Supercharger static pressure depends on rotation speed. Basic operating parameters of superchargers. Pumps connected in parallel

Pumps are usually divided into two main types: volumetric And centrifugal.
Positive displacement pumps They set the liquid in motion by changing the volume of the chamber containing 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.
transmit momentum to the liquid due to the rotation of the impeller immersed in it. The pulse causes an increase in pressure or flow at the pump outlet. This article covers only centrifugal pumps.

A centrifugal pump is a device that converts drive energy into kinetic energy of a fluid by accelerating it towards the outer rim of 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 impeller rotates or the larger its size, the higher the fluid velocity at the blade tip and the higher the energy transferred to the fluid. The formation of flow resistance regulates the kinetic energy of the fluid at the impeller outlet. The initial resistance is created by the pump's volute chamber (casing), into which the liquid enters and slows down. As the fluid slows down in the pump body, some of the kinetic energy is converted into pressure energy. It is the pump supply 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 stream of water directed straight up into the air. The pressure will be 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 created by the pump. Head is the height of the water column that the pump can create due to the kinetic energy that is transferred to the fluid. 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 as the weight of the fluid changes, but the head does not.

Therefore, using the term head, we can always indicate the pump performance for any Newtonian fluid, heavy (sulfuric acid) or light (gasoline). Remember that head is related to the speed that the fluid acquires as it passes 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 reservoir is below the centerline of the pump. Thus, the geometric suction lift is the vertical distance from the centerline of the pump to the free level of the liquid to be pumped.

BACKUP occurs when the supply reservoir (suction lift) is above the centerline of the pump. Thus, the geometric head is the vertical distance from the centerline of the pump to the free level of the liquid to be pumped.

GEOMETRIC HYDROSTATIC HEAD is the vertical distance between the centerline of the pump and the free flow point or surface of the liquid in the receiving reservoir.

TOTAL HYDROSTATIC HEAD is the vertical distance between the free level in the supply tank and the free flow point or surface of the pumped liquid (in the receiving tank).

FRICTION LOSS (hf)- losses to overcome the flow resistance that occurs in the pipeline and pipes. Resistance depends on the size, condition and type of pipeline, number and type of pipes, flow rate and type of fluid.

VELOCITY HEAD (hv) is the pressure generated as a result of the movement of fluid at speed V. The velocity pressure can be calculated using the following formula:
h v = v 2 / 2g, where: g = 9.8 m/s, V = fluid speed, m/s
The velocity head is usually negligible and can be ignored in most high-pressure systems. However, it can play a significant role in low-pressure systems and must be taken into account.

PRESSURE RATE must be taken into account when the pumping system begins or ends in a non-atmospheric pressure tank. The supply tank vacuum or the positive pressure in the receiving tank must be added to the system head, 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, friction head loss, velocity head and pressure head together form the system head at a certain flow rate.

VACUUM SUCTION HEIGHT (hs) is the geometric suction height taking into account losses and velocity pressure. The vacuum suction lift is determined by the readings of the device on the suction flange. If the permissible vacuum height is exceeded, cavitation occurs in the pump.

OUTLET HYDRODYNAMIC HEAD (hd)- this is the geometric hydrostatic head, plus the velocity head at the pump outlet flange, plus the total friction head loss in the discharge pipeline. The total discharge head (determined during pump testing) is the reading from the meter at the outlet flange.

TOTAL HYDRODYNAMIC HEAD (TDH) is the hydrodynamic pressure at the outlet taking into account the vacuum suction height:
TDH = hd + hs (when liquid rises to suction height)
TDH = h d - h s (if there is support)

POWER The work done by a pump is a function of the total head and the weight of the pumped liquid over a certain time. Formulas usually use pump volumetric flow and specific gravity of the liquid, rather than the actual weight of the liquid being pumped. Power input (N) is the actual power supplied to the pump shaft. Pump flow or net hydraulic power (Nn) is the power that the pump transfers to the fluid. These two quantities are determined by the following formulas:

Pump characteristics such as flow, head, efficiency and power consumption are shown graphically on pump operation curves.

The pump size, 2x3-8, is shown at the top of the graph. The numbers 2x3-8 indicate that the outlet (exhaust port) is 2 inches (can be represented in mm), the inlet (suction port) 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 numbers is the inlet port. 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. Productivity or volumetric flow is shown along the bottom of the curve. All different flow levels are shown at an operating speed of 2960 rpm, but show the effect of head when throttling the output. The left side of the performance curves shows the head created when different speeds flow.

The graph compares several flow and pressure curves, each characterizing a different (cut-down) impeller size. For this pump, the impeller range ranges 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. Power consumption is shown with a dotted line drawn diagonally from the bottom right to the top left. Power consumption curves are shown for the range 80 - 325 kW. When using an 8-inch impeller with a flow rate of 250 m/h, the power consumption will be about 270 kW.

Pump and system performance

The pump performance curve is a simple function of the physical characteristics of the pump. The operating 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 prolonged changes, it is necessary to change the pump characteristics or system parameters.
There are two methods that are used to provide variable flow. One of the methods is throttling, which leads to a change in the characteristics of the system due to the throttle valve. Another method is to change the rotation speed of the pump, which changes the operating characteristic of the pump.

With this method, additional flow resistance increases the pressure. The system characteristics at 2 different valve positions are shown below.

