Picture 1 – Chart of the NK OVG breaking up on areas
Vitaly
Berkovsky
Faculty: Physico-metallurgical
Speciality: Industrial heating technology's
Subject of master's work: Development of the thermal mode of the impulsive heating
well with one overhead gas-ring on the basis of the
complex zonal attended model.
Scientific adviser: Ph.D. Yu. Kurbatov
E-mail: bervit07@rambler.ru In rental
production of black metallurgy for heating of steel purveyances before
treatment by pressure the fuel stoves of periodic action are
used, thus some of them thanks to the compactness of location in
a workshop are had by the high group indexes of productivity being on a 1 m2 area of
workshop. Such indexes turned out possible due to the assimetrichnogo location of
torch and teploispolzuyushih devices (recuperators), that in same queue defined
the substantial failing - considerable unevenness of
distributing of temperature on a volume working chamber. For
example, in some chamber stoves for heating of steel bars
which in metallurgy are accepted to name nagrevatelnimi
wells with heating by one overhead gasring (NK
OVG), the most high temperature is observed in overhead part of
well vblizi a frontal wall, where usually produce
measuring of temperature by termoparoy of the system of adjusting,
(t9, the pic. 1), and the most cold region is
disposed in lower part of
the working chamber NK OVG – vblizi dimootvodyashego channel
(t18, pic.1). The overfall of temperatures between these points arrives at 300ºС
(at the level of the temperatures 1250 - 1350ºС) in the initial period of heating,
that results in the uneven heating of bars in sadke consisting of 16 – 20 bars,
to the increase of duration of heating of all sadki, and,
consequently, and rise of specific expense of fuel.
For the of many years
period of the industrial use NK OVG the row of methods of decline of
unevenness of the temperature field is offered: application of swinging gasrings;
application of the swinging torch declined by the
visokoskorostnoy stream
of the compressed air; setting of protective wall before a dimootvodyashim
channel; setting of additional ploskoplamennih gas-rings in
the lateral walls of working chamber and dr. The
offered methods partly decided a task, but turned out either enough difficult in
exploitation, or resulted in worsening of the use of useful area of stove, or
resulted in the loss of the above all NK OVG dignity – compactness of location in
a workshop.
One of the known methods
of decline of unevenness of the temperature field in NK OVG is the
impulsive heating which consists in the continuous serve of fuel in the
period of self-control of metal in the set interval of
temperatures. Switching from the minimum expense of fuel (Bmin) to maximal (Bmax) one is carried out at the
overfall of temperatures in working space of stove between hot and cold points,
equal ∆tк = ∆tн*k, and
switching from the maximal value (Bmax) to minimum (Bmin) one – under reaching the set
temperature in the hot point of working space of stove, where ∆tн - overfall of
temperatures in hot (t9)
and cold (t18)
points in the moment of switching with Bmax on Bmin; ∆tк - overfall of temperatures in hot and cold points in the moment of
switching with Bmin on Bmax; k - coefficient of
smoothing. Switching are produced with
forestalling allowing to eliminate sharp skachki
of pressure in a working chamber. Dignity of
the impulsive heating NK OVG consists in absence of necessity of some changes
in construction of stove for the receipt of the even heating, and the
poperemennoe heating of sadki by «long and «short» torches» is instrumental in
smoothing of temperature in a working chamber. Depending on
quality of management by the impulsive heating it is possible increase of
productivity and specific cost cutting of fuel on 6 – 10%.
Complication in
realization of the impulsive heating is insufficiency
of information about the temperature field of stove and heated metal, necessary
for determination of moment of the timely switching of
fuel. It is possible for
the receipt of complete information to apply the mathematical attended zonal
model of burning of fuel and heat exchange, which consists of joint decision of
tasks of the unstationary temperature fields of metal and obmurovki (laying),
thermal zonal balance and function of burning down of
fuel. A model foresees the division of working chamber on
by a volume computation areas (the pic. 1):
on a vertical line – on overhead and lower, on
a horizontal line – on the number of bars which are located in one row, for
example, for NK OVG with sadkoy 100 t and mass of bar a 5, 56
t common number of areas equally 18.
Picture 1 – Chart of the NK OVG
breaking up on areas
In accordance with the chart of breaking up of well on areas
(pic.1) can be selected
on three types of equalizations of thermal balance for overhead and
lower areas:
For extreme, fellow
creature to the gasring,
the areas 1:
for areas 2 –
8:
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for the extreme
distant area 9:
for the area 10:
for the areas
11-17:
for the area 18:
where a - coefficient of
burning down of fuel in an area; В - expense
of fuel; Qнр - warmth of combustion
of fuel; Vг, сг - output of products of combustion (gases) on unit of fuel and
heat capacity of gases; tг - temperature of gas; Lд, св - actual
expense of air on unit of fuel and heat capacity of air; tв - temperature of
air; Q - power of radiation from an area in an area; м - is
a metal; г - gas; к - laying (obmurovka); u - number of area.
