Peculiarities of the Leidenfrost effect application for drag force reduction/Leidenfrosto efekto ypatumai pasipriesinimo jegos mazinimui.
Gylys, Jonas ; Skvorcinskiene, Raminta ; Paukstaitis, Linas 等
1. Introduction
A movement of body in the fluid is affected by a drag force which
resists and slows the motion. In general this resistance depends on the
body's (or liquid flow) velocity, body's shape and on the
physical characteristics of the liquid. Usually a drag force is
characterized by the drag coefficient [C.sub.D], which is influenced by
the velocity (Reynolds number) and for the spherical body are
investigated quite well [1]. In order to overcome drag force and to
maintain body's motion it is required a sufficient amount of
energy. Therefore drag force reduction is one of the most important
hydrodynamic tasks. Nowadays are known a lot of different methods
allowing drag force reduction and energy economy as well. In some cases
methods are used that enables density or viscosity reduction of the
liquid, in other cases--methods allowing alteration of the body's
surface properties. Up to today various techniques have been proposed:
polymer injection or air lubrication, wall oscillation or elastic
(hydrophobic and compliant) coating and etc. Main features of some of
the mentioned methods are as follows:
--The polymer fluid is inserted into the boundary layer between the
liquid and the body (vessel) [2]. Such polymer initially must be
"preconditioned" in order to elongate its molecules. This
technique enables quell turbulence and reduce skin friction immediately
upon injection.
--Various air lubrication techniques are applied in order to reduce
drag force [3]:
* bubble drag reduction (BDR)--small bubbles are injected into the
boundary layer;
* air layer drag reduction (ALDR)--gas creates a lubricating layer
between hull and liquid;
* partial cavity drag reduction (PCDR)--gas creates a lubricating
layer between the part of the hull and liquid.
--Method, which was proposed by A. Vand [4] in 1945, is based on
the possibility to reduce drag force by vibration of the body. As a
result of that a speed of body (boat) can be higher or the same speed
can be kept using less power.
--Drag reduction through elastic coating [5] with both flow and
material properties considered.
One of the newest methods which help to reduce the drag force and
to increase velocity of body without increasing energy consumption is so
called supercavitation [6]. Supercavitation effect is based on the use
of cavitation to create a large bubble of gas inside a liquid, allowing
an object to move at great velocity through the liquid by being wholly
enveloped by the bubble. The cavity (bubble) reduces the drag on the
object, since drag is normally about 1000 times greater in liquid
(water) than in a gas (air). Cavitation happens when water pressure is
lowered below its vapor pressure or vapor pressure is increased to water
pressure. Usually this happens at the extremely high speed although
often it can happen at any speed [6]. The one of the possible
modification of this method is to generate supercavitation by injecting
a hot gas in front of the moving object [6]. The hot gas will vaporize
water and will reduce the friction of the body to a mixture of gas and
vaporized water.
Authors [7] proposed to reduce the drag force by using boiling
crisis or Leidenfrost effect. In 1756 year J. G. Leidenfrost [8]
observed that water droplets supported by the vapor film evaporate much
slower. The Leidenfrost effect is a phenomenon in which a liquid, in
near contact with a body significantly hotter than the liquid's
boiling point, produces an insulating vapor layer keeping that liquid
separately from the body's surface [7]. The experiments [7], which
were performed by dropping spherical body into the liquid (electrolyte
FC-72), showed that the spherical hot body (wrapped by the vapor film)
moves 2.5 times faster than the cold body. Authors chose the electrolyte
FC-72 thanks to its specific thermodynamic features: electrolyte boiling
temperature at the atmospheric pressure is 56[degrees]C; density is 1680
kg/[m.sup.3] at the temperature 38[degrees]C and heat capacity is 1.1
kJ/kg K at the same (38[degrees]C) temperature.
Due to the fact that the analogical parameters of the other
liquids, for example, water, are sufficiently different from those,
mentioned above, it is reasonable to estimate the hydro and
thermodynamic limits showing the acceptability of the body's
heating in order to reduce drag force (or increase body's
velocity).
