Pressure characteristics of the pipeline network. Dependence of flow, head and power on the number of revolutions of the pump Dependence of head and power on speed
One of the ways to expand the scope of centrifugal pumps is to change their speed.
The speed of rotation of the rotor of a centrifugal pump significantly affects its main indicators: flow Q, head H and power on the pump shaft N.
When changing the speed of rotation of the rotor of a centrifugal pump from n1 to n2 revolutions per minute, the flow, head and power on the shaft 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:
According to these formulas, the pump characteristics are recalculated for a new number of revolutions.
To build a new pump characteristic at a speed of rotation n2, one should take several arbitrary points at a given pump characteristic H = f (Q) at a speed of rotation n1 at different feeds Q and the corresponding values of H. Next, using the laws of proportionality, one should calculate the flow rates Q2 and pressure H2. Based on the new values of Q2 and H2, construct new points and draw a new pump characteristic H=f (Q) through them at a new number of revolutions n2.
When constructing the efficiency curve (η-Q), they use the fact that the efficiency of the pump remains practically constant when the speed changes over a fairly wide range. Reducing the speed to 50% causes practically no change in the efficiency of the pump.
Determining the speed of the pump shaft, which provides the supply of a predetermined flow of water.
The speed n2 corresponding to the desired flow rate Q2 should be found using the proportionality laws given above.
At the same time, you should know that if you take on a given pump characteristic H at a speed of rotation n1, then it will be characterized by certain values of the flow rate Q1 and the pressure H1. Further, when the rotation frequency decreases 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 will obtain new values of Q3 and H3 characterizing the point, and so on.
If we connect all the points of a smooth curve, we get a parabola coming out of the origin. Consequently, when the pump shaft speed is changed, the value of the pressure and the pump flow will be characterized by the position of the points lying on the parabola emerging from the origin and called the parabola of similar 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 is calculated by the formula:
where Hg is the geometric height of the lift; S is the coefficient of resistance 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 number of revolutions n1 determines the values of Q1 and H1, and the rotational speed is determined as
The required speed of rotation of the pump rotor can be determined analytically:
for plumbing centrifugal pumps according to the formula:
where n1 and ncons are, respectively, the normal and required number of revolutions per minute;
Hg is the geometric height of the lift;
Q cons - the required supply;
n and m are the number of conduit lines and the number of pumps, respectively;
a and b are pump parameters;
S is the resistance of one line of the conduit;
for fecal centrifugal pumps according to the formula.
- density (“gravity” of a liquid)
- saturated vapor pressure (boiling point)
- temperature
- viscosity (“thickness” 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, a “heavier” liquid will require more energy to pump a given volume. To describe how much one liquid is “heavier” than another, such concepts as “density” or “specific gravity” are 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 the lower pressure (even possibly under vacuum) that may be present on the suction side of the pump, the liquid will have a lower boiling point. If it is near or especially below the current liquid temperature, steam may form and cavitation may occur in the pump, which in turn may have a negative effect on its performance and may cause serious damage (see chapter on cavitation). The viscosity of the fluid causes frictional losses in the pipes. The numerical value of these losses can be obtained from the manufacturer of a particular pump. It must be taken into account that the viscosity of “thick” liquids, such as oil, decreases with increasing temperature. Water consumption It is defined as the volume that must be supplied in a specified time, and is denoted as “Q”. Applied units of measurement: as a rule, it is liters per minute (l / min) for pumps of small capacity / capacity, cubic meters per hour (m 3 / h) for pumps of medium capacity, and finally, cubic meters per second (m 3 / s) for the most powerful pumps.
The dimensions of the cross-section 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 liquid surface in the lowest located tank, measured in meters (m) (fig. 3, pos. 1).Static feed height (static head)
It is defined as the difference in geodetic level between the outlet and the highest point of the hydraulic system to which fluid must be supplied (fig. 3, item 2).
Suction pressure loss
These are friction losses between the liquid and the pipeline walls and depend on the viscosity of the liquid, the quality of the surface roughness of the pipeline walls and the fluid flow rate. With an increase in the flow rate by a factor of 2, the pressure loss increases to the second degree (Fig. 4, pos. 1). Information about pressure losses in pipelines, elbows, fittings, etc. at various flow rates available from your supplier. Pressure loss in the pressure pipe See description above (fig. 4, item 2).final overpressure
This is the pressure that must be at the point where the liquid must be supplied (Fig. 5, pos. 1).Initial overpressure
This is the pressure on the free surface of the liquid at the point of intake. For an open reservoir or tank, this is simply atmospheric (barometric) pressure (Fig. 5, item 2).Relationship between head and pressure
As can be seen from fig. 6, a column of water 10 m high exerts the same pressure as a column of mercury (Hg) 0.7335 m high. Multiplying the height of the column (pressure) by the density of the liquid and the acceleration of gravity (g), we get the pressure in newtons per square meter ( N / m 2) or in pascals (Pa). Since this is a very small value, a unit of measurement equal to 100,000 Pa, called the bar, was introduced into the practice of operating pumps.
The equation in fig. 6 can be solved in meters of liquid column height: 
Thus, the height of the column of liquids with different viscosities can be reduced to the equivalent height of the water column. On fig. 7 shows conversion factors for many different pressure units. Below is an example of calculating the total hydraulic head with a pump installation diagram. 
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 level of the pump installation; the final pressure in the tank must be 2 bar. The frictional pressure loss in the suction pipeline is assumed to be 0.4 m, and in the discharge pipeline it is 1.3 m including losses in the elbows. The density of water is assumed to be 1000 kg/m 3 and the acceleration due to gravity is 9.81 m/s 2 . Solution: Total head (H): Suction lift - 4.00 m Suction head loss - 0.40 m Discharge head - 16.00 m Discharge line pressure loss - 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 an absolute pressure, i.e. as pressure measured relative to absolute vacuum. ** If the final overpressure is given as absolute, then the initial overpressure must be subtracted as this pressure “helps” the pump to draw liquid. 
Water enters the impeller inlet through the suction pipe of the pump and experiences positive acceleration under the action of rotating blades. In the diffuser, the kinetic energy of the flow is converted into potential pressure energy. In multistage pumps, the cross section of the diffuser with integral fixed vanes is referred to as the “vane”. 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 (the kinetic energy of the flow velocity) is converted into potential pressure energy in the diffuser. 
Pump Performance
On fig. 11 shows a typical performance curve for 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 outlet is closed. As soon as the flow in the pump increases (the volume of the pumped liquid increases), the discharge head drops.
