- Email: [email protected]
Reprint of: Rod bundle vortex networks, gap vortex streets, and gap instability: A nomenclature and some comments on available methodologies
Nuclear Engineering and Design 241 (2011) 4612–4614
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Reprint of: Rod bundle vortex networks, gap vortex streets, and gap instability: A nomenclature and some comments on available methodologies夽 Stavros Tavoularis Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada
a r t i c l e
i n f o
Article history: Received 18 January 2011 Received in revised form 20 March 2011 Accepted 25 March 2011
a b s t r a c t This note introduces the following terms, which apply to large-scale, vortical, coherent structures, appearing in flows through tightly packed rod bundles and other channels that have narrow gap regions: the term gap instability describes the mechanism of generation of such structures in the gap region in laminar and turbulent flows; the term gap vortex street describes the chain of counter-rotating vortices which from on either side of a single gap; and the term rod bundle vortex network describes the set of mutually dependent gap vortex streets that appear in rod bundles and other channels with multiple gaps. Moreover, this notes summarizes the capabilities and limitations of available CFD methods for simulating flows in rod bundles. © 2011 Elsevier B.V. All rights reserved.
Flows in tightly packed nuclear reactor rod bundles have been known for a long time to have peculiar patterns, which are not encountered in pipe flows or flows in other simple channels. These patterns, demonstrated by strong, transverse, large-scale motions across the narrow gaps between adjacent fuel elements or between a fuel element and the wall of a containing vessel, enhance drastically the mixing between flows in neighbouring subchannels. Large-scale inter-subchannel mixing has been accounted for in widely employed one-dimensional subchannel codes with the use of empirical correlations, which have been based on measurements in simple systems under drastically simplified conditions. Motivated by the recent intensification of global interest in nuclear power generation, and following enabling advances in computer capabilities, numerical simulation technology and fluid mechanical instrumentation, studies of flow and heat transfer in rod bundles have been appearing at an accelerating pace. Some recent advances in this area have been presented by several research groups in a special session on Mixing in Rod Bundles in NURETH-13 and two articles (Merzari and Ninokata, in press; Piot and Tavoularis, in press) that contain material from these presentations have been included in this special NURETH-13 issue of Nuclear Engineering and Design; a third article (Meyer, 2010) from the special NURETH13 session has already been published in an earlier volume of the same journal.
DOI of original article: 10.1016/j.nucengdes.2011.03.052. 夽 This editorial has previously been published in Nuclear Engineering and Design Vol. 241, issue 7, pages 2624–2626. E-mail address: [email protected] 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.09.043
As our understanding of large-scale motions in rod bundles and their effects has evolved through the course of several decades, the associated literature contains diverse hypotheses, explanations and terminology. Occasionally, obsolete explanations, as for example the association of these large-scale motions with secondary flows in the subchannels, reappear in new references. Research on this topic has now reached a state at which a consensus seems to be necessary, and is in fact within reach. Therefore, it is time for the nuclear research community to establish a universal nomenclature that is true to the corresponding physical phenomena; such a nomenclature should be free of influences that may be of historical value, but may also lead to misunderstandings or to confusion with other types of phenomena. Moreover, it is even more important to establish some quality standards for future research. The flow patterns of concern are very strong, and may indeed dominate all other transport mechanisms, at least locally and under certain conditions. As a result, the signature of large-scale motions in rod bundle flows (e.g., an oscillatory cross-stream velocity in the gap region) is detectable by even crude experimental and CFD methods, as long as they have some basic temporal and spatial resolution capabilities. The mere detection of these motions was of value during the long pioneering period of rod bundle research, but this era has passed. From now on, one may justifiably anticipate that any new computational or experimental work on this topic should not be confined to qualitative descriptions, but also meet quantitative standards for uncertainty, as they have been established by the fluid mechanics research community. Furthermore, researchers should keep in mind that the nuclear industry requires accurate predictions of local flow and heat transfer in nuclear systems under actual operating conditions and under different accident scenarios; the usability of information collected in experimental or computational
