T4 - VORTEX TUBE
Objective
Th e objective of this experiment is: to obtain performance characteristics of a vortex tube (Ranque-Hilsch Tube); to practice first law and second law analysis of a thermodynamic system.
Background
The Vortex Tube is a device without moving parts. It expands a high-pressure gas stream converting it into a cold and a hot stream. Figure 1 illustrates schematically the system. The throttle valve located at the end of the hot tube is used to control the system. The Vortex Tube can be used as a refrigeration device when the cold pipe wall is used to reduce the temperature of an enclosure or as a heating device when the hot pipe wall is used to increase the temperature of an enclosure. Note that opposite to what is normally viewed in Thermodynamics, the Vortex Tube in the present case is an open circuit (control volume) device.
Figure 1 - Vortex Tube
An examination of the system at steady state indicates that from the First Law of Thermodynamics
D
H= Q (1)where
D
is the system enthalpy change and
is the heat exchanged between the system and its surroundings. Let’s assume that 
is approximately zero even though the cold tube may have frost on it and the hot tube is very warm (remember that is the total heat exchanged). If this is the case then
D
H= DHc+ DHH= 0 (2)where
DHcis the enthalpy change of cold stream and DHHis the enthalpy change of hot stream. Assuming the air as an ideal gas, the total enthalpy change can be written asD
H= mccp (Tc – Ti) + mhcp (Th – Ti) = 0 (3)where:
m
c= mass flow rate at cold tubem
h= mass flow rate at hot tubeT
c = cold air temperatureT
i = inlet air temperatureT
h = hot air temperaturec
p = specific heat of air at constant pressureThe inlet and hot outlet mass flow rates are measured through a float type meter (restriction of cold tube to measure flow will prevent device from operating properly in most cases). The mass flow rate from the cold tube is obtained by applying the conservation of mass principle to the whole system.
Now let us examine the Second Law of Thermodynamics as applied to this system. Assuming the process as reversible and adiabatic then
D
S =
= 0 (4)
where
DS is total entropy change, q is heat transfer and T is absolute temperature. The actual entropy change of the control volume at steady state is
(5)
where DSc and DSh are the entropy change from entrance to exit of the portion of entering air which leaves the cold tube, and the portion of entering air which leaves the hot tube, respectively.
For an ideal gas with constant specific heat, the entropy change can be written as
(6)
where the subscripts i, c and h are respectively inlet stream, cold stream and hot stream and R is the ideal gas constant. Notice that in reality the vortex tube process is irreversible so DS should be greater than zero.
Since the appearance of a cold (or hot) effect upon the pipe wall without moving parts would tempt to consider this device as competition for a refrigerator (or heat pump), it is instructive to estimate its coefficient of performance (COP). Focusing on the cooling effect that can be achieved by placing the cold pipe within an enclosure, the COP can be calculated by
(7)
where DHcis obtained from
(8)
D
in the present case is the work done to compress the air from atmospheric pressure and temperature to the inlet conditions of the tube. Assuming reversible compression (isentropic, minimum work), 
then obtained from:
(9)
where T2 is the compressor exit temperature, and T1 is the compressor inlet temperature (Reversible, Polytropic process; air: n=1.4). If we consider a complete system, P1 and T1 are the atmospheric pressure and temperature, P2 and T2 are the compressor exit conditions,
(10)
After the air is compressed, it is kept in the high pressure tank where then it cools down to the atmosphere temperature T1, so the inlet temperature of the sonic nozzle, Ti, is equal to T1. By noting that
(11)
Equation (9) can be simplified to
(12)
with T2 calculated from Eq. (10). This is an ideal work value so it is less than the actual work needed to drive the compressor.
The comparison between vortex tube COP with the conventional refrigeration COP will show that unless high pressure air is inexpensive or the vortex tube simplicity is more important than the cost of operation, the conventional system is better.
The refrigeration effect of the vortex tube is simply equal to DHc,
(13)
Note:
In working with a vortex tube (that is to obtain experimental data) be reminded of the following:
a. Do not use large diameter tubes that will exceed the capacity of your air storage system. If you do, you will not be able to reach or maintain steady state and the previous analyses will not apply
b. Remember it is necessary to measure the incoming flow rate of gas and the flow rate leaving the hot tube. This requires some experience with flow measurements.
c. Outlet streams should be well mixed in order to assume average temperature readings.
d. The hot tube valve must be partially closed in order to force air out of the cold tube. If the hot tube valve is in the wide-open position, room air will actually be drawn into the cold tube. This is interesting to observe in this experiment.
Procedure
Before running air through the vortex tube, verify that the knob at the hot outlet exit is fully closed. Open it by turning the knob two full turns.
Air flows from the high-pressure tank outside the building through a series of valves. Locate the main valve and the two secondary valves. Open the first secondary valve so that the pressure meter reads 80 psig. The second secondary valve behind the vortex tube apparatus should control the inlet pressure to the apparatus. Select a pressure for the inlet flow into the vortex tube around 70 psig. A gauge mounted on the Vortex Tube Test Board indicates the vortex tube inlet pressure.
The objective of the experiment is to measure several parameters of interest for different hot outlet mass flow rates. This can be obtained for the chosen inlet pressure by adjusting the knob at the hot end of the vortex tube. This changes the proportion of hot flow to cold flow. It should not alter the inlet pressure.
For a given inlet pressure, a set of measurements (perhaps 8 to 20 points) should be taken over the full range of the hot flow rotameter (mounted on the right side of the Vortex Tube Test Board). For example, if the inlet pressure is 85 psig, the maximum hot rotameter reading might be 81% so the readings should be made within the range 0-81%. These are numbers read directly off of the rotameter.
Air temperatures are measured by four type K thermocouples connected directly to a digital thermometer. The digital thermometer reads the temperatures in degrees Celsius. The following temperatures can be measured by switching the control: the inlet temperature, the outlet cold temperature, and outlet hot temperature, and the exhaust hot temperature.
You must also record:
%h : number read on the hot flow rotameter (right hand side)
%in : number read on the inlet rotameter (left hand side)
PATM : barometer (with corrections for latitude, 35° N, and temperature)
Pin : inlet pressure psig
Calculate the following:
COP : coefficient of performance (Eq. (7))
in : mass flow rate of input flow
c : mass flow rate of cold flow
h : mass flow rate of hot flow
: refrigeration (Eq. (14))
DS : entropy change (Eq. (6))
DTc : temperature drop at cold end
%c : ratio of cold end mass flow rate and inlet mass flow rate
D: enthalpy change (Eq. (3))
To find % cold fraction using [P] in psi, and [T] in °F so [
] in lb/min:
These equations are derived from the ideal gas law and from the properties of rotameters so they are valid only for the specific rotameter being used with air.
Report
The lab write up should include 5 graphs:
1. temperature drop at the cold end vs. % c
2. refrigeration vs. % c
3. entropy gain vs. % c
4. Coefficient of performance vs. % c
5.
vs. % c
The analysis of the results should include a discussion on the option of having the system working at its most efficient point according to the second law or having it working at its most efficient point according to the first law.
References
(useful for learning and preparation of Lab Report)