Efficiency and Feasibility Analysis of Wind Turbines in Tandem in a Vortex Tube

Polar scientific research is of great importance for the human. The exploitable wind energy of the polar region accounts for more than 20% in the worldwide sense. However, the harsh polar storms, extreme wind speed (up to 100 m/s), ice crystals and sand in the wind all hinder the exploitation of wind resources. Therefore, in order to protect the power generation infrastructure and to maximize the power generation window, this paper proposes an innovative concept of power generation first. This concept, placing multi wind turbines in tandem in a vortex tube, is based on the Venturi principle which allows the wind in a funnel-shaped air inlet to accelerate. Meanwhile, the large-scale vortices and associated turbulent kinetic energy in the tube are diminished through the inlet honeycomb grid, thus driving the multi-turbines in tandem to generate more power. Second, to verify the efficiency of this concept, the CFD simulation technology is employed to investigate the wake characteristics in two distinct flow fields, namely the open space and the vortex tube space. The simulation results are then compared with prototype site tests. The comparison confirms the superior performance of this vortex tube scheme accommodating multi-turbines and the use of a honeycomb at the inlet.


Introduction
The polar scientific research represents a country's comprehensive strength for global governance, and has a profound impact in many fields, such as economy and politics [1].Wind resources in the polar region are abundant and widely distributed, with about 100 GW of feasible technology, accounting for 20% of the global wind resources [2].
However, the development of wind power in the polar region also faces many hazards.Firstly, although stable high-speed wind is an ideal condition, the wind speed in the Antarctic Continent is too high, with an annual average wind speed of 19.4 m/s.An extreme speed of 100 m/s was observed at the France Dilvere station [3] [4], which is the highest wind speed recorded in the world so far.At present, the wind speed for turbines to stop working is generally 20 m/s for onshore turbines and 25 m/s for offshore turbines.Both two speeds cannot adapt to polar conditions.Also, the too heavy wind loads on a wind turbine are not friendly to structural safety.Secondly, there are approximately 65 million birds in 33 species in the Antarctic region.Towering wind turbines can easily involve flying organisms and affect the safety of the turbines simultaneously, which imposes a potential threat to the ecological environment.Finally, when placing turbines, it is required that the distance between two turbines should be at least 3-4 times the blade diameter.Employing an overly dispersed layout scheme in the polar region will obviously increase the difficulty and cost of installation and maintenance.Thereby, how to utilize wind energy in extreme weather areas such as the polar region has become a challenge in the wind industry.
The academic community has conducted comprehensive studies on the Venturi vortex tube scheme.Allaei and Andreopoulos [5] first proposed the pioneering INVELOX concept (Figure 1) and indicated that the concept has an outstanding performance in capturing, accelerating and concentrating the air.Then, Allaei et al. [6] carried out a field omnidirectional INVELOX test to verify the concept's strong ability in per output watt cost reduction.Anbarsooz et al. [7] optimized the original design of INVELOX by extending the guiding curtains, and evaluated the aerodynamic performance.Zhang et al. [8] improved the wind collection effect of the INVELOX system by optimizing the outlet structure.Guan et al. [9] proposed an efficient breeze generator with a vertical multi-layer wind gathering component.Compared with the INVELOX system, this generator has a lower cost advantage.For the polar region electricity power generation, the authors have registered a patent in China.This patent aims at developing a vortex tube to resist heavy wind loads and meanwhile maximize power generation with multi horizontal-axis turbines in this tube.Though this tube also utilizes the Venturi principle, it differs from the INVELOX in four aspects, i.e., a much smaller height in geometry, a greater number of turbines, an aligning system and an inlet honeycomb device.Therefore, this paper is devoted to technically verifying the efficiency and feasibility of this innovative concept.

Tandem layout of turbines in a vortex tube
The proposed concept is shown in Figure 2. Its main structure is an accelerating vortex tube with a funnel-shaped air inlet.Based on the Venturi principle, the wind is accelerated by such an inlet and then drives the multi-turbines in tandem in the tube to generate power.This device is equipped with an overall yaw system.The yaw system includes an anemometer, a rigid yaw bearing and several aided rollers.The anemometer persistently captures wind field information throughout the entire lifecycle of this device.Under normal wind speed, the anemometer at the top of the air inlet receives wind field information and makes the device's orientation accurately follow the wind direction.Upon encountering the extreme wind speed, the yaw system will revolve the vortex tube to the orthogonal direction of the wind.By the time, strong pipe walls are expected to resist wind loads and to protect the turbines in tandem inside the tube.

