Solar Thermal Power Plants - Renewable Energy: Technology, Economics and Environment - page 213

Determination of the main parameters of the tower efficiency η Tower , by con-
trast, is much more complex. For this purpose it is assumed that the tower con-
verts the heat energy supplied by the collector into kinetic energy (convection
flow) and into potential energy (pressure drop at the turbine). The difference be-
tween the air density inside the tower ρ Air,Tower and the ambient air ρ Air,amb acts as
the driving force. The lighter air column of warm air inside a tower of a height h T
is connected to the neighbouring atmosphere at the tower bottom (collector exit
and thus tower entry) and consequently gets buoyancy. There is thus a pressure
difference ∆ p between the tower bottom and the environment which is described
by Equation (5.8); the pressure difference increases proportionally with tower
height. g stands for acceleration of gravity.

h

T
∫

∆ p = g ( ρ − ρ ) dh

(5.8)

Air , amb Air , Tower T

0

The pressure difference ∆ p consists of a static ∆ p s and a dynamic ∆ p d compo-
nent. The static portion of the pressure difference drops at the turbine whereas the
dynamic component describes the kinetic energy of the flow. The distribution of
the pressure difference depends on the amount of energy which the turbine with-
draws from the flow.
The power contained in the flow P Flow can be described according to Equation
(5.9) by the pressure difference ∆ p , calculated according to Equation (5.8), the
flow speed of the air inside the tower v Air and the tower diameter d T .

P = ∆ p ⋅ v ⋅ d (5.9)

Flow Air T

On this basis, the tower efficiency η Tower is calculated as the ratio of the power
contained in the flow P Flow (Equation (5.9)) and the power supplied by the collec-

tor P Abs , which is calculated by the solar energy supplied to the plant G . g,abs , re-
duced by the collector efficiency η Coll (Equation (5.10)).

P P
PG

η =

Flow

=

Flow

(5.10)

&

Tower

⋅ η

Abs g ,abs Coll

Inside the collector the flowing air is warmed up by a certain temperature ∆ θ Air

in dependence of the mass flow m . Air and the specific heat capacity of the air c p,Air .
On this basis, the thermal power output of the collector P Abs can be calculated
according to Equation (5.11).

&

P = m c ∆ θ

(5.11)

Abs Air p , Air Air