Dependence of pressure and power on speed. The main operating parameters of the blowers. Suction pressure loss
The centrifugal compressor is widely used in transport and aircraft engines (GTE), in closed-cycle gas turbine plants (CGTU), as well as in stationary installations and on helicopter gas turbine engines as the last stage of an axial centrifugal compressor.
When the wheel rotates, air is pumped through the channels formed by the blades to the periphery. A vacuum is formed in front of the wheel and the outside air is continuously supplied to the wheel through the inlet device. In the impeller, mechanical energy is supplied to the flow, under the action of which the working fluid is compressed in the impeller (>) and the kinetic energy of the flow in absolute motion (>) increases. From the impeller, gas enters the diffuser, in which the cross-sectional area increases with increasing radius. According to the continuity equation, the flow rate gradually decreases. In accordance with the Bernoulli equation, the kinetic energy in the diffuser is converted into pressure energy.
Rice. 1. Scheme of constructive types of impellers:
a) -open; b) -semi-open; c) -closed
Figure 1 shows the diagrams of the applied designs of impellers of centrifugal compressors. The open impeller has individual blades mounted on a bushing. When using an open-type RK, there are increased end losses associated with air overflow. Therefore, despite the relative structural simplicity, this type of wheel is of limited use. Closed impellers provide the highest efficiency. The cover disc reduces end loss. However, this type of wheel is structurally much more complicated than others and has a lower circumferential speed of rotation, allowed by strength conditions. Until recently, the most commonly used RK of a semi-open type, combining the advantage of open (ease of manufacture) and closed (reduced end losses) wheels.
When studying the working process in a centrifugal compressor, the concept of the degree of reactivity is used:
The speed triangles for wheels with different degrees of reactivity are shown in Fig. 2.
Rice. 2.The speed triangles of the RK centrifugal compressors with different degrees of reactivity:
a - blades bent against rotation; b — radial blades; c-blades curved in rotation
For radially located blades we get: and. The velocity triangle at the outlet from the RK in this case is shown in Fig. 2, b. In reality,< и < при и степень реактивности рабочего колеса с радиальными лопатками при несколько больше величины . Если угол выхода потока < (лопатки загнутые против вращения), то скорость в абсолютном движении на выходе из РК существенно меньше, чем при , и увеличивается степень реактивности . Именно в связи с ростом при уменьшении угла < РК с лопатками, загнутыми против вращения, получили название реактивных рабочих колес. Хотя в таких колесах, по сравнению с радиальными на выходе лопатками, при одинаковых окружных скоростях уменьшается величина (теоретический напор компрессора), использование их позволяет существенно улучшить эффективность работы выходной системы (безлопаточного и главным образом лопаточного диффузора) в результате уменьшения скорости потока. Кроме этого, протекание характеристик ступени с РК, имеющим загнутые против вращения лопатки, более благоприятно. В РК с лопатками, загнутыми по вращению >, there is a significant increase in the absolute flow rate and, consequently, a decrease in the degree of reactivity. In connection with a decrease in the degree of reactivity in wheels with> they are called active. At the highest theoretical head coefficient and, therefore, at a higher head at a given peripheral speed, the RK c> have the most gentle flow of the stage characteristics and the efficiency of the blade diffuser is difficult to ensure due to the high value of the air flow on the blades of the diffuser.
Figure 3 shows the dependence of the total theoretical work on the productivity at different outlet angles of the blades:
Rice. 3. Dependence of the total theoretical work on productivity at different outlet angles of the blades
2. SCHEME AND DESCRIPTION OF THE STAND
The tests are carried out at the "Centrifugal compressor stage" stand, the structural diagram of which is shown in Fig.4.
Rice. 4. Layout of the "Centrifugal compressor stage" stand:
1 – input device; 2 – impeller; 3 – electric motor; 4 – tachometer sensor; 5 – throttle; 6 – reverse radial guide vanes; 7-output capacity
The impeller 2 is driven into rotation by the electric motor 3. The air enters the compressor through the inlet 1, the measuring part of which is made along the lemniscate in accordance with GOST 27-64. This creates a uniform velocity field in front of the compressor. At the outlet of the compressor there is a reverse radial vane 6, from which air flows around the electric motor into the outlet container 7, then passing through the throttle valve 5.
By changing the speed of the electric motor and the position of the throttle valve, it is possible to set the compressor operating mode in the required range of parameters.
Rice. 5. Compressor impeller
The impeller of a semi-open centrifugal radial compressor has the following parameters (Fig. 5):
Inlet diameter;
Outlet diameter;
Blade height at the wheel entrance;
Height of the blade at the exit from the wheel;
Stream entry angle;
Angle of flow out of the impeller;
The number of blades;
Blade thickness;
Blade bending radius;
The radius of the circle at which the centers of the arcs of the bending of the blades are located.
During the experiment, the following are measured:
differential pressure across the inlet meter
ambient temperature
total compressor inlet pressure
air temperature at the outlet of the impeller
compressor outlet air temperature
stagnant flow pressure at the compressor outlet
static pressure at the outlet of the compressor
rotor speed
amperage
voltage
3.LABORATORY WORK No. 1
EXPERIMENTAL CHARACTERISTICS OF A STAGE OF A CENTRIFUGAL COMPRESSOR
3.1 PURPOSE OF THE WORK
Experimentally obtain the characteristics of a centrifugal compressor stage in the form of dependencies:,,,,.
3.2 GENERAL INFORMATION
When the compressor is operating in any system, due to a change in the operating modes of the system, the parameters at the compressor inlet change and the properties of the working fluid (air) change. For example, when a compressor is operating in an aircraft engine, in connection with a change in altitude and flight speed, the parameters at the inlet change: pressure, temperature, working fluid flow rate, rotation speed, air viscosity, its thermal conductivity and heat capacity, and, consequently, the ratio of heat capacities. For the efficiency and the degree of increase in total pressure in the general case, the following functional dependencies can be written:
The given dependencies, which are called compressor characteristics, are inconvenient in their practical use. This is due to the fact that and depend on many variables, which makes it almost impossible to represent them graphically.
In this regard, the construction of characteristics is based on the provisions of the theory of similarity, which allows, by introducing dimensionless parameters or similarity criteria, to reduce the number of variables that determine the characteristics of blade machines.
The phenomena are similar if geometric, kinematic and dynamic similarity is observed.
If one and the same machine is examined, then the change in dimensions due to thermal expansion and elastic deformations is not taken into account and the assumption is made that the geometric similarity is preserved.
To fulfill the kinematic similarity, it is necessary that the similarity of the velocity triangles be preserved, that is, the ratio of the peripheral speed to the absolute at similar points would be the same
It is known from the similarity theory that the gas-dynamic similarity in geometrically similar systems will be satisfied if the similarity criteria are equal. Applying the provisions of the theory of dimensions or considering the equations describing the phenomena in the initial and similar modes, it can be established that the gas-dynamic similarity is determined by the equality of the following criteria:
Adiabatic exponent;
Characterizing the effect of flow compressibility;
Characterizing the ratio of inertial and viscous forces in the flow to the nature of the flow and friction losses;
Characterizing the effect of the field of gravitational forces on the flow;
Characterizing the physical properties of the working fluid and does not depend on the flow parameters.
