Research on Operation Characteristics of Heater Directly Driven by Vertical Axis Wind Turbine

Abstract

Direct heating of wind turbine is a form of heating production using wind energy. Because of its low requirements for wind quality, relatively simple device structure and high heating efficiency, the wind turbine-driven heating devices can take the place of traditional fossil energy for winter heating and achieve the purpose of reducing carbon emissions to a certain extent. Through the heater experimental platform constructed at Northeast Electric Power University, it is concluded that the liquid stirring heater can operate at 7 m/s, however; the efficiency is extremely low in the low-temperature environment. The permanent magnet eddy current heater must operate at the wind speed above 13 m/s, but it also can operate normally under the low-temperature condition. Combining the advantages and disadvantages of the two experimental devices and setting the vertical axis wind generator as the original motor, the heating efficiency of the two types of heating devices are analyzed under different working conditions, and then the adaptability of the wind turbine and the heating efficiency of the heating device are also studied.

1. Introduction

In addition to achieving the energy conversion, wind energy heating system can also get the thermal energy needed by users through the “wind energy-mechanical energy-thermal energy” route [1]. The kinetic energy of the natural wind is captured and converted to mechanical energy by the wind turbine firstly, and then the heater converts the mechanical energy to the desired thermal energy. Compared with the first type of energy conversion, the second form is called the wind energy direct heating system and it saves the power generation equipment (as shown in Figure 1) and reduces the number of energy conversion time. The system will further reduce the initial investment cost and significantly improve the energy utilization coefficient.

Figure 1.

Schematic diagram of the “wind energy-mechanical energy-thermal energy” conversion pathway.

The vertical axis wind turbine has attracted more and more attention due to its simple structure, low cost, and no yaw system required. The vertical axis wind turbine is divided into lift-type and drag-type vertical axis wind turbines, between which the lift-type one has a higher wind energy utilization coefficient under the high blade tip speed ratio, and thus the wind turbine has higher power. Lift-type vertical axis wind turbines are usually designed with two-or three-bladed wind turbines, and the three-bladed turbine has a lower shaft torque ripple and better self-starting characteristics compared to the two-bladed turbine [2].

The basic principle of the permanent magnet eddy current heater (Figure 2) is that when the rotor of the eddy current heater starts to rotate, the stator heating element is in the changing magnetic field. Since the stator heating element is generally a solid metal structure, many free loops can be formed inside it. Under the action of changing magnetic field, the magnetic flux of each circuit will change, which will produce an induced current. The impedance value formed in the stator heating body is small, so the circuit current will be large, so as to achieve the effect of heating.

Figure 2.

Model of the permanent magnet eddy current heater.

For the study of wind energy heating, the authors in reference [3] set up an outdoor mixing heating experimental platform powered by natural wind and calculated the heating efficiency by the recorded wind speed, rotational speed, and temperature of working fluid. The authors in reference [4] compared the heating effects of the flat blade and the cylindrical blade and found that the heating effect of the flat blade is much better. The authors in reference [5] established a mathematical model to match the torque and the power, which provides a theoretical basis for the design of the stirred wind heating device. The authors in reference [6] optimized the structure of the wind turbine by using the Fluent software according to the relevant theory of wind turbine. The authors in reference [7] used Computational Fluid Dynamics (CFD) method to analyze the thermal efficiency of wind energy heating, and verified the feasibility of using CFD to analyze the mixing heating device.

The basic principle of the liquid stirring heater (Figure 3) is that the wind turbine directly drives the agitator to rotate the liquid at high speed and make the liquid heat.

Figure 3.

Model of liquid stirring heater.

The authors in reference [8] studied the relationship between the torque required in the starting stage of the liquid stirring heater and the stirring impeller radius, angular acceleration. The liquid stirring heater is accompanied by a higher torque when starting.

