Author: Takeo Kajishima
Publisher: Springer
ISBN: 3319453041
Category : Technology & Engineering
Languages : en
Pages : 364
Book Description
This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.
Computational Fluid Dynamics
Author: Takeo Kajishima
Publisher: Springer
ISBN: 3319453041
Category : Technology & Engineering
Languages : en
Pages : 364
Book Description
This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.
Publisher: Springer
ISBN: 3319453041
Category : Technology & Engineering
Languages : en
Pages : 364
Book Description
This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.
Unsteady Computational Fluid Dynamics in Aeronautics
Author: P.G. Tucker
Publisher: Springer Science & Business Media
ISBN: 9400770499
Category : Technology & Engineering
Languages : en
Pages : 432
Book Description
The field of Large Eddy Simulation (LES) and hybrids is a vibrant research area. This book runs through all the potential unsteady modelling fidelity ranges, from low-order to LES. The latter is probably the highest fidelity for practical aerospace systems modelling. Cutting edge new frontiers are defined. One example of a pressing environmental concern is noise. For the accurate prediction of this, unsteady modelling is needed. Hence computational aeroacoustics is explored. It is also emerging that there is a critical need for coupled simulations. Hence, this area is also considered and the tensions of utilizing such simulations with the already expensive LES. This work has relevance to the general field of CFD and LES and to a wide variety of non-aerospace aerodynamic systems (e.g. cars, submarines, ships, electronics, buildings). Topics treated include unsteady flow techniques; LES and hybrids; general numerical methods; computational aeroacoustics; computational aeroelasticity; coupled simulations and turbulence and its modelling (LES, RANS, transition, VLES, URANS). The volume concludes by pointing forward to future horizons and in particular the industrial use of LES. The writing style is accessible and useful to both academics and industrial practitioners. From the reviews: "Tucker's volume provides a very welcome, concise discussion of current capabilities for simulating and modellng unsteady aerodynamic flows. It covers the various pos sible numerical techniques in good, clear detail and presents a very wide range of practical applications; beautifully illustrated in many cases. This book thus provides a valuable text for practicing engineers, a rich source of background information for students and those new to this area of Research & Development, and an excellent state-of-the-art review for others. A great achievement." Mark Savill FHEA, FRAeS, C.Eng, Professor of Computational Aerodynamics Design & Head of Power & Propulsion Sciences, Department of Power & Propulsion, School of Engineering, Cranfield University, Bedfordshire, U.K. "This is a very useful book with a wide coverage of many aspects in unsteady aerodynamics method development and applications for internal and external flows." L. He, Rolls-Royce/RAEng Chair of Computational Aerothermal Engineering, Oxford University, U.K. "This comprehensive book ranges from classical concepts in both numerical methods and turbulence modelling approaches for the beginner to latest state-of-the-art for the advanced practitioner and constitutes an extremely valuable contribution to the specific Computational Fluid Dynamics literature in Aeronautics. Student and expert alike will benefit greatly by reading it from cover to cover." Sébastien Deck, Onera, Meudon, France
Publisher: Springer Science & Business Media
ISBN: 9400770499
Category : Technology & Engineering
Languages : en
Pages : 432
Book Description
The field of Large Eddy Simulation (LES) and hybrids is a vibrant research area. This book runs through all the potential unsteady modelling fidelity ranges, from low-order to LES. The latter is probably the highest fidelity for practical aerospace systems modelling. Cutting edge new frontiers are defined. One example of a pressing environmental concern is noise. For the accurate prediction of this, unsteady modelling is needed. Hence computational aeroacoustics is explored. It is also emerging that there is a critical need for coupled simulations. Hence, this area is also considered and the tensions of utilizing such simulations with the already expensive LES. This work has relevance to the general field of CFD and LES and to a wide variety of non-aerospace aerodynamic systems (e.g. cars, submarines, ships, electronics, buildings). Topics treated include unsteady flow techniques; LES and hybrids; general numerical methods; computational aeroacoustics; computational aeroelasticity; coupled simulations and turbulence and its modelling (LES, RANS, transition, VLES, URANS). The volume concludes by pointing forward to future horizons and in particular the industrial use of LES. The writing style is accessible and useful to both academics and industrial practitioners. From the reviews: "Tucker's volume provides a very welcome, concise discussion of current capabilities for simulating and modellng unsteady aerodynamic flows. It covers the various pos sible numerical techniques in good, clear detail and presents a very wide range of practical applications; beautifully illustrated in many cases. This book thus provides a valuable text for practicing engineers, a rich source of background information for students and those new to this area of Research & Development, and an excellent state-of-the-art review for others. A great achievement." Mark Savill FHEA, FRAeS, C.Eng, Professor of Computational Aerodynamics Design & Head of Power & Propulsion Sciences, Department of Power & Propulsion, School of Engineering, Cranfield University, Bedfordshire, U.K. "This is a very useful book with a wide coverage of many aspects in unsteady aerodynamics method development and applications for internal and external flows." L. He, Rolls-Royce/RAEng Chair of Computational Aerothermal Engineering, Oxford University, U.K. "This comprehensive book ranges from classical concepts in both numerical methods and turbulence modelling approaches for the beginner to latest state-of-the-art for the advanced practitioner and constitutes an extremely valuable contribution to the specific Computational Fluid Dynamics literature in Aeronautics. Student and expert alike will benefit greatly by reading it from cover to cover." Sébastien Deck, Onera, Meudon, France
