Working out the universal algorithm of consumed characteristics calculation for control and management of discharged production
Table of contents: The KazakhAmerican Free University Academic Journal №1  2010
Author: Abitova Gulnara, Eurasian National University in honor of L. Gumilyov, Kazakhstan
The basis of any automation system is devices to control the
technological parameters which determine the course of technological process.
Such parameters are temperature, pressure, discharge and amount, chemical
formulation, concentration, density etc.
As we know, while controlling the technological process the
information goes from sensors set on technological conduits to logical
controller (the drop of pressure on narrowing device, temperature and pressure
in conduit). The values of flow rate of substances and energy loss are determined.
Considering this, in this work was set the target to create the
universal algorithm for calculation the flow rate and the software to determine
the mentioned above parameters which are fundamental as in the process of
tellurium extraction so in other technological processes of metallurgical
complex. [12].
The task of work included studying the process of measuring the
pressure drop on narrowing device and the behavior of measuring substances at
this process. The following results were acquired after construction of
algorithm for calculation the flow rate of substances and energy with some of
them and summarizing some authors’ research data:
1. The algorithm of calculation the flow rate of steam, condensed
air, cold and hot water and thermal energy accumulated with steam and hot water
was worked out and realized on computer.
2. The behavior model of liquids and gaseous substances at passing
through narrowing device of flowmeter was analyzed.
Developed in the course of this work and realized on computer
algorithm on IBM provides an opportunity to get precise data for calculation
the fundamental consumed characteristics of technological processes of
metallurgical complex with maximum speed which lets in turn to optimize and
automate the process of control and quality management of discharged
production.
The created interface visually reflects calculated data, considers
given peculiarities of controlled process and is maximally comforted to
consumers’ needs.
The showed below calculation formulas as the methods of calculation
are valid for all narrowing devices including standard diaphragm. But the
values of flow rate coefficient Q_{m} and corrective multipliers Q for change of gas or steam density will be different for various narrowing
devices. However, most commonly used narrowing device is a diaphragm representing
itself a thin disc with round hole with diameter d axis of which coincides with
axis of pipe.
Calculation formulas. For the comfort of
calculation showed above formulas (19) and (20) for massive Qm and volume Q
were modified.
First of all, the square of hole of narrowing device Fo should be
found through diameter d coming from equality F0 = πd2/4. It is necessary
to keep in mind that initial units of measurement in formulas (19) and (20)
are: kilogram (kg), meter (m), and second (s). It is more convenient to measure
diameter not in meters but in millimeters and time not in seconds but in hours.
Then mentioned formulas should be multiplied by 3600 and divide by 106.
Considering that
_{}
(1),
We will get
_{}
(2).
In these equations d is in millimeters, p in kg/m^{3} and (р_{1} – р_{2}) in Pa.
Till present time devices which measure pressure are calibrated in kgs/m^{2}^{ }or kgs/sm^{2} and so are the maximum drops of differential pressure gages working in compliance
with narrowing devices. So we transformed the equation of flow rate that the
pressure drop would be in kgs/m^{2}. In order to this we must
multiply equation (2) by (9. 81)^{1/2}.
If 4*10^{3}*(9,81)^{1/2 }= 0,01252 we will
get:
_{}
(3).
These formulas are basic when calculating narrowing devices.
When measuring volume flow rate of gas it is reasonable to bring the
results to normal conditions (p_{n}=760 mm of m.c., T_{n}=293
K). Let’s call the adapted flow rate of gas through Q_{n} and
density of dry gas at normal conditions through p_{n}. Then we
can write that
Q_{n }=
Qρ/ ρ_{n} = Qp_{1}Т_{n} / (р_{n}Т1К), (4),
Where:
k is the coefficient of coercibility 121
characterizing its failure from laws of perfect gas.
Using this
expression and also changing density p to ρ_{n}р_{1}Т_{n}/р_{n}Т_{1}К in equation of flow rate we will get from formula (2) the
following:
Q_{n} = 2,151*10^{4} α ε d^{2} (p_{1}(p_{1} – p_{2})/ρ_{н}Т_{1}К)^{1/2} (5),
Where:
p_{2} is in Pa.
