Benchmarking of Non-Linear Wake Interactions of Two ... · The eddy viscosity model is a wake model...

ObjectivesWind Turbine WakesEddy viscosity modelActuator Disc modelValidation Exercise

ConclusionQuestions

Benchmarking of Non-Linear Wake Interactionsof Two Turbines of Marine and Wind

Bahri Uzunoglu

Uppsala University Gotland Campus

July 24, 2013

Bahri Uzunoglu


ConclusionQuestions

Bahri Uzunoglu


ConclusionQuestions

Objectives

The eddy viscosity model is a wake model that is widely employed byindustry for wind farm far wake calculations and energy outputpredictions. In this presentation, we are outlining a validation exercise to:

benchmark eddy viscosity wake model to single turbine and twoturbine configurations,

show dependence of eddy viscosity model on different parameterssuch as turbulence intensity, Reynold stresses, filter parameters for atwo turbine configuration.

comparison is made to full three dimensional Phoenics solver RANSwith closure models k-ε and RNG k-ε

bring to your attention the importance of this topic on everydayindustrial and business applications.

Modelling of wake losses is an important part of the productionestimation for wind farms. Next slide;

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Wind Turbine Wakes

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Wind Turbine Wakes

Wake modelling and wind farm designLinear wind resource grid

Wasp, Windfarm, WindFarmer, Openwind, WaspEngineeringPark Model and its variants

Non-linear wind resource grid

Fluent, MeteoDyn, WindSim, Ellips3D etcActuator disc, Eddy Viscosity

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Wind Farm Design

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Park model

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Eddy viscosity model

mass :1

r

∂

∂r(rUr ) +

∂

∂z(Uz) = 0 (1)

z−momentum :

(Ur∂Uz

∂r+ Uz

∂Uz

∂z

)= (2)

ε

[1

r

∂

∂r

(r∂uzur∂r

)]

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Field conditions

For eddy-viscosity model boundary conditions The Uz boundaryconditions are chosen as Uo which is free stream boundary condition atthe radial direction. As result of the symmetry, the gradient of the Uz

will equal to zero at the center line. The boundary condition for Ur isequal to zero at the boundary.

For eddy-viscosity model initial conditions which is for a singleturbine configuration; inlet or initial center line velocity deficit field is a

Gaussian curve

D = Uz/Uo = Uo

(1 − Dme

(−3.56 r2

b2)

)(3)

that employs the following semi-empirical relation: This function at theinitial iteration Dm = Dmi has the following definition for velocity deficit:

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Boundary conditions, field conditions and closure for eddyviscosity

Dmi = Ct − 0.05 − (16 Ct − 0.5)Io

1000= Uz/Uo (4)

Herein Io is the ambient turbulence intensity which is defined inpercentage. Through this relationship a semi empirical closure for eddy

viscosity can be obtained:

ε = F K1 b Dm Uo + F κ2Io

1000(5)

The parameters F ,K1, b, κ are filter coefficients, dimensionless constantbased on experimental data and wake width b and von Karman constant

κ respectively. Wake width b is defined as

Bahri Uzunoglu


ConclusionQuestions

Boundary conditions, field conditions and closure for eddyviscosity

Wake width b is defined as

b =

√3.56 Ct

8 Dm (1 − 0.5 Dm)(6)

and F term for the filter is defined as

F−z > 5.5 : F = 1.0 (7)

F−x < 5.5 : F =

(x − 4.5

23.32

)1/3

(8)

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Eddy viscosity model

[a] [b]

Figure : a) Figure a illustrates wind speed contours for a turbine placed on theleft inlet. Notice that numerical solution of eddy-viscosity is a propagatingsolution on the x-axis. b) Figure b on the right illustrates the computationaldomain with turbine placed at the origin. The grid on the right figures is toemphasize that the solution is computed on a regular and uniform grid.

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Actuator Disc model

[a] [b]

Figure : a) Figure a illustrates wind speed contours for 80m height. b) Figure bon the right illustrates the computational domain with turbine placed on themesh where the triangle is located.

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Validation Exercise

[a] [b] [c]

[d]

Figure : a) Downstream profile b) Cross stream profile at rotor diameterdistance 2.5 c) Cross stream profile at rotor diameter distance 5 d) Crossstream profile at rotor diameter distance 10

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Effects of ambient turbulence intensity on the profile

[a] [b]

[c] [d]

Figure : Ambient turbulence intensity variations effect wake

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Effect of filter on ambient turbulence intensity and wake

[b] [c]

[d]

Figure : Effect of filter on ambient turbulence intensity and wake;

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Effect of two turbine wake interaction

Figure : Effect of two turbine wake interactionBahri Uzunoglu


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Turbulence Intensity

Figure : Turbulence Intensity at RANSBahri Uzunoglu


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Effect of two marine turbine wake interaction

Figure : Effect of two turbine wake interactionBahri Uzunoglu


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Conclusions

Ambient turbulence intensity has significant effect on eddy viscositycalculations.

The turbulence intensity influences the eddy viscosity calculationthrough the eddy viscosity term.

The eddy viscosity demonstrated a reasonable accuracy compared tothe model’s simplicity for two turbine configuration.

The eddy viscosity model was benchmarked to nonlinear wake model.Averaging of wake showed reasonable results considering simplicity.

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Questions?

Questions?

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Windfarmer, The wind farm design software, Theory Manual(11/2006) Garrad Hassan and Partners LTD..

Openwind, Theoretical basis and validation Version 1.3 (04/2010)AWSTRUEPOWER LLC.

J.F.Ainslie Calculating the velocity field in the wake of wind turbines.Journal of Wind Engineering and Industrial Aerodynamics, 27,213–224 (1988).

WindSim. History. http://windsim.com/about-windsim/history.aspx.Accessed: 2010-07-15.

Windfarmer 4.1, Validation report (11/2006) Garrad Hassan andPartners LTD..

Benchmarking of Eddy Viscosity Model with nonlinear wake models ,Uzunoglu, B. , Zou. F and Ivanell, S CFD Optimization -ECCOMAS, Antalya, Turkey. (2011)

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Benchmarking of Non-Linear Wake Interactions of Two ... · The eddy viscosity model is a wake model...

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