Aviation GTE compressors. Saving energy with frequency control Main operating parameters of blowers
The main technical indicators of superchargers include: flow, pressure (pressure), power, efficiency, suction lift and speed.
Feed - the amount of liquid or gas supplied through the section of the outlet pipe of the supercharger per unit time. To measure the flow, volumetric values \u200b\u200bof Q [m 3 / s] and mass Q m [kg / s] are used.
They are related
where is the density of the working medium, kg / m 3.
Head (H) - the energy imparted by the supercharger to a unit mass of the pumped liquid or gas.
For positive displacement pumps, the main parameter is usually not the head, but the total pressure they create.
Head and pressure are related
[ 
]
For fans, the pressure is often indicated in mm of water. pillar - h.
1 mm. water. Art. = 9.81 Pa
1 atm. \u003d 10 m. of water. Art. » 100 kPa (98067 Pa).
Power and efficiency
The energy supplied to the supercharger from the engine per unit time represents its power
Part of the energy is lost in the supercharger in the form of losses and determines its efficiency. - h naked.
The other part of the energy transferred to the working medium per unit time determines the useful power of the blower, which is proportional to pressure and flow.
Efficiency is the ratio of useful power to spent power.
It can be represented as a product of three efficiency factors.
h Г - hydraulic efficiency, which characterizes the power loss to overcome hydraulic resistance in the supercharger;
h 0 - volumetric efficiency due to leakage of the working medium inside the blower;
h fur - mechanical efficiency - from friction losses in the supercharger.
Rotation frequency - n[rpm]
The choice of blower speed depends on conditions such as blower type, weight and size restrictions, and economy requirements.
The rated speed is indicated in the supercharger passport.
The power of the rotational movement is determined by the moment and the angular velocity (c -1) - w.
[kW]
Angular velocity ω and speed n related by the ratio [ - number of revolutions per second in different measures]
From here 
[kW]
Vacuum suction head (H in).
For some marine pumps, this is an important parameter.
Vacuum suction lift is understood as the difference between atmospheric pressure and pressure - at the inlet to the pump, i.e.
The suction height is limited by the minimum absolute pressure min that occurs in the area of the pump inlet, which must be greater than the saturation vapor pressure of the pumped liquid
Otherwise, the liquid boils in places where the minimum pressure occurs and the normal operation of the pump is disrupted.
The power of pumps with suction capacity is determined by the total head H \u003d H load ± N in
Dynamic superchargers
Centrifugal blowers
3.1.1 General arrangement and principle of operation
Consider the scheme of a cantilever centrifugal pump.
When the impeller rotates, a reduced pressure is formed in its central part, as a result of which the liquid from the intake pipeline continuously enters the pump through the inlet 1, made in the form of a conical pipe (confuser) with a straight axis.
The blades of the impeller exert force on the fluid flow and transfer mechanical energy to it. The increase in fluid pressure in the wheel is created mainly under the action of centrifugal forces.
Flowing around the blades, the liquid moves in the radial direction from the center of the wheel to its periphery. Here, the liquid is ejected into the spiral outlet channel 12 and is directed to the diffuser outlet 6, where its velocity decreases and the kinetic energy of the flow is converted into pressure potential energy.
The movement of fluid in the impeller.
Operating characteristics
In the impeller of a centrifugal pump, fluid particles move relative to the wheel itself and, in addition, they make a portable movement with it.
The sum of the relative W and translational U motion gives the absolute motion of the fluid, i.e. its movement relative to the stationary pump housing. The speed of absolute movement V (absolute speed) is equal to the geometric sum of the fluid speed relative to the impeller W (relative speed) and the circumferential speed U of the impeller
The absolute speed can be decomposed into V u - circumferential and V p radial.
The first component determines the pressure, the second determines the flow of the pump. In the theory of centrifugal pumps, it is proved that the head is a linear function of the flow and depends on the outlet angle of the blades.
If the blades are bent against the stroke (< 90 0), то характеристика Н-Q в начале будет восходящей. При радиальных лопастях ( = 90 0) значение напора будет оставаться неизменным, а при >90 0 , when the blades are bent along the way, the H - Q characteristic will be falling.
On ships, as a rule, centrifugal superchargers with radial blades and blades curved along the course (> 0) are used.
The operational characteristics of H-Q are significantly different from the calculated ones and in the region of high feeds in all cases of profiling the blades, the H-Q characteristics are falling.