The authors in reference [9] studied the permanent magnet eddy current heater directly driven by the vertical axis resistance differential wind turbine and analyzed the work of the permanent magnet eddy current heater under a certain wind speed. The authors in reference [10] simulated the permanent magnet eddy current heater model using the finite element method, determined the relevant geometric parameters and material properties of the model and obtained the heater power. The authors in reference [11] set up a permanent magnet eddy current heater experiment device, through which the relevant data were obtained. By using the test device, the temperature changes under different rotating speeds, working times, and different import and export water temperatures were measured, and then the corresponding conversion efficiency was obtained. The authors in reference [12] show that the increase of the thermal energy of the permanent magnet eddy current heater is roughly proportional to the square of the rotational speed increase. The authors in reference [13] pointed out that for the instability and intermittent nature of wind energy, connecting the thermal energy storage device after the permanent magnet eddy current heater can ensure the stable output of thermal energy.

In this study, the operation characteristics of the heater directly driven by a vertical axis wind turbine (Figure 4) under different working conditions are studied. The heating efficiencies of the two types of heaters are analyzed, and the matching relationship between the wind turbine and heater is optimized (see Figures 2–4).

Figure 4.

Model of vertical axis wind turbine in wind tunnel test.

2. Physical model and numerical simulation method

2.1 Physical model of the wind turbine

The wind turbine model is a three-blade vertical axis wind turbine adopting the NACA0018 symmetrical airfoil. The string length ($c$) of the blade is 0.25 m, the rotating diameter (D) of the wind turbine is 0.55 m. The blade height of the vertical axis wind turbine is 1 m. The geometric model and parameters are shown in Figure 5 and Table 1. The computational domain is mainly divided into two parts, the outside is the static domain and the inner is the internal rotating domain, and sliding grid calculations are applied to rotate the wind turbine in the inner rotating domain. These domains are connected by the interface connection. To eliminate the effect of the inlet blocking on the wind turbine performance and to ensure the continuity of the fluid flow during the simulation, the diameter of the rotating domain inside is set to be 1.5D (see Figure 6) [14].

Figure 5.

Geometric model of vertical axis wind turbine.

The parameter name	Value	Unit
Blade height/$H$	1	m
Airfoil	NACA0018	—
Chord length/$c$	0.25	m
Blade number	3	—
Rotor rotating diameter/$D$	1.1	m

Table 1.

Dimension parameters of the vertical axis wind turbine.

Figure 6.

Schematic diagram of the 3D Computational domain.

The aerodynamic characteristics of the vertical axis wind turbine can be expressed as follows:

The following speed relation is satisfied when the wind turbine blades are in each position as Eq. (1):

$$\overrightarrow{\mathit{V}}=\overrightarrow{\mathit{U}}+\overrightarrow{\mathit{W}}$$E1

where, $\overrightarrow{V}$—inflow wind speed, m/s; $\overrightarrow{U}$—wind turbine blade line speed, m/s; $\overrightarrow{W}$—relative speed between airflow and blade, m/s.

The force analysis of a certain determined blade is shown in Figure 7. The central point of the vertical axis wind turbine is the $O$ point, and the height is $2H$. The $\mathit{\text{Oxyz}}$ coordinate frame is defined in Figure 7, where $\mathit{Oz}$ is perpendicular to the vertical rotation axis of the rotor, $\mathit{Ox}$ is in the same direction as the wind speed passing through the rotor. And the midpoint of this element in the blade is defined as $M$, string length is $l$.

Figure 7.

Force analysis of the element on the blade.

$\overrightarrow{W}$is perpendicular to the blade direction and is expressed as Eq. (2):

$${\mathit{W}}_{\mathit{n}}=\mathit{V}\text{sinθ cos}\mathit{\delta }$$E2

The other component can be expressed as Eq. (3):

$${\mathit{W}}_{\mathit{t}}=\mathit{U}+\mathit{V}\text{cos}\mathit{\theta }=\mathit{r\omega }+\mathit{V}\text{cos}\mathit{\theta }$$E3

