# Chapter 12 Turbomachines

The two types of Pumps seen in the Lecture Slides

*Dynamic* (such as Centrifugal Pumps) and *Positive Displacement* (work with large pressures so are large or heavy) Pumps.

Velocity Triangles

Absolute Fluid Velocity (V) = Relative Velocity (W) + Blade Velocity (U). Have to assume fluid enters and leaves the fan at the same distance from the axis of rotation. The axial Absolute Vector (V) that enters is turned during its flow as the tangential force exerted by the blades gives it a nonzero tangential velocity component as it exits.

Actual Head-Flowrate Curve

Actual curve differs from ideal due to losses such as fluid friction, separation, and leakages.

Turbomachines

Are dynamic fluid machines that add or extract flow energy. Involve the parameters of force, torque, work, and power.

What are Turbomachines classified as?

As axial, mixed, or radial-flow, depending on the predominant direction of the fluid motion relative to the rotor's axis.

Cavitation

Associated with suction (low pressure side of the pump). Occurs when liquid pressure drops below vapor pressure, which causes liquid to "boil" and form vapor bubbles. These bubbles collapse and produce shock waves that damage equipment and lower efficiency.

Velocity Triangles for Turbines (Energy Extraction)

Blades move in the direction of the lift force exerted on each blade. The fluid moves *opposite to the direction of blade motion*. The fluid does work on the blades (a turbine).

Various Characteristics of Centrifugal Pumps

Can have open or enclosed impeller, where blades are revealed or covered. Can also be single or double suction. Double suction would have a larger inlet area and a reduced inlet velocity. Pumps can also be single or multistage. Multistage has several impellers. Kinetic Energy is converted by the pumps into an increase in pressure.

Net Positive Suction Head (NPSH)

Characterizes potential for cavitation by finding the difference between the total head on the suction side and the liquid vapor pressure head.

Pump-System Characterization

Considers the pump equation/curve and system equation/curve. The operation point is decided by the intersection of the pump and system curve. The operating point should be near a best efficiency point (BEP). The operating point will shift with any change in the system.

The Centrifugal Pump

Consists of the Casing and Impeller. Fluid is sucked in and flows radially outwards. Can be single stage or multistage. Uses the three "basic" Turbomachine equations, plus the energy equation which accounts for head developed.

Pump Performance Curves

Designer's objective: a flat efficiency curve. Overall efficiency depends on: Hydraulic Efficiency, Mechanical Efficiency (Bearings, Seals), Volumetric Efficiency (Leakages).

Pumps in Series and Parallel

For pumps in series, add head; For two in parallel add flowrates.

Energy Addition to Fluid

Generally consist of *Pumps*, Compressors, or Fans.

Energy Extraction From Fluid

Generally consist of *Turbines*. Steam turbine, Gas turbine, Impulse Turbine (Pelton Wheel).

Overall Pump Efficiency

Is the ratio of power actually gained by the fluid to the shaft power supplied.

Required and Available NPSH

Pumps are tested to determine the value for Required NPSH by detecting cavitation or observing a change the head-flowrate curve. Required NPSH must be maintained or exceeded so Cavitation does not occur. The Available NPSH represents the head that actually occurs for the particular flow system. For proper pump operation, Available NPSH has to be greater than the Required NPSH.

What are the three Pump Performance equations?

The Head-Energy equation, Fluid Power, and Overall Pump Efficiency which accounts for brake horsepower (bhp).

The Three "Basic" Turbomachine Equations from the Lecture Slides

The Shaft Torque equation (also called the Euler Turbomachine Equation, from Moment-of-Momentum equation). The Shaft Power equation, and the Shaft Power equation in terms of work per unit mass.

Velocity Triangles for Pumps (Energy Addition)

The blades exert a tangential force *in the same direction of the motion of the blade*. The blade does work on the fluid (a pump).