Centrifugal pump

Warman centrifugal pump in a coal preparation plant application

Centrifugal pumps are a sub-class of dynamic axisymmetric work-absorbing turbomachinery.[1] Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from where it exits.

Common uses include water, sewage, petroleum and petrochemical pumping. The reverse function of the centrifugal pump is a water turbine converting potential energy of water pressure into mechanical rotational energy.

History

According to Reti, 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.[2] True centrifugal pumps were not developed until the late 17th century, when Denis Papin built one using straight vanes. The curved vane was introduced by British inventor John Appold in 1851.

How it works

Cutaway view of centrifugal pump

General explanation: Like most pumps, a centrifugal pump converts rotational energy, often from a motor, to energy in a moving fluid. A portion of the energy goes into kinetic energy of the fluid. Fluid enters axially through eye of the casing, is caught up in the impeller blades, and is whirled tangentially and radially outward until it leaves through all circumferential parts of the impeller into the diffuser part of the casing. The fluid gains both velocity and pressure while passing through the impeller. The doughnut-shaped diffuser, or scroll, section of the casing decelerates the flow and further increases the pressure.

Fluid dynamic principles

Figure 2.1 -- the forces affect on a mass going along an impeller vane.

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

Figure 2.2 -- triangle velocity of a curved backward vanes impeller (a).
File:Color trigle velocity 2.jpg
Figure 2.2 -- triangle velocity of a radial straight vanes impeller (b).

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)

Applying Bernoulli principle: The first force causes the absolute velocity of the object as circumferential speed which means dynamic head pressure

$H_d=\frac{U_2^2}{2g}$

The second force creates the static pressure. If a mass moves radially outward along a vane of the impeller, its orbit will be a spiral-shaped curve. One can easily calculate its angular speed. In two dimensions the angular velocity ω is given by

$\omega = \frac{d\phi}{dt}$

So during its movement the centrifugal force Fc is always present as

$F_c=m\omega^2R$

The centrifugal acceleration increases linearly on the radius of rotation R (variable). In constant gravitational acceleration g, static pressure of a column of water h is

$H_s=gh$

In the centrifugal acceleration increase linearly from the R1 position to the 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 its 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=2 cm=.02 m; R2=8 cm=.08 m; ω=50.2π

$a_1=1971m/s^2=201g$

Apply similar calculation; one will have

$a_2=804g$

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

Head pressure created by straight vanes impeller

rotating impeller 1
Rotating impeller 2

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

Fractional rotary angular speed of the flow and rotary angular speed of the impeller are called the rotary transfer coefficient, where

fω=1 for the straight vane impeller

0<fω<1 variable from 0 to 1 depending on the discharge of the pump for the backward curved vane impeller

Figure 1 rotating impeller shows a block m moved through the impeller. During 1/4 rotation, element m moves from the inner edge to the outer edge of the impeller. Seemingly working separately, in this case the impeller does not rotate element m at all. This means the impeller transfers 0 angular velocity coefficient for element m. 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.

Figure rotating impeller 2 shows if element m move with 1/2 speed than before it will rotate 1/8 of round, means the impeller transfer 50% angle velocity coefficient for element m.

Head pressure created by backward curved vanes impeller

$H'=f\omega^2H$

This is the formula

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.

The old description

By Sir Euler in 19th Century

Conservation of momentum

Another consequence of Newton’s second 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:[3]

$\rho Q(c_2 u .r_2 - c_1 u .r_1) = M + M_\tau$ (1.13)

Euler's pump equation

Based on Eq.(1.13) 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.

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 called "velocity triangle". 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 illustrates rather clearly energy added 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*0.746). 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.

Vertical centrifugal pumps

Vertical centrifugal pumps are also referred to as cantilever pumps. They utilize a unique shaft and bearing support configuration that allows the volute to hang in the sump while the bearings are outside the sump. This style of pump uses no stuffing box to seal the shaft but instead utilizes a "throttle bushing". A common application for this style of pump is in a parts washer.

