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AIR CHAMBER AS WATER SHOCK ABSORBER
Sobir Jonkobilov, Murodilla Ulugmuradov
Karshi institute of irrigation and agrotechnologies, Xonobod 19, 180119, Karshi, Uzbekistan.
E-mail:
,
Abstract:
The article is devoted to the study of a water shock absorber - an air chamber, used in
long pressure systems and in pressure pipelines of pumping stations. The work provides an
analysis of scientific works. The efficiency of pressure pipelines depends on ensuring their
trouble-free operation - the reliability of pressure hydraulic systems. The reliability of long
pressure pipelines is ensured using the proposed design of a water shock damper.
As a result of a joint solution of the equation of unsteady pressure motion of the liquid, the
equation of flow continuity and the equation of the state of air in the chamber, dependencies
were obtained for calculating the volume of the proposed absorber, taking into account the
isothermal and adiabatic laws of air compression.
To check the reliability of the obtained dependencies for calculating the chamber parameters,
experimental studies of the shock absorber were carried out. In this case, modern scientific
instruments were used. The authors of this work have developed a special pressure sensor to
record changes in hydrodynamic pressure in pressure systems during unsteady fluid flow.
At the same time, a reliable agreement between the results of calculations of the shock absorber -
the air chamber - and the experimental data was obtained. The completed research experiments
prove that the proposed damper is a very effective and economical water shock damper for long
pressure pipeline systems.
Keywords
: water shock, air chamber, pressure system, positive water shock, water shock with
pressure reduction, pumping unit, check valve.
1. Introduction
One of the effective means of protecting pipelines from water shock is an air chamber installed
during positive water shock at the end of the pressure pipeline before the valve or water shock
with a decrease in pressure at the beginning of the pressure pipeline after the check valve of the
pumping unit and station [1,2,3,4,5].
Calculation of water shock in a pressure pipeline with an air chamber comes down to
determining the required volume of air in the chamber to maintain the pressure within acceptable
limits [6,7,8,9,10,11].
N.E. Zhukovsky [1] gave an analysis of the processes occurring in the air chamber during direct
water shock and formulas for determining the volume of air in the chamber.
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I.A. Charny [12] gives a more general solution to the problem using linearized equations of
hydromechanics of a viscous fluid.
L.B. Zubov [13] gives an approximate formula for determining the volume of air in the chamber.
However, the author's assumption that liquid flows into the chamber occurs during one phase of
the impact raises objections.
Alliev theoretically proved that the increase in pressure in the chamber occurs over a time
exceeding the impact phase, which was later confirmed by the experiments of A.F. Mostovsky
[2].
The listed solutions to the problem of water shock in a pipeline with an air chamber are
applicable for direct water shock under condition
a
Z
t
2
. Therefore, the formulas obtained in
these works are in good agreement with experiment only for small volumes of water shock
absorbers - the air chamber [10,11].
2. Materials and methods
Disregarding the wave nature of the hydrodynamic processes occurring in the pipeline and in the
chamber, to solve the problem we used the equation of unsteady motion of an ideal
incompressible fluid in a rigid pipe [10,11,12].
Let's consider a pressure system consisting of a pipeline of length Z with a valve at the end, a
reservoir and an air chamber in front of the valve (Fig. 1). The movement of liquid through the
pipeline occurs under a pressure of P
0
with an initial speed of ϑ
0
. The volume of air in the
chamber in this mode is W
0
.
At time t=0, the instantaneous closing of the valve causes unsteady motion, which is described
by the equation [10,11]
dt
d
g
Z
P
P
J
g
+
=
0
,
(1)
where P is the maximum absolute air pressure in the chamber, P
0
is the absolute air pressure
before closing the valve.
To determine the dependence of P on ϑ, we use the continuity equations
ϑωdt=-dW
(2)
and ideal gas states [10,11,12,13,14]
P
0
W
0
= PW,
(3)
k
k
PW
W
P
=
0
0
,
(4)
where dW is the change in air volume in the chamber; W
0
is the volume of air in the chamber.
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3. Results and Discussion
The above equations (1), (2), (3) and (4) form closed systems, the solution of which, under the
condition P(ϑ
0
)=P
0
, is represented as:
Fig.1
. Experimental setup diagram: 1 - reservoir; 2 - pressure pipeline; 3 - air chamber; Ω is the
transverse area of the chamber.
+
-
=
-
P
P
P
P
P
W
W
g
p
0
0
0
0
0
2
0
1
ln
2
g
J
J
,
(5)
+
-
-
-
=
-
-
k
k
k
p
P
P
P
P
k
P
W
W
g
1
0
1
0
0
0
0
2
0
1
1
1
1
2
g
J
J
,
(6)
where W
p
is the volume of the pipeline, ϑ
0
is the initial speed of water movement.
Using equations (2), (3), (5), (6), one can obtain the dependence of pressure on time – P(t).
However, the derivation of this dependence is associated with certain mathematical difficulties,
so we limit ourselves only to determining the volume of air in the chamber. The flow of liquid
into the chamber stops at ϑ = 0, which corresponds to the maximum compressed state of the air
[15,16,17,18,19]. Let us denote the pressure of this state by P
1
.
Then from equations (5) and (6) we find the required volume of air to obtain the predetermined
pressure P
1
:
in the case of an isothermal process
1
0
0
1
0
2
0
0
1
ln
2
P
P
P
P
W
P
g
W
p
+
-
=
g
J
,
(7)
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in the case of an adiabatic process
k
k
k
p
P
P
P
P
k
W
P
g
W
1
1
0
1
0
1
0
2
0
0
1
1
1
1
2
+
-
-
-
=
-
g
J
.