Under the performance characteristics of centrifugal (vane) superchargers understand the dependence of pressure, power, efficiency on the supply H = f (Q), N = f (Q), h = f (Q). Characteristics are taken experimentally at a constant nominal speed.
The construction of the characteristic H - Q for an angular velocity other than the nominal one, possibly using the laws of proportionality for this.
Typically, pumps are measured when operating on water, but the operation of a centrifugal pump is greatly influenced by the viscosity of the pumped liquid. With an increase in the viscosity of the liquid, the flow and pressure of the pump decrease, and the power increases: so the efficiency h drops from 75% to 35% when switching from working on water to working on oil.
3.1.2. Operating characteristic
pipeline networks
The graphical dependence of the required pressure in the pipeline network on the flow rate at a constant position of the regulatory bodies is called the characteristic of the pipeline network.
The required pressure is determined by the sum of the pressure losses
H c \u003d H pr + H g + H tr + H m + H q
where N pr - back pressure head, available when the system has
pressure tank;
H g - geometric head, determined by the liquid column,
overcome by the pump on the suction side N us and co
discharge side N p.
H tr - loss of pressure due to friction in the pipeline;
N m - pressure loss due to local resistance, due to
the presence of various fittings in the pipeline;
H q - additional head loss due to the flow rate of liquid or gas.
The sum of the first two components is the static head Hco, i.e. constant component of pressure loss in the network
H co \u003d H pr + H g
The other three loss components are proportional to the square of the flow rate, and hence to the delivery. They are the dynamic component of the resistance of the pipeline, thus
H e \u003d H co + H dyn \u003d
where K c is the system resistance coefficient.
3.1.3. Pump operation on pipeline network
Having a characteristic of the pump and the pipeline connected to the pump, it is easy to determine the mode that has been established in the pump-pipeline system, i.e. flow and pressure developed by the pump when working on this pipeline.
In many cases, in accordance with the operating conditions of the elements of the ship's power plant, as well as, for example, changes in water consumption in domestic systems, it is necessary to regulate the flow of the pump, in particular in the direction of its reduction.
Feed change can be achieved:
1. throttling;
2. bypass;
3. change in rotational speed;
In the first and second methods, the characteristic of the system changes,
in the third - the pump.
Throttling- is carried out by changing the position of the valve installed near it, on the pressure pipeline. When the valve is partially closed, from the working (.) A they moved to (.) B. In this mode, the pressure H in will be the sum of the pressure H in ’, which would be consumed in the network with a fully open valve and the pressure loss H 3 in the valve, therefore, efficiency. installation is reduced.
Bypass control is carried out by a valve installed parallel to the pump.
Since over the entire control range the pump flow will be greater than the flow Q A with the valve closed, regulation by bypass is more economical than throttling for pumps whose power decreases with increasing flow.
Bypass control as well as throttling is often used to avoid overloading the drive motor.
Speed control leads to a change in the characteristics of the pump. It is the most economical, but in general the drive is more expensive, more complicated and less reliable in operation. Applied if necessary for pumps of high power.
Joint operation of pumps on a common system
The pump control methods discussed above make it possible to reduce the flow or pressure compared to those provided by the pump when operating at rated speed. However, during operation, it becomes necessary to increase the pressure or flow in the system. This is possible when the pumps are connected in series or in parallel.
In this case, pumps with different pressures can be used, but preferably with the same design flow, otherwise the efficiency will increase. settings will be low.
The total characteristic can be represented as a characteristic of one pump, the flow of which at a given pressure is approximately equal to the sum of the flows of both pumps. Q A \u003d Q B + Q C
Due to the fact that with an increase in the supply, the pressure loss in the pipeline of the system increases, Q A< Q 1 + Q 2.
The increase in feed will be the more significant, the more positive the characteristic of the system. For parallel operation, pumps with a similar head value at zero flow are most suitable.
3.1.4. Designs of centrifugal pumps. Application area
The centrifugal pump considered by us has one impeller with a one-way fluid inlet. The use of several impellers in one pump allows you to significantly expand the scope of use of centrifugal pumps and creates a number of design advantages.
Pumps with a serial connection of the impellers are called multistage. The pressure of such a pump is equal to the sum of the pressures of the individual wheels (stages), and the feed is equal to the feed of one wheel. All wheels of a multistage pump are mounted on a common shaft and form a single rotor.
