Chapter 3: Results and Discussions
3.2 Optimization of The Vortex Tube Energy Separation
3.2.4 Effect of the Cold Mass Fraction
59 Figure 39: Energy Separation Performance for Different Inlet Pressure (a) Outlet
Temperature Differences between the Hot and Cold Outlets (b) Coefficient of Performance of Heating and Refrigeration (Continued)
Figure 39 shows that the low Coefficient of Performance (COP) of a vortex tube is due to the absence of an external energy source to power the device, unlike traditional refrigeration systems. In conventional refrigeration systems, the compressor is powered by an external energy source, such as electricity or fuel, which compresses the refrigerant and facilitates a temperature difference. In contrast, in a vortex tube, the high- pressure flow that enters the tube is the sole driving force behind the energy separation process. This constraint results in the energy efficiency of the vortex tube being limited by the properties of the compressed air that enters the tube, including its pressure, temperature, and flow rate. Moreover, the design parameters of the vortex tube, such as its diameter, length, number, and size of tangential inlets, and the angle of the conical nozzle, can significantly impact the device's efficiency, leading to changes in its COP.
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Additionally, the cold mass fraction plays a vital role in the vortex tube's energy separation performance. Specifically, the energy separation performance increases as the cold mass fraction increases, but only up to a specific point; any further increments in the cold mass fraction can adversely affect the vortex tube's performance, as outlined in Table 6. Notably, the cold mass fraction's impact on the vortex tube is critical, given the hot outlet pressure's influence on it. This pressure can cause mass flow separation in the tube, resulting in energy separation, which manifests as a cooling effect due to the different kinetic energy levels of the separated fluids.
3.2.4.1 Velocity Distribution Total Velocity
According to the findings presented in Figure 40, the total velocity is sensitive to the cold mass fraction. The results demonstrate that an increase in the cold mass fraction can lead to a considerable decrease in the total velocity, given that the velocity depends on the cold mass fraction. The data highlights that the optimal velocity profile is achieved when the cold mass fraction is 0.05.
Figure 40: Radial Distribution of Total Velocity for Different Cold Mass Fraction
0 50 100 150 200 250 300 350
0 0.2 0.4 0.6 0.8 1
Vtotal (m/s)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
61 Tangential Velocity
Based on the findings presented in Figure 41, the tangential velocity inside the vortex tube is also influenced by the cold mass fraction. Specifically, an increase in the cold mass fraction can significantly reduce the tangential velocity, as the velocity is a function of the cold mass fraction. The maximum velocity profile is attained at a cold mass fraction of 0.05. Additionally, the results suggest the presence of vortex regions inside the vortex tube.
Figure 41: Radial Distribution of Tangential Velocity for Different Cold Mass Fraction Axial Velocity
Figure 42 illustrates the effect of changes in the cold mass fraction on the axial velocity distribution within the vortex tube. The results indicate that an increase in the cold mass fraction can increase the effective length of the cold region, leading to a significant decrease in the axial velocity towards the hot side while causing a growth in the axial velocity within the core region. This behavior is consistent with the cold mass fraction being a velocity function. The data further suggests that the optimal velocity profile can be achieved when the cold mass fraction is at 0.56.
0 50 100 150 200 250 300 350
0 0.2 0.4 0.6 0.8 1
Vtangentail (m/s)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
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Figure 42: Radial Distribution of Axial Velocity for Different Cold Mass Fraction Radial Velocity
Figure 43 presents the impact of the cold mass fraction on the radial velocity component within the vortex tube. The results indicate that changes in the cold mass fraction can significantly impact the fluid's radial velocity. Moreover, flow turbulence can further influence the radial velocity component. In turbulent flows, the velocity fluctuations can cause the fluid to move unpredictably, resulting in the unusual and erratic behavior of the radial velocity component.
Figure 43: Radial Distribution of Radial Velocity for Different Cold Mass Fraction
-100 -80 -60 -40 -20 0 20 40 60 80
0 0.2 0.4 0.6 0.8 1
Vaxial (m/s)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
-5 -4 -3 -2 -1 0 1 2 3
0 0.2 0.4 0.6 0.8 1
Vradial (m/s)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3
63 3.2.4.2 Pressure Distribution
Static Pressure
Figure 44 illustrates the impact of changes in the cold mass fraction on the static pressure distribution within the vortex tube. The results demonstrate that an increase in the cold mass fraction can increase the static pressure within the vortex tube. This phenomenon is due to the decrease in mass flow rate towards the hot side, which causes a reduction in the total velocity. As a result, the Bernoulli effect causes a drop in pressure within the vortex tube's core or annular regions. The data indicate that the maximum static pressure occurs at a cold mass fraction of 0.99.
