© 2014
Ivanov O. N., PhD, Senior Lecture,
Arendarenko V. N., PhD, Associate Professor
Poltava State Agrarian Academy
COMPUTATIONAL MODELS HYDROINJECTION INSTALLATION TUNNEL TYPE
Reviewer – PhD, Associate Professor R. N. Harak
The results of theoretical studies on the preparation of the computational model hydro spray
tunnel designed for spraying high-pressure plants in the tunnel chamber. Studies were carried out using
the theory of hydrodynamic and hydrostatic calculations for complex pipelines and multi-hydraulic
systems. To achieve the objectives of the study were divided into components of hydraulic systems, each
of which is a more simplified version of a complex pipeline. According to the results of computational
studies were compiled analytical equations that determine the magnitude of hydraulic parameters at
nodes and establish the relationship between the main components of the hydraulic system, and outlines
the framework for the selection of a pressure pump for the amount of required pressure and flow.
Keywords: pipeline, hydraulic system, hydrostatics, jet, hydrodynamic parameters estimated
model.
Statement of the problem. Providing the population with high-quality and environmentally
friendly products - the main task of agricultural production. However, for quality products producers use
various pesticides that are applied by spraying on plants.
Spraying potato plants performed several times (depending on the occurrence of adult beetles and
their larvae). For this purpose, Rod sprayers, equipment nozzles. This involves spraying the spray fluid to
transport droplets formed air flow to treatment facilities. In this case, part of the fluid hits the ground, and
the other from the tops of potatoes flowing again on the soil, increasing its pesticide load.
To address this shortcoming offered hydroinjection plant tunnel type, in which the spraying potato
plants in a closed volume. This scheme provides for the collection hanging spraying fluid and its reuse.
Analysis of recent research and publications, which discuss the problem. Collect and dispose
of Colorado beetle on potato plantings involved various researchers. Thus, in [1, 2, 3] proposed by
pneumatic cleaning pest and destroy it mechanically. However, this principle does not allow collecting
and destroying the larvae of the beetle first and second generations.
To solve the problem of collecting adult beetles and their larvae we proposed and patented utility
model Ukraine [6]. The proposed installation shaking larvae and adult beetles’ stream is compressed
working fluid. The installation consists of the working chamber Five of this type, injectors, located in the
middle tier of the working chamber, pump, tank, filter, jet pump and piping.
1
Purpose and objectives of the research. The goal of the proposed research is to design a model
drawing hydraulic tunnel injection installation using guidelines theories of hydrostatics and
hydrodynamics for use in further theoretical studies of the identification and coordination of hydraulic
parameters and characteristics of the main components of the installation.
The objective of the proposed research is prompting a clear mathematical algorithm to identify
key points in hidroparametriv designs with complex pipelines and varied in character and principle of the
hydraulic elements.
Results. Schematic diagram of hydraulic tunnel hydroinjection installation is shown in Fig. 1 as
well. The installations of large volume tank, from which by means of centrifugal pump is the selection of
fluid and pumping it under high pressure to a large number of nozzles in the spray chamber (Fig. 1b).
Number of nozzles and the nature of their location in the middle of the camera meets the requirements of
effective spraying process. In order to save injection fluid of the installation is collecting tank, the use of
which allows to collect and store the portion of liquid that does not get the object spraying and naturally
flows down from the surface of the object. For pumping the collected fluid is introduced to the
installation jet pump and filter which cleans the flow of fluid from mechanical and plant additives.
Injection flow jet pump is forked part of the main hydraulic flow supplied to staff centrifugal pump
installation to the injectors spraying chamber.
а)
b)
Figure 1. Schematic diagram of the hydraulic unit (a)
and general view of the camera injection (b)
Addressing the task of drawing up computational model of hydraulic system with complex
pipelines involves partitioning a single design into elementary parts, which would represent a set of
common piping and the calculation is reduced to the application of the law (equation) Bernoulli [4] and
the continuity equation flow fluid. In this regard, hydraulic diagram of the apparatus (Fig. 1,a) is divided
into separate components (Fig. 2). Consider each component in particular.
2
a)
b)
d)
c)
e)
f)
g)
Figure 2. Separation of the components of the hydraulic system
The first component in Fig. 2, and is a hydraulic rod with multiple nozzles that is connected to the
input node C. Calculate the nodal point for a given hydraulic pressure Pc and the value of working fluid
(QC).
The total value of expenses QC is defined as the total cost of liquid through each nozzle, which are
attached to the rod [5]:
QC  Qô 1  Qô 2  ...  Qô n ,
(1)
where Qô 1 , Qô n − magnitude of fluid flow through the first and n-well injector.
If the nozzles are the same type and have the same regulation, the flow rate through each of them
will be the same. Then the total cost is equal to QC:
QC  n  Qô ,
(2)
where n – number of nozzles on the boom.
To determine the pressure Pc compose the Bernoulli equation for the two sections of the plane of
comparison that passes through the point P. The first section passing through point C, the other - in the
cross section of the output of the first injector nozzle. Weighing pressures neglected as a starting point C
and injector nozzle lie on a horizontal plane. With this in mind, the Bernoulli equation has the form:
pc 

