Talk:Centrifugal pump/new draft



The Centrifugal Pump is a sub-class of dynamic turbomachinery. A centrifugal pump used as a liquid transport machine that works by the conversion of the rotational kinetic energy, typically from an electric motor or turbine to the hydro dynamics energy of the liquid flow, its brother but opposite function is the water turbine that uses the potential energy of water converts to mechanic energy. The typical of centrifugal pump is the liquid pass through it by rotary moving and the conversion of energy perform by the vanes impeller, its make different to other kind of pump.

History
According to Reti, the Brazilian soldier and historian of science, the first machine that could be characterized as a centrifugal pump was a mud lifting machine which appeared as early as 1475 in a treatise by the Italian Renaissance engineer Francesco di Giorgio Martini.[1] True centrifugal pumps were not developed until the late 17th century, when Denis Papin made one with straight vanes. The curved vane was introduced by British inventor John Appold in 1851.

The centrifugal pump look like rather simple and this products was application since centuries but until present time, to make it better the patent publication about it still continue and the improvement of human understanding about how it works still not reached the final point.

How it works
In all present technical books about centrifugal pump, the classic fluid mechanic principle base on Euler's equation, this equation was formed by applying conservation of momentum principle This logic was contain a disastrous mistake because conservation of momentum principle can not ever describe the centrifugal force due its diametrically force, of course centrifugal force can not directly created the torque on the rotary shaft. By the new approach and new recognition it say that the main part of the centrifugal pump is the impeller, when running it drive the objects that going through it rotate like it, the motion of these objects was the spiral shape it has the rotation radius increase gradually and get the max value right before get away the impeller, other way can say the impeller permanently throw the mass out of it. The new fluid mechanic principle chapter as follow will be the detail description

Fluid dynamic principles


Applying classical mechanics theory, assuming viscosity of the liquid equal 0 and no energy loss for the work of energy transferring from impeller to the streamlines which means that, all separate flow will be uniforms (this approximations of physical reality to get the simpler as solid state mechanism than hydraulic mechanism)

The new description
Observe a mass going along a straight vane impeller (the oldest and simplest impeller), there are these forces impact on it :

1-	The impeller vane push on it a force Fc, it reflect an anti force F' on the vane

2-	The centrifugal force Fc pull it fly out (follow centrifugal direction)

Dynamic head pressure
Applying Bernoulli principal: The first force cause the absolute velocity of the object as circumferential speed which means dynamic head pressure
 * $$H_d=\frac{U_2^2}{2g}$$

Static head pressure
The second force create the static pressure. If a mass moves radially outward along a vane of the impeller it orbit will be a spiral-shaped curved we can easily calculated it’s angular speed In two dimensions the angular velocity ω is given by
 * $$\omega = \frac{d\phi}{dt}$$

So during it movement the centrifugal force Fc always present as
 * $$F_c=m\omega^2R$$

The centrifugal acceleration increase linearity on the radius of rotary R(variable) In constant gravitational acceleration g, static pressure of a column of water h is
 * $$H_s=gh$$

In the centrifugal acceleration increase linearity from R1 position to R2 position static pressure of a column of water R2 -R1 is
 * $$H_s=\frac{a_c1+a_c2}{2}R_2-R_1	$$
 * $$H_s=\frac{\omega^2R_1+\omega^2R_2}{2}R_2-R_1=\frac{U_2^2-U_1^2}{2}$$

In the case the discharge of the pump is 0 static pressure save it’s original value In the outlet of the pump is open air of static pressure created by the impeller drop to 0 static pressure transfer all to the dynamic pressure in vector  which is highest value.

For example: R1=2cm=.02m; R2=8cm=.08m;ω=50.2π
 * $$a_1=1971m/s^2=201g$$

Apply similar calculation we will have
 * $$a_2=804g$$

6 cm column of water present in that area will give the static pressure = 3bar (10m column of water in gravitational acceleration g give 1bar static pressure)

Head pressure created by straight vanes impeller
Depend on this logic the head pressure created by the straight vane impeller is
 * $$H=\frac{U_2^2}{2g}+\frac{U_2^2-U_1^2}{2}$$

the head pressure created by the backward curved vane impeller is

Rotary transfer factor
fraction rotary angular speed of the flow and rotary angular speed of the impeller call rotary transfer coefficient fω=1 for the straight vane impeller fω<1 it variable from 0 to 1 depend on the discharge of the pump for the backward curved vane impeller