Main task of this work is to analytically determine thermal and
hydrodynamic conditions under which a boiling crisis (Leidenfrost
effect) is reasonable to use for the drag force reduction of the
spherical body moving in the water and electrolyte FC-72. For the main
analytical analysis the body was considered that is made from the
stainless steel, diameter was 0.02 m. Body's velocity was changed
from 0.03 to 32.5 m/s; liquid and cold body temperature was kept at
20[degrees]C; hot body temperature was equal to 500[degrees]C.
2. Analytical analysis of drag force
Let assume a spherical body, which falls in the liquid vertically.
In general a body can be affected by the following main forces: gravity,
fluid resistance, and buoyancy (Archimedes force). If the force of
gravity is greater than the Archimedes force, body moves vertically
downwards, and otherwise--upwards. Initially body moves with
acceleration. When a gravity force becomes equal to the sum of the
friction (resistance) force and the buoyancy (Archimedes force), the
body begins to move at a constant velocity (gradually).
Spherical cold body stabilized falling velocity can be expressed by
the Eq.(1) [9], m/s:
[w.sub.1] = [d.sup.2]([[rho].sub.sphere] -
[[rho].sub.L])g/18[[mu].sub.L], (1)
where d is body's diameter (0.02 m); [[rho].sub.L],
[[rho].sub.sphere] are water and spherical body densities at the
temperature 20[degrees]C (999.7 and 7800 kg/[m.sup.3] respectively);
[[mu].sub.L] is coefficient of the dynamic viscosity (1.308 Pa x s).
Drag force of the spherical body can be calculated using the Eq.
(2) [10], N:
[F.sub.D] = [C.sub.D] [pi][R.sup.2] [[rho].sub.L][w.sup.2.sub.1]/2,
(2)
where [C.sub.D] is drag coefficient of the spherical body (Fig. 1);
R is body's radius (0.02 m); [w.sub.1] is stabilized velocity of
the body's fall, m/s.
Cold body drag coefficient [1] for the region 500 [less than or
equal to] Re [less than or equal to] 200000 (velocity w = ~0.03/~13.06
m/s) is almost constant [C.sub.D] = 0.46. Thus, the drag force of the
cold spherical body falling in the liquid, according to the Eq. (2), is
equal to 0.0474 N, where [w.sub.1] is equal to 0.81 m/s (Eq. (1)).
As it was mentioned before, authors [7] (Fig. 1) determined that
the stabilized falling velocity of the body, wrapped by vapor film, in
comparison with velocity of the cold body, increases by 2.5 times in the
electrolyte FC-72.
[FIGURE 1 OMITTED]
Let's consider that the stabilized velocity of the hot
spherical body falling in the water increases by the same ratio, i.e.
2.5 times. In such a case falling velocity of the hot body in water will
be [w.sub.2] = 2.5 x 0.81 = 2.03m/s.
It is assumed, that a vapor film enables increase falling velocity
by 2.5 times if the drag force is the same as for the cold body case:
[F.sup.cold1.sub.D] = [F.sup.hot.sub.D] = 0.0474N
The hot body's drag force coefficient [C.sup.hot.sub.D] =
0.074 can be obtained from the Eq. (2):
[C.sup.hot.sub.D] =
2[F.sup.hot.sub.D]/[pi][R.sup.2][[rho].sub.2][w.sup.2.sub.2]. (3)
At the same time drag force of the cold body, moving at the
velocity [w.sub.2] = 2.03 m/s, will be 0.296 N (according to the Eq.
(2)).
Table shows drag force calculation options and results for the
different velocities of the spherical body which d = 0.02 m.
2. Energy consumption of hot and cold bodies
The minimal value of the heat flux, necessary for the formation of
a stable vapor film on the surface of the spherical body placed in the
large volume of the water, can be estimated using N. Zuber equation [11,
12]:
[q.sub.2] = [q".sub.min] = 0.09 [[rho].sub.v][i.sub.fg]
[[[sigma]g([[rho].sub.L] - [[rho].sub.V])/[([[rho].sub.L] +
[[rho].sub.V]).sup.2]].sup.1/4], (4)
where [[rho].sub.V], [[rho].sub.L] are vapor and liquid density at
the boiling temperature (0.595 and 958 kg/[m.sup.3] respectively);
[sigma] is surface tension coefficient (0.0589 N/m); g is acceleration
of gravity (9.81 m/[s.sup.2]); [i.sub.fg] is evaporation heat (2260
kJ/kg).
