Transcript Mathematical model EXCEL SHEET
Acknowledgement: Research is subsidized by International Atomic Energy Agency in Vienna (No.: 11557 and by Ministry of Education of Czech Rep. No. J04/98: 212200008
J.Thýn, M. Nový, P. Houdek, G. Borroto Portela
*)
and R.Žitný Department of Process Engineering CTU in Prague, Faculty of Mechanical Engineering,
*)
ISCTN Avenida Salvador Allende, La Habana, Cuba
E-mail: [email protected]
1. CASE STUDY - CONTINUOUS OHMIC HEATER
Direct ohmic heater with three parallel channels: Reynolds number in central channel 1300, in lateral channel 1600, inlet/outlet pipes 3000.
2. EXPERIMENTS
Radiotracer Tc 99m was injected into inlet pipe.
detected by Local responses were collimated scintillation detectors D1, D2, D3 and D4 (see Fig).
RTD (residence time distribution) of the heater was determined by stimulus response method using the conductivity probes C1 and C2 measuring KCl concentration at inlet and outlet:
3. CFD MODEL and RESPONSE EVALUATION
CFD model (Fluent 5.2, laminar, k , RNG and low Reynolds flow models) predicts distribution of tracer
c
(
t,x,y,z
) in time
t
. While the RTD is given directly by Fluent, the theoretical responses of detectors D1,2,3 and 4 must be calculated according to :
J
(
t
)
e
e c
(
t
,
x
,
y
,
z
)
D
(
x
,
y
,
z
)
d
where
D
(
x,y,z
) is the response of collimated detector to the unite activity situated in
x,y,z
(PSR-Point Source Response). The function
D
(
x,y,z
) can be evaluated theoretically (using view factor/ Monte Carlo method) or by interpolation of values
D
(
x
k
,y
k
,z
k
) determined experimentally (the locations
x
k
,y
k
,z
k
of unit activity tracer have nothing to do with position of CFD nodes) :
D
(
x
,
y
,
z
)
k n
1
D
(
x k
,
l k m y k
1
k n
1
l k m
,
z k
)
l
k
is distance between (
x,y,z
) and (
x
k
,y
k
,z
k
) points.
PSR experiment
4. COMPARISON of EXPERIMENT WITH CFD PREDICTION
0.04
0.09
0.08
0.07
0.06
0.05
0.04
1
0.03
0.02
0.03
0.01
0.02
3
0.01
2
0.00
0.00
0 10 20 30 40
t [ s ]
50 60 70 80 0 20 Local responses of collimated detectors: Experimental response (1), RNG k
2 1 3
40 60 80
t [ s ]
model (2) and laminar flow (3) 0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0 10 20
2
30
3
40
t [ s ]
50
1
60 70 80 Comparison of RTD: CFD prediction and conductivity method CFD Models Lam flow (LD) Lam flow (HD) Low Re flow (HD) Experiment Flow [ ml/s ] 80 79.3
Time step [ s ] 1 0.25
1 0.25
0.25
0.5
T mean
[ s ] 50.74
49.91
49.42
49.8
49.72
49.87
2 [ 1 ] 0.04
0.04
0.088
0.07
0.03
0.09
Y i
Y
exp [ 1/s ] 0.0028
0.0021
0.0012
0.0008
0.0038
/
n where LD - Low density ( 178 932 nodes, 160 560 elements ) HD - High density (834 432 nodes, 790 400 elements )
100
5. CONCLUSIONS:
• New method of CFD postprocessing enables prediction of collimated detector responses to a gamma radiation tracer distribution.
• A case study predicts only small difference between the laminar and turbulent flow model with small advantage for
RNG k-
. An effect of real injection, inaccuracy of collimation algorithms as well as effects of operational parameter ambiguities are to be analysed in future.