MAE 598 Topic: Wind Energy

My notes that I have derived from Reading the text and studying Wind Energy over the internet on my own can be seen below:

Project rough draft title for wind energy 30% of final grad: “Small turbine analysis via micro air vehicle wings using CFD to measure impact on lift and drag”

differential form, integral form and cartesian form of the continuity or conservation of mass equation http://www.ae.metu.edu.tr/~ae244/docs/FluidMechanics-by-JamesFay/2003/Textbook/Nodes/chap03/node12.html

low wavelength inversely proportional to high frequency

c=lambda*f

http://web.pdx.edu/~jduh/courses/geog493f11/Week04.pdf

VAD assumes that the wind field at a given altitude is uniform

http://kkd.ou.edu/Mean_Retrieval.pdf

VAD Velocity–azimuth display is a method for deriving profiles 

 of mean wind speed and direction from PPI data (Browning 

 and Wexler 1968)

http://journals.ametsoc.org/doi/pdf/10.1175/BAMS-86-6-825 

Dual-lidar for vertical wind profiles

http://www2.mmm.ucar.edu/imagearchive/episodes/ROC/WSR-88D_algorithms/pdfs/velocity_azimuth_display.pdf

turbulence is generated by shear and destroyed by negative buoyancy and viscosity. 

buoyancy does not allow turbulence to mix

http://www4.ncsu.edu/~sbasu5/basu_sbl-les.pdf

page 571, Kundu book chap 12 turbulence

From R. Stull's BLM book defines the atmospheric boundary layer as follows: 

     "that part of the troposphere that is directly influenced by the presence of the earth's surface and responds to surface forcings with a time scale of about an hour or less"

Boundary Layer

what are the continuity and NS equations for incompressible flow

http://en.wikipedia.org/wiki/Boundary_layer

http://www.wind-power-program.com/turbine_characteristics.htm

Design Modeler

http://www.ansys.com/Products/Workflow+Technology/ANSYS+Workbench+Platform/ANSYS+DesignModeler/Video+Series

ANSYS Comprehensive Solutions for Advanced Materials

watch at about 20.00 min the windmill CFD set up

CFD

what is optimal interpolation?

The equation for lidar

P(r) = C/r^2* beta(r) e^-2integral(from 0 to r) k(r')dr'

Lidar power is inversely proportional to the range squared.

beta represents the amount of light back scattered at a given range to the reciever

k is the extinction coefficient

http://lidar.ssec.wisc.edu/papers/dhd_thes/node10.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/deriv.html

Taylors hypothesis states that when an eddy-cloud is moved the properties stay the same (like the diameter of the 

eddy and temperature is like frozen or the same after  moving from one place to another place.

we call zeta = 0 for taylors hypothesis so the derivative of zeta is also 0.

So, we have dzeta/dt = partialzeta/partial t + u*partialzeta/partialx + V*partialzeta/ partial y +Wpartialzeta/partialz

The wake behind a wind turbine rotates in the opposite direction of the turbine

The convective mixed layer occurs during the day due to the sun

The radial velocity magnitude will be a sine wave

radial velocity is the component of the wind vector in the "look" direction of the lidar

http://www.hydrol-earth-syst-sci.net/13/651/2009/hess-13-651-2009.pdf

VADs (Velocity Azimuth Display)

http://apollo.lsc.vsc.edu/classes/remote/lecture_notes/radar/doppler/vads2.html

Solving for V2=(V1+v4)/2, by using conservation of momentum (F=ma or Thrust=mdot*changeinvelocity)

and using conservation of mass (mdot = density*velocity*Area)

and Force = Pressure*Area

Where Pressure is from Bernoulli Equation, deltaP=0.5*rho*V^2

Force=(0.5*rho*Area*(V1^2-V4^2)

Thrust=Force=rho*V2*A*(V1-V4

Set both Forces equal to eachother

(0.5*rho*Area*(V1-v4)*(V1+V4) = rho*V2*A*(V1-V4)

The V1-V4 cancels!!!

leaving, V2 = (V1+V4)/2

Wind power is the conversion of wind energy into a useful form of energy

http://en.wikipedia.org/wiki/Wind_power

The watt (W) is a measure of electric power. (Power is the rate of doing work or producing or expending energy.) One watt is equal to 1 joule (J) per second. A megawatt (MW) is one million watts. 

http://www.aweo.org/windunits.html

Wind power in the United States, Texas produces the most wind energy-power with 12,355 MW of capacity, then California with 5,830 MW then Iowa with 5,178 MW of wind power-energy capacity.

http://en.wikipedia.org/wiki/Wind_power_in_the_United_States

log law-best for wall bounded flows

log law equation, pg 586 in Kunu Fluid Mechanics, U=(u*/k)ln(y+)+B, k=von karman log constant, B is log constant.

The divergence of a vector field is zero, pg 555 in Kundu Fluid Mechanics 

http://mathworld.wolfram.com/Divergence.html

Proof that the divergence of the velocity field is zero

https://www.khanacademy.org/math/multivariable-calculus/partial_derivatives_topic/divergence/v/divergence-2

Governing equations of fluid dynamics

http://www.eng.auburn.edu/~tplacek/courses/2610/fluidsreview-1.pdf

http://farside.ph.utexas.edu/teaching/336L/Fluid.pdf

Betz law states that a wind turbine can only be 59% (=0.59) efficient

http://web.mit.edu/windenergy/windweek/Presentations/Wind%20Energy%20101.pdf

Wind power energy is 1/2*rho*u^3, if the wind speed doubles then you energy increases by a factor of 8.

http://www.raeng.org.uk/education/diploma/maths/pdf/exemplars_advanced/23_Wind_Turbine.pdf

A sonic anemometer usage of ultrasonic sound waves is more accurate than cup anemometer.

http://en.wikipedia.org/wiki/Anemometer

http://www.benthamscience.com/open/toascj/articles/V002/131TOASCJ.pdf

Isotropic velocity fluctuation turbulent field is when direction does not matter!

You can make a simple cup aneometer to measure the wind speed

Emission Reduction via wind turbines

The big picture for Wind Turbines

RPM

Power depends on wind speed cubed!!

Top 10 wind power countries[7]CountryTotal capacity

end 2013 (MW)

China 91,424

United States 61,091

Germany 34,250

Spain22,959

India20,150

United Kingdom 10,531

Italy8,552

France8,254 

Canada 7,803

Denmark 4,772

Rest of world 48,351

Total 318,137

http://en.wikipedia.org/wiki/Wind_power_by_country

largest windmills

http://www.windpowermonthly.com/10-biggest-turbines

Lidar (also written LIDAR or LiDAR) is a remote sensingtechnology that measures distance by illuminating a target with a laser and analyzing the reflected light.

http://en.wikipedia.org/wiki/Lidar