Calculations according to the Eq. (4) give a value equal to 19 x
[10.sup.3] W/[m.sup.2]. Taking into account a small reserve let's
assume, that the heat flow, necessary for reaching boiling crisis and
forming a stable vapor film is equal to [q.sup.sphere] = 20 x [10.sup.3]
W/[m.sup.2].
Drag force of the hot body, moving at the velocity [w.sub.2] (2.5
times faster than a cold body), will remain the same as that for the
cold body, moving at the velocity [w.sub.1] (0.81 m/s) only in the case
if the drag coefficient [C.sub.D] will be equal to 0.074 (instead of
0.46). Distance, which the body moving at the same velocity ([w.sub.2] =
2.03 m/s) passes during one second (t =1 s) is equal to L = 2.03 m. In
that case energy consumption, necessary for the hot body to overcome
distance L, will be 0.096 J (according to the Eq (5)):
[Q.sub.1] = [F.sup.hot.sub.D]L. (5)
Besides that it is necessary to evaluate an amount of energy
(26.000 J) spent for the heating of the body which can be obtained from
the equation:
[Q.sub.2] = [q.sup.sphere]At, (6)
where A is area of the spherical body's surface (A =
4[pi][r.sup.2]), [m.sup.2]; r = d/2 = 0.01 m; t = 1 s.
Total energy consumption (26.096 J) for the hot body is calculated
as follows:
[Q.sup.hot] = [Q.sub.1] + [Q.sub.2] (7)
Cold body moves at an increased velocity [w.sub.2] = 2.03 m/s; the
drag force is [F.sup.cold2.sub.D] = 0.296N. Energy consumption (0.601 J)
of the cold body moving at the same velocity as the hot body (t = 1 s, L
= 2.03 m) is obtained from:
[Q.sup.cold2] = [F.sup.cold2.sub.D]L. (8)
The difference of the energy consumption (25.5 J) for the hot and
cold bodies', moving at the same velocity 2.03 m/s, is obtained
from the equation:
[DELTA]Q = [Q.sup.hot] - [Q.sup.cold2]. (9)
[FIGURE 2 OMITTED]
Energy consumption change, depending on the body's velocity,
is calculated according to the Eqs. (1) to (8).
Fig. 2 shows the hot and cold bodies' energy consumption
dependence on the velocity. This graph is drawn assuming, that the
velocity of the hot body has no influence on a stability of the vapor
film.
Fig. 2 shows that the increase of the cold or hot body's
velocity influences on the energy consumption grow. For the case, if the
body's velocity is greater than 7.5 m/s, the total energy
consumption, required for the hot body movement, is less than that for
the cold body at the same velocity. The hot body (wrapped with a vapor
film) achieves the same velocity using less energy than the cold body.
Otherwise the hot body moves faster using the same energy amount like
the cold body. Higher velocity corresponds to the higher energy savings.
3. Energy relative consumption of the hot and cold bodies, moving
in the water
Comparison of the energy relative consumption of the hot and cold
body's, allows us better present the process mechanism and examines
the limits where the Leidenfrost effect can be used as a measure for
drag force reduction.
[FIGURE 3 OMITTED]
Fig. 3 shows the influence of the velocity relative increment
[DELTA][w.sub.i]/[DELTA][w.sub.const] on the energy relative increment
[DELTA][Q.sub.i]/[DELTA][Q.sub.const]. Here an initial stabilized
velocity of the hot body ([w.sub.2] = 2.03 m/s) is taken as a starting
point. In Fig. 3 segment AB, which is below zero axes, shows an area,
where the energy relative consumption of the cold body is lower than
that of the hot body. The curve segment BC, which is above zero axes,
shows an area, where the energy relative consumption of the hot body is
lower than that of the cold body.
Energy relative increment [DELTA][Q.sub.i]/[DELTA][Q.sub.const] is
calculated as a ratio of the cold and hot bodies energy consumption
difference at the ith point ratio to the initial (i = 1 point) energy
consumption difference, where the velocity of the hot body is considered
as a stabilized ([w.sub.2] = 2.03 m/s) velocity.
