The aerodynamic characteristics of an ASWT are usually described by a set of dimensionless aerodynamic performance curves [24].

The ASWT test torque is calculated from Eq. (1):(1) T=Pω´ where T is the generated torque, P is the output power, and ω is the angular velocity of the wind turbine.

The power coefficient Eq. (2), the torque coefficient Eq. (3), the force coefficient Eq. (4), and the tip speed ratio Eq. (5) can be calculated from the following equations:(2) CP=P0.5ρSV3 (3) CT=T0.5ρSV2R (4) Cd=FX0.5ρSV2 (5) TSR=ωRν=2πRnν where V is the incoming wind speed, and S is the swept area of the wind turbine when it is facing the incoming wind. ρ is the air density (ρ = 1.225 × 10⁻⁵ kg/m³).

The measurement equipment includes a power analyzer, as shown in Fig. 5, of type NORMA 4000CN. It has a maximum input voltage of CATII 1000 V and a maximum input current of CATII 1000 A, with an accuracy of ±0.2%. The power values obtained are accurate to two decimal places, which can be used to satisfy the test process by completely measuring the rotational speed and the output power of the ASWT under different working conditions. Aerodynamic performance tests are conducted at a distance from the ASWT. The experiments were conducted in the closed section, specifically 10D from the left side of the open section. The power analyzer and load meter were used in series, and the electronic load meter is shown in Fig. 5, of type IT8512A+.

The ANSYS-Fluent 2020 R2 software provides a feasible approach to establishing a reasonable meshing and calculation for this computational domain. To obtain accurate calculation results, the meshes in the stationary and rotating domains are refined, respectively. The ANSYS-Fluent 2020 R2 solver, which employs the Navier-Stokes equations (RANS) and the Finite Volume Method (FVM), is capable of meeting the requirements for the accurate prediction of flow fields in the stationary and rotating domains. The rotation domain mesh is refined to ensure the accuracy of predicting the flow field. Additionally, Fig. 6 shows boundary condition settings, such as velocity inlets and pressure outlets.

In Fig. 6, the stationary domain section features a rectangular cross-section (5D), where “D” represents five times the turbine diameter, serving as the velocity inlet. With the downwind direction as the reference, the stationary domain area is delineated both in front of and behind the rotating area, denoted as (5D) and (10D), respectively. The rotating domain dimensions are divided by a cylindrical region with a height of (1.6D) and diameter of (2D). This division is to ensure that the mesh around the blades maintains a skewness less than 0.7 and to guarantee that the final generated body mesh has a minimum orthogonal mass greater than 0.2. The wind speeds flowing through the stationary domain are 4, 6, 8, and 10 m/s, respectively. To obtain accurate calculated values, the above channel data were constructed based on the reference values recommended by Zhang et al. [12]. The actual wind tunnel closed section model.

The meshing of the complete computational region is illustrated in Fig. 7a. Notably, the inflation layer cells around the blade peripheral surface and near the rotating axis surface, as well as the Prism cells, are highlighted in Fig. 7b. The model cell mesh region conditions are based on the method of the rotating coordinate system (MRF). The delineated mesh regions in ANSYS-Fluent include the stationary domain and encrypted region, the rotating domain and mesh interface, the blade surface mesh, and the expansion layer mesh.

In this case, the growth rate of all the blades and the rotating axis boundary is 1.2. The height of the first layer is 2 × 10⁻⁵ m. The direction of the incoming flow is distributed in the normal direction, so the number of layers of the prismatic layer around the blades is set to 18 to ensure computational convergence, all of which remain unchanged in the mesh independence verification, as shown in Table 2. To ensure that the changes in the size of the cell do not affect the accuracy of the results of the calculations. The gradual incremental increase in the number of grids obtained is 4543073, 7667253, 5321106, and 6276041 cells. All the models above keep y⁺ < 1 for calculation. The relative error is a minimum of 0.1803%, as shown in Table 2. The prototypical ASWT has a total of 6276041 grid cells, of which the static domain grid cells are about 2701284. The rotational domain grid cells are about 3574757, and the relative error of the grid is 0.1803%, indicating sufficient computational accuracy.

An error analysis of the actual measurement results is also a crucial step. Test errors may arise from imperfections in the test program, personal reading errors, instrument errors, and various other factors. Taylor’s theory is employed for the error analysis of the measurement results. The findings indicate that the relative errors of the torque coefficients at 10 and 8 m/s are 1.44% and 0.90%, respectively, and the errors of the power coefficients at 10 and 8 m/s are 98.56% and 99.1%, respectively.(22) uM=(ux1∂M∂x1)2+(ux2∂M∂x2)2+...+(uxn∂M∂xn)2 where M is the measured result, x is the variable, μ and is the error.(23) RE=100n∑in|CT,exp−CT,numCT,num|

Here, the relative error is RE, CT,exp is the tested wind power coefficient, CT,num is the calculated power coefficient, i is the number of times it was tested, n and is the number of total measurements.

