Implementation of the ‘smart’ rotor concept - Wind Power Generation and Wind Turbine Design - page 486

a

− 2ln10 ,

M

a = b =

( 15 )

M M

MM − C

s f M

The shape functions for phase transition are valid on certain stress-dependent
temperature domains which can thus be plotted on the T , s -plane (see Fig. 13).

s

M

C M

C A

A

M

f M s

A s A f T

Figure 13: T , s -phase diagram from the Tanaka model. The arrows indicate in
which direction of the T , s -path the phase change occurs.

Here the graphical representation of the Clausius Clapeyron constant can
also be seen. Tanaka actually defi nes b A and b M in terms of the height of the
transition band:

2ln10
b

Δ= s

( 16)

A

A

s −

2ln10
b

Δ=

( 17)

M

M

This constitutes the same as eqns (14) and (15) because of the defi nition of the
Clausius Clapeyron constants:

Δ s

A

C =

( 18)

A

AA −

f s

Δ s

M

C =

( 19)

M

MM −

s f

Liang and Rogers propose a similar model, but with a cosine-shaped dependency
of x on T and s .
For

CTM ( −− ) ( p / | b |) ≤≤ s CTM ( − ) :

M f M M f

1 − x 1 + x

(20)

A A

x = cos( aTM ( − ) + b s ) +

M f M

2 2

for the AM transition. For the MA transition the following holds.