# 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 air, 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
Inlet velocity triangles for radial discharge centrifugal pump impeller
Exit velocity triangles for radial inlet centrifugal pump impeller

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

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

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 factor 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

#### Head pressure created by back ward curved vanes impeller

$H'=f\omega^2H$

This is the formula

#### The necessity of the new theory

Compare the two way the old and the new description how the impeller supply energy for the object going through it we see: New way shows how the centrifugal force appear and it's effective on an object going through the impeller. while the old way only mentioned about the inertial force interaction between the impeller van and the object, which means that conservation of momentum principal can not ever describe centrifugal force including energy relation with it because it is the diametrically force it can not make the torque on the rotary shaft.

### 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

Figure 2.2 -- triangle velocity of a curved backward vanes impeller (a).
Figure 2.2 -- triangle velocity of a radial straight vanes impeller (b).

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.

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:

$P_i= \cfrac{\rho\ g\ H\ Q}{\eta}$

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[clarification needed]

## 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

Main article: magnetic coupling

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 Giant of 1MW. The material construction includes metallic and nonmetallic executions. Commonly magdrive metallic pumps are less efficient than traditional mechanical seals pumps. The reason is a power loss in the magnetic trasmission. This loss is called Eddy Current and for a magnetic drive pump can reach 20% and more of the installed power. This is due to the presence of the metallic containment shell into the transmission magnetic field. Last innovation in magnetic drive pump technology minimized efficiency lack, between magnetic drive pumps and mechanical seals pumps. In some cases today there are no more difference between this two category of pumps. In fact the introduction of nonmetallic containment shells reduced or eliminated the Eddy currents generated in the coupling.

Below a resume of the containment shells materials actually present on the market.

The comparison is based on a centrifugal magnetic drive pump with 18.5 kW installed, rotating at 2900 RPM.

Material / Technology Approx. Thickness [mm] Pressure Rating [bar] Temp. Field [°C] Magnetic Losses [kW] Comment
Hastelloy / other metallic alloys 1.2 – 1.7 PN 16 to PN 50 -90°C / +350°C 2.6 Most common, less efficient
Hybrid Containment shell 1.6 PN 50 -90 / +250 0.78 innovative
PEEK composite 3.5 – 5.5 3.5 – 5.5 -40°C / +120°C 0 High thickness, cost and temp. limits
Zirconium oxide 4 - 7 PN 16 -190°C / +350°C 0 High thickness, High cost
Borosilicate glass 3-7 PN 10 -40°C / +180°C 0 Weathering, high thickness, Pressure/Temp. limits

The only solution available on the market capable to minimize Eddy current losses and keep metallic shell in contact to pumped liquid is the Hybrid containment shell. This has a minimum magnetic losses, but high temperature and pressure resistance, for this reason more adapt to the heavy duty application.

Magnetic Drive pump with Hybrid containment shell, 400kW motor, 9kW losses; Courtesy of M PUMPS

• There are no drive seals, therefore the risk of leaks is completely eradicated. This means that hazardous liquids can be pumped without spillages.
• Less heat transfer from the motor—the pump chamber is separated from the motor by an air gap; this provides a thermal barrier.
• Complete separation of the liquid means that liquid cannot seep into the motor from the pump.
• Reduced friction.
• Magnetic coupling can be broken—if the load of the pump is too great. By the magnetic coupling 'breaking', it means the pump does not overload and get damaged.[7]

Eliminating the drive seals gets rid of leaks, friction loss, wear and noise. It provides complete separation of fluid from the pump drive, and nearly 100% transfer of motor power into pumping power.

• Liquids containing ferrous particles are problematic when a magnetic drive pump is used. This is due to the particles collecting on the impeller magnet, and over time causing the pump to stop working.
• Some energy is lost in the coupling. This is primarily due to some magnetic resistance called "Eddy currents".
• Traditionally Eddy currents reduce magnetic drive pump efficiency of about 20%. This disadvantage has been minimized by recent innovation Hybrid containment shell, and other non metallic containment shell systems, even if the latter have some limitations.
• If unexpectedly heavy loads occur it may cause the coupling to slip.

### Principle of operation

The impeller of such a pump is magnetically coupled with the motor, across a separation wall which is resistant to the fluid pumped. The motor drives a rotor carrying one or several pairs of permanent magnets, and these drag around a second pair(s) of permanent magnets attached to the pump impeller.

### Containemnt shells for Magnetic Drive pumps

Containment shell is one of the most important components of magnetic drive pumps. Various studies have been done during last 5 decades to improve the quality and performance of this component for the application in the chemical process. Considering metallic process pumps, single metallic containment shells are installed in most of magnetic drive pump in the field. In the last 10 years pump manufacturers has developed alternative solutions to realize these components. Going in depth and considering how this can be realized and with which performance, the main concern in containment shell design is not given by the mechanical resistance itself, but typically from the magnetic losses generated by the rotating magnetic field during pump operation. From design and construction point of view, guideline for a right containment shell design is given by ASME BPVC, Section VIII, Division 2. 2nd Edition of API 685 standard specify that containment shell must have a minimum corrosion allowance of 0.4mm (0.015 in.), the minimum cont. shell thickness has to be 1mm (0.040 in.), it must be able to withstand to a hydrostatic test of 1.5 times the MAWP, that for process pumps is 50 bar (725 psi). These guidelines requires manufacturers a series of restrictions in magnetic coupling design and some of these gives a negative impact onto magnetic losses. To better understand these restrictions here mentioned the most important: -containment shell has to be “relatively thick” to comply to mentioned standards. -clearance reduction between containment shells and magnets, to compensate the increasing of distance consequent to the containment shell thickness increasing. -increasing of magnetic coupling length and diameter reduction, in order to minimize containment shell thickness ( at same pressure rating [pi], smaller diameter [d] will need smaller wall thickness respect to a bigger diameter, following the equation: s= (pi * d) / (2f_adm - pi) ). Even when the manufacturer has made a proper design, some magnetic losses will be present. This is the simple reason why the research is following to investigate alternative technology to produce the containment shell. From the other point of view we have to say that for critical application and when people and environmental reason requires an hermetic solution, magnetic drive pumps are the solution. As said above, many alternative introductions have been proposed to improve this pump design. Listed below containment shell solution seen on the market, divided in single and double containment shells.

