VAWT Aeroacoustics — Full Technical Report

01

Project setup

Reproducing a published aerodynamic model before extending it into acoustics

Aim and scope

This project began as a replication study.

My starting point was Syawitri, Yao, Yao and Chandra (2020), Assessment of stress-blended eddy simulation model for accurate performance prediction of vertical axis wind turbine . Their study used Transition SST + Stress-Blended Eddy Simulation (SBES) in ANSYS Fluent to predict the unsteady aerodynamic performance of a three-bladed Darrieus vertical-axis wind turbine.

My first objective was to reproduce that aerodynamic behaviour as closely as possible. Once I had a transient model running, I extended the study beyond the original paper by applying the Ffowcs Williams-Hawkings (FW-H) acoustic analogy and analysing the predicted sound at four receiver positions around the turbine.

That made the project a two-stage investigation: reproduce the aerodynamic behaviour of the reference model, then use the resulting unsteady flow field as the basis for an aeroacoustic analysis.

The second stage depended on the first. The acoustic model could only be as reliable as the transient aerodynamic solution feeding it.

The project generally proceeded as follows:

01 Reproduce

Rebuild the published turbine geometry and computational domain.

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02 Simulate

Apply the Transition SST + SBES methodology.

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03 Compare

Assess forces, power and vortex behaviour against published results.

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04 Extend

Use the transient solution for FW-H acoustic prediction.

Reference study and geometry

The project used the standard three-bladed Darrieus VAWT geometry associated with the Castelli benchmark, while the simulation strategy was aligned primarily with Syawitri et al. (2020).

Syawitri et al. investigated tip-speed ratios between 1.44 and 3.3 using Transition SST + SBES. I concentrated the final study on TSR = 3.3 and used the same approximate 1° rotor movement per timestep adopted in the reference work.

The reference paper therefore gave me more than a general methodology. It provided a specific aerodynamic result and flow-field behaviour against which I could assess my own model before attempting the acoustic extension.

External computational domain used in the Syawitri VAWT simulation — External computational domain, including the velocity-inlet and pressure-outlet boundaries. Source: Syawitri et al. (2020).

Three-bladed Darrieus rotor and rotating control sub-domain from Syawitri et al. — Three-bladed rotor geometry and rotating control sub-domain used as the basis of my model. Source: Syawitri et al. (2020).

Freestream velocity 9 m/s

Tip-speed ratio 3.3

Reynolds number ≈ 172,465

Air density 1.225 kg/m³

Timestep ≈ 3 × 10⁻⁴ s

Angular increment ≈ 1°

02

Numerical approach

Developing a transient model capable of resolving blade-wake interaction

Solver and turbulence treatment

A Darrieus turbine experiences strongly unsteady flow. As each blade rotates, its relative velocity and angle of attack change continuously, while the blade also encounters the disturbed wake generated earlier in the rotor cycle.

The resulting flow contains dynamic stall, vortex shedding and rapidly changing aerodynamic loads.

I therefore followed Syawitri et al. in using Transition SST + SBES.

Transition SST provides the near-wall RANS treatment, while SBES allows more LES-like resolution in separated regions where the mesh can support it. This was particularly relevant because the vortex structures were important to both the aerodynamic performance and the later acoustic calculation.

The turbine itself was modelled using a sliding mesh, with the blades contained within a rotating core surrounded by a stationary far-field domain.

Mesh structure

I divided the mesh into three broad levels of refinement: the static far-field, the rotating core, and local bodies of influence around each aerofoil.

The BOIs provided additional resolution around the blades and their wakes, where the vortex structures relevant to the SBES solution were expected to develop.

Far-field mesh used in the Darrieus VAWT CFD simulation — Static far-field surrounding the rotating turbine domain.

Rotating-core mesh containing the three Darrieus turbine blades — Sliding-mesh rotating region containing all three blades.

Refined body-of-influence mesh surrounding a Darrieus turbine aerofoil — Local BOI refinement used to increase resolution around each aerofoil and its developing wake.

Source: Author's own ANSYS mesh. Domain and meshing strategy based on Syawitri et al. (2020).