For comparison, let's use an example to determine the power consumption of a system when throttling, then for a system with speed control. A pump (with an 8-inch impeller) operating at a nominal speed of 2960 rpm is used. The pump is designed to operate in a system requiring a head of 250 meters at a flow of 250 m3/h. See pump performance curve below

Based on the information presented in the graph, the various power requirements at the flow rates shown in the table below can be determined for the throttling system.

Where,
Nn- hydraulic power (kW)
N- power consumption (kW)

Variable speed system

Unlike the above method, when regulating the speeds change.

Lower pump speed changes the pump operating curve based on the velocity head generated by the speed of the fluid being pumped. Remember that this head is equal to v 2 / 2g.

Laws of similarity

The set of formulas used to predict the performance of a centrifugal pump at any operating point based on the pump's initial characteristics are called similarity laws.

Where,
n= Pump rotation speed
Q= Feed (m/h) R= Pressure (m) N= Power (kW)
Using the same example as for throttling, it is possible to 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 flow mode is significantly 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 load is not full (as in the case of throttling), while the efficiency of an adjustable electric drive remains unchanged, which provides additional savings. Energy savings will depend on the amount of time the pump runs at each reduced speed setting.

To calculate real savings, 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 consumption from the throttling power consumption to obtain the difference in energy cost.

In our example, with a flow rate of 200 m/h, 240 kW is consumed during throttling, and during speed control, only 136.2 kW is required for the same flow. If it is necessary to provide such a mode for 2000 hours per year at a price of 2 rubles per kWh, the cost comparison will be as follows:

Throttle system:
240 x 2000 = 480000 kWh
480,000 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 pressure does not affect the characteristics of the system and the power consumption when regulating the flow. The higher the hydrostatic head of the system, the lower the energy saving opportunities. This is due to the fact that the characteristics of the system are flatter, because Most of the energy is used to lift the liquid to the required height.

based on materials from Rockwell Automation, Inc.[Cancel reply]
Pages:

There is a relationship between mass and volume feed:

Measure The pump can be supplied using various devices:

2. Application of injection machines

3. Operating parameters of injection machines

4. Fundamentals of the theory of centrifugal superchargers

5. Actual characteristics of the centrifugalsupercharger at constant frequency rotation

6. Similarity to centrifugal machines. Formulasproportionality

7. Regulation of the supply of centrifugal blowers

8. Summary graphs of fields (zones) of supercharger performance characteristics

9. Parallel and serialconnectionssuperchargers

10. Centrifugal pumps

11. Centrifugal fans

12. Centrifugal compressors

13. Piston pumps

14. Piston compressors

15. Gas compressor stations 59

15.1. Purpose and description of the compressor station

15.2. Layout of gas pumping units at station 62

15.3. Natural gas blowers. 64

15.4. Power supply for gas turbine compressor stations and gas compressor units 65

15.5. Maintenance of the unit and KS systems during operation 67

15.6. Oil supply system for compressor stations and gas compressor units, oil purification systems

oil air cooling machines and apparatus 69

15.7. Design and operation of the control system 75

15.8. PC work of OPERATOR'S workstation 78

16. Oil pumping station 81

17. Selection of pumping equipment and its operating modes 88

18. Pumping equipmentWestern companies 100

19. Analysis and comparison adjustable electric drives 103

1. Types and classification of superchargers

Blowers are machines used to move liquids and gases and increase their potential and kinetic energy.

It is known that most modern technological processes are associated with the movement of flows of liquid and gaseous media, and therefore superchargers are very widely used in all industries, agriculture and public utilities.

Depending on the type of moving working fluid, injection machines are divided into two large groups: pumps - machines that supply liquids; fans and compressors - machines that supply air and technical gases.

Fan- a machine that moves a gas medium at a degree of pressure increase e p< 1,15 (степень повышения давле­ния е р - отношение давления газовой среды на выходе из маши­ны к давлению ее на входе).

Compressor- a machine that compresses gas with e p » 1.15 and has artificial (usually water) cooling of the cavities in which the gases are compressed.

According to GOST 17398-72, blowers (pumps) are divided into two main groups: dynamic and volumetric pumps.

In dynamic superchargers, the transfer of energy to a liquid or gas occurs through the work of mass flow forces in a cavity permanently connected to the inlet and outlet of the supercharger.

In positive displacement superchargers, an increase in the energy of the working fluid (liquid or gas) is achieved by the force action of solid bodies, for example, pistons in piston machines in the working space of the cylinder, periodically connected by means of valves to the inlet and outlet of the supercharger.

Rice. 1. Classification of superchargers

Classification of superchargers is also made according to design characteristics, pressure developed by the machine, and purpose in the technological process.

N and fig. 1 presents the classification of superchargers according to their operating principle and design features.

Rice. .2. Centrifugal blower:

1 - body; 2 - pipeline; 3 - pressure pipe; 4 - blades; 5 - pipe

In Fig. Figure 1.2 shows a diagram of a dynamic centrifugal supercharger. The impeller, equipped with curved blades 4, is rotated by a motor located in the housing 1. The working fluid (liquid or gas), entering the central cavity of the wheel through the pipe 5, fills the entire housing and the linear channels of the wheel between the blades 4. When the impeller rotates under the influence of centrifugal forces, the mass of the working fluid located in these channels increases the energy of the flow and is thrown out by the flow into the spiral channel surrounding the impeller. Next, the flow enters the pressure pipe 3 and pipeline 2.

