The science of making more torque from wind: Diffuser experiments and theory revisited.

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1 Journal of Physics: Conference Series The science of making more torque from wind: Diffuser exeriments and theory revisited. To cite this article: Dr Gerard J W van Bussel 7 J. Phys.: Conf. Ser. 75 View the article online for udates and enhancements. Related content - A suersonic gas target for a bundle divertor lasma F.R. Chang and J.L. Fisher - Assessment of low-order theories for analysis and design of shrouded wind turbines using CFD Aniket C Aranake, Vinod K Lakshminarayan and Karthik Duraisamy - Angular Momentum Theory for Diatomic Molecules P W Atkins Recent citations - Determining Diffuser Augmented Wind Turbine erformance using a combined CFD/BEM method JE Kesby et al - Flow interaction of diffuser augmented wind turbines U Göltenbott et al - Ducted turbine theory with right angled ducts S McLaren-Gow et al This content was downloaded from IP address on /5/8 at 4:57

2 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// The science of making more torque from wind: Diffuser exeriments and theory revisited. Dr. Gerard J.W. van Bussel section Wind Energy Faculty of Aerosace Engineering, Delft University of Technology, Kluyverweg, 69 HS, Delft, The Netherlands. tel: fax: g.j.w.vanbussel@tudelft.nl Abstract. History of the develoment of DAWT s stretches a eriod of more than 5 years. So far without any commercial success. In the initial years of develoment the conversion rocess was not understood very well. Exerimentalists strived at maximising the ressure dro over the rotor disk, but lacked theoretical insight into otimising the erformance. Increasing the diffuser area as well as the negative back ressure at the diffuser exit was found rofitable in the exeriments. Claims were made that erformance augmentations with a factor of 4 or more were feasible, but these claims were not confirmed exerimentally. With a simle momentum theory, develoed along the lines of momentum theory for bare windturbines, it was shown that ower augmentation is roortional to the mass flow increase generated at the nozzle of the DAWT. Such mass flow augmentation can be achieved through two basic rinciles: increase in the diffuser exit ratio and/or by decreasing the negative back ressure at the exit. The theory redicts an otimal ressure dro of 8/9 equal to the ressure dro for bare windturbines indeendent from the mass flow augmentation obtained. The maximum amount of energy that can be extracted er unit of volume with a DAWT is also the same as for a bare wind turbine. Performance redictions with this theory show good agreement with a CFD calculation. Comarison with a large amount of exerimental data found in literature shows that in ractice ower augmentation factors above 3 have never been achieved. Referred to rotor ower coefficients values of C P,rotor =.5 might be achievable according to theory, but to the cost of fairly large diffuser area ratio s, tyically values of β >4.5.. Nomenclature V V V 3 V e 3 velocity far in front of diffuser velocity at wind turbine inside diffuser velocity at diffuser outlet velocity in the wake of DAWT ressure in front of diffuser ressure at nozzle before wind turbine ressure at nozzle after wind turbine ressure at diffuser exit c 7 Ltd