If we take into account that for gas the influence of the gravitational field is small, for air, and in most cases the blades operate in such an area of (self-similar) change in the number that the loss coefficients do not change with change, then the functional dependence (1) can be represented in the following form:
If, instead of numbers, we use reduced speeds uniquely associated with them, and instead of the value of a function, then we get the compressor characteristic presented in the form of dependencies:
where is the reduced peripheral speed.
Characteristics (3) are valid for the entire family of geometrically similar compressors and it is convenient to use them, for example, to determine the dimensions and parameters of a new compressor, for which the characteristics of its geometrically similar model are known.
For compressors of certain sizes, it is more convenient to use the characteristics of the compressor, in which, instead of and, complex parameters uniquely associated with them are used and are called, respectively, the reduced flow rate and the reduced speed. The use of these parameters seems to be more convenient, since they are directly related to such important parameters of the compressor as air flow rate, rotational speed and parameters of air at the compressor inlet, etc.
And the temperature and pressure value under standard conditions at the compressor inlet,
It is called the reduced flow rate, and since it corresponds to a certain value, then it can be considered as a similarity parameter.
The condition can be written for two similar modes:
It is called the reduced number of revolutions.
Compressor characteristics plotted as dependencies:
are called universal characteristics and allow, under the same inlet conditions, to compare the parameters of different compressors.
Rice. 6. Typical compressor characteristic
The characteristic of the compressor in the form of dependencies determined by the relationship (4) is shown in Fig. 6. An important feature of the compressor characteristics is the presence of a boundary of stable operation, called the pump boundary. To the left of this limit, due to a sharp drop in parameters and an increase in dynamic loads, the operation of the compressor is unacceptable. To the right is the area of stable modes, which are used when the compressor operates as part of a gas turbine engine. On such a characteristic, lines are usually applied in the form of topographic lines.
Under given operating conditions, the centrifugal stage has a capacity, and the total theoretical work is determined by the equation (PPM with< ):
The dependence of work on productivity (air flow) is straightforward. The slope of the straight line is determined by the outlet angle of the impeller blades. Figure 7. the straight line represents the theoretical characteristic of a centrifugal stage with outlet angles of the impeller blades< . Эффективная работа меньше, чем теоретическая. Величина работы в расчетной точке определяется уровнем потерь: профильных (трения и вихреобразования в пограничном слое на профиле, кромочные, волновые), вторичных (парный вихрь, вихрь от перетекания в радиальном зазоре, радиальное течение в пограничном слое вдоль лопатки) и концевых (боковое трение диска и бандажа, перетекание воздуха в радиальном зазоре). На нерасчетном режиме характер изменения работы определяется характером изменения профильных потерь, т.к. уровень концевых и вторичных потерь с изменением расхода не меняется. Профильные потери возрастают при отклонении от расчетного режима из-за отрывных явлений пограничного слоя с корытца профиля при малых расходах и из-за отрывных явлений со спинки профиля и роста волновых потерь при больших расходах.
Rice. 7. Characteristics of the centrifugal stage:
1 – terminal losses; 2 – secondary losses; 3-profile losses
3.3 EXPERIMENTAL PROCEDURE
3.3.1. Get acquainted with the experimental setup and the necessary measuring equipment.
3.3.2. Prepare blank tables of measured parameters.
3.3.3. Enable installation.
3.3.4. Set the preset compressor rotor speed with the rotational speed control knob. Withstand the mode.
3.3.5. Covering the throttle, measure the parameters of the compressor stage at intermediate points (6 - 7 points), while maintaining the given speed and maintaining the setting in each mode before measuring the parameters.
3.3.6. Enter the measurement results in the table (see table 1).
3.3.7. Turn off the installation.
Table 1
Measurement results
3.4 PROCESSING OF EXPERIMENTAL DATA
3.4.1. The translation of the obtained values, and in Pa is carried out taking into account the following ratios:
3.4.2. Determination of air flow:
From Bernoulli's equation:
where is the pressure loss in the inlet device.
In the first approximation, we assume that, and - due to low velocities in the input device.
The absolute value of the speed at the entrance to the wheel:
Static flow temperature at the wheel inlet:
where is the heat capacity,
Flux density at the wheel inlet:
Knowing the flow density, we specify the speed value:
The air flow rate is determined from the continuity equation:
where is the area of the inlet section of the compressor.
Where is the diameter of the inlet section.
3.4.3. Pressure loss in the inlet device:
where (design of the inlet device) is the coefficient of frictional resistance.
3.4.4. Retarded flow pressure at the wheel inlet:
3.4.5. Static pressure at the wheel inlet:
3.4.6. Specific work with insignificant heat exchange with the environment can be determined by the difference in total temperatures at the inlet and outlet of the compressor:
3.4.7. The work spent on rotating the wheel for each kilogram of air mass:
where is the work of friction of the disk on the gas,.
3.4.8. Compressor power:
3.4.9. Electric motor power:
The power of the electric motor can also be defined as:
where is the power spent on heating the air that cools the electric motor.
3.4.10. Out-of-wheel peripheral speed:
3.4.11. The peripheral component of the speed at the outlet of the centrifugal compressor wheel:
3.4.12. Wheel outlet area:
The number of blades;
3.4.13. Density of the decelerated flow at the outlet of the impeller:
3.4.14. The radial component of the flow velocity at the exit from the wheel:
As a first approximation, we assume that From the continuity equation:
3.4.15. The absolute value of the speed at the exit from the wheel:
3.4.16. Static air temperature at the wheel outlet:
3.4.17. Static pressure at the exit from the wheel:
3.4.18. Flux density at the outlet of the wheel:
3.4.19. We clarify the value of the speed at the exit from the wheel:
3.4.20. Pressure loss at the outlet of the installation:
3.4.21. Decelerated flow pressure at the outlet of the centrifugal compressor wheel:
3.4.22. Compressor pressure ratio:
3.4.23. Compressor adiabatic operation:
3.4.24. Compressor adiabatic efficiency:
3.4.25. Flow rate and speed values referred to standard atmospheric conditions
3.4.26. Enter the calculation results in the table (see table 2).
table 2
Calculation results
3.4.27. Build characteristics in the form of dependencies:,,,,.
3.4.28. Draw conclusions.
3.5 REQUIREMENTS FOR THE REPORT
4.LABORATORY WORK No. 2
KINEMATICS OF FLOW AT THE ENTRANCE OF A CENTRIFUGAL COMPRESSOR WHEEL
4.1 PURPOSE OF THE WORK
Investigation of the flow kinematics at the inlet to the wheel of a centrifugal compressor at design and non-design operating modes.
4.2 GENERAL INFORMATION
The absolute speed at the inlet to the impeller is equal to. The peripheral speed at this radius is. In relation to the wheel, the gas has a relative velocity. Direction and magnitude is defined as the vector sum of the relative speed and the peripheral speed.
If the impeller of a centrifugal compressor is radial, then the velocity triangle at the inlet is drawn in the plane perpendicular to the axis of rotation.
