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UDC 681.5: 519.6
FUNCTIONAL ASPECTS OF PUMPS AND CENTRIFUGAL PUMP MODELS
1
Xalikov Abdiravub Mamarahimovich, SRIF, dotsent,
Uzbekistan
;
2
Matmuradov Farhod Matniyazovich, CHHTCESCH, professor;
Uzbekistan
.
Abstract.
This article presents the principle of operation of a centrifugal pump and the
classification of impellers. The geometric and kinematic parameters of the impeller
were calculated, the spiral outlet was calculated, the axial force acting on the rotor and
the radial force acting on the impeller were found. The impeller was designed based on
the calculation results. A strength calculation of the shaft connection with the impeller
was performed. The pump drive and the centrifugal pump model were selected.
Keywords:
hydraulics, centrifugal pump, aspect, component, efficiency, performance,
rotation frequency, design.
Introduction.
Hydraulic power engineering is the field of study and practice
concerned with the transmission and control of energy (in the form of fluid under
pressure) for the purpose of moving and applying forces to machine elements. This field
currently employs new technologies related to hydraulic power engineering.
The amount of fluid that a pump can deliver is determined by two main
parameters: the pump displacement and the drive shaft speed. The pump displacement
mainly depends on the design geometry. This paper provides analytical procedures for
determining the pump functions of specific positive displacement pumps [1]
Of these, centrifugal pumps are widely used in water supply systems, wastewater
disposal, thermal power engineering, food industry, chemical industry, petrochemical
industry, nuclear industry, aviation and rocket engineering, etc. A centrifugal pump is
a mechanical device that uses a rotating impeller to create a flow inside the pump
casing, thereby increasing the fluid pressure; it is commonly used for pumping liquids
in various industries.
The principle of operation of a centrifugal pump is to create a centrifugal force
that moves the liquid through the pump. This is achieved by the rotation of a central
rotor inside the stator or by using a difference wheel, which creates a pressure difference
and moves the liquid.[4] Small centrifugal pumps (e.g. aquarium pumps) are capable
of developing a maximum pressure of 0.05 bar (i.e. creating a water head of up to 0.5
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meters). Some industrial positive displacement pumps (e.g. plunger pumps) are capable
of developing pressures of up to 200 bar or even more. There are no seals between the
suction and discharge sides of the pump. This means that centrifugal pumps are
ineffective with gases and are not capable of pumping air out of the suction line when
the liquid level is below the impeller. The method of regulating the performance of a
centrifugal pump is to bypass a portion of the fluid being pumped from the pump outlet
to its inlet through a bypass line with a regulating gate valve and a suction gate valve
on the pump inlet pipe to the bypass line[11]. The simplest way to change the flow rate
of a centrifugal pump is to adjust the opening of the pump outlet valve, while the pump
speed remains constant (usually rated). The idea is to change the position of the pipeline
characteristic curve to change the pump's operating point. Almost all centrifugal pumps
will consume more power as the head decreases and the flow increases. So, if your head
(pressure) decreases, your flow increases and the operating point shifts to the right of
the pump curve where more power is required. The most common method of
controlling the pump discharge pressure is to use a regulating valve . This valve is
installed in the discharge line and is used to restrict the flow of fluid, thereby increasing
the pressure[10]. Regulating valves can be manually or automatically controlled,
depending on the system requirements [5].
Almost all centrifugal pumps will use more power when the head drops and the
flow increases. So if your head (pressure) decreases, your flow increases, and the
operating point shifts to the right of the pump curve, where more power is required.
Almost all centrifugal pumps will use more power when the head drops and the flow
increases. So if your head (pressure) decreases, your flow increases, and the operating
point shifts to the right of the pump curve, where more power is required.[2]
Method and methodology of the research.
The material uses the methods of
mathematical statistics and analysis. The main components of a centrifugal pump are
the impeller, casing, suction and discharge nozzles, shaft, bearings and mechanical
seals.
The functional aspects of the pump are related to the performance of the layout
of the elements of the hydraulic system of a given machine. In addition, how well does
the pump meet the performance requirements as a converter of mechanical energy into
fluid energy? If the selected pump does not satisfy the functional aspects of the
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application, there is no need to worry about how well it resists damage to the structure
and the environment.
The efficiency of energy conversion by a pump is determined by its performance
characteristics. Theoretically, at low pressure, the output flow of a positive
displacement pump is equal to the product of the pump displacement (cc/rev, or cu.
in./rev) and the shaft speed [4]. As the pressure increases and the viscosity of the fluid
decreases (temperature increases), internal leakage paths in the pump lead to flow losses
due to slippage, which are reduced from the output flow. Since volumetric efficiency is
the ratio of actual flow to theoretical flow, the term reflects the severity of this volume
loss.