3 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// a β γ c i C T,diffuser C T,,total C T,,rotor C P,,rotor C P,,exit axial induction factor diffuser area ratio (ratio of exit area to nozzle area) back ressure velocity ratio ressure coefficient at location i thrust coefficient of diffuser (non dimensionalised with swet rotor area) total thrust coefficient of diffuser lus rotor thrust coefficient of rotor erformance coefficient of rotor (non dimensionalised with swet rotor area) erformance coefficient of diffuser (non dimensionalised with DAWT exit area). DAWT history The first assessments on ducted windmills were erformed by Lilley an Rainbird in 956 []. In the seventies a significant amount of wind tunnel exeriments were carried out by Foreman et al [3,5] from Grumman Aerosace Det. USA, and by Kogan, Seginer and Igra [,4] from the Ben- Gurion University in Israel. Conclusions from these early studies varied significantly. The Lilley and Rainbird study [] concluded that no erformance imrovements were ossible, when erformance is referred to the exit area, where Foreman et al [3] conclude that the DAWT roduced 4.5 times the ower of the same turbine oerating as a conventional turbine and Igra [4] even concluded that the shrouded wind turbine is suerior to any similar horizontal axis wind turbine of the same diameter. Aart from exeriments these researchers also develoed basic theoretical models to analyse their exeriments. These models however lacked a coherent and comlete descrition of the major henomena in the flow field of a DAWT. Diffuser augmented wind turbine (DAWT) geometries were a hot toic at the Wind Energy Innovative Systems Conference 979 in the USA. One of the conclusions from this conference in general was that interesting ower augmentations are ossible, but economic alication of DAWT s seemed not feasible because of the high costs of the configuration. Many research grous shared this oinion and with the raid develoment of horizontal axis wind turbine technology in the second art of the eighties and the nineties the R&D of DAWT s disaeared from the research agenda s. About years after the initial activities of Forman et al [3] and Igra [4] the DAWT concet revived, through an intensive develoment, romotion and ublic relation camaign by a comany called Vortec Energy from New Zealand. This comany claimed ower coefficients of above (referred to the rotor swet area) which claim was based on former wind tunnel exeriments of Grumman Aerosace (Foreman et al [3]) backed by wind tunnel exeriments erformed by Flay and Nash from the University of Auckland NZ. Vortec Energy realized a 7.3 m diameter DAWT in 997 and started exerimenting with this full scale configuration. In an article of Flay et al ublished on the former website of Vortec Energy one of the conclusions is.field measurements on the full scale DAWT gave erformance which was lower than redicted in the Grumman ublications. From CFD calculations erformed by Flay et al it was found that the maximum ower coefficient was found of around referred to the rotor swet area. Comared to the diffuser exit area the ower coefficient was significantly below the Betz value. Recently DAWT windturbines have regained new attention: Several aers are ublished by Abe et al on a flanged diffuser geometry; Mertens [5] ublished a PhD thesis in 6 where he addresses diffuser like concentrator effects that building may have on urban wind turbines and several new small DAWT wind turbines have entered the market. Time to revisit the exeriments as well as the theories for DAWT in more detail. 3. DAWT theoretical models De Vries [6] was one of the first to develo a consistent theory for DAWT s. He distinguishes simle diffuser theory from shrouded turbine theory. In the simle diffuser theory he models the

4 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// dimensional flow through a diffuser, but anticiated on the fact that the exit ressure should be equal to ambient. He incororated negative backressure values as found in the earlier exeriments by introducing an emirical exit ressure coefficient. In his shrouded turbine aroach he makes an attemt to model the radial forces on the shroud in a momentum aroach. That results into the conclusion that.otimum values of about C P = can be obtained. What was not found by De Vries was the fact that the otimal ressure dro over the rotor equals the otimal ressure dro over a bare windturbine. In 999 Hansen et al [9,] showed by means of CFD comutations that the Betz limit can be exceeded with the ratio corresonding to the relative increase in mass flow through the rotor. A simle momentum theory for DAWT s was also derived, at that time by the author [] using a number of straight forward assumtions. It is assumed that there is no viscous wake mixing rocess behind the diffuser but the effect of negative backressures are taken into account in the erformance rediction. From this DAWT momentum theory it can be seen that the achievable ower is comarable with the ower of a normal HAWT (horizontal axis wind turbine) having a diameter equal to the exit diameter of the diffuser. But from this momentum model it can also be seen that larger erformances are ossible when a substantial low back ressure level can be achieved at the diffuser exit. 4. Pressures and velocities inside an emty diffuser In one dimensional momentum theory the velocity and ressure relations in an emty diffuser are directly related to its geometry, i.e. to the variation of cross sectional area. Figure shows the indexes used at the various locations. The cross sectional area of the exit of the diffuser is used as reference. Ambient ressure is found far in front of the diffuser and in the far wake behind the diffuser. Throughout the diffuser the velocity and ressure relations can found by alication of the continuity equation and by Bernoulli s law for the total ressure: tot = + ρ V = + ρv = 3 + ρv3 = o + ρv e () inlet nozzle exit ressure 3 = velocity V V = V V 3 Figure : Pressure and velocity relations in an emty diffuser Using the continuity equation it can be seen easily that the relation between the velocity at the nozzle and the velocity at the diffuser exit is roortional to the diffuser area ratio β: V = β V 3 () 3

