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Production of hydrogen and carbon by solar thermal methane splitting. IV. Preliminary simulation of a confined tornado flow configuration by computational fluid dynamics
International Journal of Hydrogen Energy 32 (2007) 4800 – 4810 www.elsevier.com/locate/ijhydene
Production of hydrogen and carbon by solar thermal methane splitting. IV. Preliminary simulation of a confined tornado flow configuration by computational fluid dynamics A. Kogan a,b,∗ , M. Israeli c , E. Alcobi d a Department of Aerospace Engineering, Technion-IIT, Israel b Solar Research Facilities Unit, Weizmann Institute of Science, Israel c Department of Computer Science, Technion-IIT, Israel d Department of Electrical Engineering, Technion-IIT, Israel
Received 9 January 2006; received in revised form 21 June 2007; accepted 11 August 2007
Abstract The confined tornado flow configuration has been developed at the Solar Research Facilities Unit, Weizmann Institute of Science, as a means for protection of the window of a solar reactor from contact with incandescent solid particles in gas suspension in the reactor cavity. The results of a computational fluid dynamics (CFD) simulation of a tornado flow confined in a simplified reaction chamber are compared in this paper with information about such a flow obtained by gas dynamics experimentation. All the information obtained by experiment was corroborated by CFD. Moreover, the CFD simulation brought to view some important unexpected features of the confined tornado flow, which are discussed in detail. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Hydrogen production; Thermal methane splitting; Confined tornado flow
1. Introduction In the development of a solar reactor based on direct gas heating by seeding the volume of the reaction chamber with carbon powder, we were guided by our previous experience with flow of solid–gas suspensions, by theoretical and experimental information on prevention of fluid flow detachment and by intuition. In this way we succeeded to conceive the tornado flow configuration, which enables protection of the reactor window surface from contact with incandescent solid particles suspended in the flow [1]. The characteristics of the tornado flow configuration were observed in the course of laboratory experiments performed at room temperature and at elevated temperatures. On these occasions we noted the existence of a secondary flow effect by ∗ Corresponding author at: Solar Research Facilities Unit, Weizmann Institute of Sciences, Israel. Tel.: +972 8 934 3782; fax: +972 8 934 4117. E-mail address: [email protected] (A. Kogan).
which small amounts of floating solid particles are carried toward the reactor window. Some intuitive solutions were tried to counteract the suspected cause of the stray particles migration, with various degrees of success [2,3]. At this point we came to the decision to engage in a detailed computational fluid dynamics (CFD) simulation of the tornado flow pattern in the solar reactor under development at our laboratory. We solicited the cooperation of Prof. Moshe Israeli from the Department of Computer Sciences, Technion-IIT in this work. The present report describes results of a preliminary CFD simulation of a tornado flow performed in a reaction chamber of a simplified geometry. The purpose of this preliminary exercise was to get acquainted with the capabilities of the FLUENT CFD code currently in use at the Technion. At this stage we were interested in particular to learn whether there exists at least a qualitative agreement between certain results of practical significance that were arrived at by CFD and the corresponding phenomena observed during our experiments. All the information gained by experiment were confirmed by CFD
0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.08.016
A. Kogan et al. / International Journal of Hydrogen Energy 32 (2007) 4800 – 4810
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simulation. Moreover, some important unexpected features of the confined tornado flow became evident by CFD simulation. These features are discussed below. 2. An abbreviated description of the tornado flow pattern A detailed description of the tornado flow pattern, which enables effective screening of the reactor window from incandescent solid particles, may be found elsewhere [1]. The following brief explanation of the phenomenon is given here for ease of reference. When a fluid flows along a solid stationary boundary, its motion is retarded within a thin boundary layer by friction. The retarded fluid boundary layer may thicken progressively in the direction of flow and ultimately it may detach from the solid boundary and mix with the main flow. Boundary layer detachment can be averted if care is taken to maintain a uniformly decreasing pressure in the direction of flow. The accelerated main flow then entrains the fluid in the boundary layer strongly enough to counteract the flow retardation caused by friction with the stationary boundary. Turning to our particular application, the axisymmetric chamber of the solar reactor illustrated in Fig. 1 is provided with a transparent window located at one end of the chamber, transversally to the longitudinal axis. The main gas flow F1 is introduced into the chamber in a manner whirling around the axis, while the reaction products are withdrawn at the opposite end of the chamber through a narrow central tube oriented along the longitudinal axis. The gas flow inside the chamber then approximates a free vortex flow, characterized by a drop of pressure from the periphery of the chamber to its axis. A secondary flow F2 of protecting gas introduced at the periphery of the window is directed toward the window central area. It is accelerated by the negative pressure gradient generated by the free vortex flow. The secondary gas boundary layer flow at the window surface is thereby stabilized and it remains attached to the surface all the way to the center of the window. The radially converging streamlines then turn into the axial direction, forming a typical tornado-like funnel along the reactor axis. Synergy between the free vortex flow of the main gas and the boundary layer flow of the secondary gas is here exploited in order to protect effectively the reactor window. The synergy is expressed by the fact that the secondary flow, which is desired to form a stable, continuous and non-separated protective layer on the window surface, is not disturbed by the whirling main stream. It is rather stabilized by it. Consequently, the secondary flow does not need to be injected with high velocity or with a great flow rate in order to adhere to the surface to be protected, because it uses the energy of the whirling mainstream against which protection is sought. The tornado effect has been demonstrated in a series of simulation tests at room temperature with the reactor model shown in Fig. 1. The main gas stream was flown from an annular plenum chamber through a narrow annular gap toward the upper part of the reaction chamber. An impeller-like ring was implanted in the annular gap. The main gas stream acquired an angular
Fig. 1. Cross-section of reactor M2a.
