⚡ electrical engineering

Time-Domain Two-Way Fluid–Structure Interaction Analysis of the HIRENASD Transonic Wing: Static Aeroelastic Response and Flutter Prediction

This study validates a time-domain, loosely-coupled Fluid–Structure Interaction framework in ANSYS Workbench against NASA benchmarks to accurately predict the static aeroelastic response and flutter boundaries of the HIRENASD transonic wing, demonstrating its viability as a reproducible, industry-accessible tool for preliminary aircraft wing assessment.

Original authors: Siddalingappa P Kodigaddi

Published 2026-07-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Siddalingappa P Kodigaddi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, flexible wing soaring through the sky, dancing with the wind. Now, imagine that wind isn't just blowing past it; it's actually pushing and pulling the wing, while the wing bends and twists back, changing how the wind flows. This invisible dance is called Fluid–Structure Interaction (FSI), and when it gets out of hand, the wing can start shaking violently until it breaks. This scary shaking is called flutter.

In this study, a researcher named Siddalingappa P. Kodigaddi built a super-accurate virtual wind tunnel inside a computer to watch this dance happen on a specific wing called the HIRENASD. This isn't just any wing; it's a high-tech, "supercritical" wing designed for fast, transonic jets (flying just below the speed of sound). The goal was to see if a standard, commercial computer program (ANSYS) could predict exactly when this wing would start to flutter, without needing a super-expensive, custom-made code.

The Virtual Wind Tunnel Test

First, the researcher had to prove his virtual wind tunnel was real. He set up a simulation at a speed of Mach 0.8 (about 614 mph) and a very high air density (Reynolds number of 7×10⁶). He compared his computer's results against a famous benchmark from NASA.

The Result: The computer predicted the lift, drag, and twisting forces with incredible accuracy, missing the NASA numbers by less than 4%. It was like guessing the weight of a cat and being off by only a few grams.
The Wing's Natural Rhythm: Before the wind blew, the researcher checked how the wing vibrated on its own (like plucking a guitar string). The wing's main bending frequency was measured in real life at 26.0 Hz. The computer predicted 26.504 Hz. That's a difference of only 1.94%, proving the virtual wing was stiff and heavy just like the real one.

The Static Stretch (Before the Shaking)

Next, they pushed the wing to different angles (from -1.5° to +4.5°) to see how much it would bend under steady pressure.

The Bend: At the highest angle (4.5°) and speed (Mach 0.8), the tip of the wing bent down by 12 mm.
The Twist: Because the wing is swept back (angled like a boomerang), this bending actually twisted the wing slightly, which helped reduce the load on the root. It's like a flexible tree branch bending in the wind to avoid snapping. The computer matched these bending numbers almost perfectly with other high-end simulations.

The Big Moment: Finding the Flutter Speed

This is the main event. The researcher turned off the "damping" (the internal friction that usually stops shaking) and slowly increased the wind speed in the simulation to see when the wing would go crazy. They tested two different "atmospheres":

High Altitude (Thin Air): Speed Mach 0.8 with a density of 0.2525 kg/m³.
Lower Altitude (Thick Air): Speed Mach 0.7 with a density of 0.50 kg/m³.

The Findings:

At Mach 0.8 (Thin Air): The wing stayed calm until the speed hit 266.56 m/s. At this exact speed, the wing started shaking with a constant, steady rhythm (neither growing nor dying out). This is the flutter speed. The shaking happened at a frequency of about 22 Hz.
At Mach 0.7 (Thick Air): The wing stayed calm until 230.46 m/s. Here, the shaking frequency was about 25.5 Hz.

The "Aha!" Moment:
You might think, "Wait, the wing fluttered at a higher speed in the thin air (266.56 m/s) than in the thick air (230.46 m/s). Does that mean it's safer at high altitudes?"
Not exactly. The paper explains that while the speed was higher, the force of the wind (dynamic pressure) was actually much stronger in the thick air case.

The "flutter pressure" at the lower speed (thick air) was 13.27 kPa.
The "flutter pressure" at the higher speed (thin air) was only 8.97 kPa.
This means the wing is actually 47.9% more stressed in the thick air scenario, even though it was moving slower. The paper confirms a rule of thumb: the danger scales with density times speed squared. So, a wing that is safe at a low altitude might become dangerous as it climbs, even if it keeps the same speed, because the air gets thinner and the aerodynamic "stiffness" drops.

