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H-Darrieus Cp Values

Hello QBlade Community,

Recently I tried to replicate the experimental results for calculating the Cp and Ct of an H-Darrieus Turbine inside a wind tunnel from this study (https://doi.org/10.1115/1.4030448). I recreated the turbine in QBlade and ran it under the same conditions as in the mentioned study (TSRs of 1.5 to 3.5 at 400 rpm while varying the wind speed).

The results I obtained for the Ct had good agreement with the closed chamber configuration of the wind tunnel (CC) and slightly overestimated the open chamber configuration of the wind tunnel (OC). As for the Cp, all the values I obtained significantly overestimated the Cp given by both CC and OC wind tunnel configurations. I tried all the available dynamic stall models, but only the IAG model had a significant impact in bringing down the Cp values to agree more with the experimental data. I also tried other methods for increasing the accuracy of the simulation such as more blade elements (up to 40 per blade), smaller time step (down to 1.25 ms), using the Himmelskamp effect, incorporating the drag from the tower and struts, and using different wake integration methods. Most of these methods had no significant effect on the calculated Cp. Other than the IAG dynamic stall model, incorporating the drag from the struts (which had a diameter of 1 cm) had a huge and unrealistic impact in decreasing calculated Cp. It seemed as if adding tiny struts to the VAWT model on QBlade only decreased the Cp, but not the Ct, which I found strange.

I have attached a copy of the rotor and turbines I was using for these simulations alongside the plotted data for the obtained Cp and Ct values. The dashed lines represent the obtained experimental data while the full lines represent the data from my QBlade simulations. Each case has three data points for TSRs of 1.5, 2.5 and 3.5, with the line representing a quadratic fit of these 3 points. The baseline simulation uses 13 elements per blade, a time step of 2.5 ms and no dynamic stall models. The black line represents a combined case that used 30 elements per blade, 2.5 ms time step, incorporated the drag from the tower, and used the IAG dynamic stall model. Its black line on the plot is created by using a cubic polynomial fit with data points at 1.5, 2, 2.5, 2.75, 3, 3.25 and 3.5.

If anyone can take a look at the QBlade files I have shared and explain what I’m doing incorrectly or at least provide a good explanation for how to run accurate simulations for VAWTs with dimensions of around H x D:  1.5m x 1m, it would be greatly apreaciated.

Thank you and best!

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Hi,

I ran a quick test of this model, and found a converged Cp of ~0.45 (no struts) and ~0.25 (with struts) at a TSR of 3.0.

The main issue I am seeing with this model is that for the NACA 0021 the polar data was calculated by XFoil for a Reynolds number of 1,000,000. At this turbine size, at 10m/s wind speed and at a TSR of 3 the Reynolds number at the blades is in the range between 100,000-200,000. At such low Reynolds numbers the airfoils operate at a much lower efficiency – and this is most likely the main reason for the “overprediction” that you are seeing.

I would suggest to recalculate the polars for the appropriate Reynolds number range and define a “multi-polar” blade, so that during the simulation the polar data can be interpolated based on the instantaneous Reynolds number.

I dont think that the effect of struts is not correctly predicted. While the struts are quite “thin” there are 6 struts in total connected to the three blades and they cause significant parasitic torque at the high rotational speeds. The drag created by the struts is solely based on the local relative velocities over the struts, their diameter and the strut drag coefficient, which in your case is 1.2. You can carry out a quick calculation by hand to estimate this local parasitic torque and compare it to the aerodynamic torque generated by the blades.

Also have a look at this thread, as it contains some useful information on the wake settings and required simulation times to get “converged” power coefficients from a simulation.

BR,

David

cq123 has reacted to this post.
cq123

Hello David,

Thank you very much for your feedback, indeed I had not considered that the only polar I was using was meant for much higher Reynolds numbers than I was anticipating in the simulations. This indeed helped with the results we are getting so I thank you for that. I hence defined a rotor with a multipolar that had about 20 different polars which encompassed the range of the expected Re numbers to be faced by the blades throughout the simulations (Re = 40k – 220k). I also defined a rotor with only a single polar of 100k = Re for testing purposes. As I ran these two new rotors for the same conditions as explained in the original post I made of this thread, I still did not get sufficiently accurate results with respect to the paper I was trying to emulate (https://doi.org/10.1115/1.4030448). The 100k polar had good agreement with low TSRs but not as much with higher TSRs, while the multipolar had better performance with TSRs but worse with low TSRs, as seen in the figure below. I have also tried running the multipolar blade with other dynamic stall models and tower drag but none have made a significant difference.

I have attached the project file here for further reference. Am I defining my 360 polars correctly? Usually, I run the xfoil analysis for +/- 15 deg of the angle of attack.  Is there anything else with the turbine setups that could be changed to help with the accuracy of the simulations? Any feedback would be greatly appreciated once again.

Best regards,

Daniel Roman

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Hi Daniel,

glad to hear that you have made some progress.

looking at your setup, nothing appears fundamentally incorrect. However, when generating XFoil polars for very low Reynolds numbers, we often initiate the boundary layer transition at the leading edge, whereas you’ve opted for free transition. This could be worth investigating.

Another aspect to consider is the “virtual camber effect.” Although, for your rotor design, this effect might be minimal due to the rotor’s low solidity and operational tip-speed ratio (TSR).

Regarding the experimental results: the OC and CC results show significant differences, making it challenging to assess their accuracy. Achieving good correlation with experimental data largely hinges on the quality of that data. Small variations in measuring the rotor’s operating conditions, such as wind speed and RPM, can significantly impact the results.

Has this experimental data been verified, for instance, compared to another measurement of the same rotor or to computational fluid dynamics (CFD) or lower fidelity simulations?

In general, we could accurately predict the performance of quite a few different VAWT designs in the past, thats why I’m wondering about this large discrepancy in your comparison.

BR,

David

danirmn has reacted to this post.
danirmn

Hello David,

Thank you once again for your feedback. We are currently constructing a 3D CFD model to verify these results as well, but it is not done yet.

I would like to ask though what do you consider low Re numbers for these purposes? As in, for what range of Re numbers should I enforce the boundary layer separation at the leading edge?

Thank you once again and best,

Daniel Roman

Hello Daniel,

what “low” means in this context if of course highly subjective, but I would say anything < ~ 300,000 Re could be considered “low”. This range of Reynolds numbers is often seen in wind tunnel experiments. To reduce the sensitivity of the results to surface roughness effects, and also to prevent laminar separation bubbles, tripping is often used.

But also when simulating airfoil data with XFoil in a similar Reynolds numbe range I often use forces leading edge transition for the same reasons.

BR,

David

danirmn has reacted to this post.
danirmn

Hello David,

Thanks again for your feedback, this as well has improved our results. Could you provide an explanation or some literature which could explain why forcing the boundary layer transition in the leading edge instead of having it be free is more accurate for low Reynolds number cases?

Thanks again and best,

Daniel Román

Hi Daniel,

in this range of Reynolds numbers the boundary layer will transition from laminar to turbulent somewhere along the airfoil chord.

This transition point is highly sensitive to inflow turbulence and also to surface roughness effects, both of which are hard to control exactly in an experiment, but also in a simulation (turbulence models play a big role there). For a turbine operating in the field it is often assumed that the surface roughness increases over its lifetime (erosion, bugs, etc), which will cause an earlier transition than in a coressponding experiment.

Removing this “transition point sensitivity” from the experiment or simulation by means of tripping or forced transition helps to eliminate this sensitivity of the transition point and aligns experimental and numerical results more closely with real-world data.

BR,

David

 

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danirmn