Theoretical Demonstration of Diffuser Augmented wind Turbine Performance

World Renewable Energy Congress VI (WREC2000)

© 2000 Elsevier Science Ltd. All rights reserved. Editor: A.A.M. Sayigh

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THEORETICAL

DEMONSTRATION

OF DIFFUSER AUGMENTED

WIND TURBINE PERFORMANCE M. T. S. BADAWY & M. E. ALY" *Mech. Eng. Dept., National Research Center, Dokki, Cairo, EGYPT. ABSTRACT: The present paper aims to find a theoretical demonstration of diffuser augmentedwind turbine (DAWT)by using theoretical analysis, mathematical models, assumptions, in addition to computer program for calculations and drawings. The final results show that the power coefficient (Cpdo) of DAWT reaches 1.5 at Co -=--0.5, No _= 1.0 and Cr --- 0.5, but the augmentation ratio (Rb) reaches 6.0 at Co --- -0.5, Cr --- 0.9 and reaches 7.0 at No _=_1.0 and Ct = 1.0, which gives a good application for DAWT systems. KEYWORDS: Diffuser flow, Diffuser augmented wind turbine, Theoretical demonstration, Design and performance mathematical models. 1-INTRODUCTION: The optimal performance of wind turbine system has been studied (Badawy et al., 1995.), whereof the optimal power coefficients is Cp_=_0.435. Further investigations of DAWT and experimentat demonstration for increasing augmentation has been studied (Forman et. al., 1978, 1979) Turbomachinary diffuser design technology and review of diffuser analysis had been studied (Japikse et. al., 1984, and Johnston et. al., 1998). Finally the' unified integral method has been demonstrated to produce results which are equal or better in accuracy to the performance parameters. It is obvious from the previous work, that the optimum configuration regarding numbers, positions, pressure recovery and overall factors of diffuser, suitable area ratio and the diffuser efficiency in addition to velocity ratio must be considered to get the optimum performance of DAWT system. In the present paper, a theoretical demonstration of DAWT performance has been realized. Modeling and analysis of DAWT system were estimated and improved for finding the power coefficient and augmentation ratio by changing area ratio, diffuser efficiency, velocity ratio, turbine factor, pressure recovery and overall factor in computer program.

2- MODELING AND ANALYSIS: The analysis of DAWT performance depends on some assumptions such as, one-dimensional, potential incompressible and inviscid flow, whereon the power coefficient (see fig. (1)) is given by:

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Cpd=APt_ 2

(1)

V2 2 2 9A2V°

by using of some mathematical operations then: AP,_2//lpv~ = (APo_3- AP2_3)/2PV2 = ( 1 - C o ) - N 2 ( 1 - C r )

(2)

Substituting equation (2) into equation (1), then the power coefficient of DAWT is: 3 N[Ct + ( l - N 2 ) ] , Cpd = _2-3N[(1- C o ) - N2(1- Cr)] = -~

(3)

where C r = ( P 3 - P 2 ) / l p V2 = r I ( 1 - m 2 ) , N = V 2 / V 0 , l"I=(,P3-P2

p,V.-Vj,

Co:(P3-Po)/2PV2

,in= 12/13=

2L

l+~tan

, Ct= (Po-P2)/lpv~

8Cpd The maximum power coefficient of DAWT (at ON ~ 0) is given by:

Cpd0 = No (1-Co)= No (1+3 Ct), No = [(1 + Ct)/3] g =[(1- Co)D0- Or)]g

(4)

The augmentation ratio relative to Betz limit (Rb) is given by: R b : Cpd 0/ Cp (Betz) = (27/16)Cpd 0

(5)

From the above modeling and analysis of DAWT performance, it is clear that, the power output can be increased significantly by the satisfaction of the following parameters: 1- Maximum area ratio (m), optimum L/D and suitable vertex angle (0) of diffuser to get optimum Cr. 2-Optimum diffuser efficiency (1"!)to find optimum Cr. 3-Optimum speed ratio (N) for optimum Cpd. 4- Maximum and suitable pressure recovery factor (Cr). 5- Maximum overall factor (Co) for optimum Cpd. 6-Optimum and suitable turbine load factor (Ct) 3- RESULTS AND DISCUSSIONS:

The effect of area ratio (m) and diffuser efficiency (11) on the pressure recovery factor is shown in fig. (2), whereon Cr is directly proportional to 11, but inversely with (m), for good choosing of suitable Cr for optimum power coefficient of DAWT system. The relation between power coefficient (Cpd) and N, Ct is shown in fig.(3) whereby it is directly proportional to N, Ct to a maximum value and then decreases, the optimum value increases with N and Ct. The effects of Cr, Co and No on the optimum power Coefficient (Cpdo) are shown in fig. (4). It is clear that, Cpdo is directly proportional to No and Co, it has a value of 1.5 at No ~ 1, Co ~, -0.5 and Cr ~ 0.5. The effects of Cr, Co, Ct and No on the augmentation ratio (Rb) are shown in figs.(5,6). One can see that Rb is directly proportional to Cr, Co and No, whereon the optimum value of ~ 6 for Rb at Cr ~ 0.9, Co ~ -0.5, No ~ 1.0 and Ct ~ 1.0.

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4- CONCLUSIONS: The conclusions of this paper are as follows: 1- The power coefficient of DAWT (Cpd) is directly proportional to Cr, Co, Ct, N and q, but inversely proportional to m, whereon the suitable choosing must be considered to get optimal power for good applications. 2- The maximum power coefficient (Cpdo) of DAWT is directly proportional to Cr, Co, Ct and No, and reaches a value of 1.5 at Co = -0.5, Cr = 0.5, Ct = 1.0 and No = 1.0. 3- The augmentation ratio relative to Betz (Rb) is directly proportional to Cr, Co, Ct and No, and reaches a value of 6 at Ct~ 1.0, No~ 1.0, Cr= 0.9 and Co~-0.5. REFERENCES" Badawy, M.T.S. and M. F. Abd-Raboo. (1995). Some investigations on the performance of wind turbine. J. of Eng. Researches. 46, 1-11, Cairo, Egypt. Forman, K.M. and B.L. Gilbert. (1978). Experimental demonstration of the diffuser augmented wind turbine concept. SAE. 3, 2083. Forman, K.M. and B.L. Gilbert. (1979). Further investigations of diffuser augmented wind turbines., Gruman Aerospace Corporation, New York, USA. 1/714. Japikse, D. (1984). Turbomachinary diffuser design technology. DTS-1, Concepts, ETI, Inc., Pox 643, Norwish, VT, 05055. Johnston, J.P. (1998). Review; diffuser design and performance analysis by a unified integral method. Trans. of ASME, No.6. 120. 1

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.

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