MASS , ENERGY , ENTROPY AND EXERGY RATE BALANCE IN A RANQUE-HILSH VORTEX TUBE

The objectve of this paper is to present a laboratory program designed for the Thermodynamics course offered in the Department of Thermal Engineering at the University of the Basque Country. With reference to one of the examples given in the textbook by Moran, Shapiro, Boettner and Bailey (2012), the balances of mass, energy, entropy and exergy are applied to a partcular control volume, and the ideal gas model is used. Using a Ranque-Hilsh vortex tube (Ranque, 1934), the division of a compressed air fow into two streams at a lower pressure is achieved: one hot stream, where the temperature can exceed 100 °C, and another cold stream, in which temperatures can fall below -40 °C. Therefore, an air fow is divided into two separate hot and cold streams, without any thermal interacton with hot or cold focuses. The vortex tube is used to demonstrate the basics of the First and Second Law of Thermodynamics. In additon, this practcal laboratory program can even be used to make sense of one of the best-known theoretcal experiments in thermodynamics, the so-called Maxwell's demon experiment (Lewins & Bejan, 1999; Liew, Zeegers, Kuerten & Michalek, 2012). It should also be noted that once a compressed air source has been provided, the material needed to prepare the practcum is simple and affordable, and the lab itself is very interestng and appeals to students.

outlet fow, the thermocouple used to measure the temperature at the exit cold stream was placed near the vortex generator so the length of the cold branch tube was very short. The installaton and details of the instrumentaton used for the measurement of temperatures are shown in Figure 1.
Furthermore, the way in which the vortex tube works has an unusual appeal in and of itself, due to the temperatures that can be achieved and how they are reached.

THE MEASUREMENT
In order to achieve the proposed balances, the temperature and pressure of the air at the inlet and exit sectons of the vortex tube have to be known, as well as the fracton of the input fow in each of the output streams. The speed of the air at the inlet and exit sectons must be known if the kinetc energy is to be included into the energy balance. By applying the expression ( A· V v =ṁ ) , the values of the air speed and kinetc energy may be obtained, if the mass fow, the cross sectonal area and the specific volume of the air are known. The material necessary to perform the proposed analysis is the tube itself and different vortex generators, which make it possible to vary the air fow and the cooling power of the tube. Manometers and temperature sensors are also needed to measure pressures and temperatures at the inlet and outlet sectons. Both the inlet and exit fows can be measured by means of mass air fow meters. If these fow meters are not available, the input fow and the distributon of this fow between the cold (referred to as the fracton) and hot outlows can be calculated using the tables provided by the manufacturer, which are based on the inlet pressure and temperature variaton between the inlet and outlet air streams. Using these data, air velocites and kinetc energy can also be obtained, as explained above.

Figure 1. A general view of the laboratory equipment and details of the K-class thermocouples used
Vol. 3(3), 2013, pp 123 σ In the proposed practcal laboratory experience, the use and understanding by students of the thermodynamic concepts is prioritzed over a highly accurate system design. Therefore, the operatng model is simplified, even though a certain degree of accuracy in the data may be lost when tables are used. As will be seen later, we will check if the data recorded are appropriate, and if the calculatons are correct.

THE VORTEX TUBE
The Raque-Hilsch vortex tube is a heat apparatus with no moving parts that divides a high-pressure fuid fow into two separate fows (hot and cold) at lower pressures. It was designed in 1930 by George J. Ranque, and improved in 1945 by Rudolf Hilsch. Its operaton is based on the vortex effect created when a spin movement is induced in the pressurized inlet air by a vortex generator. Some generator models are shown in Figure 2.

