OPEN ACCESS
The purpose of this study is to analyze the parameters of cold temperature and coefficient of performance refrigeration (COP_{ref}) 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 COP_{ref} 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 performance_{}with 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.
could temperature, coefficient of performance refrigeration (COP), cooling machine, natural cooling, forced cooling, parameter design, efficient experimental and reliable statistics
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 (COP_{ref}) are also influenced by mass fractions [36]. Other vortex tube performance parameters are pressure, whereas the higher pressure results in lower temperature [45, 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 COP_{ref} 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 COP_{ref} vortex tube. This analysis is also used to predict the optimal cold value of temperature and COP_{ref} 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.
2.1 Mathematical analysis method of COP_{ref}
COP_{ref} 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)
$Pd=PPv$ (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 Rvalue, 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 Fvalue 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].
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: D_{in} 5mm, D_{outc} 5mm D_{outh} 8.5mm, L_{tubec} 40mm, L_{tubeh} 105mm, α_{plug} 70 ±2^{o}, 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 (H_{2}O) with contraflow flow direction and flow velocity 7 liters/minute. The incoming water temperature is controlled at 27 ^{o}C.
Figure 3. Dimension of vortex tube type 2
Figure 4. Size of generator specifications
Tests were carried out in T_{r} 27 ^{o}C conditions. The variables used are ε_{cn} 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 
^{o}Celcius (${{T}_{in}}$) 
3 
Dew point Meter 
Measuring the inlet air dew point 
^{o}Celcius ($T{{d}}$) 
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 
^{o}Celcius (T_{c}) and (T_{h}) 
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 
^{o}Celcious 
11 
Flow meter (water) 
Measuring water discharge 
Liter/min 
12 
Pump 
pumping cooling water 
 
13 
Vessel 
Cooling water container 
 
4.1 Presentation of experimental data
The experimental results of cold outlet temperature data and COP_{ref} of vortex tube are presented in the following diagram:
Figure 7. Cold temperature chart
Figure 8. COP_{ref} 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 (ε_{c}) produces a better COP_{ref}. 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 COP_{ref} the better [1]. In this experiment, higher pressure produces lower COP_{ref}. The forced cooling treatment produces a better COP_{ref}. 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 COP_{ref} 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 (ε_{c}) 
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 (ε_{c}) 
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 COP_{ref} data
Tube Type (TT) Natural Cooling (1) 

Fraction (ε_{c}) 
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 (ε_{c}) 
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 (2^{1} 3^{2}), where:
L : Latin square design,
36 : number of lines or experiments,
2^{1} : onefactor column for two level, and
3^{2} : twofactor 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] Signaltonoise formula used for the cold temperature produced the smaller is better with equation (15), and for the COP_{ref} 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 (2^{1}×3^{2})
Exsperiment Number 
Coloum Number 
[S/N] Rasio 

1 (TT) 
2 (P) 
3 (ε_{c}) 
T_{c} 
COP_{ref} 

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 (ε_{c}) 
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 COP_{ref} from the most influential are type of tube, fraction, and pressure. The optimum COP_{ref} 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 COP_{ref}
Level 
Tube Type (TT) 
Pressure (P) 
Fraction (ε_{c}) 
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 COP_{ref}. The pvalue shown in the ANOVA table shows the significance of each variable in the results. Factors are said to have a significant effect if the pvalue is <0.05 [1415]. In the table all pvalues are 0, so all factors have a significant effect on cold temperature and COP_{ref}.
The Ftest concept states that the higher the Fvalue, 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 
FValue 
PValue 
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 

LackofFit 
6 
1.604 
0.267 
* 
* 
Pure Error 
24 
0.000 
0.000 

Total 
35 
260.294 
Table 8. Analysis of variance COP_{ref}
Source 
DF 
Adj SS 
Adj MS 
Fvalue 
Pvalue 
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 

LackofFit 
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 
COP_{ref} 

Tube Tipe 
8.25% 
62.34% 
Pressure 
89.36% 
10.13% 
Fraction 
1.78% 
23.96% 
Error 
0.62% 
3.57% 
LackofFit 
0.62% 
3.32% 
Pure Error 
0.00% 
0.25% 
Total 
100% 
100% 
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 T_{c} and COP_{ref} 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)
$RCO{{P}_{ref}}=0.0911980.012237T{{T}_{1}}+0.012237T{{T}_{2}}\\0.006656{{P}_{1}}0.001517{{P}_{2}}0.005139{{P}_{3}}\\0.009439{{F}_{1}}+0.000303{{F}_{2}}+0.009136{{F}_{3}}$ (23)
where,
P = 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:
${{T}_{c\_op}}=17.51940.7722~T{{T}_{\text{2}}}~2.7486~{{P}_{\text{3}}}+~0.0681~{{F}_{\text{1}}}\\{{T}_{c\_op}}=17.51940.77222.7486+0.0681\\{{T}_{c\_op}}=14.07℃$ (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 
TT_{2};P_{3};F_{2} 
13.45 
TT_{2};P_{3};F_{1} 
14.07 
4.61% 
COP_{ref} 
TT_{2};P_{1};F_{3} 
0.123 
TT_{2};P_{1};F_{3} 
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 COP_{ref}.
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:
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.
COP 
coefficient of performance refrigeration 
$\dot{Q}$ 
heat flow 
$\dot{W}$ 
total energy 
$\dot{m}$ 
mass flow rate 
Cp 
heat capacity 
T 
Temperatur 
$\dot{V}$ 
volume flow rate 
Es 
saturation vapor pressure 
C 
coefficient 
eso 
Herman Wobus constant (6.1078) 
P 
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 j^{th} 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 
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