Computational Fluid Dynamics (CFD) has become one of the most widely adopted numerical tools for analysing wind turbine aerodynamics. Despite its growing application, the reliability of CFD predictions depends heavily on numerical settings, particularly mesh resolution. An inadequate mesh may lead to inaccurate predictions of aerodynamic performance and flow behaviour, ultimately reducing confidence in simulation-based engineering decisions. The reviewed study investigates how grid refinement influences both turbine performance and fluid-dynamic characteristics of H-Darrieus vertical-axis wind turbines with different blade configurations. By combining Grid Convergence Index (GCI) analysis with aerodynamic evaluation, the research presents a systematic framework for verifying CFD accuracy and identifying mesh resolutions that provide dependable engineering results.
Bibliographic Information
| Item | Information |
|---|---|
| Article Title | Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations |
| Authors | Sanjaya Baroar Sakti Nasution; Dian Morfi Nasution; Elang Pramudya Wijaya; Oki Suprada Ompusunggu |
| Journal | Teknomekanik |
| Volume | 9 |
| Issue | 1 |
| Publication Date | February 2026 |
| Pages | 42–59 |
| DOI | https://doi.org/10.24036/teknomekanik.v9i1.45272 |
| Publisher | Universitas Negeri Padang |
| License | Creative Commons Attribution 4.0 International (CC BY 4.0) |
| Online ISSN | 2621-8720 |
| Print ISSN | 2621-9980 |
| Keywords | CFD; Darrius wind turbine; grid convergence index; vorticity |
Research Background
Computational Fluid Dynamics (CFD) has become an indispensable engineering tool for analysing complex fluid-flow phenomena in numerous engineering disciplines, including aerodynamics, turbomachinery, manufacturing, healthcare, and renewable energy systems. Compared with full-scale experimental testing, CFD enables engineers to investigate flow behaviour under various operating conditions while reducing development time and experimental costs.
Within wind energy research, CFD plays a particularly important role in understanding aerodynamic interactions between airflow and turbine blades. It enables detailed investigation of blade geometry, dynamic stall behaviour, wake development, pressure distribution, turbulence characteristics, and overall turbine performance. These capabilities have made CFD one of the primary numerical methods for designing and optimising modern wind turbines.
Although CFD provides substantial advantages, simulation accuracy depends heavily on numerical modelling decisions. Previous research has shown that computational domain size, turbulence models, boundary conditions, and especially mesh quality strongly influence numerical predictions. Among these factors, mesh refinement is frequently recognised as one of the most critical determinants of simulation reliability because discretisation errors directly affect the accuracy of calculated aerodynamic parameters.
Many previous investigations have evaluated mesh independence using only a single turbine configuration and typically assessed convergence through one performance indicator, such as torque coefficient or power coefficient. While useful, this approach provides only a limited understanding of numerical accuracy because it does not consider whether important flow-field characteristics exhibit similar convergence behaviour.
The reviewed study addresses this limitation by evaluating multiple H-Darrieus blade configurations and examining not only aerodynamic performance but also pressure coefficient and vorticity distributions. Through the application of the Grid Convergence Index (GCI), the research establishes a quantitative framework for estimating discretisation errors and verifying simulation robustness across different mesh resolutions.
Research Objective
- To investigate the influence of mesh resolution on CFD simulations of H-Darrieus vertical-axis wind turbines with different blade configurations.
- To evaluate grid convergence behaviour using the Grid Convergence Index (GCI) as a quantitative indicator of discretisation error.
- To analyse how mesh refinement affects both aerodynamic performance and important flow-field characteristics, including pressure coefficient and vorticity.
- To compare numerical behaviour among three-, four-, and five-bladed H-Darrieus wind turbine configurations.
- To determine an appropriate mesh resolution capable of producing reliable CFD predictions while maintaining acceptable computational efficiency.
Why This Research Matters
- Improves CFD verification practices. The study demonstrates that mesh sensitivity should be evaluated using both aerodynamic performance indicators and detailed flow-field characteristics rather than relying on a single numerical parameter.
- Enhances confidence in numerical simulation. Quantitative estimation of discretisation error through the Grid Convergence Index provides engineers with objective evidence regarding simulation reliability.
- Supports wind turbine optimisation. Accurate CFD predictions are essential for improving blade geometry, turbine efficiency, and aerodynamic performance.
- Reduces uncertainty in engineering design. Proper grid convergence analysis helps ensure that numerical results reflect physical behaviour rather than artefacts introduced by insufficient mesh quality.