What Kind of Shaking Was It?

The researcher looked closely at the shaking to see how it happened.

One-Mode Wobble: The wing didn't twist and bend together in a complex knot. Instead, it was a simple up-and-down bending motion (like a diving board).
Why? The wing's twisting frequency is way higher (279.13 Hz) than its bending frequency (26.504 Hz). They are so far apart that they never "coalesce" (merge) to create a complex, deadly flutter. It's a simple, single-mode bend.
The Shift: At the higher speed (Mach 0.8), the air pressure actually made the wing feel "softer," dropping its shaking frequency from 26.504 Hz down to 22 Hz. At the lower speed (Mach 0.7), the air was less "softening," so the frequency only dropped to 25.5 Hz.

What This Means for the Future

The paper doesn't claim to have "solved" flutter for all planes forever. Instead, it shows that commercial, off-the-shelf software (ANSYS Fluent and ANSYS Mechanical) can be used to predict these dangerous speeds with high confidence, without needing secret, government-only code.

The Confidence: The results are based on simulations that have been rigorously checked against real-world data and other super-computer benchmarks. The authors estimate their method is accurate within 5–8%.
The Limit: The simulation didn't account for the extreme cold of the wind tunnel (which makes the metal slightly softer) or complex temperature changes, but the main bending mode was accurate enough to trust the flutter prediction.

In short, this study built a digital twin of a high-tech wing, proved it behaves like the real thing, and used it to find the exact speed where the wing starts to dance uncontrollably. It showed that while the wing might fly faster before shaking in thin air, the force of the wind is the real danger, and this new computer method can help engineers design safer wings for the future.

Technical Summary: Time-Domain Two-Way Fluid–Structure Interaction Analysis of the HIRENASD Transonic Wing

Problem Statement
The structural integrity of transport aircraft wings in the transonic regime is governed by complex aeroelastic couplings, particularly flutter, which can lead to catastrophic failure. Linear frequency-domain methods, such as the Doublet Lattice Method (DLM), often lack the fidelity to capture critical nonlinear phenomena inherent to transonic flow, including moving shock waves, shock-induced boundary layer separation, and strong fluid-structure interactions. While the High Reynolds Number Aero-Structural Dynamics (HIRENASD) project provides a comprehensive experimental database for a supercritical wing (BAC3-11 airfoil), significant gaps remain in the open literature regarding the validation of these configurations using commercially available, general-purpose CFD-CSD solvers. Furthermore, systematic time-domain identification of flutter boundaries across multiple Mach numbers and the quantitative analysis of how free-stream density and Mach number jointly influence flutter dynamic pressure have not been fully addressed for this benchmark.

Methodology
The study employs a time-domain, loosely-coupled, two-way Fluid–Structure Interaction (FSI) framework implemented within ANSYS Workbench. The approach partitions the solution between:

CFD: ANSYS Fluent (density-based solver) utilizing the Reynolds-Averaged Navier–Stokes (RANS) equations with the SST $k-\omega$ turbulence model. The fluid domain features an unstructured tetrahedral mesh (~600,000 cells) with prismatic layers to achieve $y^+ \approx 1$ .
CSD: ANSYS Mechanical utilizing a hexahedral finite element model (41,923 elements) of the HIRENASD wing structure (nickel maraging steel). Modal analysis uses the Block-Lanczos algorithm, and transient integration employs the Newmark- $\beta$ method.
Coupling: ANSYS System Coupling manages the data exchange via the General Grid Interface (GGI) for force conservation and Smart Bucket interpolation for displacement mapping. Mesh deformation is handled via spring-analogy smoothing with local remeshing.

The study validates the framework against NASA FUN3D aerodynamic benchmarks and HIRENASD experimental structural frequencies. Static aeroelastic analyses are performed at Mach numbers ( $M$ ) of 0.7 and 0.8 across angles of attack from $-1.5^\circ$ to $+4.5^\circ$ . Dynamic flutter analysis identifies the flutter boundary by systematically varying free-stream velocity to characterize sub-critical (damped), critical (neutral), and super-critical (divergent) response regimes at two distinct flight conditions: $M=0.8$ ( $\rho = 0.2525$ kg/m³) and $M=0.7$ ( $\rho = 0.50$ kg/m³).