Rotating-core element size 12 mm

Far-field element size 50 mm

Aerofoil divisions 174

Trailing-edge divisions 14

Near-wall treatment

I targeted y+ ≈ 1 around the aerofoils.

The inflation-layer setup used 15 layers, a first-layer height of approximately 1.95 × 10⁻⁵ m and a growth rate of 1.16.

This was intended to maintain sufficient near-wall resolution for the Transition SST component of the model and capture the blade-surface behaviour feeding the transient aerodynamic solution.

During the project, I began to think of y+ less as another mesh-quality target and more as part of the underlying physics. Poor near-wall resolution could alter separation and unsteady blade loading before the acoustic calculation had even begun.

Inflation-layer mesh around a Darrieus VAWT aerofoil — Inflation-layer structure used around the aerofoil to target y+ ≈ 1. Source: Author's own ANSYS mesh.

Mesh-selection strategy

I tested four mesh resolutions by varying the BOI element size.

The mesh cases were used as an early screening study rather than being taken through the entire final transient run. Their early force histories showed that the 2 mm BOI mesh produced effectively the same aerodynamic response as the finer 1.5 mm case.

I therefore selected the 2 mm mesh for the full simulation. The full case was then run through repeated rotor revolutions while monitoring lift, drag, moment and power coefficients.

Comparison of force behaviour from different VAWT mesh resolutions — Comparison of the candidate mesh resolutions used to select the final BOI size. Source: Author's own simulation and post-processing.

Lift, drag, moment and power coefficients over repeated rotor revolutions — Average force and power coefficients over successive rotor revolutions. Source: Author's own simulation and MATLAB post-processing.

03

Aerodynamic results

The solution became periodic, but did not fully reproduce the reference aerodynamics

My predicted Cp ≈ 0.13

Syawitri et al. ≈ 0.27

Force histories and power coefficient

The simulation initially produced large startup fluctuations in the aerodynamic coefficients. Over successive revolutions, the lift, drag, moment and power histories settled into repeatable periodic behaviour.

That gave me a stable basis from which to calculate aerodynamic performance and compare the model with the reference study.

The most significant quantitative discrepancy was the power coefficient. At TSR = 3.3, my simulation predicted approximately Cp ≈ 0.13, compared with approximately Cp ≈ 0.27 in Syawitri et al.

Power coefficient from the current VAWT simulation compared with published CFD and experimental results — My calculated power coefficient at TSR = 3.3 compared with the published aerodynamic results used for validation. Reference data: Syawitri et al. (2020) and Castelli et al. (2010). Current-study result and comparison plot: author's own work.

Vorticity comparison

The flow-field comparison showed that the difference was not limited to a single performance coefficient.

At corresponding rotor positions, the vorticity contours from Syawitri et al. showed strong vortex structures developing around the blades and clear interaction between turbulence shed from one blade and the next blade in the rotor cycle.

My simulation showed noticeably weaker vortex structures and less developed turbulence in the rotating region.

This became particularly important because the same unsteady flow field subsequently formed the basis of the acoustic calculation.

Current study

Weaker vortex development and reduced turbulence within the rotating region.

Vorticity magnitude scale for the current simulation

Current simulation vorticity field at 135 degrees rotor position — 135°

Current simulation vorticity field at 150 degrees rotor position — 150°

Current simulation vorticity field at 180 degrees rotor position — 180°

Source: Author's own ANSYS Fluent simulation.

Syawitri et al. (2020)

Stronger vortex structures and more pronounced blade-to-blade wake interaction.

Vorticity magnitude scale used in the Syawitri reference results

Source: Syawitri et al. (2020).

04

Acoustic extension

Using the unsteady flow field to investigate far-field acoustic behaviour

FW-H setup

After completing the aerodynamic simulation, I extended the model using Fluent's Ffowcs Williams-Hawkings acoustic analogy .

I used four omnidirectional receivers, each positioned 1 m from the rotor centre.

Receiver 1 was downstream, Receiver 4 upstream, with Receivers 2 and 3 positioned above and below the rotor respectively.

The aim was not to produce a detailed polar directivity map, but to compare wake-side, upstream and lateral acoustic behaviour.