(8)
Formulas (7) and (8) are very convenient for calculations, since they do not contain the time
during which the air pressure in the chamber reaches its greatest value. From these formulas it
follows that the required volume of air to maintain pressure P
1
is directly proportional to the
square of the initial velocity and the volume of the pipeline. Formulas (7) and (8) satisfy the
condition P→P
0
, W0→∞.
To verify theoretical dependencies (7) and (8), experiments were carried out on an experimental
setup (Fig. 2).
Fig.2.
Pumping installation diagram: 1-reservoir; 2-suction pipeline; 3-pump; 4.8-valves; 5-
check valve;
6-pressure pipeline; 7-air chamber; 9-pressure pool.
The design diagram of the air chamber and its elements are shown in Fig. 3.
The experiments were carried out in the following sequence. A stationary mode of water
movement through the pressure pipeline was created, the flow rate was measured by volumetric
method, the initial pressure P
0
was determined using the M
1
pressure gauge and the volume of air
in the chamber using a rotometer. The required volume of air was supplied by the compressor.
Then, by quickly closing the valve, a water shock was caused and the change in pressure in the
chamber and in the pipeline was recorded using pressure sensors D-1 and D-2. Before the next
experiment, the volume of air was changed by passing it through a tap. As a result of the
research, a number of diagrams were obtained (Fig. 4). Using calibration graphs [6,7], the
parameters of steady-state fluid motion were determined: flow rate Q, speed ϑ
0
, air volume W
0
in
the absorber at absolute pressure P (Fig. 2).
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Fig.3.
Scheme of the air chamber design and its elements: 1 – pressure pipeline; 2 – level
indicator; 3 – level sensor; 4 – pressure gauge; 5 – valve; 6– air chamber; 7 – plug valve; D-1, D-
2 – pressure sensors.
The block diagram of the instrumentation used is shown in Fig. 4.
Figure 5 shows records of pressure changes for different volumes of air in the chamber.
As a result of the research, a number of diagrams were obtained (Fig. 4). Using calibration
graphs [10,11], the parameters of steady-state fluid movement were determined: flow rate Q,
speed ϑ
0
, air volume W
0
in the chamber at absolute pressure P. Using water shock diagrams (Fig.
4), extreme pressure values in the pressure pipeline with an air chamber were determined [10,11].
From these diagrams it can be seen that as the volume of air increases, the pressure decreases
and the time t
1
increases, during which the air pressure reaches its greatest value.
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Fig.4.
Block diagram for connecting control and measuring equipment: D-1 and D-2 - pressure
sensors; WLS - water level sensor; TS - time sensor; SC-1 - secondary converter.
Air chamber 6 was equipped (Fig. 2) with level indicator 2 for visually determining the water
level in the chamber, valve 6 for connection to the compressor (brand 155-2V5UCH), which
provided the required volume of air to the damper [10,11].
Changes in the water level in chamber 7 were recorded on a computer using a specially designed
low-inertia electronic sensor level 3 (Fig. 3).
Pressure sensors D-1 and D-2 (Fig. 4) were used to record pressure fluctuations over time in the
pressure pipeline 1 and in the absorber 6 (Fig. 3), b). Signals from pressure sensors D-1 and D-2
were recorded on a computer (Fig. 4).
For comparison with experimental data, Fig. 5 shows in relative coordinates the dependence of
100
0
tr
W
W
on
0
1
P
P
at ϑ
0
=0.973 m/s (curves 1,2) and ϑ
0
=0.5 m/s (curves 3,4) for isothermal (curves
1,3) and adiabatic (curves 2,4) processes of air compression. As can be seen from these graphs,
to maintain pressure P
1
, the required volume of air is obtained more during the adiabatic
compression process.
Fig.5.
Curve dependences of the relative volume of air
100
0
tr
W
W
on the relative pressure
0
P
P
during isothermal and adiabatic processes of air compression.
Results of experiments conducted by A.F. Mostovsky [2]. and are plotted by the author in Fig. 5.
The experimental points coincide well with the theoretical curves and are mainly located
between them. It should be noted that the wings asymptotically approach the x-axis, since
neglecting the compressibility of water in the absence of air in the chamber should lead to an
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unlimited increase in pressure. In fact, due to the compressibility of water, water shocks are
accompanied by a final increase in pressure, determined by the well-known formula of N.E.
Zhukovsky [1]. Therefore, the discrepancy between the experimental results and the theoretical
curves for small volumes of air is quite natural.
Experiments carried out by the author on chambers having different cross sections and shapes
revealed that the magnitude of the pressure increase does not depend on the cross section and
shape of the chamber. This circumstance allows you to freely choose the design of the camera
depending on local conditions [20,21]. The use of air chambers in pressure systems and pipelines
of pumping stations helps to soften and reduce the force of water shocks that occur when starting
pumps and during an emergency shutdown of the power supply to pump motors [22,23].
Compared to other means of protecting pipelines from water shock, air chambers are very
economical in that when they are installed in pressure systems, there is no liquid discharge and
no special care is required during their operation.
4. Conclusions
Based on the above, the following conclusions can be drawn:
A method has been developed for calculating the volume of an air chamber installed at the end of
a pressure pipeline during a water shock, taking into account the isothermal and adiabatic laws of
air compression in the chamber.
Calculation dependencies were obtained to determine the optimal volume of air in the proposed
means of protecting pressure systems from water shock.
A comparison of the calculated values based on the proposed dependence of the volume of the
chambers shows good agreement with the results of experimental data. This indicates the
reliability of the obtained dependencies for calculating pressure systems under water shock.
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American Academic publishers, volume 05, issue 02,2025
Journal:
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