Statistical Turbulence Modelling For Fluid Dynamics - Demystified: An Introductory Text For Graduate Engineering Students
Author: Michael Leschziner
Publisher: World Scientific
ISBN: 1783266635
Category : Science
Languages : en
Pages : 424
Book Description
This book is intended for self-study or as a companion of lectures delivered to post-graduate students on the subject of the computational prediction of complex turbulent flows. There are several books in the extensive literature on turbulence that deal, in statistical terms, with the phenomenon itself, as well its many manifestations in the context of fluid dynamics. Statistical Turbulence Modelling for Fluid Dynamics — Demystified differs from these and focuses on the physical interpretation of a broad range of mathematical models used to represent the time-averaged effects of turbulence in computational prediction schemes for fluid flow and related transport processes in engineering and the natural environment. It dispenses with complex mathematical manipulations and instead gives physical and phenomenological explanations. This approach allows students to gain a 'feel' for the physical fabric represented by the mathematical structure that describes the effects of turbulence and the models embedded in most of the software currently used in practical fluid-flow predictions, thus counteracting the ill-informed black-box approach to turbulence modelling. This is done by taking readers through the physical arguments underpinning exact concepts, the rationale of approximations of processes that cannot be retained in their exact form, and essential calibration steps to which the resulting models are subjected by reference to theoretically established behaviour of, and experimental data for, key canonical flows.
Publisher: World Scientific
ISBN: 1783266635
Category : Science
Languages : en
Pages : 424
Book Description
This book is intended for self-study or as a companion of lectures delivered to post-graduate students on the subject of the computational prediction of complex turbulent flows. There are several books in the extensive literature on turbulence that deal, in statistical terms, with the phenomenon itself, as well its many manifestations in the context of fluid dynamics. Statistical Turbulence Modelling for Fluid Dynamics — Demystified differs from these and focuses on the physical interpretation of a broad range of mathematical models used to represent the time-averaged effects of turbulence in computational prediction schemes for fluid flow and related transport processes in engineering and the natural environment. It dispenses with complex mathematical manipulations and instead gives physical and phenomenological explanations. This approach allows students to gain a 'feel' for the physical fabric represented by the mathematical structure that describes the effects of turbulence and the models embedded in most of the software currently used in practical fluid-flow predictions, thus counteracting the ill-informed black-box approach to turbulence modelling. This is done by taking readers through the physical arguments underpinning exact concepts, the rationale of approximations of processes that cannot be retained in their exact form, and essential calibration steps to which the resulting models are subjected by reference to theoretically established behaviour of, and experimental data for, key canonical flows.
IUTAM Symposium on Physicochemical and Electromechanical, Interactions in Porous Media
Author: Jacques P. Huyghe
Publisher: Springer Science & Business Media
ISBN: 9781402038648
Category : Science
Languages : en
Pages : 412
Book Description
In the last decades, new experimental and numerical techniques have taken many advanced features of porous media mechanics down to practical engineering applications. This happened in areas that sometimes were not even suspected to be open to engineering ideas at all. The challenge that often faces engineers in the field of geomechanics, biomechanics, rheology and materials science is the translation of ideas existing in one field to solutions in the other. The purpose of the IUTAM symposium from which this proceedings volume has been compiled was to dive deep into the mechanics of those porous media that involve mechanics and chemistry, mechanics and electromagnetism, mechanics and thermal fluctuations of mechanics and biology. The different sections have purposely not been formed according to field interest, but on the basis of the physics involved.
Publisher: Springer Science & Business Media
ISBN: 9781402038648
Category : Science
Languages : en
Pages : 412
Book Description
In the last decades, new experimental and numerical techniques have taken many advanced features of porous media mechanics down to practical engineering applications. This happened in areas that sometimes were not even suspected to be open to engineering ideas at all. The challenge that often faces engineers in the field of geomechanics, biomechanics, rheology and materials science is the translation of ideas existing in one field to solutions in the other. The purpose of the IUTAM symposium from which this proceedings volume has been compiled was to dive deep into the mechanics of those porous media that involve mechanics and chemistry, mechanics and electromagnetism, mechanics and thermal fluctuations of mechanics and biology. The different sections have purposely not been formed according to field interest, but on the basis of the physics involved.
