Parameters Optimization of Tube Type, Pressure, and Mass Fraction on Vortex Tube Performance Using the Taguchi Method

Parameters Optimization of Tube Type, Pressure, and Mass Fraction on Vortex Tube Performance Using the Taguchi Method

Alfan SarifudinDanar Susilo Wijayanto Indah Widiastuti 

Department of Mechanical Engineering Education, Faculty of Teacher Training and Education, Universitas Sebelas Maret, Sutami No.36 A Road, Pucangsawit, Jebres, Surakarta City, Central Java Province, Zip Code 57126, Indonesia

Corresponding Author Email: 
alfansarifudin@merahputih.id
Page: 
597-604
|
DOI: 
https://doi.org/10.18280/ijht.370230
Received: 
20 May 2019
|
Accepted: 
28 June 2019
|
Published: 
30 June 2019
| Citation

OPEN ACCESS

Abstract: 

The purpose of this study is to analyze the parameters of cold temperature and coefficient of performance refrigeration (COPref) of the vortex tube cooling machine and how much the contribution of each parameter to the performance. This analysis also aims to predict the optimal value of cold temperature and COPref of the vortex tube as well as to predict the condition of how the optimal value is obtained. To find out whether the analysis is suitable for optimizing the performance, then the confirmation data verification is done to know the error level. The parameters considered in the experiment were the tube type consisting of natural cooling and forced cooling, the pressures are 0.5bar, 1.0bar, and 1.5bar, and fractions are 30 %, 40 %, 50 %, 60 %, and 70 %. The results of the experimental test optimized using the Taguchi method where data is reduced by selecting the three optimal fractions in each response. Obtained that tube type, pressure, and fraction are factors that influence performancewith the level of error for predicting the optimal value at cold temperatures is <5 %. This study provides an analysis of the contribution of improved design of vortex tube performance parameters that are efficient experimental and reliable statistics.

Keywords: 

could temperature, coefficient of performance refrigeration (COP), cooling machine, natural cooling, forced cooling, parameter design, efficient experimental and reliable statistics

1. Introduction

Current cooling machine needs cannot be separated from daily life. One of the cooling devices used in the industrial world is vortex tube.  This tool can only be used with compressible air that is sprayed, so this tool is very environmentally friendly because it does not produce dangerous freon emissions. Vortex tube in a works system has no moving parts therefore it does not require maintenance costs for wear components due to friction, which makes it more economical in maintenance [1].

Many research efforts to improve the performance of this tool have been carried out. It was found that forced cooling by flowing water on the tube surface with conductor material can reduce the cold temperature of the vortex tube and increase its thermal efficiency [2]. Changes in temperature and coefficient of performance refrigeration (COPref) are also influenced by mass fractions [3-6]. Other vortex tube performance parameters are pressure, whereas the higher pressure results in lower temperature [4-5, 7].

For the purposes of optimization, parameters that have been found are not yet known for the contribution to the performance of vortex tubes simultaneously. To solve the case requires effort, cost and time are expensive if tested in a thorough experiment. Based on these problems an efficient design of experiments is needed. Considering this reason system testing and modeling using numerical analysis, or optimizing the test numbers based on the Taguchi method is more appropriate and very popular today [8].

Experimental Design by optimizing control parameters to get the best results is achieved by the Taguchi Method. The Taguchi method is an effective technique for completing instrument test processes that work reliably and ideally solve various conditions [9]. "Orthogonal Array" (OA) provides a series of experiments that are balanced (minimum) well and the ratio Taguchi [S/N], which is a log function of the desired output, serves as an objective function for optimization, helps in data analysis and optimum prediction results [10].

In this study, data parameters were obtained by taking data using experiments and mathematical analysis. Cold air temperature is obtained from taking experimental data and COPref is obtained from experimental data which is then processed with mathematical analysis. Taguchi analysis is used to estimate the parameters that contribute to factor response of cold temperature and COPref vortex tube. This analysis is also used to predict the optimal cold value of temperature and COPref of vortex tube, also to predict the condition of how the optimal value is obtained. To find out whether the Taguchi analysis is suitable for optimizing the performance of vortex tube, verification of the data is carried out to find out the error.

