CONTENT
INTRODUCTION
6
1 GENERAL INFORMATION ON THE INFLUENCE OF AN EXTERNAL
ELECTRIC FIELD ON THE CHARACTERISTICS OF IGNITION AND
COMBUSTION
7
1.1 Problems of modern burner devices
8
1.2 The physical nature of the process of exposure of an external electric field
to a flame
10
1.3 The process of ionization in an electric field
13
1.3.1 Ionization in a collision
15
1.4 Effects of an external electric field on the main combustion parameters
17
1.5 Goals and objectives of the study
22
2 DEVELOPMENT OF A MATHEMATICAL MODEL
23
2.1 Ionization
24
2.2 Heat transfer
31
3 EXPERIMENTAL UNIT
37
3.1 Schematic diagram of the experimental setup
38
3.2 Equipment selection
40
3.2.1 Gas injection torch UG-16
40
3.2.2 Gas cylinder
42
3.2.3 Digital thermometer
44
3.2.4 Propane reducer BPO-5M
45
3.2.5 Gas meter SGBM-1.6 BETAR
47
3.2.6 Ionizer
48
3.2.7 Gas analyzer DAG-500
50
3.2.8 Industrial dryer
52
4 EXPERIMENTAL STUDIES
54
4.1 Test sequence and experimental design
4.1.1 Progress of the experiment
54
55
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4.2 Planning an experiment
56
CONCLUSION
67
REFERENCES
68
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INTRODUCTION
Heat power engineering in the modern world requires the creation and
implementation of new and modern solutions in production processes that will lead
to an increase in the efficiency of obtaining heat energy with an equivalent economic
effect.
The combustion process of fuel in heat power engineering is an integral part
of obtaining a hot heat carrier. The most common type of burned organic fuel in
Russia is natural gas. It, in turn, is used for a variety of technological processes in
various industries, as well as premises heating. All this entails large emissions of
harmful substances into the air.
Thus, focusing on the natural gas combustion is a reasonable solution that is
designed to increase the efficiency of burners and reduce the amount of nitrogen
oxide and carbon monoxide released into the atmosphere.
Based on the experience of the past years, it is possible to create a model and
conditions under which the control of combustion processes at the molecular level
will become real. When this effect is achieved, most processes that burn natural gas
will become more economical and environmentally friendly.
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1 General information on the influence of an external electric field on
the characteristics of ignition and combustion
It was established in [1], [2] that the combustion process of various types of
fuels, including natural gas, proceeds simultaneously with the ionization of
molecules and the separation of positive and negative charges along the entire
flame front.
Combustion is a complex process of conversion of starting materials into
combustion products, proceeding both from a physical and chemical point of view,
during exothermic reactions, accompanied by intense heat generation. This
phenomenon is used in almost all areas of life [3].
If we consider the flame as a stationary homogeneous system, then it will
not have any charge, i.e. is neutral. If we consider the flame as a laminar system, it
turns out that the distribution of charges occurs unevenly. The inner cone is a
region of flame with a negative charge, the outer cone is a region with a positive
charge [4]. From this it is concluded that flame is an electrical system with a
distributed electric charge. Therefore, if it is an electric system, then when it is
exposed to an electric field, a geometric change in the direction of the flame will
occur. Therefore, we can conclude that a chemical reaction occurs only at the
interface of the flame front, taking into account the different speeds of unlike
charges.
All this causes interest in studying the effect of an external eclectic field on
the combustion process. In the case of achieving a certain efficiency, it is fair to
say that this will increase the efficiency of power plants in which the application of
this solution is possible and appropriate.
At present, there is a rather large base of studies of previous years, which
have, in the majority, empirical data [2], [5]. Based on them, data that is obviously
fair and proven to have no result will not be considered in this paper.
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1.1 Problems of modern burner devices
One of the key aspects of the combustion process is mixture formation. As a
rule, it is carried out in the burner, which means that the mixture formation
precedes the occurrence of the flame front [6].
As it is known, the finished combustible mixture burns, but not its individual
components. Its formation requires time, which will be the determining parameter
of mixture formation and, therefore, will determine the speed of the process. This
gives reason to consider this process as a regulator of the burning rate and becomes
the principle of regulation of all main combustion processes. [7]
Until the mixture reaches the state in which it fully ignites, another stage
passes, that is called primary mixture formation. The ignition front arises already at
this stage, due to the fact that the fuel and oxidizer reach the minimum required
temperatures for ignition, provided that the required concentration is reached. In
order to accelerate the effect of increased temperature on the occurrence of the
ignition front, it is necessary to limit the supply of air, which requires heating, at
the initial stage (in the primary zone). Due to this, the total heat capacity of such a
mixture will decrease, which means that its heating will occur faster along with the
achievement of the required fuel concentration [6], [8].
All known manufactured burners, including multi-fuel ones, due to the lack
of quality of mixture formation require the supply of excess air, thereby spending
some of the combustion energy on its heating and significantly reducing the
temperature of the torch and flue gases. The disadvantages include the fact that in
case of incomplete combustion of the fuel, a significant amount of carbon
monoxide, soot and other harmful volatile substances are emitted. The use of
injection, swirling flows, artificial blasting and even the introduction of a pure
oxidizing agent (oxygen) do not solve the problem of complete burning of fuel.
This is due to the cluster nature of the gas structure. It is known that the reaction of
combustion (oxidation) of fuel begins on the contact surface of clusters with
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oxidizer clusters and moves relatively slowly towards the center of the clusters.
Theoretically, the simultaneous oxidation of fuel molecules is required. At present,
the problem of the destruction of clusters to structural molecules has been partially
solved [9], [10], [11] [12], [13]. In this case, the Coulomb forces with the speed of
propagation of the electromagnetic wave crush and mix the combustible mixture
into smaller clusters.
There are various ways to increase the efficiency of combustion processes,
for example, by ionizing an oxidizing agent (air) involved in the combustion
process. In the patent [12], it is proposed to ionize it before passing the oxidizing
agent into the combustion zone by passing it through an electrode grid equipped
with electric charge expanders. The use of the device according to this patent
makes it possible to reduce fuel costs by an average of 0.5-1.5%, increase the
efficiency of thermal units by 0.5-3%.
The solutions used in these patents allow a slight increase in the efficiency
of combustion processes, lower fuel costs, and increase the efficiency of fuel and
energy plants. However, in all these patents very complex electrode designs are
offered; there are no instructions on the placement of electrodes in the furnace
volume. There is no reference to the scientific research of these devices. Such
designs are difficult to technically put into practice and use. Moreover, in most
cases, it is proposed to conduct electric field treatment directly with a torch
(flame), where temperature ionization is already deeply developed.
This goal can be achieved due to the fact that ionized air is already present in
the burner region and, in the ignition start region, respectively, an ionized fuel
mixture is already present, which leads to the destruction of the cluster system of
vapors and gases [14].
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1.2
The physical nature of the process of exposure of an external
electric field to a flame
A stationary homogeneous flame is a system that has a neutral charge.
However, in a flame, particles are divided into charged and uncharged, which can
interact with an electric field [15].
The application of an external electric field to the flame leads to the
appearance of an ordered and directed movement of ions and electrons in the
combustion zone. Ions present in the flame begin to move toward oppositely
charged electrodes to achieve equilibrium of the system. This phenomenon in the
flame is called the ionic wind [2].