The exact characteristic of the dependence of the supply Q on the head H is determined by the manufacturer empirically on a test bench. For example (Fig. 11), with a pressure of H 1, the pump will supply a volume of Q 1 and similarly with H 2 - Q 2. Pump Performance
As already shown above, the friction pressure loss in the pipeline depends on the quality of the surface roughness of the pipeline walls, and the square of the fluid flow velocity and, of course, on the length of the pipeline. Friction pressure loss can be represented on the “H/Q” graph as a hydraulic system characteristic curve. In the case of closed systems, such as central heating systems, the current discharge head may not be taken into account, since it is balanced by the positive pressure on the suction side.
Pressure loss [Pa/m] at t = 60°C. The recommended losses in pipes are no more than 150 Pa/m. Operating point
The duty point is the intersection point of the pump characteristic curve with the hydraulic system characteristic curve. It is clear that any changes in the hydraulic system, such as a change in the flow area of the valve when it is opened or the formation of deposits in the pipeline, affect the characteristics of the hydraulic system, as a result of which the position of the operating point changes. Likewise, changes to the pump, such as impeller wear or speed changes, will cause a new duty point to occur.
Pumps in series
Multistage pumps can be seen as an example of single stage pumps in series. Of course, in this case it is not possible to isolate the individual stages, which is sometimes desirable when checking the condition of the pump. Since a non-working pump creates significant resistance, a bypass line and a check valve must be provided (fig. 14). For pumps operating in series, the total head (Fig. 15) at any given flow is determined by the sum of the discharge heights of each individual pump.
Parallel connected pumps.
This installation scheme is used to monitor the condition of the pumps or to ensure operational safety when ancillary or redundant equipment is required (eg twin pumps in a heating system). In this case, it is also necessary to install check valves for each of the pumps in order to prevent backflow through one of the non-working pumps. These requirements in twin pumps are met by a flap type changeover valve. For pumps operating in parallel, the total flow (fig. 17) is determined as the sum of the flow values of the individual pumps at a constant head.
pump efficiency
The pump efficiency shows how much of the mechanical energy transferred to the pump through its shaft is converted into useful hydraulic energy.
Efficiency is affected by: - the shape of the pump body;
- the shape of the impeller and diffuser;
- quality of surface roughness;
- sealing gaps between the suction and discharge chambers of the pump.
In order for the user to be able to determine the efficiency of the pump at a particular duty point, most pump manufacturers attach diagrams with efficiency curves to the pump performance curves (Fig. 18).
Typical patterns
GivenFurthertypicallawnumbersdemonstratetheoreticalinfluencediameter ( d ) working wheels on thepressure, filing andconsumedpower. The pressure is proportional to the diameter to the second power:
According to this pattern, doubling the diameter will increase the pressure 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 by 32 times. 
Typicalpatterns
GivenFurthertypicallawnumbersdemonstratetheoryticinfluencefrequencies spin nia (n) working wheels on thepressure, filingandconsumedpower. The feed is proportional to the speed:
According to this pattern, doubling the RPM 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 pressure. 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 motor from the mains. For motors that are directly connected to the pump shaft, as is the case with the drive of circulation pumps, the maximum power consumption is indicated on the rating plate. P 1 can also be determined using the following formula: (3-phase motors) (1-phase motors) where: V = voltage (V) I = current (A) cos ϕ = power factor (-) P2: power at the motor shaft. When the motor and pump are separate units (including standard and submersible motors), the rating plate indicates the maximum shaft power of the motor. P3: Power absorbed by the pump The current motor load can be determined from the pump power curve. In case of direct connection of the electric motor to the pump shaft: P 3 = P 2 . P4: Pump power (P hydraulic) The value of the pump power is determined by the formula:
Adaptationpumpsto variablesmodesexploitation
Pressure losses in the hydraulic system are 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 incorporated into the hydraulic system. The duty point of a hydraulic system with a pump is always the intersection point of the pump characteristic curve with the hydraulic system characteristic curve, therefore, the flow is usually higher than required for a new hydraulic system. This mismatch can create problems in the hydraulic system. Flow noise can occur in heating circuits, cavitation in condensate systems, and in some cases an unnecessarily large supply 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 adjusting the hydraulic system. In practice, one of the following methods is used:- Changing the characteristics of the hydraulic system by covering the throttle valve (throttling) (Fig. 22).
- Changing the characteristics of the pump 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 orifice of the throttle valve in the hydraulic system causes an increase in pressure loss (hydrodynamic head H dyn), making the curve of the hydraulic system steeper, causing the operating point to shift in the direction of lower flow (see Fig. 25). As a result, power consumption is reduced, since centrifugal pumps have a power characteristic that decreases as the flow decreases. However, power losses during throttling in a hydraulic system with a high power input will be significant, therefore, in such cases, it is necessary to carry out special calculations to assess the profitability of the method of flow control using a throttling valve.
Worker modificationwheels
In cases where a reduction in pump performance and head is required permanently, the most optimal solution may be to reduce the outer diameter of the impeller. At the same time, 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 reduction in efficiency is usually more significant in those pumps that operate at high speeds. With low-speed pumps, it is not so noticeable, especially if the reduction in the outer diameter is insignificant.
When the decrease in the outer diameter is insignificant, then with a sufficiently high degree of accuracy, the following relationships can be used: 
On fig. 27 shows a method for determining the underestimated diameter Dx using the "H/Q" curve in linear coordinates. The origin (Q = 0, H = 0) is connected to the new operating point (Q x , H x ) by a straight line continuing until it intersects with the characteristic 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 reduced to a size slightly larger than the D x value calculated as indicated above. After that, the pump is subjected to tests, after which the final diameter can be determined. In mass production, this can be avoided. Performance graphs are available for pumps equipped with impellers with different outside diameter reductions (see fig. 28) from which the D x value can be calculated directly using the formulas above. 
Frequency controlrotation
Changing the speed will cause changes in the performance of the centrifugal pump. Let's use the typical regularities indicated earlier:
cavitation
The most common problems encountered in pump operation are related to suction conditions at the inlet of the hydraulic system and are almost always caused by too low hydrostatic pressure (boost) 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 errors made in the design of the hydraulic system. The rotation of the impeller throws the liquid to the surface of the pump housing, resulting in a vacuum from the side of the suction cavity of the impeller. This causes liquid to be sucked through the suction valve and pipeline, which enters the impeller, where it is again thrown to the surface of the pump casing. The vacuum at the pump inlet depends on the difference between the level of the inlet and the surface of the pumped liquid, on the pressure loss due to friction in the suction valve and pipeline, as well as on the density of the liquid itself. This rarefaction is limited by the saturation 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 less than the saturation vapor pressure will cause the liquid to react by forming vapor bubbles as it begins to boil.