The prototypical ASWT is initially validated numerically at steady incoming wind speeds of 4, 6, 8, and 10 m/s. Figs. 8 and 9 illustrate the comparison between the experimental and numerically calculated results for C_T and C_p, respectively. The results demonstrate a good agreement between the experimental values and the numerically calculated results in the corresponding TSR range at different wind speeds of 4, 6, 8, and 10 m/s.

The predicted values of C_T and C_p were found to be slightly higher than those measured experimentally for the low wind conditions 6 and 8 m/s. To prevent the accumulation of excessive turbulent kinetic energy in the stagnation region, the SST k-ω turbulence model [30] is constrained by the use of the Kato-Launder limiter [26,30]. Under operating conditions with wind speeds up to 10 m/s, the numerical and experimental results agreed when the production limiting correction factor was applied. At high wind speeds of 10 m/s, where the Reynolds number reaches 2.47 × 10⁵, and the flow is in a fully developed turbulent state, the SST k-ω turbulence model alone is sufficient for accurate performance prediction of the ASWT.

However, in the transition region with Reynolds numbers of 1.48 × 10⁵ and 1.98 × 10⁵ at wind speeds of 6 and 8 m/s, respectively, it is more appropriate to use the SST k-ω turbulence model with the Kato-Launder limiter. As shown in Fig. 8, numerical calculations reveal that the maximum values of C_T are 0.244, 0.249, and 0.252 at TSR equal to 0.5 at wind speeds of 6, 8, and 10 m/s, respectively. Experimental results show slightly higher maximum values of C_T at 0.260, 0.252, and 0.248 for the corresponding TSR under the same operating conditions. As shown in Fig. 9, the maximum values of C_P are 0.219, 0.223, and 0.227 at TSR equal to 1.58, 1.58, and 1.58 when the wind speed is 6, 8, and 10 m/s, respectively. As a result, the maximum C_P value is enhanced by 3.65% when the incoming wind speed is 8 and 10 m/s compared to the incoming wind speed of 6 m/s, and the maximum C_P value is enhanced by 1.79% when the incoming wind speed is 10 m/s compared to the incoming wind speed of 8 m/s. The experimental results exhibit maximum values of C_P at 0.213, 0.226, and 0.228 for the same operating conditions at TSR equal to 1.6, 1.6, and 1.5, respectively. Therefore, the maximum values of C_P are enhanced by 7.04% when the incoming wind speed reaches 8 and 10 m/s compared to that at the incoming wind speed of 6 m/s. As shown in Fig. 8, the thrust coefficient decreases gradually with the increase of TSR due to the dominant role of torque in the case of fixed incoming wind speed. When the aerodynamic force in the X-direction increases gradually with the increase of incoming wind speed, the trend of thrust coefficient is significantly higher than that under low wind speed, and the overall trend remains the same, as shown in Table 5.

Under completely turbulent conditions, the ASWT exhibits unique peak-like curves that are plotted by the dimensionless parameters (C_P, C_T, TSR). These curves follow similar characterization principles as other wind turbine aerodynamic characteristics, showing distinct peaks unless there is a change in the flow pattern [31].

The boundary layer mesh height is specified according to the range of values of the dimensionless number y⁺ to ensure a reasonable range of y⁺ values for analyzing prototypical ASWT wind turbine models. The ASWT generates power by relying on both lift and drag to produce rotational motion. The results of numerical calculations comparing y⁺ < 3 and y⁺ < 1 are shown in Fig. 10. It is verified and discussed that the value of y⁺ < 1 is more suitable for the results of the experimental tests than the numerical case of y⁺ < 3.

Under the premise of keeping y⁺ < 1,the improved ASWT is divided into eleven groups of blade models for numerical simulation and comparison. Three groups of the blade spread angles α₁, α₂, and α₃ were grouped and numerically analyzed in the simulation. Firstly, the angle of α₂ is discussed basded on α₁ = 30°, α₂ = 45°, α₃ = 60°, and α₂ varies in the ranges of 40°, 45°, 50°, 55°, while α₁ and α₃ remain constant at 30° and 60°, respectively. When α₂ = 55°, the simulated range of TSR during the operation of this wind turbine is (0.5~3.0) and the C_P reaches a maximum value of 0.263 when TSR is equal to 2, V = 10 m/s. Therefore, it is concluded that the optimal angle of α₂ is 55°, as shown in Fig. 11a.