momentum during its passage through slanted grooves in the impeller ring and it entered the reactor cavity in a whirling motion. The secondary gas stream was flown radially from a second annular plenum chamber through a second narrow annular gap toward the periphery of the inner surface of the window. Both streams consisted of nitrogen gas. The secondary stream was made visible by charging it with smoke, while the gas in the mainstream was left in its natural transparent condition. In order to enable visual inspection of a cross-section of the flow inside the reaction chamber, a laser beam directed toward the reactor window was diffracted by passage through a transverse cylindrical glass rod. The monochromatic laser beam emerged from the glass rod as a planar sheet of light that illuminated a cross-section of flow inside the reaction chamber. The four tornado configuration tests illustrated in Fig. 2 were performed with a secondary smoke-charged gas maintained at a constant flow rate of 1 L/min. With a whirling main gas stream at a flow rate of 3 L/min (Fig. 2a), the secondary flow separated from the window surface immediately upon its entry into the reaction chamber. When the whirling main stream was introduced into the reaction chamber at successively higher flow rates (Fig. 2b–d), the secondary stream became progressively stabilized as a thin boundary layer. For a main gas flow rate of 20 L/min, the secondary gas moved at high speed in the thin boundary layer near the window surface. It covered the entire window surface area and it left finally the reaction chamber through a narrow axially oriented funnel. 3. Degeneration of the tornado flow configuration when F1 is increased beyond a certain transition value By increasing the flow rate F1 of the main gas stream without changing the other test parameters, the test Ekman
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Fig. 2. Consecutive stages in the evolution of a “tornado” flow pattern in a reaction chamber. (a) Main flow — 0 L/M; (b) Tangential Main flow — 5 L/M; (c) Tangential Main flow — 10 L/M; (d) Tangential Main flow 2 L/M.
number [4] E= (1) L2 is diminished. Is there a limit to the permissible increase of F1 , beyond which the tornado flow pattern will break down? In order to answer this question we performed a prolongated smoke visualization tornado flow configuration test at room temperature similar to the test described above. The reactor illustrated in Fig. 3 served us in this test. The streams F1 and F2 consisted likewise of nitrogen. The smoke-charged stream F2 was maintained at a low constant value throughout the test duration, F2 = 2 L/min. The mainstream, F1 , was varied over a wide range. At low F1 flow rates the flow pattern in the reaction chamber resembled that of a regular tornado flow pattern. By increasing F1 a point of transition was reached, when the flow pattern became unstable, flipping at random between the regular tornado flow pattern and a degenerate pattern, as illustrated in Fig. 4. When F1 was increased beyond the transition point, the flow pattern in the reaction chamber stabilized in the diffuse flow configuration, illustrated in Fig. 5, which suggests a transition or a turbulent flow pattern. Fig. 3. Cross-section of reactor D1 .
4. Exploratory tornado flow configuration tests with powder seeding into the reaction chamber. The existence of a weak torroidal flow perturbation was postulated in order to explain a slight powder deposition on the window surface Some exploratory tornado flow configuration tests with powder seeding were performed at room temperature in order to
gain experimental information about the paths followed by solid particles entrained by the gas flow. During these tests neither one of the two gas streams entering the reaction chamber were stained by smoke, but the main gas stream was charged with a small amount of carbon black (CB) powder before its entry into the reactor [3].
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Fig. 4. Smoke flow visualization of an unstable tornado flow configuration.
Fig. 6 is a picture of the reactor window taken at the end of one such test. It shows two concentric rings of powder sediment. The outside diameter of the diffuse outer ring equals the diameter of the circle along which the powder is admitted into the reactor cavity (6 cm). The more concentrated inner powder ring is confined between two concentric circles with diameters of about 2.5 and 0.5 cm, respectively. The test was repeated with the inner surface of the window wetted by a thin layer of lubrication oil. At the end of the test, a narrow, high-density powder ring was observed at the periphery of the window and a circular spot of CB of about 0.3 cm in diameter was spread around the window center, with vestiges of streak lines connecting the outer ring to the central spot (Fig. 7). By the time the picture shown in Fig. 7 was taken, about 30 min after the end of the test, the central spot of CB-stained oil spread over the area of a circle about 1.3 cm in diameter. Figs. 6 and 7 suggest a flow of CB particles entrained by an upwelling stream of gas along the periphery of the reactor cavity. Upon reaching the top of the cavity, the gas stream turned apparently abruptly from the axial into the radial direction,
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Fig. 5. Smoke flow visualization of a degenerated tornado flow configuration.
shedding CB particles onto the window surface by centrifugal force. Solid particles coming into close proximity to the window surface may also have been attracted to it by electrostatic force. Some of the particles formed the outer black ring, while most of them were swept by the accelerated gas stream along the lubricated window surface toward the center of the window. The following mechanism was suggested as a plausible explanation of the observed powder flow behavior. The ascending gas current along the reactor cavity wall is part of a weak flow perturbation generated by friction between the energetic gas stream in the tornado funnel and the gas surrounding it. The fast axial flow of gas in the tornado funnel entrains by friction the relatively quiescent gas around it. Fig. 8 is an intuitive picture of the streamlines in the perturbed quiescent region. These are helical streamlines wrapped around torroidal surfaces. This flow perturbation is, of course, a very weak effect that could be neglected, were it not for the presence of the very fine powder particles that may be entrained by the postulated torroidal flow toward the reactor window. At close proximity to the entraining jet, solid particles suspended in the perturbed gas are expected to move downwards, concurrent with the entraining funnel jet.
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reactor illustrated in Fig. 1, which was heated by concentrated solar radiation up to 1320 ◦ C. The main gas stream consisted of methane and the secondary stream was helium. With increasing test temperature, the slight powder deposition on the window surface diminished. No powder deposition could be discerned at all when the reactor inner wall temperature came close to 1000 ◦ C [2]. We note that by increasing the temperature from ambient to above 1000 ◦ C the gas kinematic viscosity goes up by an order of magnitude, with a corresponding increase in Ekman number. It appears reasonable to assume that during the initial low temperature tests in this test series the flow in the reaction chamber was turbulent and with increasing test temperature the Ekman number increased beyond the critical value and the flow in the reaction chamber became laminar. 6. Some results of a CFD simulation of a tornado flow configuration maintained in a reaction chamber of a simplified geometry
Fig. 6. Reactor window stained by powder deposition after a 10-min seeding tornado flow test.
Fig. 7. CB deposit on reactor window at the end of a test similar to the one illustrated in Fig. 6, when the window surface was wetted by lubrication oil, before start of test.
