation, depending on the number of data to be
displayed (depending on the time period for the report and the
period of entry in the database). For faster generation a shorter
period should be chosen or lower frequency of entries in the
database.
NIGOS Manager can be used to adjust the device,
because through communication interface can access their
parameters. Current setting can be saved to a file (setting all
parameters). It is possible to enter previously recorded settings
to other devices of the same type.
C. 4.4 Thermal imaging camera Flir E30
For comparison of data measured on the PT100
temperature probes, parallel periodical measuring of the
temperature field is executed with thermal camera Flir E30
[29]. Cameras specifications are given in Table 4.1. The
camera data shows that the reading accuracy of temperature
field is ±2°C or ±2% of reading, however, since the
temperature was up to a level of 50°C, it follows that the
accuracy level is ±1°C, which is an order of magnitude smaller
than the accuracy of the used probe PT100. The use of thermal
camera was limited to a comparison with the measured
temperature fields and visualization, but not really measuring.
However, the obtained results are consistent with the
measured, and as comparative values they can be taken into
account within the specified accuracy.
TABLE 1 Thermal imaging camera flir E30 technical data [30]
Model FLIR E30
Optical performance
Resolution 160 × 120 pixels
Global resolution 19,200 pixels
Temperature sensitivity < 0.10°C
Accuracy ±2°C or ±2% reading
Temperature range -4°F to 662°F (-20°C to
350°C)
Video camera w/lamp 2.0 MP
Video output Composite
Sampling frequency 60 Hz
IV. RESULTS AND DISCUSSIONS
The aim of the experiment was to determine the
influence of external conditions on the fluid contained in the
parallelepiped tank. In order to facilitate the comparison of
results, the same heat flux is brought to the water in the
chamber, and the surrounding air is left to the influences of the
atmosphere. The chamber is tested with air as the working
fluid. Fig. 4 shows the preliminary results of the
measurements for a period of 5 days.
Fig. 4 The five-day temperature changes of air as the working fluid
Fig. 5 shows a typical daily temperature change. It can be
concluded that all the temperatures show similar behaviour in
relation to environment temperature change.
Fig. 5: Typical daily temperature change
Fig. 6 shows the hourly change in temperature during the
parallel measurements with the IC camera. Period of 30
minutes before and 30 minutes after the measurement with
thermal camera (results shown in Figs. 7 & 8). Measurement
with the thermal camera lasted for 4 minutes, during which
layer after layer of insulation was removed. As the probes
located in the chamber showed no noticeable temperature
differences (other than those along the cold plates, which
show a very slight increase in the level of up to 0.4° C), it can
be concluded that this is due to increased convective heat
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exchange caused by increased room air velocity (opening the
door, the movement during the measurement, removing and
restoring the insulation, etc.)
Fig. 6 Typical hourly changes in temperature (during the thermal camera
measurement)
The chamber used in the experiment has shown great
flexibility. The probes are placed at appropriate locations so
that there are 3 or 4 probes that measure temperature in 3
different vertical sections. This arrangement allows
measurement with various hydraulic fluids at different
temperature regimes and positions of the warmer and cooler
plates. The experiment has shown that the relative stability of
the surrounding air has allowed the cooler plate to be directly
exposed to external conditions. The measuring system has
shown an appropriate response to external conditions,
enabling a variety of experiments. Selected Probe TS-05, due
to the massive threaded part somewhat increased measurement
inertia; yet this has allowed control measurements with the
thermal camera. Thermal camera measurements have shown
no significant heat loss in the insulated part of the chamber.
Fig. 7: The temperature profile in the left, middle and right vertical cross-
section of the chamber with air in case of RBC (left) for temperatures
TS01=41.3°C and TS16=30.3°C
As at this time for technical reasons it was not possible
to perform measurement of velocity field in the experimental
chamber (although it same is equipped with transparent
openings to allow the possible application of laser-Doppler
anemometry), the measurement of temperature profiles was
carried out in multiple cross sections, both horizontal and
vertical for all of the working fluids (air). For comparison,
there was a series of measurements with the warmer plate
positioned on the upper side (which simulated the impact of
solar radiation as a source of the temperature gradient in the
fluid) – the RRBC case, and then to a warmer plate positioned
on the lower side (a classic setting for Rayleigh-Bénard
convection) – the RBC case.
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International Journal of Computation and Applied Sciences IJOCAAS, Volume 3, Issue 2, October 2017, ISSN: 2399-4509
231
Fig. 8 The temperature profile in the left, middle and right vertical cross-
section of the chamber with air in case of RRBC (right) for temperatures
TS01=51°C and TS16=33°C
The natural convection in enclosed spaces has been
studied for a long time in energetics. It emerges in a wide
range from the smallest scales (in various vessels and devices)
to the largest ones (atmosphere, molten planet core). The
occurring processes depend on geometric relations and
temperature of respective surfaces, which defines the type of
flow that would occur.
A special group of these flows occurs when the flow
takes place between two parallel plates with different
temperatures, most often when the lower plate temperature is
higher than that of the upper – a well-known case is that of the
Rayleigh-Bénard convection. This case was first experim-
entally investigated by Henry Bénard in 1900, while the Nobel
Prize winner for physics, Lord Rayleigh (John William Strutt,
3rd Baron Rayleigh) was the first to lay the theoretical
foundations based on the temperature gradient. In the later
studies this problem was theoretically better described,
especially after the introduction of the model based on surface
tension. These studies are mainly based on the study of flow
between 2 infinite parallel plates, which left space for the
study of the impact of the real side walls in real tanks, without
process idealization and in the real three-dimensional
domains.
V. CONCLUSIONS
All the research results can be summarized in the form
of several characteristic findings:
- The chamber used in the experiment has shown great
flexibility. The probes are placed at appropriate locations
so that there are 3 or 4 probes that measure the
temperatures in 3 different vertical cross sections. This
arrangement allows measurement with various hydraulic
fluids with different temperature regimes and warm and
cool plate positions.
- The experimental results have indicated that the relative
stability of the surrounding air allows the cooler plate to
be directly exposed to external conditions.
- Measuring system showed an appropriate response to
external conditions, enabling a variety of experiments.
Probes carriers have somewhat increased measurement
inertia, but allowed the control measuring with the
thermal camera. Thermal camera measurements showed
no significant loss of heat on the insulated part of the
chamber
- This chamber construction, through transparent
openings, enables the use of non-contact methods for
temperature and velocity field measurement, such as
laser-Doppler anemometry, various optical methods, etc.
- On the basis of experimental data numerical experiment
was performed. Validation is done through the
temperature field in several sections. The values of
Rayleigh number are in accordance with the obtained
velocity field.
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