Energy consumption difference [DELTA][Q.sub.i] (at the ith point)
is equal to, J:
[DELTA][Q.sub.i] = [Q.sup.hot.sub.i] - [Q.sup.cold2.sub.i], (10)
where [Q.sup.hot.sub.i] is hot body energy consumption at the
initial (i = 1) point, J; [Q.sup.cold2.sub.i] is cold body, moving at
the same velocity as a hot body, energy consumption at the initial point
(i = 1), J.
Energy consumption difference [DELTA][Q.sub.const] for the velocity
[w.sup.2] = 2.03 m/s can be found from the equation, J:
[DELTA][Q.sub.const] = [Q.sup.host.sub.const] -
[Q.sup.cold2.sub.const], (11)
where [Q.sup.host.sub.const] is energy consumption of the hot body
at the velocity [w.sub.2] = 2. 03 m/s, J; [Q.sup.cold2.sub.const] is
energy consumption of the cold body, moving at the same velocity as a
hot body ([w.sub.2] = 2.03 m/s), J.
Velocity relative increment [DELTA][w.sub.i]/[DELTA][w.sub.const]
is the cold and hot bodies velocity difference at the ith point ratio to
the initial (i = 1) point velocity difference, where the velocity of the
hot body is considered as a stabilized ([w.sub.2] = 2.03 m/s) velocity.
Cold and hot bodies' velocity difference [DELTA][w.sub.i] at
the ith point, is found from the equation, m/s:
[DELTA][w.sub.i] = [w.sub.2i] - [w.sub.1i], (12)
where [w.sub.2i], [w.sub.1i] are velocity of the hot and the cold
bodies at the ith point, m/s.
Velocity relative increment [DELTA][w.sub.i]/[DELTA][w.sub.const]
is the cold and hot bodies velocity difference at the ith point ratio to
the initial (i = 1) point velocity difference, where the velocity of the
hot body is considered as a stabilized ([w.sub.2] = 2.03 m/s) velocity.
Cold and hot bodies' velocity difference [DELTA][w.sub.const]
at the initial (i = 1) point is found from the equation, m/s:
[DELTA][w.sub.const] = [w.sub.2const] - [w.sub.1const], (13)
where [w.sub.2const] is stabilized velocity of the hot body
([w.sub.2] = 2.03 m/s); [w.sub.1const] is stabilized velocity of the
cold body ([w.sub.1] = 0.81 m/s).
[FIGURE 4 OMITTED]
Fig. 4 shows the velocity relative increment
[DELTA][w.sub.i]/[DELTA][w.sub.i-1] influence on the energy relative
increment [DELTA][Q.sub.i]/[DELTA][Q.sub.i-1]. Here a preceding
(previous) velocity is assumed as an initial starting point. Point B can
be considered as a critical point, which separates an area, where energy
consumption of the hot body is higher than that of the cold body, from
the area, where the energy consumption of the hot body is less than that
of the cold body.
The Point B, which is below zero axes, shows an area, where the
energy relative consumption of the cold body is lower than that of the
hot body.
Energy consumption difference [DELTA][Q.sub.i] at the ith point for
the various velocities can be found from the Eq. (9). Energy consumption
difference [DELTA][Q.sub.i-1] at the initial point is found from the
equation:
[DELTA][Q.sub.i-1] = [Q.sup.hot.sub.i-1] - [Q.sup.cold2.sub.i-1],
(14)
where [Q.sup.hot.sub.i-1] is hot spherical body energy consumption
at the initial point (i = 1), J; [Q.sup.cold2.sub.i-1] is cold spherical
body energy consumption at the initial point (i = 1), J.
Relative increment of the velocity
[DELTA][w.sub.i]/[DELTA][w.sub.i-1] is the ratio of the hot and cold
bodies' velocity difference at the ith point to the difference at
the initial (i = 1) point.
Velocity difference [DELTA][w.sub.i] at the ith point can be found
from the Eq. (11). Velocity difference [DELTA][w.sub.i-1] at the
preceding (i = 1) point is found using Eq. (15):
[DELTA][w.sub.i-1] = [w.sub.2(i-1)] - [w.sub.1(i-1)] (15)
where [w.sub.2(i-1)] is hot body velocity at the (i = 1) point,
m/s; [w.sub.1(i-1)] is cold body velocity at (i = 1) point, m/s.