To obtain a shockless entry into the wheel, the angle of inclination of the wheel blades must be equal to the angle of the flow entry onto the blades. To reduce the energy losses associated with the conditions of flow entry onto the lattice of the working and guide vanes, attempts are made to provide a flow around the lattice profiles with an optimal angle of attack, usually close to the condition of the so-called shockless entry, i.e. ... It can be provided in two ways: the first is to direct the input edges of the wheel blades in the direction of rotation of the wheel in the absence of an input guide vane. In the semi-open type axial radial wheels, this is done by correspondingly bending the trailing edges of the blades and making these folded edges, often separately from the rest of the disc with blades, in the form of a so-called slat. The second method is a combination of a slat (but with a smaller bend of the blades) with the installation of an NNA (fixed guide vane), which swirls the flow in the direction of the wheel rotation. Conditions when, can be achieved by other methods as well, for example, by installing only NNA with positive flow swirl, in the absence of a slat; by a combination of a slat and an NNA with negative flow swirl. These methods are characterized by relatively large values of speeds or and the corresponding numbers and.
The design mode is the only operating mode of the compressor for which the gas-dynamic calculation is performed and the main geometrical dimensions of the stage, the angles of the blades, the density of the gratings, etc. are determined. The design mode is characterized by the fact that only in this mode the blade apparatus best matches the flow kinematics, i.e. provides uninterrupted flow around the blades of the impellers and the guide vanes of the compressor stages. However, during operation, most of the time the compressor operates under conditions different from the design mode, or, as they usually say, in non-design modes (Fig. 8.)
Rice. 8. Velocity triangles at the inlet to the centrifugal compressor stage at design and off-design operating modes
With a decrease in gas consumption at a constant rotor speed, instability of the compressor operation is also noted, associated with a change in the nature of the flow around the grilles of the impellers and fixed diffuser channels. When flowing around a blade at a certain value of the angle of attack> 0, a noticeable separation of the boundary layer occurs. This does not take place in the entire lattice at the same time, but in one of its channels. The resulting stall leads to blockage of this channel and spreading of the flow on both sides of it. On the one side of the channel, the angles of attack increase, on the other, they decrease. An increase in the angles of attack leads to a breakdown of the flow in the outlet part of the wheel blades. In this case, rotating separation zones are formed. The angular speed of their rotation is 2-3 times less than the angular speed of the wheel. This flow is called rotating stall. A further decrease in the gas flow rate through the compressor stage is associated with the intensification of disruptive phenomena and the excitation of vibrations.
With an increase in the flow rate in excess of the calculated one, the angle of attack decreases and becomes negative due to an increase in the radial velocity component. This leads to flow disruptions from the concave surface of the profile, a sharp increase in losses and, "locking" of the compressor. It should be noted that, in centrifugal compressors with vane diffusers, "closing" is determined, as a rule, by the flow mode around the diffuser blades, significantly reducing the range of stable operation of the compressor in terms of flow.
4.3 PROCESSING OF EXPERIMENTAL DATA
4.3.1. Experimental data processing is carried out on the basis of experimental data obtained in laboratory work No. 1.
4.3.2. The absolute value of the flow rate at the inlet to the wheel of a centrifugal compressor is taken from laboratory work No. 1.
Since (axial entrance to the wheel).
4.3.3. Peripheral speed at the entrance to the wheel:
where is the diameter of the flow inlet into the wheel,
Diameter of the flow exit from the wheel,
4.3.4. Flow entry angle into the wheel:
4.3.5. Attack angle:
where is the geometric angle of the flow into the wheel.
4.3.6. The relative value of the flow rate at the inlet to the wheel:
4.3.7. The absolute value of the flow rate at the wheel inlet at the optimal (design) compressor operating mode:
4.3.8. The relative value of the flow rate at the wheel inlet at the optimal (design) compressor operating mode:
4.3.9. Enter the calculation results in the table (see table 3).
Table 3
Calculation results
4.3.10. On graph paper, build the speed triangles at the inlet to the wheel of a centrifugal compressor, build a dependence.
4.3.11. Draw conclusions.
4.4 REPORTING REQUIREMENTS
The experiment is carried out in subgroups of 6 people. Each student in a subgroup has a detailed calculation of one flow rate mode. The report should contain the following parts:
5.LABORATORY WORK No. 3
KINEMATICS OF FLOW AT THE OUTLET OF THE CENTRIFUGAL COMPRESSOR WHEEL
5.1 PURPOSE OF THE WORK
Study of the flow kinematics at the outlet of the centrifugal compressor wheel.
5.2 GENERAL INFORMATION
The study of the flow kinematics at the outlet is reduced to the construction of a velocity triangle for various operating modes. The velocity triangle, with a known wheel geometry and rotation frequency, can be constructed if the radial component and the circumferential component of the absolute speed at the exit from the wheel are known.
If we assume that the flow path of the impeller consists of an infinite number of channels formed by an infinite number of blades of zero thickness, then the flow direction will fully correspond to the profile of the blades. Gas will exit the impeller at a relative velocity at an angle equal to the angle of inclination of the vane when exiting the impeller.
The work spent on the rotation of the wheel for each kilogram of air mass, according to the Euler equation (without taking into account the friction of the side surfaces of the wheel disc), is determined by the formula:
and for the axial entrance to the wheel:
Here the value depends on the number and length of the blades. At a finite number of blades, it decreases. When considering the movement of gas in the impeller in the proposal for an infinite number of blades, it is assumed that all streamlines have the same shape, and the blades are segments of streamlines. Hence it follows that the speed at any radius of the impeller is constant along the entire circumference. However, to transfer energy from the impeller blades to the flow, a pressure difference between both sides of the blade is required, which is possible only with a difference in speed on these sides. Thus, in contrast to the jet theory, the speed of movement is not constant around the circumference and changes periodically, since in each channel bounded by two adjacent blades, the flow pattern should be the same. In the channel of a rotating wheel with a finite number of blades, due to Coriolis acceleration, the relative velocities on an arc of a given radius vary linearly depending on the polar angle. As a result, at the front side of the blades, the speed is lower and the pressure is higher, and at the rear side - vice versa (Fig. 9).
Rice. 9. Change of speeds and pressure in the channel of a centrifugal compressor
The smaller the number of blades, the greater the difference in velocities at the front and rear walls of the blades. The appearance of an additional circumferential component can be explained by considering the process of equalizing the velocities at the exit from the wheel, where the flow flows freely, without the influence of external forces. When the velocities are equalized, the jets with a higher speed decrease their speed to a certain average value, and the jets with a lower speed increase it to this average value. As a result of this, some movement of air masses occurs at the periphery in the direction opposite to the rotation of the wheel, as a result of which a certain circumferential component appears. Due to the presence, the theoretical head, or work, imparted by 1 kg of air passing through the wheel decreases and, consequently, decreases. A decrease in the circumferential component is usually taken into account using a coefficient. The coefficient (it is usually called the coefficient of reduction of the transmitted energy) on the basis of theoretical and experimental studies for radial blades can be determined by the Kazanjan formula:
where is the average diameter of the inlet section of the wheel.
According to the Stodolla formula, the coefficient is
The average value of the coefficient fluctuates within
The velocity triangle at the outlet of the centrifugal compressor wheel is shown in Fig. ten.
Rice. 10. Speed triangle at the outlet of the centrifugal compressor stage
5.3 PROCESSING OF EXPERIMENTAL DATA
5.3.1. Experimental data processing is carried out on the basis of experimental data obtained in laboratory work No. 1.
5.3.2. The peripheral component of the speed at the exit from the wheel:
where is the work spent on the rotation of the wheel for each kilogram of air mass;
Out-of-wheel peripheral speed.
