Inverse Design of Single- and Multi-Rotor Horizontal Axis Wind Turbine Blades using Computational Fluid Dynamics

A method for inverse design of horizontal axis wind turbines (HAWTs) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds Averaged Navier Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM); this approach is referred to as RANS/ADM. The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; the desired performance is prescribed as angle of attack ($\alpha$) and axial induction factor ($a$) distributions along the blade. An iterative approach is used. An initial estimate of blade geometry is used with the direct solver (RANS/ADM) to obtain $\alpha$ and $a$. The differences between the calculated and desired values of $\alpha$ and $a$ are computed and a new estimate for the blade geometry (chord and twist) is obtained via nonlinear least squares regression using the Trust-Region-Reflective (TRF) method. This procedure is continued until the difference between the calculated and the desired values is within acceptable tolerance. The method is demonstrated for conventional, single-rotor HAWTs and then extended to multi-rotor, specifically dual-rotor wind turbines. The TRF method is also compared with the multi-dimensional Newton iteration method and found to provide better convergence when constraints are imposed in blade design, although faster convergence is obtained with the Newton method for unconstrained optimization.Comment: 19 pages, 12 figure

Numerical Investigations of Bio-Inspired Blade Designs to Reduce Broadband Noise in Aircraft Engines and Wind Turbines

Simplified representations of the leading edge serrations in owl feathers are modeled numerically to investigate their effectiveness in reducing inflow turbulence noise. The rod wake-airfoil interaction problem is selected for this investigation. Two numerical methods utilizing compressible- and incompressible large eddy simulation techniques are used for the analyses. The methods are first validated against experimental results for the baseline airfoil (no serrations). Good agreement is observed between measurement and predictions for mean surface pressure, near-field velocity spectra, and far-field sound spectra. Two serrated leading edge blade designs are then analyzed for noise. The leading edge serrations are found to give a noise reduction of up to 5 decibels in the mid-to-high frequency range

Numerical investigation of the effect of airfoil thickness on onset of dynamic stall

Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack (= 4 degrees). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness

A Prescribed-Wake Vortex Line Method for Aerodynamic Analysis and Optimization of Multi-Rotor Wind Turbines

This paper extends the prescribed wake vortex lattice/line method (VLM) to perform aerodynamic analysis and optimization of dual-rotor wind turbines (DRWTs). A DRWT turbine consists of a large, primary rotor placed co-axially behind a smaller, secondary rotor. The additional vortex system introduced by the secondary rotor of a DRWT is modeled while taking into account the singularities that occur when the trailing vortices from the secondary (upstream) rotor interact with the bound vortices of the main (downstream) rotor. Pseudo-steady assumption is invoked and averaging over multiple relative rotor positions is performed to account for the primary and secondary rotors operating at different rotational velocities. Our implementation of the VLM is first validated against experiments and blade element momentum theory results for a conventional, single rotor turbine. The solver is then verified against Reynolds Averaged Navier-Stokes (RANS) CFD results for two DRWTs. Parametric sweeps are performed using the proposed VLM algorithm to optimize a DRWT design. The problem with the algorithm at high loading conditions is highlighted and a solution is proposed that uses RANS CFD results to calibrate the VLM model

Noise Reduction Mechanisms due to Bio-Inspired Airfoil Designs

This paper presents numerical analysis of an airfoil geometry inspired by the down coat of the night owl. The objective is to understand the mechanisms of airfoil trailing edge noise reduction that has been observed with such designs in previous experiments. The bioinspired geometry consists of an array of “fences” that are applied near the trailing edge of the NACA-0012 baseline airfoil. Wall-resolved large eddy simulations are performed over the baseline and the bioinspired airfoil geometries and the aeroacoustic performance of the two geometries are contrasted. Both models are simulated at chord-based Reynolds number Rec = 5 × 105 , flow Mach number, M∞ = 0.2, and angle of attack, α = 0◦ . Farfield noise spectra comparisons between the baseline and the bioinspired airfoil near the airfoil trailing edge show reductions with the fences of up to 10 dB. The simulations reveal that the fences lift turbulence eddies away from the airfoil trailing (scattering) edge hence reducing scattering efficiency. These findings suggest that one of the mechanisms of noise reduction is the increased source-scattering edge separation distance

On Predicting the Phenomenon of Surface Flow Convergence in Wind Farms

A systematic analysis of a single-rotor horizontal axis wind turbine aerodynamics is performed to obtain a realistic potential maximum efficiency. It is noted that by including the effects of swirl, viscosity and finite number of blades, the maximum aerodynamic efficiency of a HAWT is within a few percentage points of the efficiency of commercially-available turbines. The need for investigating windfarm (as a unit) aerodynamics is thus highlighted. An actuator disk model is developed and implemented in the OpenFOAM software suite. The model is validated against 1-D momentum theory, blade element momentum theory, as well as against experimental data. The validated actuator disk model is then used to investigate an interesting microscale meteorological phenomenon called “flow convergence” caused by an array of wind turbines. This phenomenon is believed to be caused by the drop of pressure in wind farms. Wind farm numerical simulations are conducted with various approximations to investigate and explain the flow convergence phenomenon