In the case of combustion of two pre-mixed environs, for example, in the
case of an injection burner, in the zone of the onset of reaction formation (preflame reaction), which develops at the flame front, the highest concentration of
positive ions is observed on the inside, and negative ions on the outside (on the
front). From this condition, if a negative potential is applied to the burner, positive
ions will move to the inner part of the flame, and negative ions - to the external,
along the flame front at the phase boundary [16].
In the case of combustion in a laminar flame, mainly everything happens
vice versa. In the zone of the onset of reaction formation, the highest concentration
of positive ions is also noted, where they subsequently remain, that is, on the outer
cone, and negative ions mainly move into the inner cone.
Such a separation of unlike charges is caused by different degrees of
mobility of positive and negative particles. The positive ions formed during the
chemical reaction have low mobility and therefore create mainly positive charges
at the place of origin, and the electrons formed as a result of the same reaction have
greater mobility, as a result of which they quickly leave the flame front, i.e. the
reaction formation zone, and form mostly negative charges on the inner cone [17].
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It is worth noting that in both cases the charged particles are distributed
unevenly and have a statistical distribution.
There is a general phenomenological feature by which an unstable state of a
nonequilibrium plasma differs from a stable one. It is most convenient to recognize
it by referring to the equation of electron kinetics written in symbolic form [18]:
dne
Z Z ,
dt
(1)
Where Z - the rate of appearance of electrons;
Z - the rate of disappearance of electrons.
These speeds are the result of the complex kinetics of collision processes.
The steady state corresponds to equality Z Z which satisfies the
stationary state of electron density ne . Resulting speeds Z , Z depend not only on
the electron density itself ne , but also, from other parameters:
- electronic temperature Т e ;
- negative electron density n (if sticking occurs);
- densities of excited atoms N * if the ionization of the latter by electron
impact plays a role.
Since all these parameters on which the speeds depend Z , Z are connected
by a system of differential equations, in the general case it is impossible to express
the quantities Z , Z through only the electron density at a given point in time.
If the number of parameters m is counted, which describe the state of a
weakly ionized molecular gas in a field: ne , n , n (taking into account space
charges n ne n ), Te , T vibrational temperature of molecules Tv , N , N * , E ,
typed ten quantities. It is clear that the analysis of the corresponding dispersion
equation, even if we obtain it, presents insurmountable difficulties [19], [20].
The way out of this situation is suggested by the assessment and comparison
of various parameters. In the study of a certain type of instability associated with
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the action of some main process and developing over time , usually it is possible
to process “fast” processes, which take much less time than . In some cases, it
can be processed and "slow" processes. Parameters that can be quickly established
can be considered quasistationary, assuming that they “follow” the slower change
in the determining parameters, instantly adjusting to their current values, as if the
latter were unchanged in time. Relatively slower processes, if they exist, we can
say that during the development of this instability, the corresponding parameters
do not have time to change at all and remain as if “frozen” [21], [22]. The situation
is completely analogous to that which takes place when considering relaxation
processes leading to the establishment of thermodynamic equilibrium in various
degrees of freedom of a heated gas.
The mechanism of propagation of a combustion wave in a gaseous medium,
which is associated with the process of molecular transfer, occurs as follows. The
heat contained in the reaction zone due to heat transfer between the particles in
contact, which plays a role at a sufficiently large temperature gradient in the
boundary layer, is transferred to the reagent region. Due to this, new volumes of
pre-mixed gas mixture are formed (primary mixture formation). The combustion
mode in this case is kinetic, since as soon as in this mode the rate of chemical
reactions depends only on the kinetics of the chemical reactions themselves. As a
result of all processes, flames are formed. These are modes with the ability to selfsustain the spread of the chemical transformation zone in space. The disadvantages
of this principle are:
- the inability to control the burning rate;
- problems of burning gas with preheated air;
- low flame resistance to its breakdown;
- low flame resistance to the phenomenon of slip [23].
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1.3 The process of ionization in an electric field
Ionization is the process of formation of ions from neutral atoms or
molecules while absorbing heat from the environment [24].
In a simple form, the ionization process is as follows (Picture 1.3.1).
Picture 1.3.1 - Ionization
The degree of ionization is the ratio of the number of ionized particles to the
total number of neutral particles per unit volume. For example, an ionization
degree of 30% will mean that 30% of the original particles have decayed into
positive ions and electrons. It is determined by the formula:
S
n
,
N
(2)
Where n - the number of ionized particles, pcs ;
N is the number of neutral particles, pcs .
Since ions of both positively and negatively charged, as well as free
electrons are located in a unit of conditional volume, it is necessary to understand
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their concentration. For this, the concept of unipolarity is introduced, which is
found as:
Sx
n p nn
N
,
(3)
Where n p - the number of negatively charged particles, pcs ;
nn - the number of positively charged particles, pcs ;
Depending on the calculated polarity, a plus sign is determined in the case of
finding the concentration of positive ions or a minus sign in the case of finding the
concentration of negatively charged ions [4].
The process of formation of positively charged ions: occurs only if sufficient
energy is obtained to overcome the potential barrier in an atom or electron. The
potential barrier is equal to the ionization potential.
The process of formation of negatively charged ions: occurs by the
formation of an additional electron, which is formed when it is captured by an
atom. The process takes place with the release of energy. The final product of this
reaction has more energy than individual source components. Visually, this process
is presented in Picture 1.3.2.
Picture 1.3.2 - The process of formation of a negative ion
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The ionization process, as a rule, requires a significant expenditure of
energy. For each substance, the ionization potential is different, but they all lie in
the range from 5 to 20 eV. In Table 1.3.1 the ionization potentials of the most
frequently occurring particles that are involved in the combustion process are given
[25].
Table 1.3.1 - Ionization Potentials
Substance
Potential, eV
Substance
Potential, eV
Substance
Potential, eV
H
13,595
Sr
5,692
CH 2
11.82 and 10.396
N
14,530
Ba
5,210
CH 3
9,905± 0,075
O
13,614
Pb
7,415
CH 4
13.06± 0.06
Ci
13,010
H2
15,427
CH 3O
9.2
Br
11,840
OH
13.18± 0.1
C2
12.0± 0.6
Li
5,390
H 2O
12.60± 0.01
C2 H
11.3
Na
5,138
CO
14.05± 0.05
C2 H 2
11.41± 0.02
K
4,339
O2
12,20± 0.2
C2 H 4
10.5± 0.1
Rb
4,176
CO2
13.84± 0.11
C2 H 6
11.65
Cs
3,893
NO
9.25± 0.02
C2 H 8
11.14± 0.07
Ca
6,111
CH
11.13± 0.22
CHO
9.88± 0.05
1.3.1 Ionization in a collision
If a particle of mass M 1 collides with a direct hit with a particle of mass M 2
at initial relative speed ur , it can be calculated the maximum amount of kinetic
energy that is converted into internal energy [26].
From the condition of conservation of momentum in the reference frame in
which the particle M 2 originally movable:
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M1ur M1u1 M 2u2 ,
(4)
i.e.:
u2
M u
2
1 r
M 1u12
M2
,
(5)
Where u1 - particle velocity M 1 after the collision m / s ;
u2 - particle velocity M 2 after the collision m / s ;
ur - constant speed m / s .
The amount of kinetic energy converted into internal energy, J :
U
1
M1ur M1u1 M 2u22 .
2
(6)
Substituting instead u2 in (6) expression (5) and differentiating U by u1 at
constant speed ur , we find the maximum condition U :
u1 u2
1 M 1M 2 2
ur ,
2 M1 M 2
(7)
i.e.:
U max
1 M1M 2 2
ur .
