-
REACTOR DYNAMICSFrontsSpontaneous Oscillations and Patterns :
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Luss et al (1991)Above: mult. of homogeneous and front solutions in controlled wireBelow: A back-and-forth travelling pulse
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Left: A hot pulse rotating around Ni ring during H2 oxidationRight: A travelling pulse during CO oxidation in a bed (feed from left; Hlavacek et al)
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Spatiotemporal patterns in CO oxidation on Pd/GFC(Sheintuch et al, 2003)
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CO oxidation over a disk (1.4 % CO;Tg= 225; Ts=245-251)
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1 2 3
3
214216220
214217.5228
214.5218.5230.2
213228.7232
215228.8230.2
225.5229.8231
228.5231.5233
230.8232.7234.3
230.5233234.5
233.5235236.8
233.5234.8236.3
230.2232.5234
229.5231.5232.8
224.5225226
218220221
1st frame
after 7 sec
after 28 sec
Relative radial distance
Temperature oC
1
-7214216220
-6214217.5228
-5214.5218.5230.2
-4213228.7232
-3215228.8230.2
-2225.5229.8231
-1228.5231.5233
0230.8232.7234.3
1230.5233234.5
2233.5235236.8
3233.5234.8236.3
4230.2232.5234
5229.5231.5232.8
6224.5225226
7218220221
1
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
1st frame
after 7 sec
after 28 sec
Relative radial distance
Temperature oC
2
3
-
CO oxidation over a ring (35/22 mm,1% CO;Tg= 225; Ts=245- 251 )
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1
0.1150.8
0.1030.75
0.1320.69
0.1760.632
0.2060.647
0.2350.676
0.2790.692
0.3240.706
Lower peak
Upper peak
Exit CO2 concentration, %
1
2150.1150.8
2200.1030.750.4265
2240.1320.690.411
2300.1760.6320.404
2360.2060.6470.4265
2420.2350.6760.4555
2480.2790.6920.4855
2540.3240.7060.515
1
000
000
000
000
000
000
000
Reactor temperature,oC
CO2 concentration, %
2
00
00
00
00
00
00
00
ixtinguished state
ignited state
Exit CO2 concentration, %
3
1
239
232
236
246
252
258
271
Hot spot temperature, oC
1
224239
215232
220236
230246
236252
242258
254271
1
232
236
246
252
258
271
Tignited state, oC
2
3
1
2
3
4
5
7
10
20
Feed gas temperature, oC
Number of secondary oscillations
1
2542
2483
2424
2365
2307
22410
21420
1
2
3
4
5
7
10
20
Fed gas temperature, oC
Number pulses
2
3
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Figure 2: Propagating reaction waves on catalytic surfaces. (A) Temperature wave observed in CO oxidation on the surface of a supported Pd catalyst. The wave arises from coupling of the autocatalytic heat generation to heat conduction. (B) Spirals and target patterns in the isothermal NO reduction on Rh single crystal. The wave is arises from to coupling of the autocatalytic generation of empty
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The Phenomenology of the Belousov-Zhabotinsky Reaction
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Anodic oxidation of Nickel
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Anodic oxidation of aluminum
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Fig. 1Schematic drawing showing the difference between the morphogen gradient model and Turing model. (A) A morphogen molecule produced at one end of an embryo forms a gradient by diffusion. Cells know their position from the concentration of the molecule. The gradient is totally dependent on the prepattern of the morphogen source (boundary condition). (B) Adding a second morphogen produces a relatively complex pattern; but with no interactions between the morphogens, the system is not self-regulating. (C) With addition of the interactions between the morphogens, the system becomes self-regulating and can form a variety of patterns independent of the prepattern. [Art work by S. Miyazawa]
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Fig. 2Schematic drawing showing the mathematical analysis of the RD system and the patterns generated by the simulation. (A) Six stable states toward which the two-factor RD system can converge. (B) Two-dimensional patterns generated by the Turing model. These patterns were made by an identical equation with slightly different parameter values. These simulations were calculated by the software provided as supporting online material. (C) Reproduction of biological patterns created by modified RD mechanisms. With modification, the RD mechanism can generate more complex patterns such as those seen in the real organism. Simulation images are courtesy of H. Meinhardt [sea shell pattern (5)] and A. R. Sandersen [fish pattern (13)]. Photos of actual seashells are from Bishougai-HP (http://shell.kwansei.ac.jp/~shell/). Images of popper fish are courtesy of Massimo Boyer (www.edge-of-reef.com).
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Flow reversal operation Direct heat exchange The bed acts as regenerative heat exchanger Accumulation of the heat generated Simple design and small dimensions High temperatures for low concentrations
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: 15 , : 0.5% -
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Flow rate of 15 l/min and feed concentration of 0.5%Reverse-flow operation
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Maximal temperature vs. Flow rateSimulationExperimental
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Maximal temperature vs. ConcentrationFlow rate of 10 l/min
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Inner-recirculationFlow rate of 5.7 l/min and feed concentration of 0.5%ToTnTn (Exp.)To(Exp.)
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ConclusionsReverse flow and inner recirculation operations exhibit higher temperatures than the once-through operation.No difference was seen between the homogeneous and heterogeneous models.Reverse flow operation is favorable at high flow rates, and inner-recirculation operation at low flow rates.Parameter analysis showed that heat transfer coefficient and bed conductivity affect the most.
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* * * * -. . . , . , . . .