Fig. 5 shows the energy consumption difference change for the two
cases. In the first case hot body moves with the increased velocity,
body's energy consumption difference depends on the velocity
difference. In the second case cold body moves with the increased
velocity. Similarly like in the first case, body's energy
consumption difference depends on the speed difference as well. An
initial (i = 1) point is a starting point for the both cases. The third
(middle) curve of the Fig. 5 demonstrates hot body's (lower curve)
and cold body's (top curve) energy consumption difference change.
It is clear that the increase of the hot body's velocity influences
on the energy consumption growth more slowly than in the case of a cold
body.
In the Fig. 5 used the following designations: [Q.sup.hot.sub.i] -
[Q.sup.hot.sub.const]; [Q.sup.cold2.sub.i] - [Q.sup.cold2.sub.const],
and [DELTA][Q.sub.i] - [DELTA][Q.sub.const] - present the hot body, cold
body, and hot and cold bodies' energy consumption difference at the
ith and at the initial (i = 1) points; [w.sub.2i] -
[w.sub.2const]--presents the body's velocity difference at the ith
point and at the initial point (i = 1). Here the stabilized velocity
([w.sub.2] = 2.03 m/s) of the hot body is considered as an initial
velocity of the hot and cold bodies.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Fig. 6 shows the hot and cold bodies' velocity changes over
the time under the same energy consumption. Hot body velocity grows
faster than that of a cold body. On the other hand, it can be stated,
that a hot body reaches the same velocity as a cold body using less
energy, moreover, during the same time period a hot body goes a longer
distance than a cold body.
4. Dynamics of the spherical body drag coefficient changes
As it was already mentioned above, it can be assumed that the drag
coefficient of the spherical body is constant ([C.sub.D] = 0.46) for the
low velocity w [less than or equal to] 13 m/s (500 [less than or equal
to] Re [less than or equal to] 200000). Meanwhile, bodies can move at
the velocity faster than 13 m/s. In such a case drag coefficient of the
spherical body suddenly decreases (Fig. 7). This figure represents an
expanded part of the Fig. 1, covering range of 200000 [less than or
equal to] Re [less than or equal to] 500000.
Using data from the Fig. 7 one can provide the analogous
calculation (chapter 3) of the energy consumption for the hot and cold
bodies' moving at the velocity greater than 13 m/s. Fig. 8 presents
the calculation results. This graph shows that the energy consumption
declines if the body's velocity reaches ~18 m/s. Energy consumption
declination is directly related to the reduction of the drag coefficient
[C.sub.D] (Fig. 7).
[FIGURE 7 OMITTED]
It is possible to stress two turning points (C and D) in the Fig.
8. The first point (C) shows a decrease, and the second one (D) matches
an increase of the energy consumption.
Fig. 9 shows a dependence of the relative energy increment on the
relative velocity increment. The stabilized velocity ([w.sub.2] = 2.03
m/s) is taken as an initial velocity of the hot body.
The relative increment of the energy
[DELTA][Q.sub.i]/[DELTA][Q.sub.const] represents a ratio of the energy
consumption difference for the cold and hot bodies at the ith point to
the initial energy consumption difference at the initial (i = 1) point.
Hot body's stabilized velocity ([w.sub.2] = 2.03 m/s) is considered
as an initial velocity. The relative increment of the velocity
[DELTA][w.sub.i]/[DELTA][w.sub.const] represents a ratio of the velocity
difference at the ith point to the initial stabilized velocity
([w.sub.2] = 2.03 m/s) difference at the initial (i = 1) point.
[FIGURE 8 OMITTED]
The relative increment of the energy
[DELTA][Q.sub.i]/[DELTA][Q.sub.const] represents a ratio of the energy
consumption difference for the cold and hot bodies at the ith point to
the initial energy consumption difference at the initial (i = 1) point.
Hot body's stabilized velocity ([w.sub.2] = 2.03 m/s) is considered
as an initial velocity. The relative increment of the velocity
[DELTA][w.sub.i]/[DELTA][w.sub.const] represents a ratio of the velocity
difference at the ith point to the initial stabilized velocity
([w.sub.2] = 2.03 m/s) difference at the initial (i = 1) point.