So, the force on the blade is expressed as Eq. (4):

$${\mathit{W}}_{\mathit{u}}^2={\mathit{W}}_{\mathit{n}}^2+{\mathit{W}}_{\mathit{t}}^2={\mathit{V}}^2{sin}^2\mathit{\theta }{cos}^2\mathit{\delta }+{\left(\mathit{r\omega }+\mathit{V}\text{cos}\mathit{\theta }\right)}^2$$E4

Based on the above velocity decomposition relationship, the attack angle of blade is as Eq. (5):

$$tan\mathit{\alpha }=\frac{\mathit{V}\text{sin}\mathit{\theta }\text{cos}\mathit{\delta }}{\mathit{r\omega }+\mathit{V}\text{cos}\mathit{\theta }}$$E5

The aerodynamic pressure acting on the blade can be expressed as Eq. (6):

$$\mathit{Q}=\frac{\mathit{1}}{\mathit{2}}\mathit{\rho }{\mathit{W}}_{\mathit{u}}^{\mathit{2}}$$E6

The Lilienthal aerodynamic coefficient at this blade element is expressed as Eq. (7):

$$\left\{\begin{array}{c}{\mathit{C}}_{\mathit{t}}={\mathit{C}}_{\mathit{l}}sin\mathit{\alpha }-{\mathit{C}}_{\mathit{d}}cos\mathit{\alpha }\\ {\mathit{C}}_{\mathit{n}}={\mathit{C}}_{\mathit{l}}cos\mathit{\alpha }+{\mathit{C}}_{\mathit{d}}sin\mathit{\alpha }\end{array}\right.$$E7

where $C_l$ is the lift coefficient, and $C_d$ is the drag coefficient.

Component forces of normal direction and wing string direction of the blade are given as Eq. (8):

$$\left\{\begin{array}{c}\mathit{dN}={\mathit{C}}_{\mathit{n}}\mathit{Qlds}\\ \mathit{dT}={\mathit{C}}_{\mathit{t}}\mathit{Qlds}\end{array}\right.$$E8

Decompose the above component forces to the flow wind speed direction, the resultant force received by the rotor in that direction is as Eq. (9):

$$\mathit{F}=\frac{\mathit{bL}}{\mathit{2}\mathit{\pi }}{\int }_{-\mathit{H}}^{+\mathit{H}}{\int }_0^{2\mathit{\pi }}\mathit{Q}\left({\mathit{C}}_{\mathit{n}}sin\mathit{\theta }\text{cos}\mathit{\delta }-{\mathit{C}}_{\mathit{t}}cos\mathit{\theta }\right)\mathit{d}\theta \mathit{ds}$$E9

where $b$ is the number of blades.

The torque formula provided by the force acting on the blade for the rotor rotation axis is expressed as Eq. (10):

$$\mathit{dM}=\mathit{dTr}={\mathit{C}}_{\mathit{l}}\mathit{QLrds}$$E10

Integrating the above formulas, the torque of the whole rotor is expressed as Eq. (11):

$$\mathit{M}=\frac{\mathit{bl}}{\mathit{2}\mathit{\pi }}{\int }_{-\mathit{H}}^{+\mathit{H}}{\int }_0^{2\mathit{\pi }}{\mathit{C}}_{\mathit{l}}\mathit{Qrdsd\theta }$$E11

Therefore, the power is expressed as Eq. (12):

$$\mathit{P}=\mathit{M\omega }=\frac{\mathit{bl}}{\mathit{2}\mathit{\pi }}{\int }_{-\mathit{H}}^{+\mathit{H}}{\int }_0^{\mathit{2}\mathit{\pi }}{\mathit{C}}_{\mathit{l}}\mathit{Qr\omega dsd\theta }$$E12

The wind energy utilization coefficient $C_P$ is expressed as Eq. (13):

$${\mathit{C}}_{\mathit{P}}=\frac{\mathit{P}}{\frac{\mathit{1}}{\mathit{2}}\mathit{\rho }{\mathit{V}}^{\mathit{3}}\mathit{A}}$$E13

2.2 Grid division and verification of numerical simulation results

Grid division is a very important part in numerical simulation. Good grid division can improve the accuracy of the wind turbine performance prediction. In order to ensure the accuracy of the simulation, this study adopts the 3D structured grid for the wind turbine as shown in Figure 8.