Froth pumps

In the mineral industry, or in the extraction of oilsand, froth is generated to separate the rich minerals or bitumen from the sand and clays. Froth contains air that tends to block conventional pumps and cause loss of prime. Over history, industry has developed different ways to deal with this problem. In the pulp and paper industry holes are drilled in the impeller. Air escapes to the back of the impeller and a special expeller discharges the air back to the suction tank. The impeller may also feature special small vanes between the primary vanes called split vanes or secondary vanes. Some pumps may feature a large eye, an inducer or recirculation of pressurized froth from the pump discharge back to the suction to break the bubbles.[4]

Multistage centrifugal pumps

Multistage centrifugal pump[5]

A centrifugal pump containing two or more impellers is called a multistage centrifugal pump. The impellers may be mounted on the same shaft or on different shafts.

For higher pressures at the outlet, impellers can be connected in series. For higher flow output, impellers can be connected parallel.

A common application of the multistage centrifugal pump is the boiler feedwater pump. For example, a 350 MW unit would require two feedpumps in parallel. Each feedpump is a multistage centrifugal pump producing 150 l/s at 21 MPa.

All energy transferred to the fluid is derived from the mechanical energy driving the impeller. This can be measured at isentropic compression, resulting in a slight temperature increase (in addition to the pressure increase).

Energy usage

The energy usage in a pumping installation is determined by the flow required, the height lifted and the length and friction characteristics of the pipeline. The power required to drive a pump ($P_i$), is defined simply using SI units by:

File:Centrifugal Pump-mod.jpg
$P_i= \cfrac{\rho\ g\ H\ Q}{\eta}$

where:

$P_i$ is the 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 (kW = hp/0.746). 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.

The energy usage is determined by multiplying the power requirement by the length of time the pump is operating.

Problems of centrifugal pumps

These are some difficulties faced in centrifugal pumps:[6]

Open Type Centrifugal Pump Impeller
• Cavitation—the net positive suction head (NPSH) of the system is too low for the selected pump
• Wear of the impeller—can be worsened by suspended solids
• Corrosion inside the pump caused by the fluid properties
• Overheating due to low flow
• Leakage along rotating shaft
• Lack of prime—centrifugal pumps must be filled (with the fluid to be pumped) in order to operate
• Surge
Pie chart showing what causes damage to pumps.

Centrifugal pumps for solids control

An oilfield solids control system needs many centrifugal pumps to sit on or in mud tanks. The types of centrifugal pumps used are sand pumps, submersible slurry pumps, shear pumps, and charging pumps. They are defined for their different functions, but their working principle is the same.

Magnetically coupled pumps

Magnetically coupled pumps, or magnetic drive pumps, vary from the traditional pumping style, as the motor is coupled to the pump by magnetic means rather than by a direct mechanical shaft. The pump works via a drive magnet, 'driving' the pump rotor, which is magnetically coupled to the primary shaft driven by the motor.[7] They are often used where leakage of the fluid pumped poses a great risk (e.g., aggressive fluid in the chemical or nuclear industry, or electric shock - garden fountains). They have no direct connection between the motor shaft and the impeller, so no gland is needed. There is no risk of leakage, unless the casing is broken. Since the pump shaft is not supported by bearings outside the pump's housing, support inside the pump is provided by bushings. The pump size of a magnetic drive pumps can go from few Watts power to a giant 1MW.

Priming

Most centrifugal pumps are not self-priming. In other words, the pump casing must be filled with liquid before the pump is started, or the pump will not be able to function. If the pump casing becomes filled with vapors or gases, the pump impeller becomes gas-bound and incapable of pumping. To ensure that a centrifugal pump remains primed and does not become gas-bound, most centrifugal pumps are located below the level of the source from which the pump is to take its suction. The same effect can be gained by supplying liquid to the pump suction under pressure supplied by another pump placed in the suction line.