Chemical Engineering June 2018 - 52

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Substrate solution
Radiation source
C1
hv
C2
100%
80%
60%
40%
20%
0%
x
FIGURE 7. This graph of the Lambert-Beer law shows the decrease in radiant power with distance x due
to absorption (c2 > c1)
This pressure is not constant,
it fluctuates substantially around
its mean value due to the velocity
fluctuations of the turbulent flow.
Local velocities may be calculated
by computational fluid dynamics
(CFD), and the corresponding flow
simulation shows their variation in
the vicinity of the tubes (Figure 8).
CFD may also be used to optimize
the impeller arrangement to equalize
the flow around the inserted
wells avoiding stagnant zones.
Additionally, the high energetic
vortices from the turbulence spectrum,
vortex shedding according
to the Karman principle and blade
passing frequencies of the impeller
cause the lamp units to vibrate at its
resonance frequency, if it coincides
with the exciting frequency [13]. The
vortex shedding frequency, f, may be
evaluated from the inflow velocity v,
the tube diameter d and the Strouhal
number Sr [15]:
(11)
The Strouhal number assumes
characteristic values for different
geometric forms, such as cylinders.
The blade passing frequency
fB is calculated from the impeller
speed, n, and the number of impeller
blades, zB:
(12)
The concept used for the fixation
and stabilization of the well's housing
ensures that the natural frequency of
the tubes will be sufficiently higher
than the exciting frequencies. Calculations
by finite element analysis
(FEA) and modal analysis must also
take into account that the fluid-structure
coupling leads to conditions
where the liquid surroundings of the
wells reduce the natural frequencies
to approximately half [13]. The challenge
linked to the construction of
the fixation is threefold:
1. The well holders must be designed
in a way that gaps between holder
and tube are excluded to avoid
space for vibrations.
2. Stress on the mounted quartz or
glass tubes must be excluded,
even if the tubes are not perfectly
straight upon delivery and nozzles
and holders are not perfectly
aligned due to tolerances in the
tank manufacturing process.
3. The support must allow for the
thermal dilatation of the tubes
without stress.
Agitator design
Beside the permanent renewal of the
fluid within the irradiated zones, as
described above, stirring of the reacCHEMICAL
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51
Glass or quartz

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Chemical Engineering June 2018

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