BMW Research Center, BMW AG, Muenchen, Germany b. Department of Physics, Univ. od Udine, Via delle Scienze 208, Udine, Italy

Transcription

1 Renewable Energy (2002) Upgrading conventional wind turbines F. Bet,a, H. Grassmann b,* 6 7 a BMW Research Center, BMW AG, Muenchen, Germany b Department of Physics, Univ. od Udine, Via delle Scienze 208, 3300 Udine, Italy 8 9 Abstract 0 When approaching a conventional wind turbine, the air flow is slowed down and widened. This effect causes a loss in the efficiency of the turbine. By creating a field of low pressure 2 behind the turbine, this effect and the corresponding loss in efficiency can be avoided. In order 3 to maintain this low pressure field, the air passing near, but not through the turbine needs to do work. 6 Based on these considerations we have made a model of a wind turbine with a wing profiled 6 ring around it. We present various fluidodynamical calculations in order to study the resulting 7 increase in power and in order to estimate what the geometrical size of such an apparatus 8 would need to be and whether it could be of advantage compared to conventional devices 9 from an economic point of view. 200 Published by Elsevier Science Ltd. 60 Keywords: Electric energy from wind; Wind turbine; Wind turbine efficiency; Economic analysis Introduction 6 Conventional wind turbines extract kinetic energy from a flow of air by means of 6 a rotor, which is exposed to the otherwise undisturbed air flow. The turbine slows 66 the air down from its original ambient velocity v to a final velocity v 2. This deceler- 67 ation causes an increase of the static pressure before and after the turbine, while 68 within the turbine, where energy gets extracted from the air, its static pressure drops 69 in correspondence. 70 While the air gets decelerated, the flow of air correspondingly widens * Corresponding author. Tel.: ; fax: address: hans.grassmann@fisica.uniud.it (H. Grassmann) Tel.: F. Bet participated privately in this project, it is not a BMW research activity /02/$ - see front matter 200 Published by Elsevier Science Ltd. PII: S0960-8(0) RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P DTD v..0 / RENE8

2 2 2 2 F. Bet, H. Grassmann / Renewable Energy (2002) 3 7 Due to this effect the power which can be extracted from the air flow is at 72 maximum only 9% of the power of an air flow of cross-section equal to the area 73 covered by the rotor []. This maximum value of 9% is reached when v 2 =/3v. 7 For different values of v 2, the efficiency is lower. If one can avoid this effect of 7 widening, the efficiency of a wind turbine could increase. For the ideal case of 76 v 2 =/3v, the increase would be somewhat less than a factor of.7, for all other 77 cases the increase would be higher than that. This increase could make the use of 78 wind energy more economic [2]. 79 Therefore there have been several attempts in the past to augment the power of 80 wind turbines by means of shroud systems, some examples are found in Refs. [3 8 ]. In one case [] even several millions of New Zealand dollars have been invested 82 in the construction of several prototypes. But none of the reported attempts has 83 proven successful. 8 The reason is found in the fact, that for increasing the power of the wind turbine, 8 the pressure drop at the propeller must be increased, by means of a decrease of 86 pressure behind the propeller. To maintain this pressure sink in a flow of air, work 87 must be done, either by the flow of air which passes the turbine, or by another flow 88 of air, which does not pass the turbine. In all applications known to us, the first 89 choice was made: then the same flow from which one wants to extract energy, also 90 must do work for maintaining the pressure drop at the propeller, and consequently 9 the efficiency of the device cannot improve very much. For example, we have created 92 a model of the shrouded turbine presented in Ref. [] and we found from a fluidody- 693 namical simulation an increase in power by only 20%, in spite of the fact, that the 9 shroud in this model is much larger than the turbine itself. 9 In our studies, instead, we extract the energy for maintaining an increased pressure 96 drop at the propeller from the flow of air which passes near to the turbine, but does 97 not pass through it: if one brings a wing close to a wind turbine, with the bended 98 side of the wing pointing to the wind turbine, then the field of low pressure which 99 forms over the bended side of the wing decreases the pressure behind the turbine. 00 As a consequence, the air passing between the wing and turbine will be decelerated. 0 This in brief is this concept, which we want to study in more detail in this paper Simulation 03 For a given wind speed a turbine can rotate the slower, the more blades it has. 0 Slowly moving blades are less demanding from an aerodynamic point of view. For 0 our simulation we wanted to use a very simple blade, in order to save computing 06 time, and therefore we chose to use a slowly rotating propeller consisting of blades. We simulated a segment of this propeller of 0 degrees width, and imposed 08 cyclic conditions on the side walls of the simulated domain. The blade is a bended 09 two-dimensional baffle. We therefore could limit the number of cells in our models 0 to about 20,000. For two of the models (one propeller without shroud and one shrouded system) we have made test runs with the grid density in the region around 2 the propeller and the shroud being increased by about a factor of ten, for a total of 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

