Wind site and limit of Betz

[Bibiphoque]

Hello,
I found this site / forum, it is not bad at all !

Down

[Christophe]

not bad indeed, at random I click and I can read:

The Betz limit is applicable to any type of sensor of the kinetic energy of a moving fluid.

This value is worth 16/27 or 0,59259

We can only capture 59,259% of the kinetic energy of a moving fluid (air, water, ...).



However, some pumps (many) have an efficiency higher than 60% ditto for the turbines (pelton for example) .... maybe this is because part of the energy captured by the hydraulic turbine is also potential ... ?

To complete your link: http://fr.wikipedia.org/wiki/Limite_de_Betz

[State]

Hello,

Indeed, the yields of certain hydraulic turbines (the pumps, not recovering energy, do not lend themselves to "Betzian" considerations ...) can reach values ​​higher than the "fateful" 59% of the Betz limit, due to the pressure difference between the infinite upstream and downstream flows to the pump (away from the turbine). Therefore, these closed flows make it possible to recover, in addition to the kinetic energy (dynamic pressure = 1 / 2.rhô.V²), the pressure energy (static pressure = P), or even the potential energy ( rhô.gh) contained in the fluid. This is impossible to achieve with open flows: the static pressures upstream and downstream of the rotror disc remain substantially equal to atmospheric pressure (10exp5 Pascals). The pressure jump used in the Betz demonstration only considers the pressures measured in the immediate vicinity of the rotor disc.

Small precision to bring to the yields of wind turbines: their values ​​are always expressed as a function of this Betz limit, and not as a function of the reference power. Let me explain: for a reference surface (or master-torque) corresponding to the surface swept by the rotor, and noted S, the power "transported" by the wind is Pref = 1 / 2.rhô.S.V3. The maximum power that can be recovered by a wind turbine is therefore worth Pbetz = Pref.0,59. Or a Peol power wind turbine. Its performance is then worth Peol / Pbetz, and not, as one might think, Peol / Pref ..... which has led to more than one being mistaken, me first ....

[Christophe]

thank you for the clarification !

Regarding the pump / turbine even if one recovers and the other provides energy to the fluid, the dimensioning calculations and the general theory remain the same!

Ok for the yield relative to the Betz limit ... this means that to have the "absolute" yield it would be necessary to apply a coef. 0.6 to the yields given in wind power?

[State]

Not exactly...

... What I mean is that two cases arise: either the announced yield is already calculated with respect to the Betz limit (yield = Peol / Pbetz), or it is calculated with respect to the overall power (yield = Peol / Pref), and we must then multiply this overall yield by 1,67 (1 / 0,6) to fall back on the yield based on Betz (because Pbetz = 0,6.Pref). So the efficiency of a wind turbine is 1,67 times higher when we calculate it compared to the Betz limit. This corresponds on the one hand to a logical approach, since part of the reference power (0,4.Pref) can never be recovered, but on the other hand to higher yield values ​​to present to buyers wind turbines .... watch out, everyone does it, including us ...

For example, a wind turbine recovering 30% (for the best ...) of the overall power will be considered to have a yield of 50% compared to the Betz limit. Furthermore, this yield obviously varies with the wind speed, which means that a yield must imperatively be associated with a wind speed.

In the end, what matters is not really good performance at a certain speed, but rather correct performance for the whole range of machine speeds. This leads to optimal annual energy production: we will rather rely on kW.h produced than on instantaneous powers (kW) ..... because we must not forget that these are indeed kW.h that EDF buys (or that we consume ...), and not kW .... This is why we must take into account more parameters than the efficiency or the power curve of a wind turbine to study the feasibility of an implantation. Indeed, it will for example be necessary to correctly choose the wind turbine model which will be adapted to the types of winds encountered on such or such site, or to position the machine judiciously, because a bad location can lead to considerable differences in production.

[Christophe]

So speaking of my 0.6 coefficient I was right ...