Figure beside shows a block m moved through the impeller while rotating, with appropriate speed of m, the impeller transfer 0% angle velocity coefficient for it. For this situation it is not real, but only used to demonstrate the transfer velocity coefficient of the impeller to the streamlines of variation that according to the flow of the pump. Nguyen thanh chinh (talk) 03:56, 9 April 2016 (UTC)

Head pressure created by back ward curved vanes impeller

 * $$H'=f\omega^2H$$

The necessity of the new theory
For centuries, people have trusted and used Euler equation as a basic to explain how the impeller work. But it was not correct. Because: The old description shows only the interactive force between the impeller van and the mass of liquid going through it, namely the force generated torque on its axis,that means only circumferential force was mention. The centrifugal force not created torque on the shaft so it was outside that scope.this description was the major shortcomings was also serious mistakes.Nguyen thanh chinh (talk) 03:59, 9 April 2016 (UTC)

The old description
By Sir Euler in 19th Century

Conservation of momentum
Another consequence of Newton’s 2nd law of mechanics is the conservation of the angular momentum (or the “moment of momentum”) which is of fundamental significance to all turbomachines. Accordingly, the change of the angular momentum is equal to the sum of the external moments. Angular momentums ρ×Q×r×cu at inlet and outlet, an external torque M and friction moments due to shear stresses Mτ are acting on an impeller or a diffuser.

Since no pressure forces are created on cylindrical surfaces in the circumferential direction, it is possible to write Eq. (1.10) as:

ρ Q (c_2u r2 – c_1u r_1) = M + Mτ  (1.13)

Euler's pump equation


Base on Eq.(1.13) Sir Euler developed the head pressure equation created by the impeller see Fig.2.2


 * $$Yth.g=H_t= c_2u.u_2 - c_1u.u_1 $$    (1)


 * $$Yth=1/2(u_2^2-u_1^2+w_1^2-w_2^2+c_2^2-c_1^2)$$       (2)

In Eq. (2) the sum of 4 front element number call static pressure,the sum of last 2 element number call velocity pressure look carefully on the Fig 2.2 and the detail equation. It is so hard ! to study and understand it. Especially and very strange that the curved respond of this equation is always linearity.

Ht theory head pressure  ;    g = between 9.78 and 9.82 m/s2 depending on latitude,conventional standard value of exactly 9.80665 m/s2     barycentric gravitational acceleration

u2=r2.ω the peripheral circumferential velocity vector u1=r1.ω the inlet circumferential velocity vector

ω=2π.n  angular velocity

w1   inlet relative velocity vector

w2   outlet relative velocity vector

c1   inlet absolute velocity vector

c2   outlet absolute velocity vector

Triangle velocity
The color triangle formed by velocity vector u,c,w call 'triangle velocity" this is an important role in old academic, this rule was helpful to detail Eq.(1) become Eq.(2) and wide explained how the pump works.

Fig 2.3 (a) shows triangle velocity of forward curved vanes impeller ; Fig 2.3 (b) shows triangle velocity of radial straight vanes impeller. it's illustrate rather clearly energy add to the flow (shown in vector c) inversely change upon flow rate Q (shown in vector cm).

Efficiency factor
$$\eta = \frac{\rho.gQH}{P_m}$$,

where:
 * $$P_m$$ is the mechanics input power required (W)
 * $$\rho$$ is the fluid density (kg/m3)
 * $$g$$ is the standard acceleration of gravity (9.80665 m/s2)
 * $$H$$ is the energy Head added to the flow (m)
 * $$Q$$ is the flow rate (m3/s)
 * $$\eta$$ is the efficiency of the pump plant as a decimal

The head added by the pump ($$H$$) is a sum of the static lift, the head loss due to friction and any losses due to valves or pipe bends all expressed in metres of fluid. Power is more commonly expressed as kilowatts (103 W, kW) or horsepower (hp = kW*0.736). The value for the pump efficiency, $$\eta_{pump}$$, may be stated for the pump itself or as a combined efficiency of the pump and motor system.

Components of A Simple Centrifugal Pump
A simple centrifugal compressor is comprised of the following 4 components, inlet, impeller/rotor, diffuser, and collector. If you look carefully at Figure 1.1 you will be able to identify each of these 4 components of the flow path. The flow (working gas) enters the centrifugal impeller axially from right to left. As the impeller spins at high speed it pulls the gas into the impeller blades then turning through the annulus (from axial to radial approximately 90°) discharges the flow at high velocity outward into the diffuser (a short passage with parallel walls). In this case the collector is the trumpet shaped device outside the diffuser.