Single containment shells Hastelloy / other metallic alloys Hybrid Containment shell PEEK composite Zirconium oxide Borosilicate glass Carbon fiber-PTFE Double containment shells Zirconium oxide – metallic Double containment shell metallic Sandwich double containment shell

Focusing more on the metallic containment for process pumps, previous list become: Single metallic containment shells Hastelloy C / other metallic alloys Hybrid Containment shell Double metallic containment shells Zirconium oxide – metallic Double containment shell metallic Sandwich double containment shell Metallic containment shell characteristics

### Hastelloy C / other metallic alloys

Metallic containment shells has been the first to be made and still are the most present on the market. Technically speaking design procedure is widely known and reliability too. Foto bicchieri old style e cn mag-m. Its limits is given by magnetic losses, that even in case of adoption of Titanium alloy still is a quite high value of the installed power (10-15%). Economic construction, welding free design available. Applied in the high pressure up to 1500 bar.

### Hybrid Containment shell

Innovative design that couples metallic shell in contact to the liquid (in the inside) to an external carbon composite reinforcement. Corrosion allowance comply to API 685 2nd Ed. Reliability of this design is given by the knowledge in cold metal deep drawn process, and from carbon composite materials that nowadays are applied in the most different technology fields.

Magnetic losses still present but in a minimum quantity, in reason of the relatively low metallic shell thickness adopted (from 2 to 5% of the installed power). In the field applied in units of 500 kW, and system pressure up to 250 bar. Energy efficiency and extremely low liquid temperature rising are the strongest point of this design. Application field showed that hybrid containment shell can reduce magnetic losses of more than 70%. Temperature rising into the pumped liquid has been reduced up to 90%. This great advantage allow the pumping of low boiling liquids without any risk of flashing.

 CN MAG-M magnetic drive pump with hybrid containment shell cross section - Courtesy of M PUMPS Hybrid Containment Shell - Courtesy of M PUMPS 500 kW High system pressure magnetic drive pump with hybrid containment shell - Courtesy of M PUMPS

### Zirconium oxide – metallic

Double containment shell introduced to comply to API 685 2nd Ed. The external zirconium oxide shell provide the mechanical resistance, and the internal metallic shell is the primary containment. Limit of this construction is given by the high cost of Zirconium oxide casing. Magnetic losses of this containment shell system is around 50% less than the traditional metallic double containment shells system. Zirconium oxide has a great temperature resistance, but again, pressure resistance is low, and it requires high wall thickness. This provides magnetic coupling characterize by oversizing, in order to keep same torque value at consequent clearance increasing.

### Double containment shell metallic

This kind of containment shells has been the first to be developed to comply to API 685 2nd Ed. Different technology have been adopted to realize these shells, with different performance. Are characterized by low efficiency and generally speaking have been of two main category. The first category is composed by double shells made with two separated shells, sealed by gaskets. When failure of the first shell, process liquid go inside the thin way between the two shells and reach the monitor port, where is detected the failure. The weak point of this is given by the fact that the external wall has a poor cooling system, cause is not in contact to the internal one, and from the process liquid. So this configuration can be applied only in small units and with low rotation speed. Production cost of this solution is the lowest for this kind of components, due by the simplicity. The second family is composed by the shells coupled between them, in order to create a single piece. With this, the two cylindrical walls have been in contact in different ways, and this increases vertically conduction and cooling of the external shells. This kind of shells present more complication from the manufacturing point of view, and the various manufacturers, during the years have developed their own way to produce these components. Not all of them has the same performance, anyway on the field we can find double containment shells up to 230 bar system pressure.

 High pressure centrifugal pump according to API 685 2nd Ed. provided by double containment shell - Courtesy of M PUMPS

### Sandwich double containment shell

Designed at the end of eighties by a Canadian Engineer named Taiani, this was an ingenious solution to reduce magnetic losses in the magnetic drive pump transmission. Main characteristic of this design was the reduction of current generation on the surface of the shell by the adoption of a series of electric insulators. Weak points of this containment shell system were the impossibility to apply a frequency inverter to the pump, and the high gaskets number adopted in it. In case of accidental overheating of the transmission ( decoupling), gasket material melts and sealing went lost. Due to the construction requirement the application to standard designed pumps was almost impossible because of the big thickness of it. This was also the reason why magnetic coupling has to be oversized. In the last years this design has been updated but still keep weak point never solved, as the high gaskets number and the high thickness that decrease coupling performance, with consequent needed oversizing in terms of rear earth quantity. The last updates improved energy efficiency, so, considered “100” the losses given by a traditional Hastelloy C containment shell, the sandwich shell can give a reduction of around 50-60%.

## 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.