Designing wind turbine rotor blades to enhance energy capture in turbine arrays

An inverse design approach is proposed to compute wind turbine blade geometries which maximize the aggregate power output from a wind farm. An iterative inverse algorithm is used to solve the optimization problem. The algorithm seeks to minimize the target function, f = -CP,av, where CP,av is the average normalized mechanical power of all the turbines in the wind farm. An upper bound on the blade planform area, representative of the blade weight, is imposed to demonstrate how to incorporate constraints in the design process. The power coefficients (CP) of the turbines in the farm are computed by solving the Reynolds Averaged Navier Stokes equations with the turbine rotors modeled as momentum sources using the actuator disk model. The inverse design is carried out using the trust-region-reflective method, which is a nonlinear least squares regression solver. The computation cost is reduced by computing the Jacobian once every few iterations and approximating it using Broyden\u27s method in between. The proposed design approach is first demonstrated to maximize the isolated performance of single- and dual-rotor wind turbines and subsequently used to design the blades for a 3-turbine array and a ten-turbine array in which the downstream turbines operate directly in the wake of the upstream turbines. For a turbine-turbine spacing of four rotor diameters, the farm-optimized blade designs increase the farm power output by over five percent and the optimized blade geometries are found to be considerably different from the blade geometry optimized for isolated turbine operation. As the turbine-turbine spacing is increased to eight rotor diameters, the difference between the blade geometry optimized for farm operation versus that for isolated operation, is reduced

Numerical analysis of aerodynamic noise mitigation via leading edge serrations for a rod–airfoil configuration

Noise produced by aerodynamic interaction between a circular cylinder (rod) and an airfoil in a tandem arrangement is investigated numerically using incompressible large eddy simulations. Quasi-periodic shedding from the rod and the resulting wake impinges on the airfoil to produce unsteady loads on the two geometries. These unsteady loads act as sources of aerodynamic sound and the sound radiates to the far-field with a dipole directivity. The airfoil is set at zero angle of attack for the simulations and the Reynolds number based on the rod diameter is Red = 48 K. Comparisons with experimental measurements are made for (a) mean and root mean square surface pressure on the rod, (b) profiles of mean and root mean square streamwise velocity in the rod wake, (c) velocity spectra in the near field, and (d) far-field pressure spectra. Curle’s acoustic analogy is used with the airfoil surface pressure data from the simulations to predict the far-field sound. An improved correction based on observed spanwise coherence is used to account for the difference in span lengths between the experiments and the simulations. Good agreement with data is observed for the near-field aerodynamics and the far-field sound predictions. The straight leading edge airfoil is then replaced with a test airfoil with a serrated leading edge geometry while maintaining the mean chord. This new configuration is also analyzed numerically and found to give a substantial reduction in the far-field noise spectra in the mid- to high-frequency range. Source diagnostics show that the serrations reduce unsteady loading on the airfoil, reduce coherence along the span, and increase spanwise phase variation, all of which contribute to noise reduction

Prediction of Aerodynamic Tonal Noise from Open Rotors

A numerical approach for predicting tonal aerodynamic noise from ‘‘open rotors’’ is presented. ‘‘Open rotor’’ refers to an engine architecture with a pair of counter-rotating propellers. Typical noise spectra from an open rotor consist of dominant tones, which arise due to both the steady loading/thickness and the aerodynamic interaction between the two bladerows. The proposed prediction approach utilizes Reynolds Averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations to obtain near- field description of the noise sources. The near-to-far-field propagation is then carried out by solving the Ffowcs Williams–Hawkings equation. Since the interest of this paper is limited to tone noise, a linearized, frequency domain approach is adopted to solve the wake/vortex–blade interaction problem. This paper focuses primarily on the speed scaling of the aerodynamic tonal noise from open rotors. Even though there is no theoretical mode cut-off due to the absence of nacelle in open rotors, the far-field noise is a strong function of the azimuthal mode order. While the steady loading/thickness noise has circumferential modes of high order, due to the relatively large number of blades (~10-12), the interaction noise typically has modes of small orders. The high mode orders have very low radiation efficiency and exhibit very strong scaling with Mach number, while the low mode orders show a relatively weaker scaling. The prediction approach is able to capture the speed scaling (observed in experiment) of the overall aerodynamic noise very well