Mathematical description of the action of the device elements and the results of
the study. The pump suffers not only volume losses but also torque losses. Torque
losses occur due to the relative movement of the pump working elements, which are
accompanied by energy (power) losses due to friction of the mechanical parts and fluid
movement. The theoretical torque required by the pump is equal to the product of the
pump working volume and the pressure difference in the pump. Obviously, the actual
torque must be greater than the theoretical one to compensate for any losses occurring
in the pump. Mechanical efficiency or torque efficiency is the ratio of the theoretical
torque to the actual torque. The overall efficiency of the pump is equal to the product
of the volumetric efficiency and the mechanical efficiency. The pump characteristics
table shown in Fig. 1 illustrates the information on the type of energy conversion needed
to properly match the pump to the workload. The only thing missing is a reflection of
the pressure effect. In fact, three curves for each parameter should display different
pressures to facilitate the pump selection process, as shown in Fig. 2.
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Fig. 1. Efficiency and performance graphs and the effect of discharge pressure on
pump performance.
It is important to understand the penalty for poor overall pump efficiency. As shown
in Figure 3, the penalty for poor efficiency can be significant. Note that a pump with
66% efficiency requires 50% more horsepower. When you translate this loss into the
cost of the extra horsepower required to do the job, the results are dramatic. The type
of hydraulic fluid used with a given pump can have serious consequences if the pump
and fluid are incompatible. Too low a viscosity can result in excessive slippage, which
can lead to inadequate lubrication.[8] Too high a vapor pressure at the pump suction
can result in vapor cavitation and subsequent metal surface erosion. If the air exhaust
performance is poor, pumping efficiency is greatly reduced, leading to high
temperatures and the formation of a porous medium.
The strength of the pump, as reflected by the strength and burst pressure, is an
important indication that the pump casing can withstand accidental overpressure
without creating a safety hazard. The allowable pressure is usually 1.5 times the
nominal pressure, and the burst pressure is at least 2.5 times. In some engineering
circles, the working pressure is half the allowable pressure and one-quarter the burst
pressure. The flow and pressure characteristics of variable displacement pumps are
important for their successful application. The maximum system pressure (standby or
ultimate), as shown in Fig. 4, is determined by the compensator spring setting. The
slope of the curve between the initial
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Fig.3.Reduction of energy consumption due to low efficiency of pumps.
pressure and cut-off pressure depends on the constant spring of the compensator. The
flow from the pump to the full stroke condition depends on the ability of the pump to
respond to the required flow, as well as on the load on the drive for acceleration. To
accelerate loading, full ultimate pressure can be applied, but the volume of the delivered
flow cannot exceed the load offset and leakage in the system [7]
Fig. 4. Dependence of flow rate on pressure for pumps with adjustable working
volume.
Another important factor in pump selection is its filling characteristics. In theory,
for a positive displacement pump, the flow rate is directly (linearly) related to the pump
speed. However, if sufficient fluid cannot be supplied to the pump chamber before the
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suction port closes, the chamber will only be partially filled and the pump will operate
in the idle mode. This situation is illustrated in Figure 5 for a given pump, fluid, inlet
temperature, and pressure, and shows that the pump speed must not exceed a certain
value or the flow will be "choked off" and the pump will not operate.[6] Another way
to obtain the required inlet pressure for a given pump speed is shown in Figure 5.
Similarly, for a given pump, fluid temperature, and speed, the system must maintain a
certain inlet pressure to avoid cavitation. The point at which deviation from linearity
occurs depends on the viscosity of the fluid, the geometry of the pump inlet
(restrictions), and the inlet pressure. A pump with poor filling
Fig.5-6. Flow rate versus pressure for pumps with adjustable displacement.
characteristics may require pressurization or at least a flooded inlet port to properly fill
its pumping chambers. Most pumps have limited speed, both low and high. At low
speeds, volumetric efficiency is extremely low, and the clutch and sealing
characteristics of the plates, which may wear, are completely inadequate. At high
speeds, mechanical efficiency may be reduced to such an extent that failure becomes
inevitable. The speed characteristics of the prime mover must be taken into account in
the pump specifications. The idle speed of a diesel engine or the auxiliary drive of a jet
engine represent practical speed limits of importance.
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Fig. 6. Requirements for inlet pressure at a given pump speed
Serious difficulties arise when using positive displacement pumps at sub-zero
temperatures. Under such conditions, the viscosity of the liquid increases significantly.