- Promotes efficient computational modelling. Identifying an appropriate mesh density enables engineers to balance numerical accuracy with computational cost.
- Provides a systematic verification framework. The proposed methodology can serve as a reference for future CFD studies involving vertical-axis wind turbines and similar rotating aerodynamic systems.
Research Methodology
The study employed a quantitative Computational Fluid Dynamics (CFD) approach to evaluate the influence of mesh resolution on the numerical accuracy of H-Darrieus vertical-axis wind turbine simulations. Rather than focusing exclusively on turbine performance, the researchers investigated how different mesh densities affected both aerodynamic outputs and detailed flow-field characteristics. Grid convergence was assessed using the Grid Convergence Index (GCI), allowing numerical uncertainty to be quantified systematically.
Wind Turbine Configurations
Three H-Darrieus wind turbine configurations were analysed using identical overall dimensions but different blade numbers. The investigated models consisted of three-, four-, and five-bladed turbines equipped with a symmetrical NACA 0015 airfoil. Because blade chord remained constant while blade number varied, each configuration possessed a different solidity, enabling comparison of grid convergence behaviour across multiple turbine geometries.
Numerical Simulation
Two-dimensional transient CFD simulations were performed using ANSYS Fluent. The computational domain consisted of stationary and rotating regions connected through a sliding-mesh interface to capture the transient interaction between rotating blades and surrounding airflow. A uniform inlet velocity of 8 m/s was prescribed, while pressure outlet and symmetry boundary conditions completed the computational domain.
The simulations employed the SST k–ω turbulence model because of its capability to predict near-wall flows, adverse pressure gradients, and flow separation more accurately than several alternative Reynolds-Averaged Navier–Stokes (RANS) models. Second-order discretisation schemes were applied to improve numerical accuracy throughout the transient simulations.
Mesh Sensitivity Analysis
Five different mesh resolutions were generated for every blade configuration. The mesh was intentionally refined around the rotating domain and blade surfaces using inflation layers to improve the resolution of boundary-layer flow and near-wall aerodynamic phenomena. The total number of computational cells ranged from approximately twenty thousand to more than three hundred thousand, depending on blade configuration and refinement level.
Instead of relying solely on traditional mesh independence analysis, the researchers evaluated discretisation error quantitatively through the Grid Convergence Index (GCI). Richardson extrapolation was applied to estimate numerical uncertainty and determine whether further mesh refinement produced meaningful improvements in simulation accuracy.
Performance Evaluation
Simulation results were evaluated using several complementary indicators. Aerodynamic performance was assessed through torque coefficient and torque generation, while pressure coefficient and vorticity distributions were analysed to examine detailed flow behaviour surrounding turbine blades. This broader evaluation enabled the researchers to determine whether mesh refinement consistently improved both global turbine performance and local fluid-dynamic characteristics.
Key Findings
Mesh Refinement Improves Numerical Stability
The study demonstrated that increasing mesh density consistently reduced discretisation errors and produced more stable CFD predictions. Finer computational grids generated smoother convergence behaviour and improved agreement among successive numerical solutions, confirming the importance of adequate mesh refinement for reliable aerodynamic analysis.
Grid Convergence Was Consistent Across Blade Configurations
Although the three turbine models differed in blade number and solidity, all configurations exhibited similar grid-convergence behaviour. As mesh resolution increased, numerical uncertainty decreased steadily, indicating that the adopted verification procedure remained robust regardless of turbine geometry.
Torque Prediction Became More Reliable
Torque coefficient calculations became increasingly stable as additional computational cells were introduced. Coarse meshes produced greater variation in predicted torque, whereas refined meshes generated smoother and more consistent aerodynamic performance. These results confirm that mesh quality directly influences predicted turbine efficiency.
Flow-Field Resolution Improved Significantly
Beyond aerodynamic performance, finer meshes provided considerably better resolution of important fluid-flow characteristics. Pressure coefficient distributions and vorticity patterns surrounding turbine blades became more detailed and physically consistent as mesh refinement increased, demonstrating that numerical verification should include flow-field analysis rather than relying exclusively on global performance indicators.
Discretisation Errors Declined with Increasing Grid Density
Grid Convergence Index calculations showed a continuous reduction in numerical error as computational grids became finer. The smallest GCI values were obtained using the highest mesh resolutions, confirming that discretisation error decreases systematically with mesh refinement.
An Efficient Mesh Resolution Was Identified
The study found that a computational grid containing approximately 1.6 × 105 cells provided an effective balance between numerical accuracy and computational efficiency. At this resolution, discretisation errors remained below five percent while avoiding the substantially higher computational cost associated with much finer meshes.