In a pump, cavitation occurs when the pressure on the side of the impeller blades that faces the suction cavity (usually near the pump inlet) drops below the saturation vapor pressure of the liquid, causing the formation of gas bubbles. When transported to areas of high pressure in the impeller, these bubbles collapse (explode) and the resulting pressure wave can cause damage to the pump (fig. 31). This damage, which can occur within a few minutes or after a few years, is so severe 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 a stainless steel impeller is only 5% of the damage caused to a cast iron impeller. The lossinmassvarious materials(Based on cast iron = 1.0 for comparison): Cavitation is also associated with increased noise levels, head drops and operational instability. Often, damage is not detected until the pump and motor are disassembled. 
Calculationsoneliminationdangercavitation
The NPSH of the pump, Hmax, required to eliminate the risk of cavitation is calculated as follows: Hmax: NPSH of the pump (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 will become positive. H b: Atmospheric pressure on the pump side; this is the theoretical maximum suction lift. This value of H b depends on the density of the liquid and the “g” value on the pump side (fig. 32).
H fs: The friction pressure loss in the suction valve and the connected pipeline also depends on the density of the liquid. 
NPSH: N et P positive S uction H head
This parameter reflects the minimum suction pressure required for trouble-free operation. It characterizes the frictional pressure loss from the suction port of the pump to the point of the first impeller where the pressure is minimum, and defines the hydraulic conditions under which the pump is not able to suck up 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 circulation pumps, the NPSH schedule is not used; instead, in Fig. 34 is a table showing the minimum suction pressure required at various fluid temperatures. H v: This parameter reflects the saturation vapor pressure of the pumped liquid. It is included in the equation because at a higher temperature, the liquid begins to evaporate faster. H v also depends on the density of the liquid:
Hs: This parameter is a margin of safety, which must be determined in specific conditions, depending on the degree of reliability and reliability of the calculation methodology used. 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 to be 2 m. 
Howto avoidcavitation
This argumentation 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 terms of the equation. Hmax: The pump must always be installed as low as possible or it will be necessary to raise the liquid level on the suction side. The latter method is often the cheapest solution. The positive suction pressure generated by the pump (if any) or expansion tank must be kept as high as possible. Hb: This indicator is constant when pumping a certain liquid in a given place. hfs: Suction piping should be as short as possible and have a minimum number of bends, valves, taps and fittings. NPSH: The pump with the lowest required NPSH should be selected. H v: This setting may decrease as the fluid temperature (ambient temperature) drops. Hs: Set individually. The easiest way to avoid cavitation is to reduce the flow of the pump by partially closing the discharge (or discharge) valve; as a result of this, the required value of NPSH and H fs will decrease, hence the value of H max will increase.Alternativemethodologycalculationforeliminatedangercavitation
Many people prefer to convert the formula to NPSH functions like this:
This gives the available NPSH available for the given hydraulic system, which can then be compared with the required NPSH required shown on the respective pump performance curves. Thus, if NPSH available ≥NPSH required, cavitation can be avoided. However, if NPSH available ≤NPSH required, then the risk of cavitation remains. Connectionelectric motor "GRUNDFOS» inaccording to the designation on its nameplate
Decryptiondesignations: “ - “ 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 motor windings according to the “star” scheme. 1 X220-230 / 240V- The motor can be connected to a single-phase AC network with voltage U = 1 x 220-230V.
- The motor can be connected to a single-phase AC network with voltage U = 1 x 240V.
3
X220
–
240D / 380–
415YV
- The motor can be connected to a three-phase AC network with voltage U = 3 x 380-415V according to the "star" scheme.
- The motor can be connected to a three-phase alternating current 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 voltage U = 3 x 220-240V in a star-delta configuration.
3
X380
–
415DV
- The motor can be connected to a three-phase alternating current network with voltage U = 3 x 380-415V according to the "triangle" scheme.
- The motor can be connected to a three-phase AC network with voltage U = 3 x 380-415V in a star-delta configuration.
The topic today is quite difficult due to its initial vastness and complexity of the theory of the axial compressor. At least for me, it has always been like that in certain aspects :-). But based on the site’s policy, I’ll try to reduce it to basic concepts, simplify and squeeze it into one article. I don’t know what will happen ... We’ll see :-) ...
At the same time... Speaking about such complex devices as an aircraft gas turbine engine, despite the constant desire for simplicity of the story, one has to periodically turn to the exact technical sciences. Fortunately, this does not happen often, not deeply, and usually a school course in physics is enough. Just like now :-).
So, a little bit of theory.
VJ-Advance video endoscope by RF System Lab.
Such devices are quite perfect, have a large number of functions and allow you to reliably detect and comprehensively evaluate any damage in the compressor in almost any part of its air path.
In order for the probe of the video endoscope to get into the flow part, small-diameter holes (ports) are made in the compressor housing (usually between the HA blades), which are closed with hermetic 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 according to the design can be of three types: drum, disk or disco drum. When choosing the type of construction, various parameters are taken into account: mass, complexity, rigidity of the assembly, bearing capacity, circumferential speeds of the rotor. Disco-drum constructions are most often used. The disks, depending on the parameters of the engine, are connected to each other and to the shaft by welding, bolted connections, using special splines.
Design diagrams OK. 1 - drum type, 2 - disco drum type, 3 - disk type.
An example of an engine with a disk-drum compressor (Rolls-Royce RB.162-86).
Vanes are fixed at the ends of the disk rims. The mounting method typical for the compressor is the so-called "dovetail" with an individual socket for each blade. The blades can also be recruited into the annular groove on the disc rim. This is also a dovetail, but with annular working surfaces.
Blades OK with shanks "dovetail" of various configurations.
Much less often, the method of fastening with a herringbone-type lock is used. This method is most often used to fasten turbine blades.
In addition, long blades (usually of the front stages) can be fixed in the annular grooves of the disk rim with special pins to reduce the load on the feather and eliminate excess vibration.
Such blades under the action of centrifugal force during engine operation are radially oriented independently (AL-21F-3 engine). To reduce vibration loads, long blades of the front stages can have special shroud shelves mating with each other (usually in the upper half of the blade airfoil or at several levels).