Four FW-H acoustic receivers positioned one metre from the centre of the VAWT — Four omnidirectional FW-H receiver positions, each located 1 m from the rotor centre. Source: Author's own ANSYS Fluent acoustic setup.

Receivers 4

Receiver distance 1 m

Sound speed 340 m/s

Reference pressure 2 × 10⁻⁵ Pa

Pressure-time histories

Before analysing the spectra, I inspected the raw pressure-time histories from all four receivers to confirm that the exported signals contained coherent transient data.

Receiver 1, positioned downstream in the wake, showed the largest pressure excursions, reaching a peak of approximately 155 Pa in the recorded history.

Pressure-time histories recorded at the four acoustic receiver locations — Pressure-time histories recorded at the four FW-H receiver positions. Source: Author's own ANSYS Fluent acoustic results.

Blade-passing frequency

For a three-bladed rotor, I calculated the theoretical blade-passing frequency using:

BPF = (blade count × RPM) / 60

At TSR = 3.3, this gave:

BPF ≈ 27.54 Hz

This gave me a physically expected tonal frequency against which to compare the spectra.

Receiver 4, located upstream, produced the clearest tonal component near the expected BPF. The observed peak was approximately 25.82 Hz, corresponding to a difference of roughly 6.2%.

Receiver 1 behaved differently. Because it sat directly in the wake, its spectrum was more strongly dominated by low-frequency content and the blade-passing tone was less clearly defined.

My interpretation was that the wake-side signal contained a greater contribution from wake turbulence and unsteady blade loading, while the upstream receiver provided a cleaner view of the rotor-periodic tonal component.

Sound pressure level spectra calculated for the four VAWT acoustic receivers — Calculated SPL spectra showing differences between the upstream, downstream and lateral receiver signals. Source: Author's own ANSYS Fluent acoustic results.

05

Limitations

Why the model diverged from the reference study

The limitations were closely connected rather than independent. Most ultimately traced back to the computational resources available for the project.

01

Computational resources

The Transition SST + SBES model was computationally expensive.

Greater BOI refinement increased the cell count, while reducing the timestep increased the number of solver steps required for every revolution. Fully converging several mesh cases, testing additional timesteps and repeating the simulation across several TSRs would have multiplied that cost further.

I did not have the computational access required to carry out all of those studies at the fidelity I would have preferred within the time available.

02

Mesh fidelity and aerodynamic underprediction

The Cp comparison and vorticity fields suggested that my local flow solution was more dissipative than that of Syawitri et al.

Weaker vortex structures, reduced turbulence within the rotating region and smoother pressure gradients were consistent with insufficient local resolution contributing to numerical damping.

The mesh-selection study was also a practical screening exercise rather than a fully converged formal grid-independence study.

03

Timestep and Courant number

The final timestep was approximately 3 × 10⁻⁴ s, corresponding to about 1° of rotor movement.

In my case, this produced local Courant numbers of approximately 10 in parts of the domain.

A smaller timestep would have improved temporal resolution and reduced numerical damping, but it would also have substantially increased the computational cost of every rotor revolution.

This became particularly important because the same timestep was later inherited by the acoustic analysis.

Cell convective Courant number from the final VAWT transient simulation — Cell convective Courant-number output from the final transient simulation. Values in parts of the domain reached approximately 10. Source: Author's own ANSYS Fluent simulation.

04

Acoustic bandwidth

Once I extended the model into acoustics, the CFD timestep also became an acoustic sampling interval.

Using the Nyquist criterion:

f_max = 1 / (2Δt)

the maximum theoretical resolvable frequency was approximately 1.67 kHz.

The model therefore could not represent the full human-audible range of approximately 20 Hz–20 kHz, limiting the analysis of higher-frequency acoustic behaviour.

05

Two-dimensional modelling

The simulation was two-dimensional and therefore could not reproduce genuinely three-dimensional flow behaviour.

Effects such as spanwise flow, blade-tip vortices, finite-height losses and the full three-dimensional development of turbulent structures were absent from the model.

This limited both the aerodynamic fidelity and the range of acoustic source mechanisms that could be represented.

06

Acoustic validation

The FW-H spectra were not validated against a directly corresponding experimental microphone dataset.