5.3.3. Wheel outlet area:
where is the thickness of the blade at the exit from the wheel;
The number of blades;
Height of the vane at the exit from the wheel.
5.3.4. Density of the decelerated flow at the outlet of the impeller:
5.3.5. The radial component of the flow velocity at the exit from the wheel:
As a first approximation, we assume that. From the equation of continuity:
5.3.6. The absolute value of the flow rate at the outlet of the wheel:
5.3.7. Static air temperature at the wheel outlet:
5.3.8. Static pressure at the exit from the wheel:
5.3.9. Flux density at the outlet of the wheel:
5.3.10. We clarify the value of the speed at the exit from the wheel:
5.3.11. The relative value of the speed at the exit from the wheel:
5.3.12. Flow exit angle from the wheel:
5.3.13. The angle of exit of the flow from the wheel in absolute motion:
5.3.14. Flow lag angle:
where is the geometric angle of the flow exit from the wheel of the centrifugal compressor.
5.3.15. Transmitted energy reduction factor:
where is the circumferential component of the speed at the exit from the wheel with an infinite number of blades.
According to the Stodolla formula, the coefficient is determined as:
5.3.16. The absolute value of the speed at the exit from the wheel with an infinite number of blades:
5.3.17. The relative value of the speed at the exit from the wheel with an infinite number of blades:
5.3.18. Geometric angle of flow out of the wheel in absolute motion:
5.3.19. Enter the calculation results in the table (see table 4).
Table 4
Calculation results
5.3.20. On graph paper, build the speed triangles at the outlet of the centrifugal compressor wheel, build a dependence.
5.3.21. Draw conclusions.
5.4 REPORTING REQUIREMENTS
The experiment is carried out in subgroups of 6 people. Each student in a subgroup has a detailed calculation of one flow rate mode. The report should contain the following parts:
Bibliography
1. Kholshchevnikov KV, Emin ON, Mitrokhin VT, Theory and calculation of aircraft blades: A textbook for university students in the specialty "Aircraft engines". 2nd ed., Rev. and additional - M.: Mechanical Engineering, 1986.432 p., ill.
2. Den GN Designing the flow part of centrifugal compressors: Thermogasdynamic calculations. - L: Mechanical engineering. Leningrad. branch, 1980. - 232 p., Ill.
3. Cherkassky VM Pumps. Fans. Compressors. Textbook for heat power engineering specialties of universities. M., "Energy", 1977
4. Seleznev KP Podobuev Yu. S. Theory and calculation of turbocompressors-L: Mechanical engineering, 1968.-408 p., Ill.
15.1. Delivery, head and power of the pump
The operation of the pump is characterized by its flow rate, head, power consumption, useful power, efficiency and speed.
Pump flow called the amount of liquid supplied by the pump per unit of time, or the flow rate of the liquid through the discharge pipe, usually denoted by the Latin letter Q.
Pump head is the energy difference of the weight of the liquid in the flow section in the discharge pipe (after the pump) and in the suction pipe (in front of the pump), referred to the weight of the liquid, i.e. energy per unit weight of a liquid, usually denoted by the Latin letter N. The pump head is equal to the difference in the total liquid head after the pump and in front of the pump
where the indices "n" and "sun" are the pressure and suction lines. The head is expressed in units of the column of fluid being displaced.
Power consumption of the pump called the energy supplied to the pump from the engine per unit of time, denoted N d .
Useful pump power or the power developed by the pump is called the energy that the pump imparts to the entire fluid flow per unit of time, denoted by -Nп.
For a unit of time, a liquid with a weight ofG w = ( Qρ )* g ... Each unit of this weight acquires energy in the amountH ( m).
This energy or useful power of the pump is
N n = QρgH = QP (15.2),
where because P = ρgH .
Power consumption of the pump N d more useful power N NS by the amount of losses in the pump. This power loss is estimated by the efficiency of the pump.
The pump efficiency is the ratio of the effective pump power to the engine power consumed by the pump :
η= N NS/ N etc. (15.3)
If the efficiency is known, the power consumption of the pump can be determined. N d = QρgH / η (15.4)
The value of power is expressed in SIvwatt system, in the technical system of units in kgm / s.
15.2 Working process of a vane pump
The moment of resistance forces about the axis opposes the rotation of the impeller, therefore the blades are profiled, taking into account the amount of feed, the frequency of rotation, the direction of movement of the fluid.
Overcoming the moment, the impeller does the work. Most of the energy supplied to the wheel is transferred to the fluid, and some of the energy is lost when overcoming resistances.
If the stationary coordinate system is associated with the pump casing, and the moving coordinate system with the impeller, then the trajectory of the absolute motion of the particles will be made up of the rotation (portable movement) of the impeller and the relative motion in the moving system along the blades.
The absolute speed is equal to the vector sum of the portable speed U - the speed of rotation of the particle with the impeller and the relative speed W movement along the blade relative to the movable coordinate system associated with the rotating wheel.
In fig. 15.2 the dash-dotted line shows the trajectory of the particle from the entrance to the exit from the pump in relative motion - AB, the trajectories of the transfer movement coincide with the circles at the wheel radii, for example, at the radii R 1 and R 2. The trajectories of particles in absolute motion from the pump inlet to the outlet - AS. The motion of a moving system is relative, in a moving system it is portable.
Parallelograms of speeds for entering and exiting the impeller:
(15.5)
The sum of the relative speed W and portable U will give absolute speed V .
Parallelograms of velocities in Fig. 15.2 show that the moment of velocity of a liquid particle at the outlet of the impeller is greater than at the inlet:
V 2 Cosα 2 R 2 > V 1 Cosα 1 R 1
Therefore, when passing through the wheel angular momentum increases. The increase in the angular momentum is caused by the moment of forces with which the impeller acts on the liquid in it.
For the steady motion of the liquid, the difference between the moments of the moment of momentum of the liquid leaving the channel and entering it per unit of time is equal to the moment of external forces with which the impeller acts on the liquid.
The moment of forces with which the impeller acts on the liquid is:
M = Q ρ( V 2 Cosα 2 R 2 - V 1 Cosα 1 R 1 ), where Q is the liquid flow rate through the impeller.
We multiply both sides of this equation by the angular velocity of the impeller ω.
M ω= Q ρ( V 2 Cosα 2 R 2 ω - V 1 Cosα 1 R 1 ω),
Work M ω called hydraulic power, or the work that the impeller produces per unit of time, acting on the liquid in it.
It is known from the Bernoulli equation that the specific energy , transferred to a unit of weight of a liquid is called a head. In the Bernoulli equation, the source of energy for the movement of the fluid was the difference in pressure.
When using a pump, energy or head is transferred to the liquid by the impeller of the pump.
The theoretical head of the impeller is H T called specific energy , transferred to a unit of fluid weight by the impeller of the pump.