2. Analytical Method

2.1 Mathematical analysis method of COPref

COPref is a dimensionless number to express the value of the cooling effect that can be done by a cooler or a heat pump. To calculate the coefficient value of vortex tube cooling performance as follows [3]:

$CO{{P}_{ref}}={{\dot{Q}}_{c}}/\dot{W}$ (1)

The value of heat flow in cold air on the vortex tube is [7]:

${{\dot{Q}}_{c}}={{\dot{m}}_{outc}}Cp({{T}_{c}}-{{T}_{in}})$ (2)

By using mass flow equilibrium the equations become [7]:

${{\dot{m}}_{in}}={{\dot{m}}_{outc}}+{{\dot{m}}_{outh}}$ (3)

The value of incoming mass flow on the vortex tube is [13]:

${{\dot{m}}_{in}}=\rho {{\dot{V}}_{in}}$ (4)

The nature of the air is that it can be compressed, while the value of ρ changes according to the conditions of pressure, temperature and dew point. In the vortex tube inlet channel, the thermodynamic system is isochoric and isothermal. The equation in this condition has been developed by Herman Wobus as follows [11]:

$\rho =\frac{Pd}{287.0531({{T}_{in}}+273.15)}+\frac{Pv}{461.4964({{T}_{in}}+273.15)}$ (5)

$Pd=P-Pv$ (6)

$Pv=Es(T{{d}})$ (7)

$Es=eso/{{P}^{8}}$ (8)

The total energy entering the vortex tube can be shown as follows [3, 12]:

$\dot{W}={{\dot{m}}_{in}}R{{T}_{in}}\ln ({{P}_{in}}/{{P}_{atm}})$ (9)

To get the R-value, it employed the following equation [13]:

$R={{P}_{in}}/\rho {{T}_{in}}$ (10)

The equation for taking the valve opening ratio data variable is [3, 12]:

${{\varepsilon }_{c}}={{\dot{m}}_{outc}}/{{\dot{m}}_{in}}$ (11)

${{\varepsilon }_{c}}={{\vec{v}}_{cn}}/{{\vec{v}}_{cmax}}$ (12)

Figure 1. Mathematical method analysis diagram

2.2 Taguchi method

Taguchi developed a special orthogonal array design to study all parameter spaces with only minimum experiments. The Taguchi method uses a measure of performance statistics called the [S/N] ratio [14]. This method is used to reduce the number of experiments needed to achieve the goal depending on various parameters [15].

The [S/N] ratio is used to measure the characteristic quality deviating from the desired value. There are three categories in the signal to ratio analysis, namely [14]:

larger is better,

$\frac{S}{N}ratio(\eta )=-10\times {{\log }_{10}}\frac{1}{n}\sum\nolimits_{i=1}^{n}{\frac{1}{y_{1}^{2}}}$ (13)

nominal is best,

$\frac{S}{N}ratio(\eta )=-10\times {{\log }_{10}}\sum\nolimits_{i=1}^{n}{\frac{1}{n}}\frac{{{\mu }^{2}}}{{{\sigma }^{2}}}$ (14)

smaller is better,

$\frac{S}{N}ratio(\eta )=-10\times {{\log }_{10}}\sum\nolimits_{i=1}^{n}{y_{1}^{2}}$ (15)

Techniques of Analysis of variance (ANOVA) is used to test the adequacy of the model. This method is very useful to reveal the level of significance of the influence of factors or factors of interaction on a particular response. This separates the total variability of responses into the contributions given by each parameter and error [16].

$S{{S}_{Tot}}=S{{S}_{F}}+S{{S}_{e}}$ (16)

where,

$S{{S}_{Tot}}=\sum\nolimits_{j=1}^{p}{({{\gamma }_{j}}}-{{\gamma }_{m}})$ (17)

The mean square deviation in the ANOVA table is defined as [16]:

$MS=\frac{SS}{DF}$ (18)

The F-value of the Fisher ratio (variance ratio) is defined as:

$F=\frac{M{{S}_{t}}}{M{{S}_{et}}}$ (19)

The contribution of each factor is calculated by the following formula [14]:

$C\%=\frac{S_A}{S_z}$(20)

where,

${{S}_{z}}={{S}_{A}}+{{S}_{B}}+{{S}_{C}}$ (21)

In the last step of Taguchi's analysis, a data confirmation is performed to verify the most optimal parameters [16].

