Introduction to Fluid Machines & Centrifugal pump

Classification of fluid machines Positive displacement machine(Static type) Positive displacement machines force a fluid into or out of a chamber by changing the volume of the chamber. The pressures developed and the work done are a result of essentially static forces rather than dynamic effects. Positive-displacement pumps are ideal for high-pressure applications like pumping viscous liquids or thick slurries, and for applications where precise amounts of liquid are to be dispensed or metered, as in medical applications.

Turbomachines (Dynamic type) Pumps and turbines in which energy is supplied or extracted by a rotating shaft are properly called turbomachines Turbomachines are dynamic fluid machines that add (for pumps) or extract (for turbines) flow energy. The increase in fluid energy is usually felt as an increase in the pressure of the fluid. The purpose of a pump is to add energy to a fluid, resulting in an increase in fluid pressure, not necessarily an increase of fluid speed across the pump. turbine extract energy from the fluid and transfer most of that energy to some form of mechanical energy output, typically in the form of a rotating shaft The fluid at the outlet of a turbine suffers an energy loss, typically in the form of a loss of pressure. The purpose of a turbine is to extract energy from a fluid, resulting in a decrease of fluid pressure, not necessarily a decrease of fluid speed across the turbine.

In dynamic machines(turbomachines) rotating blades supply or extract energy to or from the fluid. For pumps, these rotating blades are called impeller blades, while for turbines, the rotating blades are called runner blades or buckets. Examples of dynamic pumps include enclosed pumps and ducted pumps (those with casings around the blades such as the water pump in your car’s engine, and open pumps (those without casings such as the ceiling fan in your house, the propeller on an airplane, or the rotor on a helicopter). Examples of dynamic turbines include enclosed turbines, such as the hydro turbine that extracts energy from water in a hydroelectric dam, and open turbines such as the wind turbine that extracts energy from the wind

Pump Fluid machines that move liquids are called pumps When used with gases, pumps are called fans, blowers, or compressors, depending on the relative values of pressure rise and volume flow rate.

The Euler turbomachine equation is the axial component of the moment- of-momentum equation.

Turbine Pump The torque applied to the contents of the control volume

& Euler turbomachine equation. In case of turbine Euler turbomachine equation. In case of a pump The sign of the component depends on the direction of and the blade motion, U. If and U are in the same direction, then is positive. The shaft torque is directly proportional to the mass flow rate It takes considerably more torque and power to pump water than to pump air with the same volume flow rate & Shaft power

For steady flow continuity equation Finally, in terms of work per unit mass This is the basic governing equation for pumps or turbines whether the machines are radial-, mixed-, or axial-flow devices and for compressible and incompressible flows. Note that neither the axial nor the radial component of velocity enter into the specific work (work per unit mass) equation.

The velocity component Vx is the generic through-flow component of velocity and it can be axial, radial, or in-between depending on the rotor configuration

The Centrifugal Pump (Radial-flow turbomachines)

Components An impeller attached to a rotating shaft, consists of a number of blades (usually curved), also sometimes called vanes, arranged in a regular pattern around the shaft A stationary casing, housing, or volute enclosing the impeller

Centrifugal pumps come in a variety of arrangements (open or shrouded impellers, volute or diffuser casings, single- or double-suction, single- or multistage) but the basic operating principle remains the same. Work is done on the fluid by the rotating blades (centrifugal action and tangential blade force acting on the fluid over a distance) creating a large increase in kinetic energy of the fluid flowing through the impeller. This kinetic energy is converted into an increase in pressure as the fluid flows from the impeller into the casing enclosing the impeller.

Centrifugal pump impellers involve an increase in blade velocity along the flow path. The head that a pump adds to the fluid is an important parameter. The pump ideal head rise is the work per unit weight added to the fluid by the pump.

the pressure head rise that develops across the impeller due to the centrifugal effect the increase in the kinetic energy of the fluid, the pressure head rise that develops across the impeller due to the diffusion of relative flow in the blade passages

Flow rate and the pump ideal head rise Often the fluid has no tangential component of velocity or swirl, as it enters the impeller Flow rate impeller blade height at the radius r2 ideal or maximum head rise for a centrifugal pump varies linearly with Q for a given blade geometry and angular velocity

For actual pumps, the blade angle falls in the range of 15°-35° with a normal range of and with . Blades with are called backward curved, whereas blades with are called forward curved.

