05.04.2016 Views

Modern Engineering Thermodynamics

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

574 CHAPTER 14: Vapor and Gas Refrigeration Cycles<br />

The following example illustrates the use of this material.<br />

EXAMPLE 14.12<br />

A company manufactures the cryogenic Stirling refrigeration cycle<br />

microcooler shown in Figure 14.30. The microcooler has a mass<br />

of only 0.300 kg and is used to replace liquid nitrogen in infrared<br />

thermal imaging cameras. With a power input of only<br />

3.00 W from a 12.0 V battery, the microcooler can reach a temperature<br />

of 65.0 K in an environment at 22.0°C. The refrigerating<br />

capacity of the microcooler at these conditions is 0.100 J/s. For<br />

this design, determine<br />

a. The Stirling ASC coefficient of performance of this refrigeration<br />

unit.<br />

b. The actual coefficient of performance of this unit.<br />

Solution<br />

a. The Stirling ASC coefficient of performance of a refrigeration<br />

unit is given by Eq. (14.27) as<br />

COP reversed Stirling<br />

ASC R/AC<br />

T<br />

= L<br />

T H − T L<br />

=<br />

65:0K<br />

ð273:15 + 22:0KÞ − 65:0K = 0:282<br />

FIGURE 14.30<br />

Example 14.12, microcooler.<br />

b. The actual coefficient of performance can be calculated from its definition as<br />

COP reversed Stirling<br />

actual R/AC<br />

=<br />

_Q L<br />

_W compressor<br />

=<br />

_Q cooling<br />

_W input<br />

=<br />

0:100 J/s<br />

3:00 J/s = 0:0333<br />

The actual efficiency of Stirling cycle systems is often much lower than the idealized ASC predictions. In addition to<br />

the fact that real systems have losses and entropy production that are not accounted for in an ASC analysis, the large<br />

dead space within the reciprocating piston mechanism prevents all the gas in the system from passing through<br />

the cycle. Also, a reciprocating piston mechanism cannot provide a truly constant volume process at any point in<br />

the cycle. It can provide only approximate constant volume conditions when the piston is near the top or bottom<br />

dead center positions while the crankshaft is rotating. Figure 14.31 illustrates this volume change for a compression<br />

ratio of 8.0.<br />

5.0<br />

5.0<br />

R<br />

Θ<br />

Compression<br />

ratio = 8.0<br />

Clearance<br />

volume<br />

L<br />

% Change in volume<br />

4.0<br />

3.0<br />

2.0<br />

1.0<br />

L/R= 1.0<br />

L/R= 2.0<br />

4.0<br />

3.0<br />

2.0<br />

1.0<br />

0.0<br />

0.0<br />

1.0 2.0 3.0 4.0<br />

Crankshaft angle, degrees<br />

0.0<br />

5.0<br />

FIGURE 14.31<br />

Example 14.14, volume change.<br />

Exercises<br />

34. If the microcooler described in Example 14.12 is used to produce a temperature of 75.0 K instead of 65.0 K at the same<br />

environmental temperature, determine the ASC coefficient of performance of the unit under these conditions. Answer:<br />

COP reversed Stirling ASC R/AC = 0.341.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!