3. Experimental Conditions

This study uses a type 1 vortex tube which uses no forced cooling and a type 2 which uses forced cooling on the heat tube. The dimensions of this tool are as follows: Din 5mm, Doutc 5mm Douth 8.5mm, Ltubec 40mm, Ltubeh 105mm, αplug 70 ±2o, and Ng 4. The size of the generator specifications is shown in Figure 4.

Figure 2. Dimension of vortex tube type 1

In Vortex tube type 1 forced cooling is developed by adding a tube that covers the hot tube. The material is made of PVC. Furthermore, in the tube flowed aquades (H2O) with contraflow flow direction and flow velocity 7 liters/minute. The incoming water temperature is controlled at 27 oC.

Figure 3. Dimension of vortex tube type 2

Figure 4. Size of generator specifications

Tests were carried out in Tr 27 oC conditions. The variables used are εcn 30 %, 40 %, 50 %, 60 %, and 70 % and pressure 0.5 bar, 1.0 bar, and 1.5 bar. In each of these variables, data was taken four times randomly with a duration interval of at least 5 seconds.

The series of experimental device for vortex tube type 1 is shown in Figure 5. The series of experimental tool for vortex tube type 2 shown in Figure 6.

Figure 5. Experiment series of vortex tube type 1

Figure 6. Experiment series of vortex tube type 2

Table 1. Information on Figures 5 and 6

No

Name

Function

Unit (Symbol)

1

Compressor

Pressurized air supply

-

2

Digital Thermometer

Measuring the temperature of the air inlet

oCelcius

(${{T}_{in}}$)

3

Dew point Meter

Measuring the inlet air dew point

oCelcius

($T{{d}}$)

4

Flow meter

Measuring air flow

Liter/min

5

Pressure Gauge

Measuring inlet air pressure

Bar

(P)

6

Vortex tube

Test instrument

-

7

Thermocouple

Measuring hot and cold outlet air temperature

oCelcius

(Tc) and

(Th)

8

Anemometer

Measuring the speed of cold outlet air

meter/sec

$({{v}_{\max }})$ and

$({{v}_{n}})$

9

Computer

Processing observation data from each measuring instrument

-

10

Digital Thermometer

Measuring water temperature

oCelcious

11

Flow meter (water)

Measuring water discharge

Liter/min

12

Pump

pumping cooling water

-

13

Vessel

Cooling water container

-

4. Results and Discussion

4.1 Presentation of experimental data

The experimental results of cold outlet temperature data and COPref of vortex tube are presented in the following diagram:

Figure 7. Cold temperature chart

Figure 8. COPref chart

Cold temperature data presented in Figure 7 shows the tendency for the 40 % fraction to be the best. Higher pressure results in lower temperature of the cold outlet. Hamdan which has performed an experiment with different dimensions and forms of vortex tube also found for the pressure at 2bar, 3bar, and 4bar [7]. However an anomaly was found at 5bar pressure. The forced cooling on the heat tube affects the decreasing of temperature produced. These results are in accordance with the results of Eimsa's research in which cooling the heat tube by flowing water on the surface can reduce the temperature of the cold tank [2].

Based on Figure 8, it is found that the increasing cold fraction (εc) produces a better COPref. These results are also in accordance with Aydın's research with vortex tube dimensions and different generator forms found that cold fractions (20 % to 80 %) the greater the yield of COPref the better [1]. In this experiment, higher pressure produces lower COPref. The forced cooling treatment produces a better COPref. Eimsa by measuring isotropic efficiency found that cooling the surface of a hot tube by flowing water can improve its efficiency value [2].

