Theory Notes

VorLap Methodology Summary (From the Paper)

The NAWEA paper describes VorLap as a workflow with two primary outputs:

  • A frequency-overlap screening metric to identify likely shedding-mode alignment.
  • Reconstructed time-domain nodal loads for one-way structural coupling.

At a high level, the methodology is:

  1. Spectral preprocessing of source data:
  2. Start from lift/drag (or force/moment) time series from CFD/experiments.
  3. Convert frequencies to Strouhal form (St = f c_n / V_inf) and force levels to coefficient form (C_L, C_D).

  4. Compute FFT amplitude/phase and rank non-DC peaks by PSD using combined-force magnitude (C_F = sqrt(C_L^2 + C_D^2)), retaining only the top ranked peaks.

  5. Local kinematics for each structure node:

  6. For each inflow speed and azimuth, resolve local angle of attack and effective speed from inflow projected on local chord/normal directions.

  7. Compute local Reynolds number from effective speed and local chord.

  8. Interpolation in aerodynamic parameter space:

  9. Interpolate St, amplitude, and phase over Reynolds number and angle of attack grids (per ranked peak index).

  10. Use this to map source spectral data onto the local conditions at each node.

  11. Combinatorial overlap reduction:

  12. For each candidate shedding frequency, compare against each structural natural frequency and selected harmonics.
  13. Track the minimum absolute percent difference as the “worst-case overlap” metric for each inflow/azimuth point.
  14. Apply practical filters:
  15. Peak-depth limit (only top N ranked frequencies).

  16. Amplitude cutoff (ignore low-energy peaks).

  17. Optional signal reconstruction:

  18. Reconstruct local lift/drag time signals from interpolated frequency, amplitude, and phase.

  19. Rotate and assemble these nodal loads into global force time histories for downstream structural models.

  20. Time-varying inflow reconstruction:

  21. For nonstationary inflow files (time, inflow_speed, direction), VorLap evaluates local Re/AOA at each time sample.
  22. It interpolates Strouhal/amplitude/phase at each sample and converts Strouhal to instantaneous shedding frequency.
  23. Harmonics are synthesized with phase continuity (dphi/dt = 2*pi*f(t)), using FFT phase as the initial condition.
  24. Optional cycle-based smoothing can be applied to frequency/amplitude trajectories to avoid non-physical jumps under rapid inflow changes.

This is the bridge the paper emphasizes: from high-dimensional unsteady spectral datasets to practical, design-stage VIV screening and load synthesis on arbitrary beam-type multi-body structures.

Core Load Model

At each component node, VorLap computes:

  • Effective speed from local inflow projection on chord/normal directions.
  • Reynolds number from effective speed and local chord.
  • FFT coefficient lookup/interpolation for CL, CD, and CF.
  • Nodal force from dynamic pressure scaling.

Spanwise Nodal Weighting

Nodal load weighting uses half-segment averaging:

  • End nodes: half of adjacent segment length.
  • Interior nodes: average of left/right adjacent segment lengths.

This avoids dropping first-node contribution and keeps total nodal span weighting consistent.

Moments

Global moments are computed as:

M = r × F

where r is the node position relative to rotation_axis_offset.

Frequency Overlap

Shedding frequencies are estimated from Strouhal form:

f = St * V_eff / L_st

with L_st = chord * |sin(AOA)| and a small epsilon floor to avoid divide-by-zero at near-zero AOA.