DRAG-TYPE WIND ENERGY TECHNOLOGY

[VERSION 2]

Part B Module 1 – Wind Energy

[Version 2]

SAILING DOWNWIND

• Sailors have known for millennia that the wind will push you downwind

• Force due to drag of object exposed to wind

• Cannot exceed wind speed Wind

Wind

DRAG-TYPE WIND ENERGY TECHNOLOGY • Panemones

– (a) cup type – (b) paddle type – (c) s –type

• Wind capturing element has to go upstream as it rotates back to starting point

(a) (b)

(c) Wind

Wind Wind

Screen

CUP-TYPE PANEMONE

• Rotating cup anemometer used to measure wind speed

• Convex shape on back side has less resistance to air than concave side facing the wind

• Wind direction doesn’t matter

"Cup-Anemometer-Animation" by Jan Barani

CUP-TYPE PANEMONE (2)

• Creative practical example – Oil drum halves acting as cups – Drives water pump – 1936 North Dakota farm

Torrey, 1976

PADDLE-TYPE PANEMONE • Paddles with screen

– 9th century Persia – Wood poles with reeds tied to

them – Masonry screen – Fixed screen requires prevailing

winds from consistent direction – Mill grain, pump water

Torrey, 1976

S-TYPE Variation on cup-type

• Convex surface has lower drag than concave surface

"Savonius-rotor en" by Ugo14

Wind

Savonius rotor (split S-type) • Flow on back of rotor assists rotation • Higher torque

PADDLE CONFIGURATION

• Basic geometry for analysis • Wind acts normal to

paddle • Paddle rotates

counterclockwise • Screened on return loop

R

WIND AGAINST A PLATE • Force on paddle is given by:

𝐹 = 𝐶𝐹12𝜌𝜌 𝑉0 − 𝑣 2

where: CF = pressure coefficient that accounts for form and nature of surface • If v = 0 (paddle not moving)

𝐹 = 𝐶𝐹12𝜌𝜌 𝑉0 2

Wind

Paddle

Paddle speed

v

POWER APPLIED TO PADDLE • Power = Force x paddle velocity

𝑃𝑃𝑃𝑃𝑃 = 𝐶𝐹12𝜌𝜌 𝑉0 − 𝑣 2 𝑣

Normalize by upstream wind velocity

𝑃𝑃𝑃𝑃𝑃 = 𝐶𝐹12𝜌𝜌𝑉03

𝑣𝑉𝑜

− 2𝑣𝑉𝑜

2

+𝑣𝑉0

3

MAXIMUM POWER FROM DRAG-TYPE WIND DEVICE

• To find maximum,

𝑑 𝑣𝑉𝑜

− 2 𝑣𝑉𝑜

2+ 𝑣

𝑉0

3

𝑑 𝑣𝑉0

= 0

• maximized when 𝑣 = 𝑉03

,

• when 𝑣 = 𝑉03

, 𝑣𝑉𝑜

− 2 𝑣𝑉𝑜

2+ 𝑣

𝑉0

3= 4/27 = 0.148 (1/4 of Betz limit)

𝑃𝑚𝑚𝑚 𝑑𝑑𝑚𝑑 𝑡𝑡𝑡𝑡 𝑤𝑖𝑖𝑑 𝑑𝑡𝑣𝑖𝑑𝑡 =12𝜌𝜌𝑉03𝐶𝐹

427

PADDLE CONFIGURATION

• Torque = Force x R

𝑇 = 𝐶𝐹12𝜌𝜌𝜌𝑉0

2 1 −𝑣𝑉0

2

R

PADDLE CONFIGURATION

• High starting torque • Common to drag

type devices

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Dim

ensi

onle

ss to

rque

v/V0

DRAG-TYPE WIND ENERGY TECHNOLOGY SUMMARY

• Power = force x paddle or cup velocity

• Max power that can be extracted from the wind

𝑃𝑚𝑚𝑚 𝑑𝑑𝑚𝑑−𝑡𝑡𝑡𝑡 𝑤𝑖𝑖𝑑 𝑑𝑡𝑣𝑖𝑑𝑡 =12𝜌𝜌𝑉03𝐶𝐹

427

• Low performance compared to Betz limit • High starting torque is an advantage

PRACTICE EXERCISES

REFERENCES AND PHOTO CREDITS Reference • Golding, E.W., “The Generation of Electricity by Wind Power,” E.& F. N. Spon Ltd, London,1976 • Torrey, Volta, “Wind-Catchers; American Windmills of Yesterday and Tomorrow,” The Stephen Greene

Press, Brattleboro, Vermont, 1976. Photo credits • "Cup-Anemometer-Animation" by Jan Barani - Own work. Licensed under Creative Commons Attribution-

Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Cup-Anemometer-Animation.gif#mediaviewer/File:Cup-Anemometer-Animation.gif

• "Savonius-rotor en" by Ugo14 - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Savonius-rotor_en.svg#mediaviewer/File:Savonius-rotor_en.svg