3 2 F. Bet, H. Grassmann / Renewable Energy (2002) ,000 cells, and we found no significant changes between the model with a large number and the model with a smaller number of cells. This study is to explore a new procedure for increasing the power of a wind 6 turbine, little attempt for optimization and no study of systematic errors was done 7 yet. The program Star-CD was used for the fluidodynamic simulation [6]. This is a 8 highly professional and widely used program in industry, for instance for the simul- 9 ation of engines, cars, airplanes and other technical devices. While a detailed study 20 of systematic errors for our models remains a high priority, the experience with the 2 program Star-CD in industry suggests, that those uncertainties most likely will not 22 be much larger than a few percent. 23 In our simulation the wind velocity is always m/s, in our figures the wind enters 2 from the left and in the horizontal direction, the horizontal axis is referred to as 2 x-axis The turbine 27 The simulated turbine has a radius of 0.6 m and covers an area of r 2 π=0.98 m At m/s air has a power of 7 W per m 2. From the simulation the turbine is found 29 to have a power of 29 W (at w=90 rotations/min). That means, it absorbs 30 29/7=39% of the energy which flows through an area as large as is covered by its 3 propeller (0.98 m 2 ). 632 Betz has shown [], that for reasons of mass conservation, a turbine can at 33 maximum absorb 9% of the energy which flows through an area as large as is 3 covered by the rotor. With respect to this theoretical limit our turbine is therefore 3 39/9=66% efficient. 36 In Fig. we show the static pressure in a cross-section along the x-axis of the 37 pressure field around this turbine. The air is decelerated before the turbine and there- 38 fore its static pressure increases. The air pressure drops sharply within the turbine, 39 because the turbine is extracting energy from the flow of air. Also behind the turbine 0 the air continues to slow down, in correspondence its pressure again increases, till finally the normal environmental pressure is again reached. 2. Creating a field of low pressure 3 The turbine is inserted into a cylindrical structure with a profile similar to an air plane wing, as indicated in Fig. 2. (The opening of the cylinder formed by the wing structure is 0.77 m, corresponding to an area of.7 m 2.) Fig. 2 shows how the field 6 of low pressure, which forms over the bended side of a wing, is coupling with the 7 field of low pressure behind the turbine. We find, that the power of the turbine is 8 increased by the wing system by a factor of.6. This increase in power therefore 9 is approximately as large as the increase in the area covered by the device, which 0 is a factor of.7. In Fig. 2 we see, that the pressure field around the turbine is modified by the wing 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

4 2 2 F. Bet, H. Grassmann / Renewable Energy (2002) Fig.. Static pressure around the propeller. A cross-section along the x-axis is shown. Wind flows from the left to the right with v= m/s. The position of the propeller is indicated as a black line. 2 in such a way, that immediately before the turbine, the air now remains on ambient 3 pressure the air does not get decelerated anymore, when approaching the turbine. If the turbine were fully efficient (if it would be able to extract all of the kinetic energy from the air), then an air flow of velocity v would cause a pressure drop in 6 the turbine of /2rv 2. A larger pressure drop cannot be produced: if the pressure 7 in the turbine would drop by more than /2rv 2, then one would extract from a 8 volume of air more energy than what corresponds to its kinetic energy density, which 9 is /2rv 2. That would be in violation of energy conservation, since at some distance 60 behind the turbine, the air must return to ambient pressure. 6 However, our turbine is not ideal, a flow of air of velocity v does not cause a 62 pressure drop of /2rv 2. Therefore it should be possible, to further increase the 63 velocity of the air through the turbine and to augment the power of the turbine. 6 In Fig. 3 therefore an additional, outer cylindrical wing structure is added. Again, 6 the field of low pressure, created by this structure, is coupling to the low pressure 66 field inside the first cylinder, behind the turbine. Compared to the bare turbine, the 67 power again increases to 8 W, that is a factor of 2.0, compared to the bare turbine. 68 Up to now our only goal was the study of some physics effect. Therefore the 69 geometrical configuration for the models in Figs. 3 and was chosen quite arbitrarily. 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