Attaching the blades of an axial compressor.
PW4000 engine with two shrouds on the fan.
However, in modern turbofan engines with a high bypass ratio, they have found application wide-chord blades(in fan steps) without shrouds. This makes it possible to increase the aerodynamic efficiency of the fan (up to 6%), increase the total air flow and improve engine efficiency (up to 4%). In addition, the mass of the fan and its noise level are reduced.
Banded shoulder blades OK.
Wide-chord blades are manufactured using the latest advances in technology. Special composite materials based on polymers (PCM) are used, hollow blades are made from titanium alloys with honeycomb cores, as well as blades from 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 vanes are mounted in the outer housing, usually in the connecting ring.
Fan blades. Wide-chord and regular with a bandage shelf.
Depending on the loads, vibration and purpose, they are either cantilevered, or (more often) along the inner case they are also united by a ring with seals (honeycomb or easily abraded ( e.g. alumographite- Al 2 O 3 + 8-13% graphite)). Counter seals (usually comb-shaped with a labyrinth) are in this case on the rotor. This prevents harmful air overflows on the SE.
Compressor materials - aluminum alloys, titanium, and steel.
On some modern engines, compressor impellers made using the technology "Blisk"(short for bladed disk), otherwise called IBR (integrally bladed rotor). In this case, the rotor blades and the disk body itself are made as a single unit. This is one unit, most often cast, or welded and processed accordingly.
Mounting blades ON axial compressor.
Such designs are noticeably stronger than prefabricated disks. They have significantly fewer stress concentrators, such as, for example, which are inevitably present when using dovetail blade mounting. In addition, the mass of the entire structure is less (up to 25%).
In addition, the surface quality of the assembly and its streamlining are much better, which helps to reduce hydraulic losses and increase the efficiency of a stage with such a disk (up to 8%). There is, however, the "bliss" and a significant drawback. In the event of any damage to the blades, the entire disk must be replaced, and this inevitably entails disassembling the engine.
Disc with rotor blades made using "Blisk" technology.
In such a situation, along with borescopes, the use of special equipment (for example, Richard Wolf GmbH) for cleaning nicks and local elimination of arising blade defects. Such operations are performed using all the same viewing windows that are available on almost all stages of modern compressors.
Blisks are installed most often in the HPC of modern turbofan engines. An example is the SaM146 engine.
You can do it without a compressor.
A modern aviation gas turbine engine, together with all the systems and components 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 a ground gas turbine compressor.
However, as soon as the plane takes off and starts accelerating, conditions change. After all, air is compressed not only in the compressor, but also in the inlet, that is, in the air intake. With increasing speed, it can reach and even exceed the amount of compression in the compressor.
At very high speeds (several times the speed of sound), the pressure ratio reaches its optimum value (corresponding to maximum traction or maximum economy). After that, the compressor, as well as the turbine that drives it, become unnecessary.
TRD and ramjet in comparison.
The so-called "degeneration" of the compressor or otherwise "Degeneration" TRD, because the engine ceases to be a gas turbine and, remaining in the air-breathing 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 in supersonic) occurs in the air intake of the MiG-25.
However, these are topics for other articles.
Thank you for reading to the end.
See you again.
Photos are clickable.
At the end, a few more pictures on the topic that “did not fit” into the text……….
Speed triangles for the axial compressor stage.
CFM56 dovetail fan blade sockets.
An example of a hinged attachment of the blades of an axial compressor.
Hollow titanium fan blade with honeycomb core.
The operation of the supercharger in the network.
The characteristic of the supercharger determines the entire set of possible modes of operation of the supercharger. But, if the supercharger is connected to the network, then the specific mode of its operation (parameter values p-Q ) is also determined by the characteristics of the network. The latter is the dependence of pressure losses in the network on the flow. The mode of operation of the blower-network system is determined by the equality of the pressure (pressure) created by the blower to the network resistance.
The pressure losses in the network are equal to the total friction losses (losses along the length l ) and local resistances (with coefficients ) in all its elements:
But since c=Q/F (see Equation 2.1*) p = kQ 2 , (6.1)
where k some constant for the given network.
Let's consider the simplest ventilation network, consisting of one section of an air duct of constant cross section at the inlet to the fan and one at the outlet (Fig. 6.1). Full pressure P p (excess ) at the entry into the system from the atmosphere is 0 and further along the direction of air movement decreases by the amount of losses. This pressure drop is proportional to the length of the duct p l , i.e. the plot of total pressures is an inclined straight line. dynamic pressure P d constantly (c=const ). Therefore, the plot of static pressures P c \u003d P p -P d is parallel to the plot of total pressures.
Fig.6.1 Plots of pressure in the simplest ventilation network
In the fan, the total pressure rises by p (fan pressure), becomes positive and further, due to the presence of losses, falls in proportion to the length. AT exit section into the atmosphere, the total pressure is equal to the dynamic pressure, and the static pressure is equal to 0.
It follows from the diagrams that the fan pressure is equal to the pressure loss in the air ducts plus the dynamic pressure at the outlet. However, the latter can also be attributed to losses, since the corresponding kinetic energy is irretrievably dissipated in the atmosphere.
If the fan works for suction and discharges air directly into the atmosphere, then only part of the pressure goes to overcome the hydraulic losses with the exception of the dynamic pressure at the outlet p a.i. : p c =p-p a.i. .
This is the so-called. static pressurefan and it should be taken into account when selecting it for a given network.
From formula 6.1 it follows that for fans the network characteristic is a quadratic parabola. If we impose a fan characteristic on it, then the point of intersection of the graphs of the network characteristic and the pressure characteristic of the fan (it is usually called operating point ) determines the parameters of the fan operation mode for this network (Fig. 6.2).
The characteristic of the network is determined differently for the network working on it. pump . If we apply the Bernoulli equation (2.4) for the installation, the scheme of which is shown in fig. 6.3 and assume that, as is most often the case in practice, P I \u003d P II \u003d P a , then the pressure that needs to be created by the pump will be H=H g + H , i.e. pump pressure is used not only to overcome hydraulic losses ( H ), but also on rise of liquid H g . Since the hydraulic losses, as before, are proportional to Q2 , the characteristic of the network for the pumping unit will look like:
H \u003d H g + kQ 2, (H g \u003d z 2 -z 1 ) .
Fig.6.2 Finding the operating point for Fig.6.2. 6.3 Diagram of the pumping unit
fan
Now this parabola must be combined with the pump characteristic to determine the operating point (Fig. 6.4).