The process of suction and delivery in such superchargers occurs continuously and evenly (at a constant speed of rotation of the impeller).

D Axial-type dynamic blade superchargers are also used to supply liquids and gases (Fig. 3). The supercharger consists of a wheel with working blades 4 mounted at a certain angle on the wheel hub with a fairing 1, a housing 2 and a straightening blade apparatus 5, fixedly fixed in the housing. When the wheel rotates, the blades transfer energy to the working fluid and move the working fluid (nozzle 3 - suction, nozzle 6 - pressure).

Rice. 3. Axial supercharger: 1- fairing; 2 - body; 3 - suction pipe; 4 - blades; 5 - blade apparatus; 6 - pressure pipe

In Fig. Figure 4 shows a diagram of a vortex supercharger. In the housing 4, a wheel with flat radial blades 3 is located concentrically. The working fluid enters through the suction pipe into the annular channel 2, is carried away by the blades 3, performing a complex vortex movement and increasing energy, and exits through the pressure pipe 1 into the pipeline.

The diagram of the simplest volumetric supercharger-pump is shown in Fig. 5. Cylinder 3 and valve box 7 are tightly connected into a single unit. The box contains 5 suction and 2 pressure valves. Piston 4, moving back and forth, produces suction and delivery.

The acceleration of a piston moving sinusoidally causes the appearance of inertial forces that affect the strength of the supercharger running system and cause discontinuities in the flow continuity. This limits the permissible rotation speed of the crank shaft. Therefore, rotary-type positive displacement superchargers are used, allowing direct connection to high-speed engines.

Rice. 6 gives an idea of ​​the design and principle of operation of a vane rotary supercharger. A massive rotor 2 with radial slots is placed eccentrically in the housing 1. Rectangular steel plates 7 are inserted into the slots and are freely pressed against the body by centrifugal forces. When the rotor is rotated by the engine, the working fluid will be sucked through the cutting section 5 and fed through the cavities of variable cross-section 6 and 3 into the pressure pipe 4 of the pipeline system. The supercharger is reversible: when the direction of rotation of the rotor changes, the supercharger changes the direction of flow of the working fluid.

Jet blowers are used to move liquids and gases in industrial and laboratory installations (Fig. 7). The flow of working fluid exits at high speed through a convergent nozzle 1 into chamber 2, where low pressure is established. Under the influence of the pressure difference on the surface of the liquid and in the chamber, the liquid rises through pipe 5 and mixes it with working fluid, ejected from the nozzle. The mixture of liquids - working and rising through pipe 5 - is transported through diffuser 3 and pressure pipe 4 to a height of H g.

Rice. 4. Vortex blower:

1- pressure pipe; 2 - ring channel; 3 - shoulder blades; 4 - body

R is. 5. Piston supercharger:

1- discharge pipeline; 2 - pressure valve; 3 - cylinder; 4~ piston; 5- suction valve; 6- suction pipeline; 7 - valve box

Rice. 6. Rotary blower:

1 - body; 2 - rotor; 3, 6 - cavities of variable cross-section; 4- pressure pipe; 5- suction pipe; 7 - movable

records

Rice. 7. Jet supercharger: 1- nozzle; 2 - camera; 3 - diffuser;

4 - pressure pipe; 5-pipe

In industrial water supply systems, oil production, agriculture and municipal services, special types of superchargers are used - airlifts and gas lifts, which use compressed air or gas to lift liquids (Fig. 8). This type of lift is used to lift water and oil from deep wells.

A riser pipe 2 is lowered into the casing pipe 1. Air or technical gas flows from the compressor K through an air line (shown by a dotted line) to the lower end of the riser pipe through a bubbling device. Here a bubble mixture of air or gas with liquid is formed. The density of this mixture is less than the density of the pure liquid in the casing.

According to the law of communicating vessels, a column of liquid of height H in the casing pipe displaces a column of mixture in the riser pipe to height H2. When hitting the impact cone 4, air (gas) is removed from the mixture, the liquid is collected in reservoir 3 and sent by pumps to the pipeline system.

Based on the flow and total pressure specified for the fan or pump, and for the compressor - the flow and specific compression work, the power on the shaft is determined, according to which the power of the drive motor can be selected.

For a centrifugal fan, for example, the formula for determining shaft power is derived from the expression of the energy imparted to the moving gas per unit time.

Let F be the cross-section of the gas pipeline, m2; m - gas mass per second, kg/s; v - gas velocity, m/s; ρ - gas density, m3; ηв, ηп - efficiency of the fan and transmission.

It is known that

Then the expression for the energy of the moving gas will take the form:

where does the power on the drive motor shaft come from, kW,

In the formula, we can distinguish groups of values ​​corresponding to flow, m3/s, and fan pressure, Pa:

From the above expressions it is clear that

Respectively

here c, c1 c2 are constant quantities.

Note that due to the presence of static pressure and design features For centrifugal fans, the exponent on the right side may differ from 3.

In the same way as was done for the fan, we can determine the shaft power of a centrifugal pump, kW, which is equal to:

where Q is pump flow, m3/s;

Нг - geodetic pressure equal to the difference between the discharge and suction heights, m; Ns - total pressure, m; P2 - pressure in the tank where the liquid is pumped, Pa; P1 - pressure in the tank from where the liquid is pumped, Pa; ΔН - pressure loss in the main line, m; depends on the cross-section of the pipes, the quality of their processing, the curvature of the pipeline sections, etc.; ΔН values ​​are given in reference literature; ρ1 - density of the pumped liquid, kg/m3; g = 9.81 m/s2 - free fall acceleration; ηн, ηп - efficiency of the pump and transmission.