Pumps with parallel connection of wheels are called multi-flow. The head of such a pump is equal to the head of one wheel, and the pump flow is equal to the sum of the flows of the individual wheels. The most widespread are double-flow pumps with a double-sided impeller, which is a connection in one piece of two ordinary wheels.
According to the location of the shaft, centrifugal pumps are horizontal and vertical.
According to the location of the supports, the pumps are divided into cantilever with supports located at the ends of the shaft, and monoblock. For monoblock pumps, the impeller is mounted directly on the shaft of the flange motor; for fastening to the electric motor the pump has the flange.
Centrifugal pumps are used in various ship systems:
fire-fighting, ballast, drainage, drainage, sanitary. They are used as coolants in internal combustion engines, trucks - on tankers, etc.
Advantages of centrifugal superchargers:
speed;
Small weight and overall dimensions;
Simplicity of design;
Uniform supply of liquid;
Relatively low sensitivity to contaminated liquid;
Limited pressure (can be started with closed valves).
Flaws:
Little pressure;
Lack of self-priming ability.
As required by the Register Rules, ships must be equipped with self-priming centrifugal pumps or equipped with a vacuum system.
For general ship systems, centrifugal pumps with self-priming devices of water ring and recirculation types are used in accordance with GOST 7958-78.
Axial superchargers
The housing is the flow part of the pump and is a section of a curved cylindrical pipe. The pump can be easily integrated into the common pipeline to which it is connected.
Approach and retraction are fixed elements. A fairing 7 is installed in the inlet for a smooth supply of fluid to the blades or a guide vane, which serves to eliminate flow swirling, which may occur due to flow asymmetry before entering the pump. Behind the impeller is a straightening apparatus, which consists of fixed blades. It destroys the flow swirl and the kinetic energy of the flow is converted into pressure energy.
The blower impeller has two to six blades. Marine pumps are made with vertical and horizontal shaft arrangement, single-stage (with one impeller). According to the method of fastening the impeller blades on the sleeve, rigid-vane and rotary-vane pumps are distinguished. Due to the rotation of the blades, the angle of attack changes, which leads to a change in feed at a constant speed, while the pressure remains constant. The regulation of the supply by changing the speed of the electric motor also leads to a change in pressure. However, the presence of a device for turning the blades greatly complicates the design of the pump.
Feed control is carried out by changing the rotational speed or turning the blades, efficiency = 0.7 - 0.9 ..
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. Therefore, when the pump shaft speed is changed, the value of the pressure and 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.
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.
Pumps are usually divided into two main types: voluminous And centrifugal.
Positive displacement pumps set the liquid in motion by changing the volume of the chamber with the liquid by mechanical means. Positive displacement pumps represent a load with a constant torque on the shaft, while the design of centrifugal pumps assumes a variable torque depending on the speed.
transfer the momentum of the liquid due to the rotation of the impeller immersed in it. The impulse leads to an increase in pressure or flow at the pump outlet. This article only deals with centrifugal pumps.
A centrifugal pump is a device that converts the drive energy into the kinetic energy of the liquid by accelerating it to the outer rim of the impeller - the impeller. The point here is that the energy created is kinetic. The amount of energy transferred to the fluid corresponds to the speed at the tip of the impeller blade. The faster the rotation of the impeller or the larger its size, the higher the speed of the fluid at the edge of the blade and the higher the energy transferred to the fluid. The formation of flow resistance regulates the kinetic energy of the liquid at the outlet of the impeller. The initial resistance is created by the pump's volute chamber (casing), into which the liquid enters and slows down. When the fluid slows down in the pump casing, some of the kinetic energy is converted into pressure energy. It is the pump flow resistance that is recorded on a pressure gauge installed on the discharge pipeline. The pump creates flow, not pressure. Pressure is a measure of resistance to flow.
Head - Flow resistance
Example:
Imagine a pipe with a jet of water pointing straight up into the air. The pressure is the height to which the water rises.
FOR NEWTONIAN (TRUE) fluids (non-viscous fluids such as water and gasoline), we use the term head to measure the kinetic energy generated by a pump. The head is the height of the water column that the pump can create due to the kinetic energy that is transferred to the liquid. The main reason for using head instead of pressure to measure the energy of a centrifugal pump is that the pressure at the pump outlet changes with a change in the weight of the liquid, but the head does not.