Rice. 6.4 Finding the operating point 6.5 Toward a sustainability study
for the blower-network pump
It should be noted that in settings with smoke exhausters there is also a gravitational pressure associated with the difference in densities of the gas in the chimney and the outside air p e the so-called self-draught, which “helps” the fan, and when determining the characteristics of the network, is subtracted from the losses in the gas path p \u003d kQ 2 - p e.
Combining the characteristics of the network and the supercharger also makes it possible to consider the very important question of the stability of the operation of the supercharger-network system.
AT blower-network systemsthere may be periodic or random changes in operating modes (obstacles at the output of the network, fluctuations in engine speed, etc.).
If the constant mode corresponds to point A (Fig. 6.5), then in the case of an increase in feedblower pressure decreases, a network resistance increases. This will cause the flow to slow down and return the regime to point A. Here, the tangent of the slope of the network characteristic is greater than the tangent of the slope of the blower characteristic. Such a system is stable.
At point B this condition is not metand the regime is unstable. With such a combination of forms of characteristics of the supercharger and the network, the removal of excitations does not lead to the stability of the regime, and the system remainsspontaneous vibrationsparameters. Such self-oscillations are called surge .
The occurrence of this phenomenon in modern high-speed installations poses a great danger in terms of fatigue failure of machines and pipelines, and therefore operation under surge conditions is unacceptable.
Combination of superchargers
The need to install several blowers working together may arise in the following cases:
1) The performance or pressure of installations during operation require significant abrupt changes.
2) One supercharger does not provide the required mode of operation, and replacement with a large one is not possible.
3) It is required to increase the reliability of operation of the installation by creating a certain reserve (not one hundred percent).
Consistent operation of superchargers. When the blowers are switched on in series, the displaced flow first passes through the first blower (in the direction of the flow), and then enters the second blower, and so on. Usually, they try to include no more than two superchargers in sequential operation, and the most optimal option is to include identical fans in operation.
Let curve 1 be the characteristic of the first supercharger, and curve 2 of the second supercharger (Fig. 7.1). To build the overall characteristics of a plant consisting of two blowers in series, it is necessary to take into account that at each particular moment in time the supply of blowers is the same Q 1 \u003d Q 2 , and the total pressure is equal to the sum of the pressures of both superchargers at the specified flow P 1.2 = P 1 + P 2.
The efficiency of the serial connection of superchargers significantly depends on the shape of the network characteristic. From fig. 7.1 it can be seen that with a flat network characteristic (curve I), the feed gain is very small, or not at all. At the same time, with a steep characteristic (curve II), this gain is significant.
Rice. 7.1 Characteristics of blowers, Fig. 7.2 Characteristics of blowers,
operating in series operating in parallel
At parallel operation of superchargers(Fig. 7.2) through each of the superchargers passes its own flow. At the same time, the system must have at least one section through which the total flow passes.
The total characteristic of the installation is based on the fact that the pressure in each of the branches is the same R 1 = R 2 = R 1.2 . The total flow of the installation during the operation of two machines is equal to the sum of the feeds of each of the blowers Q 1,2 \u003d Q 1 + Q 2 . In contrast to the case of sequential operation, in this case, with a steep characteristic of network II, the joint operation of blowers is clearly inappropriate.
If we draw a horizontal line through the point of intersection of the network characteristic with the total characteristic of the blowers, then it turns out that it intersects the characteristic of blower 2 in the area of negative feeds, which means the movement of fluid in it in the opposite direction. About the section of the characteristic, drawn in Fig. 7.2 to the left of the P axis by a dotted line, they say that it is in the second quadrant. In the case of sequential operation, shown in Fig. 7.1, when the network characteristic I changes in the direction of decreasing network resistance, blower 2 operates at negative pressure, or, in other words, it provides resistance that blower 1 has to overcome. The corresponding section of the characteristic, drawn in Fig. .7.1 located in quadrant IV by dotted line.
The need for the characteristics of blowers in the II and IV quadrants arises in the design of installations for joint operation and some other cases encountered in practice.
Cases of off-design characteristics of the network.
In the practice of designing and operating ventilation, heating and other systems, there may be cases when the actual network characteristic differs from the calculated one.
a) the network is calculated with an excessive pressure margin. In this case, the actual network characteristic has a flatter shape (Fig. 7.3). Performance is higher than expected Q>Q p . To determine the appropriate power and efficiency values. it is necessary to draw a vertical line through the operating point (i.e. the point of intersection of the compressor pressure curve and the network characteristics) until it intersects with the curves N(Q) and (Q) . In doing so, it may turn out that N>N p and there is a danger of overloading the motor. This is especially true for fans with forward curved blades, where the power curve increases monotonically. The same happens in the case of increased leakage of the network.
b) the network is calculated with underestimation of losses. The network characteristic runs more steeply. The performance becomes lower than the calculated one, which may be unacceptable from the point of view of the system performing its main function, for example, providing the required air exchange.
Rice. 7.3 Cases of off-design network characteristic
Regulation of blowers.
The actual performance of the blower may differ from the calculated one due to changes in the characteristics of the network. In some cases, it may be necessary to change the actual performance.
In some cases, the need to change performance arises due to changes in the technological process of installations that include a supercharger. So, for example, when the load of boilers is reduced, it is necessary to reduce the performance of smoke exhausters and blowers. Thus, superchargers must have the means regulation performance.
In principle, such regulation can be achieved:
1) changing the characteristics of the network;
2) change in the characteristics of the supercharger;
3) change in the number of jointly (parallel) working machines.
In the first case, a change in the resistance of the network is applied using the so-called throttling devices (“throttling"). In pumping units, these are usually gate valves (valves), in fan dampers, gate valves, throttles. As will be shown below, this is the least economical method of regulation, but, unfortunately, it is the most common in practice (especially for pumps) due to its simplicity.
In some cases, depending on the shape of the power curve, its use is generally unacceptable. We are talking about superchargers whose power curve is falling in a certain range, i.e. . However, in cases where throttling is also extremely uneconomical.
Rice. 8.1 Throttling control
On fig. 8.1 the initial characteristic I corresponds to the operating point R 1 , Q 1 . As a result of throttling (increase in network resistance), the network characteristic takes the form II, and the operating point coordinates P 2 , Q 2 . At the same time, the pressure R dr \u003d R 2 -R 1 is lost in the throttle device, i.e. only pressure is used to overcome losses in the pipeline network I R c1 . Therefore, the efficiency installation (fan + throttle) will be:
and efficiency fan at performance Q2:
Then:
Considering that the value R dr / R 2 often exceeds 50%, then the low efficiency of the considered method of regulation becomes obvious.