Figure 44: Radial Distribution of Static Pressure for Different Cold Mass Fraction Total Pressure
Figure 45 presents the impact of changes in the cold mass fraction on the total pressure within the vortex tube. The data indicates that an increase in the cold mass fraction can significantly impact the total pressure, where the total pressure increases with an increase in the cold mass fraction. For example, the maximum total pressure is observed at a cold mass fraction of 0.99. However, when the hot outlet flow rate is reduced, resulting in a decrease in velocity within the vortex tube, the pressure on the hot side increases, leading to a significant increase in pressure in either the core or annular
10000 110000 210000 310000 410000 510000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pstatic (Pa)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
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regions of the vortex tube. Additionally, the total pressure and static pressure at the wall are equal due to the non-slip condition, where the velocity is zero at the wall.
Figure 45: Radial Distribution of Total Pressure for Different Cold Mass Fraction 3.2.4.3 Thermal Distribution
Static Temperature
Based on Figure 46, it can be observed that changes influence the static temperature inside the vortex tube in the cold mass fraction. The results show that an increase in the cold mass fraction can result in a higher static temperature in the core region. This temperature change is accompanied by a reduction in the forced vortex region and an expansion of the transition and free vortex regions. At the core region, the lowest temperatures are observed at a cold mass fraction of 0.05, while the highest is at 0.99. However, it should be noted that choosing the optimal cold mass fraction is more appropriate than choosing the one with the lowest or highest temperature.
10000 110000 210000 310000 410000 510000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ptotal (Pa)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
65 Figure 46: Radial Distribution of Static Temperature for Different Cold Mass Fraction Total Temperature
Figure 47 demonstrates that alterations in the cold mass fraction can affect the total temperature. Specifically, an increase in the cold mass fraction results in higher temperatures in the core region. At the core region, the data shows that the lowest temperatures are observed at a cold mass fraction of 0.05, while the most elevated temperatures occur at a cold mass fraction of 0.99. However, it is essential to note that selecting the optimal cold mass fraction is not a straightforward process and must consider other factors, such as the Coefficient of Performance (COP). Moreover, the static and total temperatures are equivalent at the wall due to the no-slip condition, resulting in zero velocity.
240 250 260 270 280 290 300 310 320 330
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Tstatic (K)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
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Figure 47: Radial Distribution of Total Temperature for Different Cold Mass Fraction Performance of the Energy Separation
This section investigated the impact of changes in the cold mass fraction on the performance of the optimal vortex tube obtained from Case 3. The optimal vortex tube had an internal tapering angle of 1.75o convergent, a tube length-to-diameter ratio of 3, and an inlet pressure of 6 MPa. Figure 48 (a) indicates that the optimal temperature separation occurs at the cold mass fraction of 0.56. Additionally, Figure 48 (b) demonstrates that the highest coefficient of performance is attained at a cold mass fraction of 0.56.
In Figure 48 b, it is essential to note that the low Coefficient of Performance (COP) of a vortex tube is due to the absence of an external energy source to power the vortex tube, unlike traditional refrigeration systems. Conventional refrigeration systems use an external energy source, such as electricity or fuel, to power the compressor, compressing the refrigerant and facilitating a temperature difference. However, in a vortex tube, the high-pressure flow that enters the tube is the sole driving force behind the energy separation process. This restriction results in the energy efficiency of the vortex tube being limited by the properties of the compressed air that enters the tube, including its pressure, temperature, and flow rate. Moreover, the design parameters of the vortex tube, such as its diameter, length, number, and size of tangential inlets, and
240 250 260 270 280 290 300 310 320 330
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ttotal (K)
r/Rt
α=0.05 α=0.1 α=0.17 α=0.3 α=0.43
α=0.56 α=68 α=0.78 α=0.91 α=0.99
67 the angle of the conical nozzle, can also significantly impact the efficiency of the vortex tube, leading to changes in its COP.
Figure 48: Energy Separation Performance for Different Cold Mass Fraction (a) Outlet Temperature Differences between the Hot and Cold Outlets (b) Coefficient of
Performance of Heating and Refrigeration
250 270 290 310 330 350 370
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
T (K)
Cold Mass Fraction (α) T_hot [K] T_cold [K]
(a)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
COP
Cold Mass Fraction (α)
COP_R COP_HP
(b)
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