A curve part ABC at the Fig. 9 was analyzed previously talking
about the curve at the Fig. 5. A curve part CD (Fig. 9), according to
the corrected values of the drag coefficient [C.sub.D] (Fig. 7),
reflects a reduction of the energy consumption. The energy consumption
for both hot and cold bodies decreases and the relative increment
[DELTA][Q.sub.i]/[DELTA][Q.sub.const] of the energy consumption
decreases at the same time also. Further augmentation of the relative
velocity influences on the energy consumption increase (curve part DE at
the Fig. 9).
[FIGURE 9 OMITTED]
Fig. 10 reflects a change of the hot and a cold body's energy
consumption difference for the curve ABCDE (Fig. 9). The third (middle)
curve shows a change of the hot body (lower curve) and cold body (upper
curve) energy consumption difference. A starting point, like it was for
the previous cases, was considered an initial (i = 1) point. A curve
part ABC at the Fig. 10 was analyzed more in detail discussing about the
curves in the Fig. 5. Similarly, as it was mentioned talking about the
Fig. 8 and Fig. 9, the change tendency of the real drag coefficient
[C.sub.D] (Fig. 7) reflects on the energy consumption decrease (or
increase) at the critical points C and D.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
Figs. 11 and 12 show an influence of the hot and cold bodies'
diameter on the energy consumption changes. Here also can be noticed the
energy consumption decrease (or increase) at the critical points C and
D. Those critical points appear at the same vertical line for all the
changes of the body's diameter. This can be explained by the fact
that the spherical body's drag coefficient does not depend on the
diameter of the body. Meanwhile, spherical body's velocity depends
directly on the body size (diameter). Therefore drag force and energy
consumption for bigger bodies are higher.
[FIGURE 13 OMITTED]
The first curve at the Figs. 11 and 12 was analyzed more in detail
discussing about the curves in the Fig. 8. It can be noticed that a
shape of the curves in the Figs. 11 and 12 are similar each to other,
but a magnitude of the energy consumption scale is different. Hot
body's energy consumption (Fig. 11) is lower than that of the cold
body (Fig. 12). Fig. 13 represents a comparison of the hot and cold
body's energy consumption using the same energy scale magnitude.
Figures 11-13 show that the bigger body requires more energy
consumption. But the hot body moving in the fluid under the boiling
crisis conditions (surrounded by the vapour layer) can achieve higher
velocity at the lower energy consumption.
5. Real case for the body moving in the water
Our experiments [13], which were performed on the hot and cold
bodies' moving in water which temperature is less than
20[degrees]C, do not show that the hot body's velocity increases by
2.5 times in comparison with the cold body [7]. Investigation showed
that hot body moves in water only 1.2 times faster [11]. For this case
hot and cold bodies' energy consumption dependence on the velocity
is shown in the Fig. 14. The Fig. 2 and Fig. 8 comparison with the Fig.
14 shows that in this case energy consumption saving starts at higher
velocity (w = 11.5 m/s). Furthermore, energy consumption economy Such
difference between conditions of the body movement in electrolyte FC-72
and water can be explained by difference in the evaporation heat which
is [i.sup.FC-72.sub.fg] = 88kJ/kg for electrolyte FC-72 and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for water.
Otherwise, heat capacity difference influences on the energy consumption
as well.
The amount of heat (320.490 MJ), which is required for the 1
[m.sup.3] water heating from 20 to 100[degrees]C, can be calculated by
equation:
[[??].sub.sot] = m[c.sub.p] [DELTA]T = [rho]V [c.sub.p] ([T.sub.3]
- [T'.sub.3]), (16)
where m is water density at the average temperature (958.4
kg/[m.sup.3] at 60[degrees]C); cp is water heat capacity at the same
temperature (4.18 kJ/(kg x K)).
Using the same Eq. (16) can be found an amount of heat (66.530 MJ),
which is required for the 1 [m.sup.3] electrolyte FC-72 heating from 20
to 56[degrees]C. In that case: 56[degrees]C is an electrolyte boiling
temperature at the atmospheric pressure; m is electrolyte density at the
average temperature (1680 kg/[m.sup.3] at 38[degrees]C); cp is
electrolyte heat capacity at the same temperature (1.1 kJ/(kg x K)).
