Turbomachinery

Motivation. The most common practical engineering application for fluid mechanics
is the design of fluid machinery. The most numerous types are machines that add
energy to the fluid (the pump family), but also important are those that extract energy
(turbines). Both types are usually connected to a rotating shaft, hence the name turbomachinery.
The purpose of this chapter is to make elementary engineering estimates of the
performance of fluid machines. The emphasis will be on nearly incompressible flow: liquids or low-velocity gases. Basic flow principles are discussed, but not the detailed construction of the machines.

11.1 Introduction and Classification

Turbomachines divide naturally into those that add energy (pumps) and those that
extract energy (turbines). The prefix turbo- is a Latin word meaning “spin” or “whirl,”
appropriate for rotating devices.
The pump is the oldest fluid energy transfer device known. At least two designs
date before Christ: (1) the undershot-bucket waterwheels, or norias, used in Asia and
Africa (1000 B.C.) and (2) Archimedes’ screw pump (250 B.C.), still being manufac-
tured today to handle solid–liquid mixtures. Paddlewheel turbines were used by the
Romans in 70 B.C., and Babylonian windmills date back to 700 B.C. [1].
Machines that deliver liquids are simply called pumps, but if gases are involved,
three different terms are in use, depending on the pressure rise achieved. If the pres-
sure rise is very small (a few inches of water), a gas pump is called a fan; up to 1 atm, it is usually called a blower; and above 1 atm it is commonly termed a compressor.

Classification of Pumps

There are two basic types of pumps: positive-displacement and dynamic or momentum-
change pumps. There are several billion of each type in use in the world today.
Positive-displacement pumps (PDPs) force the fluid along by volume changes. A
cavity opens, and the fluid is admitted through an inlet. The cavity then closes, and
the fluid is squeezed through an outlet. The mammalian heart is a good example, and
many mechanical designs are in wide use. References 35–38 give a summary of PDPs.

A brief classification of PDP designs is as follows:
A. Reciprocating
1. Piston or plunger
2. Diaphragm
B. Rotary
1. Single rotor
a. Sliding vane
b. Flexible tube or lining
c. Screw
d. Peristaltic (wave contraction)
2. Multiple rotors
a. Gear
b. Lobe
c. Screw
d. Circumferential piston
All PDPs deliver a pulsating or periodic flow as the cavity volume opens, traps, and
squeezes the fluid. Their great advantage is the delivery of any fluid regardless of its
viscosity.
Figure 11.1 shows schematics of the operating principles of seven of these PDPs.
It is rare for such devices to be run backward, so to speak, as turbines or energy
extractors, the steam engine (reciprocating piston) being a classic exception.
Since PDPs compress mechanically against a cavity filled with liquid, a common
feature is that they develop immense pressures if the outlet is shut down for any rea-
son. Sturdy construction is required, and complete shutoff would cause damage if
pressure relief valves were not used.
Dynamic pumps simply add momentum to the fluid by means of fast-moving
blades or vanes or certain special designs. There is no closed volume: The fluid
increases momentum while moving through open passages and then converts its high
velocity to a pressure increase by exiting into a diffuser section. Dynamic pumps can
be classified as follows:
A. Rotary
1. Centrifugal or radial exit flow
2. Axial flow
3. Mixed flow (between radial and axial)
B. Special designs
1. Jet pump or ejector (see Fig. P3.36)
2. Electromagnetic pumps for liquid metals
3. Fluid-actuated: gas lift or hydraulic ram
We shall concentrate in this chapter on the rotary designs, sometimes called rotody-
namic pumps. Other designs of both PDP and dynamic pumps are discussed in spe-
cialized texts [for example, 3, 31].

Fig. 11.1 Schematic design of
positive-displacement pumps:
(a) reciprocating piston or plunger,
(b) external gear pump, (c) double-
screw pump, (d) sliding vane,
(e) three-lobe pump, (f ) double
circumferential piston, (g) flexible-
tube squeegee.

Dynamic pumps generally provide a higher flow rate than PDPs and a much stead-
ier discharge but are ineffective in handling high-viscosity liquids. Dynamic pumps
also generally need priming; if they are filled with gas, they cannot suck up a liquid
from below into their inlet. The PDP, on the other hand, is self-priming for most appli-
cations. A dynamic pump can provide very high flow rates (up to 300,000 gal/min)
but usually with moderate pressure rises (a few atmospheres). In contrast, a PDP can

Fig. 11.2 Comparison of perform-
ance curves of typical dynamic and
positive-displacement pumps at
constant speed.

operate up to very high pressures (300 atm) but typically produces low flow rates
(100 gal/min).
The relative performance (-
p versus Q) is quite different for the two types of
pump, as shown in Fig. 11.2. At constant shaft rotation speed, the PDP produces nearly
constant flow rate and virtually unlimited pressure rise, with little effect of viscosity.
The flow rate of a PDP cannot be varied except by changing the displacement or the
speed. The reliable constant-speed discharge from PDPs has led to their wide use in
metering flows [35].
The dynamic pump, by contrast in Fig. 11.2, provides a continuous constant-speed
variation of performance, from near-maximum -
p at zero flow (shutoff conditions) to
zero -
p at maximum flow rate. High-viscosity fluids sharply degrade the performance
of a dynamic pump.
As usual—and for the last time in this text—we remind the reader that this is
merely an introductory chapter. Many books are devoted solely to turbomachines: gen-
eralized treatments [2 to 7], texts specializing in pumps [8 to 16, 30, 31], fans [17 to
20], compressors [21 to 23], gas turbines [24 to 26], hydropower [27, 28, 32], and
PDPs [35 to 38]. There are several useful handbooks [29 to 32], and at least two
undergraduate textbooks [33, 34] have a comprehensive discussion of turbomachines.
The reader is referred to these sources for further details.

The Centrifugal Pump

Let us begin our brief look at rotodynamic machines by examining the characteris-
tics of the centrifugal pump. As sketched in Fig. 11.3, this pump consists of an
impeller rotating within a casing. Fluid enters axially through the 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.
The impeller blades are usually backward-curved, as in Fig. 11.3, but there are also
radial and forward-curved blade designs, which slightly change the output pressure.

Fig. 11.3 Cutaway schematic of a
typical centrifugal pump.

The blades may be open (separated from the front casing only by a narrow clearance)
or closed (shrouded from the casing on both sides by an impeller wall). The diffuser
may be vaneless, as in Fig. 11.3, or fitted with fixed vanes to help guide the flow
toward the exit.

Basic Output Parameters

Assuming steady flow, the pump basically increases the Bernoulli head of the flow
between point 1, the eye, and point 2, the exit. From Eq. (3.73), neglecting viscous
work and heat transfer, this change is denoted by H:

where hs is the pump head supplied and hf the losses. The net head H is a primary
output parameter for any turbomachine. Since Eq. (11.1) is for incompressible flow,
it must be modified for gas compressors with large density changes.
Usually V2 and V1 are about the same, z2 z1 is no more than a meter or so, and
the net pump head is essentially equal to the change in pressure head:

The power delivered to the fluid simply equals the specific weight times the discharge times the net head change:

This is traditionally called the water horsepower. The power required to drive the pump is the brake horsepower

where -
 is the shaft angular velocity and T the shaft torque. If there were no losses,
Pw and brake horsepower would be equal, but of course Pw is actually less, and the
efficiency of the pump is defined as

Conversion factors may be needed: 1 hp 550 ft. lbf/s 746 W.

The chief aim of the pump designer is to make as high as possible over as broad a range of discharge Q as possible.
The efficiency is basically composed of three parts: volumetric, hydraulic, and
mechanical. The volumetric efficiency is