S. Tavoularis / Nuclear Engineering and Design 241 (2011) 4612–4614
laboratories to actual nuclear systems cannot be taken for granted. The objectives of the present note are to introduce a nomenclature for large-scale motions in rod-bundles and to identify certain pitfalls that may distract future work from meeting quality standards. The generation of these large-scale motions has been attributed to an instability mechanism that is particular to rod bundles and other channels having narrow gaps that connect larger subchannels. The cross-sectional velocity distribution in such channels is inflectional, a condition that is well known to be hydrodynamically unstable. Although there are some similarities between this type of hydrodynamic instability and those in other kinds of flows, including wakes and boundary layers, they are not sufficient for one to categorize them all together using the same term. In the absence of any previous term to denote the flow instability process in gaps connecting larger subchannels, it is suggested to adopt the term gap instability (this term is now used in the article by Piot and Tavoularis, in press). Concerning the large-scale motions across an individual gap, the most commonly used term is flow pulsations. This term correctly expresses the oscillatory state of flow velocity in the gap region. Nevertheless, pulsations are only a symptom of the condition of the flow and this term provides no physical insight into the overall structure of the velocity field. The pulsations are the result of the interactions between sequences of counter-rotating vortices on either side of the gap. An appropriate term to characterize these flow patterns is gap vortex street, which fittingly reminds one of the well-known von Kármán vortex street in two-dimensional wakes. The use of this term should not necessarily imply periodicity, but a general recurrence of vortices with specific senses of rotation and typical recurrence rates. When multiple gaps are present in a channel, as in the case of a rod bundle, the vortex streets from different gaps are coupled with each other, according to the laws of fluid dynamics. This coupling must be taken into consideration in the analysis of rod bundle flows and it would not be appropriate to consider gap regions in isolation. For example, the distortion of flow in a single gap (e.g., by deformation or displacement of a rod or by the presence of some local obstruction) would have implications on the flow patterns in other gaps as well. The interactions between the vortex streets forming in several gaps with different sizes and shapes have only recently been investigated and much work remains to be done. Nevertheless, when referring to large-scale motions in rod bundles, it is deemed appropriate to acknowledge the interactions between gap vortex streets by using the term rod bundle vortex network. Studies of flows in rod bundles are currently conducted by several research teams worldwide. Most of the ongoing research seems to be computational, and the rates of presentation and publication of numerical results are ever increasing. Nevertheless, this research topic is far from being saturated. Although several powerful CFD methods have been developed and tested successfully in a variety of engineering applications, their use for the accurate simulation of realistic rod bundle flows remains a challenge. The most accurate CFD method is undoubtedly the Direct Numerical Simulation (DNS), which employs no modelling or other approximation for the solution of the equations of motion. To qualify as DNS, a numerical simulation must satisfy two strict requirements. First, a DNS must resolve motions with a scale comparable to the size of the smallest dynamically important eddies, which by convention is described by the Kolmogorov microscale of turbulence. This scale diminishes with increasing Reynolds number. The Reynolds numbers of flows in the rod bundles of operating CANDU reactors and PWR exceed 500,000. Simple analysis using established scaling laws predicts that, to meet this requirement, a DNS of an operating rod bundle must have a mesh with a number of elements that would exceed 1012 ; this is clearly an impossible task, not only for current computers but also for any computer system
4613