With some approximation, for centrifugal pumps it can be assumed that there is a relationship between shaft power and speed P = cω 3 and M = cω 2. In practice, the speed exponents vary within 2.5-6 for different 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. Let us 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 different speeds of the mechanism.

In Fig. As an example, Figure 1 shows the characteristics (1, 2, 3, 4) of a centrifugal pump at various angular velocities of its impeller. The same coordinate axes show the characteristics of line 6 to which the pump operates. 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 productivity when the pump operates on a certain line at different speeds.

Rice. 1. Dependence of pump pressure H on its flow Q.

Example 1. Construct the characteristics H, Q of a centrifugal pump for various speeds 0.8ωn; 0.6ωн; 0.4ωн, if characteristic 1 at ω = ωн is specified (Fig. 1).

1. For the same pump

Hence,

2. Let's construct the pump characteristic for ω = 0.8ωn.

For point b

For point b"

Thus, it is possible to construct auxiliary parabolas 5, 5", 5"... which on the ordinate axis at Q = 0 degenerate into a straight line, and QH characteristics for various pump speeds.

The engine power of a piston compressor can be determined based on the air or gas compression indicator diagram. 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.

Compressing a gas requires work, which will vary depending on the nature of the compression process. This process can be carried out according to the adiabatic law without heat transfer, when indicator diagram limited by curve 1 in Fig. 2; according to the isothermal law at constant temperature, respectively, curve 2 in Fig. 2, or along the polytrope curve 3, which is shown solid line between adiabatic and isotherm.

Rice. 2. Gas compression indicator diagram.

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 compressed gas, Pa; V1 is the initial specific volume of gas, or the volume of 1 kg of gas during suction, m3.

Compressor motor power, kW, is determined by the expression

here Q is the compressor flow, m3/s; ηk is the indicator efficiency of the compressor, taking into account the power losses in it during the actual operating process; ηп - efficiency 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 power on the compressor shaft, 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 is compressor flow, m3/s; Au is the isothermal work of compressing 1 m3 of atmospheric air to pressure P2, J/m3; Aa is the adiabatic work of compressing 1 m3 of atmospheric air to pressure P2, J/m3.

The relationship between the power on the shaft of a piston-type production mechanism and speed is completely different from the corresponding relationship for mechanisms with a fan-type torque on the shaft. If a piston-type mechanism, for example a pump, operates 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 obtained formulas, the power on the shaft of the corresponding mechanism is determined. To select a motor, you should substitute the nominal values ​​of flow and pressure into the indicated formulas. Based on the power received, a continuous-duty engine can be selected.

The centrifugal compressor is widely used in transport and aircraft engines (GTE), in closed-cycle gas turbine units (CGTU), as well as in stationary installations and helicopters. gas turbine engines as the last stage of an axial-centrifugal compressor.

When the wheel rotates, air is forced through the channels formed by the blades to the periphery. A vacuum forms in front of the wheel and outside air continuously flows through the input device to the wheel. In the impeller, mechanical energy is supplied to the flow, under the influence of which the working fluid is compressed in the impeller (>) and the kinetic energy of the flow in absolute motion increases (>). From the impeller, the gas enters the diffuser, in which the cross-sectional area increases with increasing radius. According to the continuity equation, the flow velocity gradually decreases. In accordance with Bernoulli's equation, kinetic energy in the diffuser is converted into pressure energy.

Rice. 1. Scheme of design types of impellers:

a) - open; b) - half-open; c) - closed

Figure 1 shows diagrams of the applied designs of centrifugal compressor impellers. The open-type impeller has separate blades mounted on a bushing. When using an open-type valve, increased end losses associated with air flow occur. Therefore, despite the comparative simplicity of design, this type of wheel has limited use. Closed impellers provide highest value Efficiency The presence of a cover disk reduces end losses. However, this type of wheel is structurally much more complex than others and has a lower peripheral rotation speed allowed by strength conditions. Until recently, the semi-open type wheel drive was most often used, combining the advantages of open (ease of manufacture) and closed (reduced end losses) wheels.

When studying the working process in a centrifugal compressor, the concept of degree of reactivity is used:

Speed ​​triangles for wheels with different degrees of reactivity are shown in Fig. 2.

Rice. 2. Speed ​​triangles of RK centrifugal compressors with varying degrees of reactivity:

a – blades curved against rotation; b – radial blades; scapulae curved in rotation

For radially located blades we obtain: and . The velocity triangle at the exit from the RC in this case is shown in Fig. 2, b. In reality,< и < при и степень реактивности рабочего колеса с радиальными лопатками при несколько больше величины . Если угол выхода потока < (лопатки загнутые против вращения), то скорость в абсолютном движении на выходе из РК существенно меньше, чем при , и увеличивается степень реактивности . Именно в связи с ростом при уменьшении угла < РК с лопатками, загнутыми против вращения, получили название реактивных рабочих колес. Хотя в таких колесах, по сравнению с радиальными на выходе лопатками, при одинаковых окружных скоростях уменьшается величина (теоретический напор компрессора), использование их позволяет существенно улучшить эффективность работы выходной системы (безлопаточного и главным образом лопаточного диффузора) в результате уменьшения скорости потока. Кроме этого, протекание характеристик ступени с РК, имеющим загнутые против вращения лопатки, более благоприятно. В РК с лопатками, загнутыми по вращению >, there is a significant increase in the absolute flow rate and, consequently, a decrease in the degree of reactivity. Due to the decrease in the degree of reactivity in wheels with > they are called active. At the highest coefficient of theoretical pressure and, therefore, at a higher pressure at a given peripheral speed, the RK c > have the most gentle flow of the stage characteristics and the operating efficiency of the blade diffuser is difficult to ensure due to the high value of the speed of the air flow incident on the diffuser blades.