Comprehensive Mesh Verification Produces More Reliable CFD Simulations
One of the principal outcomes of the research is the demonstration that mesh sensitivity analysis should evaluate both engineering performance indicators and detailed flow phenomena. Combining torque prediction with pressure coefficient, vorticity analysis, and GCI verification provides a more comprehensive assessment of CFD reliability than traditional single-parameter approaches.
Scientific Contribution
- The study extends conventional CFD mesh verification by evaluating both aerodynamic performance and detailed flow-field characteristics simultaneously.
- It demonstrates the application of the Grid Convergence Index as an objective method for quantifying discretisation errors in H-Darrieus wind turbine simulations.
- The research compares grid convergence behaviour across multiple blade configurations instead of limiting verification to a single turbine geometry.
- It establishes a practical mesh density capable of maintaining numerical errors below five percent while preserving computational efficiency.
- The findings provide a reproducible verification framework that can improve the credibility of future CFD investigations involving rotating aerodynamic systems.
Industrial Implications
Although the research focuses on numerical verification rather than turbine design optimisation, its findings have direct implications for engineering practice. Reliable CFD simulations enable engineers to make better-informed decisions throughout the design, optimisation, and evaluation stages of vertical-axis wind turbine development. By demonstrating how mesh refinement influences numerical accuracy, the study provides practical guidance for selecting computational settings that balance accuracy with computational cost.
- Improves engineering confidence in CFD analysis. Engineers can adopt the recommended mesh refinement strategy to reduce discretisation errors before using simulation results for design decisions.
- Supports renewable energy development. More accurate aerodynamic simulations contribute to the optimisation of H-Darrieus wind turbines intended for small-scale and distributed renewable energy systems.
- Reduces unnecessary computational expense. Identifying an appropriate mesh density allows researchers and engineers to avoid excessive computational time while maintaining acceptable numerical accuracy.
- Enhances engineering verification procedures. The combination of torque analysis, pressure coefficient evaluation, vorticity assessment, and Grid Convergence Index calculations establishes a comprehensive workflow for CFD validation.
- Benefits industrial CFD applications. The verification methodology may also be adapted to other rotating machinery, including fans, compressors, pumps, propellers, and hydrokinetic turbines where mesh quality significantly affects simulation reliability.
- Supports digital engineering. Accurate numerical verification strengthens the use of simulation-driven product development, virtual prototyping, and engineering optimisation in industrial environments.
Research Limitations
- The investigation considered only three H-Darrieus blade configurations consisting of three, four, and five blades. Additional rotor geometries were outside the scope of the present study.
- The numerical simulations were performed using two-dimensional CFD models. Although computationally efficient, two-dimensional analysis cannot fully capture all three-dimensional flow phenomena that occur in practical wind turbine operation.
- The study employed the SST k–ω turbulence model exclusively. The influence of alternative turbulence models on grid convergence behaviour was not investigated.
- Only five mesh refinement levels were evaluated. Different refinement strategies may produce different convergence characteristics depending on turbine geometry and numerical settings.
- The research focused on numerical verification and mesh sensitivity rather than experimental validation using wind tunnel measurements or field testing.
- The operating conditions were limited to the selected turbine geometry and simulation parameters adopted in the study. Different wind speeds, tip-speed ratios, or operating environments may require additional verification.
Future Research Opportunities
- Extend grid convergence analysis to fully three-dimensional CFD simulations for H-Darrieus wind turbines.
- Investigate mesh sensitivity under different operating conditions, including varying wind speeds and tip-speed ratios.
- Compare Grid Convergence Index behaviour using alternative turbulence models such as LES, DES, or hybrid RANS–LES approaches.
- Evaluate mesh convergence for different airfoil profiles, blade inclinations, rotor diameters, and turbine solidities.
- Integrate experimental measurements with CFD verification to strengthen numerical validation.
- Develop automated mesh optimisation algorithms capable of achieving target numerical accuracy with minimum computational cost.
- Investigate adaptive mesh refinement techniques for transient simulations of rotating wind turbines.
- Apply the proposed verification framework to other renewable-energy devices, including Savonius turbines, hydrokinetic turbines, marine current turbines, and axial-flow wind turbines.
- Examine the influence of mesh refinement on additional flow variables such as turbulence kinetic energy, wake recovery, flow separation, and vortex evolution.
- Explore artificial intelligence or machine learning techniques for predicting optimum mesh density before CFD simulation begins.