2 M1 M 2
(8)
In a simplified form, the chemical reaction of the two compounds will look
like this:
Collision ionization:
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A B A B e
(9)
A e A e e
(10)
A B A B
(11)
Electron transfer:
1.4 Effects of an external electric field on the main combustion
parameters
For a correct assessment of the effect of an electric field on the combustion
process, it is necessary to understand how it affects the basic parameters of the
process. The main parameters of the combustion process can be identified:
combustion temperature and flame speed.
The value of the normal flame velocity is found from the ratio according to
the theory of laminar spherical flame, m / c :
uн w f
T0
,
T*
(12)
Where w f - flame propagation speed m / с ,
T0 - initial temperature С ;
T * - fuel combustion temperature, С .
For a deeper understanding of the process, it is necessary to understand the
likelihood of a particular reaction. The probability characteristic in this case is the
cross section. Thus, the collision frequency of an electron with a neutral molecule
will be determined as, 1/ с :
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v Vn0 ,
(13)
Where V is the electron velocity (the true velocity in a collision with a molecule that is, thermal at low field strengths, directed at high intensities), m / с ;
- cross section of the reaction, m 2 ;
n0 - concentration of neutral molecules, m 3 .
Based on their unit size, we determine that the molecule is a ball. Collision
is the contact of surfaces. In this case, the collision frequency, based on the
condition that the reaction cross section will be equal to the cross-sectional area of
the ball, the mean free path will be as follows, m :
l
1
.
n0
(14)
Presented in section, in Picture1.4.1, the visual component of the molecule
gives a more detailed idea of the meaning of the cross section. The area of each
ring corresponds to the cross section of a specific reaction, and, therefore, the
larger the cross section of the reaction, the greater its probability [27], [28].
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Picture1.4.1 - A visual model of the cross section of a molecule in a section with
reaction rings
One of the most important parameters is the heat balance when an external
electric field is applied to a burning gas-air mixture [8]. It is defined as, W :
Tpn 4 T 4
Q pn ЭQk Ql Э k Fpn Tpn Ttn 5,67 Fpm
tn ,
100 100
(15)
Where Q pn - released heat power from the heating surface, W . We believe that it
is equal to the power supplied from the gases by electroconvection and
radiation;
Qk - emitted thermal power by convection, W ;
Ql - emitted thermal power by radiation, W ;
k - convection heat transfer coefficient during the movement of flue gases
at the heating surface without applying an electric field, W m 2 / К ;
Fpn - heating surface, m 2 ;
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T pn - the average temperature of the heating surface, K ;
Ttn - the average temperature of the coolant, K ;
- the degree of blackness of the heating surface.
The average temperature of the heating surface is defined as K :
Tpn1 Tpn 2 Tpn 3 ... Tpn ( n )
Tpn ( mn )
n
,
(16)
Where n - the number of thermocouples on the heating surface, pcs .
Thermal efficiency (thermal effect of applying an electric field) is defined
as, %:
Q
QЭ QPN
100,
QPN
(17)
Where QЭ - heat output with a field, W ;
QPN - heat output without field (control), W .
The effectiveness of reducing harmful substances is defined as, %:
NO
NOnO NOэ
100,
NOnO
(18)
CO
COnO COэ
100,
COnO
(19)
Where COnO - concentration of carbon oxides (carbon monoxide) in flue gases
without imposing an electric field;
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COэ concentration of carbon oxides (carbon monoxide) in flue gases in the
case of an electric field;
NOnO concentration of nitrogen oxides in flue gases without imposing an
electric field;
NOэ concentration of nitrogen oxides in flue gases in the case of an electric
field.
In [8], liquid butane gas was used as fuel with the composition: isobutane 72%, butane - 22%, propane - 6%.
The results of the experiment [8]:
- 12% reduction in gaseous fuel consumption;
- increase in the efficiency of the heat apparatus by 11.5%;
- 80% reduction in flue gas (CO) toxicity;
- reduction of nitric oxide and sulfur by 32-40%.
Based on these equations, we can conclude that an external electric field has
a positive effect on the process of burning gas fuel by bringing it to a more intense,
almost instantaneous mixing of oxygen and gas, which leads to an increase in
intensity, and as a result, the course of the combustion process in the most
complete volume, relative to a similar process without the participation of an
electric field.
Another undoubted advantage is the increase in the heat transfer coefficient
due to the same simultaneous combustion of fuel in the entire volume. This
parameter is variable and has a spasmodic character [29]. Due to ionization, it is
possible to increase the luminosity of the torch and increase heat transfer due to
radiation.
The application of an external electric field makes it possible to reduce the
coefficient of excess air in the combustion chamber by about 15% as mentioned in
[30], and it should be noted that the coefficient of excess air is initial 1.4. This
feature, together with the simultaneous combustion of fuel in full, leads to a
decrease in the amount of flue gases. In proportion to this, the volume of cold air
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drawn in, which no longer needs additional heating, is reduced. All this allows us
to conclude that the electric field increases the overall efficiency of the system.
1.5 Goals and objectives of the study
The aim of the dissertation research is to conduct experimental studies on
the effect of air ionization on the combustion process in an atmospheric type
burner.
The objectives of the dissertation research:
- do a comparative literature analysis of the
influence of the
electromagnetic field on the combustion process in atmospheric-type gas burners;
- on the basis of literature sources, analyze the mechanisms of air
ionization, as well as analyze the effect of ionized air and the electromagnetic field
on the combustion process;
- put a mathematical model of the process of ionization of air for
combustion, based on the theory of energy chains;
- make an elementary diagram of the experimental setup for studying the
effect of air ionization on the coefficient of excess air of a gas burner of
atmospheric type;
- mount an experimental setup for studying the effect of air ionization on
the coefficient of excess air of a gas burner of atmospheric type;
- conduct a complete factorial experiment and, on its basis, obtain a
regression equation for the dependence of the coefficient of excess air on the
burner load, temperature of the supplied air, voltage on the ionizer electrode.
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2 Development of a mathematical model
The development of the power system requires the introduction of new
economically sound and easy-to-use principles. devices and systems. Nowadays, the
use of the combustion process to generate energy when burning various types of fuels
plays a large role in the field of energy, metallurgy and other industries. Thus, 70% of
all energy currently produced comes from burning fossil fuels. It follows that the
efforts aimed at optimizing the combustion process, in order to increase its efficiency,
are very relevant, and at the same time should remain at the same level, and it is
better to reduce, the amount of harmful emissions from combustion products into the
atmosphere.
Electric charge is one of the ways to increase the enthalpy of combustion
products of various types of fuels. Based on the study of the peculiarities of the
influence of electric fields on combustion, it is possible to create new methods of
controlling combustion processes in power and technological installations that reduce
fuel consumption, reduce harmful emissions into the atmosphere and intensify the
combustion process [31].
In order to increase the efficiency of gas combustion and reduce the size of the
thermal units of the equipment, it is proposed to burn gas in the form of an ionized
mixture by acting on it with an electric field. In this case, instantly in the entire
volume at any point of the furnace, Coulomb repulsive forces begin to act, destroying
the cluster structure of the combustible mixture. Due to intense mixing, the process of
simultaneous burning of the torch, a significant increase in temperature, and its
luminosity increase.
The heating of the working surface already occurs to a greater extent due to
radiation in the infrared, visible and ultraviolet spectrum than by convective means
from hot gases. The amount of carbon monoxide is reduced.