This increase in viscosity leads to excessive hydraulic resistance to flow in the pipeline
and increases friction forces in moving joints, makes it difficult to start the pump,
disrupts the continuity of flow in the suction line, leads to incomplete filling of the
pump chambers of the pump and excessive wear of the rubbing surfaces. The design
features of the pump and the properties of hydraulic fluids determine the practical level
of the operating temperature. Reducing the pump speed leads to a significant increase
in temperature to ensure stable operation, and also increases the pumpability of working
fluids compared to their viscosity level [8],
Flow or pump pulsations contribute to a variety of problems in hydraulic power
systems, including:
• Noise (fluid-borne)
• Oscillations in flow meters, gauges, and controllers
• Unwanted amplification of disturbances on highly sensitive components.
Flow pulsations created by hydraulic pumps are caused by three things, namely:
• The volume of fluid being pumped does not decrease at a constant rate.
For example, in a piston pump, the volume of fluid being pumped is time-
dependent or a function of the angular displacement of the shaft, so the flow rate is
also time-dependent.
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• Gas locks, which occur due to a restriction in the inlet flow - the outlet pressure
drops rapidly when the gas lock enters the high-pressure line.
• Reverse flow (slip) from the high-pressure side of the pump to the low-pressure
side is constant.
Each type of pump has its own flow pulsation characteristics and before making a
final pump selection it is necessary to obtain information from the pump manufacturer
or conduct actual tests[4].
In practice, the most important characteristic of a centrifugal pump is the
relationship between head (or pressure) and capacity (or flow). Knowing the pressure-
flow function makes the centrifugal pump model compatible with models of
conventional hydraulic components. Thus, the centrifugal pump model can be
integrated into any standard hydraulic circuit for simulation. Figure 7 shows the
velocity components of a centrifugal pump having an inner radius r1 and an outer radius
r2 and rotating with an angular velocity ω. As can be seen in this figure, there are three
critical velocity components, labeled u, w and v. The quantities u and u2 represent the
tangential (linear circumferential) velocities at the inner and outer ends of the blade,
respectively. The quantities w1 and w2 represent the fluid velocities relative to the
blade at the inlet and outlet of the impeller. The quantities V1 and V2 are the absolute
velocities of the fluid at the inlet and outlet, vectorially composed of their
corresponding linear and relative velocities. The velocity angles (α1, αß) and the blade
pitch angles (ß1, ß2) are determined as shown in the figure. If we look at Fig. 7, these
velocity values have the following relationships:
U
1
=
ω
1
r
1
(1а)
U
2
=
ω
2
r
2
(1б)
V
t1
=W
1
sin ß
1
(2а)
V
t2
= w
1
sin ß
2
(2б)
Vu =v
1
cosα
1
= u
1
-w
1
cos ß
1
(3а)
V
12
= v
2
cosα
2
= u
2
-w
1
cos ß
2
(3ь)
Note that in the above equations the absolute velocities of the fluid are
represented by their tangential components (V
t1
, V
t2
) and normal components (V n
1
and
Vn
2
).
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Fig. 7. Diagram of impeller speeds
This is a convenient way to obtain a pressure-flow model using these velocity
components.
Assuming that the flow is steady, one-dimensional, and incompressible, the
volumetric flow rate Q passing through the pump, according to the law of continuity,
is
Q=2πr
1
b
1
, V
n1
=2πr
2
b
2
,V
n2 (4)
where: b1 (b2) - blade width at the inner (outer) end.
In the general design configuration, the arrangement of the blades results in the
velocity of the fluid entering the pump having a tangential component. Since the
magnitude and direction of the velocity constantly changes as the fluid passes through
the impeller, the angular momentum of the fluid also changes. This creates a torque on
the impeller. In other words, this is the amount of torque that must be applied to the
fluid to achieve the required flow characteristics. Based on angular momentum theory
and assuming an ideal system (i.e. no energy loss), the required torque T is
T = ρ Q(r
2
V
t1
-r
2
V
t2
) (5)
where ρ is the density of the liquid
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In addition, the power P transmitted from the shaft (=ωT) must be completely
transmitted to the liquid under ideal conditions, as shown below:
P =ωT= ρg Q h
р
(6)
where hр -pressure
h
1
=
) (7)
Equation 7 is the well-known Euler equation. Using a triangle, this equation
can be rewritten as
+
(8)
The first term on the right side of Equation 8 represents the pressure energy created
by the centrifugal force. The second term represents the flow effect of changing the
trajectory (shape and arrangement of the blades) as a function of the pressure energy.