As opposed to throttling, the most economical way to regulaterotation speed changeimpeller, because if the network characteristic passes through the origin, in this case, the similarity of the velocity triangles is preserved, and thus the efficiency value is preserved. If, for example, the efficiency was in the region of the maximum value, then it will remain just as high when the speed of rotation of the blower impeller changes (this applies, as already mentioned, to the self-similar interval of the number Re ). In this case, however, part of the energy is lost in the devices for regulating the rotation speed itself.
As a rule, in superchargers, AC motors with a squirrel-cage rotor are used as a drive, which practically cannot be economically controlled at all. However, there are such motors with a variable number of pole pairs two-speed . It is they who should be tried to order if it is necessary to regulate superchargers.
Abroad, to drive pumps and fans, electric drives with frequency regulation using semiconductor converters (thyristors) are increasingly being used.
An affordable and very economical way to change the speed of rotation of the impellers of blowers is the use of replaceable belt drive pulleys. This is useful if the feed rate changes infrequently, for example during seasonal adjustment.
Much more economical than throttling is regulation by changing the characteristics of the supercharger usingguide vanes. The action of the guide vanes is to change the moment of momentum c 1u r at the entrance to the impeller. However, the theoretical pressure P t \u003d c 2u r 2 - c 1u r 1 decreases if the swirling of the flow is directed towards the rotation of the impeller ( c 1u >0 ). It might be expected that at c 1u<0 (twisting against wheel rotation) the pressure will increase, however, this does not actually occur. Therefore, only “down regulation” is applied, i.e. c 1u >0 .
Fig.8.2 Axial guide vane Fig.8.3 Simplified guide vane
Typically appliedaxial guide vanes(Fig. 8.2), which are a system of flat blades that rotate on axes passing through the holes in the body. The blades simultaneously rotate at the same angles and, by deflecting the flow, create its twist.
Simplified guide vanes are known, the blades of which are installed parallel to each other in the inlet boxes of the fans (Fig. 8.3).
8.1 Selection of fans
As a result of the calculation of the ventilation network, the fan operation mode is determined ( p-Q ), and then you should choose a fan that most economically provides this mode.
Designation of types of radial (centrifugal) fans contains:
The letter B, which means "fan";
The letter C, which means "centrifugal" ("radial");
A number equal to five times the pressure coefficient at nominal mode;
A number equal to the speed of the fan in nominal mode.
Nominal mode is the fan mode at which the maximum efficiency value is achieved.
Currently, fans V.Ts4-75, V.Ts4-76, V.Ts14-46, V.Ts10-28, etc. are being manufactured.
Fans are manufactured in various designs depending on the physical properties of the medium being transported. Fans in standard designgeneral purpose fansdesigned to move air and other non-aggressive gas mixtures with a temperature not exceeding 80 C, not containing dust and other solid impurities in the amount of more than 100 mg/m 3 or sticky and fibrous materials.
If these conditions are not met, fans are usedspecial purpose. These include:
Corrosion-resistant fans that can move aggressive gas mixtures;
Spark-proof fans are used to move explosive gas mixtures. These fans are equipped with explosion-proof electric motors, and the housings and impellers of such fans are most often made of aluminum;
Dust fans for moving dust-gas-air mixtures containing solid impurities up to 1000 g/m 3 . The flow part of dust fans is made in such a way as to reduce the abrasive wear of the fan parts, as well as to prevent the possibility of dust sticking. Their designation contains the letter P (“dusty”) V.TsP6-45, V.TsP7-40, etc.
The design features of all the above fans will be described below.
For ventilation systems that require low pressures with significant performance, it is advisable to select not radial, but axial fans. For general industrial ventilation, axial fans of the following types V.O-06-300 and V.O2.3-130 are most widely used.
Fans of each type are manufactured with standard impeller diameters, forming a range of diameters or a range of standard sizes. This range includes: 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600 mm. The fan of each of these diameters is usually denoted by a “number” by the size of the diameter expressed in decimeters, i.e. row of numbers: No. 2, 2.5, 3.15, 4, etc.
The choice of the fan number and rotation speed starts according to the summary characteristics (Fig. 5.3). In this case, the curve closest to the point is taken. p-Q , obtained according to the calculation of the ventilation system. Further, the operating mode is specified, based on where the network characteristic (according to the calculated data p-Q ) will cross the accepted curve of the summary graph.
It is clear that the closer the neighboring values of the diameters of the impellers, the more accurately it is possible to select a fan for a given task and ensure this task with the greatest efficiency. Therefore, factories produce fans with intermediate diameters: less and more than the above nominal values by 5 or 10%.
Each of the curves of the summary graph presented in Figure 5.3 has a designation that contains the following information:
1. Fan type symbol. For example, for fans V.Ts4-75 the letter E.
2. Designation of impeller diameter: 090 at D=0.9D nom ; 095 at D=0.95D nom ; 100 at D=D nom etc.
3. The serial number of the operating characteristic corresponding to the rotation speed for a given fan, denoted by an Arabic numeral.
4. In some cases, this fan at a given rotation speed can be equipped with motors of different power for different sections of the characteristic. The power index is indicated by a capital letter (a, b, etc.).
If, for example, the symbol of the characteristic is E3.15.105-1a, then we are talking about a fan V.Ts4-75 No. 3.15 with an impeller diameter of 1.05D nom , with rotation speed n=1365 rpm, with 0.25 kW motor.
The final decision on the choice of a fan (with specification of all its parameters supply, developed pressure, efficiency, power) is made using the individual characteristics of this fan. Engine parameters are usually given in the table attached to the characteristic.
It should be kept in mind that fans are recommended to be used with the following actual efficiency values: f 0.85 max . The range of fan operation modes in which the specified condition is met is commonly calledworking area characteristics fan.
The summary and individual characteristics are given for the fan operating conditions corresponding to normal atmospheric conditions: barometric pressure 101.3 kPa (760 mm Hg), temperature 20 C, air density 1.2 kg/m 3 .
For other atmospheric conditions, the pressure must be converted to the actual density by formula 5.3. Wherein:
where in actual barometric pressure (mm Hg); t temperature in С; 0 \u003d 1.2 kg / m 3.