Combined with the aerodynamic underprediction and limited acoustic bandwidth, this means I would not present the calculated SPL values as experimentally validated absolute noise levels for a physical turbine.

I am more confident using the acoustic results to discuss frequency behaviour, the location of the blade-passing tone, differences between upstream and wake-side receivers, and the way limitations in the CFD solution propagate into an acoustic prediction.

06

Reflections

What changed in the way I approach numerical modelling

01

Convergence is not validation

The aerodynamic coefficients eventually became periodic, but the model still underpredicted Cp substantially and produced weaker vortex structures than the primary paper.

A solver reaching a repeatable solution does not mean that the physical model has been validated.

02

Matching a published setup is not the same as reproducing the published result

I began the project expecting that reproducing the geometry, turbulence model and approximate timestep would put my result reasonably close to the reference study.

The aerodynamic comparison showed how strongly high-fidelity CFD depends on local mesh resolution, timestep, numerical dissipation and available compute.

03

The acoustic model inherited the aerodynamic weaknesses

Initially, I thought of FW-H as a somewhat separate analysis stage added after the CFD.

By the end of the project, I saw it as being fundamentally dependent on the quality of the preceding flow solution.

If a vortex is under-resolved, its associated pressure fluctuation is weakened. That weakened pressure field then becomes the acoustic source.

04

The timestep acquired a second physical meaning

For the aerodynamic simulation, the timestep primarily controlled rotor movement and transient-flow resolution.

For the acoustic analysis, the same timestep became a sampling interval and directly limited the highest frequency that could be resolved.

05

Compute is an engineering resource

The highest-fidelity setup I could imagine was not necessarily the setup I could realistically run.

I had to decide where additional computation would provide the most value, what could be simplified and how those compromises would limit the claims I made from the results.

07

Future work

What I would change with greater computational access

Treat successful aerodynamic replication as a gate before beginning the acoustic extension.
Refine the BOI mesh until both Cp and vortex development more closely match Syawitri et al.
Run all mesh cases to periodic convergence and perform a formal mesh-convergence study.
Perform a dedicated timestep-sensitivity study.
Reduce the timestep to improve Courant number and scale resolution.
Choose the acoustic timestep based on the frequency range I intend to resolve rather than simply inheriting the aerodynamic timestep.
Move to a three-dimensional simulation.
Use Q-criterion or λ₂ visualisation to link vortex structures more directly with acoustic events.
Compare the predicted spectra with experimental microphone measurements.
Investigate several tip-speed ratios rather than restricting the final acoustic analysis to TSR = 3.3.

08

References

Principal literature used in the project

Primary replication study

Syawitri, T.P., Yao, Y., Yao, J. and Chandra, B. (2020). Assessment of stress-blended eddy simulation model for accurate performance prediction of vertical axis wind turbine. International Journal of Numerical Methods for Heat & Fluid Flow, 31(2), pp. 655–673.

Geometry and aerodynamic validation

Castelli, M.R., Ardizzon, G., Battisti, L., Benini, E. and Pavesi, G. (2010). “Modeling strategy and numerical validation for a Darrieus Vertical Axis Micro-Wind Turbine.” Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition, Vol. 7, pp. 409–418.

Additional literature

Ma, L., Wang, X., Zhu, J. and Kang, S. (2019). Dynamic Stall of a Vertical-Axis Wind Turbine and Its Control Using Plasma Actuation. Energies, 12(19), 3738.

Viqueira-Moreira, M. and Ferrer, E. (2020). Insights into the Aeroacoustic Noise Generation for Vertical Axis Turbines in Close Proximity. Energies, 13(16), 4148.

Pearson, C.E. and Graham, W.R. (no date). Noise from a Model-Scale Vertical-Axis Wind Turbine.

Wang, W.-Y. and Ferng, Y.-M. (2024). Numerical model for noise reduction of small vertical-axis wind turbines. Wind Energy Science, 9(3), pp. 651–664.

09

Original deliverable

Project presentation

The presentation below was the final assessed deliverable for the project. It contains the original methodology, ANSYS setup, aerodynamic histories, flow-field comparisons and acoustic results.

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