Therefore, using the term head, we can always indicate the performance of the pump for any Newtonian liquid, heavy (sulfuric acid) or light (gasoline). Remember that the head is related to the speed that the liquid acquires when passing through the pump. All types of energy available in a fluid flow system can be characterized by the height of the water column. The sum of the different heads is the total head of the system, or the work that the pump will do in that system. The following types of pressures are distinguished:
Pump Terms
SUCTION HEIGHT exists when the supply tank is below the centerline of the pump. Thus, the geometric suction head is the vertical distance from the centerline of the pump to the free level of the fluid to be pumped.
SUPPORT occurs when the supply tank (suction lift) is above the center line of the pump. Thus, the geometric head is the vertical distance from the centerline of the pump to the free level of the fluid to be pumped.
GEOMETRIC HYDROSTATIC HEAD is the vertical distance between the center line of the pump and the point of free flow or the surface of the liquid in the receiving tank.
TOTAL HYDROSTATIC HEAD is the vertical distance between the free level in the supply tank and the point of free flow or the surface of the pumped liquid (in the receiving tank).
FRICTION LOSS (hf)- losses to overcome the flow resistance that occurs in the pipeline and branch pipes. The resistance depends on the size, condition and type of pipeline, the number and type of nozzles, the flow rate and the type of liquid.
SPEED HEAD (hv)- this is the head resulting from the movement of a fluid with a speed V. Velocity head can be calculated using the following formula:
h v = v 2 / 2g where: g = 9.8 m/s, V = fluid velocity, m/s
Velocity head is usually negligible and can be ignored in most high head systems. However, it can play a significant role in low pressure systems and must be taken into account.
PRESSURE HEAD must be considered when the pumping system starts or ends in a tank having non-atmospheric pressure. The supply tank vacuum or the positive pressure in the receiving tank must be added to the head of the system, while the positive pressure in the supply tank or the vacuum in the receiving tank must be subtracted. The above types of heads, namely hydrostatic head, frictional head, velocity head and pressure head together form the head of the system at a certain flow velocity.
VACUUM SUCTION HEIGHT (hs) is the geometric suction height, taking into account losses and velocity head. Vacuum suction lift is determined from the gauge on the suction flange. If the permissible vacuum height is exceeded, cavitation occurs in the pump.
HYDRODYNAMIC HEAD OUTLET (hd) is the geometric hydrostatic head, plus the velocity head at the pump outlet flange, plus the total frictional head loss in the discharge piping. The total hydrodynamic head at the outlet (determined when testing the pump) is the reading of the meter on the outlet flange.
TOTAL HYDRODYNAMIC HEAD (TDH) is the hydrodynamic head at the outlet, taking into account the vacuum suction height:
TDH = h d + h s
(when liquid rises to suction height)
TDH = h d - h s
(if there is backwater)
POWER The work done by the pump is a function of the total head and the weight of the pumped liquid in a certain time. The formulas usually use the volumetric flow of the pump and the specific gravity of the liquid, and not the actual weight of the pumped liquid. Power input (N) is the actual power supplied to the pump shaft. Pump delivery or net hydraulic power (Nn) is the power that the pump delivers to the fluid. These two quantities are defined by the following formulas:
Pump characteristics such as flow, head, efficiency and power consumption are shown graphically on the pump curves.
The pump size, 2x3-8, is shown at the top of the graph. The numbers 2x3-8 indicate that the outlet (outlet) is 2 inches (may be expressed in mm), the inlet (suction) is 3 inches and the impeller is 8 inches in diameter. Some manufacturers indicate this code as 3x2-8. The larger of the first two digits is the inlet. The pump speed (rpm) is also shown at the top of the graph, and shows the output at 2960 rpm.
All information is presented for a given operating speed. The capacity or volume flow is shown along the bottom of the curve. All different flow rates are shown for operating speed of 2960 rpm, but show the effect of head when output is throttled. The left side of the performance curves shows the head generated at different flow rates.
The graph compares several flow and head curves, each characterizing a different (truncated) impeller size. For this pump, the impeller range varies from 5.5 to 8.375 inches. Efficiency curves are superimposed on the graph (vertical lines) and characterize the efficiency of this pump from 64 to 45 percent. As head increases, flow and efficiency decrease. The power consumption is shown as a dotted line drawn diagonally from the lower right to the upper left. Power consumption curves are shown for the range 80 - 325 kW. When using an 8" impeller with a flow of 250 m/h, the power consumption will be about 270 kW.