that may be developed in the foreseeable future. At present, the most powerful computers would accommodate the DNS of simple rod bundle at Reynolds numbers of up to a few thousand. Compromising the small-scale resolution of a DNS, a process that has been referred to as coarse DNS or, more appropriately, as pseudo-DNS, would result in unpredictable errors. The second requirement for a proper DNS is that it must ensure a very high accuracy for spatial and temporal discretization of the governing equations. This is usually accomplished by the use of spectral methods in specialized codes, whereas the solution of time-dependent dynamic equations with commercial or open-source CFD codes, which generally have a second-order accuracy, fails to satisfy this requirement. The results of low-accuracy pseudo-DNS in rod bundles should be treated with caution, even if they predict the formation of gap vortex streets. Another powerful CFD method is the Large Eddy Simulation (LES), consisting of the solution of low-pass filtered dynamic equations, in which the fine structure has been modelled by a SubGrid-Scale (SGS) model. Proper application of this method requires that its spatial resolution be comparable to eddy sizes within the inertial spectral subrange. This should be the case not only for the core of the flow, but also for the near-wall regions, where the inertial-subrange scales are very small. Consequently, the computational cost of LES of high Reynolds number flows is also extremely high. For example, one may easily estimate that the LES of an operating CANDU or PWR rod bundle should have a mesh with a number of elements that would be of the order of 1010 , which is also beyond the reach of current computers, although it may come into range in the future. Another limitation is that estimates of turbulence properties by LES would miss the SGS components, although averages of these can be roughly recovered with the simultaneous solution of some modelled equations for the SGS turbulence. On the positive side, because the energy of the SGS motions is small when compared to the energy of the resolved motions, the distortion of the latter by the filtering process is not significant, at least as far as the energy containing motions and the gap vortices are concerned. As a result, LES would likely resolve gap vortex streets that appear to be quite irregular. In other words, the diversity of individual members of such vortex streets may be such that no single member may be taken as representative of the process. To extract typical vortex features, statistical methods including phase averaging and the Proper Orthogonal Decomposition (POD) would be required. To compensate for the fact that the vast majority of mesh elements for proper LES would be in the near-wall regions, a number of hybrid methods have been developed, in which LES equations are solved away from solid walls, whereas wall functions or solutions of modelled equations are employed near the walls. Popular hybrid methods include the Detached Eddy Simulation (DES) and the Scale-Adaptive Simulation (SAS). Early enthusiasm for the application of LES to industrial problems has been replaced by cautious optimism, and much more research would be required before hybrid LES simulations of realistic rod bundle flows become an acceptable routine. In general, the most widely used CFD method for industrial applications is the solution of the Reynolds-Averaged Navier Stokes (RANS) equations, combined with modelled equations for turbulence properties. This method has proved to be notoriously inaccurate for tightly packed rod bundle flows, as it cannot resolve time-dependent motions. On the other hand, the recent use of Unsteady RANS (URANS) methods has resulted in realistic predictions of average gap vortex streets and rod-bundle vortex networks as well as fair estimates of mean velocity and turbulence distributions in rod bundles. Like RANS, URANS suffer from the drawback that they are heavily based on empirical models. Moreover, they employ a decomposition of turbulent motions into resolved and unresolved ones, a distinction that is arbitrary and not based on solid mathematical and physical foundations. Nevertheless, in the
4614
S. Tavoularis / Nuclear Engineering and Design 241 (2011) 4612–4614
particular case of rod bundle flows, because the length and time scales of the large-scale vortices are much larger than those of non-coherent turbulence, the former turn out to be represented fairly well, on the average, by the resolved velocity field. URANS methods are analogous to strong low-pass filtering and so they predict gap vortex streets and rod bundle vortex networks, which are more regular and periodic than in reality. One should definitely take this exaggeration of regularity into consideration when investigating vortex phenomena in rod bundles. On the other hand, if one is merely interested in predicting time-averaged properties, such as the average mixing rate between subchannels, the degree of regularity of predicted vortex streets and even the average vortex spacing would be of secondary importance, as long as the predicted average velocity fields are in fair agreement with experimental results. As more results on the application of URANS methods to rod bundle flows will likely become available in the near future, the powers and limitations of such methods are expected to become better known. The accuracy of all CFD studies must undergo two sets of tests. The first test is verification, which must demonstrate that the solution converges within acceptable bounds and that its dependence on the mesh size (and the time-step, if applicable) is also at an acceptable level, thus quantifying the numerical uncertainty. The second test is validation, which signifies that CFD predictions must be in agreement with experimental results. As long as CFD results remain non-validated, any assessment of their accuracy would be inconclusive. This point brings forward a difficulty that is not always appreciated by CFD analysts: the assessment of the conditions of experimental studies and the accuracy of experimental results. A comparison between the results of CFD and experimental studies may only be appropriate if the corresponding geometries