Design of centrifugal blowers
DESIGN OF FANS
Radial fans of small sizes (up to No. 10) consist of the following main components (Fig. 9.1): impeller 1 mounted on the motor shaft 5, housing 2, inlet pipe 3 and frame 4. For fans of large numbers, the impeller sits on its own shaft , fixed in bearings and connected to the electric motor by a coupling or belt drive (Fig. 9.2)
Rice. 9.1 Radial fan design 9.2 Structural diagrams fan-
New installations
The impellers of V.Ts4-75 fans have 8 backward-curved leaf blades, V.Ts14-46 fans have 32 forward-curved blades. The blades 1.1 are attached on the one hand to the rear disc 1.2, on the other hand to the front 1.3. The rear disc is mounted on a 1.4 hub sitting on the shaft.
The body is a welded sheet steel structure consisting of a spiral shell and flat side walls. The spiral wall is drawn using the "designer square" method (Fig. 9.3). Here is the side of the square a equal to 1/4 of the "opening" of the body BUT . The latter is usually A=0.6D 2 .
Rice. 9.3 Volute casing 9.4 Dust fan V.TsP-6-45-8
The inlet branch pipe is also made by welding from sheet steel and has a conical shape in V.Ts4-75 fans. The bed has a welded structure made of sheet and angle steel.
There are several different schemes for connecting a fan with an electric motor - these are the so-calleddesigns(Fig. 9.2).
In design version 1, all V.Ts4-75 fans up to and including No. 10 are manufactured. Larger sizes, from 12.5 most often in the 6th version. Fans V.Ts14-46 - in the 1st version.
Fans of the 5th and 7th versions are double-inlet fans, which are distinguished by significantly higher flows than fans of other versions.
Fans are classified according to the direction of rotation.right rotation(the impeller rotates clockwise when viewed from the suction side) and left rotation (wheel rotates counterclockwise).
The location of the fan exhaust pipe is determinedbody position. The position of the housing is indicated by the angle measured from the direction "vertically up" in the direction of rotation of the impeller (when viewed from the side of the suction pipe). Regular values 0 , 90 , 180 , 270 ; less common 45 , 135 , 215 etc.
The most widely used dust fans are manufactured in two types: TsP6-45 and TsP7-40. TsP6-45 fans have impellers with 8 flat blades located radially (Fig. 9.4). The front and rear discs are missing. These design features are associated with the need to prevent settling and sticking of dust on the surface of the impeller parts.
In design corrosion resistant fansused: stainless steel, titanium alloys, plastics.
As intrinsically safe fansfans made of aluminum alloys and dissimilar metals are used. The latter are made of ordinary carbon steel, except for the inlet pipe, the part of which facing the wheel is made of brass, which eliminates sparking when parts of a rotating wheel touch the fixed surface of the pipe.
For installation directly on the roofs of buildings, they are usedroof fans; most often they are used without a network of air ducts to provide general exhaust ventilation. The scheme of the radial roof fan is shown in fig. 9.5, where 1 is the impeller, 2 is the engine, 3 is the housing.
Rice. 9.5 Radial roof fig. 9.6 Centrifugal pump type K
fan
PUMPS DESIGN
The most common type of centrifugal pump is the single-stage, end-suction pump. On fig. 9.6 shows a pump type K (console). Here 1 is the housing cover, 2 is the housing, 3 is the front seal. The impeller 4 sits on the shaft 9 and is fastened with a nut 5. The seal assembly includes an stuffing box packing 6, which is pressed by the cover 8, a sleeve 7 serves to protect the shaft from wear. The shaft 9 is installed in rolling bearings 11.
Pumps are used in heat supply systems:
1) SE for superheated water with temperatures of 120 and 180 .
2) SD double suction for superheated water with the same parameters.
3) D with double-sided flow supply (double-sided);
4) K and KM cantilever single-stage with a horizontal shaft;
5) Ks, KsD, KsV, KsVD condensate (with temperatures up to 120 ).
The impeller is cast iron or, in special cases, bronze.
The pump housing is used to supply and discharge the flow from the impeller, convert kinetic energy into potential energy, and also to combine all the fixed parts of the pump into one common unit - the stator.
To perceive the radial and axial loads acting on the rotor, rolling or sliding bearings are used.
In places where the shaft exits the housing, seals are installed, usually of the stuffing box type. The action of the stuffing box seal is that the packing compressed by the sleeve is distributed to the sides and pressed against the moving surface of the shaft. This achieves a seal between the rotating shaft and the stationary housing.
According to the number of impellers, pumps can be single- and multi-stage. According to the position of the shaft - vertical and horizontal. By appointment for water (cold, hot, clean or with impurities), for liquid chemicals, viscous liquids.
Fight against axial forces in centrifugal pumps.
Axial forces arise in centrifugal superchargers as a result of the presence of pressures of different magnitude and direction acting on the impellers from the front (facing suction) and rear sides. In addition, the axial force results from the dynamic action of the flow entering the impeller. In large multistage centrifugal pumps, axial forces can reach several tens of tons.
One way to reduce the axial force is topressure equalizationon both sides of the impeller. This can be achieved by drillingmultiple holesin the rear disk of the impeller near the hub, or with the help of specialconnecting tubes, connecting the area with low pressure (inlet to the impeller) and the area of high pressure (behind the impeller). The disadvantage of this method is the reduction in volumetric efficiency. pump due to the overflow of part of the flow through the holes (or tubes).
Another way is to useunloading disk (hydraulic heel).
The most rational design of centrifugal pumps, in which axial pressure is almost imperceptible, is the design of pumpsdouble suction(type D). The flow supply to the two-sided wheels is carried out from two sides and the axial forces are mutually compensated. Usually these are pumps with a horizontal casing split, and the outlet pipe is located in the lower part, which allows the pump to be repaired with the upper casing removed without disconnecting the pipelines. In addition, the seal has been reinforced.
The impellers of all pumps have backward-curved blades..
Aero-hydrodynamics and structural elements of axial superchargers.
To consider the operation of axial superchargers, the theory of flat profile gratings is used. If a cylindrical section with a radius r and then deploy it on a plane, you get the so-called flat lattice of profiles. The main geometric parameters of the lattice: t - blade pitch equal to the distance between similar points of adjacent profiles (Fig. 10.2); b - profile chord; - blade angle. Each of the profiles is also characterized by a thickness With , and the deflection arrow f . The calculations use relative values: c=c/b and f=f/b , as well as the lattice density \u003d b / t.
All relative dimensions are obtained by dividing the dimension by the blade chord.
