Modern Engineering Thermodynamics

304 CHAPTER 9: Second Law Open System Applications
EXAMPLE 9.9 (Continued )
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
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.
Then,
ð1:209Þ _S 0:5
P / _m 3 vortex = ½0:240 Btu/ ðlbm.RÞŠln
1 + 0:500ð0:209Þ + ½ 0:0685 Btu/ ð lbm .RÞŠln 34:7
14:7
tube
= −0:0011 + 0:0588 = 0:0577 Btu/ ðlbm.RÞ
Notice that the first term (which corresponds to isobaric separation) in this calculation is negative while the second term
(resulting from the pressure loss) is positive and dominant. Therefore, if the vortex tube is required to be isobaric, it could
not work, because to do so would violate the second law of thermodynamics. However, isobaric mixing is possible because
then the lead term in this equation is positive and the second term is zero. The remaining results are in Table 9.3. These
values are plotted Figure 9.20.
0.20
0.18
0.16
0.14
Btu
lbm •R
0.12
0.10
S P
m 3
0.08
0.06
0.04
m
y = 1
= 0.5
m 3
0.02
0 20 40 60 80 100 120 140 160
Inlet pressure (psig)
S P /m 3 vs. inlet pressure for a vortex tube
FIGURE 9.20
Example 9.9, results.
CAN VORTEX TUBES BE USED FOR AIR CONDITIONING?
In factories where compressed air is readily available, vortex tubes are often used to cool parts during machining or to
provide cool air to workers in enclosed environments. But, when you take into account the energy needed to compress the
air, vortex tubes are not very efficient cooling devises.
Vortex tubes also work with liquids as well as gases, but only at very high inlet pressures. Using the incompressible liquid
equations of state in the entropy balance equation, you can show that indeed a temperature separation occurs in a vortex
tube, providing the inlet pressure is very high. 7
7 See: R.T. Balmer, “Pressure-Driven Ranque-Hilsch Temperature Separation in Liquids,” ASME Journal of Fluids Engineering (1988), pp. 161–164.