Regarding kwh and kw fully agree unfortunately this does not seem to be the current development policy which advocates powers installed increasingly gigantic and therefore necessarily inaccessible to individuals .... and where is the micro wind recovering winds weak power ?

[State]

Not very far to tell the truth ....

As you have very well underlined, these are the "big projects" which are favored by design offices, and especially by investors .... normal, these are the most profitable, since they offer the returns on investment the weakest (around 5 years on a 2-3MW fleet). Conversely, the small wind turbine intended for individuals does not (not yet ...) achieve such a break-even point, whether with conventional wind turbines or other. Of course, the financial aspect should not be the first argument of a feasibility study, but current mentalities bring us back to earth brutally. Especially in France, where the first question we are asked is: "how much does it cost and how much does it bring in", without knowing if we will be able to reduce CO2 emissions, without knowing that we will be able to produce inexhaustible energy .... in short, mentalities are far from changing. Not to mention that the legislation has practically nothing at the level of aid (ADEME, Europe ...) intended to promote small wind turbines in the home, as is the case for photovoltaics .... it's not won ....

In addition, I often see you talking about low wind speeds, and the means to be used to recover them. Know that we (GUAL Industrie / www.gual-industrie.com) do not share the same opinion, especially since the manufacturers of propeller wind turbines benefit from this (suggested power limitation from 15m / s, due to the efforts on the blades ...). Indeed, an "all stupid" example will surely make you change your mind ...

Take the power carried by the wind, and crossing a unit area (1m²). This power is then equal to 1 / 2.rhô.V3 (because S = 1m²). Let's compare the total amount of energy (in kW.h) that can be recovered over a year, by considering two different cases: either we observe a constant wind of 5m / s all year (12 months), or a wind of 10m / s for 6 months and zero wind for the other 6 months. Obviously, the average annual speed remains the same (5m / s). In the first case, we obtain an instantaneous power of 0.5 * 1.225 * 5 * 5 * 5 = 76.56 W, i.e. an energy produced by P * time (24 * 365 hours) = 76.56 * 8760 = 671 kW.h approximately. In the second case, the instant = 0.5 * 1.225 * 10 * 10 * 10 = 612.5 W, and an energy P * time (24 * 182.5 hours) = 2683 kW.h .... therefore 4.4 times more energy . We immediately see the advantage of recovering high wind speeds when we transpose this example to what happens during an hour of wind, especially when it is very turbulent and we observe very violent gusts: the energy produced will strongly depend on the power peaks recorded ... if they can be recovered .... which is of course not the case for all wind turbines. One downside, however: being able to recover "more" instantaneous power of course makes it possible to produce more over a year, but this implies oversized power electronics, technically, but also financially ..... it is therefore necessary to make a compromise between the additional cost a chain of such power (generator, inverter ...), and the benefits it will allow to realize during strong winds which are obviously rarer. Such considerations lead, by considering the data provided by Meteo France on a given site, to improvements of 30 to 40% in annual production: recovering more but less often is more profitable ....

[Bibiphoque]

Hello,
A small question by the way, are there any technical studies on high efficiency generators, using for example neodymium magnets?
A+

[State]

Hello,

Yes yes, there are ...... well hidden in the boxes of the manufacturers ....
I am talking about either the manufacturers of generators (direct drive neodymium synchronous for example), or the manufacturers of wind turbines themselves. At the same time, if we had developed such machines, we would be very happy to be the only ones to benefit from them ....

This is why it is so difficult to find detailed studies on this, not to mention that certain generator manufacturers (LS to name no name ...) sign exclusive contracts with wind turbine manufacturers, which eliminates any chance. to others if only to obtain information on their products ... there again, it is good war, but it is not war (economic of course ...) that will advance renewable energies. ..

[Misterloxo]

Thank you for these Stato details. This forum is wide open for you to share your knowledge.

MisterLoXo