The third term represents the increase in pressure energy as a result of the increase in
absolute fluid velocity.[9]
Fig.8. Curves of actual pressure dependence on productivity
If the fluid enters the impeller radially, then the angle a is equal to 90".
Substituting this value into equation 8 and combining it with equations (1b), (2b), (3b)
and (4) yields
(9)
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Therefore, for a given centrifugal pump operating under certain conditions (i.e.
the quantities ω, g2, b2, ß2 are known), the two coefficients on the right-hand side of
equation 9 are constant. When replacing the head h with a pressure p (= p g h), equal to
9, we get
(10)
where
K =
(11)
Some applications have different requirements for the pump performance. For
example, the pump may need to act as a motor due to the application of negative
external loads that create a backflow into the pump. Such an application may require
extremely low noise levels but still operate at relatively high pressures, say 300 bar
(4500 psi).
Obviously, a centrifugal pump has a linear pressure-flow relationship under the
assumed conditions specified in this section.
This is because the efficiency of a conventional pump drops off at high flows.
This characteristic means that two different pump flows can be used to produce the
same head. Having two delivery points at the same pressure can cause instability in a
pump with forward-curved vanes, so most centrifugal pumps have backward-curved
vanes.
Hydraulic efficiency depends on the design of the flow path and the way the fluid
passes through it. It is defined as the actual head (h) achieved compared to the ideal
head (h) delivered by the pump.
Friction losses are generally proportional to the square of the outlet flow.
Imperfect matching of the flow to the outlet vane angle b2 results in a circulating flow,
A centrifugal pump can be designed for a specific flow rate at a given speed when
the relative velocity is tangential to the inlet vane. Turbulent losses at this optimum
operating point are negligible. At other discharges, the head loss varies approximately
as the square of the deviation in approach angle.
Volumetric efficiency takes into account the loss of flow due to leakage. It is the
ratio of the actual flow rate (Q) delivered by the pump to the theoretical flow rate (Q)
calculated using equations 4. The actual flow rate is the theoretical flow rate minus the
leakage flow rate (Q)[12].
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(12)
Mechanical efficiency is the fraction of the mechanical power supplied to the
pump that is used to move the fluid. It is the ratio of the input power minus the power
losses (PL) to the input power (P). Mechanical power losses are mainly due to friction
in mechanical components such as bearings. The general trend is for mechanical
efficiency to decrease with increasing speed and flow capacity.[12]
(13)
Therefore, the overall efficiency is
(14)
Conclusions.
It was determined that a pump with an efficiency of 66% requires
50% more power. When these losses are translated into the cost of the additional power
required to do the job, the results are astounding. The type of hydraulic fluid used with
a given pump can have serious consequences if the pump and fluid are incompatible.
Too low a viscosity can result in excessive slippage, which can lead to inadequate
lubrication. Too high a vapor pressure at the pump suction can result in vapor cavitation
and subsequent destruction of the metal surface.
An important factor in selecting a pump is its filling characteristics.
Theoretically, for a positive displacement pump, the flow rate is directly (linearly)
related to the pump speed,
However, if sufficient liquid cannot be supplied to the pump chamber before the
suction port closes, the chamber is only partially filled and the pump operates in the
idle mode. This situation is illustrated in the figure for a given pump, liquid, temperature
and inlet pressure, and shows that a certain pump speed must not be exceeded,
otherwise the flow will be "choked off" and the pump will not operate. Another way to
obtain the required inlet pressure for a given pump speed. Similarly, for a given pump,
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liquid temperature and speed, the system must maintain a certain inlet pressure to avoid
cavitation.
References
1.
Fluid Power Communication Standards. Milwaukee, WI. National Fluid Power
Association. inc.1977
2.
Golygin A. Yu. Calculation and Design of a Centrifugal Pump. National
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3.
Tumakov A.A., Poleshkin M.S. Calculation and Design of a Centrifugal Pump.
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4.
Guyon M. Analysis and Design of Hydraulic Servo Systems
5.
New York, NY. PLENUM Press, 1969.
6.
Hutton R.E. Introduction to Hydraulic Fluids. New York, NY: Reinholp
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Rzhebaeva N.K., Rzhebaev E.E. Calculation and design of centrifugal pumps. -
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Yarashevich, P. N. J. (2023). Factors for Choosing a Marketing Strategy in
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13.
Nurillayev, J. Y. (2022). The role of corporate management system in
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14.
Махмудова, Г. Н., & Гуломова, Н. Ф. (2023). Unlocking the potential of the
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π-Economy, 16(4), 7-25.
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15.
Mikhailova S.V., Pogrebnaya I.A. Increasing the productivity of centrifugal
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