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2.1 Ionization
The processes taking place, in the circuit with the ionizer, are considered using
the theory of chains. The energy circuit of one circuit, consisting of three links, is
presented in Picture 2.1:
Picture 2.1 - The energy chain of three links
The equation of the chain links:
2
P rV
P1
1
Z1)
,
V
l
P
V
1 1
1
(20)
2
2
P2 rV
rV
P4
2 2
3 3
Z2)
.
V
l
P
V
2 2 3
3
(21)
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We make calculations for Z1.
Equation on P :
(22)
V l1P1 V10 V1 ,
(23)
2
P 2V10V1 rV
1 10 2V10 l1 P1 P1 P10 .
(24)
P r1 V102 2V10 l1 P1 V1 P10 P .
Equation on V :
We introduce the coefficients:
a1 2V10 ,
2
a2 rV
1 10 ,
b1 2V10l1 ,
b2 1 ,
b3 P10 .
Equation on P taking into account the coefficients has the following form:
P a1V1 a2 b1 P1 b2 P1 b3 .
(25)
Applying the Laplace transform, we obtain the equation for the image:
(a1 1)V1 ( s) (b1P b2 1) P1 ( s) .
(26)
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Integrated circuit resistance:
Z1 ( p )
P1 ( p )
a1 1
,
V1 ( p )
(b1 P b2 1)
(27)
After substituting the entered coefficients:
Z1 ( p )
P1 ( p )
21
.
V1 ( p )
(0,04 P 2)
(28)
We make calculations for Z1.
Equation on P3 :
2
P3 rV
3 3 P4 ,
P3 2rV
3 30V3 P4 ,
(29)
(30)
V2 V30 2l2 rV
3 30V3 l2 P4 V3 .
Equation on V2 :
V22 V302 2 2l2 rV
3 30V3 l2 P4 V3 V30 .
Equation on P2 :
2
P2 r2V302 4r2 r3l2V302V3 2l2V30 PV
4 2 2V30V3 r2 rV
3 30 2rV
3 30V3 P40 P4 ,
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2
P2 4r2 r3l2V302V3 2r2V30 2rV
3 30 V3 r2 r3 V30 2l2 r2V30 P4 P40 .
(31)
We introduce the coefficients:
a1 4r2 r3l2V302 ,
a2 2r2V30 2rV
3 30 ,
a3 ( r2 r3 )V302 ,
b1 2l2 r2V30 ,
b2 P40 .
Equation on P2 taking into account the coefficients has the following form:
P2 a1V3 a2V3 a3 b1 P4 b2 .
(32)
Applying the Laplace transform, we obtain the equation for the image:
(a1P a2 1)V1 ( s) (b1 1) P1 ( s) .
(33)
Integrated circuit resistance:
Z1 ( p )
P4 ( p )
a P a2 1
.
1
V3 ( p )
(b1 1)
(34)
After substituting the entered coefficients:
Z1 ( p )
P4 ( p )
69,12 P 265
.
V3 ( p )
1,48
(35)
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Joint system solution:
Z12
a1 1
a P a2 1
1
ZZ
(b P b2 1)
(b1 1)
1 2 1
,
a1 1
a1 P a2 1
Z1 Z 2
(b1 P b2 1)
(b1 1)
(36)
a1 1
a P a2 1
1
(b P b2 1)
(b1 1)
Z Z12 r4 1
r
a1 1
a1 P a2 1 4
(b1 P b2 1)
(b1 1)
(37)
( a1 1)( a1 P a2 1)
(b1 P b2 1)(b1 1)
Z
r
( a1 1)(b1 1) ( a1 P a2 1)(b1 P b2 1) 4
(b1 P b2 1)(b1 1)
a12 P a1a2 a1 a1P a2 1
r4
a1b1 a1 b1 1 a1b1P 2 a1b2 P a1P a2b1P a2b2 a2 b1P b2 1
a
2
1
a1 P a1a2 a1 a2 1
a1b1 P 2 a1b2 a1 a2b1 b1 P a1b1 a1 b1 a2b2 a2 b2 2
r4
525P 2012,8
8.
P 2 53,8339 P 202,937
(38)
Frequency circuit function:
Z ( j )
a
2
1
a1 j a1a2 a1 a2 1
a1b12 a1b2 a1 a2b1 b1 j a1b1 a1 b1 a2b2 a2 b2 2
525 j 2012,8
8.
53,8339 j 202,937
2
r4
(39)
The real part of the frequency function:
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Re( j)
2012,8
8.
2 202,937
(40)
The imaginary part of the frequency function:
Im( j)
525
j 8.
53,8339
(41)
Frequency response of a circuit:
A( j) Re2 ( j) Im2 ( j) .
(42)
Phase-frequency characteristic of the circuit:
( j) arctg
Im( j)
.
Re( j)
(43)
Table 2.1.1 - the source data of the circuit
r1
r2
r3
r4
l1
l2
V10
V30
P10
P30
4
5
6
8
0,002
0,004
10
12
100
200
Table 2.1.2 - Values of the entered coefficients Z1
a1
a2
b1
b2
b3
20
40,000
0,04
1
100
Table 2.1.3 - Values of the entered coefficients Z 2
a1
a2
a3
b1
b2
69,12
264
4320
0,48
200
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Table 2.1.4 - Received data Z
Re
Im
A
1
-1,869714667
-1,752219326
2,562441317
-0,75296959
2
-1,726631777
-1,752219326
2,459985744
-0,792753203
3
-1,497161892
-1,752219326
2,304726947
-0,863731703
4
-1,193512289
-1,752219326
2,120081166
-0,972838352
5
-0,830510185
-1,752219326
1,939077032
-1,128183685
6
-0,423977869
-1,752219326
1,802783903
-1,333393053
7
0,010701088
-1,752219326
1,752252003
1,56468924
8
0,459644036
-1,752219326
1,811503577
1,314255406
9
0,911103519
-1,752219326
1,974938528
1,091299735
10
1,355714224
-1,752219326
2,215453368
0,912291052
We construct the amplitude-frequency characteristic (AFC) and phasefrequency characteristic (PFC) of the circuit.
Picture 2.1.1 - Frequency response of a circuit
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Picture 2.1.2 - Phase-frequency characteristic of the circuit
The frequency response graph has a clearly defined minimum, which
corresponds to a frequency of 7 rad / s, which is the most optimal for the ionization
process under consideration.
The phase response curve has two clearly defined inflection points of the
function: maximum and minimum in the frequency range from 6 to 7 radian per
second.
2.2 Heat transfer
A diagram of the energy chain is drawn:
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Picture 2.2.1 - Energy circuit for heat transfer
The equation of the chain links:
r2 q1 t2
t rq
1
q lt1 q1
,
(44)
t2 t20 t2
q1 q10 q1 .
(45)
The increment equation:
t1 r2 q1 t2 ,
t1 r2 q1 t2 .
(46)
q lt1 q1 lr2 q1 lt2 q10 q1 lt2 lr2 q1 q1 q10 .
(47)
Equation on q :
We introduce the coefficients:
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a1 l ,
b1 lr2 ,
b2 1 ,
b3 q10 .
Equation on P taking into account the coefficients has the following form:
P a1 t2 b1q1 b2 q1 b3 .
(48)
Applying the Laplace transform, we obtain the equation for the image:
(a1P)t2 ( p) (b1P b2 1)q1 ( p) .
(49)
Integrated circuit resistance:
Z ( p)
t2 ( p )
b P b2 1
.
1
q1 ( p )
a1P
(50)
Frequency circuit function:
Z ( j )
b1 j b2 1
b (b2 1) j
.