5 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// The total ressure at the nozzle, using the above relation can thus be written as: tot = V + ρ( β ) At first it is assumed that there is no back ressure at the diffuser exit, thus 3 = and V =V 3. Then the ressure at the nozzle equals: = This shows that an under ressure will exist at the nozzle, whenever the diffuser area ratio β is larger than. This is evidently the case when the exit area is larger than the nozzle area, and no flow searation is resent. (5) V + ( ) V = γv 3 β ρ At the diffuser exit however a back ressure may exist, e.g. when, through the Kutta condition, the flow is forced to deflect in radial direction. Then the velocity at the exit will differ from the undisturbed velocity V in front of the diffuser. Writing the back ressure relation as a relation between V and the velocity V 3 at the diffuser exit (3) (4) yields the following exression for the ressure at the nozzle: = + ( βγ ) ρv (6) Thus for a diffuser area ratio β larger than and for zero or negative back ressure (γ ), there will be an under ressure at the nozzle. The velocity relations inside the diffuser are rather simle once its geometry is known. Starting from the velocity V 3 at the exit of the diffuser the velocities at other locations can be directly calculated from the local area to exit area ratio, with alication of the continuity equation, and under the assumtion of a uniform velocity distribution at each diffuser section. With resect to the axial forces on the emty diffuser, the situation is in fact quite straightforward. Alying the axial momentum conservation law uon the volume of air in a surrounding stream tube at large distance from the diffuser will show that there is no net force in axial direction on the diffuser. An equivalent way of stating this is that Bernoulli s law can be alied along all streamlines and that this shows that far in front of the diffuser as well as far behind the diffuser, both undisturbed ressure as well as undisturbed velocity V are established again. Of course this is only valid for an emty diffuser, where no energy extracting device is resent. In several references dealing with diffusers for wind turbines, e.g. De Vries [6] and Dick [8] this result is also resented. The ratio of the velocity found in the nozzle of the diffuser (without wind turbine) and the inflow velocity V far in front of the diffuser is very often the cause for erroneous redictions of the achievable ower from a DAWT. Combining the equations () and (5) does show that the nozzle velocity is equal to βγv o. The maximum achievable ower however is not equal to β 3 γ 3 C max, where C max is the maximum achievable ower of the wind turbine without diffuser. The actual maximum will be significantly lower, as will be derived below. 5. Velocity and ressure relations within DAWT s When a windturbine is located in the diffuser, things start to become more comlex. The velocity relations within a DAWT are still rather straightforward since they are, in this one dimensional theory, determined by the shae of the diffuser. Although the shae of the inlet should be adequate for achieving a smooth inflow and for revention of flow searation, the recise shae is not 4

6 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// very imortant for the understanding of the DAWT energy conversion rocess. The velocity at the diffuser exit V 3 will, in general, be lower than V.. Behind the diffuser exit the velocity might reduce further until the final velocity in the wake V e is established at ambient ressure. In the resent momentum theory aroach the exact location of the windturbine inside the diffuser is not relevant for understanding the energy extraction rocess. The effect of the windturbine will be a dro in total ressure, somewhere inside the diffuser, which can be reresented by a reduced total ressure level at the exit of the diffuser. The most suitable location for the windturbine from a constructional oint of view is inevitable the nozzle of the diffuser. Here the smallest cross sectional area is found and thus use can be made of the smallest rotor diameter In the one dimensional momentum theory develoed by Van Bussel [] it is strived to develo a theory having the closest equivalency with momentum relations for ordinary windturbines. Hence it is assumed that at the exit of the diffuser the same conditions aly as just after an ordinary wind turbine (assuming no extra back ressure). Thus the following exression is introduced: V a 3 = ( ) V (7) So the axial induction factor a is defined at the exit of the diffuser. Just as in ordinary wind turbine momentum theory this induction is half the induction factor found in the far wake behind the DAWT (thus V e =( - a)v ). From the continuity equation in then follows, using the diffuser area ratio β, that the velocity at the windturbine in the nozzle of the DAWT equals V = βv 3, and thus: V ( a V = β ) (8) The velocities at other locations inside the diffuser can, as in the situation without windturbine, be determined by alication of the continuity equation. When an extra back ressure at the exit of the diffuser is resent, the exression for the velocity at the exit yields: V ( a V (9) 3 = γ ) analogue to equation (5) for the emty diffuser. The velocity at the nozzle then equals V ( a V () = βγ ) The ressure relations can easily be obtained by alication of Bernoulli s law in the flow in front of the rotor and similarly in the flow behind the rotor. When it is assumed that the rotor is located in the nozzle this leads to: = + [ β γ ( a) ] ρv () for the ressure in front of the rotor and to: = for the ressure behind the rotor. + [( a) β γ ( a) ] ρv Thus the following exression for the ressure jum over the rotor can be written down: = 4a( a) ρv () (3) 5