N =M ω = H T * Q ρ g
Considering that u 1 = R 1 ω - portable (circumferential) speed of the impeller at the inlet and u 2 = R 2 ω - the speed of the impeller at the outlet and that the projections of the vectors of absolute speeds on the direction of the transport speed (perpendicular to the radii R1 and R2) are equal V u 2 = V 2 Cosα 2 and V u 1 = V 1 Cosα 1 , where V u 2 and V u 1 , we get the theoretical head in the form
H T * Q ρ g = Q ρ( V 2 Cosα 2 R 2 ω - V 1 Cosα 1 R 1 ω), where
(15.6)
Actual pump head 
less than the theoretical head since it takes real values of speeds and pressures.
Vane pumps are available in single-stage and multi-stage. In single-stage pumps, the liquid passes through the impeller once (see fig. 15.1). The head of such pumps at a given speed is limited. To increase the pressure, multistage pumps are used, which have several series-connected impellers fixed on one shaft. The pump head rises in proportion to the number of wheels.
The topic today is quite complex due to its original vastness and complexity of the theory of axial compressors. At least for me, it has always been like that in certain aspects :-). But based on the site's policy, I will try to reduce it to basic concepts, simplify it and squeeze it into one article. I don’t know what will happen ... We will see :-) ...
At the same time ... Speaking of such complex devices as an aircraft gas turbine engine, despite the constant striving for the simplicity of the story, one has to periodically refer to the exact technical sciences. Fortunately, this does not happen often, not deeply, and usually the school physics course is enough. Just like it is now :-).
So, a little bit of theory.
Video endoscope VJ-Advance from RF System Lab.
Devices of this kind are quite sophisticated, have a large number of functions and make it possible to reliably detect and comprehensively assess any damage in the compressor in almost any part of its air path.
In order for the probe of the video endoscope to enter the flow path, small-diameter holes (ports) are made in the compressor casing (usually between the blades of the HA), which are closed with sealed easily removable plugs. In this case, the compressor rotor rotates either manually (by the blades) from the air intake, or with the help of a special device (usually large engines on pylons).
A little about the design.
Rotors axial compressors by design, there can be three types: drum, disc or disco drum... When choosing a type of structure, various parameters are taken into account: mass, complexity, rigidity in the assembly, bearing capacity, circumferential speeds of the rotor. Disco-drum designs are more often used. The discs, depending on the parameters of the engine, are connected to each other and to the shaft by welding, bolted connections, using special splines.
Construction diagrams are OK. 1 - drum type, 2 - disco-drum type, 3 - disk type.
An example of an engine with a disco-drum compressor (Rolls-Royce RB.162-86).
Blades are fixed at the ends of the disc rims. The mounting method typical for a compressor is the so-called "dovetail" with an individual seat for each blade. The vanes can also fit into an annular groove on the rim of the disc. This is also a "dovetail", but with annular working surfaces.
OK blades with dovetail shanks of various configurations.
The fastening method with a herringbone lock is used much less frequently. This method is more often used for attaching turbine blades.
In addition, long blades (usually of the front steps) can be hinged in the annular grooves of the disc rim with fixation with special fingers to reduce the load on the pen and eliminate unnecessary vibration.
Such blades are radially oriented independently under the action of centrifugal force during engine operation (AL-21F-3 engine). To reduce vibration loads, long blades of the front steps can have special shroud flanges mating with each other (usually in the upper half of the blade airfoil or at several levels).
Attachment of axial compressor blades.
PW4000 motor with two shroud shelves on the fan.
However, in modern turbojet engines with a high degree of bypass, they have found application wide-chord shoulder blades(in the fan steps) without retaining shelves. This allows to increase the aerodynamic efficiency of the fan (up to 6%), increase the total air consumption and increase the engine efficiency (up to 4%). In addition, the weight of the fan and its noise level are reduced.
Bandaged shoulder blades OK.
Wide chord blades are manufactured using the latest technology. Special polymer-based composite materials (PCM) are used, hollow blades are made of titanium alloys with honeycomb fillers, as well as blades of non-polymer composite materials (for example, boron fiber in an aluminum matrix with titanium sheathing).
Stator the compressor is made either in the form of solid sections, or assembled from two halves (top-bottom). The vanes of the guide vane are mounted in an outer casing, usually in a connecting ring.
Fan blades. Wide-chord and regular with a bandage shelf.
Depending on the loads, vibration and purpose, they are either cantilever or (more often) along the inner casing are also combined with a ring with seals (honeycomb or easily erasable ( e.g. aluminographite- Al 2 O 3 + 8-13% graphite)). In this case, counter seals (usually comb-type seals with a labyrinth) stand on the rotor. This makes it possible to prevent harmful overflows of air onto the AN.
Compressor materials - aluminum alloys, titanium alloys, as well as steel.
On some modern engines, compressor impellers made using the technology "Blisk"(short for bladed disk), otherwise also called IBR (integrally bladed rotor). In this case, the rotor blades and the disc body itself are made as one piece. This is a single unit, most often cast or welded and processed accordingly.
Attachment of blades ON axial compressor.
Such designs are significantly stronger than composite discs. They have significantly fewer stress concentrators, such as, for example, which are inevitably present when using the blade attachment according to the "dovetail" principle. In addition, the weight of the entire structure is less (up to 25%).
In addition, the surface quality of the assembly and its streamlining are much better, which contributes to a decrease in hydraulic losses and an increase in the efficiency of a stage with such a disk (up to 8%). There is, however, the "blisk" and a significant drawback. In case of any damage to the blade, the entire disc must be replaced, and this inevitably entails the disassembly of the engine.
Blisk disc with blades.
In such a situation, along with borescopes, the use of special equipment (for example, firms Richard Wolf GmbH) for cleaning nicks and local elimination of emerging blade defects. Such operations are carried out using all the same viewing windows that are found in almost all stages of modern compressors.
Blisks are most often installed in the HPC of modern turbojet engines. An example is the SaM146 engine.
It is possible without a compressor.
A modern aviation gas turbine engine, together with all systems and assemblies that ensure its operation, is a very complex and delicate unit. Compressor in this regard, perhaps in the first place (maybe it shares it with the turbine :-)). But it is impossible to do without it.
In order for the engine to do work, there must be an apparatus for compressing air. And besides, it is necessary to organize the flow in the gas-air path while the engine is on the ground. In these conditions aircraft gas turbine compressor is no different from the compressor of a ground-based gas turbine.
However, as soon as the plane takes off and starts accelerating, the conditions change. Compression of air takes place not only in the compressor, but also in the inlet device, that is, in the air intake. As the speed increases, it can reach or even exceed the compression value in the compressor.
At very high speeds (several times the speed of sound), the pressure rise reaches an optimal value (corresponding to maximum traction performance or maximum efficiency characteristics). After that, the compressor, as well as the turbine driving it, become unnecessary.
Turbojet and ramjet engines in comparison.
The so-called Compressor degeneration or else "Degeneration" of the turbojet engine, because the engine ceases to be a gas turbine and, while remaining in the air-jet class, it should already be ramjet engine.
Aircraft MiG-25RB.
TRDF R15B-300.
An example of an engine that is, so to speak, on the way to compressor degeneration is the R15B-300 engine, which was installed on MiG-25 aircraft and was originally intended for flights with large ones. This engine has a very "short" compressor (5 stages) with a compression ratio of 4.75. A large proportion of compression (especially at supersonic) occurs in the air intake of the MiG-25.
However, these are already topics for other articles.
Thanks for reading to the end.
Until next time.