Pump and system performance
The pump curve is a simple function of the physical characteristics of the pump. The performance curve of the system depends entirely on the size of the pipeline, its length, the number and location of elbows and other factors. The intersection of these two curves is the actual operating point. At this point, the pump pressure matches the system losses and everything is balanced.
If the system is subject to frequent or continuous changes, it is necessary to change the pump characteristics or the system parameters.
There are two methods that are used to provide variable flow. One method is throttling, which results in a change in the characteristics of the system by means of a throttling valve. Another method is to change the speed of rotation of the pump, which changes the performance of the pump.
With this method, the additional resistance to flow increases the head. The characteristics of the system at 2 different valve positions are shown below.
For comparison, let's use an example to determine the power consumption of a throttling system, then for a speed controlled system. A pump is used (with an 8" impeller) running at a nominal speed of 2960 rpm. The pump is designed to work in a system requiring a head of 250 meters at a flow of 250 m/h. See pump curve below.
Based on the information provided in the graph, you can find out the different power requirements at the flow rates shown in the table below for the throttling system.
Where,
Nn- hydraulic power (kW)
N- power consumption (kW)
Variable speed system
In contrast to the above method, when speed is controlled, .
A lower pump speed changes the pump curve based on the velocity head generated by the speed of the fluid being pumped. Remember that this pressure is v 2 / 2g.
Similarity laws
The set of formulas used to predict the operation of a centrifugal pump at any duty point, based on the original characteristics of the pump, are called scaling laws.
Where,
n= Pump rotation speed
Q= Feed (m/h) R= Pressure (m) N= Power (kW)
Using the same example as for throttling, you can calculate the power consumption for systems when the pump speed is:
Where N- power consumption on the shaft in kW.
Use the laws of similarity to calculate the values at the remaining operating points.
It is obvious that when regulating the speed, the power consumption in the partial supply mode is much less than when throttling. To determine the actual electrical power consumed, it is also necessary to take into account the efficiency of the electric drive. The efficiency of an electric motor operating from the network decreases when the shaft is not fully loaded (as in the case of throttling), while the efficiency of an adjustable electric drive remains unchanged, which gives additional savings. Energy savings will depend on the amount of time the pump will run at each reduced speed setting.
To calculate the real savings, the power consumption must be multiplied by the number of hours of operation. This value is then multiplied by the cost per kWh to show the cost of running the pump at each flow rate. Subtract the speed control power draw from the throttling power to get the difference in energy cost.
In our example, at a flow rate of 200 m/h, 240 kW is consumed when throttling, and at speed control, only 136.2 kW is required for the same flow. If it is necessary to provide such a regime for 2000 hours per year at a price of 2 rubles per kWh, the cost comparison will be as follows:
Throttling system:
240 x 2000 = 480000 kWh
480000 x 2 = 960 thousand rubles
Variable speed system:
136.2 x 2000 = 272400 kWh
272400 x 2 = 545 thousand rubles
Saving:
960-545 = 415 thousand rubles
This example was not tied to pressure. The head does not affect the characteristics of the system and the power consumption when regulating the supply. The higher the hydrostatic head of the system, the lower the potential for energy savings. This is due to the fact that the characteristic of the system is flatter, because most of the energy is used to lift the liquid to the required height.
Adapted from Rockwell Automation, Inc.[Cancel reply]
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Based on the flow and total head specified for the fan or pump, and for the compressor - flow and specific work of compression - the shaft power is determined, in accordance with which the power of the drive motor can be selected.
For a centrifugal fan, for example, the formula for determining the power on the shaft is derived from the expression of the energy imparted to the moving gas per unit time.
Let F be the section of the gas pipeline, m2; m - gas mass per second, kg/s; v - speed of gas movement, m/s; ρ - gas density, m3; ηv, ηp - fan and transmission efficiency.
It is known that
Then the expression for the energy of the moving gas will take the form:
where is the power on the drive motor shaft, kW,
In the formula, groups of values can be distinguished corresponding to the supply, m3 / s, and the pressure of the fan, Pa:
It can be seen from the above expressions that
Respectively
here c, c1 c2 are constants.
Note that due to the presence of static pressure and the design features of centrifugal fans, the exponent on the right side may differ from 3.
