We should be consistent with the spelling of Diffuser ...

DESIGN PRINCIPLES FOR A DIFFUSOR AUGMENTED WIND-TURBINE BLADE Alois P. Schaffarczyk CFD Laboratory University of Applied Sciences Kiel, Mech. Eng. Dept. Grenzstr. 3, D-24103 Kiel, Germany Phone: +49 431 210 2610, Fax: +49 431 210 2611 Email: [email protected] D. Phillips Department of Mechanical Engineering The Universty of Auckland Private Bag 92019 Auckland, New Zealand Email: [email protected] ABSTRACT: Research has been undertaken by Vortec Energy on the development of an efficient Diffusor Augmented Wind Turbine (DAWT). An extensive programme of both computational and experimental work has been undertaken to characterise the DAWT performance. As part of this work, the integration of a matched rotor within the diffusor has been investigated. The comparison of three types of blades, a truncated conventional wind turbine blade, a genuine turbo-machinery type blade and an empirically designed DAWT blade, was performed. Wind tunnel and controlled field tests showed that the ordinary bladeelement/momentum theory, in which the usual thrust induction factor relationship was replaced by one empirically derived from DAWT wind tunnel tests, provides the best results to date. Keywords: Innovative Concepts, Wind Tunnels, Actuator Disk Models. 1

INTRODUCTION

Research into a commercially viable DAWT by Vortec Energy has resulted in the development of a double skinned, multi-slotted diffusor (Fig. 1).

diameter model was chosen which has an exit-to-inlet area ratio of 3. Initial evaluation of the diffuser was performed using hot wire anemometry with calibrated gauze screens to simulate the pressure drop across the blade plane. A 2m prototype (V2) was used in a controlled field testing programme. Both models utilised full variable speed and pitch control, which enabled various blade sets to be tested over a range of pitch angles and tip speed ratios. Three classes of blades were examined in the study. These comprised blades from a conventional bare wind turbine, those from a ducted axial turbine, together with blades designed using an empirical relation derived from the DAWT wind tunnel testing. A modified blade element method (BEM) was developed by incorporating an empirical equation describing the velocity at the blade plane as a function of the local thrust coefficient and radial position of the blade element. At the design point, good comparison between the modified BEM prediction and measurement was shown for the 2m V2 prototype. 2

Figure 1: Back view of V37 Engine. An investigation of the diffuser performance was undertaken in The University of Auckland Twisted Flow Wind Tunnel (Flay, R. G. J.) which was modified to produce an open jet flow of 3 by 3 metres with wind speeds up to 12 m/s. To minimise any effect of blockage, a 0.48m

DIFFUSER PERFORMANCE

The results indicate the operating conditions of a rotor in a DAWT are significantly different from those of a conventional HAWT (Fig. 2) and also from ordinary (long length to diameter ratio) diffusers whose divergence angle is typically less than 12 degrees. Therefore only very limited knowledge is available in the open literature [10]. Wind tunnel testing has shown that the axial velocity is approximately doubled and the radial velocity distribution is significantly altered. It should be noted however, that the increase in power output is not related to a larger energy

extraction per unit mass flow, but only due to the increased mass flow. This is shown when the optimal local thrust loading coefficient measured of 1.0 is defined in the more conventional sense, that is relative to the ambient flow velocity. For an average velocity at the blade plane of 1.1 times ambient, the thrust loading coefficient equals 0.82, just below the optimal value of 8/9 for a bare turbine.

2

4 U0 cj·r=G= · . 9 W ®wake expansion ® Glauert Theory [1] Loading concentrated at the outer half of the blade. Power Estimate (Hansen, et.al., [2]): WT

1.600

cP=cP ×e=0.4·hdiffusor·Ar»0.6

Local Disc Loading 0

0.5

0.68

0.75

0.9

1

1.24

1.4

1.5

1.7

2.3

2.6

Axial Turbines Axial velocity components » constant by geometric constraints. Potential vortex (free vortex) assumed for induced tangential velocities.