Under the same condition of wind speed V = 10 m/s, the effect of α₁ on the C_P value is analyzed, and α₁ varies in the range of 25°, 30°, 35°, and 40°, while α₃ and α₂ are kept constant at 60° and 55°, respectively. A regular change of the data can be found in Fig. 11b, where α₁ varies from the range of 25° to 40° with an initial increase and then a decrease in the C_P value. At the same time, it validates Nawar et al. [22] designed the improved ASWT with the spread angles of α₁ = 30°, α₂ = 45°, and α₃ = 60° for good aerodynamic performance. It is worth noting that changing the spread angle at the three sets of blades does not have any effect on the range of TSR. It can form a good interval of aerodynamic curves during the change of α₁, and it also shows that ASWT was characterized by a wide speed range. When α₁ = 30°, the TSR ranges from (0.5~3.0), and TSR is equal to 2, V = 10 m/s with C_P reaches a maximum value of 0.263. Therefore, it is concluded that the optimum angle of α₁ is 30°. α₃ varies in the range of 60°, 65°, and 70°, and meanwhile, α₁ = 30°, α₂ = 55° are selected to keep the same as shown in Fig. 11c. It found that the variation of α₃ has a more significant enhancement for the ASWT in the TSR range of (0.5~3.0) has a more significant enhancement. It is worth noting that reducing α₃ from 70° to 60° finds that the aerodynamic performance in the TSR range of (0.5~3.0) is enhanced with the reduction of the angle and 60° is taken at α₃ as the best.

Finally, it was concluded that the optimum blade spread angle of the improved ASWT was α₁ = 30°, α₂ = 55°, α₃ = 60°. Fig. 12 shows the maximum C_P of the improved ASWT is 0.263 at TSR = 2. In addition, the analysis of the figure shows that the TSR speed range of the improved ASWT is wider, and the maximum C_P value of the improved ASWT is 17.93% higher than that of the prototypical ASWT. In addition, Fig. 13 summarizes the effect on the retrofitted ASWT under the variation of each parameter.

According to the design prototye, ASWT generates aerodynamic sources that are distributed in three dimensions. Therefore, it is particularly important to analyze the aerodynamic forces on the forward-looking datum. The aerodynamic analysis of the prototypical ASWT shown in Fig. 14 is performed by vector translation from the rotation axis to the tip area, C, U, and W represent the absolute velocity in the inflow direction, the linear velocity in the apical region, and the relative velocity synthesized from the absolute and linear velocities, respectively. β is between the absolute and relative velocities angle. The forces F_X and F_Y generated in the incoming flow direction are decomposed into the lifting force F_L and the drag force F_D, F_X can be decomposed into F_Lx, F_Dx, and F_Y can be decomposed into F_Lx, F_Dy. Therefore, the rotational motion of the ASWT is mainly dominated by F_Y. It is concluded that during the rotation of the ASWT. The three parts of the blades are arranged in alternating rows of 120°, so that the airflow is uniformly and repeatedly acted on each group of blades under the dominant effect of F_Y, thus achieving the purpose of power generation.

Table 6 shows the ASWT before and after the improvement when TSR is equal to 2, V = 10 m/s, with C_P reaching its maximum value. The aerodynamic F_Y value of the prototypical ASWT is 0.70 N, and the aerodynamic F_Y value of the improved ASWT is 0.84 N. The F_Y value of the improvement is 20% higher than that of the prototypical ASWT. The aerodynamic F_X value of the prototypical ASWT is 4.11 N, and the aerodynamic F_X value of the improvement ASWT is 4.78 N. The F_X value of the modification is 16.3% higher than that of the prototypical ASWT.

(24) FX=FLx+FDx (25) FY=FLx+FDY

In this paper, the study of the velocity flow field and pressure field contours can effectively help to understand the effect of ASWT on aerodynamic performance before and after the modification. At TSR = 2, V = 10 m/s, Figs. 15a, 15b reveal the comparison of velocity and pressure contours of prototypical and improved ASWT, respectively. When the turbulent kinetic energy starts to impinge on the surface of the blades, it generates different When the turbulent kinetic energy starts to flow into the blade surface, different high and low-pressure regions in the windward and leeward directions of the incoming velocity. With the improvement of the blade, the high-pressure region is shifted from the second and third blades before the improvement to the first and second blades after the modification, and the low-pressure region is also smaller with the modification.

As shown in Fig. 11, the improved ASWT as α₁ decreases in the range of (35° to 30°) and the blade spread angle α₂ increases in the range of (40° to 45°), as in Figs. 15a and 15c. Therefore, a certain high-pressure region is formed upstream of the spread angles α₁, α₂ at the first and second blades. The formation of a corresponding low-pressure region downstream of the blades is conducive to the improvement of the ASWT’s ability to capture wind energy. As shown in Figs. 15b and 15d, the comparison of the velocity contours and flow field streamlines found that the improved ASWT forms an extremely low-velocity region in the downstream region of the incoming wind speed, implying that more efficiency can be obtained when the improved ASWT operates in comparison with the prototypical ASWT, which is verified with each other and with the analysis of the above results.