4.2 Data reduction

For processing data with the Taguchi method, data reduction is done on the fraction factor to three levels that produce the best value. The cold temperature data that is produced smaller is the best and the COPref data the larger is the best. The selected data reduction is as follows:

Table 2. Reduction of cold temperature average data

Tube Type (TT) Natural Cooling (1)

Fraction (εc)

Pressure (P) (bar)

0.5 (1)

1.0 (2)

1.5 (3)

30%(1)

21.65

18.05

15.525

40%(2)

21.1

17.05

14.925

50%(3)

21.9

18.35

16.125

Tube Type (TT) Forc Cooling (2)

Fraction (εc)

Pressure (P) (bar)

0.5 (1)

1.0 (2)

1.5 (3)

30%(1)

20.600

16.375

13.950

40%(2)

20.200

15.525

13.450

50%(3)

20.400

16.125

13.625

 Table 3. Reduction of COPref data

Tube Type (TT) Natural Cooling (1)

Fraction (εc)

Pressure (P) (bar)

0.5 (1)

1.0 (2)

1.5 (3)

40%(1)

-0.074

-0.074

-0.070

60%(2)

-0.081

-0.081

-0.079

70%(3)

-0.085

-0.083

-0.083

Tube Type (TT) Force Cooling (2)

Fraction (εc)

Pressure (P) (bar)

0.5 (1)

1.0 (2)

1.5 (3)

40%(1)

-0.096

-0.093

-0.087

60%(2)

-0.112

-0.104

-0.097

70%(3)

-0.123

-0.111

-0.100

 

4.3 Determining the orthogonal matrix

The orthogonal matrix is determined using statistical software Minitab 18. The orthogonal matrices used are L36 (21 32), where:

L       : Latin square design,

36     : number of lines or experiments,

21     : one-factor column for two level, and

32     : two-factor column for three level.

4.4 Calculating the ratio of [S/N]

The data obtained from the experimental results are processed into the form of [S/N] ratio to determine the factors that influence the temperature of the vortex tube cold outlet. The [S/N] Signal-to-noise formula used for the cold temperature produced the smaller is better with equation (15), and for the COPref the larger is better with equation (13).

The most decisive parameter for vortex tube performance results for cold temperature show in Figure 9 and Table 5. The most determining parameters for the least related are pressure, tube type, and fraction. The value of cold temperature based on the calculation of [S/N] ratio is reached on the factor of tube type 2 (forced cooling), pressure 3 (1.5 bar) and fraction 1 (30 %).

 Table 4. [S/N] Rasio Ortogonal Matriks L36 (21×32)

Exsperiment Number

Coloum Number

[S/N] Rasio

1

(TT)

2

(P)

3

c)

Tc

COPref

1

1

1

1

-26.709

-22.587

2

1

2

2

-24.634

-21.814

3

1

3

3

-24.150

-21.638

4

1

1

1

-26.709

-22.587

5

1

2

2

-24.634

-21.814

6

1

3

3

-24.150

-21.638

7

1

1

1

-26.709

-22.587

8

1

2

2

-24.634

-21.814

9

1

3

3

-24.150

-21.638

10

1

1

1

-26.709

-22.587

11

1

2

2

-24.634

-21.814

12

1

3

3

-24.150

-21.638

13

1

1

2

-26.486

-21.805

14

1

2

3

-25.273

-21.612

15

1

3

1

-23.821

-23.107

16

1

1

2

-26.486

-21.805

17

1

2

3

-25.273

-21.612

18

1

3

1

-23.821

-23.107

19

2

1

2

-26.107

-19.031

20

2

2

3

-24.150

-19.628

21

2

3

1

-22.891

-21.197

22

2

1

2

-26.107

-19.031

23

2

2

3

-24.150

-19.090

24

2

3

1

-22.891

-21.197

25

2

1

3

-26.193

-18.216

26

2

2

1

-24.284

-20.677

27

2

3

2

-22.574

-20.279

28

2

1

3

-26.193

-18.216

29

2

2

1

-24.284

-20.677

30

2

3

2

-22.574

-20.279

31

2

1

3

-26.193

-18.216

32

2

2

1

-24.284

-20.677

33

2

3

2

-22.574

-20.279

34

2

1

3

-26.193

-18.216

35

2

2

1

-24.284

-20.677

36

2

3

2

-22.574

-20.279

 
 
 

Figure 9. Main effects plot for [S/N] ratio for cold temperature

 Table 5. Response table for signal to noise ratios for cold temperature

Level

Tube Type (TT)

Pressure (P)

Fraction (εc)

1

-25.18

-26.37

-24.43

2

-24.37

-24.59

-24.95

3

 

-23.36

-24.94

Delta

0.81

3.01

0.52

Rank

2

1

3

The parameters that have the most influence on COPref are shown in Figure 10 and Table 6. The parameters that most influence COPref from the most influential are type of tube, fraction, and pressure. The optimum COPref is achieved in tube type 2 (force cooling), pressure 1 (0.5 bar) and fraction 3 (70 %).