Rice. 10.1 Scheme of the axial supercharger 10.2 Lattice of axial profiles
Supercharger
Figure 10.2 also shows the velocity triangles at the inlet and outlet of the airfoil array: u 1 ; w1; c 1 - respectively, portable, relative and absolute speeds at the input and u 2 ; w2; c 2 - at the exit, w cf. - geometric mean relative velocity in the grating: w cf. =(w 1 + w 2 )/2 .
If you draw a closed contour around the profile S (Fig.10.2) and denote by angle between speed w and tangent to the contour, then to determine the circulation speed G it is necessary to calculate the integral (Fig. 10.3)
Or through the tangential components of the relative velocity at the input w 1u and output w 2u circulation for the entire vane system of the impeller:
G k \u003d (w 2u -w 1u) t.
But from the Euler equation (3.4), which applies equally to centrifugal and axial machines
w 2u -w 1u \u003d p t / u
since for an axial supercharger u 2 \u003du 1 \u003d u; w 1u -w 2u =с 2u -с 1u .
In this way,
P t \u003d rG to u / t.
Or, going to dimensionless quantities:
t \u003d 2G to,
where t =P t / u 2 /2; G to \u003d G to / ut.
Calculation of G to and theoretical aerodynamic characteristics of an axial supercharger for given geometric parameters are described in the book by I.V. Brusilovsky “Aerodynamic calculation of axial fans”.
The amount of circulation makes it possible to calculate the lift force of the airfoil, i.e. component of the force acting from the side of the flow on the profile in the direction perpendicular to the vector w cf (fig.) using the well-known theorem of N.E. Zhukovsky:
R y \u003d w cf G
When changing from theoretical pressure P t to p It is also necessary to take into account pressure losses in the elements of the flow path: p=P t - P .
Losses in the flow path are associated, on the one hand, with the flow around the blade system (profile losses), on the other hand, with friction on the cylindrical surfaces of the housing and the impeller bushing, as well as with fluid overflows through the gaps between the ends of the blades and the housing (secondary). In the calculation, the magnitude of losses can be determined from the experimental data given, for example, in the above-mentioned book by I.V. Brusilovsky.
Currently, axial fans for general industrial use with leaf blades are produced according to two aerodynamic schemes: V.06-300 and V.2.3-130.
The impeller of the B.06-300 fan consists of a cylindrical sleeve with three welded sheet blades. The angle of the scapula is =22 on the middle radius.
Unlike them, B.2.3-130 fans have, in addition to the impeller, an outlet directing vane. The impeller has 12 sheet blades with an angle =36.
A number of standard sizes of these fans includes numbers from 4 to 10.
15.1. Flow, head and pump power
The operation of the pump is characterized by its flow, pressure, power consumption, useful power, efficiency and speed.
pump feed called the amount of fluid supplied by the pump per unit time, or the flow rate of fluid through the pressure pipe, usually denoted by the Latin letter Q.
pump head is the difference between the energies of the liquid weight in the flow cross section in the discharge pipe (after the pump) and in the suction pipe (before the pump), related to the weight of the liquid, i.e. the energy of a unit weight of a liquid, usually denoted by the Latin letter H. The pump head is equal to the difference between the total head of the liquid after the pump and before the pump
where the indices "n" and "sun" denote the pressure and suction lines. The head is expressed in units of the column of fluid being moved.
Pump power input is called the energy supplied to the pump from the engine per unit of time, denoted N d .
Net power of the pump or the power developed by the pump is the energy that the pump communicates to the entire fluid flow per unit time, denoted by -Np.
In a unit of time, a liquid weighingG f = ( Qρ )* g . Each unit of this weight gains energy in the amountH ( m).
This energy or useful power of the pump is equal to
N n = QρgH = QP (15.2),
where because P = ρgH .
Pump power input N d more usable power N P to the pump losses. These power losses are estimated by the efficiency of the pump.
The efficiency of the pump is the ratio of the useful pump power to the motor power consumed by the pump :
η= N P/ N d. (15.3)
If the efficiency is known, the power absorbed by the pump can be determined N d = QρgH / η (15.4)
The power value is expressed in the Civwatt system, in the technical system of units in kGm / s.
15.2 Vane pump workflow
The moment of resistance forces relative to the axis counteracts the rotation of the impeller, so the blades are profiled, taking into account the amount of feed, rotation frequency, and direction of fluid movement.
Overcoming the moment, the impeller does work. The main part, brought to the wheel of energy, is transferred to the liquid, and part of the energy is lost when overcoming resistances.
If the fixed coordinate system is associated with the pump housing, and the moving coordinate system with the impeller, then the trajectory of the absolute motion of particles will be the sum of the rotation (translational motion) of the impeller and the relative motion in the mobile system along the blades.
The absolute speed is equal to the vector sum of the translational speed U - the speed of rotation of the particle with the impeller and the relative speed W movement along the blade relative to the moving coordinate system associated with the rotating wheel.
On 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 portable movement coincide with the circles on the radii of the wheel, for example, on the radii R 1 and R 2. Particle trajectories in absolute motion from the pump inlet to the outlet - AC. The motion of the mobile system is relative, in the mobile system it is portable.
Speed parallelograms for entering and exiting the impeller:
(15.5)
Relative speed sum W and portable U will give absolute speed V .
Speed parallelograms in fig. 15.2 show that the moment of fluid particle velocity 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 moment of momentum increases. The increase in the moment of momentum is caused by the moment of forces with which the impeller acts on the liquid in it.
For a steady motion of a fluid, the difference in the moments of the momentum of the fluid leaving the channel and entering it per unit time is equal to the moment of external forces with which the impeller acts on the fluid.
The moment of forces with which the impeller acts on the liquid is equal to:
M = Q ρ( V 2 Cosα 2 R 2 - V 1 Cosα 1 R 1 ), where Q is the fluid flow through the impeller.
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 is called hydraulic power, or the work that the impeller produces per unit time, acting on the liquid in it.
It is known from the Bernoulli equation that the specific energy , transferred to the unit weight of the liquid is called head. In Bernoulli's equation, the source of energy for fluid movement was the head difference.
When using a pump, energy or pressure is transferred to the liquid by the pump impeller.
Theoretical pressure of the impeller - H T called specific energy , transmitted to the unit weight of the liquid by the pump impeller.
N =M ω = H T * Q ρ g
Given 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 translational 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 obtain 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 the real values of velocities and pressures are taken in it.
Vane pumps are 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 impellers connected in series, mounted on one shaft. The pump head increases in proportion to the number of wheels.
