Simulating wind and marine hydrokinetic turbines with actuator lines in RANS and LES¶

Motivation¶

Sought array modeling strategy for capturing a vertical-axis cross-flow turbine's (VAT/CFT) vertical mean velocity field (dominant near-wake recovery mechanism for high-solidity VAT, see Bachant and Wosnik (2015, J. Turbulence))
- 2-D blade-resolved RANS can't resolve vertical velocity
- 3-D blade-resolved RANS too expensive ($\sim 10^4$ CPU hours per case)
- Potential flow doesn't include turbulent transport
- ALM for cross-flow turbine and array analysis/design?
  - NREL's SOWFA?

turbinesFoam ¶

New open-source ALM library for OpenFOAM
Models CFTs, AFTs, standalone actuator lines
Compatible with standard solvers
Inflow sampled away from element using cell-point interpolation
Smearing parameter $\epsilon$ either $c/2$ or $2 \sqrt[3]{V_\mathrm{cell}}$ (whichever larger)
Lifting-line based end effects model (see Anderson (2001)):

$$ \alpha(\theta) = \frac{2b}{\pi c(\theta)} \sum_1^N A_n \sin n \theta + \sum_1^N n A_n \frac{\sin n \theta}{\sin \theta} + \alpha_{L=0}(\theta) $$$$ \Gamma(\theta) = 2b U_\infty \sum_1^N A_n \sin n \theta \hspace{1in} F = \Gamma(\theta)/\Gamma_\max $$

UNH-RVAT cross-flow turbine validation case¶

Open datasets from tow tank measurements:
github.com/UNH-CORE/RVAT-baseline
github.com/UNH-CORE/RVAT-Re-dep

3-D standard $k$–$\epsilon$ RANS model

Leishman–Beddoes dynamic stall model modified by Sheng et al. (2008)

Flow curvature correction from Goude (2012)

Added mass model from Strickland (1981)

Preliminary results: UNH-RVAT performance¶

Wake profiles at $x/D = 1$¶

Mean velocity at $x/D=1$ (ALM vs. experiment)¶

UNH-RVAT cross-flow turbine LES¶

Preliminary results with one equation eddy viscosity model

UNH-RVAT near free surface¶

Using OpenFOAM's interFoam volume of fluid solver

NTNU dual in-line HAWTs¶

Extensive axial-flow turbine validation case by Pierella et al. (2014)

NTNU HAWTs performance¶

Preliminary results with standard $k$–$\epsilon$ RANS model

NTNU HAWTs wake profiles¶

$1D$ behind downstream turbine

NTNU HAWT large eddy simulation¶

Preliminary results with one equation eddy viscosity model

Conclusions¶

New open-source ALM developed for both AFTs and CFTs in OpenFOAM
- Compatible with RANS, LES turbulence models and VOF solvers
Predicts performance reasonably well
CFT near-wake predictions need work
- Turbulence generated by dynamic stall
- Three-dimensionality from vortex shedding