Inlet
The inlet to a centrifugal compressor is typically a simple pipe. It may include features such as a valve, stationary vanes/airfoils (used to help swirl the flow) and both pressure and temperature instrumentation. All of these additional devices have important uses in the control of the centrifugal compressor.

Centrifugal Impeller
The key component that makes a compressor centrifugal is the centrifugal impeller. (ref Figure 1.2) It is the impellers rotating set of vanes (aka blades) that gradually raises the energy of the working gas. This is identical to an axial compressor with the exception that the gases can reach higher velocities and energy levels through a centrifugal impeller. This as a result of the increasing radius. In many modern high-efficiency centrifugal Pump the gas exiting the impeller is traveling near the speed of sound. Impellers are designed in many configurations includeing "open" (as shown), "covered", "with splitters" and "w/o splitters". Most modern high efficiency imppeller use "backsweep" in the blade shape.

Euler’s “Pump and Turbine” equation plays an important role in understanding impeller performance.

Diffuser
The next key component to the simple centrifugal compressor is the diffuser. Downstream of the impeller in the flow path, it is the diffuser's responsibility to convert the kinetic energy (high velocity) of the gas into pressure by gradually slowing (diffusing) the gas velocity. Diffusers can be vaneless, vaned or an alternating combination. High efficiency vaned diffusers are also designed over a wide range of solidities from less than 1 to over 4. Hybrid versions of vaned diffusers include: wedge, channel, pipe and pipe diffusers. There are turbocharger applications that benefit by incorporating no diffuser.

Bernoulli's “Fluid dynamic” principal plays and important role in understanding diffuser performance.

Collector
The collector of a centrifugal compressor can take many shapes and forms. When the diffuser discharges into a large empty chamber the centrifugal Pump collector may be referred to as a Plenum. When the diffuser discharges into a device that looks somewhat like a snail shell, bull's horn or a French horn, the collector is likely to be referred to as a volute or scroll. As the name implies, a collector’s purpose is to gather the flow from the diffuser discharge annulus and deliver this flow to a downstream pipe. Either the collector or the pipe may also contain valves and instrumentation to control the compressor. For example, a turbocharger blow-off valve.

Applications
Below, is a partial list of centrifugal compressor applications each with a brief description of some of the general characteristics possessed by those centrifugal Pump. To start this list two of the most well-known centrifugal compressor applications are listed; gas turbines and turbochargers. In their simple form, modern gas turbines operate on the Brayton cycle. (ref Figure 3.1) Either or both axial and centrifugal Pump are used to provide compression. The types of gas turbines using centrifugal Pump include turboshaft, turboprop, auxiliary power units, and micro-turbines. The industry standards applied to all of the centrifugal Pump used in aircraft applications are set by the FAA and the military to maximize both safety and durability under severe conditions.
 * In Gas Turbines and auxiliary power units. Ref. Figures 2.1 - 2.2

Centrifugal Pump used in conjunction with reciprocating internal combustion engines are known as turbochargers if driven by the engine’s exhaust gas and superchargers if mechanically driven by the engine. Standards set by the industry for turbochargers may have been established by SAE. Ideal gas properties often work well for the design, test and analysis of turbocharger centrifugal compressor performance.
 * In automotive engine and diesel engine Turbo-Chargers and Super-Chargers. Ref. Figure 1.1

Centrifugal Pump used in these applications may be single or multi-stage and driven by large gas turbines. Standards set by the industry (API, ASME) result in large thick casings to maximize safety. The impellers are frequently if not always of the covered style which makes them look much like pump impellers. This type of compressor is also frequently referred to as an API-style. The power necessary to drive these Pump is most often measured in the thousands of HP. Use of real gas properties is required to properly design, test and analyze the performance of pipeline centrifugal Pump.
 * In Pipeline Pump of natural gas to move the gas from the production site to the consumer.

Centrifugal Pump used in these applications are frequently single shaft multi-stage and driven by large steam or gas turbines. Their casings are often referred to as horizontally split or barrel. Standards set by the industry (API, ASME) for these Pump result in large thick casings to maximize safety. The impellers are frequently if not always of the covered style which makes them look much like pump impellers. This type of compressor is also frequently referred to as API-style. The power necessary to drive these Pump is most often measured in the thousands of HP. Use of real gas properties is required to properly design, test and analyze their performance.
 * In oil refineries, natural gas processing, petrochemical and chemical plants.

