Towards a knowledge base for a wind electric

pumping system design

Abdelaziz ARBAOUI1,2(*)

1 M2I, Ecole N ationale superieure d' Arts et Metiers BP 4024, Meknes Ismai:lia, Morocco.

abdelaziz3rbaoui@yahoo.fr

Abstract-A knowledge base tool for wind electric pumping

system design has been presented. In this paper, the used

approach is illustrated through the rotor component. The

performance of the rotor is predicted using the axial momentum

theory combined with the blade element theory. The design

variables of the blade are its geometry and the airfoil

aerodynamic characteristics which are introduced into the tool

using the analytic model AERODAS. To validate the developed

model, it is formulated as a Mixed Complementarity (Problem

and is solved using the GAMS software (Generalized Algebraic

Modeling System). The model validation refers to the

experimental data of NREL (National Renewable Energy

Laboratory) obtained using the NASA Ames wind tunnel. The

validated model is then used to design a new blade for a small

wind turbine which we attempt to manufacture locally.

Keywords: Small wind turbine; Pumping; Design; Knowledge base; Model validation; GAMS software.

I. INTRODUCTION

A wind electric pumping system is a technology that combines small wind turbines and standard electric centrifugal or submersible pumps. The small wind generator emulates an alternative current (AC) with a variable voltage and variable frequency drive according to the wind speeds. This enables a direct connection with standard 50 hertz induction motors [1]. The power available from a wind turbine varies as the cube of the wind speed. Following the affinity laws, the power required by a centrifugal pump varies as cube of its speed. Therefore, if a pump is optimally matched to a wind turbine at one speed or frequency, it is also optimally matched at all speeds or frequencies [2].

These configurations allow choosing the location of the pump independently of the wind turbine one. This system will be boon to small scale farming.

A 2.5 HP pump along with a 3.3 kW wind generator is currently tested at the ENSAM School. This test bench has been installed as part of the 'Sahara Trade Winds to Hydrogen' project financed by NATO. It is instrumented by a set of sensors and a data acquisition system for performance monitoring.

Our work aims to build a knowledge base system for supporting decisions in the design process of wind turbine water pumping systems. The development of the knowledge base system has been performed through four main steps displayed on the figure 2 [3] [4].

Mohamed Allae BENNINI2 and Mohamed ASBIK2

2 LP2MS, URAC 08, FacuIte des Sciences

BP 11201, Zitoune, Meknes, Morocco

asbik_m@yahoo.fr, bennini.allae@gmail.com

The models used are based on the development of a set of relations derived from engineering knowledge. These models are then verified, validated, processed, and exploited using the GAMS software (Generalized Algebraic Modeling System). This platform is equipped with several solvers adapted to design problems solving [5]. The validation and the verification of models refer either to experimental data obtained using the test bench and/or to those available in the scientific literature.

Figure 1: Test bench installed at the ENSAM School, Meknes.

Analysis and structuring of the design problem

Models formulation

Models verification and validation

Models processing and utilization

Figure 2: Applied approach.

In this investigation, the used approach is illustrated through the rotor component only. The aerodynamic behavior model of the rotor is presented in the following section. The verification and validation of the formulated model is the subject of Section 3. Finally, the present model is then used to

978-1-4673-6374-7/13/$31.00 ©2013 IEEE

design a new blade for a small wind which we attempt to manufacture locally.

II. ROTOR MODEL FORMULATION

The performance of the rotor is predicted using the axial momentum theory combined with the blade element theory [6] [7]. The first theory is based on a global description of the flow by using the conservation of the linear and angular momentum. It assumes the wind to be a one dimensional, incompressible nonviscous flow. The thrust and the torque undergone by the annular element are expressed, using this theory, as:

dM = 4rrpr3Vo wa'(1 - a)Fdr dT = 4rrpVo2a(1 - a)Frdr

(1) (2)

These two relationships involve, first, the axial induction factor "a" and the tangential induction factor "a'" to take into account the variation of the wind speed of the upstream flow. According to the 3 which shows the wind airfoil interaction, the effective wind speed and orientation relative to the airfoil at r section are respectively expressed by:

Vr = JVo2(1- a)2 + w 2r 2(1 + a')2 (3) Vo(1 - a)

tan <p = <p = f3 + a (4) wr(1 + a')

Rotor plane

Figure 3 : Blade geometry for flow analysis.

The equations (I) and (2) entail, also, the Prandtl factor which is a correction factor for both the finite blade number and the finite blade radius [8]:

(2) 2 _ N R -r _ N r- Rr F = -;: arccos(e 2rsin<p) arccos(e 2rsin<p) (5)

The blade element theory uses the definition of the lift and drag to obtain the thrust and the torque; it employs the airfoil geometry and aerodynamic characteristics. In this case the torque and the thrust are respectively given by:

1 Vo(1- a)wr(1 + a') dM = -pN . lCtFrdr (6) 2 sm <p cos <p

1 Vo2(1- a)2 dT = -pN . 2 lCnFdr 2 sm <p

(7)

Where normal and tangential coefficients are derived from the lift and drag ones:

Ct = C1 sin <p - Cd cos <p

Cn = C1 cos <p + Cd sin <p

(8) (9)