Upon approaching the reactor cavity bottom, they diverge toward the periphery, turning in sequence upwards toward the reactor window, then inwards along the window. 5. Cessation of powder deposition on reactor window at elevated temperatures The above described room temperature tests with powder seeding were followed by a series of tests with the unseeded
The postulation of the existence of a weak torroidal flow perturbation in order to explain the observed slight powder deposition on the window surface during the room temperature tests was based on scanty experimental evidence. During the above mentioned exploratory tornado flow configuration tests with powder seeding we were unable to follow the paths of single particles. By observation of the powder deposition pattern in Figs. 6 and 7, one can conclude with confidence that some powder particles in gas suspension were entrained toward the window surface, that some of them settled on the surface and that some others were entrained by the surface boundary layer flow within a stretch between the center of the window and its periphery. In order to obtain a more detailed description of the tornado flow configuration, we decided to back up our experimental work by CFD simulation. In the preliminary CFD simulation study described below, the simplified cylinder–frustum geometry illustrated in Fig. 9 was chosen for the outline of the reaction chamber. The main gas is introduced into the reactor cavity through the annular entrance of width w1 as an axi-symmetric whirling stream at a flowrate F1 . The secondary gas stream F2 is introduced into the cavity radially through the annular entrance of width w2 . Both streams are simulated by air. The air viscosity and density are functions of temperature. The kinematic viscosity of air increases significantly with temperature (Fig. 10). Figs. 11–13 illustrate contours of stream function and of swirl velocity of air flow in the reactor cavity of Fig. 9, as calculated by FLUENT CFD simulation code for a case of high viscosity, corresponding to T = 1200 ◦ C. The stream function contours shown in Fig. 11 were attained for a tornado flow configuration established by introducing a main stream of air tangentially into the reaction chamber at a flowrate F1 = 10 L/min through the main annular entrance of width w1 = 2 mm and a secondary stream of air F2 = 0.5 L/min through the secondary annular entrance of width w2 = 0.2 mm, the air leaving the reaction
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Fig. 8. Schematic representation of torroidal flow perturbation induced by friction between the gas moving at high speed in the tornado funnel and the surrounding gas.
chamber through the exit section at the bottom of the chamber. These contours were attained at time 1075 s after start of flow. Fig. 12 is an enlarged picture of the air entry region in Fig. 11. Fig. 13 shows contours of swirl velocity (m/s) of the flow. At short distance from the entrance annuli the stream divides into two distinct streams. The seven streamlines marked by A in Fig. 11 flow roughly radially, toward the reactor axis of symmetry, then they make sharp turns of almost 90◦ , forming a funnel-like jet of air. Yet the major part of the entering air stream represented by the 41 streamlines marked by B proceed toward the axis of symmetry along a distance less than a third of the cylinder radius before making a sharp U-turn toward the wall of the cylinder. A concentrated annular vortex E located just below air entrance w1 is powered by friction with the sharply curved stream. After completion of the U-turn, the 34 outer streamlines marked by C flow down the cylinder and frustum walls toward the chamber exit section. The remaining 7 inner streamlines marked by D diverge one by one from the bulk of 34 streamlines, trying to ascend toward the top of the chamber. But they do not quite make it all the way to the top. The first of this set of streamlines reaches up to a distance G from the top. They all turn downwards toward the exit section after reaching their maxima. An oblong widespread annular vortex marked F is formed in the fold of this streamline and is powered by friction with it.
Fig. 14 illustrates stream function contours for a tornado air flow configuration in the simplified reactor of Fig. 9 for an intermediate air temperature. It exhibits all the features of Fig. 11. We notice that the shortest distance G reached by an upwelling streamline in Fig. 14 is less than half the value of G in Fig. 11. Figs. 15–17 illustrate stream function and swirl velocity contours for a tornado air flow configuration in the same reactor when the air is at room temperature. They suggest the existence of a transition or turbulent flow. It is interesting to notice the row of annular vortices generated by friction with the abundant stream of air flowing down along the cylindrical boundary of the reaction chamber. Most of these peripheral streamlines turn successively along the frustum boundary layer upwards, some of them reaching the top of the chamber, where they join the attached boundary layer flow. 7. Interpretation of the CFD simulation results in light of the facts established by experiment The ability to prevent separation of the boundary layer flow from the reactor window surface by maintaining a tornado flow configuration in the reaction chamber is corroborated by the CFD simulation. The extreme set of stream function lines marked by A in Fig. 11, e.g., do not detach from the window surface, in accord with our experimental evidence.
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Fig. 9. The cylinder–frustum geometry of a simplified combustion chamber.
The existence of a minimum gas kinematic viscosity (or temperature) for a given reactor geometry and flow parameters, beyond which the tornado flow pattern breaks down is also predicted by the CFD simulation, as may be seen by comparing the flow patterns in Figs. 10 and 15. The simulated low viscosity flow illustrated in Fig. 15 exhibits a set of nine streamlines marked by D which follow a path reminiscent of the flow path of the corresponding set of streamlines D in the high viscosity flow diagram of Fig. 11. They start their journey inside the reaction chamber by flowing down along the cylindrical boundary of the chamber as part of the set of streamlines B. Upon reaching the vicinity of frustum boundary at the bottom of the chamber, they diverge one by one from the mainstream, turning upwards, toward the reactor window. The subset of four streamlines marked by D in Fig. 15 reach a maximum before touching the window surface. They make a final turn downwards to the exit port. Yet unlike in the case of the high viscosity flow of Fig. 11, the remaining set of five streamlines marked by D in Fig. 15 reach all the way to the window surface, where they join the set of streamlines A along that surface. The gas flowing along streamlines in subset D in Fig. 15 is capable of entraining powder particles and of shedding them on that surface. The experimental observation of formation of a slight deposit of solid particles on the reactor window when a powder suspension in a low viscosity fluid is flowing inside the reaction chamber in a tornado flow configuration (a low Ekman number flow) and the absence of formation of such a powder deposit during a similar flow of a powder suspension in a high viscosity gas (a high Ekman number flow) seems thus to be in accord with results obtained by CFD simulation.
Fig. 10. Kinematic viscosity of air vs. temperature.
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Fig. 11. Contours of stream function (kg/s) (time = 1.0750e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at 1200◦ C.
Fig. 12. An enlarged picture of the region of air entry in Fig. 11.
Fig. 13. Contours of swirl velocity (m/s) (time = 1.0750e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady).
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Fig. 14. Contours of stream function (kg/s) (time = 2.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at 600◦ C.
Fig. 15. Contours of stream function (kg/s) (time = 1.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at room temperature.
Fig. 16. An enlarged picture of the region of air entry in Fig. 15.
A. Kogan et al. / International Journal of Hydrogen Energy 32 (2007) 4800 – 4810
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Fig. 17. Contours of swirl velocity (m/s) (time = 1.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady).