1.400

Velocity Speed-Up

1.200

1.000

cj·r=G=2p·P/(w·m).

0.800

Approx. constant loading Hub - tip ratio 0.5 Estimate for Power (Igra [4]): cP=1.2

0.600

0.400

0.200 0.150

0.250

0.350

0.450

0.550

0.650

0.750

0.850

0.950

Normalised Radius

DAWT Coupled system made of Diffuser + Turbine blades. All in all this means that the flowfield of the whole system has to be investigated. Another important design parameter is solidity

Figure 2: Velocity speed-up as a function of radial position. 3

BLADE SHAPE SELECTION RULES

From [1] the power-increment of an small radial ring element of length dr can be calculated from the forceincrements by: dP = WdQ = (1-a) U0 dT - aW dQ , dT = L (j) + D (j) , dQ = -L (j) + D (j) . Minimizing losses means therefore minimizing swirl losses. This is the starting-point for an optimized windturbine-blade as described in [1]. To design a blade the flow pattern (axial as well as tangential flow as function of radius) has to be known at least in the rotor-plane at least in principle. Two totally opposite design methods are known and used: free wind-turbine [1], axial turbines [3]. Main assumptions of these methods are: Wind Turbines Mainly axial flow velocities are reduced. Induced tangential components much smaller [1].

s =

BcC L . 4pr

To choose Cl one usually takes an aerodynamic profile at an angle of attack (AOA) where the lift-to-drag ratio is high (er than 80-100).

4

CFD MODELLING

In conjunction with the wind tunnel testing, development of computational fluid dynamic models using the full 3D Navier-Stokes solvers CFX and FLUENT was undertaken at the University of Applied Sciences Kiel. An actuator disc approach in an extended form was implemented in both codes and validated against standard BEM calculations with WT-PERF. The influence of boundary conditions, cell type (tetrahedral and hexahedral) and 2D or 3D models was investigated. Results were compared with wind tunnel gauze screen measurements validating the use of a 2D, axi-symmetric model with 24,000 cells. A high level of agreement with experimental result was obtained with rapid execution times. Evaluation of the entire flow field for three blade geometries was examined. Comparison of both computational models with wind tunnel and V2 prototype measurements was performed. It can be seen in Figure 3 that a slight overestimation in velocity at the blade plane was predicted by the CFD compared with wind tunnel measurements for the gauze screen modelling.

blade tip with the diffuser wall, it was assumed for the initial modified BEM model, that the Prandtl tip loss correction could be neglected.

Figure 3: Thrust coefficient vs induction factor for local disc loading coefficients between 0.5 and 2.6. The difference could be attributed to delayed separation prediction by the CFD model together with separation sensitivity due to the low Reynolds numbers inherent in wind tunnel testing. Close agreement in predicted shaft power output was found between the actuator disc CFD model and experimental measurements.

5

WIND TUNNEL TESTS

Wind tunnel investigations of the Multi-Slotted Diffuser using hotwire anemometry and flow visualisation were used to establish the diffuser performance over a range of constant disc loading coefficients. Velocity traverses across the blade plane for all constant disc loading screens showed similar trends. A section of relatively uniform velocity was found over the inner third of the screens with the velocity increasing towards the diffuser wall. The effect of an increase in disc loading was to reduce the magnitude of the velocity at the blade plane. The results from the velocity traverses are shown in Figure 4 where the normalised velocity, termed speed-up, is plotted against the normalised radial position. In order to use the blade element method (BEM), an equation describing the velocity at the blade plane with the diffuser was required. This equation should be a function of the local forces acting on the element and the radial position of that element. The assumption was made that the radial loading of the blade for optimum performance would be approximately constant and that small radial variation of thrust coefficient would not alter the flow conditions in the diffuser. This assumption allowed the use of hotwire velocity results for constant thrust coefficient screens (Fig. 4) to be used in determining an equation describing the local velocity for each blade element. The Glauert correction was therefore not necessary into the empirically modified BEM model. Due to the close proximity of the