1
a1 j
a1
(51)
The real part of the frequency function:
Re( j)
b1
.
a1
(52)
The imaginary part of the frequency function:
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Im( j)
b2 1
j.
a1
(53)
Frequency response of a circuit:
A( j) Re2 ( j) Im2 ( j) .
(54)
Phase-frequency characteristic of the circuit:
( j) arctg
Im( j)
.
Re( j)
(55)
Table 2.2.1 - the source data of the circuit
n/n
r2
l
q10
1
10
50
500
2
5
70
200
3
20
20
900
Table 2.2.2 - Values of the entered coefficients Z1
n/n
a1
b1
b2
b3
1
50
500
1
500
2
70
350
1
200
3
20
400
1
900
Table 2.2.3 - Received data Z1
Re
Im
A
1
-10
0,04
10,00008
0,003999979
2
-10
0,02
10,00002
0,001999997
3
-10
0,013
10,00000889
0,001333333
4
-10
0,01
10,000005
0,001
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End of table 2.2.3
5
-10
0,008
10,0000032
0,0008
6
-10
0,0067
10,00000222
0,000666667
7
-10
0,0057
10,00000163
0,000571429
8
-10
0,005
10,00000125
0,0005
9
-10
0,004
10,00000099
0,000444444
10
-10
0,004
10,0000008
0,0004
We construct the amplitude-frequency characteristic (AFC) and phasefrequency characteristic (PFC) of the circuit.
Picture 2.2.1 - Chart response of a circuit
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Picture 2.2.2 - Phase-frequency characteristic of the circuit
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3 Experimental unit
In order to increase the efficiency of burning natural gas, compared with
traditional methods, and to improve burner devices without making a big change in
the design, it is proposed to burn natural gas in the form of an ionized gas-air
mixture. This process is carried out due to the influence of an external electric field
on the flame, or due to the preliminary ionization of the air supplied to the nozzle.
Regardless of the chosen ionization method, the Coulomb repulsive forces
begin to act in the entire volume of the flame, or rather, at each of its points. Due to
this, intense mixing of the gas-air mixture occurs [32], [33].
This leads to two key factors [34]:
- the amount of carbon monoxide (CO) at the outlet is reduced;
- increased heating of the working surface due to simultaneous radiation in
the infrared, visible and ultraviolet spectra.
Moreover, during ionization, the luminosity of the flame is enhanced due to
the burning of the flame and a simultaneous increase in temperature against this
background [35].
The novelty of this work is that we propose to burn the gas-air mixture not in
a standard way, but with preliminary ionization of the air, which will participate in
the mixture formation and subsequent combustion. The option of applying an
electric field to the flame is not considered due to the fact that this method has
limitations on use, and therefore cannot be applied in some cases. The conditions
under which pre-ionized air will be involved in the process of mixing are much
easier to create, which is the reason for the choice.
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3.1 Schematic diagram of the experimental setup
The schematic diagram of the installation is shown in Picture 3.1.1. which
includes 11 positions: gas cylinder 1, atmospheric type injection burner 2, pressure
reducer 3, pressure gauge 4, gas flow meter 5, combustion chamber 6, air ionizer 7,
industrial dryer 8, chimney 9, temperature sensors 10, 11.
The processes in the circuit are as follows. From a gas cylinder 1 through a
flexible connection, natural gas (propane) is supplied to an atmospheric-type
injection burner 2. A pressure reducer 3 with a pressure gauge 4 and a gas flow
meter 5 are installed on the gas line to control the pressure of the gas mixture at the
outlet of the cylinder 1 to operating pressure necessary for the correct operation of
the gas burner 2 and its maintenance, regardless of the pressure in the cylinder 1
and the gas pipeline. Air is supplied to the combustion chamber 6 through an air
ionizer 7 to ensure that only ionized air is supplied to the burner 2. Thanks to the
industrial hairdryer 8, it is possible to control the temperature of the supplied air to
the ionizer 7. When the gas-air mixture is burned in the combustion chamber 6, the
exhaust gases with a reduced amount of carbon monoxide, passing through the
chimney 9 are removed from the combustion chamber. Temperature sensors 10
and 11 record the temperatures in front of the ionizer 7 and in the chimney 9,
respectively.
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1 - gas cylinder; 2 - gas burner; 3 - pressure reducer; 4 - pressure gauge; 5 - gas
flow meter; 6 - a combustion chamber; 7 - air ionizer; 8 - industrial dryer; 9 chimney; 10, 11 - temperature sensors.
Picture 3.1.1 - Schematic diagram of the experimental setup
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3.2 Equipment selection
3.2.1 Gas injection torch UG-16
The gas injection torch UG-16 is made according to GOST 16569-86 and is
intended for heating furnaces. It is made of steel pipes in which equidistant
technological holes are made to allow uniform distribution of the flame throughout
the furnace volume. As a result, the design of the burner provides the declared
passport data on power with the optimal amount of heat received. The appearance
of this burner is shown in Picture 3.2.1.1.
Picture 3.2.1.1 - Appearance of an injection torch UG-16
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Variable nozzle throughput ensures stable flame burning without forced air
supply to the burner, which in turn ensures complete combustion of natural gas.
More deliberately, the burner, as one of the most important components, is
represented schematically in Picture 3.2.1.2.
1– valve; 2 - crane; 3 - gas distributor; 4 - nozzle; 5 - gas supply regulator; 6 frontal shield; 7 - main burner; 8 - ignition burner; 9 - reflector; 10 - inspection
damper; 11 - temperature sensor with a fixing screw; 12 - node mounting lever; 13
- spring; 14 - lever; 15 - bracket; 16 - valve button; 17 - gas pipeline ignition
burner;
Picture 3.2.1.2 - Gas injection torch UG-16 in isometry
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Technical characteristics are presented in table 3.2.1.
Table 3.2.1 - Technical characteristics of UG-16
Parameter Name
Values
Rated thermal power kW
16
Thermal power, kW
12
Nominal working gas pressure in the network, Pa
1274 or 1960
Heating area m 2
Up to 120
Fuel consumption, m3 / h
No more than 1,8
Gas pressure mb
13
Du connection for gas supply, mm
15
Dimensions, mm
300x340x415
Weight, kg
6
3.2.2 Gas cylinder
A gas cylinder is a vessel operating under excessive internal pressure. It is
designed to transport and store industrial gases such as propane ( C3 H 8 ), butane (
C4 H10 ) and mixtures thereof. This gas cylinder is welded and consists of a shell,
bottom and neck. It is made of steel that can withstand internal and external loads,
while not violating the original properties of the technical gases that are in it. In
accordance with GOST 949-73 has a red color and a white inscription. In
accordance with safety rules and operating rules, a valve VB-2 and a valve KB-2
are installed on it. The appearance of the gas cylinder is shown in Picture 3.2.2.
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Picture 3.2.2 - Gas cylinder NZGA 27 liters
Technical characteristics of this cylinder are presented in table 3.2.2.
Table 3.2.2- Technical characteristics of the gas cylinder NZGA
Parameter Name
Values
Gas type
propane
A type
welded
Volume l
27
Material
high alloy steel
Operating pressure, MPa
2,5
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End of table 3.2.2
Dimensions, mm
600x280x280
Weight, kg
12
3.2.3 Digital thermometer
A digital thermometer is a device for measuring temperature. As a
thermosensitive element, external temperature sensors are used - resistance
thermocouples. The main component of this thermometer is an analog-to-digital
converter, which operates on the principle of modulation, that is, the conversion of
one or more (up to 4) information signals of the converter in accordance with the
instantaneous values of information signals from sensors. The power supply is due
to the stable voltage by including a 9 V battery in the circuit. The appearance of the
digital thermometer is shown in Picture 3.2.3.