Photos are clickable.
At the end there are a few more pictures on the topic that did not fit into the text ……….
Speed triangles for an axial compressor stage.
Dovetail fan blades CFM56.
An example of articulated mounting of axial compressor blades.
Hollow titanium honeycomb fan blade.
One of the ways to expand the scope of centrifugal pumps is to change their speed.
The rotational speed of the rotor of a centrifugal pump significantly affects its main indicators: supply Q, head H and power on the pump shaft N.
When the rotor speed of a centrifugal pump changes from n1 to n2 rpm, the feed, head and shaft power change in accordance with the equations:
These ratios are called the law of proportionality.
From the above equations of the law of proportionality it follows:
These formulas are used to recalculate the pump characteristics for a new speed.
To build a new pump characteristic at a speed n2, on a given pump characteristic H = f (Q) at a speed n1, take several arbitrary points at different feed rates Q and the corresponding values of H. Next, using the laws of proportionality, one should calculate the flow rate Q2 and pressure H2. Using the new values of Q2 and H2, construct new points and through them draw a new characteristic of the pump H = f (Q) at a new speed n2.
When constructing the efficiency curve (η-Q), they use the fact that the efficiency of the pump remains practically constant when the number of revolutions changes over a fairly wide range. A decrease in the speed of up to 50% practically does not change the efficiency of the pump.
Determination of the speed of rotation of the pump shaft, which provides the supply of a predetermined flow rate of water.
The rotational speed n2 corresponding to the required flow rate Q2 should be found using the proportionality laws given above.
In this case, you should know that if we take on a given characteristic of the pump H at a speed of rotation n1, then it will be characterized by certain values of the flow rate Q1 and the pressure head H1. Further, with a decrease in the rotational speed to n2, using the laws of proportionality, it is possible to obtain new values of the coordinates of this point. Its position will be characterized by the values of Q2 and H2. If we further reduce the rotational speed to n3, then after recalculation we get new values of Q3 and H3, characterizing the point, etc.
If we connect all the points of a smooth curve, then we get a parabola going out from the origin. Consequently, when the pump shaft speed changes, the pump head and flow rate will be characterized by the position of the points lying on a parabola going out from the origin and called a parabola of such modes.
To determine Q1 and H1 included in the relations
Since the parabola must pass through the point with coordinates Q2 and H2, the constant coefficient of the parabola k can be found by the formula:
H2 is taken from the characteristics of the pipeline at a given flow rate Q2 or calculated by the formula:
where Hg is the geometric height of the rise; S is the resistance coefficient of the pipeline.
To build a parabola, you need to specify several arbitrary values of Q. The intersection point of the parabola with the pump characteristic H at the speed n1 determines the values of Q1 and H1, and the speed is determined as
The required rotation speed of the pump rotor can be determined analytically:
for water supply centrifugal pumps according to the formula:
where n1 and nconsum - respectively, the normal and required number of revolutions per minute;
Нг - geometrical lifting height;
Q cons - required feed;
n and m are the number of water conduit lines and the number of pumps, respectively;
a and b - pump parameters;
S is the resistance of one line of the water conduit;
for faecal centrifugal pumps according to the formula.
- density (the “weight” of the liquid)
- saturated vapor pressure (boiling point)
- temperature
- viscosity ("density" of the liquid)
Liquid characteristics
To select the optimal pump, it is necessary to have complete information about the characteristics of the liquid that should be supplied to the consumer. Naturally, the "heavier" liquid will require more energy when pumping a given volume. To describe how much "heavier" one fluid is than another, a term such as "density" or "specific gravity" is used; this parameter is defined as the mass (weight) of a unit volume of liquid and is usually denoted as “ρ” (Greek letter “ro”). It is measured in kilograms per cubic meter (kg / m 3). Any liquid at a certain temperature and pressure tends to evaporate (temperature or boiling point); an increase in pressure causes an increase in temperature and vice versa. Thus, at a lower pressure (even possibly a vacuum) that can occur on the suction side of the pump, the liquid will have a lower boiling point. If it is close to or especially below the current liquid temperature, vapor formation and cavitation in the pump can occur, which in turn can have negative consequences for pump performance and can cause serious damage (see chapter on cavitation). The viscosity of the fluid causes frictional losses in the pipes. A numerical value for these losses can be obtained from the manufacturer of the particular pump. Please note that the viscosity of “thick” liquids, such as oil, decreases with increasing temperature. Water flow This is defined as the volume that must be delivered in a specified time and is referred to as “Q”. Applied units of measurement: as a rule, these are liters per minute (l / min) for low power / capacity pumps, cubic meters per hour (m 3 / h) for medium-capacity pumps and, finally, cubic meters per second (m 3 / s) for the most powerful pumps.
The cross-sectional dimensions of the pipeline are determined by the volume that must be supplied to the consumer at a given fluid flow rate “v”: 
Geodetic (static) suction lift
It is defined as the difference in geodetic level between the pump inlet and the free surface of the liquid in the lowest-located tank, measured in meters (m) (Fig. 3, item 1).Static delivery head (static head)
It is defined as the difference in the geodetic level between the outlet pipe and the highest point of the hydraulic system to which it is necessary to supply fluid (Fig. 3, item 2).
Suction pressure loss
These are friction losses between the fluid and the pipeline walls and depend on the fluid viscosity, the quality of the pipeline wall surface roughness and the fluid flow rate. When the flow rate is doubled, the pressure loss increases to the second degree (Fig. 4, item 1). Information on pressure losses in piping, elbows, fittings, etc. at different flow rates can be obtained from the supplier. Pressure loss in the discharge line See description above (fig. 4, item 2).Final overpressure
This is the pressure that must be maintained at the point where the liquid is to be supplied (fig. 5, pos. 1).Initial overpressure
This is the pressure on the free surface of the liquid at the point of water intake. For an open tank or tank, this is simply the atmospheric (barometric) pressure (fig. 5, item 2).The relationship between head and pressure
As you can see from fig. 6, a column of water 10 m high exerts the same pressure as a column of mercury (Hg) with a height of 0.7335 m. N / m 2) or in pascals (Pa). Since this is a very small value, a unit of measurement equal to 100,000 Pa, called a bar, was introduced into the practice of operating pumps.
The equation in Fig. 6 can be solved in meters of the height of the liquid column: 
Thus, the height of the column of liquids with different viscosities can be reduced to the equivalent height of the water column. In fig. 7 provides conversion factors for many different pressure units. An example of calculating the total hydraulic head with a pump installation diagram is shown below. 
The hydraulic power (P hyd) of a pump determines the volume of fluid delivered at a given head in a given time and can be calculated using the following formula: 
Example
A volume of 35 m 3 of water per hour must be pumped from a well 4 m deep into a tank located at a height of 16 m relative to the pump installation level; the final pressure in the tank must be 2 bar. Friction head losses in the suction pipeline are taken equal to 0.4 m, and in the pressure pipeline they are 1.3 m, including losses in the elbows. The density of the water is assumed to be 1000 kg / m 3 and the value of the acceleration due to gravity is 9.81 m / s 2. Solution: Total head (H): Suction head - 4.00 m Suction head loss - 0.40 m Discharge head - 16.00 m Pressure loss in the discharge line - 1.30 m Final pressure: - 2 bar * ~ 20 , 40m Minus 1 atm ** ~ -9.87 m Total head - 32.23 m Hydraulic power is determined by the formula:
* In this example, the final gauge pressure is given as absolute pressure, i.e. as pressure measured relative to absolute vacuum. ** If the final gauge pressure is given as absolute, then the initial gauge pressure must be subtracted as this pressure “helps” the pump to suck in liquid. 