Problem Solution:

Actual head rise of the fluid (ha)

Manometric head Euler head hm= hm In most of the cases except for fans hm manometric efficiency: It represents the effectiveness of the pump in producing pressure from the energy given to the fluid by the impeller.

Efficiency of the pump Hydraulic losses Shock loss at the eye due to imperfect matching between inlet flow and blade entrance Friction losses in the blade passages Circulation loss (whirl slip) Losses in the volute casing Hydraulic efficiency Leakage losses Loss of fluid due to leakage in the impeller casing clearance Volumetric efficiency Mechanical losses Losses due to mechanical friction in bearings, packing glands and other contact points in the machine Mechanical efficiency Overall efficiency of the pump

A washing operation at a power plant requires 370 gallons per minute (gpm) of water. The required net head is about 24 ft at this flow rate. A newly hired engineer looks through some catalogs and decides to purchase the 8.25-in impeller option of the Taco Model 4013 FI Series centrifugal pump. If the pump operates at 1160 rpm, as specified in the performance plot, she reasons, its performance curve intersects 370 gpm at H ! 24 ft. The chief engineer, who is very concerned about efficiency, glances at the performance curves and notes that the efficiency of this pump at this operating point is only 70 percent. He sees that the 12.75-in impeller option achieves a higher efficiency (about 76.5 percent) at the same flow rate. He notes that a throttle valve can be installed downstream of the pump to increase the required net head so that the pump operates at this higher efficiency. He asks the junior engineer to justify her choice of impeller diameter. Namely, he asks her to calculate which impeller option (8.25-in or 12.75-in) would need the least amount of electricity to operate .Perform the comparison and discuss.

Net Positive Suction Head (NPSH) On the suction side of a pump, low pressures are commonly encountered, with the concomitant possibility of cavitation occurring within the pump. WHAT IS CAVITATION? Cavitation occurs when the liquid pressure at a given location is reduced to the vapour pressure of the liquid. When this occurs, vapour bubbles form (the liquid starts to “boil”);Then these bubbles accumulated & burst in a higher pressure region in the pump and release huge pressure wave, causing vibration & noise within the pump, this phenomenon can cause a loss in efficiency as well as structural damage to the pump.

Required net positive suction head (NPSHR) Pump manufacturers test their pumps for cavitation in a pump test facility by varying the volume flow rate and inlet pressure in a controlled manner. Specifically, at a given flow rate and liquid temperature, the pressure at the pump inlet is slowly lowered until cavitation occurs somewhere inside the pump. The value of NPSH is calculated using Eq. above and is recorded at this operating condition. The process is repeated at several other flow rates, and the pump manufacturer then publishes a performance parameter called the required net positive suction head (NPSHrequired), defined as the minimum NPSH necessary to avoid cavitation in the pump Typical pump performance curve in which net head and required net positive suction head are plotted versus volume flow rate.

Available net positive suction head (NPSHA) It represents the head that actually occurs for the particular flow system. This value can be determined experimentally, or calculated if the system parameters are known. Since irreversible head losses through the piping system upstream of the inlet increase with flow rate, the pump inlet stagnation pressure head decreases with flow rate. Therefore, the value of NPSH decreases with Q

For proper pump operation it is necessary that The volume flow rate at which the available NPSH and the required NPSH intersect represents the maximum flow rate that can be delivered by the pump without the occurrence of cavitation.

The 11.25-in impeller option of the Taco Model 4013 FI Series centrifugal pump of Fig. 14–15 is used to pump water at 25°C from a reservoir whose surface is 4.0 ft above the centreline of the pump inlet (Fig. 14–20). The piping system from the reservoir to the pump consists of 10.5 ft of cast iron pipe with an ID of 4.0 in and an average inner roughness height of 0.02 in. There are several minor losses: a sharp-edged inlet (KL = 0.5), three flanged smooth 90° regular elbows (KL = 0.3 each), and a fully open flanged globe valve (KL = 6.0). Estimate the maximum volume flow rate (in units of gpm) that can be pumped without cavitation. If the water were warmer, would this maximum flow rate increase or decrease? Why? Discuss how you might increase the maximum flow rate while still avoiding cavitation.

the maximum volume flow rate without cavitation decreases with increase of temperature How can we increase the maximum flow rate without cavitation? We can raise the height of the reservoir surface (to increase the hydrostatic head). We can reroute the piping so that only one elbow is necessary and replace the globe valve with a ball valve (to decrease the minor losses). We can increase the diameter of the pipe and decrease the surface roughness (to decrease the major losses).