Figure 3 shows the dependence of the overall theoretical work on productivity at various exit blade angles:

Rice. 3. Dependence of the overall theoretical work on productivity at various exit blade angles

2. DIAGRAM AND DESCRIPTION OF THE STAND

Tests are carried out on the “Centrifugal compressor stage” stand, the design diagram of which is shown in Fig. 4.

Rice. 4. Scheme of the stand “Centrifugal compressor stage”:

1-input device; 2–impeller; 3–electric motor; 4–tachometer sensor; 5–throttle; 6-reverse radial guide vane; 7-output capacity

Impeller 2 is driven by electric motor 3. Air enters the compressor through inlet device 1, the measuring part of which is made according to the lemniscate in accordance with GOST 27-64. This creates a uniform velocity field in front of the compressor. At the outlet of the compressor there is a reverse radial blade apparatus 6, from which air flows around the electric motor into the output tank 7, then passing through the throttle valve 5.

By changing the motor speed and position throttle valve you can set the compressor operating mode in the required parameter range.

Rice. 5. Compressor impeller

The impeller of a semi-open type centrifugal radial compressor has following parameters(Fig.5):

Inlet diameter;

Outlet diameter;

The height of the blade at the entrance to the wheel;

The height of the blade at the exit of the wheel;

Flow entry angle;

Angle of flow exiting the impeller;

Number of blades;

Blade thickness;

Blade bending radius;

The radius of the circle on which the centers of the blade bending arcs are located.

During the experiment the following are measured:

pressure drop across the inlet measuring device

ambient temperature

total compressor inlet pressure

air temperature at the impeller outlet

compressor outlet air temperature

stagnant flow pressure at the compressor outlet

static pressure at compressor outlet

rotor speed

current strength

voltage

3. LABORATORY WORK No. 1

EXPERIMENTAL CHARACTERISTICS OF A CENTRIFUGAL COMPRESSOR STAGE

3.1.PURPOSE OF THE WORK

Experimentally obtain the characteristics of a centrifugal compressor stage in the form of dependencies: , , , , .

3.2.GENERAL INFORMATION

When a compressor operates in any system, due to changes in operating modes of the system, the parameters at the entrance to the compressor change and the properties of the working fluid (air) change. For example, when a compressor operates as part of an aircraft engine, due to changes in altitude and flight speed, the input parameters change: pressure, temperature, flow of the working fluid, rotation speed, air viscosity, its thermal conductivity and heat capacity and, consequently, the ratio of heat capacities. For efficiency and degree of improvement total pressure In general, the following functional dependencies can be written:

The given dependencies, which are called compressor characteristics, are inconvenient for practical use. This is due to the fact that and depend on many variables, which makes their graphical representation almost impossible.

In this regard, the construction of characteristics is based on the provisions of the theory of similarity, which allows, by introducing dimensionless parameters or similarity criteria, to reduce the number of variables that determine the characteristics of blade machines.

Phenomena are similar if geometric, kinematic and dynamic similarity is observed.

If the same machine is studied, then changes in dimensions due to thermal expansion and elastic deformations are not taken into account and the assumption is made that geometric similarity is maintained.

To perform kinematic similarity, it is necessary that the similarity of the velocity triangles be maintained, i.e. the ratio of the circumferential to absolute velocity at similar points would be the same

From the theory of similarity it is known that gas-dynamic similarity in geometrically similar systems will be satisfied if the similarity criteria are equal. By applying the provisions of dimensional theory or considering equations that describe phenomena in the original and similar modes, it can be established that gas-dynamic similarity is determined by the equality of the following criteria:

Adiabatic exponent;

Characterizing the influence of flow compressibility;

Characterizing the relationship between inertial forces and viscous forces in the flow on the nature of the flow and friction losses;

Characterizing the influence of the field of gravitational forces on the flow;

Characterizing the physical properties of the working fluid and independent of flow parameters.

If we take into account that for gas the influence of the gravitational field is small, for air, and in most cases, blade machines operate in such a region (self-similar) of number changes that the loss coefficients do not change with changes in , then functional dependence (1) can be represented in the following form:

If instead of numbers we use the reduced speeds uniquely associated with them, and instead of the value of the function, we obtain the compressor characteristic presented in the form of dependencies:

where is the reduced peripheral speed.

Characteristics (3) are valid for the entire family of geometrically similar compressors and are convenient to use, for example, to determine the dimensions and parameters of a new compressor for which the characteristics of its geometrically similar model are known.

For compressors of certain sizes, it is more convenient to use compressor characteristics in which, instead of and, complex parameters uniquely associated with them are used - called respectively the reduced flow rate and the reduced rotational speed. The use of these parameters seems more convenient, since they are directly related to such important parameters compressor such as air flow, rotation speed and air parameters at the compressor inlet and.