8. Revision of the postulation of a torroidal flow perturbation in view of the contours of tornado flow stream function obtained by CFD simulation In a free vortex flow, the tangential velocity u and the pressure p are given by u = c1 /r
(2)
and p = p0 − c2 /r 2 ,
(3)
where r is the distance from the vortex axis of symmetry, p0 is the total pressure, c1 is a constant and c2 is a positive constant. A free vortex can persist in steady state when the centrifugal force generated by the rotation of fluid is counter-balanced by the centripetal force caused by the increase of pressure with the distance r. When a vortex flow takes place within a finite volume confined by stationary solid boundaries, the fluid friction within the boundary layer may perturb considerably the vortex flow pattern. By way of example, the centrifugal force acting on the fluid in vortex flow is sharply reduced within the boundary layer along a plane boundary normal to the axis of rotation, such as the surface of the reactor window. The centripetal force within the boundary layer is then left unbalanced and the fluid on the periphery of that boundary is accelerated toward the axis of rotation. This is the effect that we have exploited in order to obtain a natural gas dynamic windscreen to protect the reactor window from contact with solid particles floating in the gas. Upon approaching the axis of rotation, the converging streamlines turn sharply into the axial direction, forming a typical tornado funnel. We have assumed intuitively that friction between the fast funnel jet and the surrounding relatively quiescent fluid generates a torroidal flow perturbation as shown in Fig. 8, which could be the agent by which some powder particles are carried toward the window surface and are deposited on it.
The contours of streamlines in Fig. 11 obtained by CFD simulation differ considerably from those sketched in Fig. 8. They do not corroborate the postulation of the existence of a torroidal flow perturbation in a vortex flow confined by solid stationary walls. After careful examination of the confined vortex flow patterns obtained by CFD simulation, we came to realize that the assumption that the perturbed flow pattern of the confined vortex in the simplified reaction chamber of Fig. 9 is not determined solely by the interaction between the rotating fluid and the boundary layer flow adjacent to the chamber ceiling, which is perpendicular to the axis of rotation. In fact, the centrifugal force acting on the fluid within the boundary layer along the surface of the frustum shaped wall is also sharply reduced and the fluid inside this boundary layer is also accelerated toward the chamber exit port by the unbalanced centripetal force. Two natural routes are thus available for delivery of the rotating fluid confined within the reaction chamber of Fig. 9 from the two annular entrance ports at the top of the chamber to the exit port at the bottom. The flow patterns in Figs. 11 and 15 that were obtained by CFD simulation indicate that both routes are exploited by nature. The fluid stream entering the reaction chamber splits shortly after entry into two unequal streams. A scarce stream A follows the first route described above, forming the gas dynamic windshield at the chamber ceiling and the tornado funnel, while the abundant stream B takes the second, peripheral route to the chamber exit. The behavior of a slightly viscous swirling flow entering an axisymmetric chamber at a large (outer) radius and exiting at a smaller (inner) radius near the axis can be interpreted with the help of the theory of rotating flows at very small Ekman numbers, see [4]. In such flows, the radial flow of the fluid is inhibited by the strong Coriolis force generated by the vortex which is further amplified as the swirling flow approaches the axis conserving its angular momentum. This effect is observed also in “industrial cyclones” and “rotation valves” where a huge
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pressure difference must be supplied to drive the flow as described. In a cylinder symmetrical with respect to its center plane, the vortex generates two horizontal boundary layers, called Ekman Layers (E.L.). A radial mass flux can be sustained in these thin layers. It is proportional to the difference in angular velocity between the swirling interior and the horizontal stationary top and bottom plates, and also to the square root of the Ekman number. In such a configuration, the top and bottom radial flux must be exactly the same. In a non-symmetric chamber like the cylinder–frustum combination, the radial mass flux in the frustum (inclined) E.L. is allowed to be larger (as the Ekman number depends on the slope). However, if too much flux is directed to the bottom initially, an appropriate fraction of this flux must return to the top (horizontal) plate E.L. before it can proceed to the axis (as can be seen for example in Figs. 11 and 15). It is interesting to observe that both in the case of the laminar flow (Fig. 11) and of the turbulent (or transition) flow (Fig. 15) some of the streamlines that started on the second route separate at some point from their original mainstream B, trying to ascend along isobars toward the chamber ceiling. Yet almost all of these stray streamlines make a U-turn before reaching the ceiling and they rejoin their original mainstream B. These streamlines will not contaminate the reactor window with any solid particles that they may carry in suspension. Only in the case of transition or turbulent flow (Fig. 15), a part of the stray streamlines does succeed to reach the chamber ceiling. They join the set of streamlines A that followed the first route. These particular streamlines carry the danger of deposition of entrained powder on the surface of the reactor window. 9. Conclusion The above described comparison of certain characteristics of a confined tornado flow, that were observed previously during laboratory tests, with corresponding characteristics of such flows obtained by CFD simulation is of a preliminary nature. For the sake of simplicity, a rudimentary geometry was chosen for the outline of the reaction chamber used in the CFD calculation. This geometry was different from the geometries of
the reaction chamber models used in the laboratory tests. The comparison of our previous experimental results with predictions derived from the described CFD work is therefore only of a qualitative nature. Yet despite this limitation, we were able to identify by CFD simulation certain basic characteristics of the confined tornado flow that were observed in the laboratory. Moreover, the CFD simulation helped us to clarify some intricate features of the flow under study that were previously obscure. CFD simulation can thus certainly become an important auxiliary tool in the development of an effective solar reactor that exploits the confined tornado flow configuration. To this end we will have to choose a reaction chamber model with a standard geometry. Some of CFD simulation and laboratory test work will be performed with the standard reaction chamber model under strict similarity conditions. A quantitative comparison will then be made between the CFD simulation predictions and the test results. If small systematic discrepancies will be found between the two results, the data will be reconciled by the introduction of calibration factors. CFD simulation will then become an important aid in our R&D work. Acknowledgments This study was supported by the Heineman Foundation for Research, Education, Charitable and Scientific Purposes and the Rose Family Foundation, NY, USA. The authors gratefully acknowledge the steadfast support of these foundations. References [1] Kogan A, Kogan M. The tornado flow configuration—an effective method for screening of a solar reactor window. J Solar Energy Eng 2002;124:206 –14. [2] Kogan M, Kogan A. Production of hydrogen and carbon by solar thermal methane splitting. I. The unseeded reactor. Int J Hydrogen Energy 2003;28:1187–98. [3] Kogan A, Kogan M, Barak S. Production of hydrogen and carbon by solar thermal methane splitting. II. Room temperature simulation tests of seeded solar reactor. Int J Hydrogen Energy 2003;29:1227–36. [4] Greenspan HP. Theory of rotating fluids. Cambridge: Cambridge University Press; 1968 p. 3.