Figure 4: 1/77th scale wind tunnel model of the double skinned, multi-slotted diffuser. The modified BEM model was subsequently used to design a third blade set for testing. At the design point, good comparison between prediction and measurement is shown for the V2 data (Fig. 5). The agreement reduces at pitch angles away from optimal as can be seen in Figure 6. It can be noted at higher pitch angles, the peak shaft power coefficient magnitudes are similar although the tip speed ratio it occurs at differs. The loss in prediction accuracy may be attributed to a change in flow conditions within the diffuser due to the non-uniform radial thrust loading at off design pitch angles highlighting a limitation of the empirical approach used.

both computational predictions with wind tunnel and field data validate the blade design methodology for a diffuser augmented wind turbine

1.2 V2 12.7m/s 6.7deg V2 12.8m/s 7deg 1

Pred V2 12.6m/s 6.7deg Pred V2 12.8m/s 7deg

0.8

BIBLIOGRAPHY CoP

0.6

0.4

0.2

0 -2

0

2

4

6

8

10

12

14

-0.2 Tip Speed Ratio

Figure 5: Comparison of Shaft Power Coefficient with Tip Speed Ratio for V2 data and blade element prediction at the design pitch. 0.9 V2 11.55m/s 10.7deg Predicted V2 11.55m/s 10.7 deg

0.8

0.7

0.6

CoP

0.5

0.4

0.3

0.2

0.1

0 0

2

4

6

8

10

Tip Speed Ratio

Figure 6: Comparison of Shaft Power Coefficient with Tip Speed Ratio for V2 data and blade element prediction 4 degrees off the design pitch. 6

SUMMARY AND CONCLUSIONS

Research has been undertaken by Vortec Energy on the development of an efficient Diffuser Augmented Wind Turbine (DAWT). A comprehensive programme of wind tunnel, controlled field testing and computational modelling of a diffuser augmented wind turbine has been undertaken. Computational models using the Navier-Stokes solvers CFX and FLUENT with the turbine modelled as an actuator disc have successfully predicted the performance of the DAWT. The development of a modified blade element method incorporating empirical relations from wind tunnel data has enabled blades to be designed for a DAWT. Evaluation of three blade geometries and comparison of

12

[1] H. Glauert, in: F. Durand, Ed., Aerodynamic Theory, Vol. IV, J. Springer, Berlin, Germany, 1936 [2] M.O.L. Hansen, N.N. Sørensen, R.G.J. Flay, Effect of placing a Diffusor around a Wind Turbine, European Wind Energy Conference, Nice, France, 1999 [3] J.H. Horlock, Axial Flow Turbines, Krieger, 1973 [4] O. Igra, Research and Development for Shrouded Wind Turbines, European Wind Energy Conference,1984, Hamburg, Germany [5] FLUENT 5 User’s Guide, Volume 1 - 4, Fluent Incorporated, Centerra Resource Park,10 Cavendish Court, Lebanon, NH 03766, 1998 [6] CFX-4.2: Solver, CFX International, 8.19 Harwell, Didcot, Oxfordshire 0X11 ORA, UK,1997 [7] A.P. Schaffarczyk and J.T. Conway, Comparison of a Nonlinear Actuator Disk Theory with Numerical Integration Including Viscous Effects, CASI J. 46, pp 209 - 215, Dec. 2000 [8] A.P. Schaffarczyk, Prediction of Airfoil Characteristics for Wind Turbines Blades with CFX, Proc. 5th int. CFX-Users Conf., Friedrichshafen, Lake Constance, Germany, June 1999 [9] A.P. Schaffarczyk, Aerodynamic Blade Investigations for V37 with 3D Navier-Stokes-Solvers CFD Laboratory Internal Report, 19, UAS Kiel, Kiel, Germany, December 2000 (Confidential) [10] A.E. Zaryankin, E.F. Kasilov, Aerodynamic control offlow in short diffusors, Energetica, 57-61, 1978 (in Russian)