 Figure 10. Main effects plot for [S/N] Ratio for COPref

Table 6. Response table for signal to noise ratios for COPref

Level

Tube Type (TT)

Pressure (P)

Fraction (εc)

1

-22.09

-20.41

-21.89

2

-19.79

-20.87

-20.73

3

 

-21.56

-20.21

Delta

2.30

1.15

1.68

Rank

1

3

2

4.5 ANOVA test

The ANOVA results for the [S/N] ratio were obtained using Minitab 18 statistical software as shown in Table 7 for cold temperatures, and Table 8 for COPref. The p-value shown in the ANOVA table shows the significance of each variable in the results. Factors are said to have a significant effect if the p-value is <0.05 [14-15]. In the table all p-values are 0, so all factors have a significant effect on cold temperature and COPref.

The F-test concept states that the higher the F-value, the more significant the factor is [15]. The results show that the order of influence for each factor for the ANOVA test whit the [S/N] ratio test is the same. 

Table 7. Analysis of variance cold temperature

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Tube Type

1

21.468

21.468

401.48

0.000

Pressure

2

232.588

116.294

2174.85

0.000

Fraction

2

4.633

2.317

43.33

0.000

Error

30

1.604

0.053

   

Lack-of-Fit

6

1.604

0.267

*

*

Pure Error

24

0.000

0.000

   

Total

35

260.294

     

Table 8. Analysis of variance COPref

Source

DF

Adj SS

Adj MS

F-value

P-value

Tube Type

1

0.005391

0.005391

522.59

0.000

Pressure

2

0.000876

0.000438

42.46

0.000

Fraction

2

0.002072

0.001036

100.42

0.000

Error

30

0.000309

0.000010

   

Lack-of-Fit

6

0.000287

0.000048

51.52

0.000

Pure Error

24

0.000022

0.000001

   

Total

35

0.008648

     

Equations (20) and (21) are utilized to find out how much the contribution of each factor is used on. The magnitude of the contribution of each factor is shown in the following Table 9:

Table 9. Contributions of each factor

Factor

Response

Cold Temperature

COPref

Tube Tipe

8.25%

62.34%

Pressure

89.36%

10.13%

Fraction

1.78%

23.96%

Error

0.62%

3.57%

Lack-of-Fit

0.62%

3.32%

Pure Error

0.00%

0.25%

Total

100%

100%

 
The contribution of a factor is an absolute value that illustrates how a test factor influence the responses. The greater the contribution value of the factor, the more influential the response factor will be. Based on Table 9, the contribution of each factor to the cold temperature of the most influential is tube type 8.25%, pressure 89.36 %, and fraction 1.78 %. The contribution of factors in COPref from the most influential is the tube type 62.34 %, pressure 10.13 %, and fraction 23.96 %.

4.6 Regression analysis

The regression equation is used to determine the value of the predictive response of each factor tested. To get the regression equation, Minitab 18 statistical software is used. The regression equation for cold temperatures Tc and COPref is as follows:

 $R{{T}_{c}}=17.5194+0.7722T{{T}_{1}}-0.7722T{{T}_{2}}+\\ 3.3806{{P}_{1}}-0.6319{{P}_{2}}-2.7486{{P}_{3}}+\\0.0681{{F}_{1}}-0.4694{{F}_{2}}+0.4014{{F}_{3}}$ (22)

$RCO{{P}_{ref}}=0.091198-0.012237T{{T}_{1}}+0.012237T{{T}_{2}}\\0.006656{{P}_{1}}-0.001517{{P}_{2}}-0.005139{{P}_{3}}-\\0.009439{{F}_{1}}+0.000303{{F}_{2}}+0.009136{{F}_{3}}$ (23)

where,

       =   pressure factor

F         =    fraction factor

TT       =   tube type factor

The regression equation above does not apply to all factor variables on vortex tube. This equation applies only to the factors and levels specified in this analysis.