7 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// which is the classical relation for the ressure dro over a normal windturbine. In other words: the ressure dro over the windturbine is indeendent of the diffuser area ratio, the back ressure ratio and even the location inside the diffuser, as can be shown easily! This means that the amount of energy extracted er unit of volume is identical to the amount of energy extracted for an unaugmented turbine. The amount of air assing the turbine in the diffuser has however been increased with a factor βγ comared to a normal windturbine of the same size. And as the case with momentum theory for ordinary windturbines otimal values are found for for a = /3. Figure : Otimal velocity and ressure relations in a DAWT obtained from momentum theory Left: diffuser without extra backressure (γ =) Right: diffuser with extra backressure (γ >) 6. Power and thrust exressions for a DAWT. With the exressions in the revious section it is easy to write down the equations for the ower obtained from a DAWT. Based uon the area of the windturbine the ower coefficient of the DAWT follows from the equations (8) and (3): (4) C P, rotor = βγ 4a( a) And consequently the ower coefficient based uon the diffuser exit area: C P, exit = γ 4a( a) (5) From the exressions above an interesting conclusion can be drawn with regard to the distribution of the total thrust acting uon the DAWT. The thrust on the rotor inside the diffuser is exactly the same as the thrust on a bare rotor, as can be seen from equation (3): Alication of the rincile of conservation of momentum for the flow through the DAWT leads to the following exression: C T total, = βγ 4a( a) (6) Where, for the resent urose, the rotor area is used for non-dimensionalising the total thrust. This leads to the conclusion that the thrust on the diffuser is deendent uon the thrust of the rotor: CT, diffuser = CT, total CT, rotor = ( βγ )4a( a) (7) 6

8 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// Note again that in (7) the diffuser thrust coefficient is non-dimensionalised with the rotor area!! Hence the thrust on the diffuser is roortional to the extra mass flow obtained in the DAWT, where the thrust on the rotor is not!! Otimal ower coefficients are obtained for a = /3, just as in the situation of ordinary windturbines. In his aroach Van Bussel [] stresses that the develoed theory does not cover the determination of the maximum achievable back ressure ratio γ. Values might be obtained however by examining exeriments. 7. Comarisons with Grumman Aerosace exeriments In the seventies researchers from Grumman Aerosace, erformed an extensive series of model exeriments in their free jet wind tunnel facility which can be used for comarison with the theoretical exressions resented above. The first exerimental results were ublished for slotted diffusers with a half angle of, [3]. In these exeriments the rotor was relaced by a screen, see fig 3 left. Figure 3: Comarison of centre line ressure distributions Left: exerimental results from Foreman et al slotted diffuser half angle Right: redicted distribution from DAWT momentum theory by Van Bussel A comarison is shown in figure 3 between the exerimental results obtained with one of the Foreman diffusers and the basic momentum theory model. The measured back ressure value c 3 = -.4 gives, according to the above DAWT momentum theory, rise to an augmentation of %. Hence the theoretical (inviscid) uer value for this diffuser yields a C P value of.66 (referred to the diffuser exit area). Yet the exeriments revealed an exerimental value of only.35. In a survey aer ublished in some year s later [5] they resent the results of more exeriments in a fairly concise way. Diffuser Area Ratio:.78 3 degree diffuser 4 degree diffuser Velocity at nozzle/screen Pressure coefficient at exit Disk loading Coefficient Rotor Power Coefficient Diffuser Power Coefficient Table : overview of exerimental results obtained by Oman et al [3]. 7