By grouping terms G = Nlj2nr representing the local solidity, the relationships (1) and (6) on the one hand and (2) and (7) on the other hand give:

a= 1

4 Fsin2 cp + 1 GCn

1 a'= ��----------4F sincpcoscp _ 1

GCt

(10)

(11)

Equation (9) gives acceptable results when a <ac = 0.4, beyond this value the blade element theory is not valid. Reference [9] proposes to use the following relationship to avoid numerical instability when the Prandtl factor is not equal to 1:

a = � [2 + K(1-2a) -.j(K(1-2a) + 2)2 + 4(Ka2 -1)] (12) 4 F sin2 <p

K = -----:-­aCn (13)

The power generated by the rotor is given by the integral of the product of the elementary torque and the angular velocity along the blade:

P = 4 fR

w 2 rrpr3Voa'(1- a)Fdr Rr

(14)

The power coefficient which characterizes the performance of the rotor is given by:

8 fR 2 3 , Cp = 2 3 W rrpr Voa (1 - a)Fdr prrr Vo Rr (15)

To satisfy the need for algebraic equations which express the lift and drag coefficients variation with the angle of attack, we used the AERODAS model [10]. In this model the lift coefficient is given by:

(16) with

(17)

and

(a - 92)N2 C/2 = -0.032(a - 92) + RC/2 ----s1 (18)

The drag coefficient is given by:

with

and

Cd = max(Cd1, Cd2) (19)

(20)

[ 90 - a ] Cd2 = +(Cd2max - Cdlmax) sin .90 (21) 90 - ACd1

These analytical equations are developed based on the experimental data obtained using a wind tunnel or those obtained by CFD simulation [10]. These last data are used to determine the aerodynamic characteristics of the airfoil: S), Ao, ACII , N), N2, RCII , RC12, CdO, Cd)max,M,ACdv Cd2max'

The figure 4 compares the obtained lift and drag coefficients for the NREL S809 airfoil using AERODAS model with experimental data of the Delft University [11].

--CI

1,2 1,8 ... 1,6

"" t-

t �-

-A I--' IDra ill

1,4 ... 1,2 c ., .;:;

:e ., 0,8 8

OJ) 0,6 '"

C

... c 0,8 ., .;:; :e 0,6 ., 0 " � 0,4

� 0,4 0,2

0,2

° °

° 20 40 60 80 100

Angle of attack (Oeg)

Figure 4 : Simulated lift and drag coefficients for the S809 airfoil using AERODAS model compared with experimental

data of Delft University [11 J.

III. MODEL VERIFICATION AND VALIDATION

In order to verify and validate the formulated model, we refer to the experimental data of NREL (National Renewable Energy Laboratory) obtained using the NASA Ames wind tunnel. These data relate to a wind turbine with a diameter of 10m. The rotor configuration was, constant speed (72 rpm), upwind, and stall regulated. The blade is twisted with the chord variable along it and with an S809 airfoil [12].

To simulate the power curve of the NREL wind turbine, the developed model, it is formulated as a Mixed Complementarity Problem and is solved using the PATH solver with GAMS software (Generalized Algebraic Modeling System). Mathematically, the Mixed Complementarity Problem looks, in our case, like:

Solve for z E IR\.N such that:

Where:

Fj(z) = o and Ii < zi <ui,iE{l, ... N}

• zi is a set of variables to be set

• F(z) is a (possibly nonlinear) function

• Ii and ui are a set of upper and lower bounds on the variables, where li may be -inf and ui may be +inf

• The number of zi variables and the number of relations Fi(z) is equal.

Briefly, solving this problem is to find the axial and the tangential induction factors along the blade. The input variables of the global model are:

• Blade tip and root radius R, Rr , number of blade N, Chord l and pitch angle f3 along the blade, and the rotational speed w,

• Airfoil aerodynamic characteristics : Sv Ao, ACu ,

N),N2,RCII, RC12, CdO, Cd)max,ACd),M , Cd2max'

The simulated power curve is compared to the experimental one [12] in the Figure 5. This result shows that there is a good agreement between the power curve obtained in the present work and the experimental data, for most of the wind speeds. For a predicted power, in the worst case, the observed deficiency is about 17,5% for the range of wind speed between 8mJs and 10mJs and reaches its maximum at 9mJs

"" Experimental-Power -- Simulated-Power - - - Simu l ated-Cp 12 0,45

10 .... r- 0,4 0,35

== =-." ---f- 0,3

:2 � 6 � o ... 4

°

-

4 9

'So;

"'"-- - --

14 19 Wind speed (m/s)

0,25 0,2 0,15 0,1 0,05

- !--f-- ° 24

Figure 5 Comparison of the simulated power with the experimental data [ 12 J.

IV. MODEL PROCESSING AND UTILIZATION

Q. v

Now, the model can be used to design a blade for a small wind turbine which we attempt to manufacture locally. The goal is to find, the pitch angle distribution along the blade that maximizes the power coefficient (c p) of the rotor.

