Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

7–12 ■ ISENTROPIC EFFICIENCIES

OF STEADY-FLOW DEVICES

We mentioned repeatedly that irreversibilities inherently accompany all

actual processes and that their effect is always to downgrade the perfor-

mance of devices. In engineering analysis, it would be very desirable to

have some parameters that would enable us to quantify the degree of degra-

dation of energy in these devices. In the last chapter we did this for cyclic

devices, such as heat engines and refrigerators, by comparing the actual

cycles to the idealized ones, such as the Carnot cycle. A cycle that was com-

posed entirely of reversible processes served as the model cycleto which the

actual cycles could be compared. This idealized model cycle enabled us to

determine the theoretical limits of performance for cyclic devices under

specified conditions and to examine how the performance of actual devices

suffered as a result of irreversibilities.

Now we extend the analysis to discrete engineering devices working

under steady-flow conditions, such as turbines, compressors, and nozzles,

and we examine the degree of degradation of energy in these devices as a

result of irreversibilities. However, first we need to define an ideal process

that serves as a model for the actual processes.

Although some heat transfer between these devices and the surrounding

medium is unavoidable, many steady-flow devices are intended to operate

under adiabatic conditions. Therefore, the model process for these devices

should be an adiabatic one. Furthermore, an ideal process should involve no

irreversibilities since the effect of irreversibilities is always to downgrade

the performance of engineering devices. Thus, the ideal process that can

serve as a suitable model for adiabatic steady-flow devices is the isentropic

process (Fig. 7–48).

The more closely the actual process approximates the idealized isentropic

process, the better the device performs. Thus, it would be desirable to have

a parameter that expresses quantitatively how efficiently an actual device

approximates an idealized one. This parameter is the isentropicor adia-

batic efficiency,which is a measure of the deviation of actual processes

from the corresponding idealized ones.

370 | Thermodynamics

The compressor work across each stage is also the same. Thus the total

compressor work is twice the compression work for a single stage:

Discussion Of all four cases considered, the isothermal compression requires

the minimum work and the isentropic compression the maximum. The

compressor work is decreased when two stages of polytropic compression are

utilized instead of just one. As the number of compressor stages is increased,

the compressor work approaches the value obtained for the isothermal case.

215.3 kJ/kg



21 1.3 21 0.287 kJ>kg#K 21 300 K 2

1.3 1

¬ca

300 kPa

100 kPa

b

1 1.3 1 2>1.3

 1 d

wcomp,in^2 wcomp I,in^2 ¬

nRT 1

n 1

¬ca

Px

P 1

b

1 n 1 2>n

 1 d

P 1 , T 1

P 2 P 2

P 1 , T 1

ACTUAL

(irreversible)

IDEAL

(reversible)

FIGURE 7–48

The isentropic process involves no
irreversibilities and serves as the ideal
process for adiabatic devices.

SEE TUTORIAL CH. 7, SEC. 12 ON THE DVD.

INTERACTIVE

TUTORIAL