Production of hydrogen and carbon by solar thermal methane splitting. IV. Preliminary simulation of a confined tornado flow configuration by computational fluid dynamics A. Kogan a,b,∗ , M. Israeli c , E. Alcobi d a Department of Aerospace Engineering, Technion-IIT, Israel b Solar Research Facilities Unit, Weizmann Institute of Science, Israel c Department of Computer Science, Technion-IIT, Israel d Department of Electrical Engineering, Technion-IIT, Israel
Received 9 January 2006; received in revised form 21 June 2007; accepted 11 August 2007
Abstract The confined tornado flow configuration has been developed at the Solar Research Facilities Unit, Weizmann Institute of Science, as a means for protection of the window of a solar reactor from contact with incandescent solid particles in gas suspension in the reactor cavity. The results of a computational fluid dynamics (CFD) simulation of a tornado flow confined in a simplified reaction chamber are compared in this paper with information about such a flow obtained by gas dynamics experimentation. All the information obtained by experiment was corroborated by CFD. Moreover, the CFD simulation brought to view some important unexpected features of the confined tornado flow, which are discussed in detail. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Hydrogen production; Thermal methane splitting; Confined tornado flow
1. Introduction In the development of a solar reactor based on direct gas heating by seeding the volume of the reaction chamber with carbon powder, we were guided by our previous experience with flow of solid–gas suspensions, by theoretical and experimental information on prevention of fluid flow detachment and by intuition. In this way we succeeded to conceive the tornado flow configuration, which enables protection of the reactor window surface from contact with incandescent solid particles suspended in the flow [1]. The characteristics of the tornado flow configuration were observed in the course of laboratory experiments performed at room temperature and at elevated temperatures. On these occasions we noted the existence of a secondary flow effect by ∗ Corresponding author at: Solar Research Facilities Unit, Weizmann Institute of Sciences, Israel. Tel.: +972 8 934 3782; fax: +972 8 934 4117. E-mail address: [email protected] (A. Kogan).
which small amounts of floating solid particles are carried toward the reactor window. Some intuitive solutions were tried to counteract the suspected cause of the stray particles migration, with various degrees of success [2,3]. At this point we came to the decision to engage in a detailed computational fluid dynamics (CFD) simulation of the tornado flow pattern in the solar reactor under development at our laboratory. We solicited the cooperation of Prof. Moshe Israeli from the Department of Computer Sciences, Technion-IIT in this work. The present report describes results of a preliminary CFD simulation of a tornado flow performed in a reaction chamber of a simplified geometry. The purpose of this preliminary exercise was to get acquainted with the capabilities of the FLUENT CFD code currently in use at the Technion. At this stage we were interested in particular to learn whether there exists at least a qualitative agreement between certain results of practical significance that were arrived at by CFD and the corresponding phenomena observed during our experiments. All the information gained by experiment were confirmed by CFD
0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.08.016
A. Kogan et al. / International Journal of Hydrogen Energy 32 (2007) 4800 – 4810
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simulation. Moreover, some important unexpected features of the confined tornado flow became evident by CFD simulation. These features are discussed below. 2. An abbreviated description of the tornado flow pattern A detailed description of the tornado flow pattern, which enables effective screening of the reactor window from incandescent solid particles, may be found elsewhere [1]. The following brief explanation of the phenomenon is given here for ease of reference. When a fluid flows along a solid stationary boundary, its motion is retarded within a thin boundary layer by friction. The retarded fluid boundary layer may thicken progressively in the direction of flow and ultimately it may detach from the solid boundary and mix with the main flow. Boundary layer detachment can be averted if care is taken to maintain a uniformly decreasing pressure in the direction of flow. The accelerated main flow then entrains the fluid in the boundary layer strongly enough to counteract the flow retardation caused by friction with the stationary boundary. Turning to our particular application, the axisymmetric chamber of the solar reactor illustrated in Fig. 1 is provided with a transparent window located at one end of the chamber, transversally to the longitudinal axis. The main gas flow F1 is introduced into the chamber in a manner whirling around the axis, while the reaction products are withdrawn at the opposite end of the chamber through a narrow central tube oriented along the longitudinal axis. The gas flow inside the chamber then approximates a free vortex flow, characterized by a drop of pressure from the periphery of the chamber to its axis. A secondary flow F2 of protecting gas introduced at the periphery of the window is directed toward the window central area. It is accelerated by the negative pressure gradient generated by the free vortex flow. The secondary gas boundary layer flow at the window surface is thereby stabilized and it remains attached to the surface all the way to the center of the window. The radially converging streamlines then turn into the axial direction, forming a typical tornado-like funnel along the reactor axis. Synergy between the free vortex flow of the main gas and the boundary layer flow of the secondary gas is here exploited in order to protect effectively the reactor window. The synergy is expressed by the fact that the secondary flow, which is desired to form a stable, continuous and non-separated protective layer on the window surface, is not disturbed by the whirling main stream. It is rather stabilized by it. Consequently, the secondary flow does not need to be injected with high velocity or with a great flow rate in order to adhere to the surface to be protected, because it uses the energy of the whirling mainstream against which protection is sought. The tornado effect has been demonstrated in a series of simulation tests at room temperature with the reactor model shown in Fig. 1. The main gas stream was flown from an annular plenum chamber through a narrow annular gap toward the upper part of the reaction chamber. An impeller-like ring was implanted in the annular gap. The main gas stream acquired an angular
Fig. 1. Cross-section of reactor M2a.