Picture 3.2.3 - Digital thermometer 2D02
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Technical characteristics of this thermometer are presented in table 3.2.3.
Table 3.2.3 - Technical characteristics of a digital thermometer 2D02
Parameter Name
Values
Connection form
K-type
Number of channels pcs
4
Measuring range C
-50 to +1350
Accuracy of measurements, C
0.015% + 1
Working humidity%
10-90
Material
ABS plastic
Probe length m
0,95
Number of probe sensors pcs
4
Power Supply, V
9
Dimensions, mm
170x100x46
Weight, kg
0,23
3.2.4 Propane reducer BPO-5M
Propane gearbox is a device designed to control, maintain and create the
necessary pressure coming from a power source (gas bottle). The reducer joins a
cylinder with a union nut. When the adjustment screw is rotated clockwise, the
force of the compression spring is transmitted through the pressure plate,
diaphragm and pusher to the pressure reducing valve, which, moving, opens the
gas passage through the gap formed between the valve and the seat into the
working chamber. Existence of the manometer provides control of pressure in the
chamber of working pressure. The appearance of the propane gearbox is shown in
Picture 3.2.4.
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Picture 3.2.4 - BPO-5M propane gearbox
Technical characteristics of this gearbox are presented in table 3.2.4.
Table 3.2.4 - Technical characteristics of the propane gearbox BPO-5M
Parameter Name
Values
Max working pressure MPa
0,3
Max bandwidth m3 / h
5
Inlet pressure bar
25
Gas type
propane
Material
brass
Dimensions, mm
145x138x94
Weight, kg
0,43
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3.2.5 Gas meter SGBM-1.6 BETAR
Small-sized gas meters SBGB are designed to measure gas volume when
taking into account gas consumption by individual consumers in housing and
communal services. The Betar SGBM-1.6 gas meter has an electronic display that
shows the amount of gas used. The meter is powered by a built-in lithium battery.
The appearance of the counter is shown in Picture 3.2.5.
Picture 3.2.5 - Gas meter SGBM-1.6 BETAR
Technical characteristics of this counter are presented in table 3.2.5.
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Table 3.2.5 - Technical characteristics of the gas meter SGBM-1.6 BETAR
Parameter Name
Values
Air consumption, m3 / h
1,6
Measurement range, m3 / h
0,04 ... 1,6
Max working pressure kPa
5
Temperature range C
-10 ... 50
Material
steel
Dimensions, mm
70x88x76
Weight, kg
0,67
3.2.6 Ionizer
An air ionizer is a device designed to enrich air with negative ions. It works
on the basis of the electroeffluvial aeroionization method discovered by Professor
A. L. Chizhevsky. Working bodies - high-voltage voltage generator (GVN). The
operation diagram of the high voltage generator is shown in Picture 3.2.6.1.
Electroeffluvial emitter (EI)
PNZPT - voltage converter with a DC link; APU - rectifier - matching device.
Picture 3.2.6.1 - block diagram of the GVN
The ionizer works as follows: when the ionizer is connected to the network
220 V with a frequency of 50 Hz , PNZPT is converted into a sequence of highvoltage pulse voltages of increased frequency and, according to Picture 3.2.6.1, is
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fed to a rectifier-matching device (APU). From the output of the APU, a constant
negative voltage, which is necessary for the effective operation of the ionizer, is
supplied to the electro-effusive emitter (EI). As a result of this, electrons flow into
the air, which, when combined with oxygen molecules, then form negatively
charged oxygen ions. They are under the influence of a constant electric field
equidistant from the source in all directions. Due to this, the air mass is filled with
negative air ions. Electric charges flow from all dead-end surfaces to all grounded
objects.
The appearance of the ionizer is shown in Picture 3.2.6.2.
Picture 3.2.6.2– Appearance of an air ionizer
Technical characteristics of this ionizer are presented in table 3.2.6.
Table 3.2.6- Technical characteristics of the Effluvion-02 air ionizer
Parameter Name
Values
AC voltage V
220
Frequency, Hz
50
The voltage at the output of the high voltage source (IVN), kW
20 5
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End of table 3.2.6
Effective air ionization volume not less than m 3
50
Continuous operation time, no more h
8
Ionizer power consumption from the network no more W
30
Dimensions, mm
364x281x66
Weight, kg
2
3.2.7 Gas analyzer DAG-500
A gas analyzer is a device designed to control emissions of harmful
substances and optimize the operation of fuel installations by monitoring the
content of the following components in the exhaust gas: oxygen, carbon monoxide,
nitric oxide, sulfur dioxide, nitrogen dioxide.
The DAG-500 gas analyzer is a high-end multifunctional measuring
instrument, the wide possibilities of which can be most fully manifested under the
condition of competent instrument maintenance. It can be used for technical
monitoring and use in various fields, including chemistry, the development of
various technologies, the creation of fuel plants and engines. The device provides
optimization of technological processes, thereby reducing fuel consumption and
emissions of harmful substances.
The DAG-500 gas analyzer is a complete portable multifunctional device
with means for sampling, data processing and recording the result on thermal paper
and electronic information carriers. The instrument kit includes:
- the actual gas analyzer, which includes all the main components of the
measurement, processing and registration;
- a probe with a thermocouple, a compensation wire, a gas hose, a
condensate trap with an integrated filter for cleaning the measured gas;
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- a power supply unit that ensures the operation of the device and charging
the internal battery from the network;
- a case intended for laying the gas analyzer kit inoperative.
The appearance of the gas analyzer is shown in Picture 3.2.7.
Picture 3.2.7 - Appearance of the DAG-500 gas analyzer
Technical characteristics of this gas analyzer are presented in table 3.2.7.
Table 3.2.7 - Technical characteristics of the gas analyzer DAG-500
Parameter Name
Values
Memory
internal non-volatile, capacity of 200 records
Interface
RS-232
200 seconds at O2-20.9%
Calibration
СО-SO2-NO-NO2 = 0 ppm in fresh air
network - 220 V /50 Hz via remote source 12 V - 500 mA
Power supply
autonomous - from the built-in battery 6 V , 1.2 Ah
Battery Charge Time
no more than 14 hours, with protection against recharge
Battery life
at least 5 hours (without backlight), with discharge control
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End of table 3.2.7
Operating temperature C
+10 ... + 40
Storage temperature C
-20 ... + 50
probe length 300..1500 mm with heat insulating handle
Gas intake probe
type K (XA) built-in thermocouple and support cone
Device dimensions mm
220x110x70
Instrument weight kg
1.3
Case sizes mm
390x150x150
The total mass of the kit, kg
5,0
3.2.8 Industrial dryer
An industrial dryer is a tool with many names, probably for the reason that it
is one of the most common and widely used tools in everyday life and in
production.
Its structure is simple: an industrial dryer consists of a spiral heating an air, a
fan supplying air heated by a spiral, and an electric motor with which the fan
works. An industrial dryer is distinguished from an ordinary dryer by which hair is
dried, with a power of 930-2300W , temperature and amount of air blown out.
Typically, industrial dryers have the same characteristics: delivers heated to a
temperature of 500-600 C air, and blows - from three hundred to five hundred
liters per minute.
The appearance of the industrial dryer is shown in Picture 3.2.8.
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Picture 3.2.8 - Appearance of the industrial dryer Interskol FE-2000E
Technical characteristics of the Interskol FE-2000E industrial dryer are
presented in table 3.2.8.