Because of the wide variety of vapor compression cycles (Thermodynamic cycle, Thermodynamics) and the wide variety of workings gases (refrigerants), centrifugal Pump are use in a wide range of sizes and configurations. Use of real gas properties is required to properly design, test and analyze the performance of these machines. Standards set by the industry for these Pump include ASME.
 * Air-conditioning and refrigeration: Centrifugal Pump quite often supply the compression in Water Chillers cycles.

The centrifugal Pump used in these applications are often multistage and driven by electric motors. Inter-cooling is often required between stages to control air temperature. Note that the road repair crew and the local automobile repair garage find screw Pump better adapt to their needs. Standards set by the industry for these Pump include ASME and government regulations that emphasize safety. Ideal gas relationships are often used to properly design, test and analyze the performance of these machines. Carrier’s equation is often used to deal with humidity.
 * In industry and manufacturing to supply compressed air for all types of pneumatic tools.

The centrifugal Pump used in these applications are often multistage using inter-cooling to control air temperature. Standards set by the industry for these Pump include ASME and government regulations that emphasize safety. Ideal gas relationships are often used to properly design, test and analyze the performance of these machines when the working gas is air or nitrogen. Other gases require real gas properties.
 * In air separation plants to manufacture purified end product gases.

Centrifugal Pump used in these applications are frequently single shaft multi-stage and driven by gas turbines. With discharge pressures approaching 700 bar, casing are of the barrel style. Standards set by the industry (API, ASME) for these Pump result in large thick casings to maximize safety. The impellers are frequently if not always of the covered style which makes them look much like pump impellers. This type of compressor is also frequently referred to as API-style. Use of real gas properties is required to properly design, test and analyze their performance.
 * In oil field re-injection of high pressure natural gas to improve oil recovery.

Performance
The test measurement of centrifugal compressor performance is a very complex matter. Professional societies such as ASME (i.e. PTC – 10, Fluid Meters Handbook), ASHRAE (ASHRAE Handbook) and API (API – 617) have established detailed analysis and experimental techniques to standardize the understanding and management of turbomachinery testing and performance. Despite this complexity there are a few basic concepts that can be presented in a simplified form. Centrifugal Pump are used in to raise the pressure of a gas. In practice this requires knowledge of the quantity of gas (flow). Additionally, this requires knowledge of the operating speed and the input power required to drive the compressor.

Pressure, Flow, Speed and Power are the only parameters required to apply a centrifugal compressor to a simple application. Figure 3.2 can be used to easily to illustrate this.

Performance Maps
As is standard practice, Figure 3.2 has a horizontal axis labeled with a flow parameter. While flow measurements use a wide variety unit specifications, all fall into one of 2 categories:


 * Mass Flow per unit time
 * Volume Flow per unit time
 * Mass flows, such as kg/s, are the easiest to use in practice as there is little room for confusion. Questions remaining would involve inlet or outlet (which might involve leakage from the compressor or moisture condensation). For atmospheric air, the mass flow may be wet or dry (including or excluding humidity).


 * In contrast, all volume flow specifications require the additional specification of density. Bernoulli's fluid dynamic principal is of great value in understanding this problem. Confusion arises through either inaccuracies or misuse of pressure, temperature and gas constants.

Also as is standard practice, Figure 3.2 has a vertical axis labeled with a pressure parameter. The variety of pressure measurement units is also vast. In this case, they all fall into one of three categories:


 * The delta increase or rise from inlet to exit (Manometer style)
 * The measured discharge pressure (Force)
 * The force ratio (Ratio, Exit/Inlet)

A detailed inspection of Figure 3.2 shows:
 * Flow -- kg/s (range: 0.04 - 0.34 kg/s)
 * Pressure -- Pressure Ratio (t-t) (range 1.1 - 2.6 PR_t-t)
 * "t-t" implies the discharge total pressure is divided by the inlet total pressure (Pt_discharge/Pt_inlet).


 * ''Constant Speed Lines’’
 * The two most common methods used for testing centrifugal Pump is to test along lines of constant shaft speed or along lines of constant throttle. If the shaft speed is held constant, test points are taken along a constant speed line by changing throttle positions. In contrast, if a throttle valve is held constant, test points are established by changing speed (common gas turbine practice). The map shown in Figure 3.2 illustrate most common method; lines of constant speed. In this case we see data points connected via straight lines at speeds up 59,967 RPM, 84,832 RPM, 103,896 RPM, and 119,952 RPM. The first three speed lines have 6 points each while the highest speed line as five.