momentum during its passage through slanted grooves in the impeller ring and it entered the reactor cavity in a whirling motion. The secondary gas stream was flown radially from a second annular plenum chamber through a second narrow annular gap toward the periphery of the inner surface of the window. Both streams consisted of nitrogen gas. The secondary stream was made visible by charging it with smoke, while the gas in the mainstream was left in its natural transparent condition. In order to enable visual inspection of a cross-section of the flow inside the reaction chamber, a laser beam directed toward the reactor window was diffracted by passage through a transverse cylindrical glass rod. The monochromatic laser beam emerged from the glass rod as a planar sheet of light that illuminated a cross-section of flow inside the reaction chamber. The four tornado configuration tests illustrated in Fig. 2 were performed with a secondary smoke-charged gas maintained at a constant flow rate of 1 L/min. With a whirling main gas stream at a flow rate of 3 L/min (Fig. 2a), the secondary flow separated from the window surface immediately upon its entry into the reaction chamber. When the whirling main stream was introduced into the reaction chamber at successively higher flow rates (Fig. 2b–d), the secondary stream became progressively stabilized as a thin boundary layer. For a main gas flow rate of 20 L/min, the secondary gas moved at high speed in the thin boundary layer near the window surface. It covered the entire window surface area and it left finally the reaction chamber through a narrow axially oriented funnel. 3. Degeneration of the tornado flow configuration when F1 is increased beyond a certain transition value By increasing the flow rate F1 of the main gas stream without changing the other test parameters, the test Ekman
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Fig. 2. Consecutive stages in the evolution of a “tornado” flow pattern in a reaction chamber. (a) Main flow — 0 L/M; (b) Tangential Main flow — 5 L/M; (c) Tangential Main flow — 10 L/M; (d) Tangential Main flow 2 L/M.
number [4] E= (1) L2 is diminished. Is there a limit to the permissible increase of F1 , beyond which the tornado flow pattern will break down? In order to answer this question we performed a prolongated smoke visualization tornado flow configuration test at room temperature similar to the test described above. The reactor illustrated in Fig. 3 served us in this test. The streams F1 and F2 consisted likewise of nitrogen. The smoke-charged stream F2 was maintained at a low constant value throughout the test duration, F2 = 2 L/min. The mainstream, F1 , was varied over a wide range. At low F1 flow rates the flow pattern in the reaction chamber resembled that of a regular tornado flow pattern. By increasing F1 a point of transition was reached, when the flow pattern became unstable, flipping at random between the regular tornado flow pattern and a degenerate pattern, as illustrated in Fig. 4. When F1 was increased beyond the transition point, the flow pattern in the reaction chamber stabilized in the diffuse flow configuration, illustrated in Fig. 5, which suggests a transition or a turbulent flow pattern. Fig. 3. Cross-section of reactor D1 .
4. Exploratory tornado flow configuration tests with powder seeding into the reaction chamber. The existence of a weak torroidal flow perturbation was postulated in order to explain a slight powder deposition on the window surface Some exploratory tornado flow configuration tests with powder seeding were performed at room temperature in order to
gain experimental information about the paths followed by solid particles entrained by the gas flow. During these tests neither one of the two gas streams entering the reaction chamber were stained by smoke, but the main gas stream was charged with a small amount of carbon black (CB) powder before its entry into the reactor [3].
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Fig. 4. Smoke flow visualization of an unstable tornado flow configuration.
Fig. 6 is a picture of the reactor window taken at the end of one such test. It shows two concentric rings of powder sediment. The outside diameter of the diffuse outer ring equals the diameter of the circle along which the powder is admitted into the reactor cavity (6 cm). The more concentrated inner powder ring is confined between two concentric circles with diameters of about 2.5 and 0.5 cm, respectively. The test was repeated with the inner surface of the window wetted by a thin layer of lubrication oil. At the end of the test, a narrow, high-density powder ring was observed at the periphery of the window and a circular spot of CB of about 0.3 cm in diameter was spread around the window center, with vestiges of streak lines connecting the outer ring to the central spot (Fig. 7). By the time the picture shown in Fig. 7 was taken, about 30 min after the end of the test, the central spot of CB-stained oil spread over the area of a circle about 1.3 cm in diameter. Figs. 6 and 7 suggest a flow of CB particles entrained by an upwelling stream of gas along the periphery of the reactor cavity. Upon reaching the top of the cavity, the gas stream turned apparently abruptly from the axial into the radial direction,
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Fig. 5. Smoke flow visualization of a degenerated tornado flow configuration.
shedding CB particles onto the window surface by centrifugal force. Solid particles coming into close proximity to the window surface may also have been attracted to it by electrostatic force. Some of the particles formed the outer black ring, while most of them were swept by the accelerated gas stream along the lubricated window surface toward the center of the window. The following mechanism was suggested as a plausible explanation of the observed powder flow behavior. The ascending gas current along the reactor cavity wall is part of a weak flow perturbation generated by friction between the energetic gas stream in the tornado funnel and the gas surrounding it. The fast axial flow of gas in the tornado funnel entrains by friction the relatively quiescent gas around it. Fig. 8 is an intuitive picture of the streamlines in the perturbed quiescent region. These are helical streamlines wrapped around torroidal surfaces. This flow perturbation is, of course, a very weak effect that could be neglected, were it not for the presence of the very fine powder particles that may be entrained by the postulated torroidal flow toward the reactor window. At close proximity to the entraining jet, solid particles suspended in the perturbed gas are expected to move downwards, concurrent with the entraining funnel jet.
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reactor illustrated in Fig. 1, which was heated by concentrated solar radiation up to 1320 ◦ C. The main gas stream consisted of methane and the secondary stream was helium. With increasing test temperature, the slight powder deposition on the window surface diminished. No powder deposition could be discerned at all when the reactor inner wall temperature came close to 1000 ◦ C [2]. We note that by increasing the temperature from ambient to above 1000 ◦ C the gas kinematic viscosity goes up by an order of magnitude, with a corresponding increase in Ekman number. It appears reasonable to assume that during the initial low temperature tests in this test series the flow in the reaction chamber was turbulent and with increasing test temperature the Ekman number increased beyond the critical value and the flow in the reaction chamber became laminar. 6. Some results of a CFD simulation of a tornado flow configuration maintained in a reaction chamber of a simplified geometry
Fig. 6. Reactor window stained by powder deposition after a 10-min seeding tornado flow test.
Fig. 7. CB deposit on reactor window at the end of a test similar to the one illustrated in Fig. 6, when the window surface was wetted by lubrication oil, before start of test.