and conditions are the same. Unfortunately, the geometrical specifications of apparatus used in experimental studies reported in the literature are often incomplete. Future experimenters of rod bundle flows are advised to provide all dimensions required to model the entire apparatus, including sections upstream and downstream of the main test section where measurements are made. Equally important is the specification of boundary conditions, particularly the turbulence stresses and length scales at the inlet, because CFD analyses are known to be very sensitive to inlet conditions. It is also the duty of experimenters to report reliable estimates of the spatial, temporal and amplitude resolutions of their instrumentation as well as the uncertainties of all measurements. As important as it is for CFD analysts to be familiar with experimental limitations, it is equally important for experiments to be responsive to the needs of CFD analysis and validation. In closing, it seems fair to say that the presence and consequences of large-scale motions in rod bundle flows have been widely accepted, as unquestionable evidence has reversed early scepticism. This evidence deserves to be disseminated more widely within the nuclear community and taken into consideration in future nuclear reactor design processes and safety analyses. It is hoped that the present note makes a contribution towards this objective. References Merzari, E., Ninokata, H. Proper orthogonal decomposition of the flow in a tight lattice rodbundle. Nucl. Eng. Des., in press, doi:10.1016/j.nucengdes.2010.12.005. Meyer, L., 2010. From discovery to recognition of periodic large scale vortices in rod bundles as source of natural mixing between subchannels—a review. Nucl. Eng. Des. 240, 1575–1588. Piot, E., Tavoularis, S. Gap instability of laminar flows in eccentric annular channels. Nucl. Eng. Des., in press, doi:10.1016/j.nucengdes.2010.08.025.
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Reprint of: Rod bundle vortex networks, gap vortex streets, and gap instability: A nomenclature and some comments on available methodologies夽 Stavros Tavoularis Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada
a r t i c l e
i n f o
Article history: Received 18 January 2011 Received in revised form 20 March 2011 Accepted 25 March 2011
a b s t r a c t This note introduces the following terms, which apply to large-scale, vortical, coherent structures, appearing in flows through tightly packed rod bundles and other channels that have narrow gap regions: the term gap instability describes the mechanism of generation of such structures in the gap region in laminar and turbulent flows; the term gap vortex street describes the chain of counter-rotating vortices which from on either side of a single gap; and the term rod bundle vortex network describes the set of mutually dependent gap vortex streets that appear in rod bundles and other channels with multiple gaps. Moreover, this notes summarizes the capabilities and limitations of available CFD methods for simulating flows in rod bundles. © 2011 Elsevier B.V. All rights reserved.
Flows in tightly packed nuclear reactor rod bundles have been known for a long time to have peculiar patterns, which are not encountered in pipe flows or flows in other simple channels. These patterns, demonstrated by strong, transverse, large-scale motions across the narrow gaps between adjacent fuel elements or between a fuel element and the wall of a containing vessel, enhance drastically the mixing between flows in neighbouring subchannels. Large-scale inter-subchannel mixing has been accounted for in widely employed one-dimensional subchannel codes with the use of empirical correlations, which have been based on measurements in simple systems under drastically simplified conditions. Motivated by the recent intensification of global interest in nuclear power generation, and following enabling advances in computer capabilities, numerical simulation technology and fluid mechanical instrumentation, studies of flow and heat transfer in rod bundles have been appearing at an accelerating pace. Some recent advances in this area have been presented by several research groups in a special session on Mixing in Rod Bundles in NURETH-13 and two articles (Merzari and Ninokata, in press; Piot and Tavoularis, in press) that contain material from these presentations have been included in this special NURETH-13 issue of Nuclear Engineering and Design; a third article (Meyer, 2010) from the special NURETH13 session has already been published in an earlier volume of the same journal.