Key Contributions

Framework Validation: The study successfully establishes a reproducible, industrially accessible FSI workflow using exclusively commercial tools (ANSYS Fluent, Mechanical, System Coupling) for transonic aeroelasticity.
Static Aeroelastic Benchmarking: The framework reproduces steady-state aerodynamic coefficients ( $C_L, C_D, C_M$ ) within 1.87% to 3.52% of NASA FUN3D reference data and predicts the fundamental bending frequency (26.504 Hz) within 1.94% of experimental ground vibration test results.
Dynamic Flutter Characterization: The study provides a systematic time-domain determination of flutter boundaries, explicitly characterizing the transition from damped to divergent oscillations. It identifies that flutter is governed by a single-mode bending mechanism in both tested Mach regimes.
Physical Insight into Scaling: The research quantifies the relationship between Mach number, free-stream density, and flutter dynamic pressure, demonstrating that while flutter velocity may be higher at lower densities (higher altitude), the flutter dynamic pressure is significantly higher at higher densities due to the scaling law $q_f \propto \rho V_f^2$ .

Results

Static Response: At $M=0.8$ , the lift-curve slope is approximately 0.107 per degree. The maximum wing-tip deflection reaches 12 mm (non-dimensional $\delta/b = 0.0093$ ) at $4.5^\circ$ angle of attack. The drag polar at $M=0.8$ exhibits a sharp shock-induced drag rise, whereas the $M=0.7$ polar is more parabolic and dominated by induced drag.
Modal Analysis: The first out-of-plane bending mode is predicted at 26.504 Hz (1.94% error vs. experiment). Higher-order modes show systematic over-prediction (9–13%) attributed to structural simplifications (e.g., lack of fastener compliance) in the finite element model.
Flutter Boundaries:
- At $M=0.8$ ( $\rho = 0.2525$ kg/m³): The flutter velocity ( $V_f$ ) is 266.56 m/s with a flutter dynamic pressure ( $q_f$ ) of 8.97 kPa. The flutter frequency is ~22 Hz, representing a 16.9% reduction from the in-vacuo structural frequency due to transonic aerodynamic stiffness modification.
- At $M=0.7$ ( $\rho = 0.50$ kg/m³): The flutter velocity is 230.46 m/s with a flutter dynamic pressure of 13.27 kPa. The flutter frequency is ~25.5 Hz, showing a smaller reduction (3.8%) from the structural frequency, indicating weaker transonic nonlinearity.
Scaling Law: Despite the lower flutter velocity at $M=0.7$ , the flutter dynamic pressure is 47.9% higher than at $M=0.8$ due to the 98% higher free-stream density. This confirms the dimensional scaling $q_f \propto \rho V_f^2$ .

Significance and Claims
The paper claims that the validated ANSYS Workbench framework offers a practical, industry-relevant pathway for preliminary flutter boundary assessment of transport-category aircraft wings without requiring bespoke in-house code or proprietary solvers. The study emphasizes that the exclusive use of commercial tools allows for immediate transferability to industrial design environments.

The authors assert that the quantitative confirmation of the density-dependent scaling of flutter dynamic pressure provides a scientifically rigorous foundation for extrapolating wind tunnel model results to full-scale flight conditions, particularly regarding altitude-dependent flutter risk. The work highlights that a wing may be flutter-free at low altitudes (high density) but approach its flutter boundary at cruise altitude (low density) even at constant Mach number, due to the reduction in effective aerodynamic stiffness. The study concludes that the identified flutter velocities carry an estimated methodological uncertainty of 5–8%, based on comparisons with similar validated frameworks for the AGARD 445.6 wing, and that the single-mode bending mechanism observed is consistent with the large frequency separation between bending and torsion modes in this specific configuration.

The Virtual Wind Tunnel Test

The Static Stretch (Before the Shaking)

The Big Moment: Finding the Flutter Speed

What Kind of Shaking Was It?

What This Means for the Future

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