5 2 F. Bet, H. Grassmann / Renewable Energy (2002) Fig. 2. As Fig., with cylindrical wing structure added around propeller. The wing structure is forming a ring around the propeller. 70 For the industrial application it is important to decrease the size of the wings as 7 much as possible, in order to save construction cost. A device as shown in Fig presumably would not be cost effective. Indeed a comparison of Fig. with Figs and 3 shows, that the shroud system very much enlarges the low pressure field 7 behind the turbine in the x-direction. This is simply because the wings are rather 7 long, but it is not necessary for the operation of the turbine. This suggests, that the 76 wings can be made much smaller. However, they still need to act on a large cross- 77 section of air flow, therefore they need to have an opening angle with respect to the 78 direction of the wind as large as possible. For that reason it also would help, to give 79 them an additional bending. 80. Moving towards the technical application 8 The resulting structure is shown in Fig.. The wing profiles are now much smaller 82 than before. However, the outer cylinder covers about as much cross-section as 83 before. Also the power of the device is again about the same: the configuration 8 shown in Fig. increases the power of the wind turbine from 29 to 7 W. 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

6 2 6 2 F. Bet, H. Grassmann / Renewable Energy (2002) Fig. 3. As Fig. 2, with a second wing structure added. 8 Fig. shows a three-dimensional view of the model. The large number of blades 86 (36) was chosen in order to reduce computing time, but the system should also work 87 with a small number of propeller blades. 88 When we express the dimensions of the wings (Figs. and ) surrounding the 89 propeller in units of the radius of the propeller, r, wefind: each wing has a width 90 of about 0.2r, and is at a distance of about.3r from the axis, therefore the wings 9 have a corresponding (one-sided) surface of approximately 2(.3r)π0.2r2=.3r 2 π. 92 That means, that the surface area of the wings is equal to the area covered by the 93 propeller. Therefore, if one wants to double the power of a wind turbine, one can 9 achieve that by inserting it into a wing structure of about the same total area as the 9 area which is covered by the propeller of the turbine itself. If the price of wing 96 structure per m 2 is lower than the price for wind turbines per m 2,(which is about Euro/m 2 ) than one can decrease the price of energy produced by wind turbines Outlook 99 While the overall picture is encouraging, much work remains to be done: for 200 instance, the structure of Fig. is presumably not yet optimized, the size of the 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

7 2 F. Bet, H. Grassmann / Renewable Energy (2002) Fig.. Propeller with two small size wings. 20 wings presumably still can be reduced. The widening of the airflow in a conventional 202 turbine is not the only source of inefficiency. Power is also lost because the pressure 203 difference between the two sides of the propeller blades causes a flow of air around 20 the tip of the blade, for instance. This source of inefficiency would be avoided, if 20 one inserts the propeller tightly fitting into the inner shroud, without leaving space 206 between the tips of the propeller blades and the shroud. 207 For the discussion in this paper, we have used two wings, because this study is 208 an extension of what had been presented in Ref. [7]. Presumably one could substitute 209 the two wings either by one large wing or by a larger number of smaller wings. 20 One could then choose among the various options the one which is cheapest in 2 industrial production Conclusion 23 We have increased the power of a wind turbine by a factor of 2.0 by means of 2 a wing structure placed at some distance around the turbine. The wing structure is 2 having a size, which is about as large as the wind turbine itself. Therefore this new 26 method could result in an improvement of the ratio price/power for wind turbines. 2 RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P

8 2 8 2 F. Bet, H. Grassmann / Renewable Energy (2002) Fig.. Artist view of the propeller with wing structures. Note, that the large number of propeller blades is only for making the simulation easier, the device should be working also with a small number of blades. 27 Acknowledgements 28 This work would not have been possible without the strong support of Prof. C. 29 DelPapa and Prof. M. Ceschia, from the University of Udine. 220 References 22 [] Betz A. Wind-Energie und ihre Ausnutzung durch Windmuehlen. Oekobuch reprint, Staufen. 222 [2] Frankovic B, Vrsalovic I. New high profitable wind turbines. Renewab Energy 200;2: [3] Hau E. Windturbines. Berlin: Springer, [] Oman et al. Variable stator, diffuser augmented wind turbine electrical generation system. US pat- 22 ent,07, [] Based on the patent [], the company Vortec of New Zealand has made several prototypes. 227 [6] Documentation about Star-CD can be obtained from [7] Grassmann H. Das Denken und seine Zukunft. Hamburg: Hoffmann und Campe, RENE: renewable energy - ELSEVIER :2:28 Rev 6.03x RENE$$8P