3.1. Mesh Convergence and Domain Size Confirmation
The domain using coarse mesh is initially tested to obtain the instantaneous torque at the rotating VAWT and plotted it versus time. Then, the total number of elements is increased by approximately 20% and run with the same setup to get the corresponding instantaneous torque curve. The process of successively increasing the mesh elements continues until there is no significant change in instantaneous torque values. At this point, the result is no longer affected by the increasing number of elements, hence the mesh converged. There are three successive mesh densities that are considered as shown in detail in
Table 2.
Wall
for all simulations are monitored. Only those simulations with
for all walls are considered acceptable for the evaluation process. The
y+ monitors are reported using the mean value and the standard deviation for each time-step. For instance, presented below in
Figure 9 are the
y+ monitors taken from car case with medium mesh.
The computer used has 8 physical cores with 64 GB memory. Using all available cores, the simulations took 38 h, 46 h, and 57 h for coarse mesh, medium mesh, and fine mesh, respectively; the resulting torque versus time curve are shown in
Figure 10. The coarse mesh is not a good choice due to its inaccuracy, while the 11-h difference between the medium mesh and fine mesh gives significance when considering the number of simulations in the parametric study for the effect of windshields. Therefore, to save time on completing the simulations with a small compromise with the accuracy of the solution, the medium mesh is chosen.
For the confirmation of domain size, a velocity contour taken at
using the medium mesh density with the variable range set to only 0 to 5 m/s, is used and shown in
Figure 11. It can be seen that there is no variation in velocity magnitude exceeding 0.4 m/s in the far-field. This value is relatively small compared to the magnitude in the path of the vehicle in the VAWT area, which means that the outer boundaries are far enough to affect the area of interest within the domain. Therefore, the initial dimension of 280 m by 70 m is confirmed to be suitable for the simulation.
3.2. Wind Profile and Windshield Position
Knowing the prevailing wind direction that hits the VAWT is the key on proper positioning the windshield so that it would be effective in blocking the incoming wind causing the reduction of torque in the VAWT. From the monitors set, the plots for the instantaneous velocity magnitude and direction are obtained and shown in
Figure 12.
The plots show that the wind direction has an increasing slope until
which is the timing to which the vehicle approaches the VAWT location. Then, the wind direction changes rapidly between
to
and becomes stable in an almost horizontal direction from
and beyond. The behavior of the wind relative to the VAWT as shown in the plots can be visualized in the velocity vector field shown in
Figure 13 with the VAWT moving from right to left within the shown domain. The corresponding time on when the specific portion of the wake passes the VAWT, represented by red-outlined circle, is shown in the figure. The figure shows that the rapidly changing wind direction between
and
is due to the strong vortices created after the flow separation in the car walls that eventually dissipates in
which explains the flattening of curve to almost horizontal direction as seen in the graph.
Since there is no significant magnitude of wind detected before , the weighted-average wind direction is only taken from to with the weight factor based on its corresponding instantaneous velocity magnitude. Calculating this using Equation (2) gives the value of −1.5 degrees which can be approximated to 0 degree. The windshield must be positioned to block the incoming wind hitting against the rotation of the VAWT; therefore, based on the prevailing wind direction, the windshield is positioned where the starting location is at negative x-axis and extends in a clockwise manner.
The same procedure on determining the prevailing wind direction in car case is also done to the bus case. The bus instantaneous wind direction and magnitude are shown in
Figure 14 where it can be seen that in contrast with car case, the bus wind direction does not stabilize to any time interval within
s to
s. The same is true when seen in the velocity vector in
Figure 15, where it shows that large vortices have not yet dissipated even at
. The resulted weighted average wind direction for bus is at 15.7 degrees or approximately 16 degrees from positive x-axis. Therefore, for bus case, the windshield is positioned where the starting location is at +16 degrees from negative x-axis and extends in a clockwise manner.
3.3. VAWT CP versus TSR
A separate domain shown in
Figure 16 is prepared for the simulation to compare the
of VAWT between two conditions; the first is when induced constant rotation is applied, and second when the VAWT is freely rotating with the wind. The same meshing of rotor zone obtained from the mesh convergence study is used for this purpose. The velocity inlet is located at the left half of the domain circumference which is set to 4.4 m/s. This value is equal to the average velocity taken from the instantaneous values in
Figure 12, between
to
. The results of the simulations for the two aforementioned conditions are plotted together with the
curve from reference [
11], see
Figure 17. It can be seen that the
curve from 5 constant TSR’s of the current study is in good agreement with the literature. On the other hand, the instantaneous torque curve that corresponds to a TSR of 0.1 to 0.5 is extracted to arrive with the
curve for the freely rotating VAWT which is also plotted in
Figure 17, see green line. The result of simulation for VAWT without induced rotation are roughly agreeing with the other two
curves, only that this is based on instantaneous values while the other two are averaged, thus, the main discrepancy. For the rest of the simulations, the VAWT power is calculated in the same manner as the no induced rotation case.