Figure 2. Different vortex generators
The vortex, which may reach a rotatonal speed of 10 6 rpm, propagates through the tube to the hot output. A fracton of the air leaves this output, while the rest goes back into a lower pressure internal vortex to the cold output. The regulaton between the hot and cold fractons will be produced in the hot output, as can be seen in Figure 3.
This phenomenon is described in many different ways in the scientfic literature (Aydin & Baki, 2006;Xue, Arjomandi & Kelso, 2013a, 2013bPatño, Llopis, Sanchez, Torrella & Cabello, 2013), with some authors only providing a partal explanaton and others seemingly contradictng one another. As in other fields of fuid dynamics, the behavior of the air inside the tube has not yet been fully explained, so that for the purposes of the practcal laboratory experience, an easily understandable partal explanaton in associaton with thermodynamic concepts is proposed. More detailed explanatons can be found in the suggested references.  Figure 3 shows the vortex tube and a summary of how it works, as well as the limits of the control volume in queston. Two vortces can be observed; the outer one appertaining to the hot fow is at a higher pressure than the inner one, which appertains to the cold fracton. Even at steady state, there is air transfer between the two vortces. When air passes from the hot to the cold vortex, it expands (since the pressure is lower in the cold vortex) and therefore cools, lowering the temperature of the inner vortex. When air passes from the cold to the hot vortex, it is simultaneously compressed and heated, which raises the temperature of the outer vortex.  Table 1 is provided by the manufacturer and shows the inlet air consumpton for a specific vortex generator at the indicated pressure. For other inlet pressure values, an approximated formula is provided to calculate the consumpton based on the vortex generator type and the inlet pressure values. The value for the manufacturer's 106-4-H generator and 6.9 bars of inlet pressure is indicated. Table 2 shows the relatonship between the cold fracton of air and the temperature difference produced in each output for different inlet pressures. It is possible to estmate the cold fracton by measuring the values obtained for the temperature difference at each output and comparing them with those provided by the manufacturer in Table 2.

MASS AND ENERGY BALANCE
Once the materials and the measurements to be taken have been described, the first part of the laboratory experience can be performed. According to the law of mass conservaton for the control volume depicted in Figure 2, at steady state, the total incoming and outgoing mass fow rates are equal and therefore: The energy balance at steady state is evaluated for different values of the cold fracton, y. Due to the short length of the cold arm, the heat exchanged by the cold fow can be considered negligible so the control volume shown in Figure 2 is such that it allows considering just the heat exchanged by the hot fow.
The pressure and temperature of the incoming and outgoing fows are measured. As mentoned earlier, different tests have been performed by regulatng the outgoing cold fracton, so the temperatures of the outgoing fows vary accordingly. The cold fracton and the outgoing fows are determined using fow meters or the tables provided by the manufacturer. At steady state, the total rate at which energy is transferred into the control volume equals the total rate at which energy is transferred out and therefore: Although the tube is usually considered to be an adiabatc system, based on the obtained results and the didactc nature of the laboratory experience, the difference between the enthalpy and kinetc energy at the inlet and outlet secton is considered to be equal to the heat exchanged. As mentoned above, in order to minimize the heat transfer in the cold arm, its length has been shortened in the control volume, so the rate of heat transfer evaluated in the energy balance, Q , can be considered to be equal to the heat transfer from the hot arm. Figure 4 shows a thermal image of the vortex tube operatng with a cold fracton y = 0.75.
The additon of the kinetc energy of the air to the balance has also been consid ormuered appropriate, due to the contributon it makes (especially in the inlet stream) and to reinforce the didactc nature of the proposed practcal work.   Table 4 exhibits the values, all expressed in kJ/kg, associated with the energy balance terms for these two tests. Thermodynamics tables of the ideal gas air are used to obtain the enthalpy values in the working conditons. The ideal gas equaton of state is used to calculate the specific volume of the air at each measurement point.

T e (K) T in (K) p in (bar) T cold (K) p cold (bar) T hot (K) p hot (bar) y ṁ (kg/s)
Using these values, the air velocity and the kinetc energy are calculated for introducton into the energy balance. The use of a spreadsheet program is suggested to simplify the calculaton of the results of the different tests and to make it easier to obtain results when small changes in the input data are made.