Table 3.2.8 - Technical characteristics of the industrial dryer Interskol FE-2000E
Parameter Name
Values
Power, W
2000
Air consumption, l / min
300-500
LCD display
not
Working temperature, C
80-600
Temperature adjustment
smooth
overheat protection
Yes
Dimensions mm
260x80x200
Weight, kg
0.8
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4 Experimental studies
4.1 Test sequence and experimental design
Any research begins with goal setting. The choice of a problem for study
and its formulation affects both the research model and the conclusions that will be
drawn from its results.
After choosing the goal of work, it should be determined the dependent
variables. These are the variables that will be measured during the study.
Since there are dependent variables, there must also be independent
variables. They are called factors. The researcher operates the factors in the
experiment. The relationship between the factor and the dependent variable is
conveniently represented using a cybernetic system, often called the “black box”.
A black box is a system whose operating mechanism is unknown to us.
However, the researcher has information about what happens at the inlet and outlet
of the black box. In this case, the state of the output functionally depends on the
state of the input.
The combination of all possible states determines the complexity of the
black box. So, a system of ten factors at four levels can be in more than a million
different states. Obviously, in such cases it is impossible to conduct a study that
includes all possible experiments. Therefore, at the planning stage, the question is
solved about how many experiments and which ones are necessary to carry out to
solve the problem.
In practice, there are no fully managed objects. Both managed and
uncontrolled factors act on a real object, which leads to variability of the results
between individual objects. We can only separate random changes from natural
ones caused by various levels of independent variables using statistical methods.
The next step in planning experiments is randomization. Randomization is a
process used to group objects in such a way that each of them has an equal chance
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of falling into a control or experimental group. In other words, the choice of
research parameters should occur randomly, so that the study is not rejected in the
direction of the "preferred" result for the researcher.
Randomization helps prevent biases due to causes that were not directly
accounted for in the experiment. The randomization process is easy to implement
using specialized statistical software or tables [36].
4.1.1 Progress of the experiment
The beginning of the experiment begins with a visual inspection of all the
nodes of the experimental setup. After that, the gas supply opens on the cylinder,
which is regulated by a reducer with a pressure gauge. Gas passing through the
meter enters the burner. The valve for supplying gas to the nozzles opens and
ignition is carried out through the pilot burner. Thus, the burner enters the
operating mode. After that, the digital thermometer is turned on, and the
temperature from the probes is displayed. Next, an air ionizer and a gas analyzer
are turned on. The last one turns on an industrial dryer, on which the temperature
of the blown air is set.
To conduct an experiment, it is necessary to adjust the parameters. During
each experiment, several of them were regulated at once.
The first is a gas supply. It was controlled by opening and closing the
adjusting knob, which reduced the flow area, thereby reducing the gas supply,
which was monitored by the gas flow meter.
The second is the voltage applied to the ionizer. It is controlled by the output
voltage stage selector. Due to this, a high voltage generator is affected and the
number of ions in the air decreases in direct proportion to the output voltage.
The third is the temperature of the air supplied to the ionizer. It is regulated
by lowering the temperature on an industrial hairdryer or by removing it to a
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greater distance. To more accurately determine the temperature that enters the
input to the ionizer, a temperature sensor is installed for more precise adjustment.
Fourth is the coefficient of excess air. It is regulated thanks to the gas
analyzer. The probes are mounted above the chimney in such a way as to capture
the concentration of carbon monoxide in the exhaust products of combustion.
Thanks to these readings, the gas analyzer calculates the coefficient of excess air.
If the concentration of carbon monoxide begins to increase, then this is a sign that
less air cannot be supplied. The air supply itself is limited by a gate, which
prevents direct air from entering the burner.
After conducting all experiments, the results are recorded in the table, and
the installation is turned off in the reverse order.
4.2 Planning an experiment
It is necessary to study the influence of the parameters of the flame
ionization process on its combustion. Excessive load of the burner device, supplied
voltage must be within certain limits, deviation from which leads to an increase in
the coefficient of excess air and, as a consequence, a decrease in the efficiency of
the installation as a whole. Based on the results of tests of previous years, it was
found that the value of the coefficient of excess air most fully determines the
combustion process, and it has limitations on the lower limit at which the
efficiency decreases due to an increase in the content of carbon monoxide in the
combustion products [37], [38], [39]. Therefore, the coefficient of excess air is
selected as an effective sign. Variable factors adopted [41], [42], [43], [44]: burner
load factor K3 voltage supplied by the transformer at the output U ambient
temperature Toв . The selection of factor equations and their coding are given in
table 4.1.1.
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Table 4.1.1 - Selection of factor equations, factor coding
Level of Variable
Factors
K3 , %
U , kv
Toв , С
X1
X2
X3
Code designation
Lower level
-1
30
20
20
Upper level
+1
100
45
150
Main level
0
65
32,5
85
Range of variation
xi
35
12,5
65
To assess the influence of these factors and the mathematical description of
the process, we use a first-order model [40]:
y b0 b1 X 1 b2 X 2 b3 X 3 b12 X 1 X 2 b13 X 1 X 3 b23 X 2 X 3 b123 X 1 X 2 X 3 .
(56)
A full factorial experiment (PFE) is an experiment in which all possible,
non-repeating combinations of factor levels are realized.
The number of experiments in PFE is determined in accordance with table 2.
Usually there are plans for an experiment of the type 2k (two levels of variation of
factors), less often 3k and very rarely with p n due to the sharp increase in the
number of independent experiments (table 4.1.2).
Table 4.1.2 - the Number of experiments N p k
k
p
2
3
4
2
4
8
16
3
9
27
81
4
16
64
256
Experimental conditions are usually written in the form of experiment
planning matrices (table 4.1.3), where the rows correspond to various independent
experiments and the columns correspond to the values (levels) of factors.
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Table 4.1.3 - Experiment Planning Matrix 23
Experience
X0
X1
X2
X3
y
1
+
-
-
-
y1
2
+
+
-
-
y2
3
+
-
+
-
y3
4
+
+
+
-
y4
five
+
-
-
+
y5
6
+
+
-
+
y6
7
+
-
+
+
y7
8
+
+
+
+
y8
Number
In PFE there are various levels of interaction of factors. Table 4.1.4 shows
such interactions.
Table 4.1.4 - Planning matrix PFE 23 taking into account the interaction of factors
Experience
X0
X1
X2
X3
X1 X 2
X1 X 3
X2 X3
X1X 2 X 3
y
1
+
-
-
-
+
+
+
-
y1
2
+
+
-
-
-
-
+
+
y2
3
+
-
+
-
-
+
-
+
y3
4
+
+
+
-
+
-
-
-
y4
five
+
-
-
+
+
-
-
+
y5
6
+
+
-
+
-
+
-
-
y6
7
+
-
+
+
-
-
+
-
y7
8
+
+
+
+
+
+
+
+
y8
Number
Generally, plans like 2k geometrically represent a collection of points located
at the vertices of a hypercube located in a multidimensional space. The space
enclosed within the hypercube is the area of experimental design.
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PFE Planning Matrix 23 taking into account the interaction of factors is
presented in table 4.1.4. To determine the coefficient of excess air during the
ionization of air supplied to a gas burner of atmospheric type, it is planned to
conduct three parallel experiments in each row of the PFE matrix, a total of 24.
The experiments are randomized using a random number table. For example,
starting from the second column of the table, we write numbers from 1 to 24,
discarding more than 24 and repeating, then the table of the experiments has the
form (table 4.1.5).