Water heat capacity in comparison with the same of the electrolyte
is about 3.8 times higher. At the same time electrolyte boiling
(saturation) temperature is about twice less than for water. Therefore
the amount of the heat, necessary to reach a boiling point for
electrolyte, is about 4.8 times less than for water.
[FIGURE 14 OMITTED]
[FIGURE 15 OMITTED]
Fig. 15 shows the energy consumption for the electrolyte FC-72 when
the ratio of the hot body stabilized velocity to the cold body
stabilized velocity is 2.5 [7].
According to the Eq. (3), heat flux, necessary to achieve a boiling
crisis (Leidenfrost effect) and to form a stable vapour film in the
electrolyte is equal to 0.23 x [10.sup.3] W/[m.sup.2].
It is clear that the energy consumption, necessary to achieve
boiling crisis and to form a stable vapour film in the water
[q.sup.sphere] = 20 x [10.sup.3] W/[m.sup.2] is about 82.6 times higher
than that in the case of the electrolyte [q.sup.sphere] = 0.23 x
[10.sup.3] W/[m.sup.2]. Therefore boiling crisis application in order to
reduce drag force of the moving body, is reasonable in the case of
electrolyte, but is doubtful for the water case.
6. Conclusions
Hot and cold spherical bodies, moving in the water and electrolyte,
energy consumption preliminary comparison shows that:
1. Energy consumption of the hot body, moving in the electrolyte at
the velocity, higher than 1.0 m/s, is less than that of the cold body.
2. Energy consumption of the hot body, moving in the water at the
velocity, higher than 7.5 m/s (in the case if the hot and cold
bodies' velocity ratio is 2.5), is less than that of the cold body.
3. Energy consumption of the hot body, moving in the water at the
velocity, higher than 11.5 m/s (in the case if the hot and cold
bodies' velocity ratio is 1.2), is less than that of the cold body.
4. Energy consumption of the body, moving in the water, increases
with the increase of the velocity up to the 18 m/s. Velocity change from
18 m/s till 24 m/s acts on the energy consumption reduction. Further
velocity augmentation influences on the further energy consumption
growth.
5. Energy consumption, necessary to achieve boiling crisis on the
surface of the spherical body, moving in the water, is about 82.6 times
higher than that in the case of the electrolyte.
6. Hot body, surrounded by the vapor film, moves faster, but from
the energy economy view, boiling crisis application in order to reduce
drag force of the moving body, is reasonable in the case of electrolyte,
but is doubtful for the water case.
7. Estimation of the body's velocity influence on the
stability of the vapour film, generated on the body's surface, is
advisable to include into the further theoretical and experimental
investigations.
References
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[13.] Gylys, J.; Paukstaitis, L.; Skvorcinskiene, R. 2012.
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Received January 15, 2014
Accepted April 18, 2014
Jonas Gylys *, Raminta Skvorcinskiene **, Linas Paukstaitis ***
* Kaunas University of Technology, K. Donelaicio 20, 44239 Kaunas,
Lithuania, E-mail: jonas.gylys@ktu.lt
** Kaunas University of Technology, K. Donelaicio 20,44239Kaunas,
Lithuania, E-mail: raminta.skvorcinskiene@gmail.com
*** Kaunas University of Technology, K. Donelaicio 20, 44239
Kaunas, Lithuania, E-mail: linas.paukstaitis@ktu.lt
cross ref http://dx.doi.org/10.5755/j01.mech.20.3.6775
Table
Drag force of hot and cold spherical body
No. [w.sub.1], m/s [w.sub.2], m/s [F.sup.cold1.sub.D], N
N
1 0.81 2.03 0.047
2 1.62 4.05 0.189
3 2.43 6.08 0.426
4 3.24 8.10 0.758
5 4.05 10.13 1.184
6 4.86 12.15 1.705
No. [F.sup.cold2.sub.D], N [F.sup.hot.sub.D], N
N N
1 0.296 0.047
2 1.184 0.189
3 2.665 0.426
4 4.737 0.758
5 7.401 1.184
6 10.658 1.705