9 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// In table the results from the measurements using slotted diffusers with half angles of 3 and 4 degrees and an area ratio of.78 are summarised. It must be noted that the quoted values for the disk loading in table are different from the values given in Gilbert et al [5]. Like most of the exerimentalists they defined the non dimensional disk loading with resect to the local velocity, where the resent theory always refers to the undisturbed wind velocity V. From table it can be seen that the 3 half angle diffuser was the most successful in achieving a high ower coefficient. The maximum erformance can be found at a disk loading of.88, as is redicted by the resent theory. With a back ressure coefficient of c 3 = -.57 that leads to a back ressure velocity ratio of.4, and hence, according to the theory, a maximum rotor erformance coefficient C PMAX, Rotor =.4. This is again substantially more than the. that was found in the exeriment. In figure 4 the exerimental results for the 3 diffuser are comared to the values from the theoretical model. Gilbert et al 978 Gilbert et al 978, comasion with reduced flow rate theory Coefficients: CP, V/V and c Rotor ower coef 4, Exit ressure 3,5 Velocity at rotor Ex. Rotor ower coef. 3, Ex. velocity at rotor Ex. exit ressure,5,,5,,5,,6,7,7,8,8,9,9,,, -,5 Coefficients: CP, V/V and c Rotor ower coef,5 Exit ressure Velocity at rotor, Ex. Rotor ower coef. Ex. velocity at rotor Ex. exit ressure,5,,5,,6,7,7,8,8,9,9,,, -,5 -, Disk loading coefficient CT -, Disk loading coefficient CT Figure 4: Comarison of exerimental results from Gilbert et al [5] with results from momentum theory of Van Bussel []. Left: using the geometrical diffuser area ratio Right: using the reduced mass flow rate found in the exeriment When looking to the grah in the left hand side of figure 4 there is a fairly good similarity in shae. The most striking difference between exeriments and theory is seen in the values for the velocity ratio at the location of the rotor (screen). With a geometrical diffuser area ratio of.78 the otimal velocity ratio at the rotor disk should be around.85 for a diffuser without extra back ressure, and even to.3 with a backressure velocity ratio of.4, where actual (rotor disk averaged) values of only.6 were exerienced. The reason might be found by considering the mass flow through the slotted diffuser. Unfortunately the survey aer does not quote values for the added mass which is injected in the diffuser in order to revent boundary layer searation in the diffuse, but in the earlier ublication of Oman [3] it was stated that, for the diffuser, the exit mass flow was.86 times the mass flow through the screen. And evidently the mass flow injected in the diffuser behind the screen does not directly contribute to the ower (it does in an indirect way through establishing a lower back ressure at the diffuser exit). When the comarison of the exerimental results is recalculated with an effective reduced mass flow rate, fig 4 right, it can be seen that momentum theory does describe DAWT flow conditions quite well. As can be seen the exerimental diffuser shows a erformance break down for disk loadings above C T, rotor =.9, where theory extends u to the theoretical maximum C T, rotor =.. 8

