Machines for Doing Work on a Fluid

Machines that add energy to a uid by performing work on it are called pumps when the ow is liquid or slurry, and fans, blowers, or compressors for gas- or vapor- handling units, depending on pressure rise. Fans usually have small pressure rise (less than 1 inch of water) and blowers have moderate pressure rise (perhaps 1 inch of mercury); pumps and compressors may have very high pressure rises. Current industrial systems operate at pressures up to 150,000 psi (104 atmospheres).

Pumps and compressors consist of a rotating wheel (called an impeller or rotor, depending on the type of machine) driven by an external power source (e.g., a motor or another uid machine) to increase the ow kinetic energy, followed by an element to decelerate the ow, thereby increasing its pressure. This combination is known as a stage. These elements are contained within a housing or casing. A single pump or compressor might consist of several stages within a single housing, depending on the amount of pressure rise required of the machine. The shaft must penetrate the

housing in order to receive mechanical work from the external power source. Bearings and seals are needed to minimize frictional (mechanical) losses and prevent leakage of the working uid.

Three typical centrifugal machines are shown schematically in Fig. 10.1. The rotating element of a centrifugal pump or compressor is frequently called the impeller.

Flow enters each machine nearly axially at small radius through the eye of the impeller, diagram (a), at radius r1. Flow is turned and leaves through the impeller discharge at radius r2, where the width is b2. Diffusion of the ow is achieved in a centrifugal machine as it leaves the impeller and is collected in the scroll or volute, which gradually increases in area as it nears the outlet of the machine, diagram (b).

The impeller usually has vanes; it may be shrouded (enclosed) as shown in diagram (a), or open as shown in diagram (c). The impeller vanes may be relatively straight, or they may curve to become nonradial at the outlet. Diagram (c) shows that the diffuser may have vanes to direct the ow between the impeller discharge and the volute; vanes allow for more ef cient diffusion, but at increased fabrication cost. Centrifugal machines are capable of higher pressure ratios than axial machines, but they have a higher frontal area per unit mass ow.

Typical axial- ow and mixed- ow turbo machines are shown schematically in Fig. 10.2. Figure 10.2a shows a typical axial- ow compressor stage. In these machines the rotating element is referred to as the rotor, and ow diffusion is achieved in the stator. Flow enters nearly parallel to the rotor axis and maintains nearly the same radius through the stage. The mixed- ow pump in diagram (b) shows the

ow being turned outward and moving to larger radius as it passes through the stage. Axial ow machines have higher ef ciencies and less frontal area than centrifugal machines, but

they cannot achieve as high pressure ratios. As a result, axial ow machines are more likely to consist of multiple stages, making them more complex than centrifugal machines. Figure 10.3 shows a multiple-stage axial ow compressor. In this photo- graph, the outer housing (to which the stator vanes are attached) has been removed, clearly showing the rows of rotor vanes.

The pressure rise that can be achieved ef ciently in a single stage is limited, depending on the type of machine. The reason for this limitation can be understood based on the pressure gradients in these machines (see Section 9.6). In a pump or compressor, the boundary layer subjected to an adverse pressure gradient is not stable; so ow is more likely to encounter boundary-layer separation in a compressor or pump. Boundary-layer separation increases the drag on the impeller, resulting in a decrease in ef ciency; therefore additional work is needed to compress the ow.

Fans, blowers, compressors, and pumps are found in many sizes and types, ranging from simple household units to complex industrial units of large capacity. Torque and power requirements for idealized pumps and turbo blowers can be analyzed by applying the angular-momentum principle using a suitable control volume. Propellers are essentially axial- ow devices that operate without an outer housing.

Propellers may be designed to operate in gases or liquids. As you might expect, propellers designed for these very different applications are quite distinct. Marine propellers tend to have wide blades compared with their radii, giving high solidity. Aircraft propellers tend to have long, thin blades with relatively low solidity. These machines will be discussed in detail in Section 10.6.

Machines for Extracting Work (Power) from a Fluid

Machines that extract energy from a uid in the form of work (or power) are called Turbines. In hydraulic turbines, the working uid is water, so the ow is incompressible.

In gas turbines and steam turbines, the density of the working uid may change signi cantly. In a turbine, a stage normally consists of an element to accelerate the ow, converting some of its pressure energy to kinetic energy, followed by a rotor, wheel, or runner extracts the kinetic energy from the

ow via a set of vanes, blades, or buckets mounted on the wheel.

The two most general classi cations of turbines are impulse and reaction turbines.

Impulse turbines are driven by one or more high-speed free jets. The classic example of an impulse turbine is the waterwheel. In a waterwheel, the jets of water are driven by gravity; the kinetic energy of the water is transferred to the wheel, resulting in work. In more modern forms of impulse turbines, the jet is accelerated in a nozzle external to the turbine wheel. If friction and gravity are neglected, neither the uid pressure nor speed relative to the runner changes as the uid passes over the turbine buckets. Thus for an impulse turbine, the uid acceleration and accompanying pressure drop take place in nozzles external to the blades, and the runner does not ow full of uid; work is extracted as a result of the large momentum change of the uid.

In reaction turbines, part of the pressure change takes place externally and part takes place within the moving blades. External acceleration occurs and the ow is turned to enter the runner in the proper direction as it passes through nozzles or stationary blades, called guide vanes or wicket gates. Additional uid acceleration relative to the rotor occurs within the moving blades, so both the relative velocity and the pressure of the stream change across the runner. Because reaction turbines ow full of uid, they generally can produce more power for a given overall size than impulse turbines.

Figure 10.4 shows turbines used for different applications. Figure 10.4a shows a Pelton wheel, a type of impulse turbine wheel used in hydroelectric power plants.

Figure 10.4b is a photograph of an axial steam turbine rotor, an example of a reaction turbine. Figure 10.4c is a wind turbine farm. A wind turbine is another example of a reaction turbine, but, like a propeller, also operates without an outer housing. Modern wind turbines typically collect wind energy and convert it into electricity. Several typical hydraulic turbines are shown schematically in Fig. 10.5. Figure 10.5a shows an impulse turbine driven by a single jet, which lies in the plane of the turbine runner. Water from the jet strikes each bucket in succession, is turned, and leaves the bucket with relative velocity nearly opposite to that with which it entered the bucket.

Spent water falls into the tailrace (not shown).

A reaction turbine of the Francis type is shown in Fig. 10.5b. Incoming water ows circumferentially through the turbine casing. It enters the periphery of the stationary guide vanes and ows toward the runner. Water enters the runner nearly radially and is turned downward to leave nearly axially; the

ow pattern may be thought of as a centrifugal pump in reverse. Water leaving the runner ows through a diffuser known as a draft tube before entering the tailrace. Figure 10.5c shows a propeller turbine of the Kaplan type. The water entry is similar to that in the Francis turbine, but it is

turned to ow nearly axially before encountering the turbine runner. Flow leaving the runner may pass through a draft tube.

Thus turbines range from simple windmills to complex gas and steam turbines with many stages of carefully designed blading. These devices also can be analyzed in idealized form by applying the angular-momentum principle.

The allowable amount of pressure drop in a turbine stage is usually greater than the amount of pressure rise allowable in a compressor stage. The difference is due to the favourable pressure gradient, which makes boundary-layer separation much less likely than in the case of the compressor.

Dimensionless parameters, such as speci c speed, ow coef cient, torque coef cient, power coef cient, and pressure ratio, frequently are used to characterize the performance of turbo machines.