Then from formula (24) we will get:
Q_{n }=
0,2109 α ε d^{2} (p_{1}(p_{1} – p_{2})/ρ_{n}Т_{1}К)^{1/2} (6),
Where:
p_{1 }is in kgs/sm^{2},
(p_{1} – p_{2 })is in kgs/m^{2}.
In both previous equations Q_{n}_{ }is expressed
in m^{3}/h, d in mm, and p_{n} in kg/m^{3}.
Yet it would be more proper to start measuring the massive flow rate of gas Q_{m} instead of accepted now measuring the volume flow rate Q (as it is done
while measuring the low rate of steam). Adjusting of volume flow rate to normal
conditions doesn’t always provide necessary accuracy of result (especially when
adding different gases).
The flow rate of gas (condensed air). The
flow rate of gas is being measured using the following basic formulas:
_{}
(7),
Here:
a is the
coefficient of flow rate of diaphragm with angular way of selection _{}and
sharp entrance edge;
_{} (29),
Here:
Number Re is in limits Re_{min} ≤ Re ≤
10^{8},
Re_{min }has the following
values depending on m:
0,05 ≤ m ≤ 0,20 Re_{min} = 5*10^{3},
0,20 < m ≤ 0,59 Re_{min} = 10^{4},
0,59 < m ≤ 0,64 Re_{min} = 2*10^{4},
m is relative square equals to:
_{} (8),
e
is corrective multiplier for change of density
of measuring medium;
_{}
(9),
Where:
d_{20}_{ }is the diameter of the hole of diaphragm at temperature 20^{0}C, mm;
D_{20} is the inner diameter of
conduit at temperature 20^{0}C, mm;
< P is the pressure drop on diaphragm, kgs/m^{2};
P is the absolute pressure on diaphragm, kgs/sm^{2};
c is the
indicator of adiabatic
curve;
K_{t} is the coefficient
showing temperature expansion of the material of diaphragm:
К_{t} = 1+ β_{t} (t – 20) (10),
Here:
β_{t} is the average coefficient of
linear thermal expansion of the material of narrowing device; (steel 1Х18н10Т  β_{t} = 0,165*10^{4});
p_{nom} is the density of gas at
normal conditions, kg/m^{2};
T is the absolute temperature, К (Т = t + 273,15);
K is the coefficient of gas condensability.
The flow rate of steam. The main formula
for calculation the flow rate of steam:
_{}[kg/min]
(11),
Here:
_{} [m^{3}/kg] (12),
Where:
t is the temperature of steam, ^{o}C;
P is the absolute pressure of steam, kgs/sm^{2};
А_{1 } А_{5} are coefficients having under
pressure 1.67 kgs/sm^{2} the following values:
А_{1} = 8,394429*10^{3},
А_{2} = 1,426259*10^{5},
А_{3} = 5,3654771*10^{4},
А_{4} =
1,9958847*10^{6},
А_{5} = 223,7858.
Assessment of flow rate of thermal energy with steam. Charges of thermal energy with steam are calculated with formula:
Q_{п} = G_{m}*H , [kJoule/kg]
(13),
Where:
H is the specific enthalpy of superheated steam:
_{} (14).
When Р = 1,67 kgs/sm^{2} coefficients B_{i} has the following values:
В_{1} = 2503,798,
В_{2} =
1,895008,
В_{3} = 12,067877,
В_{4} = 3,375952*10^{2},
В_{5} =
237066,5.
The flow rate of water. The basic
formula of massive flow rate of water looks this way:
_{} [kg/min]
(15).
The density of water determined by formula approximates table data
in the range of temperature 0150 ^{0}C:
_{} (16).