Similarly to how it was done for the fan, you can determine the power on the shaft of a centrifugal pump, kW, which is equal to:
where Q - pump flow, m3/s;
Hg - geodetic head equal to the difference between the discharge and suction heights, m; Hc - total head, m; P2 - pressure in the tank where the liquid is pumped, Pa; P1 - pressure in the tank from which the liquid is pumped, Pa; ΔH - pressure loss in the line, m; depends on the section of the pipes, the quality of their processing, the curvature of the pipeline sections, etc.; ΔH values are given in the reference literature; ρ1 - density of the pumped liquid, kg/m3; g = 9.81 m/s2 - free fall acceleration; ηn, ηp - efficiency of the pump and transmission.
With some approximation for centrifugal pumps, it can be assumed that between the power on the shaft and the speed there is a relationship P = cω 3 and M = cω 2. In practice, the exponents y of speed vary within 2.5-6 for various designs and operating conditions of pumps, which must be taken into account when choosing an electric drive.
The indicated deviations are determined for pumps by the presence of line pressure. We note in passing that a very important circumstance when choosing an electric drive for pumps operating on a high-pressure line is that they are very sensitive to a decrease in engine speed.
The main characteristic of pumps, fans and compressors is the dependence of the developed pressure H on the supply of these mechanisms Q. These dependencies are usually presented in the form of HQ graphs for various speeds of the mechanism.
On fig. 1 as an example shows the characteristics (1, 2, 3, 4) of a centrifugal pump at various angular speeds of its impeller. In the same coordinate axes, the characteristic of line 6, on which the pump operates, is plotted. The characteristic of the line is the relationship between the supply Q and the pressure necessary to lift the liquid to a height, overcome the excess pressure at the outlet of the discharge pipeline and hydraulic resistance. The intersection points of characteristics 1,2,3 with characteristic 6 determine the values of pressure and performance when the pump is operating on a certain line at various speeds.
Rice. 1. The dependence of the head H of the pump on its supply Q.
Example 1. Construct characteristics H, Q of a centrifugal pump for various speeds 0.8ωn; 0.6ωn; 0.4ωн, if characteristic 1 at ω = ωн is set (Fig. 1).
1. For the same pump
Hence,
2. Let's construct the characteristic of the pump for ω = 0.8ωn.
For point b
For point b"
Thus, it is possible to construct auxiliary parabolas 5, 5", 5"... which degenerate into a straight line on the y-axis at Q = 0, and QH characteristics for different pump speeds.
The engine power of a reciprocating compressor can be determined from an air or gas compression indicator chart. Such a theoretical diagram is shown in fig. 2. A certain amount of gas is compressed according to the diagram from the initial volume V1 and pressure P1 to the final volume V2 and pressure P2.
Work is expended on gas compression, which will be different depending on the nature of the compression process. This process can be carried out according to the adiabatic law without heat transfer, when the indicator diagram is limited by curve 1 in Fig. 2; according to the isothermal law at a constant temperature, respectively, curve 2 in Fig. 2, or along the polytrope curve 3, which is shown as a solid line between the adiabat and isotherm.
Rice. 2. Gas compression indicator diagram.
The work during gas compression for a polytropic process, J/kg, is expressed by the formula
where n is the polytropic index, determined by the equation pV n = const; P1 - initial gas pressure, Pa; P2 - final pressure of compressed gas, Pa; V1 is the initial specific volume of gas, or the volume of 1 kg of gas at suction, m3.
Compressor motor power, kW, is determined by the expression
here Q - compressor flow, m3/s; ηk - indicator efficiency of the compressor, taking into account the power loss in it during a real working process; ηp - efficiency of mechanical transmission between the compressor and the engine. Since the theoretical indicator diagram differs significantly from the actual one, and obtaining the latter is not always possible, when determining the compressor shaft power, kW, an approximate formula is often used, where the initial data are the work of isothermal and adiabitic compression, as well as efficiency. compressor, the values of which are given in the reference literature.
This formula looks like:
where Q - compressor flow, m3/s; Au - isothermal work of compression of 1 m3 of atmospheric air to pressure Р2, J/m3; Aa - adiabatic work of compression of 1 m3 of atmospheric air to pressure Р2, J/m3.
The relationship between the power on the shaft of a piston-type production mechanism and the speed is completely different from the corresponding relationship for mechanisms with a fan-type torque on the shaft. If a piston-type mechanism, such as a pump, works on a line where a constant pressure H is maintained, then it is obvious that the piston has to overcome a constant average force with each stroke, regardless of the rotation speed.
Based on the formulas obtained, the power on the shaft of the corresponding mechanism is determined. To select an engine, the nominal values of flow and pressure should be substituted into these formulas. Based on the power received, a continuous duty motor can be selected.
