In order to evaluate the performance of the double-nozzle runner and characterize the main flow features, computations were performed at design flow lps per nozzle, and part-flow down to 20 lps. For all simulations, H = 1.337 m. The results are compared to the corresponding ones for the single-nozzle turbine with the same and H.
The performance comparison is shown in
Figure 6. The double-nozzle turbine achieved a slightly greater maximum efficiency than the single-nozzle: 89.12%, compared to the measured
[
5], and 88.45% from the RANS computations [
10]. Thus the double-nozzle performance is similar to that of the single-nozzle considering the numerical uncertainty mentioned above. This is a remarkable performance that justifies the use of two nozzles without having to redesign the nozzle or the runner. It is clear from
Figure 6 that adding the second nozzle does not change
for maximum efficiency. This is to be expected from the analysis of [
7] for the optimum speed if it is further assumed that the flows leaving the first stages do not interfere with each other. Therefore, the power density, which is the total power produced per unit runner volume, is doubled for the same runner.
4.2. Flow and Performance of Double-Nozzle Turbine
It was found that
for the two nozzles was the same (199 RPM) as for the single-nozzle. As the identical nozzles were
apart, the flow passing through the runner from each nozzle should be identical but similarly displaced,
Figure 8. This symmetry was not enforced on the computations and some differences, particularly in the second stage flow, are apparent. At
= 46 lps (per nozzle), the mean water velocity contours in the double-nozzle runner are slightly different than that of the single-nozzle, especially in the deflections between the the flow exiting the first-stage of Nozzle 1 and that entering the second stage of Nozzle 2, around the runner centre. As indicated by the circles in
Figure 8, a portion of the flow exiting the first stage of nozzle 1 has been deflected by the flow entering the second stage of nozzle 2 and vice versa. The similar efficiencies of the single- and double-nozzle turbines imply that the flow deflection has little overall effect on the overall runner performance. However, in general, it can be argued that the mutual deflection of the two streams should be avoided. It is noted that the flow stream is narrowed by a factor of
= 0.68 as it exits the first stage so that reducing this ratio may be effective. Further,
can be decreased to avoid any mutual deflection of the flow streams in such a way that it would not reduce the maximum efficiency, for example as demonstrated below for part-load operations. On the other hand, the ability of the second stage of Nozzle 2 to accept flow from the first stage of Nozzle 1, and vice versa, can be viewed as an outcome of the highly desirable flexibility of the crossflow turbine concept in being the only hydro-turbine that has two stages. Since the present double-nozzle design maintains the efficiency of the single-nozzle, we have not attempted to reduce the mutual deflection.
The effect of the flow deflection on the runner performance can be examined by comparing the power extraction behaviour of the runner stages with single- and double-nozzle designs which was evaluated as described in [
7,
10]. As shown in
Figure 9, the impact is reflected in the stage-performance as measured by the power extracted by each blade. Because of the slight asymmetry in the runner flow, the power was calculated for both nozzles but no substantial differences were apparent for the blades
apart so only one set of symbols are shown. According to Adhikari and Wood [
7], maximum efficiency requires conversion of head into kinetic energy in the nozzle, and the flow angles, e.g.,
and
in the first stage of the runner, to equal the blade angles
and
respectively to avoid flow separation on the blades.
is the same for both single- and double-nozzle runners, but the exit flow angle
of the first stage has deviated considerably from the inner blade angle
= 90
as a result of flow deflection in the regions indicated. Therefore, there is less power extraction in that region of the runner. It is important to note that the main difference is that the first stage performance of the double-nozzle runner had decreased whereas the second stage performance has increased. This is clearly the effect of flow deflection in the runner. Fortunately, for this particular turbine, the overall impact of this flow deflection was minimal and did not decrease the maximum efficiency. We conclude that this unoptimized crossflow turbine with two nozzles can achieve the same
as with one.
Part-load flow control is an essential design consideration. We used the slider mechanism of Sinagra et al. [
12], which is a circular segment that can be rotated across the runner entry to reduce
to be proportional to
Q for
. A key feature of the slider is that it maintains a constant
as
Q reduces [
17], which should simplify the power electronics for the generator control. At
, it is evident that the exit arc covers most of the runner periphery for the double-nozzle turbine and thus the angular range for the slider is small, especially when operating near
per nozzle. We show in the
Appendix A that the exit arc of the efficient 0.53 kW turbine is approximately half the size of the entry arc
, which the simulations show is contiguous to the first stage. As such, for
, an inflexible slider can control only a small percentage of
. However, a retractable flexible slider can be designed to reduce
for different
Q.
The part-flow operation of the double-nozzle runner was computed for
Q = 40, 30 and 20 lps with the same slider position,
, as in the single-nozzle simulations of reference [
17] and listed in
Table 3.
Figure 10 shows the part-flow efficiency. Desai [
5] and Adhikari and Wood [
7] determined that maximum efficiency occurs at
RPM for
. This compares with the value of 183 RPM from the analytical equation for
, Equation (14) of reference [
7], which also shows that slider position has no impact on
as
Q decreases. Therefore, simulations were conducted at
RPM. Remarkably, at
lps, there is no deflection between the flow streams in the runner as shown in
Figure 11 and the performance was found the same as expected. Without the slider at the runner entry, and
Q reduced to 40 lps from 46 lps,
dropped significantly, but with the slider at
lps,
was found very close to the design condition. Similarly, using the slider, with
Q reduced from 46 lps to 20 lps, which is about 43% of the design flow, the maximum efficiency of the double-nozzle runner dropped from 88% to about 85%. This demonstrates that the slider maintains high efficiency at considerably lower part-flow operations even when both nozzles are used for
. These results are consistent with Sinagra et al. [
12], who obtained similar performance of the slider in a single-nozzle turbine using RANS simulations.
At
lps and without the slider, the total velocity at runner entry,
, where
and
are the radial and tangential velocities respectively, dropped significantly from the ideal value of 5.12 m/s (=
),
Figure 12. This showed that
H was not converted into kinetic energy. As a result, the efficiency decreased considerably. In contrast, the slider maintained
close to 5.12 m/s, indicating that
H is fully converted into kinetic energy. This demonstrates that the angular momentum flux at the runner entry has increased compared to the case without the slider, which is the reason for the improved efficiency.
The contours of the mean water velocity vectors in the double-nozzle runner at
Q = 40 lps is shown in
Figure 11; there is no deflection of the two flow streams as observed at
. This indicates that a double-nozzle turbine designed with a smaller entry arc angle
at
is most likely to avoid deflection of the flow streams in the runner. Moreover,
Figure 11 shows no flow separation on the blades at both stages, which is one of the important criteria for maximum efficiency. This is due to the fact that the entry flow angle
, not shown here, is close to the outer blade angle
. At very low part-flow operation,
Q = 20 lps, the flow streams are well separated in the runner with no deflection as
Figure 13. Also there is no flow separation on the blades.
The design and performance calculations for all load cases are summarized in
Table 3. Equation (
A5) for the exit arc
agreed well with all the computed results. Provided the reduction in
by the slider preserves the conversion of
H to kinetic energy in the nozzle, Equation (
A5) is independent of
Q. It is noteworthy that the first stage extraction increases as
Q reduces, reaching a maximum of 88% at 20 lps. Increased first stage extraction, does not, however, directly relate to overall efficiency as demonstrated in
Table 3. The results demonstrate the unique capacity of the crossflow runner to extract power in both stages.