At the decision of task the period of heating
is broken up on steps at times, the values of which are determined by the
decision of internal task. From equalization of thermal balance on
every step the temperature of gas (mixtures of products of combustion and air)
in every area of tru, which is used further as a border
condition for the decision of unstationary task for a bar and obmurovki of
stove, is determined at times.
In a model the function of
burning down of fuel on length of stove is taken into account, difficult
radiation heat
exchange between the products of combustion, internal
surface of the heat-resistant laying and surface of metal. The function of
burning down of fuel is adopted on the basis of experimental data and
can be corrected at their accumulation. For example,
function of burning down for the long torch (at Bmax) aumax and for short (at Bmin) aumin are resulted on the pic. 1. Except for
it, in a model a heat exchange is taken into account between neighbouring areas and
pereizluchenie from overhead areas in lower,
and also heat exchange between the element of surface of the heated bar and
elements of surface of neighbouring bars, internal
surface of obmurovki, gas volumes of lower and overhead areas.
The
temperature field of metal is determined by the decision of three-dimensional
task of heat conductivity:
with
the scope terms of III family:
where λ - coefficient
of heat conductivity of metal, ρ - closeness of metal, c - heat capacity of metal, aлуч - coefficient
of heat emission by the radiation, aконв - coefficient
of heat emission by convection, tпеч - temperature of stove, which
the temperature of conditional absolutely black emitter giving a thermal stream
on the heated metal as a sum of thermal streams from gases and laying is, and, which is usually measured by termoparoy or radiation
pyrometer and is used in the systems of adjusting:
where εгкм – the resulted
degree of blackness in the system «gas – laying ‑ metal» εпеч м ‑ the resulted degree of blackness in the
system to be «stove ‑ metal», Тг – temperature
of gas, Тм –
temperature of metal.
At the decision of
three-dimensional task of heat conductivity the sixpoint eventual
non-obvious raznostnaya chart of variable directions is used, for the decision
which the method of breaking (method of fractional steps)up, which consists
that an intricate multidimensional problem in the process of raznostnogo
decision is replaced by the great number of more
simple odnomernih tasks, was used to. A bar is broken up on n steps on a co-ordinate, for NK OVG the
heated bar was broken-down, for example, on six
segments on three axes of co-ordinates. In the case of three-dimensional task
of heat conductivity the method of breaking up results in the following
odnomernoy chart:
In each of
raznostnih equalizations members approximating
second derivative on
the two from co-ordinates can be dropped, thus at the
decision of the system of equalizations advancement in time takes place on 1/3
temporal step. Approximating expressions adopt the following kind:
For determination of
the unstationary temperature field of bar
a co-ordinate the line of which settles accounts on the given step at
times (∆τ)comes forward as the active co-ordinate Ктек , as auxiliary – two co-ordinates
which remained
(Квсп1, Квсп2), which moving is
done on:
Квсп1 = Квсп1 + ∆Квсп1;
Квсп2 = Квсп2 + ∆Квсп2 ,
where Квсп1, Квсп2 – step on a
co-ordinate; ∆Квсп1, ∆Квсп2 – increase on a
co-ordinate.
The temperature of current
active co-ordinate settles accounts on the method of progonki. As a current
co-ordinate (Ктек) on the first step the co-ordinate of comes forward at
times (τ=1/3*∆τ) x, y and z – auxiliary (Квсп1 и Квсп2 accordingly). Sizes and quantity of knots of
bar are adopted according to co-ordinates. On the second step comes (Ктек = у) forward an at times (τ=2/3*∆τ) current co-ordinate, and
auxiliary – Квсп1 = х and Квсп2 = z. On the third step at times (τ=∆τ) Ктек = z, Квсп1 = x, Квсп2 = y. Presentation of temperatures of bar is carried
out as a three-dimensional array.
The temperature field of
obmurovki (laying) was determined by the decision of odnomernoy task of unstationary
heat conductivity for a mnogosloynoy wall with the scope terms of III family on internal and
external surfaces on the standard method of eventual differences.
Thus, in
work the principles of construction of mathematical teplofizicheskoy model of fuel
chamber stove of periodic action are resulted.
A model is
attended, in which jointly decides the external and internal tasks of heat
exchange, bound by thermal balance, and scope terms on motion of process of
heating are formed. A model is zonal
(mnogosloynoy), that allows to define distributing of parameters of warming
environment on a volume working chamber. In a model
the function of burning down of fuel, allowing to set the stake of
fuel burning in every area at the
diffusive (I.e. most difficult at the design)
burning, is entered. A model is the teplofizicheskoy
basis of the mathematical
providing of the system of automatic control, for example at
the impulsive heating
of stove.
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