2
vc2  pàòì 

2
vô21  pòð  p ì³ñ .
This pressure is equal to PC:
3
(3)
pc  pàòì 
v
2

2
ô1

 vc2  pòð  p ì³ñ ,
(4)
where: pàòì – atmospheric pressure;

– density of the fluid flow;
vô 1 – flow rate in the initial nozzle injectors;
v c – flow rate at the point of С;
pòð – pressure drop along the length of the pipeline;
p ì³ñ – loss of hydraulic pressure on local obstacles.
Pressure loss along the length and the local support can be found by formulas Veysbaha and
Darcy-Veysbaha [5]:
pòð  
 
2  dñ
p ì³ñ    
 vc2 .
  vô21
2
(5)
.
(6)
Losing the pressure p ì³ñ is defined as the total loss eneriyi fluid flow inside the nozzle flow at
him from point C to the output end of the nozzle.
We make some simplifying analytical expression that defines the flow rate in a pipe section; we
define the value of the flow rate [4]:
v
Q 4Q
.

S d 2
(7)
Then formula (5) and (6) has the form:
p òð  
8   2
 Qc .
 2  d c5
p ì³ñ    
8 
 Qô21 .
2
4
  dô1
(8)
(9)
In equations (5) and (6), (8) and (9) perform the following options:
Cô 
8 
.
 2  d ô41
(10)
Cñ 
8 
.
 2  d ñ4
(11)
4
ÊÑ  
8  
.
 2  d c5
Ê ô   
(12)
8 
.
 2  dô41
(13)
In view of the above replacements formula (4) takes the following form:
pc  pàòì  Ñô 1  Qô21  Ñc  Qc2  K c  Qc2  K ô 1  Qô21 .
(14)
By combining all common components of equation (14) and introducing provided below
replacement,
Z ô  Cô 1  K ô 1 ;
(15)
Yc  K C  CC .
(16)
final value equation hydraulic pressure Pc will form:
pc  pàòì  Z ô  Qô21  Yc  Qc2 .
(17)
Similarly equations consist of hydraulic pressure Pc against other jets. In general, the pressure Pc is
determined through the same type of equations, for each of the nozzles.
Neglect largest loss of hydraulic pressure along the length of piping from the point C to a single
injector (insignificant value hydraulic circuit for this). Then the magnitude of the pressure Pc is
determined only by equation (17).
Thus, the following system of equations to fully determine all the unknown hydraulic parameters
for point C:

QC  n  Qô ;

2
2

 pc  pàòì  Z ô  Qô  Yc  Qc .
(18)
Using the method shown above, determine the required hydraulic parameters for points A and B
(Fig. 2b):

Q A  n  Qô ;

2
2

 p A  p àòì  Z ô  Qô  YA  Q A .
(19)

QB  n  Qô ;

2
2

 p B  p àòì  Z ô  Qô  YB  QB .
(20)
We turn to the calculation of the point O1 (Fig. 2, b).
Since the point O1 is a common entrance for points A, B and C, the flow
QO1
will be determined
by the following expression:
QO1  QA  QB  QC .
5
(21)
In terms of uniformity costs through the points А, В, С
Q A  QB  QC .
(22)
Consumption QO1 will be calculated:
QO1  n  QA ,
(23)
where n – number of output lines from point O1 with the same flow.
According to Bernoulli's equation the pressure pO1 determined:
pO1  p A    g    O1 A 
where
 O A
1
8 
 Q A2 ,
2
4
 dA
(24)
− total pressure loss coefficient at the transition from point A to point O1.
To simplify the expression, do the following replacement:
8 g  2
Z A   O1 A  2 4 .
  dA
(25)
Then the pressure at point O1 is determined:
pO1  p A  Z A  QA2 .
(26)
Preparation of (26) with respect to the points B and C is carried out by the above method. Then the
pressure
pO1
value will be determined by the following system of equations:
 pO  p A  Z A  Q A2 ;
 1
2
 pO1  p B  Z B  QB ;