4.7 Prediction of optimal value

Based on the value of [S/N] ratio and regression equation 22 and 23, the optimal predictive value is obtained:

${{T}_{c\_op}}=17.5194-0.7722~T{{T}_{\text{2}}}-~2.7486~{{P}_{\text{3}}}+~0.0681~{{F}_{\text{1}}}\\{{T}_{c\_op}}=17.5194-0.7722-2.7486+0.0681\\{{T}_{c\_op}}=14.07℃$ (24)

$CO{{P}_{ref\_op}}=0.091198+0.012237T{{T}_{\text{2}}}+\\ 0.006656{{P}_{\text{1}}}+0.009136{{F}_{\text{3}}}\\ CO{{P}_{ref\_op}}=0.091198+0.012237+0.006656+0.009136\\ CO{{P}_{ref\_op}}=0.119227$ (25)

4.8 Data confirmation

Data confirmation is performed by comparing the results of predictions with the experimental results presented in Table 10 below:

Table 10. Data Confirmation

Response

Experiment

Prediction

Error (%)

Level Factor

Value

Level Factor

Value

 

Cold Temperature

TT2;P3;F2

13.45

TT2;P3;F1

14.07

4.61%

COPref

TT2;P1;F3

0.123

TT2;P1;F3

0.119

3.09%

 

Based on Table 10 the level of error using the Taguchi method to predict the optimum value is 4.61 % for predictions of cold temperatures and 3.09 % for prediction of COPref.

5. Conclusion

It can be concluded that the optimization of vortex tube performance on parameters of tube type, pressure, and mass fraction with the Taguchi method are:

  1. Tube type, pressure, and mass fraction are factors that influence cold temperatures and COPref.
  2. The contribution of the influence of each factor to the cold temperature are pressure 89.36 %, tube type 8.25 %, and fraction 1.78 %.
  3. The contribution of each factor to COPref are tube type 62.34 %, fraction 23.96 %, and pressure 10.13 %.
  4. The most optimal cold temperature is predicted at 14.07 oC which occurs in the type of tube with forced cooling, 1.5 bar pressure, and 30 % fraction.
  5. The optimal COPref is predicted to be 0.119227 for the type of forced cooling tube, 0.5bar pressure and 70 % fraction.
  6. The error rate of Taguchi method for predicting the optimal value at cold temperatures is 4.61 % and at COPref is 3.09 %.

Based on the conclusions, it is known how the influence of tube type, pressure and fraction, so that this research can be a reference for the next research about optimization of vortex tube performance. The Taguchi method will be more accurate if use more number of level on each factor. In this study, the number of levels on each factor is small so that for further research to obtain the optimization of vortex tube performance with increasingly accurate results is done by increasing the number of levels in the pressure factor and fraction. In order for testing experiments to continue with effort, cost and time that is cheap, the level of factor is determined by referring to the most optimal point in this study.

The testing of the Taguchi method to measure the influence of tube types to the performance of vortex tubes in this study has only differentiated which ones have the most optimal performance. The results showed that the vortex tube with the type of forced cooling tube produced the most optimal performance. Based on these findings, the potential for optimizing the performance of vortex tube for further research is the engineering of forced cooling on the surface of the heat tube and the engineering of the heat flow.

Nomenclature

COP

coefficient of performance refrigeration

$\dot{Q}$  

heat flow

$\dot{W}$    

total energy      

$\dot{m}$     

mass flow rate

Cp

heat capacity

 

Temperatur

$\dot{V}$  

volume flow rate

Es   

saturation vapor pressure

C    

coefficient

eso 

Herman Wobus constant (6.1078)

 

air pressure

Pv   

pressure of water vapor

Es   

saturation vapor pressure

Td   

dew point temperature

Pv

water vapor pressure

R

universal gas constan

 

$\vec{v}$

air velocity

SS

squared deviations number

$\gamma$

average response

MS

mean square deviation in the ANOVA table

DF

degre of fredom

C%

contribution of each factor

S

each factor

Greek symbols

$\rho$

density

$\varepsilon$

fraction

Subscripts

ref  

refrigeration

c

cold

outc

cold temperatures come out

outh

hot temperatures come out

in

inlet

cn

cold outlet variable to n

c max

cold outlet maximum conditions

Tot

total number

F

beacause of  each other

E

due to error

j

for the jth experiment

m

for all experimental conditions

t

MS for a term

et

MS for the error term

Z

total Sum

A, B, C

each vaktor to A, B, C,. . .