DOI of original article: 10.1016/j.nucengdes.2011.03.052. 夽 This editorial has previously been published in Nuclear Engineering and Design Vol. 241, issue 7, pages 2624–2626. E-mail address: [email protected] 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.09.043
As our understanding of large-scale motions in rod bundles and their effects has evolved through the course of several decades, the associated literature contains diverse hypotheses, explanations and terminology. Occasionally, obsolete explanations, as for example the association of these large-scale motions with secondary flows in the subchannels, reappear in new references. Research on this topic has now reached a state at which a consensus seems to be necessary, and is in fact within reach. Therefore, it is time for the nuclear research community to establish a universal nomenclature that is true to the corresponding physical phenomena; such a nomenclature should be free of influences that may be of historical value, but may also lead to misunderstandings or to confusion with other types of phenomena. Moreover, it is even more important to establish some quality standards for future research. The flow patterns of concern are very strong, and may indeed dominate all other transport mechanisms, at least locally and under certain conditions. As a result, the signature of large-scale motions in rod bundle flows (e.g., an oscillatory cross-stream velocity in the gap region) is detectable by even crude experimental and CFD methods, as long as they have some basic temporal and spatial resolution capabilities. The mere detection of these motions was of value during the long pioneering period of rod bundle research, but this era has passed. From now on, one may justifiably anticipate that any new computational or experimental work on this topic should not be confined to qualitative descriptions, but also meet quantitative standards for uncertainty, as they have been established by the fluid mechanics research community. Furthermore, researchers should keep in mind that the nuclear industry requires accurate predictions of local flow and heat transfer in nuclear systems under actual operating conditions and under different accident scenarios; the usability of information collected in experimental or computational
S. Tavoularis / Nuclear Engineering and Design 241 (2011) 4612–4614
laboratories to actual nuclear systems cannot be taken for granted. The objectives of the present note are to introduce a nomenclature for large-scale motions in rod-bundles and to identify certain pitfalls that may distract future work from meeting quality standards. The generation of these large-scale motions has been attributed to an instability mechanism that is particular to rod bundles and other channels having narrow gaps that connect larger subchannels. The cross-sectional velocity distribution in such channels is inflectional, a condition that is well known to be hydrodynamically unstable. Although there are some similarities between this type of hydrodynamic instability and those in other kinds of flows, including wakes and boundary layers, they are not sufficient for one to categorize them all together using the same term. In the absence of any previous term to denote the flow instability process in gaps connecting larger subchannels, it is suggested to adopt the term gap instability (this term is now used in the article by Piot and Tavoularis, in press). Concerning the large-scale motions across an individual gap, the most commonly used term is flow pulsations. This term correctly expresses the oscillatory state of flow velocity in the gap region. Nevertheless, pulsations are only a symptom of the condition of the flow and this term provides no physical insight into the overall structure of the velocity field. The pulsations are the result of the interactions between sequences of counter-rotating vortices on either side of the gap. An appropriate term to characterize these flow patterns is gap vortex street, which fittingly reminds one of the well-known von Kármán vortex street in two-dimensional wakes. The use of this term should not necessarily imply periodicity, but a general recurrence of vortices with specific senses of rotation and typical recurrence rates. When multiple gaps are present in a channel, as in the case of a rod bundle, the vortex streets from different gaps are coupled with each other, according to the laws of fluid dynamics. This coupling must be taken into consideration in the analysis of rod bundle flows and it would not be appropriate to consider gap regions in isolation. For example, the distortion of flow in a single gap (e.g., by deformation or displacement of a rod or by the presence of some local obstruction) would have implications on the flow patterns in other gaps as well. The interactions between the vortex streets forming in several gaps with different sizes and shapes have