MAXWELL'S DEMON
By observing the air fow splitng in two fows at different temperatures, we can gain a better understanding of one of the classic mental experiments of thermodynamics: Maxwell's Demon. James Clerk Maxwell unified the theories behind electromagnetsm and also worked in other fields, including thermodynamics. In his book "Theory of the Heat", he proposed the following example under the heading "Limitaton of the second law of thermodynamics".

"For we have seen that the molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifer molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."
The described process could be considered similar to the one that occurs inside the vortex tube, where an air fow is separated into two separate fows, hot and cold, apparently without any work applied. It therefore seems that the entropy of the system would diminish. This approach, apparently in violaton of the Second Law, is refuted in various ways, usually associated with the process of distnguishing between the two types of molecules and the entropy generated to perform the distnguishing acton (Bennett, 1982). At this point, it is possible to ask about the phenomenon which occurs in the vortex tube.
The same approach can be taken in a different way. When two fows at different temperatures are mixed, there is a positve generaton of entropy. This is a typical exercise to be discussed in class, reaching the conclusion that when a fow is separated into two streams at different temperatures, the entropy would decrease and the process should be impossible. The key point in this experiment is the pressure applied to the fow. There is a decrease in the pressure between the inlet and outlet fows, and this decrease in mechanical energy associated with pressure is converted into thermal energy. As a result, there is a significant amount of entropy generated during the process and the subsequent destructon of exergy, as we will see in the following paragraphs. Therefore, at this point, entropy and exergy balances will be created in order to study and understand the behavior of the system.

ENTROPY BALANCE
Everyday experience tells us that not every process consistent with the principle of mass and energy conservaton can occur. The Second Law of thermodynamics provides a guiding principle and shows whether partcular spontaneous processes occur and makes it possible to deduce their directons. Thus, the Second Law requires that entropy producton (σ) results in a value that is either positve or zero. In a hypothetcal process, once the entropy balance is obtained, if the value of the generated entropy is negatve, this means that the process cannot happen, i.e., it is impossible.
The steady-state form of the entropy rate balance for the system of Figure 2 is applied to obtain the value of the entropy producton. This value will be used to check the Gouy-Stodola relatonship once the exergy balance has been reached.
Vol. 3(3), 2013, pp 127 The entropy rate balance at steady state takes the following form: At this point, it is necessary to calculate the entropy change in the air between the inlet and outlet states.
Assuming the ideal gas model for the air, this calculaton has been performed based on the premise that either the specific heat at constant pressure c p is constant or taking in account its variaton with temperature as follows: These two methods are presented during the course, so their use will reinforce the work done with the ideal gas model of air.
When performing the calculatons, the difference between input and output pressures can be observed. The decrease in pressure explains why the fow splits into a hot and a cold fow; this is the reason why the entropy generaton obtained is positve, and there is no contradicton with the Second Law.
The values obtained for the entropy producton in the two tests and the two ways to consider the specific heat c p are refected in Table 5. As can be observed, both results are similar. Using a program such as TERMOGRAF (http://termograf.unizar.es/), the value for s i -s in can be calculated for the air as a real gas. Small deviatons will be observed between the different methods, which demonstrates how a simplified model such as the ideal gas model is valid under the proposed conditons.
The use of the T hot value has been simplified. The term Q / T hot is related to the entropy associated with the heat transfer. As seen in the thermography image in Figure 4, the temperature is not constant along the hot arm, even though in the calculatons, the temperature of the outer surface of the hot arm has been considered uniform, and equal to the mean value of the hot stream temperature (T hot ).

