Hydrofoil performance cannot be fully understood through lift and drag coefficients alone. Two operating conditions may produce apparently comparable global results while concealing very different flow structures, structures that can influence drag, noise, vibration, cavitation and ventilation.

Our new paper, “Direct Numerical Simulation of Flow Around Hydrofoil Section ‘A’ at Three Angles of Attack”, by Mario Caponnetto, Milovan Perić, Tomás Carreira and Andrew Baglin, investigates precisely this issue. Using Direct Numerical Simulation (DNS), the study examines the same hydrofoil section at three angles of attack and reveals how small changes in operating condition can fundamentally alter the transition from laminar to turbulent flow.

Building on our previous DNS benchmark

This study is the next step in the research programme introduced in our previous paper, summarised in “When Small Flow Details Matter: DNS for Accurate Ventilation Prediction in Foiling Yachts”.

That first paper established a high-resolution DNS benchmark for flow around hydrofoil Section A at a chord Reynolds number of 500,000 and a single angle of attack. It showed that instantaneous vortical structures can generate pressure minima far below those visible in time-averaged results. These local events may be important in the inception of cavitation or ventilation, yet they can remain hidden in lower-fidelity or steady analyses.

The new paper extends that benchmark from one operating point to three. The geometry and Reynolds number remain unchanged, but the angle of attack is increased from 0.71° to 2.55° and 4.05°, corresponding to lift coefficients of practical interest for the selected foil section. The objective is not merely to compare lift and drag, but to determine how the underlying transition mechanisms evolve as foil loading changes.

Three angles of attack, three transition mechanisms

The simulations show that a relatively narrow change in angle of attack—from 0.71° to 4.05°—produces markedly different flow behaviour.

At 0.71°, a laminar separation bubble forms on the suction side. Instabilities develop in its separated shear layer, producing intense vortex tubes that break down into turbulence near the trailing edge. Transition also occurs on the pressure side. These moving vortices generate instantaneous pressure minima that are not visible in the mean flow field.

At 2.55°, the pressure-side boundary layer remains laminar, while transition on the suction side takes a different form. Wall-attached vortices develop, travel downstream, deform, pair and eventually break down into fine turbulent structures. Once again, time-averaged results smooth this dynamic process into what appears to be a single recirculation region, concealing the actual sequence of events.

At 4.05°, the mechanism changes again. No laminar separation occurs on the suction side. Instead, the stronger adverse pressure gradient triggers natural transition much closer to the leading edge. The transition front is highly intermittent, with alternating laminar and turbulent regions, turbulent spots and elongated streaks. Despite the higher angle of attack, the flow does not simply present a stronger version of the same phenomena observed in the other cases; it develops through a different physical route.

Why instantaneous flow matters

Engineering analyses often rely on time-averaged pressure, velocity and wall-shear distributions. These quantities remain essential, but the study shows that they cannot describe the complete flow physics.

Time averaging removes moving wall-attached vortices, intermittent transition fronts and short-lived low-pressure regions from view. In some cases, the resulting mean field represents a smooth flow pattern that does not exist at any individual instant. This distinction matters because local, unsteady structures may contribute to phenomena such as cavitation and ventilation even when global coefficients appear well behaved.

By resolving the relevant spatial and temporal scales without a turbulence model, DNS provides access to these hidden dynamics. The simulations used systematically refined, locally adapted meshes containing up to approximately 140 million control volumes. Grid-dependence studies and spectral analysis were used to verify that the solutions were sufficiently accurate to serve as engineering reference data.

What does this mean for preliminary design tools?

The paper also compares the DNS results with XFOIL, a widely used tool for preliminary hydrofoil design.

XFOIL captures the overall lift trend reasonably well, predicting lift coefficients within approximately 3–7% of the DNS values. However, it systematically underpredicts drag by around 14–19% and places transition farther downstream in all three cases.

This does not diminish XFOIL’s value as a fast preliminary design tool. Rather, it clarifies its limits. Agreement in lift or in a single predicted transition location does not mean that the unsteady structures governing pressure fluctuations, viscous losses, cavitation or ventilation susceptibility have also been captured.

For designers, the practical lesson is clear: global performance indicators are necessary, but they may not be sufficient when local and transient flow phenomena determine operational risk.

A benchmark for more practical CFD methods

DNS remains too computationally demanding for routine full-scale vessel design. Its value here lies in providing a trusted reference against which more affordable methods can be assessed.

The results from these three operating points create a demanding validation dataset for LES, RANS and other lower-fidelity approaches. Future work in this research programme will compare turbulence models against the DNS solutions, examine a second hydrofoil geometry, and investigate the effects of free-stream turbulence and the free surface.

The broader aim is to identify which modelling approaches can reproduce the flow features that matter most for real hydrofoil engineering—without requiring DNS-level computational resources in everyday design work.

Download the full paper

This article provides an overview of the main findings. The full paper includes the complete numerical methodology, grid-dependence assessment, spectral analysis, pressure and wall-shear distributions, detailed visualisations of the three transition mechanisms, and the comparison with XFOIL.

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