only recently been investigated and much work remains to be done. Nevertheless, when referring to large-scale motions in rod bundles, it is deemed appropriate to acknowledge the interactions between gap vortex streets by using the term rod bundle vortex network. Studies of flows in rod bundles are currently conducted by several research teams worldwide. Most of the ongoing research seems to be computational, and the rates of presentation and publication of numerical results are ever increasing. Nevertheless, this research topic is far from being saturated. Although several powerful CFD methods have been developed and tested successfully in a variety of engineering applications, their use for the accurate simulation of realistic rod bundle flows remains a challenge. The most accurate CFD method is undoubtedly the Direct Numerical Simulation (DNS), which employs no modelling or other approximation for the solution of the equations of motion. To qualify as DNS, a numerical simulation must satisfy two strict requirements. First, a DNS must resolve motions with a scale comparable to the size of the smallest dynamically important eddies, which by convention is described by the Kolmogorov microscale of turbulence. This scale diminishes with increasing Reynolds number. The Reynolds numbers of flows in the rod bundles of operating CANDU reactors and PWR exceed 500,000. Simple analysis using established scaling laws predicts that, to meet this requirement, a DNS of an operating rod bundle must have a mesh with a number of elements that would exceed 1012 ; this is clearly an impossible task, not only for current computers but also for any computer system
4613
that may be developed in the foreseeable future. At present, the most powerful computers would accommodate the DNS of simple rod bundle at Reynolds numbers of up to a few thousand. Compromising the small-scale resolution of a DNS, a process that has been referred to as coarse DNS or, more appropriately, as pseudo-DNS, would result in unpredictable errors. The second requirement for a proper DNS is that it must ensure a very high accuracy for spatial and temporal discretization of the governing equations. This is usually accomplished by the use of spectral methods in specialized codes, whereas the solution of time-dependent dynamic equations with commercial or open-source CFD codes, which generally have a second-order accuracy, fails to satisfy this requirement. The results of low-accuracy pseudo-DNS in rod bundles should be treated with caution, even if they predict the formation of gap vortex streets. Another powerful CFD method is the Large Eddy Simulation (LES), consisting of the solution of low-pass filtered dynamic equations, in which the fine structure has been modelled by a SubGrid-Scale (SGS) model. Proper application of this method requires that its spatial resolution be comparable to eddy sizes within the inertial spectral subrange. This should be the case not only for the core of the flow, but also for the near-wall regions, where the inertial-subrange scales are very small. Consequently, the computational cost of LES of high Reynolds number flows is also extremely high. For example, one may easily estimate that the LES of an operating CANDU or PWR rod bundle should have a mesh with a number of elements that would be of the order of 1010 , which is also beyond the reach of current computers, although it may come into range in the future. Another limitation is that estimates of turbulence properties by LES would miss the SGS components, although averages of these can be roughly recovered with the simultaneous solution of some modelled equations for the SGS turbulence. On the positive side, because the energy of the SGS motions is small when compared to the energy of the resolved motions, the distortion of the latter by the filtering process is not significant, at least as far as the energy containing motions and the gap vortices are concerned. As a result, LES would likely resolve gap vortex streets that appear to be quite irregular. In other words, the diversity of individual members of such vortex streets may be such that no single member may be taken as representative of the process. To extract typical vortex features, statistical methods including phase averaging and the Proper Orthogonal Decomposition (POD) would be required. To compensate for the fact that the vast majority of mesh elements for proper LES would be in the near-wall regions, a number of hybrid methods have been developed, in which LES equations are solved away from solid walls, whereas wall functions or solutions of modelled equations are employed near the walls. Popular hybrid methods include the Detached Eddy Simulation (DES) and the Scale-Adaptive Simulation (SAS). Early enthusiasm for the application of LES to industrial problems has been replaced by cautious optimism, and much more research would be required before hybrid