A Method for Analysis of VAWT Aerodynamic Loads underTurbulent Wind and Platform Motion

Karl O. MerzDepartment of Civil Engineering

NTNU

9th Deep Sea Offshore Wind R&D SeminarJanuary 19, 2012

A dynamic inflow method for HAWTs was adapted for VAWTs.

This required the definition of “ghost blades” in order to provide a continuous record of forces (including dynamic stall) for the dynamic inflow calculation.

A study of a simplified model of a floating VAWT indicates that dynamic inflow is not required for predicting overall rotor loads and platform motion, in a turbulent windfield.

Dynamic inflow still provides some advantages, namely that iteration is not required to calculate induced velocities.

It is numerically stable.

Under anomalous conditions, dynamic inflow provides a smooth (and physically realistic) change in induced velocity under abrupt changes in operating conditions.

Conclusions

Overview of existing VAWT aerodynamic methods

Strickland JH, et al. A vortex model of the Darrieus turbine: an analytical and experimental study. Journal of Fluids Engineering 101 (1979) 500-505. Coton FN, et al. An aerodynamic prediction method for use in vertical axis wind turbine design. Proceedings of the 13th British Wind Energy Association Conference, Swansea, UK, 10-12 April 1991, pp 269-274. Scheurich F, et al. Simulating the aerodynamic performance and wake dynamics of a vertical-axis wind turbine. Wind Energy 14 (2011) 159-177. SibuetWatters C, et al. Application of the actuator surface concept to wind turbine rotor aerodynamics. Wind Energy 13 (2010) 433-447.

Blade Element MomentumSimple to implement and interpret

(can be checked with a hand calculation)Implicit representation of the wake

Wake VortexExplicit model of vorticity in the wakeSuperposition of undisturbed flow and induced velocityCan be

“simple” (prescribed wake)intermediate (free wake – lines, panels)advanced (vorticity transport – cells)

Advantage over BEM decreases when flow is stalledvortex wake is less well-defineduncertainties in dynamic stall models

Full flow domain CFDSolve Navier Stokes with a turbulence modelCan be

advanced (actuator line or surface)more advanced (blades with boundary layers)

Strickland et al.

Coton et al.

Scheurich et al.

Sibuet Watters et al.

Key: get a good estimate of induced velocity on the surface swept by the blades, when the windspeed is below rated. (Above rated induced velocity becomes less important.)

I like simple. Use BEM for initial design studies, control system analysis, etc. If needed, refine/verify/certify using more advanced methods.

Overview of existing VAWT aerodynamic methods

Sibuet Watters C, et al. Application of the actuator surface concept to wind turbine rotor aerodynamics. Wind Energy 13 (2010) 433-447.

NREL UAE research turbine (HAWT)

NS-AD: Navier-Stokes, actuator diskNS-AS: Navier-Stokes, actuator surfaceBEM: Blade element momentumHAWTDAWG: prescribed wake vortex

Single element on the swept surface: induced velocity by momentum balance

“Double-multiple streamtube”: assumptions about flow through the rotor interior

(Things get a bit uncertain when local flow is not aligned with the mean wind direction.)

BEM for VAWTs: Double-Multiple Streamtube

Existing VAWT-BEM implementations assume that the induced velocity is either:calculated upfront based upon mean flow and thereafter held constant (Homicz)orcalculated iteratively such that the momentum equation is satisfied at each timestep(Malcolm).

HAWTs: BEM with dynamic inflow

TUDk model (Snel and Schepers):

A time-lag on induced velocity which represents wake developmentNo iteration: (V0 + f Vi) is evaluated based on values from the previous timestep.

BEM for VAWTs: Existing Implementations for Turbulent Wind; HAWT Dynamic Inflow

Homicz GF. Numerical Simulation of VAWT Stochastic Aerodynamic Loads Produced by Atmospheric Turbulence: VAWT-SAL Code. Report SAND91-1124, Sandia National Laboratories, Albuquerque, NM, USA, 1991. Malcolm DJ. Darrieus rotors subject to turbulent inflow. Engineering Structures 10 (1988) 125-134. Snel H, SchepersJG. Joint Investigation of Dynamic Inflow Effects and Implementation of an Engineering Method. Report ECN-C--94-107, Energy Research Centre of the Netherlands, Petten, The Netherlands, 1995.

The HAWT TUDk method was adapted to VAWTs. Same equations, using r/R = 0.7

Why should the HAWT model be applicable to VAWTs? Similarity in wake structure.

Dynamic Inflow for VAWTs

Scheurich F, et al. Simulating the aerodynamic performance and wake dynamics of a vertical-axis wind turbine. Wind Energy 14 (2011) 159-177. Vermeer LJ, et al. Wind turbine wake aerodynamics. Progress in Aerospace Sciences 39 (2003) 467-510.

Scheurich et al. Vermeer et al.

Problem: The blades need a dynamic stall model that evolves with blade motion.Dynamic inflow needs a continuous record of forces at fixed locations on the swept surface.

Solution: ghost blades.Ghost blades rotate about the azimuth just as real blades.Forces/dynamic stall are calculated at both real and ghost blades.Forces at the surface elements (dynamic inflow) are interpolated.Forces for structural analysis are taken only from the real blades.

Ghost Blades for Dynamic Inflow Forces

Hypothesis:Dynamic inflow might influence the motions of a floating platform.

Dynamic Inflow on Floating VAWTs

Simple platform model, generic rotorD = 130 mM = 5×106 kg

Turbulent windfield (Mann)I = 0.2

Rigid blades

Simple induction generatorΩ = 0.5 rad/sdT/dΩ = 2×109 Nms/rad

Time-domain simulation

Simple Model of a Floating VAWT

Mann J. Wind field simulation. Probabilistic Engineering Mechanics 13 (1998) 269-282.

Compare:Constant Vi Dynamic inflowQuasi-steady Vi (as would be obtained by iteration at each timestep)

(Simulated by adjusting the time constants)

Induced Velocity

Rotor Load Spectra

Platform Displacement Spectra

Spring stiffness K tuned to give three platform natural frequencies: 0.03, 0.06, 0.20 Hz

Dynamic inflow is not required for predicting overall rotor loads and platform motion, in a turbulent windfield.

This is really nice, because it means that for platform and control system design studies, a table of rotor loads can be generated upfront.

Calculate the average incoming wind velocity vector, including platform motion.Find the rotor azimuth angle Ψ relative to the average wind velocity vector.Look up the first couple Fourier components in Ψ, based upon V∞ and Ω, to find global rotor loads.

Results

A dynamic inflow method for HAWTs was adapted for VAWTs.

This required the definition of “ghost blades” in order to provide a continuous record of forces (including dynamic stall) for the dynamic inflow calculation.

A study of a simplified model of a floating VAWT indicates that dynamic inflow is not required for predicting overall rotor loads and platform motion, in a turbulent windfield.

Dynamic inflow still provides some advantages, namely that iteration is not required to calculate induced velocities.

It is numerically stable.

Under anomalous conditions, dynamic inflow provides a smooth (and physically realistic) change in induced velocity under abrupt changes in operating conditions.

Conclusions