And the value of temperature and pressure under standard conditions at the compressor inlet,

It is called reduced flow rate, and since it corresponds to a certain value, then it can be considered as a similarity parameter.

From the condition we can write for two similar modes:

Called the reduced number of revolutions.

Compressor characteristics plotted as dependencies:

are called universal characteristics and allow, under the same inlet conditions, to compare the parameters of different compressors.

Rice. 6. Typical compressor characteristics

The characteristics of the compressor in the form of dependencies determined by relation (4) are shown in Fig. 6. An important feature of the compressor characteristics is the presence of a stable operation boundary, called the pump boundary. To the left of this boundary, due to a sharp drop in parameters and an increase in dynamic loads, the operation of the compressor is unacceptable. To the right is the area of ​​stable modes that are used when operating a compressor as part of a gas turbine engine. Such a characteristic is usually applied in the form of topographic lines lines.

Under given operating conditions, the centrifugal stage has a productivity of , and the overall theoretical work is determined by the equation (pulp and paper mill with< ):

The dependence of work on productivity (air flow) is straightforward. The slope of the straight line is determined by the exit angle of the impeller blades. In Fig.7. the straight line represents the theoretical characteristic of the centrifugal stage with the outlet angles of the impeller blades< . Эффективная работа меньше, чем теоретическая. Величина работы в расчетной точке определяется уровнем потерь: профильных (трения и вихреобразования в пограничном слое на профиле, кромочные, волновые), вторичных (парный вихрь, вихрь от перетекания в радиальном зазоре, радиальное течение в пограничном слое вдоль лопатки) и концевых (боковое трение диска и бандажа, перетекание воздуха в радиальном зазоре). На нерасчетном режиме характер изменения работы определяется характером изменения профильных потерь, т.к. уровень концевых и вторичных потерь с изменением расхода не меняется. Профильные потери возрастают при отклонении от расчетного режима из-за отрывных явлений пограничного слоя с корытца профиля при малых расходах и из-за отрывных явлений со спинки профиля и роста волновых потерь при больших расходах.

Rice. 7. Characteristics of the centrifugal stage:

1-end losses; 2–secondary losses; 3-profile losses

3.3. EXPERIMENTAL PROCEDURE

3.3.1. Familiarize yourself with the experimental setup and the necessary measuring equipment.

3.3.2. Prepare forms for tables of measured parameters.

3.3.3. Enable installation.

3.3.4. Set the desired compressor rotor speed using the speed control knob. Maintain the regime.

3.3.5. Covering the throttle, measure the parameters of the compressor stage at intermediate points (6 - 7 points), while maintaining the given rotation speed and maintaining the setting in each mode before measuring the parameters.

3.3.6. Enter the measurement results into the table (see Table 1).

3.3.7. Turn off the installation.

Table 1

Measurement results

3.4.PROCESSING OF EXPERIMENTAL DATA

3.4.1. The conversion of the obtained values ​​of , and to Pa is carried out taking into account the following relationships:

3.4.2. Determination of air flow:

From Bernoulli's equation:

where is the pressure loss in the inlet device.

As a first approximation, we assume that , and - due to low velocities in the input device.

The absolute value of the speed at the entrance to the wheel:

Static flow temperature at the wheel inlet:

where is the heat capacity,

Flux density at the wheel inlet:

Knowing the flux density, we specify the speed value:

Air flow is determined from the continuity equation:

where is the compressor inlet cross-sectional area.

Where is the diameter of the inlet section.

3.4.3. Pressure loss in the inlet device:

where (input device design) is the friction resistance coefficient.

3.4.4. Retarded flow pressure at the wheel inlet:

3.4.5. Static pressure at the wheel inlet:

3.4.6. Specific work with insignificant heat exchange with environment can be determined by the difference in total temperatures at the inlet and outlet of the compressor:

3.4.7. Work expended on rotating the wheel for each kilogram of air mass:

where is the work of friction between the disk and the gas, .

3.4.8. Compressor power:

3.4.9. Motor power:

The power of an electric motor can also be defined as:

where is the power spent on heating the air cooling the electric motor.

3.4.10. Peripheral speed at the wheel exit:

3.4.11. Circumferential velocity component at the exit from the wheel of a centrifugal compressor:

3.4.12. Wheel outlet area:

Number of blades;

3.4.13. Density of stagnated flow at the outlet of the impeller:

3.4.14. Radial component of the flow velocity at the wheel outlet:

As a first approximation, we assume that From the continuity equation:

3.4.15. The absolute value of the speed at the exit of the wheel:

3.4.16. Static air temperature at the wheel outlet:

3.4.17. Static pressure at the wheel outlet:

3.4.18. Flux density at the wheel outlet:

3.4.19. We clarify the value of the speed at the exit of the wheel:

3.4.20. Pressure loss at the outlet of the installation:

3.4.21. Retarded flow pressure at the outlet of the centrifugal compressor wheel:

3.4.22. Compressor pressure ratio:

3.4.23. Adiabatic compressor operation:

3.4.24. Adiabatic compressor efficiency:

3.4.25. Flow rates and rotation speeds reduced to standard atmospheric conditions

3.4.26. Enter the calculation results into the table (see Table 2).

Table 2

Calculation results

3.4.27. Construct characteristics in the form of dependencies: , , , , .

3.4.28. Draw conclusions.

3.5 REQUIREMENTS FOR THE REPORT

4. LABORATORY WORK No. 2

KINEMATICS OF FLOW AT THE INPUT TO THE WHEEL OF A CENTRIFUGAL COMPRESSOR

4.1.PURPOSE OF THE WORK

Study of the kinematics of flow at the inlet to the wheel of a centrifugal compressor in design and non-design modes of operation.