 * Constant Efficiency Islands
 * The next feature to be discussed is the oval shaped curves representing islands of constant efficiency. In this case we see 11 contours ranging from 56% efficiency (decimal 0.56) to 76% efficiency (decimal 0.76). General standard practice is to interpret these efficiencies as isentropic. Under some circumstances it may be necessary to question whether these efficiencies are isentropic or polytropic.


 * ''Design Point(s) or Guarantee Point(s)’’
 * Those familiar with gas turbine operation and performance understand that there may be a series of guaranteed points established for the gas turbine’s centrifugal compressor. It is also realized that these requirements are of secondary importance to the overall gas turbine performance as a whole. For this reason it is only necessary to summarize that in the simple case, the lowest specific fuel consumption would occur when the centrifugal Pump peak efficiency curve coincides with the gas turbine' s required operation line.


 * In contrast to gas turbines, most other applications (including industrial) need to meet a less stringent set of performance requirements. Historically, centrifugal Pump applied to industrial applications were required to achieve performance at a specific flow & pressure. In contrast modern industrial Pump are often required to achieve specific performance goals across a range of flows and pressures; thus taking a significant step toward the sophistication seen in gas turbine applications.


 * Using the assumption that an application requires performance a specific flow and pressure it would be very acceptable for the centrifugal compressor, shown in Figure 3.2, to be applied anywhere within the 76% efficiency island. In the simple case an "End User" would be very happy with the performance requirements of 2.0 pressure ratio at 0.21 kg/sec.

Shut-off

 * Shut-off
 * The Surge-line shown in Figure 3.2 is the curve that passes through the lowest flow points of each of the four speed lines. These points would be the lowest flow test points possible to record a stable reading within the test facility. In many industrial applications it would be necessary to increase the flow of this stall line to the highest pressure ratio point of each constant speed line. For example at 119,952 RPM stalling flow would increase from approximately 0.170 kg/sec. two approximately 0.215 kg/sec.


 * As stated earlier, the reason for this is that the high-speed line in Figure 3.2 exhibits a stalling characteristic or positive slope within that range of flows. When placed in a different system those lower flows might not be achievable because of interaction with that system. System resistance or adverse pressure is proven mathematically to be the critical contributor to compressor surge.

Maximum Flow Line vs Choke
Choke - occurs under one of 2 conditions. Typically for high speed equipment, as flow increases the velocity of the flow can approach sonic speed somewhere within the compressor stage. This location may occur at the impeller inlet "throat" or at the vaned diffuser inlet "throat". In most cases, it is generally not detrimental to the compressor.

However, for low speed equipment, as flows increase, losses increase such that the pressure ratio drops to 1:1. In this case, the occurrence of choke is unlikely.


 * Maximum Flow Line
 * The maximum flow line, shown in Figure 3.2, is the curve that passes through each of the highest flow points of each speed line. Upon inspection it may be noticed that each of these points has been taken near 56% efficiency. Low efficiency (~60%) is the most common practice used in terminating an industrial or commercial centrifugal compressor performance map at the highest flows of each speed line. Another factor that is use to establish the maximum flow line is a pressure ratio near or equal to 1. The 59,967 RPM speed line may be considered an example of this.


 * The speed lines of Figure 3.2 are also a good example of why it is inappropriate to use the term choke in association with a maximum flow of all centrifugal compressor speed lines.


 * Cavitation
 * The speed lines of gas turbine centrifugal Pump typically exhibit choke. This is a situation where the pressure ratio of a speed line drops rapidly (vertically) with little or no change in flow. In most cases the reason for this is that close to Mach 1 velocities have been reached somewhere within the impeller and/or diffuser generating a rapid increase in losses. Higher pressure ratio turbocharger centrifugal Pump exhibit this same phenomenon. The real choke phenomena is a function of compressibility as measured by the local Mach number within an area restriction within the centrifugal pressure stage.


 * In summary; most industrial and commercial centrifugal Pump are selected/designed to operate at or near their highest efficiencies and are selected/designed to avoid operation at low efficiencies. For this reason there is seldom a reason to illustrate centrifugal compressor performance below 60% efficiency.

Other Operating Limits

 * Minimum Operating Speed - the minimum speed for acceptable operation, below this value the compressor may be controlled to stop or go into an "Idle" condition.


 * Maximum Allowable Speed - the maximum operating speed for the compressor. Beyond this value stresses may rise above prescribed limits and rotor vibrations may increase rapidly. At speeds above this level the equipment will likely become very dangerous and be controlled to lower speeds.

Dimensionless Parameters, Similitude & Affinity Laws
under construction