Upon approaching the reactor cavity bottom, they diverge toward the periphery, turning in sequence upwards toward the reactor window, then inwards along the window. 5. Cessation of powder deposition on reactor window at elevated temperatures The above described room temperature tests with powder seeding were followed by a series of tests with the unseeded
The postulation of the existence of a weak torroidal flow perturbation in order to explain the observed slight powder deposition on the window surface during the room temperature tests was based on scanty experimental evidence. During the above mentioned exploratory tornado flow configuration tests with powder seeding we were unable to follow the paths of single particles. By observation of the powder deposition pattern in Figs. 6 and 7, one can conclude with confidence that some powder particles in gas suspension were entrained toward the window surface, that some of them settled on the surface and that some others were entrained by the surface boundary layer flow within a stretch between the center of the window and its periphery. In order to obtain a more detailed description of the tornado flow configuration, we decided to back up our experimental work by CFD simulation. In the preliminary CFD simulation study described below, the simplified cylinder–frustum geometry illustrated in Fig. 9 was chosen for the outline of the reaction chamber. The main gas is introduced into the reactor cavity through the annular entrance of width w1 as an axi-symmetric whirling stream at a flowrate F1 . The secondary gas stream F2 is introduced into the cavity radially through the annular entrance of width w2 . Both streams are simulated by air. The air viscosity and density are functions of temperature. The kinematic viscosity of air increases significantly with temperature (Fig. 10). Figs. 11–13 illustrate contours of stream function and of swirl velocity of air flow in the reactor cavity of Fig. 9, as calculated by FLUENT CFD simulation code for a case of high viscosity, corresponding to T = 1200 ◦ C. The stream function contours shown in Fig. 11 were attained for a tornado flow configuration established by introducing a main stream of air tangentially into the reaction chamber at a flowrate F1 = 10 L/min through the main annular entrance of width w1 = 2 mm and a secondary stream of air F2 = 0.5 L/min through the secondary annular entrance of width w2 = 0.2 mm, the air leaving the reaction
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Fig. 8. Schematic representation of torroidal flow perturbation induced by friction between the gas moving at high speed in the tornado funnel and the surrounding gas.
chamber through the exit section at the bottom of the chamber. These contours were attained at time 1075 s after start of flow. Fig. 12 is an enlarged picture of the air entry region in Fig. 11. Fig. 13 shows contours of swirl velocity (m/s) of the flow. At short distance from the entrance annuli the stream divides into two distinct streams. The seven streamlines marked by A in Fig. 11 flow roughly radially, toward the reactor axis of symmetry, then they make sharp turns of almost 90◦ , forming a funnel-like jet of air. Yet the major part of the entering air stream represented by the 41 streamlines marked by B proceed toward the axis of symmetry along a distance less than a third of the cylinder radius before making a sharp U-turn toward the wall of the cylinder. A concentrated annular vortex E located just below air entrance w1 is powered by friction with the sharply curved stream. After completion of the U-turn, the 34 outer streamlines marked by C flow down the cylinder and frustum walls toward the chamber exit section. The remaining 7 inner streamlines marked by D diverge one by one from the bulk of 34 streamlines, trying to ascend toward the top of the chamber. But they do not quite make it all the way to the top. The first of this set of streamlines reaches up to a distance G from the top. They all turn downwards toward the exit section after reaching their maxima. An oblong widespread annular vortex marked F is formed in the fold of this streamline and is powered by friction with it.
Fig. 14 illustrates stream function contours for a tornado air flow configuration in the simplified reactor of Fig. 9 for an intermediate air temperature. It exhibits all the features of Fig. 11. We notice that the shortest distance G reached by an upwelling streamline in Fig. 14 is less than half the value of G in Fig. 11. Figs. 15–17 illustrate stream function and swirl velocity contours for a tornado air flow configuration in the same reactor when the air is at room temperature. They suggest the existence of a transition or turbulent flow. It is interesting to notice the row of annular vortices generated by friction with the abundant stream of air flowing down along the cylindrical boundary of the reaction chamber. Most of these peripheral streamlines turn successively along the frustum boundary layer upwards, some of them reaching the top of the chamber, where they join the attached boundary layer flow. 7. Interpretation of the CFD simulation results in light of the facts established by experiment The ability to prevent separation of the boundary layer flow from the reactor window surface by maintaining a tornado flow configuration in the reaction chamber is corroborated by the CFD simulation. The extreme set of stream function lines marked by A in Fig. 11, e.g., do not detach from the window surface, in accord with our experimental evidence.
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Fig. 9. The cylinder–frustum geometry of a simplified combustion chamber.
The existence of a minimum gas kinematic viscosity (or temperature) for a given reactor geometry and flow parameters, beyond which the tornado flow pattern breaks down is also predicted by the CFD simulation, as may be seen by comparing the flow patterns in Figs. 10 and 15. The simulated low viscosity flow illustrated in Fig. 15 exhibits a set of nine streamlines marked by D which follow a path reminiscent of the flow path of the corresponding set of streamlines D in the high viscosity flow diagram of Fig. 11. They start their journey inside the reaction chamber by flowing down along the cylindrical boundary of the chamber as part of the set of streamlines B. Upon reaching the vicinity of frustum boundary at the bottom of the chamber, they diverge one by one from the mainstream, turning upwards, toward the reactor window. The subset of four streamlines marked by D in Fig. 15 reach a maximum before touching the window surface. They make a final turn downwards to the exit port. Yet unlike in the case of the high viscosity flow of Fig. 11, the remaining set of five streamlines marked by D in Fig. 15 reach all the way to the window surface, where they join the set of streamlines A along that surface. The gas flowing along streamlines in subset D in Fig. 15 is capable of entraining powder particles and of shedding them on that surface. The experimental observation of formation of a slight deposit of solid particles on the reactor window when a powder suspension in a low viscosity fluid is flowing inside the reaction chamber in a tornado flow configuration (a low Ekman number flow) and the absence of formation of such a powder deposit during a similar flow of a powder suspension in a high viscosity gas (a high Ekman number flow) seems thus to be in accord with results obtained by CFD simulation.
Fig. 10. Kinematic viscosity of air vs. temperature.
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Fig. 11. Contours of stream function (kg/s) (time = 1.0750e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at 1200◦ C.
Fig. 12. An enlarged picture of the region of air entry in Fig. 11.
Fig. 13. Contours of swirl velocity (m/s) (time = 1.0750e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady).
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Fig. 14. Contours of stream function (kg/s) (time = 2.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at 600◦ C.
Fig. 15. Contours of stream function (kg/s) (time = 1.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady). Air flow at room temperature.
Fig. 16. An enlarged picture of the region of air entry in Fig. 15.
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Fig. 17. Contours of swirl velocity (m/s) (time = 1.0000e + 03) FLUENT 6.2 (axi, swirl, segregated, lam, unsteady).