4.2.GENERAL INFORMATION

The absolute speed at the entrance to the impeller is equal to . The peripheral speed at this radius is . The gas has a relative speed relative to the wheel. The direction and magnitude are defined as the vector sum of the relative speed and the circumferential speed.

If the impeller of a centrifugal compressor is of radial type, then the speed triangle at the inlet is constructed in a plane perpendicular to the axis of rotation.

To obtain a shock-free entry into the wheel, the angle of inclination of the wheel blades must be equal to the angle of flow entry onto the blades. To reduce energy losses associated with the conditions of flow entry into the grid of the working and guide vanes, they try to ensure flow around the grid profiles with an optimal angle of attack, usually close to the condition of the so-called shockless entry, i.e. . This can be achieved in two ways: the first is to direct the inlet edges of the wheel blades in the direction of wheel rotation in the absence of an inlet guide vane. In axial wheels of a semi-open type, this is achieved by appropriately bending the outlet edges of the blades and making these curved edges often separately from the rest of the disk with blades in the form of a so-called slat. The second method is a combination of a slat (but with a smaller bend of the blades) with the installation of a FNA (fixed guide vane), which twists the flow in the direction of wheel rotation. The conditions when , can also be achieved in other ways, for example, by installing only a low-pressure pump with a positive swirl of the flow, in the absence of a slat; a combination of a slat and a low-pressure pump with a negative swirl of the flow. These methods are characterized by relatively large speeds or and the corresponding numbers and .

The design mode is the only operating mode of the compressor for which a gas-dynamic calculation is performed and the main geometric dimensions steps, blade angles, grating density, etc. The design mode is characterized by the fact that only in this mode does the blade apparatus best correspond to the flow kinematics, i.e. ensures continuous flow around the impeller blades and guide vanes of the compressor stages. However, during operation, most of the time the compressor operates in conditions different from the design mode, or, as they usually say, in non-design modes (Fig. 8.)

Rice. 8. Velocity triangles at the inlet to the centrifugal compressor stage in design and off-design operating modes

With a decrease in gas flow at a constant rotor speed, instability of the compressor operation is also noted, associated with a change in the nature of the flow around the impeller grids and fixed diffuser channels. When flowing around a blade at a certain angle of attack >0, a noticeable separation of the boundary layer occurs. This does not occur in the entire lattice at the same time, but in one of its channels. The resulting disruption leads to blockage of this channel and spreading of the flow on both sides. On one side of the channel the angles of attack increase, on the other they decrease. An increase in angles of attack leads to flow disruption in the outlet part of the wheel blades. In this case, rotating separation zones are formed. The angular speed of their rotation is 2-3 times less than the angular speed of the wheel. This flow is called rotating stall. A further decrease in gas flow through the compressor stage is associated with increased stall phenomena and the initiation of vibrations.

As the flow rate increases beyond the design angle, the angle of attack decreases and becomes negative due to an increase in the radial component of the velocity. This leads to flow disruptions from the concave surface of the profile, a sharp increase in losses and “blocking” of the compressor. It should be noted that in centrifugal compressors with bladed diffusers, “blocking” is determined, as a rule, by the flow regime around the diffuser blades, significantly reducing the range of stable operation of the compressor in terms of flow rate.

4.3.PROCESSING OF EXPERIMENTAL DATA

4.3.1. Processing of experimental data is carried out on the basis of experimental data obtained in laboratory work №1.

4.3.2. The absolute value of the flow velocity at the inlet to the wheel of a centrifugal compressor is taken from laboratory work No. 1.

Since (axial entrance to the wheel).

4.3.3. Peripheral speed at the wheel entrance:

where is the diameter of the flow inlet into the wheel,

Diameter of flow exit from the wheel,

4.3.4. Flow entry angle into the wheel:

4.3.5. Angle of attack:

where is the geometric angle of flow entry into the wheel.

4.3.6. Relative value of the flow velocity at the wheel inlet:

4.3.7. The absolute value of the flow velocity at the wheel inlet at the optimal (design) compressor operating mode:

4.3.8. Relative value of the flow velocity at the wheel inlet at the optimal (design) compressor operating mode:

4.3.9. Enter the calculation results into the table (see Table 3).

Table 3

Calculation results

4.3.10. On graph paper, draw triangles of speeds at the entrance to the wheel of a centrifugal compressor, construct a relationship.

4.3.11. Draw conclusions.

4.4.REPORT REQUIREMENTS

The experiment is carried out in subgroups of 6 people. Each student in the subgroup has a detailed calculation of one flow rate. The report must contain the following parts:

5. LABORATORY WORK No. 3

KINEMATICS OF FLOW AT THE OUTLET FROM THE WHEEL OF A CENTRIFUGAL COMPRESSOR

5.1.PURPOSE OF THE WORK

Study of the kinematics of flow at the outlet of a centrifugal compressor wheel.

5.2.GENERAL INFORMATION

The study of the kinematics of the flow at the outlet is reduced to constructing a triangle of velocities for different modes work. The speed triangle, with known wheel geometry and rotation frequency, can be constructed if the radial component and circumferential component of the absolute speed at the exit of the wheel are known.

