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Modern Engineering Thermodynamics

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304 CHAPTER 9: Second Law Open System Applications<br />

EXAMPLE 9.9 (Continued )<br />

Using Eq. (9.51) for air, with R =0.0685Btu/(lbm· R), c p =0.240Btu/(lbm· R), and y =0.500,tocalculate _S P / _m 3 gives<br />

the following results. At 20 psig = 34.7 psia, p 2 = p 3 = 14.7 psia, and from Table 9.2, we find T H /T C = T 3 /T 2 =1.209.<br />

Then,<br />

<br />

ð1:209Þ _S 0:5<br />

P / _m 3 vortex = ½0:240 Btu/ ðlbm.RÞŠln<br />

1 + 0:500ð0:209Þ + ½ 0:0685 Btu/ ð lbm .RÞŠln 34:7<br />

14:7<br />

tube<br />

= −0:0011 + 0:0588 = 0:0577 Btu/ ðlbm.RÞ<br />

Notice that the first term (which corresponds to isobaric separation) in this calculation is negative while the second term<br />

(resulting from the pressure loss) is positive and dominant. Therefore, if the vortex tube is required to be isobaric, it could<br />

not work, because to do so would violate the second law of thermodynamics. However, isobaric mixing is possible because<br />

then the lead term in this equation is positive and the second term is zero. The remaining results are in Table 9.3. These<br />

values are plotted Figure 9.20.<br />

0.20<br />

0.18<br />

0.16<br />

0.14<br />

Btu<br />

lbm •R<br />

0.12<br />

0.10<br />

S P<br />

m 3<br />

0.08<br />

0.06<br />

0.04<br />

m<br />

y = 1<br />

= 0.5<br />

m 3<br />

0.02<br />

0 20 40 60 80 100 120 140 160<br />

Inlet pressure (psig)<br />

S P /m 3 vs. inlet pressure for a vortex tube<br />

FIGURE 9.20<br />

Example 9.9, results.<br />

CAN VORTEX TUBES BE USED FOR AIR CONDITIONING?<br />

In factories where compressed air is readily available, vortex tubes are often used to cool parts during machining or to<br />

provide cool air to workers in enclosed environments. But, when you take into account the energy needed to compress the<br />

air, vortex tubes are not very efficient cooling devises.<br />

Vortex tubes also work with liquids as well as gases, but only at very high inlet pressures. Using the incompressible liquid<br />

equations of state in the entropy balance equation, you can show that indeed a temperature separation occurs in a vortex<br />

tube, providing the inlet pressure is very high. 7<br />

7 See: R.T. Balmer, “Pressure-Driven Ranque-Hilsch Temperature Separation in Liquids,” ASME Journal of Fluids <strong>Engineering</strong> (1988), pp. 161–164.

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