8. Revision of the postulation of a torroidal flow perturbation in view of the contours of tornado flow stream function obtained by CFD simulation In a free vortex flow, the tangential velocity u and the pressure p are given by u = c1 /r
(2)
and p = p0 − c2 /r 2 ,
(3)
where r is the distance from the vortex axis of symmetry, p0 is the total pressure, c1 is a constant and c2 is a positive constant. A free vortex can persist in steady state when the centrifugal force generated by the rotation of fluid is counter-balanced by the centripetal force caused by the increase of pressure with the distance r. When a vortex flow takes place within a finite volume confined by stationary solid boundaries, the fluid friction within the boundary layer may perturb considerably the vortex flow pattern. By way of example, the centrifugal force acting on the fluid in vortex flow is sharply reduced within the boundary layer along a plane boundary normal to the axis of rotation, such as the surface of the reactor window. The centripetal force within the boundary layer is then left unbalanced and the fluid on the periphery of that boundary is accelerated toward the axis of rotation. This is the effect that we have exploited in order to obtain a natural gas dynamic windscreen to protect the reactor window from contact with solid particles floating in the gas. Upon approaching the axis of rotation, the converging streamlines turn sharply into the axial direction, forming a typical tornado funnel. We have assumed intuitively that friction between the fast funnel jet and the surrounding relatively quiescent fluid generates a torroidal flow perturbation as shown in Fig. 8, which could be the agent by which some powder particles are carried toward the window surface and are deposited on it.
The contours of streamlines in Fig. 11 obtained by CFD simulation differ considerably from those sketched in Fig. 8. They do not corroborate the postulation of the existence of a torroidal flow perturbation in a vortex flow confined by solid stationary walls. After careful examination of the confined vortex flow patterns obtained by CFD simulation, we came to realize that the assumption that the perturbed flow pattern of the confined vortex in the simplified reaction chamber of Fig. 9 is not determined solely by the interaction between the rotating fluid and the boundary layer flow adjacent to the chamber ceiling, which is perpendicular to the axis of rotation. In fact, the centrifugal force acting on the fluid within the boundary layer along the surface of the frustum shaped wall is also sharply reduced and the fluid inside this boundary layer is also accelerated toward the chamber exit port by the unbalanced centripetal force. Two natural routes are thus available for delivery of the rotating fluid confined within the reaction chamber of Fig. 9 from the two annular entrance ports at the top of the chamber to the exit port at the bottom. The flow patterns in Figs. 11 and 15 that were obtained by CFD simulation indicate that both routes are exploited by nature. The fluid stream entering the reaction chamber splits shortly after entry into two unequal streams. A scarce stream A follows the first route described above, forming the gas dynamic windshield at the chamber ceiling and the tornado funnel, while the abundant stream B takes the second, peripheral route to the chamber exit. The behavior of a slightly viscous swirling flow entering an axisymmetric chamber at a large (outer) radius and exiting at a smaller (inner) radius near the axis can be interpreted with the help of the theory of rotating flows at very small Ekman numbers, see [4]. In such flows, the radial flow of the fluid is inhibited by the strong Coriolis force generated by the vortex which is further amplified as the swirling flow approaches the axis conserving its angular momentum. This effect is observed also in “industrial cyclones” and “rotation valves” where a huge
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pressure difference must be supplied to drive the flow as described. In a cylinder symmetrical with respect to its center plane, the vortex generates two horizontal boundary layers, called Ekman Layers (E.L.). A radial mass flux can be sustained in these thin layers. It is proportional to the difference in angular velocity between the swirling interior and the horizontal stationary top and bottom plates, and also to the square root of the Ekman number. In such a configuration, the top and bottom radial flux must be exactly the same. In a non-symmetric chamber like the cylinder–frustum combination, the radial mass flux in the frustum (inclined) E.L. is allowed to be larger (as the Ekman number depends on the slope). However, if too much flux is directed to the bottom initially, an appropriate fraction of this flux must return to the top (horizontal) plate E.L. before it can proceed to the axis (as can be seen for example in Figs. 11 and 15). It is interesting to observe that both in the case of the laminar flow (Fig. 11) and of the turbulent (or transition) flow (Fig. 15) some of the streamlines that started on the second route separate at some point from their original mainstream B, trying to ascend along isobars toward the chamber ceiling. Yet almost all of these stray streamlines make a U-turn before reaching the ceiling and they rejoin their original mainstream B. These streamlines will not contaminate the reactor window with any solid particles that they may carry in suspension. Only in the case of transition or turbulent flow (Fig. 15), a part of the stray streamlines does succeed to reach the chamber ceiling. They join the set of streamlines A that followed the first route. These particular streamlines carry the danger of deposition of entrained powder on the surface of the reactor window. 9. Conclusion The above described comparison of certain characteristics of a confined tornado flow, that were observed previously during laboratory tests, with corresponding characteristics of such flows obtained by CFD simulation is of a preliminary nature. For the sake of simplicity, a rudimentary geometry was chosen for the outline of the reaction chamber used in the CFD calculation. This geometry was different from the geometries of
the reaction chamber models used in the laboratory tests. The comparison of our previous experimental results with predictions derived from the described CFD work is therefore only of a qualitative nature. Yet despite this limitation, we were able to identify by CFD simulation certain basic characteristics of the confined tornado flow that were observed in the laboratory. Moreover, the CFD simulation helped us to clarify some intricate features of the flow under study that were previously obscure. CFD simulation can thus certainly become an important auxiliary tool in the development of an effective solar reactor that exploits the confined tornado flow configuration. To this end we will have to choose a reaction chamber model with a standard geometry. Some of CFD simulation and laboratory test work will be performed with the standard reaction chamber model under strict similarity conditions. A quantitative comparison will then be made between the CFD simulation predictions and the test results. If small systematic discrepancies will be found between the two results, the data will be reconciled by the introduction of calibration factors. CFD simulation will then become an important aid in our R&D work. Acknowledgments This study was supported by the Heineman Foundation for Research, Education, Charitable and Scientific Purposes and the Rose Family Foundation, NY, USA. The authors gratefully acknowledge the steadfast support of these foundations. References [1] Kogan A, Kogan M. The tornado flow configuration—an effective method for screening of a solar reactor window. J Solar Energy Eng 2002;124:206 –14. [2] Kogan M, Kogan A. Production of hydrogen and carbon by solar thermal methane splitting. I. The unseeded reactor. Int J Hydrogen Energy 2003;28:1187–98. [3] Kogan A, Kogan M, Barak S. Production of hydrogen and carbon by solar thermal methane splitting. II. Room temperature simulation tests of seeded solar reactor. Int J Hydrogen Energy 2003;29:1227–36. [4] Greenspan HP. Theory of rotating fluids. Cambridge: Cambridge University Press; 1968 p. 3.