Betzin laki on ylitetty jo moneen kertaan !

Eräässä kommentissa.

It is very interesting to read your opinion. We have build wind turbine that is vertical axis. We are now observing power efficiency in wind tunnel. However we measure much higher then 59 % - we are close to 80 - 85 %. If there is someone that has great understanding of other then Betz law explanation I would like to share video of our design and initial data. Please contact me in direct way - andrew@mastercore.ca

Please note that the Betz Limit has already been broken and see my technical note titled "Wind Energy Conversion Efficiency Limit", Wind Engineering, vol. 30, No. 5, 2006, Multi-Science Publishing Co, UK.


The momentum analysis of Sharpe [3] is considered further. It is shown that the maximum wind energy conversion efficiency limit, or the Betz limit of 59.3%, deduced from conventional actuator disc theory is the limiting stationary maximum value as wind turbine rotor speed approaches infinity and rotor outlet swirl approaches zero. Theoretically, solution of the governing equations indicates 100% conversion efficiency could be possible with suitable wind turbine design and without wake limitations for all tip-speed ratios. Analogous to the thermodynamics laws for heat engines and similar to a Pelton wheel with hydro power, the wind turbine efficiency is not limited by the laws of fluid mechanics but by physical constraints only. Low tip-speed ratio would have greater prospects in achieving higher conversion efficiency in practice. Though the set of equations derived in the present technical note has assumed uniform bound circulation along the blade span, the same approach can be used for determination of optimum conditions for other blade designs or using other assumptions.

Bill Wolf:

Betz’s Law is applicable to non-shrouded, transverse-flow turbines having a flow velocity through the turbine equal to the average of the incoming and exiting flow velocities. The assumption regarding the average flow velocities is part of the proof, so it is incorrect to apply Betz’s Law to applications where this initial assumption is not the case. Also, the theoretical efficiency of 50.26 percent is the result of theoretically removing 88.89 percent of the energy from the two-thirds of the incoming flow that passes through the turbine and removing zero energy from the remaining one-third of the incoming flow that passes around the turbine. According, the theoretical efficiency of the turbine is dependent on what is defined to be the power of the incoming flow. If the power of the incoming flow is defined in terms of the cross-sectional area of the flow that eventually passes through the turbine, then the maximum theoretical efficiency is 88.89 percent. However, if incoming power is defined in terms of a cross-sectional area equal to the cross-sectional area of the turbine, as in the case of Betz’s Law, then the maximum theoretical efficiency is 50.26 percent.

http://www.bg.pg.gda.pl/pmr/pdf/PMRes_2013_2.pdf

Jokainen H-darreus toimii näin.

Edelliseen perustuen arvioin omani toimivan näin.

Cycloturbiinien tehon syy lienee tässä pystysuuntaiset siivet vie ilmaa kärkiin muodostaen voimakkaan tyhjiön turbiinin keskelle.

Tämä nuolimuoto nopeuttaa ilman virtaamista laitteeseen.

Tieteellinen todiste 12%n ylityksen mahdollisuudesta.

https://iopscience.iop.org/article/10.1088/1742-6596/753/2/022056/pdf

;D

Edelleen kyse on kuitenkin hypoteesista:

Besides these theoretical considerations, previous numerical studies support this hypothesis. In
case of VAWTs, first approaches to estimate the power output were presented by Shankar [2] and
Strickland [3]. In comparison to experimental data, their momentum based models suffered from
an overprediction of the power output. Slight improvements could be identified by Strickland
[3] using a multiple streamtube approach, whereby Lapin [4] proposed to represent the rotor
as two halves. Using an analytical double actuator disk approach, Newman [5] determined a
maximum power coefficient of 0.64, which is 8% above the classical Betz value. For a very large
number of discs he derived that the maximum power coefficient tends to a value of 0.66, i.e.
12% above the Betz limit [6]. Loth and McCoy [7] extended the analytical double actuator disk
approach by replacing the two straight actuator disks by two semi-cylindrical actuators. For
the velocity distribution along the cylinder halves a cosine-type formulation was selected. This
closed-form approach led to a maximum power coefficient of 0.617, hence 4% above the Betz
limit. Furthermore, considering the blade incident angle in each position to be influenced by
streamline curvature, blade camber, and the attachment point of the blade Loth and McCoy
derived a value of 0.610 as the maximum power coefficient, which is 3% above the Betz limit.
To overcome the drawbacks of streamtube models, e.g. their assumption of a one dimensional
flow Madsen et al. [8] used an extended actuator cylinder flow model. For the ideal case of an
uniform rotor loading they determined a power coefficient, which is 5% above the classical Betz
value.