System Characteristics and Pump Selection Apply energy eqn between 1 & 2 represents all friction losses in the pipe and minor losses for pipe fittings and valves. the actual head gained by the fluid from the pump

where K depends on the pipe sizes and lengths, friction factors, and minor loss coefficients. This is system equation and shows how the actual head gained by the fluid from the pump is related to the system parameters. In this case the parameters include the change in elevation head, and the losses due to friction.

The most common situation is that an engineer selects a pump that is somewhat heftier than actually required. The volume flow rate through the piping system is then a bit larger than needed, and a valve or damper is installed in the line so that the flow rate can be decreased as necessary.

Pump characteristic curve

System equation

Pumps in Series and Parallel Pumps can be arranged in serial or parallel to provide additional head or flow rate capacity Pumps in Series -Heads Added When two (or more) pumps are arranged in serial, their resulting pump performance curve is obtained by adding their heads at same flow rate as indicated in the figure below. Centrifugal pump in series are used to overcome larger system head loss than one pump can handle alone. For two identical pumps in Series the head will be twice the head of a single pump at the same flow rate. With constant flow rate the combined head moves from 1 to 2. In practice the combined head and flow rated moved along the system curve to 3.

Pumps in Parallel-Flow Rate Added When two or more pumps are arranged in parallel their resulting performance curve is obtained by adding their flow rates at the same head as indicated in the figure below Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can handle alone. For two identical pumps in parallel the flow rate will double (moving from 1 to 2) compared to a single pump if head is kept constant. In practice the combined head and volume flow moves along the system curve as indicated from 1 to 3

Multistage centrifugal pump arranged in series

Dimensionless Parameters and Similarity Laws Dependent pump variables are the actual head rise, shaft power, and efficiency, head rise coefficient. power coefficient Efficiency

Practical experience reveals that effect of Reynold’s number & relative surface roughness can be neglected and then for geometrically similar pumps (all pertinent dimensions, scaled by a common length scale), the dependent pi terms are functions of only so that These three equations provide the desired similarity relationships among a family of geometrically similar pumps.

Pump scaling laws relate geometrically similar pumps. If two pumps from the geometrically similar family are operated at the same value of flow coefficient it then follows that With these so-called pump scaling laws it is possible to experimentally determine the performance characteristics of one pump in the laboratory and then use these data to predict the corresponding characteristics for other pumps within the family under different operating conditions.

Pump affinity laws Pump affinity laws relate the same pump at different speeds or geometrically similar pumps at the same speed. a geometrically similar family of pumps, operating at a given speed How pump characteristics change with change in speed of a given pump?

Change in pump speed (constant size) If a pump delivers a discharge Q1 at a head H1 when running at speed N1, the corresponding values when the same pump is running at speed N2 are given by the similarity (affinity) laws: where Q = discharge (m3/s, or l/s). H = pump head (m). N = pump rotational speed (rpm). Pi = power input (HP, or kw).

(b) Change in pump size (constant speed) A change in pump size and therefore, impeller diameter (D), results in a new set of characteristic curves using the following similarity (affinity) laws: where D = impeller diameter (m, cm). Note : D indicated the size of the pump

The effects of viscosity and surface roughness have been neglected in the foregoing similarity relationships. However, it has been found that as the pump size decreases these effects more significantly influence efficiency

Specific Speed Specific speed may be determined independent of pump size. However, for any pump it is customary to specify a value of specific speed at the flow coefficient corresponding to peak efficiency only. Centrifugal pumps typically are low-capacity, high head pumps, and therefore have low specific speeds. The concept of specific speed is very useful to engineers and designers, since if the required head, flow rate, and speed are specified, it is possible to select an appropriate(most efficient) type of pump for a particular application.

Specific speed may be used to approximate what general pump geometry (axial to radial) to use for maximum efficiency.