10 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// 8. Comarisons with CFD calculations In 999 Hansen et al [] showed by means of CFD comutations that the Betz limit can be exceeded with the ratio corresonding to the relative increase in mass flow through the rotor. This is in comlete agreement with the momentum theory as can be seen with the equations () and (4). Moreover the comarison with CFD calculation of Hansen [] shows a good agreement of the calculated rotor ower coefficients over the whole range of disk loadings. Only at the higher loads there are discreancies, most robably caused by the fact that viscous effects, which are evidently not taken into account in the momentum theory calculations. Hansen et al, CFD exeriments Coefficients: CP, Vx/V and c Rotor ower coef, Velocity at rotor Exit velocity Exit ressure,5 Hansen CFD,,5,,,,4,6,8,, -,5 Disk loading Figure 4: Comarison of momentum theory results with CFD calculations by Hansen et al. Unfortunately no other basic arameters were resented in the Hansen s, such as the diffuser exit ressure and velocities at the rotor disk, which could have been used for further validation of the momentum theory. 9. Further comarisons with exeriments Aart form the Grumman aerosace exeriments [3,5] a number of other researchers erformed model exeriments. Most of them are however only artially documented in freely accessible literature. In 997 the comany Vortec Energy realized a 7.3 m diameter DAWT based uon the exeriments erformed by the Grumman Aerosace diffuser team. Unfortunately the exerienced erformance was disaointing. For further analysis of this diffuser Flay et al erformed a number of wind tunnel tests. These seemed at first instance suitable for comarison with the momentum theory redictions. In comarison however it was found, by determination of the non dimensional disk loading with the undisturbed wind velocity V in stead of with the local velocity V that values were measured u to C T =.67. Since this is highly beyond what can be exected the exerimental conditions were re-examined. This led to the conclusion that the actual erformance of the model diffuser tested is highly affected by tunnel blockage. The exerimental set u used a 5 mm diameter screen in a diffuser with an area ratio β =.6. This means an exit area of slightly more than.5 m. With a x 3 m closed wind tunnel section this imlies a blockage factor of.85. But under otimal oerating conditions the area of the wake of a DAWT can become more than twice the DAWT exit area. In such cases the dynamic ressure in the external flow along the test section may increase with some 4%. And that evidently shows that blockage effects have strongly influenced the Flay 9

11 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// measurements, as was already seen from the extreme C T values. Thus these measurements could not be used for detailed comarison with the momentum theory. Recently DAWT windturbines have regained new attention: Several aers are ublished by Abe et al [4] on a flanged diffuser geometry. The large flange is ositioned at the exit of the diffuser erendicular to the undisturbed flow. The idea of alying this exit flange is to enhance the backressure at the diffuser exit. Figure 5 shows the comarison of the different exeriments reorted with the maximum achievable erformance based uon the resent momentum theory. Aart from the maximum CP values based uon the DAWT exit area also the line including 5% rotor losses is shown. Figure 5 Comarison of theoretical achievable C P -diffuser values as a function of the DAWT exit velocity with various exeriments. It can be seen from figure 5 that no exeriments have led to ower coefficients larger than.47 when referred to the exit area of the diffuser. It is also clear that large backressure values can be realized, but so far not together with reasonable erformances. With regard to the quoted exeriments by Flay it must be noticed again that they are obtained in a wind tunnel where blockage effects most robably are too large, hence the large backressure values. Aart from the theoretical exression (5) deicted in the figure also a line is shown for the situation that rotor losses are as large as 5% hence leading to a value C P =.75*.593=.45 for a diffuser with a backressure coefficient c 3 = It can also be seen that the flanged diffuser as roosed by Abe et al did not really yield large (negative) values for the backressure at the diffuser exit. Figure 6 shows the relation between diffuser area ratio and the achievable rotor ower coefficient C P,,rotor.