Independent meshing analysis
Near the inlet, a single turbine is placed.Its capacity is 300 W, with a rotating diameter of 1.4 m.With a basic grid size of 0.1 m and a growth rate of 10%, this paper employs 9 sets of numerical simulations individually.The wind speed of a monitoring point located in mid of the tube with the corresponding grid number is plotted in Figure 3.It can be observed that as the number of grids reaches 4×10 6 , the calculated wind speed becomes convergent.In this paper, the total mesh number is somehow denser with 5.08×10 6 .Figure 3. Calculated wind speeds converge with increasing mesh number.

A single turbine in tube
Set the inflow velocity to 10 m/s and the corresponding rated rotation speed to 1000 rpm, the simulation result of flow velocities is shown in Figure 4.It can be seen that a high-speed narrow wake belt comes into being behind the turbine in the tube while in the open space, the low-speed wake has a wider range and the corresponding average velocity is lower than 6 m/s.Flow fields of the open space and the vortex tube space are compared in Figure 5.The single turbine is placed at the position 0 m and the horizontal axis coordinates refer to the distance from this turbine (the positive direction denotes the leeward positions).In both two spaces, the inline speed at the 3/4 end of the blade is very close to the average speed of the whole rotating surface.This indicates that the 3/4 end speed is able to more truly represent the real wind energy potential than the hub speed.
Consequently, the inline speed of the 3/4 blade end is used to estimate the power of the downstream turbine.Moreover, Figure 4 shows that all critical speeds in the vortex tube are significantly faster than those in the open space, i.e., the inline speeds at the 3/4 blade end, the surface average speed and the hub speed are successfully increased respectively by 34.59%, 23.79% and 31.94% by the honeycomb.

Two turbines in tandem
The CFD results are shown in Figure 6 for the scenario of two identical turbines in tandem.Compared with the scenario of just one single turbine, the proportion of low velocity area in the flow field is obviously expanded in the open space.In the single turbine scenario, the proportion of the low-speed (≤3 m/s) along the height is about 38.58% of the wake area.When passing the downstream turbine in the open space, the flow has a low-velocity proportion noticeably increased to 59.66% which however does not happen in the vortex tube space.Accordingly, it can be inferred that a third turbine, if placed in tandem after the second turbine, will be exposed to the low-speed wake in the open space and seriously reduce the power generation capacity.
(a) Vortex tube space (b) Open space Figure 6.Velocity cloud image in the two turbines scenario.In the scenario of two turbines, the comparison of the critical wind speeds between two spaces is shown in Figure 7.At the wake area, the inline wind speeds at the 3/4 blade end and the rotating surface begin to decrease in the open space but gradually increase in the tube space.This is due to the wake dissipation in the open space without the wall constraints, therefore affirming the excellent flow concentration ability of the vortex tube.The inline wind speeds at the hub, the 3/4 blade end and the rotating surface are respectively 1.68 m/s, 3.91 m/s and 4.87 m/s in the open space, while in the vortex tube are 3.98 m/s, 7.56 m/s and 7.70 m/s, with the promotion of 136.90%, 93.49% and 58.18%.

Three turbines in tandem
The flow field information of three identical turbines in tandem is shown in Figure 8.When the third turbine is added, the wake velocity shows an apparent decrease in both the vortex space and the open space, but the latter's situation is more severe.It can be seen that almost the whole wake area is a lowspeed zone in the open space and even the velocity near the third turbine is 0 m/s.The output power results in the vortex space and the open space are summarized for three layouts (Sec 3.1, 3.2 and 3.3) in Table 1.The advantages of the vortex tube scheme become increasingly prominent with multi turbines involved.For two turbines in tandem, the power generation efficiency of the vortex tube scheme is 8.33% higher than that in the open space.For three turbines, such improvement is more than 20%.Thus, great engineering and economic advantages can be achieved by the tandem layout of turbines in a vortex tube.

Testing scheme
The prototype tests are carried out for small but real industrial turbines of rated power of 300 W each.
The tests are divided into three situations, i.e., in the vortex tube (without honeycomb), in the vortex tube (with honeycomb) and in the open space.The objective is to investigate the performance of the honeycomb and the advantages of the vortex tube scheme, and to make a comparison with the numerical results.