op

optimal predictive

  References

[1] Aydin, O., Markal, B., Avci, M. (2010). A new vortex generator geometry for a counter-flow RanqueeHilsch vortex tube. Applied Thermal Engineering, 30(16): 2505-2511. https://doi.org/10.1016/j.applthermaleng.2010.06.024

[2] Eiamsa-ard, S., Wongcharee, K., Promvonge, P. (2010). Experimental investigation on energy separation in a counter-flow Ranque–Hilsch vortex tube: Effect of cooling a hot tube. International Communications in Heat and Mass Transfer, 37(2): 156–162. https://doi.org/10.1016/j.icheatmasstransfer.2009.09.013

[3] Attalla, M., Ahmed, H., Salem Ahmed, M., AboEl-Wafa, A. (2017). Experimental investigation for thermal performance of series and parallel Ranque-Hilsch vortex tube systems. Applied Thermal Engineering, 123: 327-339. https://doi.org/10.1016/j.applthermaleng.2017.05.084

[4] Alizadeh, M. (2018). Three dimensional numerical (3D CFD) study of effect of pressure-outlet and pressure-far-field boundary conditions on heat transfer predictions inside vortex tube. Progress in Solar Energy and Engineering Systems, 2(1): 21-25.

[5] Sadeghiazad, M.B.M. (2017). Experimental and numerical study on the effect of the convergence angle, injection pressure and injection number on thermal performance of straight vortex tube. International Journal of Heat and Technology, 35(3): 651-656. https://doi.org/10.18280/ijht.350324

[6]  Sadeghiazad, M.B.M. (2017). Experimental study on thermal performance of double circuit vortex tube (DCVT) - Effect of heat transfer controller angle. International Journal of Heat and Technology, 35(3): 668-672. https://doi.org/10.18280/ijht.350327

[7] Hamdan, M.O., Al-Omari, S.A.B., Oweime, A.S. (2018). Experimental study of vortex tube energy separation under different tube design. Experimental Thermal and Fluid Scienc, 91: 306-311. https://doi.org/10.1016/j.expthermflusci.2017.10.034

[8] Pinar, A.M., Uluer, O., Kırmaci, V. (2009). Optimization of counter flow Ranque–Hilsch vortex tube performance using Taguchi method. International journal of  refrigeration, 32(6): 1487-1494. https://doi.org/10.1016/j.ijrefrig.2009.02.018

[9] Yallamati, A., Vinjavarapu, S., Ashok, K.N. (2018). Using Taguchi method & response surface methodology for examination of surface roughness. Modelling Measurement and Control B, 87(1): 42-54.

[10] Suresh Kumar, G., Padmanabhan, G., Dattatreya Sarma, B. (2014). Optimizing the temperature of hot outlet air of vortex tube using Taguchi method. Procedia Engineering, 97: 828-836. https://doi.org/10.1016/j.proeng.2014.12.357

[11] Thøgersen, M.L. (2005). Modelling of the variation of air density with altitude through pressure, humidity and temperature. EMD International A/S, Niels Jernesvej, Aalborg, USA.

[12] Gao, O. (2005). Experimental Study on the Ranque-Hilsch Vortex Tube. Technische Universiteit Eindhoven, Australia.

[13] Çengel, Y.A., Cimbala, Y.M. (2014). Fluid Mechanics: Fundamentals and Applications, Third Edition. The Mcgraw-Hill Companies Inc, New York, USA.

[14] Derdour, F.Z., Kezzar, M., Bennis, O., Lakhdar, K. (2018). The optimization of the operational parameters of a rotary percussive drilling machine using the Taguchi method. World Journal of Engineering, 15(5): 62-69. https://doi.org/10.1108/WJE-03-2017-0067

[15] Zade, S.K., Suresh, B.V., Sai, S.K.V. (2018). Effect of nanoclay, glass fiber volume and orientation on tensile strength of epoxy-glass composite and optimization using Taguchi method. World Journal of Engineering, 15(1): 312-320. https://doi.org/10.1108/WJE-08-2017-0286

[16] Sreeraj, P., Kannan, T., Subhasis, M. (2014). Analysis of flux cored arc welding process parameters by hybrid Taguchi approach. World Journal of Engineering, 11(6): 575-588.