Table 4.1.5 - the order of the experiments
Planning Matrix
Experience
1
2
3
4
five
6
7
8
24
19
4
9
5
21
7
8
10
15
2
23
12
14
13
16
22
20
1
3
17
6
11
18
Number
Random
procedure for
implementing
experiments
It is necessary to carry out statistical processing of the initial data: determine
the absolute and relative measurement errors, discard the errors and correctly
record the measurement result.
Following the algorithm for processing the results, we determine the
arithmetic mean value of the quantity y1 , y2 ... yn for the whole experiment:
y y2 ... yп 1
y 1
N
N
y
N
y ,
i 1
i
(57)
1,92 1,93 1,92
1,923 .
3
Where N - number of experiments.
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Next, it is needed to find the mean square error of the result separately for
N measurements (measurement method error):
y y
N
N
N
S
1,923 1,92
2
S
2
i
i 1
N 1
(58)
,
1,923 1,93 1,923 1,92
0,0058 .
2
2
2
Find the standard deviation of the arithmetic mean (the error of the result of
a series of measurements):
n
n
Sy
Sy
n
S
,
n
(59)
0,0058
0,003 .
3
Find confidence intervals y for y (absolute error of a series of
measurements).
We set the confidence probability (for most engineering experiments
choose 0,95 )
Table value t ( ; n ) based on the number of measurements and a given
confidence probability will be equal to 2,360.
We calculate the value of the confidence interval x :
y n S y t , n ,
(60)
y 0,003 2,360 0,0071 .
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As a result, we find relative error of the result of a series of measurements:
y
х
y
,
y
(61)
0,0071
0,0037 .
1,923
The value of the random error in the case of the number of experiments N
less than 10 is allowed in the range of 15-20%. In our case, the percentage error
was 3.7%, which satisfies the condition for a correct experiment.
The test results carried out in accordance with the planning matrix and the
data in table 4.1.5 are presented in table 4.1.6.
Table 4.1.6 - Test results
Excess air ratio
Experience
Si2
y y
i
i
2
Number
yi1
yi 2
yi 3
yi
yi
1
1,92
1,93
1,92
1,92
1,92
0,00003
2,5 105
2
1,41
1,40
1,39
1,40
1,41
0,00010
2,5 105
3
1,65
1,67
1,65
1,66
1,65
0,00013
2,5 105
4
1,35
1,34
1,33
1,34
1,35
0,00010
2,5 105
5
1,76
1,77
1,76
1,76
1,77
0,00003
2,5 105
6
1,32
1,30
1,31
1,31
1,31
0,00010
2,5 105
7
1,61
1,62
1,61
1,61
1,62
0,00030
2,5 105
8
1,28
1,27
1,25
1,27
1,26
0,00023
2,5 105
The dispersion of the entire experiment, that is, the measure of the scatter of
the values of a random variable relative to its mathematical expectation, is defined
as:
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S 2 ( y)
S 2 ( y)
1
N
N
S
i 1
2
i
,
(62)
0,00077
0,000096 .
8
Where N - number of experiments;
N
S
i 1
2
i
- the sum of the weighted average dispersion values, taking into
account the number of degrees of freedom.
After calculating all the coefficients, equation (56) takes the form:
y 1,534 0, 205 X 1 0,065 X 2 0,046 X 3 0,039 X 1 X 2
0,005 X 1 X 3 0,017 X 2 X 3 0,013 X 1 X 2 X 3 .
(63)
Error in determining the coefficients:
Sb
Sb
S ( y)
,
Nr
(64)
0,009789
0,001998.
83
Where S ( y ) - error of the whole experiment;
r - the number of parallel experiments.
To identify the significance of the coefficients of the regression equation, we
construct a confidence interval with a width of:
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2b tT Sb ,
(65)
2b 1,746 0,001998 0,00698.
Based on the value of the confidence interval, the tabular value of t-student
test 0,05 and the number of degrees of freedom d . f 16 , it turned out that the
coefficient b13 turned out to be statistically insignificant, therefore, the regression
equation is rewritten and has a new form:
y 1,534 0, 205 X 1 0,065 X 2 0,046 X 3 0,039 X 1 X 2
0,017 X 2 X 3 0,013 X 1 X 2 X 3 .
(66)
Estimated Values yi are given in table 4.1.6.
A graph of the coefficient of excess air when changing the load factor of the
burner K3 (chart 4.1.1):
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2
1,9
Excess air ratio, α
1,8
1,7
Х2=1, Х3=-1
1,6
Х2=-1, Х3=-1
Х2=-1, Х3=1
1,5
Х2=1, Х3=1
1,4
1,3
1,2
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
Х1
Picture 4.1.1 - Dependence burner load factor K3
The dependence of the coefficient of excess air when changing the voltage
supplied by the transformer at the output U (chart 4.1.2):
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2
1,9
Excess air ratio, α
1,8
1,7
Х1=1, Х3=-1
1,6
Х1=-1, Х3=-1
Х1=-1, Х3=1
1,5
Х1=1, Х3=1
1,4
1,3
1,2
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
Х2
Picture 4.1.2 - Dependence from voltage U output transformer
The graph of the coefficient of excess air from changes in ambient
temperature Toв (chart 4.1.3):
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2
1,9
Excess air ratio, α
1,8
1,7
Х1=1, Х2=-1
1,6
Х1=-1, Х2=-1
Х1=-1, Х2=1
1,5
Х1=1, Х2=1
1,4
1,3
1,2
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
Х3
Picture 4.1.3 - Dependence from ambient temperature Toв
With an increase in all factors in the accepted range, a decrease in the
coefficient of excess air in the range from 1,92 to 1,26 is observed. With fixed
factors X 1 1 X 2 1, Y varies from 1,652 to 1,618. With fixed factors
X 1 1 X 2 1, Y varies from 1.405 to 1.305. With fixed factors X 1 1 X 2 1, Y
varies from 1,345 to 1,262, which is the best result.
The greatest influence of ionization has on the coefficient of excess air while
reducing the load of the burner device, according to graph 4.1.1. Based on the
experimental data, it can be concluded that ionization has a greater effect on the
coefficient of excess air than an increase in the temperature supplied to the burner.
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CONCLUSION
Comparative analysis of literature sources, past experience in air ionization,
and means of influence on the combustion process of electric charge found that the
use of ionized air as an oxidizer was proven to have a positive effect.
Analysis of literature sources has shown that the most acceptable way to
ionize air for combustion is to influence the air with an electromagnetic field.
As a result of theoretical research, a database was formed, which later made
it possible to narrow the number of experiments and focus on the most significant
parameters.
Based on the gotten energy chains it was found that amplitude-frequency
response characteristic graph has a distinct minimum that corresponds to the
frequency of 7 radian per second, and the phase-frequency characteristic graph has
two distinct inflection points of a function: a maximum and a minimum in the
frequency range from 6 to 7 radian per second.
An elementary scheme of the experimental installation was compiled, on the
basis of which it was assembled. This installation allows to perform experiments to
determine the effect of air ionization on the combustion process.
A complete factorial experiment of the influence of the ionization process on
the excess air coefficient in an atmospheric type burner was performed. As a result,
a regression equation was constructed for the dependence of the excess air
coefficient on the burner load, the temperature of the supplied air, and the voltage at
the ionizer electrode, showing that all the factors significantly affect the excess air
coefficient. With an increase in the value of factors in the experimental range, there
is a decrease in the excess air coefficient by 34%.
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