Single streamtube model for Darrieus rotor
The single streamtube model is very different from the multiple streamtube
model in term of the calculation method (or equations) and the velocity
field. The multiple streamtube assumed a very simple one-direction velocity
field (i.e. velocity varies in 2 axis) in the rotor but the single streamtube
model is even simpler as the velocity field is replaced by only a single
velocity value. Weird enough, the resulting power coefficient curve does
not seems to differ too much except that single streamtube seem to over
predict slightly.
In single streamtube model, the flow through the rotor is modeled using
one single streamtube only as its name imply. The streamtube cross-section
area (swept area) remains constant and follows a straight path just like
the multiple streamtubes model. The wind speed decrease from upstream
velocity, U to velocity at rotor, U’ and finally settle down at
far downstream velocity. The velocity remains constant like previous model
when moving though the circular blade path.
The only streamtube experiences aerodynamics forces all the time as
opposed to pulses of forces in multiple streamtube. The variation of aerodynamic
forces are large in the whole revolution from 0 to 360 degree, so the
single tube model has to sum up all the forces at various position to
average the value off before equating it to the wind momentum loss rate.
Similarly, the induction factor for single streamtube model also has
to be solved numerically by root finding algorithm but for one single
value only. However, to find the first thrust coefficient (derived from
aerodynamic force), the value of the normalized velocity, angle of attack,
lift, drag, normal, and tangent coefficient for a set of predetermined
blade position (theta) which cover the whole revolution have to be obtained
first before the summation and averaging is carried using the above equation.
So, even though only one value of induction factor is needed, the number
of loop seems to remain at 2 roughly. Once the induction factor for the
single streamtube is found, the torque and power coefficients can be calculated
using the same previous set of equations.
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