Potential for Public Policy Citation
Although primarily intended for engineering researchers, the study also offers value for organisations responsible for renewable-energy development, engineering standards, and research funding. Reliable numerical verification contributes to greater confidence in simulation-based engineering studies, supporting the development of evidence-based renewable-energy technologies. The methodology may assist academic institutions, engineering laboratories, government research agencies, and standards organisations in promoting best practices for CFD verification and validation within computational engineering research.
- Renewable energy policy development.
- Engineering research quality assurance.
- National CFD verification guidelines.
- Wind energy technology development programmes.
- University research laboratories.
- Engineering accreditation and computational modelling standards.
Who Should Read This Paper?
- Researchers working in Computational Fluid Dynamics (CFD).
- Wind turbine engineers and aerodynamic designers.
- Renewable energy researchers.
- Mechanical engineering academics.
- Graduate students studying numerical simulation.
- Researchers conducting mesh sensitivity or verification studies.
- Engineers involved in rotating machinery analysis.
- ANSYS Fluent users seeking reliable CFD verification procedures.
- Reviewers evaluating CFD-based engineering manuscripts.
- Anyone interested in improving numerical reliability in engineering simulations.
Final Thoughts
The reviewed study makes a valuable contribution to CFD verification by demonstrating that reliable numerical simulations require more than simply increasing mesh density. Through systematic Grid Convergence Index analysis, multiple blade configurations, and simultaneous evaluation of aerodynamic performance and flow-field characteristics, the research establishes a comprehensive verification methodology that strengthens confidence in CFD results.
Rather than treating mesh independence as a routine numerical procedure, the study highlights its fundamental role in producing scientifically defensible engineering simulations. The proposed verification framework provides practical guidance for researchers seeking an effective balance between computational efficiency and numerical accuracy while offering a reproducible approach that can be adapted to future investigations involving rotating aerodynamic systems and renewable-energy technologies.
Suggested Citations
UNP–Teknomekanik Style
Nasution, S. B. S., Nasution, D. M., Wijaya, E. P., & Ompusunggu, O. S. (2026). Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations. Teknomekanik, 9(1), 42–59. https://doi.org/10.24036/teknomekanik.v9i1.45272
APA (7th Edition)
Nasution, S. B. S., Nasution, D. M., Wijaya, E. P., & Ompusunggu, O. S. (2026). Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations. Teknomekanik, 9(1), 42–59. https://doi.org/10.24036/teknomekanik.v9i1.45272
IEEE Style
S. B. S. Nasution, D. M. Nasution, E. P. Wijaya, and O. S. Ompusunggu, "Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations," Teknomekanik, vol. 9, no. 1, pp. 42–59, Feb. 2026, doi: 10.24036/teknomekanik.v9i1.45272.
Harvard Style
Nasution, S.B.S., Nasution, D.M., Wijaya, E.P. and Ompusunggu, O.S., 2026. Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations. Teknomekanik, 9(1), pp.42–59. Available at: https://doi.org/10.24036/teknomekanik.v9i1.45272.
Vancouver Style
Nasution SBS, Nasution DM, Wijaya EP, Ompusunggu OS. Grid convergence analysis of an H-Darrieus wind turbine for multiple blade configurations. Teknomekanik. 2026;9(1):42–59. doi:10.24036/teknomekanik.v9i1.45272.
Chicago (Author–Date)
Nasution, Sanjaya Baroar Sakti, Dian Morfi Nasution, Elang Pramudya Wijaya, and Oki Suprada Ompusunggu. 2026. "Grid Convergence Analysis of an H-Darrieus Wind Turbine for Multiple Blade Configurations." Teknomekanik 9 (1): 42–59. https://doi.org/10.24036/teknomekanik.v9i1.45272.
MLA (9th Edition)
Nasution, Sanjaya Baroar Sakti, et al. "Grid Convergence Analysis of an H-Darrieus Wind Turbine for Multiple Blade Configurations." Teknomekanik, vol. 9, no. 1, 2026, pp. 42–59. https://doi.org/10.24036/teknomekanik.v9i1.45272.
Editorial Note
Engineering Research Insights provides independent scholarly reviews of recently published engineering research to improve accessibility for researchers, educators, students, industry practitioners, and policymakers. This review summarizes the scientific contribution of the article using information presented in the original publication. The commentary reflects the editorial interpretation of the reviewed work and is intended solely for educational and scientific communication purposes. Readers are encouraged to consult the original article for complete methodological details, numerical formulations, datasets, and supplementary discussions.
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