A single turbine in tube and open space
The output power curves of turbines at different positions are shown in Figure 10.Without the honeycomb, black lines in LC-1 vs. LC-4 imply that placing the turbine in the middle and rear regions is better than in the front region.This is because the flow field in the front of the tube is not fully developed and the wind shearing is remarkable, causing adverse turbulence to the rotation of the blades.By contrast, in the middle and rear areas, wind shearing is basically eliminated.Nonetheless, the best position is not near the outlet where an adverse flow is triggered by the external space.More importantly, it can be seen that the turbines' generating capacity in all load cases in Figure 10 is enhanced by the honeycomb.For example, when the turbine is located at 0.5 m from the inlet, the electric power is increased by 20.93%, 28.96%, 43.49%, 27.80%, 24.27%, 14.00% and 19.83% for the 7 calibrated wind speeds.Such an increase, on average, is equivalent to 29.15 W. The reason is that the honeycomb grid allows an earlier development of the fluid in the front tube, consequently producing a lower turbulent flow.Uniform and stable flow fields could avoid the occurrence of a volatile moment during blade rotating, and simultaneously makes the blades rotate faster for higher power efficiency.11), the acquired powers in open space are merely 125 W, 154 W and 177 W, all dramatically lower than the rated power of 300 W. The output powers of turbines without the honeycomb are 25.46%, 34.39% and 41.26% higher than the open space.Such increases are even higher, i.e., 55.91%, 53.21% and 69.27% with the honeycomb.In Figure 12, the speed of the wake in the open space quickly decreases.After passing through the first turbine, the quickly diffused wake cannot form a high-speed and concentrated flow field.At the position of 2 m behind the turbine, the flow speed has decreased to 2 m/s or lower, unable to meet the cut-in wind speed and to drive additional turbines.This, therefore, manifests the significant advantages of the vortex tube scheme over the open space.

Two turbines in tandem
Figure 13 shows that with wider turbine spacing, the generating capacity of the turbines is improved.When the distance is 1 m (LC-5), the total power of the two turbines under each wind speed is 34.74 W, 55.81 W, 100.05W, 162.90 W, 208.46 W, 270.98 W and 334.88 W, respectively.When the spacing is enlarged to 4 m (LC-8), the total power at each wind speed is increased to 46.98 W, 76.24 W, 113.08 W, 212.27 W, 270.55 W, 355.71 W and 434.90 W. The percentage increases by 29.87% for a speed of 10 m/s, which is a typical wind condition in polar regions.The reason is that the wake field could develop more completely with the expansion of the turbine spacing.
Also shown in Figure 13, with the aid of a honeycomb grid, the output power of both turbines has been significantly increased.Particularly, when the incoming wind speed is high (> 8 m/s), the improvement in output power is significant.This is because when the blades of the centrifugal blower rotate more rapidly, the generated high-speed fluid contains more vortices and stronger wind shearing.Such a condition has a more adverse influence on the turbines than a low speed does.Therefore, the presence of the honeycomb grid is useful to diminish the turbulence in the flow field, resulting in a better performance in power enhancement.

Three turbines in tandem
Figure 14 compares the power of the three turbines with/without the honeycomb device.The figure shows again that the honeycomb grid has an outstanding performance to improve power generation on all turbines in tandem.For example, when the turbine spacing is 2.5 m (LC-12 & LC-24) with a wind speed of 10 m/s, the honeycomb makes the output power be promoted by 21.88% (1 st turbine), 14.27% (2 nd turbine) and 33.17% (3 rd turbine).

Figure 2 .
Figure 2. Schematic diagram of wind turbines in tandem in a vortex tube.
(a) Vortex tube space (b) Open space Figure 4. Velocity cloud image in the single turbine scenario.

Figure 5 .
Figure 5.Comparison of critical speeds between the vortex tube and the open space in the single turbine scenario.

Figure 7 .
Figure 7.Comparison of critical speeds between the vortex tube and the open space in the two turbines scenario.
(a) Vortex tube space (b) Open space Figure 8. Velocity cloud image in the three turbines scenario.

4. 2 .Figure 9 .
Figure 9. Calibrated time history curves of inlet wind speeds without and with the honeycomb.

Figure 11 .
Figure 11.Turbine power between the open space and the vortex tube.

Figure 12 .
Figure 12.Wind speed in the open space.

Table 1 .
Summary of power generation efficiency for three layouts in two spaces.

Table 2
contains 24 load cases (LC).LC-13 to LC-24 are for the presence of honeycomb.All LCs are distinguished by the location of turbines in the tube and their inter-spacing.

Table 2 .
Load cases