Water through the suction pipe of the pump enters the inlet of the impeller and experiences a positive acceleration under the action of the rotating blades. In the diffuser, the kinetic energy of the flow is converted into potential pressure energy. In multistage pumps, the cross-section of a diffuser with integral fixed blades is referred to as a “diffuser”. From the diagram in Fig. 10 it can be seen that the potential energy in the form of pressure in the pump increases in the direction from the suction to the discharge nozzle, since the hydrodynamic pressure created by the impeller (kinetic energy of the flow velocity) is converted into potential pressure energy in the diffuser. 
Pump performance
In fig. 11 shows the typical performance of a “Q / H” centrifugal pump. It can be seen from it that the maximum discharge pressure is reached when the pump flow is zero, i.e. when the pump discharge port is closed. As soon as the flow in the pump increases (the volume of the pumped liquid increases), the delivery head drops.
The exact characteristic of the dependence of the flow rate Q on the head H is determined by the manufacturer empirically on a test bench. For example (fig. 11), with a head of H 1, the pump will deliver the volume Q 1 and similarly with H 2 - Q 2. Pump performance
As already shown above, friction head losses in the pipeline depend on the quality of the surface roughness of the pipeline walls, and the square of the fluid flow rate and, of course, on the length of the pipeline. Friction pressure loss can be plotted on the “H / Q” graph as a hydraulic performance curve. In the case of closed systems such as central heating systems, the current delivery head may not be taken into account as it is balanced by the positive head on the suction side.
Pressure loss [Pa / m] at t = 60 ° C. Recommended losses in pipes - no more than 150 Pa / m. Working point
The duty point is the intersection of the pump performance curve with the hydraulic performance curve. It is clear that any changes in the hydraulic system, for example, a change in the flow area of the valve when it is opened or the formation of deposits in the pipeline, affects the characteristics of the hydraulic system, as a result of which the position of the operating point changes. Likewise, changes in the pump, such as wear on the impeller or changes in speed, will create a new duty point.
Series connected pumps
Multi-stage pumps can be considered as an example of single-stage pumps connected in series. Of course, in this case it is impossible to separate the individual stages, which is sometimes desirable when checking the condition of the pump. Since a non-running pump creates significant resistance, a bypass line and a non-return valve must be provided (fig. 14). For pumps operating in series, the total head (Fig. 15) at any given flow rate is determined by the sum of the pump head values for each individual pump.
Parallel connected pumps.
This installation scheme is used to monitor the status of pumps or to ensure operational safety when auxiliary or redundant equipment is required (for example, twin pumps in a heating system). In this case, it is also necessary to install check valves for each of the pumps to prevent backflow through one of the idle pumps. In tandem pumps, these requirements are met by a flap-type changeover valve. For pumps operating in parallel, the total flow (fig. 17) is defined as the sum of the flow rates of the individual pumps at a constant head.
Pump efficiency
The efficiency of a pump indicates how much of the mechanical energy transferred to the pump through its shaft has been converted into usable hydraulic energy.
The efficiency is influenced by: - pump casing shape;
- the shape of the impeller and diffuser;
- surface roughness quality;
- sealing gaps between the suction and discharge cavities of the pump.
In order for the user to be able to determine the efficiency of the pump at a particular operating point, most pump manufacturers attach diagrams with efficiency characteristics graphs to the pump performance charts (Fig. 18).
Typical patterns
The givenFurthertypicallawnumberingdemonstratetheoreticalinfluencediameter ( d ) worker wheels onpressure, filing andconsumedpower. The head is proportional to the diameter to the second degree:
According to this pattern, doubling the diameter will increase the head by 4 times. The feed is proportional to the diameter to the third power: 
According to this pattern, doubling the diameter will increase the feed by 8 times. The power consumption is proportional to the diameter to the fifth power: 
According to this pattern, doubling the diameter will increase the power consumption 32 times. 
Typicalpatterns
The givenFurthertypicallawnumberingdemonstratetheoryticinfluencefrequency turn niya (n) worker wheels onpressure, filingandconsumedpower. The feed is proportional to the speed:
According to this pattern, doubling the speed will double the feed. The head is proportional to the square of the speed: 
According to this pattern, doubling the speed by 4 times will increase the head. The power consumption is proportional to the rotational speed to the third power: 
According to this pattern, doubling the speed by 8 times will increase the power consumption. Consumedpower
P 1 : Power consumed by the electric motor from the mains. For electric motors directly connected to the pump shaft, as is the case for circulating pump drives, the maximum power consumption is indicated on the rating plate. P 1 can also be determined by the following formula: (3-phase motors) (1-phase motors) where: V = voltage (V) I = current (A) cos ϕ = power factor (-) P 2: power at the motor shaft. When the motor and pump are separate units (including standard and submersible motors), the maximum shaft power of the motor is indicated on the nameplate. P 3: Power absorbed by the pump The current load of the motor can be determined from the pump power curve. In the case of direct connection of the electric motor to the pump shaft: P 3 = P 2. P 4: Pump power (P hydraulic) The pump power value is determined by the formula:
Adaptationpumpsto variablesregimesexploitation
The pressure loss in the hydraulic system is calculated for certain specific operating conditions. In practice, the characteristic of the hydraulic system almost never coincides with the theoretical one due to the safety factors laid down in the hydraulic system. The duty point of a hydraulic system with a pump is always the intersection of the pump performance curve with the hydraulic performance curve, therefore, the flow is usually higher than required for a new hydraulic system. This discrepancy can create problems in the hydraulic system. In heating circuits, flow-induced noise can occur, in condensate systems, cavitation, and in some cases an unreasonably high flow leads to energy losses. As a result, it becomes necessary to shift the operating point (the point of intersection of the graphs of both characteristics) by adjusting the pump and tuning the hydraulic system. In practice, one of the following methods is used:- Changing the characteristics of the hydraulic system by closing the throttle valve (throttling) (Fig. 22).
- Change in pump characteristics by reducing the outer diameter (by machining) of its impeller (Fig. 23).
- Changing the pump characteristic by adjusting the speed (fig. 24).
Regulationfiling withhelpthrottlevalve
Reducing the flow area of the throttle valve in the hydraulic system causes an increase in pressure losses (head H dyn), making the hydraulic characteristic curve steeper, as a result of which the operating point shifts towards a lower flow (see figure 25). As a result, the power consumption is reduced, since centrifugal pumps have a power characteristic that decreases with decreasing flow. However, power losses during throttle control in a hydraulic system with a high power consumption value will be significant, therefore, in such cases, special calculations must be carried out to assess the profitability of the flow control method using a throttle valve.
Worker modificationwheels
In cases where a decrease in pump performance and head is required constantly, the most optimal solution may be to reduce the outer diameter of the impeller. In this case, either the entire impeller or only the ends of the blades are machined along the outer diameter. The greater the underestimation of the outer diameter, the lower the efficiency of the pump will become. The decrease in efficiency is usually more significant in those pumps that operate at high speeds. With slow-speed pumps, it is not so noticeable, especially if the reduction in the outer diameter is negligible.