Figure 8.

Mesh of vertical axis wind turbine: (a) top view of mesh in rotating domain; (b) mesh around blade; (c) the entire mesh in the computational domain.

For the three-blade wind turbine model studied in this paper, the pressure-velocity coupling method and SIMPLE algorithm are used to solve the transient URANS Equation, and the pressure order, momentum term, and turbulence dissipation term are all solved by the second-order windward space dissipation algorithm, and the judgment criterion of convergence is set to 10⁻⁵. The turbulence model used in the simulation is the transition $\mathrm{SST}$ turbulence model, which is the original k-ω, $\mathrm{SST}$ Equations plus two empirical formulas. It is more accurate in the turbulence rotation compared to other simulated wind turbine models. In order to avoid the influences of the grid number, the y⁺ value, the turbulence model, the algorithm, the time step, and other factors on the simulation results, it needs to verify the simulation results, as shown in Figure 9. Compared with the 2D numerical simulation results, it can be found that the wind energy utilization coefficient using the 3D numerical calculation results is close to the change trend of the wind tunnel experiment, and the accuracy of the wind energy utilization coefficient prediction is obviously better compared with the 2D numerical simulation. When the wind turbine runs at the optimal tip speed ratio (λ = 1.48), the wind energy utilization coefficient obtained from the 3D simulation is 0.297, which is 15% higher than that in the wind tunnel experiment and 19% lower than that in the 2D simulation.

Figure 9.

Comparison of 3D numerical simulation results to experimental data and 2D numerical simulation results.

3. Results and discussion

3.1 Operation characteristics and efficiency of the permanent magnet eddy current heater

It is known from experiments that when the working fluid temperature of the bulk heat exchange surface increases by 60°C under different speed conditions, the faster the speed of the permanent magnet eddy current heater, the faster the working fluid temperature of the heat exchanger surface increases. However, if the speed is too fast, it will lead to an increase in heat production absorbed by the bulk metal during the heater operation, the uniform heating of circulating working fluid, and a high energy loss. Overall, the running speed of the heater is relatively suitable at 20 rad/s. The starting torque of the permanent magnet eddy current heater is about 6.89N·m, while after the magnetic eddy current heater is used as the wind turbine load, the wind turbine tip speed is relatively low, which will deviate from the optimal tip speed ratio interval, and thus leads to a low wind energy utilization coefficient during operation.

For the permanent magnet eddy current heater, when the wind speed varies from 13 m/s to 17 m/s, the output parameters of the wind turbine are shown in Table 2.

Wind speed/(m/s)	Rotating speed/(rad/s)	Tip speed ratio	CP	Torque/(N m)	Power of wind turbine/(W)
13.0	5.76	0.24	0.027	7.01	40.39
13.5	6.80	0.27	0.033	8.09	55.09
14.0	8.37	0.33	0.044	9.61	80.54
14.5	9.94	0.38	0.045	11.33	112.78
15.0	11.51	0.42	0.067	13.23	152.45
15.5	13.08	0.46	0.080	15.24	199.60
16.0	15.70	0.59	0.127	16.70	350.34
16.5	17.79	0.60	0.128	21.54	383.52
17.0	19.89	0.64	0.150	24.89	495.21

Table 2.

Output parameters of wind turbine at 13–17 m/s wind speeds.

The rotating speed and torque curve of wind turbine under different wind speed conditions are shown in Figures 10 and 11. Clearly, the rotating speed and torque of the wind turbine both increase linearly with the wind speed increased.

Figure 10.

Curve of the rotating speed change at 13–17 m/s wind speeds.

Figure 11.

Curve of the torque change at 13–17 m/s wind speeds.