The assessment of flow rate of thermal energy with hot water is made with formula:
Q_{B} = Gm*H, [кДж/ч]
[kJoule/hour] (17),
Where:
H is the specific enthalpy of water
which approximates table data in the range of temperature 0150 ^{0}C and is calculated with formula:
Н = В_{1} + В_{2}t + В_{3}t^{2} (18),
Here:
B_{i} are coefficients with the following
values:
В_{1} В_{2} В_{3}
When t =
090^{0}С 8,1909182*10^{1}
4,1793106 5,6818181*10^{5}
When t =
91150^{0}С 7,318027 4,0298544
9,0537089*10^{4}
Determination of Reynolds’ number Re. The
Reynolds’ number Re for conduit with diameter D while knowing the
volume flow rate Q at working conditions is calculated with expressions:
Re = 0,0361 Qρ/(Dμ)  при μ = [кгс*с/м^{2}] [kgs*s/m^{2}^{ }]^{ } (19)
And
Re = 0,354Q/(Dv) = Qρ/(Dμ) при μ = [Па*с][Pa*s] и v
= [м^{2}/с] [m^{2}/s] (20),
Here:
Q is the volume flow rate;
Μ is the dynamic viscosity of measuring
medium at working conditions.
For determination the coefficient of correction of flow rate to the
number Re we calculate first flow rate of substances Q at its
working parameters and assuming that Re = 10^{6}(in this case k_{Re} = 1, and a_{y} = a_{y}^{*}, a_{y}^{*} is the coefficient of flow rate with Re = 10^{6}).
The Reynolds’ number Re is determined depending on the value
of flow rate Q. Then we find the real number Re with formula:
_{}
(21),
Where:
С =
(0,5959 + 0,0312m^{1,05} – 0,184m^{4}) / (1m^{2})^{1/2},
S = S_{1}/S_{2}^{1,75}.
At the same time S_{1} and S_{2} are determined
with formulas:
S_{1} = B Re^{*}/(a_{y}^{*}10^{6}) (22),
S_{2} = C Re^{*}/(a_{y}^{*}10^{6}) (23),
Where:
В =
0,0029 m^{1,25}/(1m^{2})^{1/2} (24).
Then we calculate the corrective coefficient to number Re in
order to get real amount of flow rate of substances:
k_{Re}
= (C + B(10^{6}/Re)^{0,75})/(C + B) (25).
So the real flow rate of substances is determined as value equal to:
Q = Q^{*} k_{Re }_{ }(26).
Thus, in this part of work have been introduced a mathematical model
and a program for calculation the consumed characteristics and parameters of
technological processes allowing to measure different flow rates of substances
and energy, their quantity and levels. Thanks to these developments the
management of technological cycle of metallurgical complex can be done more
effectively.
The developers provided fast obtaining precise data of the course of
the technological process and visual demonstration using created interface of
obtained calculated characteristics considering given peculiarities of
controlled process. [5]
Acquired information lets optimize the process of management of all
technological production and provides significant economical effect at
production of rare metals.
LITERATURE
1. Belgibayev B.A., Abitova G.A. Расчет параметров
расходомера переменного давления гидрометаллургического производства ОАО «УМЗ». // Materials of international
scientific practical conference. – Almaty city, publishing house KazGASA. 2003
– pages 123125/
2. Abitova G.A., Belgibayev B.A. Программноаппаратное обеспечение расходомера переменного давления в АСУ
гидрометаллургическими процессами ОАО «УМЗ». // The results of international conference (Almaty, March 46,
2003). – Almaty city. Publishing house Kazakh University. 2003 – pages 1215.
3. Abitova G. A. Оптимизация технологических процессов
современных промышленных предприятий на основе создания пакета прикладных программ. // Materials of international scientific practical conference. – UstKamenogorsk: publishing house of East Kazakhstan State University, 2002 – pages
192194.
4. Belgibayev B.A., Abitova G.A. Расчет параметров
расходомера переменного давления гидрометаллургического производства ОАО «УМЗ». // Materials of international
scientific practical conference. – Almaty: publishing house KazGASA, 2003 –
pages 123125.
5. Abitova G.A., Belgibayev B.A. Программноаппаратное обеспечение расходомера переменного давления в АСУ
гидрометаллургическими процессами ОАО «УМЗ». // The results of international conference – Almaty: publishing
house of Kazakh University, 2003 – pages 1215.
Table of contents: The KazakhAmerican Free University Academic Journal №1  2010