The optimum blade chord distribution is introduced by the following equation [13]:

8/9 (22)

To perform optimization of the power coefficient, some input variables need to be chosen. So, we retained: the design wind speed (Vdes=7mJs), the rotor diameter (D=0.45m), the number of blade (N=3), the tip speed ratio (A=6), the angle of attack (30) and the blade airfoil (NACA 4412). For this airfoil the maximum lift/drag ratio occurs at the lift coefficient of about 0.7. In this case, the global model is formulated as an NLP which means "Non Linear Problem" and solved using the CONOPT solver with the GAMS software.

The obtained pitch angle and chord along the new blade are shown in Figure 6. The power coefficient, which is the optimization criteria, reaches 0.39.

Finally, we use CATIA software to design the blade and the mold that will allow to manufacture it, using composite

materials. Figure 7 shows the Computer Aided Design (CAD) model of the blade, associated mold and the rotor assembly.

0,0 7

30 0,0 6

25 0,05

20 Chord (m) 0,04

15 0,0 3

10 Pitch angle (deg) 0,0 2

0,0 1

° ° 0,2 0,3 0,4 0, .5 0,6 0,7 0,8 0,9

Slade section ( ,JH I

Figure 6 : Pitch angle and chord variation along the blade of a new designed rotor.

(al

(el

Figure 7: CAD model of the blade (a), associated mold (b) and the rotor assembly ( c).

V. CONCLUSION

A new approach to design a wind electric pumping system is presented and illustrated through the rotor component. In the used model, the power of the rotor is predicted using the axial momentum theory combined with the blade element theory. To meet the need for algebraic equations which express the lift and drag coefficients variation with respect to the angle of attack, the AERODAS model is used. The global model is implemented in the GAMS software and solved using the PATH solver to simulate the power curve of a tested wind turbine. The obtained result shows that there is a good agreement between the simulated power curve and the experimental data. Finally, the global model is used to design a blade for a small wind turbine which we attempt to manufacture locally.

Currently, we develop models of the other component (generator, pump, tower ... ). The global model will be validated using the experimental data obtained with our test bench before being used to support decisions in the design process of such systems.

ACKNOWLEDGMENT

This work was supported by the NATO science for peace program under the project SfP- 982620.

REFERENCES

[I] E. Muljadi, G. Nix, and J. Bialasiewicz, "Analysis of the dynamics of a wind-turbine water-pumping system," Proceedings of the 2000 Power Engineering Society Summer Meeting IEEE, vol. 4, 2000, pp. 2506-2519.

[2] M. Velasco, O. Probst and S. Acevedo, "Theory of wind-electric water pumping," Renewable Energy, Volume 29, Issue 6, May 2004, pp. 873-893.

[3] A. Arbaoui, "Aide 11 la decision pour la definition d'un systeme eolien: Approche multidisciplinaire basee sur une formulation par contraintes," Editions universitaires europeennes EUE, 2012 - 188 pages.

[4] A. Arbaoui and M. Asbik "Constraints based decision support for site­specific preliminary design of wind turbines," Energy and Power Engineering, 2010; 2 pp. 161-170.

[5] M C. Ferris and T S. Munson "Engineering and Economic Applications of Complementarity Problems ," Journal of Economic Dynamics and Control, 2000; 24( 2), pp. 165-188.

[6] R. Lanzafame, M. Messina, "Horizontal axis wind turbine working at maximum power coefficient continuously," Renewable Energy 2010;35:301-6.

[7] R. Lanzafame, M. Messina, "Fluid dynamics wind turbine design: critical analysis, optimization and application of BEM theory," Renewable Energy, 2007;32(14).

[8] WZ. Shen, R. Mikkelsen, IN. S0rensen, C. Bak, "Tip loss corrections for wind turbine computations," Wind Energy 2005;8(4), pp.457-75.

[9] L.Buhl Jr, "A new empirical relationship between thrust coefficient and induction factor for the turbulent windmill state," NREUTP-500-36834, August 2005.

[10] David A. Spera, "Models of Lift and Drag Coefficients of Stalled and Installed Airfoils in Wind Turbines and Wind Tunnels," NASA/CR-2008-215434, October 2008.

[II] J. TangIer "The Nebulous Art of Using Wind-Tunnel Airfoil Data for Predicting Rotor Performance," NREUCP-500-31243, January 2002.

[12] J. Tangier, J. David Kocurek, "Wind Turbine Post -Stall Airfoil Performance Characteristics Guidelines for Blade-Element Momentum Methods," NREUCP-500-36900, October 2004.

[13] T. Burton, D. Sharpe, N. Jenkins and E.Bossanyi, "Wind energy handbook," by John Wiley & Sons, Ltd, 2001.

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NOMENCLATURE

Torque [Nm]

Air density [kg/m3]

Wind speed of the upstream flow [m/s]

Angular velocity [rad/s]

Axial induction factor

Tangential induction factor

Tip Loss Factor

Blade local radius [m]

Relative wind velocity (m/s)

Flow direction angle (rad)

Pitch angle (rad)

Angle of attack (rad)

Number of blades

Rotor radius [ml

Root radius [m]

Lift coefficient

Drag coefficient

Tangential coefficient

Normal coefficient

Local solidity

Blade chord (m)