According to the experimental data, the relationship between the heat absorption power $P_{a1}$ of the permanent magnet eddy current heater during normal operation and the mechanical power $P_w$ associated with the input heater is obtained as Eq. (14):

$${\mathit{P}}_{\mathit{a}\mathit{1}}=\mathit{0.0008}{\mathit{P}}_{\mathit{w}}^{\mathit{2}}+\mathit{0.3201}{\mathit{P}}_{\mathit{w}}+\mathit{2.875}$$E14

The relationship between the power of heat absorption $P_{a2}$ of liquid stirring heater and the mechanical power $P_w$ associated with the input heater is obtained as Eq. (15):

$${\mathit{P}}_{\mathit{a}\mathit{2}}=\mathit{0.0003}{\mathit{P}}_{\mathit{w}}^{\mathit{2}}+\mathit{0.366}{\mathit{P}}_{\mathit{w}}-\mathit{10.061}$$E15

Therefore, the efficiency of the heater can be expressed as Eq. (16):

$${\mathit{\eta }}_{\mathit{pth}}=\frac{{\mathit{P}}_{\mathit{a}}}{{\mathit{P}}_{\mathit{m}}}$$E16

where$P_a$—heat absorption power of working fluid, J; $P_m$—input mechanical power of heater, J; ${\eta }_{\mathit{pth}}$—heater efficiency.

The system efficiency is the ratio of the heat obtained by the circulating working fluid to the wind energy swept by the wind turbine. It can directly reflect how much energy the heating system captures from the natural wind. The expression is Eq. (17):

$${\mathit{\eta }}_{\mathit{sys}}={\mathit{C}}_{\mathit{P}}{\mathit{\eta }}_{\mathit{pth}}$$E17

According to the above formulas, the heating efficiency and system efficiency of the permanent magnet eddy current heater can be obtained (Table 3) by using the output power of the wind turbine.

Wind speed/(m/s)	Power of wind turbine/(W)	Thermal energy exchange power/(W)	Heating efficiency/(%)	System efficiency/(%)
13.0	40.39	17.11	42.36	1.14
13.5	55.09	22.94	41.64	1.37
14.0	80.54	33.85	42.02	1.85
14.5	112.78	49.15	43.58	1.96
15.0	152.45	70.27	46.09	3.09
15.5	199.60	98.64	49.42	3.95
16.0	350.34	213.21	60.68	7.73
16.5	383.52	243.31	63.44	8.12
17.0	495.21	357.58	72.21	10.83

Table 3.

The heating efficiency and system efficiency of the permanent magnet eddy current heater.

As seen from Figures 12 and 13, with the increase of the test wind speed, the heating efficiency increases at the same time. The heating efficiency and system efficiency are significantly increased when the wind speed is higher than 15.5 m/s. When the wind speed is 17 m/s, the heating efficiency and system efficiency reach the maximum values of 72.21% and 10.83%, respectively. Hence, the permanent magnet eddy current heater has higher efficiency under the condition of higher wind speed and rotating speed.

Figure 12.

Curve of the heating efficiency change at 13–17 m/s wind speeds.

Figure 13.

Curve of the system efficiency change at 13–17 m/s wind speeds.

3.2 Operation characteristics and efficiency of the liquid stirring heater

According to the experiment results, the temperature rise rate fluctuates in a certain range when the liquid stirring heater rotates at different speeds, but it does not attenuate with the increase of the working fluid temperature. Hence, with the rise of work fluid temperature, the increase of environmental thermal dissipation will not significantly affect the working fluid temperature rise rate. The changes in working fluid temperature at different heater speeds are in linear function, and the effect of heater speed on heating is significant. The strength and stiffness of mixing blade and the plate under high speed are also need to be considered.

The wind turbine can complete the start-up operation at a low wind speed, and the starting torque is much lower than the permanent magnet eddy current heater at the same power level. Therefore, compared with the permanent magnet eddy current heater, the mixing heater can use the wind energy at a lower speed and improve the wind energy utilization. Due to the small drive torque of the stirring heater, the wind turbine speed is increased, the tip speed ratio is close to the optimal tip speed ratio with a higher wind energy utilization coefficient.

When the wind speed varies from 7 m/s to 13 m/s, the output parameters are given in Table 4.