2
 pO1  pC  Z C  QC .
(27)
To the point O1 calculation of hydraulic parameters by the system:
QO1

 pO1

 pO1

 pO1
 n  QA
 p A  Z A  Q A2 ;
 p B  Z B  QB2 ;
(28)
 pC  Z C  QC2 .
Method of simultaneous equations for the bottom row of nozzles (Fig. 2) and nodal points F, E, O2
is appropriate, therefore give only the final results:
Point F:

QF  n  Qô ;

2
2

 p F  p àòì  Z ô  Qô  YF  QF .
Point E:
6
(29)

QE  n  Qô ;

2
2

 p E  p àòì  Z ô  Qô  YE  QE .
(30)
QO2  n  QE

2
 p O2  p E  Z E  Q E ;

2
 pO2  p F  Z F  QF .
(31)
Point O2:
To the point of D2 (Fig. 2, d) satisfy altitude location reference points O1 and O2 and taking as a
basis the foregoing method of calculation of hydraulic parameters, in particular for the O2 terms, we
obtain:
QD2  QO1  QO2 ;

2
 p D2  gz1  pO1  Z O1  QO1 ;

2
 p D2   gz2  pO2  Z O2  QO2 .
(32)
Consistency of the point D is the calculation of hydraulic pressure and flow rate for point H (Fig.
2, f). For her, the system of equations has the form:
QH  QD1  QK ;

2
 p H  gz3  p D1  Z D1  QD1 ;

 p H   gz4  p K  Z K  QK2 .
(33)
Define the desired amount of pressure to be a centrifugal pump to meet the needs received good
value pressure (flow rate) through nozzles with all hydraulic losses in the system.
As is known, the magnitude of the pressure pump is defined as the difference between the energy
flow of fluid between its output and input:
píàñîñ  Eâèõ  Eâõ .
(34)
Output energy flow is the expression:
Eâèõ  p H 

2
v H2 .
(35)
The value of pressure p H and velocity v H of fluid is determined from the system of equations
(33).
To find the energy flow of the liquid at the inlet up a Bernoulli equation for the two cross sections
0-0 and 1-1 (Fig. 2, f):
pàòì    g  z5  p1 

2
7
vP2  p ì³ñ .
(36)
Then Eâõ :
Eâõ  pP 

2
vP2  pàòì    g  z5  p ì³ñ .
(37)
The required pump pressure is determined by the following equation:
píàñîñ  Eâèõ  Eâõ  pH 

2
vH2  pàòì    g  z5  p ì³ñ .
(38)
Using knowledge of the desired output pressure and flow rate, by using pressure features to select
the desired discharge centrifugal pump.
For jet pump (Fig. 2, g), define the desired output pressure required to pump the collected liquid in
collective tank to the main tank installation. This will prepare the Bernoulli equation for the free surface
of the liquid in the tank and pipe the output plane of the jet pump (point N):
pN 

2
 v N2    g  z7  pàòì 

2
2
vâèõ
 p ì³ñ . .
(39)
Since the diameter of the pipeline d N  d âèõ , then v N  vâèõ , so that the desired pressure value
will be expressed by the equation:
p N    g  z7  pàòì  p ì³ñ . .
(40)
For jet pump feeding the output value is the sum of labor costs and suction fluid:
Q N  QK  QF .
(41)
For the initial section of the jet pump:
QN  QK  QL ;

2
 p N    g  z7  pàòì  Z N  QN .
(42)
Coefficient Z N is calculated by the formula (25).
Take a calculation of the jet pump suction line to determine the possible level of pressure for
suction of fluid from the tank. For this purpose we use the Bernoulli equation for the input section of the
pump suction line (point L (Fig. 2, g)) and the free surface of precast tank. After minor changes and
reductions in the value of pressure equal to:
p L     g  z 6  p àòì  Z L  QL2 .
(43)
Coefficient Z L is calculated by the formula (25).
Performance for the jet pumps suction line determined by the formula:
QL 
2
d âõ
4

2

 ðàòì
 pL  .
(44)
Combining hydraulic parameters found above, we obtain a finite system of equations estimated:
8
2

d âõ
2
 ðàòì  p L ;
Q


 L
4



2
 p L     g  z 6  p àòì  Z L  QL .
(45)
Based on these values of pressure at the outlet of the jet pump and suction line can be defined on
the basis of the theory of jet devices of its type design and narrowing element.
Conclusion. The mathematical algorithm for calculating hydraulic parameters in the main nodal
points of hydraulic tunnel injection installation setup will allow a better understanding of the processes
occurring in it, and also give a reasoned assessment of the quality of its functioning. Also developed
model will allow selecting the desired discharge and jet pumps that are required to meet the technological
needs and requirements to ensure the effective operation hydro injection installation.
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