3.4. Effects of Windshield and Vehicle Geometry to VAWT Power
The instantaneous power curves are obtained using the instantaneous torque and angular velocity from simulation monitors and applying the method stated in
Section 2.4. All the car cases are solved and plotted altogether in
Figure 18.
The power curve of each car case in
Figure 18 generally shows three main parts: (1) the first rise and fall of the curve which includes the occurrence of peak value, (2) the second rise and fall but with lower magnitude than the previous, and (3) the third rise and fall of the curve which has the lowest magnitude and extends wider until it reaches the almost flat curve in
.
In part 1, the curve rises until it reaches the peak value at near
and then falls. This relates to the passage of the portion of the rear wake that contains high-velocity magnitude as shown in the contours in
Figure 19. Upon inspection, all car cases have almost the same rear wake structure since it is only the windshield arclength that is varying between cases. The velocity contours captured at
show that the portion of rear wake which has high velocity magnitude ends at this instance which explains why the curves fall afterward. It can be noticed that the Car Case 1, which has no windshield, gives the highest peak power. This is because the direction of the wind at this instance (near
) is upward which makes the windshield ineffective in blocking the incoming wind that hits against the VAWT rotation and instead, creates stagnation in the area near the inner surface of the windshield. This stagnation causes the reduction of wind velocity from the center of the VAWT to the portion occupied by the windshield, this can be seen in the velocity contour and by comparing the length of lines of the velocity vector in
Figure 20, where longer line represents higher magnitude. The Car Case 6 which has the longest arc length of 150 degrees, creates the largest flow stagnation, hence, this case has the lowest peak value and the lowest energy captured within the duration of part 1.
In the transition from part 1 to part 2, which is the minima located at around
, the curves of car cases with windshield fall deeper compared to that in Car Case 1. This effect is due to the wind direction pointing downward at this instance, as shown in
Figure 21. For this wind direction, the chosen position of the windshield worsens the performance of VAWT since it blocks the incoming wind that supposedly pushes the blades to rotate and allows the incoming wind that hits the blades against its rotation. In the Car Case 2, the windshield is too short to totally block the wind that contributes to the positive torque, that is why the curve does not fall as deep as the other cases with the windshield.
From the minima, the curve starts to rise again and produce a smaller peak which is due to the apparent dissipation of vortices in this period. To visually show this, the wind direction on the period
to
for Car Case 3 is shown in
Figure 22. The slightly varying wind direction is observed until near
and eventually flatten to an almost horizontal direction beyond this instant. This direction is where the windshield gives an advantage. The velocity contour and vector for each car case in
Figure 23 show the effectiveness of the windshield in blocking the wind hitting against the rotation. Looking back at the curve in part 3, the Car Case 2 gives the worst performance among cases with windshield, in the entire duration of part 3 of the curve. The reason is the windshield arc length in Car Case 2 being the shortest among other cases is not effective enough on blocking the wind hitting against the VAWT rotation, therefore, the increase in power from no windshield case is relatively low.
By taking the energy produced by one pass of the vehicle, which is represented by the area under the instantaneous power curve, gives the overall comparison of the effectiveness of windshield with varying arc length for car cases. The numerical integration is applied with negative values excluded, and the results of the computation are summarized in
Table 3. It shows that having the windshield with a 60-degree arc length (Car Case 3) gives the highest increase in energy which is a 16.14% increase from no the windshield case.
The same is done in the bus case and the resulting power curves are shown in
Figure 24 followed by
Table 4 which shows the energy produced for each bus case.
Applying the same technique in getting the weighted-average wind direction in
Section 3.2 to the bus case results in a weighted-average wind direction of 15.7 degrees from positive x-axis.
As opposite to car cases, there is no improvement given by any of the bus cases with windshield and instead lowers the energy produced in the VAWT. Notice in
Figure 25 that unlike in the car case, the wind direction in bus case remains alternating throughout until
. Thus, a stationary windshield that is effective to a particular wind direction did not contribute to the improvement of VAWT performance in bus case. The wind behavior is because the bus, which is wider and has lesser curvature at the front, produces larger vortices that take longer time to dissipate. This can visually see by comparing the velocity vector of bus wake in
Figure 15 and that of car wake in
Figure 13. The existence of slow dissipating vortices in the bus case also prohibits the VAWT to effectively harness the energy in the rear wake as supported by the instantaneous power curve that shows the curve being flat at
while the car case is not.