LES simulations of realistic rod bundle flows become an acceptable routine. In general, the most widely used CFD method for industrial applications is the solution of the Reynolds-Averaged Navier Stokes (RANS) equations, combined with modelled equations for turbulence properties. This method has proved to be notoriously inaccurate for tightly packed rod bundle flows, as it cannot resolve time-dependent motions. On the other hand, the recent use of Unsteady RANS (URANS) methods has resulted in realistic predictions of average gap vortex streets and rod-bundle vortex networks as well as fair estimates of mean velocity and turbulence distributions in rod bundles. Like RANS, URANS suffer from the drawback that they are heavily based on empirical models. Moreover, they employ a decomposition of turbulent motions into resolved and unresolved ones, a distinction that is arbitrary and not based on solid mathematical and physical foundations. Nevertheless, in the
4614
S. Tavoularis / Nuclear Engineering and Design 241 (2011) 4612–4614
particular case of rod bundle flows, because the length and time scales of the large-scale vortices are much larger than those of non-coherent turbulence, the former turn out to be represented fairly well, on the average, by the resolved velocity field. URANS methods are analogous to strong low-pass filtering and so they predict gap vortex streets and rod bundle vortex networks, which are more regular and periodic than in reality. One should definitely take this exaggeration of regularity into consideration when investigating vortex phenomena in rod bundles. On the other hand, if one is merely interested in predicting time-averaged properties, such as the average mixing rate between subchannels, the degree of regularity of predicted vortex streets and even the average vortex spacing would be of secondary importance, as long as the predicted average velocity fields are in fair agreement with experimental results. As more results on the application of URANS methods to rod bundle flows will likely become available in the near future, the powers and limitations of such methods are expected to become better known. The accuracy of all CFD studies must undergo two sets of tests. The first test is verification, which must demonstrate that the solution converges within acceptable bounds and that its dependence on the mesh size (and the time-step, if applicable) is also at an acceptable level, thus quantifying the numerical uncertainty. The second test is validation, which signifies that CFD predictions must be in agreement with experimental results. As long as CFD results remain non-validated, any assessment of their accuracy would be inconclusive. This point brings forward a difficulty that is not always appreciated by CFD analysts: the assessment of the conditions of experimental studies and the accuracy of experimental results. A comparison between the results of CFD and experimental studies may only be appropriate if the corresponding geometries
and conditions are the same. Unfortunately, the geometrical specifications of apparatus used in experimental studies reported in the literature are often incomplete. Future experimenters of rod bundle flows are advised to provide all dimensions required to model the entire apparatus, including sections upstream and downstream of the main test section where measurements are made. Equally important is the specification of boundary conditions, particularly the turbulence stresses and length scales at the inlet, because CFD analyses are known to be very sensitive to inlet conditions. It is also the duty of experimenters to report reliable estimates of the spatial, temporal and amplitude resolutions of their instrumentation as well as the uncertainties of all measurements. As important as it is for CFD analysts to be familiar with experimental limitations, it is equally important for experiments to be responsive to the needs of CFD analysis and validation. In closing, it seems fair to say that the presence and consequences of large-scale motions in rod bundle flows have been widely accepted, as unquestionable evidence has reversed early scepticism. This evidence deserves to be disseminated more widely within the nuclear community and taken into consideration in future nuclear reactor design processes and safety analyses. It is hoped that the present note makes a contribution towards this objective. References Merzari, E., Ninokata, H. Proper orthogonal decomposition of the flow in a tight lattice rodbundle. Nucl. Eng. Des., in press, doi:10.1016/j.nucengdes.2010.12.005. Meyer, L., 2010. From discovery to recognition of periodic large scale vortices in rod bundles as source of natural mixing between subchannels—a review. Nucl. Eng. Des. 240, 1575–1588. Piot, E., Tavoularis, S. Gap instability of laminar flows in eccentric annular channels. Nucl. Eng. Des., in press, doi:10.1016/j.nucengdes.2010.08.025.