When the decrease in the outer diameter is insignificant, the following relations can be used with a sufficiently high degree of accuracy: 
In fig. 27 shows a method for determining an underestimated diameter D x using a diagram of the “H / Q” characteristic in linear coordinates. The origin (Q = 0, H = 0) is connected to the new operating point (Q x, H x) by a straight line, extended until it intersects with the curve of the existing pump (Q, H) at point “s”. The new diameter (D x) is then calculated using the following formula: 
However, these dependencies are not valid if a significant reduction in pump performance is required. In this case, it is recommended to lower the impeller in several stages. First, the impeller diameter is underestimated to a size slightly exceeding the D x value calculated as indicated above. The pump is then tested, after which the final diameter can be determined. This can be avoided in series production. Performance curves are available for pumps equipped with impellers with various undersizing of the outer diameter (see fig. 28), from which the D x value can be directly calculated using the above formulas. 
Frequency regulationrotation
Changing the speed will cause changes in the performance of the centrifugal pump. We will use the typical patterns indicated earlier:
Cavitation
The most common problems encountered in pump operation are related to the suction conditions at the inlet of the hydraulic system and are almost always caused by too low hydrostatic pressure (head) at the pump inlet. The reason for this may be rooted either in the choice of a pump with parameters that are not optimal for the given operating conditions, or in mistakes made in the design of the hydraulic system. The rotation of the impeller throws the liquid to the surface of the pump casing, as a result of which a vacuum occurs on the side of the suction cavity of the impeller. This causes the liquid to suck through the suction valve and pipeline, which flows to the impeller, where it is again thrown back to the surface of the pump housing. The vacuum at the pump inlet depends on the difference between the level of the position of the inlet and the surface of the pumped liquid, on the frictional pressure loss in the suction valve and pipeline, as well as on the density of the liquid itself. This vacuum is limited by the saturated vapor pressure of the liquid at a given temperature, i.e. pressure at which vapor bubbles will form. Any attempt to lower the hydrostatic pressure to a value less than the saturated vapor pressure will cause the liquid to react with vapor bubbles as it begins to boil.
In a pump, cavitation occurs when the pressure on the side of the impeller blades facing the suction cavity (usually near the pump inlet) drops below the saturated vapor pressure of the liquid, causing gas bubbles to form. When transferred to a high pressure area in the impeller, these bubbles collapse (explode), and the resulting pressure wave can damage the pump (Fig. 31). This damage, which can occur within a few minutes or after a few years, is so serious that it can adversely affect not only the pump, but also the electric motor. The most vulnerable parts are bearings, welds and even impeller surfaces. The extent of damage to the impeller depends on the characteristics of the material from which it is made; For example, the table shows that under the same conditions, the damage to the stainless steel impeller is only 5% of the damage to the cast iron impeller. A lossvmassvarious materials(when comparing, cast iron = 1.0 is taken as a basis): Increased noise level, pressure drop and operational instability are also associated with the cavitation phenomenon. Often, damage remains undetected until the pump and motor have been disassembled. 
Calculationsoneliminatingdangerscavitation
The pump cavitation margin H max, required to eliminate the risk of cavitation, is calculated as follows: H max: The pump cavitation margin (see fig. 33). If he positive, the pump can operate at a given suction lift. If he negative, for the pump to work, it is necessary to create conditions under which it becomes positive. H b: Atmospheric pressure at the pump side; this is the theoretical maximum suction lift. This H b value depends on the density of the liquid and the “g” value on the pump side (fig. 32).
H fs: The frictional pressure loss in the suction valve and the connected piping also depends on the density of the liquid. 
NPSH: N et P ositive S uction H ead
This parameter reflects the minimum suction pressure required for trouble-free operation. It characterizes the frictional pressure loss in the area from the suction pipe of the pump to the point of the first impeller at which the pressure is minimal, and determines the hydraulic conditions under which the pump is unable to suck in a solid column of water 10.33 m high.Thus, the NPSH value will increase with increasing feed, which can be seen from the characteristic graph in Fig. 35 concrete pump. For circulating pumps, the NPSH schedule is not used; instead, in fig. 34 is a table showing the minimum suction pressure required at various temperatures of the working fluid. H v: This parameter reflects the saturated vapor pressure of the pumped liquid. It is included in the equation because the higher the temperature, the liquid starts to evaporate faster. H v also depends on the density of the liquid:
H s: This parameter is a margin of safety, which should be determined in specific conditions, depending on the degree of reliability and reliability of the applied calculation method. In practice, it is taken equal to 0.5-1 m. In the case of the presence of gas in the water, this value is often chosen equal to 2 m. 
Howto avoidcavitation
This reasoning is based on the above formula: H max = H b - H fs - NPSH - H v - H s and takes into account the influence of each of the members of the equation. H max: The pump should always be set as low as possible or the liquid level on the suction side will need to be raised. The latter is often the cheapest solution. The positive suction pressure generated by the pump (if any) or expansion tank should be kept as high as possible. H b: This figure is constant when pumping a certain liquid in a given location. H fs: The suction piping should be as short as possible and have a minimum number of elbows, valves, valves and fittings. NPSH: Select the pump with the lowest NPSH requirement. H v: This parameter may decrease as the fluid temperature (ambient temperature) drops. H s: Installed individually. The easiest way to avoid cavitation is to reduce the pump flow by partially closing the discharge (or pressure) valve; as a result, the required value of NPSH and H fs will decrease, hence the value of H max will increase.Alternativemethodologycalculationforeliminatingdangerscavitation
Many people prefer to convert the formula to NPSH functions like this:
This gives the available NPSH available for a given hydraulic system, which can then be compared to the required NPSH required as shown on the performance curves of the respective pump. Thus, if NPSH available ≥NPSH required, cavitation can be avoided. However, if NPSH is available ≤NPSH required then the risk of cavitation remains. Connectionelectric motor "GRUNDFOS» vaccording to the designation on its nameplate
Decodingdesignations: “ - “Means“ from - to “; " / “Means that the motor can be connected in two different ways; " D“Designation of the connection of the motor windings according to the" triangle "scheme; " Y“Designation of the connection of the windings of the electric motor according to the" star "scheme. 1 NS220-230 / 240 V- The motor can be connected to a single-phase AC network with a voltage of U = 1 x 220-230V.
- The motor can be connected to a single-phase AC network with a voltage of U = 1 x 240V.
3
NS220
–
240D / 380–
415Y V
- The motor can be connected to a three-phase AC network with a voltage of U = 3 x 380-415V in a "star" circuit.
- The motor can be connected to a three-phase AC network with a voltage of U = 3 x 220-240V according to the "delta" scheme (for example, in Belgium, Norway, Italy, France).
- The motor can be connected to a three-phase AC network with a voltage of U = 3 x 220-240V according to the "star-delta" scheme.
3
NS380
–
415D V
- The motor can be connected to a three-phase AC network with a voltage of U = 3 x 380-415V according to the "delta" scheme.
- The motor can be connected to a three-phase AC network with a voltage of U = 3 x 380-415V according to the "star-delta" scheme.
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