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Acknowledgement: Research is subsidized by
J04/98: 212200008
R.Žitný,
J.Thýn
Department of Process Engineering CTU in Prague, Faculty of Mechanical Engineering E-mail: [email protected]
Theoretical prediction:
Problem: Nonuniform
distribution of flow into parallel
channels of heaters or heat
exchangers in the case of
buoyancy opposing flow.
Q
Case
Criterion of stability
Constant
temperature
of wall Te
gH B0
Z  ( Te  T0 )
12 fQ
3
Te
L
H
Volumetric
heat source
in central
channelL
gGH c B H L
2
ZG 
G
3
12 fc p Q
2
a-heat transfer coefficient, cp-heat capacity, H
x B -cross section of channel
1
ZG 
W
( 2  W )[1  (1  e  2 / W )]  1
2
G [W/m3]-volumetric heat source
f=1 in a wide channel
H
1
ZH 
2
gGB H L
ZH 
2
12 fc p Q
2
Volumetric
heat source
G
in lateral
channelsL
(insulated wall)
-flowrate
Z can be expressed in terms of Grashof and
Reynolds numbers as Z=Gr/Re
Stability limits of symmetric
flow
1
Z
W  (W  2)e  2 /W
Q0c p
W
aBL
G
4
H
(buoyancy opposite flow of cold
liquid in lateral channels)
Experimental verification
P
1
(buoyancy assisted flow in the
central channel-direct ohmic
heating)
umin/umax
-power
Coloured tracer (KMnOu 4
velocities in parallel channels)
min
0.5
umax
Predicted
symmetry
Predicted
instability
0
-15
5 ZG-ZGcrit
-5
L
1
Mean residence time
(conductivity method KCl)
0.9
V/Vtheor
-25
Active volume
is reduced if a
channel is
blocked
0.8
0.7
-25
H
Warm liquid (Te) stands in the right
channel if ZG>ZGcrit, see Table.
-15
-5
5 Z -Z
G
Gcrit
Temperatures in lateral channels
measured by Nortech Reflex 4
(optical fibres)
PT21
PT21
Conclusions:
Buoyancy has undesirable effects in heaters with downwards oriented parallel flows (nonuniform distribution of flow), which can be suppressed by decreasing the width of channel H
(this is the most efficient way), or by increasing viscosity . This theoretical prediction was
tested experimentally using tracer techniques (solution of KCl and KMnO4 ) and by
measurement of temperature profiles.
Thýn, J., Žitný, R., Klusoň, J., Čechák,T.,Analysis and Diagnostics of Industrial Processes by Radiotracers
and Radioisotope Sealed Sources, Ed. ČVUT, Prague (1999)
Žitný,R., Thýn, J.,Parallel flow asymmetries in continuous heaters, CVUT Workshop 2001, Praha,
Joye D.D., Wojnovich M.J.: Aiding and opposing mixed convection heat transfer in a vertical tube: loss of
boundary condition at different Grashof numbers, Int.J.Heat and Fluid Flow, Vol.17, No.5, 1996, 468-473