EXERGY BALANCE
In order to better understand and assess the results, a steady-state exergy rate balance is performed. This will allow quantfying the irreversibilites that occur in the compressed air as a result of its parttoning into two streams. This enables us to obtain the value of the rate of exergy destructon, Ḋ, and quantfy the energetc degradaton of the air passing through the vortex tube.
The exergy rate balance at steady state can be written as: where b in -b i is the difference in the specific fow exergy between the inlet state and the hot and cold outlet states, plus the kinetc energy change. Therefore: Gouy-Stodola relaton can also be verified, as the exergy destructon and the entropy generaton are described by the equatonḊ =T oσ (6) The tests results obtained are shown in Table 6. As expected, the Gouy-Stodola law is fulfilled, and the analysis that has been carried out can be considered correct.
To conclude the laboratory experience, the exergetc efficiency of the process is evaluated in two different ways: directly, comparing output exergy to the input exergy, η=ṁ in yb cold +ṁ in ( 1− y) b hoṫ m in b in ; and indirectly, through the exergy destructon and the exergy losses associated with the heat that was exchanged The values obtained by both expressions should be similar in order for the experiment to be considered successful.

DEVELOPMENT OF THE WORK
The lab program can be approached in two different ways, using either a teacher-lecture approach or a student-centered approach. In our case, a problem based-learning (PBL) methodology (Felder & Silverman, 1988;Hmelo-Silver, 2004) is applied, because we consider it much more effectve for the internalizaton of learning and skill development. This PBL methodology is widely accepted (Scott, Hadgraf & Ilic, 2003;Hsieh & Knight, 2008), and it is proposed with the aim of achieving a better understanding of the concepts behind the conservaton and non-conservaton of balances, as well as the different terms involved.
For each lab session, the entre class is divided into several four-student groups to encourage team work. Each group performs the experiment and writes down the data obtained. No later than fifeen days afer the practcum is performed, each group is required to submit a report. The content of this report is a general descripton of the experiment carried out and an analysis of the results obtained through the data measured. The aim of this report is to help students improve their critcal thinking and their written communicaton skills. There are five labs scheduled throughout the academic year, with different group members for each. The grade for the reports given for each lab accounts for 20% of the final mark for each student.
The lab session is held at a tme of the year when most of the course syllabus has already been completed, so it can be used as a review and as a way to evaluate the acquired knowledge before the final evaluaton takes place. Moreover, some transversal concepts are introduced, such as how a vortex tube works, the small errors made when using the ideal gas model under experimental conditons and historical references to Maxwell, his work and his era.

CONCLUSIONS
An attractve, easy-to-prepare and inexpensive program of laboratory experiences is proposed. During the course of the lab sessions, most of the syllabus for a course in thermodynamics is covered, including topics such as the ideal gas model, mass and energy conservaton, entropy producton and exergy destructon, as applied to a partcular control volume, such as the vortex tube and the Gouy-Stodola relatonship. In additon, Vol. 3(3), 2013, pp 129 the lab allows the introducton of some historical thermodynamic concepts that may be outside the scope of a regular course, such as the menton made of Maxwell's demon and his work in the field of thermodynamics.
Worth highlightng is the proposed introducton to the concept of irreversible processes and the entropy generaton associated with them through the concept of Maxwell's demon. The theoretcal impossibility of the process in the vortex tube is initally proposed, although this point is then clarified, taking into account the decrease in pressure between the inlet and outlet fows.
Within the ideal gas model, two methods are proposed to calculate the terms associated with the change in entropy that occurs in the entropy rate balance, followed by a comparison between them. The Gouy-Stodola relatonship is checked, and the exergetc efficiency of the process is calculated both directly and indirectly. Any deviaton would indicate an incorrect approach or errors in the calculatons.
The use of a spreadsheet to perform the calculatons allows students to evaluate different configuratons of the vortex tube in a relatvely simple manner. This can also be used to understand how the variaton of the different parameters (input pressure, y fracton, etc.) affects the results obtained and to gain a better understanding of the subject, as well as to improve critcal thinking skills.
Afer reviewing many reports written by students who have taken part in the lab sessions, we can highlight that the most common errors are in the evaluaton of the kinetc energies, as well as in the proper approach to the exergy balance.