Wind speed/(m/s)	Rotating speed/(rad/s)	Tip speed ratio	CP	Torque/(N m)	Power of wind turbine/(W)
7.0	13.61	1.07	0.202	3.62	49.30
8.0	18.84	1.29	0.264	5.10	96.17
9.0	21.98	1.34	0.281	6.63	145.75
10.0	26.17	1.43	0.292	7.94	207.76
11.0	29.30	1.46	0.295	9.53	279.37
12.0	32.44	1.49	0.297	11.26	365.15
13.0	35.59	1.51	0.295	12.96	461.13

Table 4.

Output parameters of wind turbine at 7–13 m/s wind speeds.

The rotating speed and torque curve of the wind turbine in the test wind speed interval are shown in Figures 14 and 15. It can be seen that the rotating speed and torque both change linearly in the test wind speed range. Therefore, when the rotating speed of the heater increases, the mixing resistance is borne by the blade and the flow resistance plate will also increase simultaneously. When the heater power is necessary to be further improved, the design of the mixing blade and the damping plate structure should be optimized to increase the mixing resistance and reduce the maximum rotating speed.

Figure 14.

Curve of the rotating speed change at 7–13 m/s wind speeds.

Figure 15.

Curve of the torque change at 7–13 m/s wind speeds.

Based on Eqs. (15)–(17), the heating efficiency and system efficiency (Table 5) of the liquid stirring heater can be obtained according to the output power of the wind turbine.

Wind speed/(m/s)	Power of wind turbine/(W)	Thermal energy exchange power/(W)	Heating efficiency/(%)	System efficiency/(%)
7.0	49.30	8.71	16.67	3.57
8.0	96.17	27.91	29.02	7.66
9.0	145.75	49.66	34.07	9.57
10.0	207.76	78.93	37.99	11.09
11.0	279.37	115.60	41.38	12.21
12.0	365.15	163.58	40.80	13.31
13.0	461.13	222.50	48.25	14.23

Table 5.

The heating efficiency and system efficiency of the liquid stirring heater.

According to Table 5, Figures 16 and 17, the heating efficiency increases with the wind speed increased in the test wind speed range, and the maximum efficiency is 48% when the wind speed is 13 m/s. The corresponding wind energy utilization coefficient is 0.295 with the highest system efficiency. Though the permanent magnet eddy current heater efficiency is high, while the matching characteristics with the wind turbine are poor, leading to low system efficiency. Thus, the good matching of heater and wind turbine will effectively improve the efficiency of the wind energy heating system.

Figure 16.

Curve of the heating efficiency change at 7–13 m/s wind speeds.

Figure 17.

Curve of the system efficiency change at 7–13 m/s wind speeds.

4. Conclusion

According to the existing experimental results, the numerical simulation method is applied to study the vertical axis wind turbine under different working conditions, the conclusion are as follows:

1. The input torque of the liquid stirring heater has a linear relationship with the rotating speed when its geometric structure and working fluid are determined. Therefore, replacing the working quality with high viscosity can effectively reduce the volume of the heating device. On the basis of guaranteeing the quantity of heat, optimizing the type of the stirring blade and flow resistance plate can reduce the working speed of the device, achieve a good match with the wind machine, improve the utilization coefficient of the wind turbine, and improve the heating efficiency of the system. According to the numerical simulation results, the maximum heating efficiency is up to 48.25%.

2. Compared with the liquid stirring heater in the same power level, the starting torque of the permanent magnet eddy current heater is higher, and due to the poor self-starting characteristics of the vertical axis wind turbine, the permanent magnet eddy current heater driven by the wind turbine can be put into operation at high wind speed, which cannot effectively use the wind energy at low wind speed. The wind energy utilization coefficient of the system can be improved by the cooperative operation with the liquid stirring heater. According to the numerical simulation results, the maximum heating efficiency is up to 72.21%.

3. The heater directly driven by a vertical axis wind turbine system has a certain referred significance for other permanent magnet eddy current heater and liquid stirring heater with vertical axis wind turbine.