If we assume that the flow part of the impeller consists of an infinite number of channels formed by an infinite number of blades of zero thickness, then the flow direction will completely correspond to the profile of the blades. The gas will exit the impeller at a relative speed at an angle equal to the angle of inclination of the blade as it exits the impeller.

The work spent on rotating the wheel for each kilogram of air mass, according to Euler’s equation (without taking into account the friction of the lateral surfaces of the wheel disk), is determined by the formula:

and for the axial entrance to the wheel:

Here the value depends on the number and length of the blades. With a finite number of blades it decreases. When considering the movement of gas in an impeller with an infinite number of blades, it is assumed that all streamlines have the same shape, and the blades are segments of streamlines. It follows that the speed at any radius of the impeller is constant over the entire circumference. However, to transfer energy from the impeller blades to the flow, a pressure difference is required between both sides of the blade, which is only possible if there is a difference in speed on these sides. Thus, in contrast to the jet theory, the speed of movement is not constant around the circumference and changes periodically, since in each channel limited by two adjacent blades, the flow pattern should be the same. In the channel of a rotating wheel with a finite number of blades, due to Coriolis acceleration, the relative velocities on an arc of a given radius vary linearly depending on the polar angle. As a result, at the front side of the blades the speed is lower and the pressure is higher, and at the rear side - vice versa (Fig. 9).

Rice. 9. Change in speed and pressure in the channel of a centrifugal compressor

The smaller the number of blades, the greater the difference in speed at the front and rear walls of the blades. The appearance of an additional circumferential component can be explained by considering the process of speed equalization at the exit of the wheel, where the flow flows freely, without the influence of external forces. When the speeds are equalized, the jets with higher speeds reduce their speed to a certain average value, and the jets with lower speeds increase it to this average value. As a result of this, some movement of air masses occurs on the periphery in the direction opposite to the rotation of the wheel, as a result of which a certain circumferential component appears. Due to the presence, the theoretical head, or work, imparted by 1 kg of air passing through the wheel is reduced and therefore reduced. The reduction in the circumferential component is usually taken into account using the coefficient. Coefficient (usually called the reduction coefficient transmitted energy) based on theoretical and experimental studies for radial blades can be determined using the Kazanjan formula:

where is the average diameter of the wheel inlet section.

According to the Stodolla formula, the coefficient is equal to

The average value of the coefficient fluctuates within

The velocity triangle at the exit from the wheel of a centrifugal compressor is shown in Fig. 10.

Rice. 10. Velocity triangle at the outlet of a centrifugal compressor stage

5.3.PROCESSING OF EXPERIMENTAL DATA

5.3.1. Processing of experimental data is carried out on the basis of experimental data obtained in laboratory work No. 1.

5.3.2. Circumferential velocity component at the wheel exit:

where is the work expended on rotating the wheel for each kilogram of air mass;

Peripheral speed at the exit of the wheel.

5.3.3. Wheel outlet area:

where is the thickness of the blade at the exit from the wheel;

Number of blades;

The height of the blade at the exit of the wheel.

5.3.4. Density of stagnated flow at the outlet of the impeller:

5.3.5. Radial component of the flow velocity at the wheel outlet:

As a first approximation, we assume that . From the continuity equation:

5.3.6. The absolute value of the flow velocity at the wheel outlet:

5.3.7. Static air temperature at the wheel outlet:

5.3.8. Static pressure at the wheel outlet:

5.3.9. Flux density at the wheel outlet:

5.3.10. We clarify the value of the speed at the exit of the wheel:

5.3.11. Relative value of the speed at the exit of the wheel:

5.3.12. Angle of flow exiting the wheel:

5.3.13. Angle of flow exiting the wheel in absolute motion:

5.3.14. Flow lag angle:

where is the geometric angle of flow exit from the centrifugal compressor wheel.

5.3.15. Transmitted energy reduction factor:

where is the circumferential velocity component at the exit of the wheel with an infinite number of blades.

According to the Stodolla formula, the coefficient is determined as:

5.3.16. The absolute value of the speed at the exit of the wheel with an infinite number of blades:

5.3.17. Relative value of the speed at the exit of the wheel with an infinite number of blades:

5.3.18. Geometric angle of flow exiting the wheel in absolute motion:

5.3.19. Enter the calculation results into the table (see Table 4).

Table 4

Calculation results

5.3.20. On graph paper, draw triangles of velocities at the outlet of the centrifugal compressor wheel, plot the relationship.

5.3.21. Draw conclusions.

5.4 REQUIREMENTS FOR THE REPORT

The experiment is carried out in subgroups of 6 people. Each student in the subgroup has a detailed calculation of one flow rate. The report must contain the following parts:

References

1. Kholshchevnikov K.V., Emin O.N., Mitrokhin V.T., Theory and calculation of aircraft blade machines: A textbook for university students specializing in "Aircraft engines". 2nd ed., revised. and additional - M.: Mashinostroenie, 1986. 432 p., ill.

2. Den G. N. Design of the flow part of centrifugal compressors: Thermogasdynamic calculations. – L: Mechanical engineering. Leningr. department, 1980. – 232 pp., ill.

3. Cherkassky V. M. Pumps. Fans. Compressors. Textbook for thermal power engineering specialties at universities. M., "Energy", 1977

4. Seleznev K.P. Podobuev Yu.S. Theory and calculation of turbocompressors-L: Mechanical Engineering, 1968.-408 p., ill.