Chapter 3: Results and Discussions
3.2 Optimization of The Vortex Tube Energy Separation
3.2.3 Effect of the Inlet Pressure
51 In Figure 30, The low COP of a vortex tube is the absence of an external energy source to power the vortex tube, 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 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 the angle of the conical nozzle, can also significantly impact the efficiency of the vortex tube, leading to changes in its COP.
52
temperature difference between the hot and cold outlets increases as the inlet pressure increases. Hilsch [2] achieved a temperature decrease of 68 K with an inlet pressure of 11 bar.
3.2.3.1 Velocity Distribution Total velocity
Figure 31 presents compelling evidence that the inlet pressure significantly affects the total velocity of the fluid. It is observed that an increase in the inlet pressure exerts a considerable impact on the total velocity of the fluid. As the inlet pressure elevates, so does the total velocity of the fluid due to an increase in the internal energy of particles as the inlet pressure increases. However, it is noteworthy that beyond 600 kPa, the increase in total velocity is less pronounced, suggesting that 600 kPa is the optimal pressure.
Furthermore, the maximum achievable velocity is observed at an inlet pressure of 1.3 MPa.
Figure 31: Radial Distribution of Total Velocity for Different Inlet Pressure Tangential Velocity
According to Figure 32, the inlet pressure affects the tangential velocity inside RHVT. The data indicates that an increase in the inlet pressure can significantly impact the fluid's total velocity. As the inlet pressure increases, the tangential velocity increases.
The maximum velocity is achieved when the inlet pressure is 1.3 MPa.
0 50 100 150 200 250 300
0 0.2 0.4 0.6 0.8 1
Vtotal (m/s)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a Pin=5 bar,a
Pin= 6 bar,a Pin= 7 bar,a Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a Pin= 13 bar,a
53 Figure 32: Radial Distribution of Tangential Velocity for Different Inlet Pressure Axial Velocity
According to Figure 33, the axial velocity inside RHVT is affected by the inlet pressure. The data indicates that an increase in the inlet pressure can significantly impact the fluid's axial velocity. As the inlet pressure increases, the axial velocity increases. The maximum velocity is achieved when the inlet pressure is 1.1 MPa.
Figure 33: Radial Distribution of Axial Velocity for Different Inlet Pressure
0 50 100 150 200 250 300 350
0 0.2 0.4 0.6 0.8 1
Vtangential (m/s)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a p in 11 Pin= 12 bar,a
-100 -80 -60 -40 -20 0 20 40 60
0 0.2 0.4 0.6 0.8 1
Vaxial (m/s)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a
54
Radial Velocity
Figure 34 illustrates that the radial velocity component of the fluid undergoes alterations in response to changes in the inlet pressure. The data presented in the figure denotes that an increase in the inlet pressure can considerably impact the fluid's radial velocity. Furthermore, flow turbulence can introduce irregularities in the radial velocity component. In turbulent flows, fluctuations in velocity can cause the fluid to move unpredictably, leading to abnormal and unpredictable behavior of the radial velocity component. However, as a general trend, it is observed that an increase in the inlet pressure enhances the radial velocity of the fluid.
Figure 34: Radial Distribution of Radial Velocity for Different Inlet Pressure 3.2.3.2 Pressure Distribution
Static Pressure
According to Figure 35, the inlet pressure affects static pressure. The results show that an increase in the inlet pressure can significantly impact the static pressure, which increases as the inlet pressure increases. The highest static pressure is observed at an inlet pressure of 1.1 MPa.
-4 -3 -2 -1 0 1 2 3 4
0 0.2 0.4 0.6 0.8 1
Vradial (m/s)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a
55 Figure 35: Radial Distribution of Static pressure for Different Inlet Pressure
Total Pressure
Based on Figure 36, the total pressure is affected by the inlet pressure. The results indicate that an increase in the inlet pressure can significantly impact the total pressure, which increases with an increase in the inlet pressure. The highest total pressure is observed at an inlet pressure of 1.1 MPa, which is not necessarily the same as the inlet pressure for the most elevated static pressure. This shows that the kinetic effect at an inlet pressure of 1.1 MPa significantly impacts the maximum total pressure. Beyond this point, the temperature separation performance deteriorates due to the extreme generation of shock waves in the flow, which damages the swirl flow structure. Total pressure and static pressure at the wall are equal since the velocity is zero due to the no-slip condition.
0 100000 200000 300000 400000 500000 600000 700000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pstatic (Pa)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a
56
Figure 36: Radial Distribution of Total Pressure for Different Inlet Pressure 3.2.3.3 Thermal Distribution
Static Temperature
Based on Figure 37, the inlet pressure impacts the static temperature. The results showed that increased inlet pressure can significantly affect the static temperature.
Specifically, as the inlet pressure rises, the core region's static temperature decreases while it grows in the annular region. Conversely, the core temperature rises when the inlet pressure falls, while the annular region temperature also increases. The lowest temperature in the core flow is observed at an inlet pressure of 1.1 MPa.
0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ptotal (Pa)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a Pin=5 bar,a
Pin= 6 bar,a Pin= 7 bar,a Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a Pin= 13 bar,a
57 Figure 37: Radial Distribution of Static Temperature for Different Inlet Pressure Total Temperature
According to Figure 38, the inlet pressure affects the total temperature. The results show that increased inlet pressure can significantly impact the total temperature.
As the inlet pressure increases, the total cold temperature in the cold region decreases while it grows in the annular region. The lowest temperature in the core flow is observed at an inlet pressure of 1.1 MPa. The total and static temperatures at the wall are equal since the velocity is zero due to the no-slip condition.
Figure 38: Radial Distribution of Total Temperature for Different Inlet Pressure
260 270 280 290 300 310
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Tstatic (K)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a
260 270 280 290 300 310
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ttotal (K)
r/Rt
Pin= 2 bar,a Pin= 3 bar,a Pin= 4 bar,a
Pin=5 bar,a Pin= 6 bar,a Pin= 7 bar,a
Pin= 8 bar,a Pin= 11 bar,a Pin= 12 bar,a
58
Performance of the Energy Separation
In this section, the author's investigation of the impact of inlet pressure variations on the performance of the optimal vortex tube identified in Case 3 is discussed. The optimal vortex tube had an internal tapering angle of 1.75o convergent and a tube length- to-diameter ratio of 3, with a cold mass fraction (α) of 0.56, as shown in Table 3. Figure 39 (a) presents the results, demonstrating that the highest temperature separation is achieved at an inlet pressure of 1.1 MPa. However, the temperature separation performance deteriorates beyond this point due to the generation of shock waves in the flow, leading to damage in the swirl flow structure. Additionally, Figure 39 (a) indicates that the optimal inlet pressure is 6 kPa, and any further increase in pressure has a negligible effect. The coefficient of heating and refrigeration performance, as shown in Figure 39 (b), aligns well with the results from Figure 39 (a). These findings are consistent with previous studies, such as Martynovskii and Alekseev [80].
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
0 10 20 30 40 50 60
0 2 4 6 8 10 12 14
T=TH -TC (K)
Pin [100 kPa, a]
(a)
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.