12 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// Figure 6 Comarison of theoretical achievable C P -rotor values as a function of the DAWT area ratio with various exeriments. Here it can be seen that the larger diffuser area s indeed can lead to higher wind turbine erformances. The diffuser area ratio used by Abe et al [3]: β =6.4 is beyond the range of the other exeriments. Desite this high area ratio, the resulting erformance is oor as can be seen.. Conclusions The focus in the earlier DAWT exeriments was to try to achieve large values for the ressure dro over the rotor disc (most times simulated by screens). The intuitive target was aarently an otimal ressure dro equal to 8/9 times the local dynamic ressure. Simle momentum theory has showed however that the otimal ressure dro equals 8/9 times the undisturbed dynamic ressure. With alication of simle momentum theory it is shown that the amount of energy extracted er unit of volume with a DAWT is the same as for an ordinary bare wind turbine. The increase in maximum erformance of a DAWT is roortional to the mass flow. This roortionality goes with a geometric area ratio β between nozzle and exit. Without extra back ressure at the diffuser exit this means that the maximum ower coefficient related to the exit area is equal to the Betz maximum 6/7. In ractice the maximum erformance will be significantly lower, caused by viscous effects and ossible early flow searation at the diffuser surface. Reducing back ressure behind the exit of a DAWT can have a rofitable effect on the erformance. With resect to the maximum erformance this enhancement factor is equal to the ratio between the diffuser exit velocity V 3 and /3V. The relation between disk loading and ower coefficient, as found from simle momentum theory shows a good agreement with CFD calculations erformed by Hansen et al. Comarison with a large amount of exerimental data found in literature shows that in ractice ower coefficients above C P,,exit =.5 have not yet been achieved. Momentum theory shows that values of C P,,exit =.7 or above can only be achieved with very significant back ressure reductions c 3 <-. Referred to rotor ower coefficients values of C P,rotor =.5 might be achievable, but to the cost of fairly large diffuser area ratio s, tyically values of β >4.5. So far a combination of a large value for the back ressure -c 3, together with a significant mass flow augmentation has not yet been demonstrated.

13 Journal of Physics: Conference Series 75 (7) doi:.88/ /75// References [] Lilley, G.M., Rainbird, W.J. 956 A reliminary Reort on the Design and Performance of a Ducted Windmill Reort, College of Aeronautics, Cranfield U.K. [] Kogan A. Seginer, A. 963 Shrouded Aerogenerator Design Study II, Axisymmetrical Shroud Performance Proc. 5 th Ann. Conf on Aviation and Astronautics, Tel-Aviv, Israel. [3] Oman, R.A., Foreman, K.M., Gilbert, B.L. 975, A Progress Reort on the Diffuser Augmented Wind Turbine Proc. 3rd Biennial Conference an Worksho on Wind Energy Conversion Systems Washington DC, USA [4] Igra, O., 976 Shrouds for Aerogenerators AIAA aer [5] Gilbert B.L., Oman R.A. and Foreman K.M. 978 Fluid Dynamics of DAWT's Journal of Energy Vol [6] De Vries, O., 979 Fluid Dynamic Asects of Wind Energy Conversion, AGARDograh No. 43, AGARD-AG-43. [7] Igra, O. 98 Research and Develoment for Shrouded Wind Turbines, Energy conservation and Management Vol., [8] Dick E., 986 Power Limits for Wind Energy Concentrator Systems, Wind Engineering Vol., no., [9] Hansen, M.O.L, Sørensen, N.N, Flay R.G.J. 999 Effect of lacing a Diffuser around a Wind Turbine, Proc. EWEC 999 Conference, Nice, France [] Hansen, M.O.L, Sørensen, N.N, Flay R.G.J. Effect of lacing a Diffuser around a Wind Turbine, Wind Energy, volume 3, 7-3 [] Flay, R.G.J., Phillis, D.G., Richards, P.J. 999 Develoment of Diffuser Augmented Wind Turbine Designs in New Zealand Proc. EWEC 999 Conference, Nice, France [] Van Bussel, G.J.W, 999 An Assessment of the Performance of Diffuser Augmented Wind Turbines (DAWT s), 3rd ASME/JSME Fluid Engineering Conference FEDSM99-783, San Francisco, USA. [3] Abe K. Ohya, Y, 4 An investigation of Flow Fields around Flanged Diffusers using CFD, Journal of Wind Eng. And Industrial Aerodynamics vol 9, [4] Abe K. Nishida, M, Sakurai, A., Ohya, Y, Kihara, H., Wada, E., Sato, K., 5 Exerimental and Numerical Flow Fields behind a Small Diffuser Wind Turbine with a Flanged Diffuser Journal of Wind Engineering and Industrial Aerodynamics vol 93, [5] Mertens, S. 6 Wind energy in the Built Environment, Concentrator Effects of Buildings 6, PhD Thesis Delft university of Technology, section Wind Energy, Delft, The Netherlands.