Advances in Turbulence
Author: Genevieve Comte-Bellot
Publisher: Springer Science & Business Media
ISBN: 3642830455
Category : Science
Languages : en
Pages : 597
Book Description
Since 1964 the main function of the European Mechanics Committee has been to arrange Euromech Colloquia. These are three- or four-day meetings for the discussion of current research on a specified and relatively narrow topic in mechanics, by about 50 specialists chosen for their active involvement in research in that topic. The organization of each Euromech Colloquium is entrusted by the Committee to one or two selected scientists of repute in the field, and these organizers are enjoined to achieve a friendly and informal forum for discussion, with a minimum of paper work and expenditure. Over 220 Euromech Colloquia have been held since 1964 (about 40 each in France, West Germany and Britain and the remainder in 18 countries in both western and eastern Europe) on a wide range of topics drawn from the mechanics of solid materials, hydrodynamics, gas dynamics and mechanical systems. The Committee believes that collectively, Euromech Colloquia have made a significant contribution to the exchange of ideas on topics in mechanics within Europe and have thereby helped to overcome the barriers to easy scientific communication in that sorely divided continent. A few years ago the European Mechanics Committee turned its atten tion to the possible need for European conferences on a larger scale than Euromech Colloquia.
Publisher: Springer Science & Business Media
ISBN: 3642830455
Category : Science
Languages : en
Pages : 597
Book Description
Since 1964 the main function of the European Mechanics Committee has been to arrange Euromech Colloquia. These are three- or four-day meetings for the discussion of current research on a specified and relatively narrow topic in mechanics, by about 50 specialists chosen for their active involvement in research in that topic. The organization of each Euromech Colloquium is entrusted by the Committee to one or two selected scientists of repute in the field, and these organizers are enjoined to achieve a friendly and informal forum for discussion, with a minimum of paper work and expenditure. Over 220 Euromech Colloquia have been held since 1964 (about 40 each in France, West Germany and Britain and the remainder in 18 countries in both western and eastern Europe) on a wide range of topics drawn from the mechanics of solid materials, hydrodynamics, gas dynamics and mechanical systems. The Committee believes that collectively, Euromech Colloquia have made a significant contribution to the exchange of ideas on topics in mechanics within Europe and have thereby helped to overcome the barriers to easy scientific communication in that sorely divided continent. A few years ago the European Mechanics Committee turned its atten tion to the possible need for European conferences on a larger scale than Euromech Colloquia.
Turbulence and Interactions
Author: Michel O. Deville
Publisher: Springer
ISBN: 366243489X
Category : Science
Languages : en
Pages : 196
Book Description
The book presents a snapshot of the state-of-art in the field of turbulence modeling and covers the latest developments concerning direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and other related topics. It provides readers with a comprehensive review of both theory and applications, describing in detail the authors’ own experimental results. The book is based on the proceedings of the third Turbulence and Interactions Conference (TI 2012), which was held on June 11-14 in La Saline-les-Bains, La Réunion, France and includes both keynote lectures and outstanding contributed papers presented at the conference. This multifaceted collection, which reflects the conference ́s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a practice-oriented guide for students, researchers and professionals in the field of computational fluid dynamics, turbulence modeling and related areas.
Publisher: Springer
ISBN: 366243489X
Category : Science
Languages : en
Pages : 196
Book Description
The book presents a snapshot of the state-of-art in the field of turbulence modeling and covers the latest developments concerning direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and other related topics. It provides readers with a comprehensive review of both theory and applications, describing in detail the authors’ own experimental results. The book is based on the proceedings of the third Turbulence and Interactions Conference (TI 2012), which was held on June 11-14 in La Saline-les-Bains, La Réunion, France and includes both keynote lectures and outstanding contributed papers presented at the conference. This multifaceted collection, which reflects the conference ́s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a practice-oriented guide for students, researchers and professionals in the field of computational fluid dynamics, turbulence modeling and related areas.
Handbook of Atomization and Sprays
Author: Nasser Ashgriz
Publisher: Springer Science & Business Media
ISBN: 1441972641
Category : Technology & Engineering
Languages : en
Pages : 922
Book Description
Atomization and sprays are used in a wide range of industries: mechanical, chemical, aerospace, and civil engineering; material science and metallurgy; food; pharmaceutical, forestry, environmental protection; medicine; agriculture; meteorology and others. Some specific applications are spray combustion in furnaces, gas turbines and rockets, spray drying and cooling, air conditioning, powdered metallurgy, spray painting and coating, inhalation therapy, and many others. The Handbook of Atomization and Sprays will bring together the fundamental and applied material from all fields into one comprehensive source. Subject areas included in the reference are droplets, theoretical models and numerical simulations, phase Doppler particle analysis, applications, devices and more.
Publisher: Springer Science & Business Media
ISBN: 1441972641
Category : Technology & Engineering
Languages : en
Pages : 922
Book Description
Atomization and sprays are used in a wide range of industries: mechanical, chemical, aerospace, and civil engineering; material science and metallurgy; food; pharmaceutical, forestry, environmental protection; medicine; agriculture; meteorology and others. Some specific applications are spray combustion in furnaces, gas turbines and rockets, spray drying and cooling, air conditioning, powdered metallurgy, spray painting and coating, inhalation therapy, and many others. The Handbook of Atomization and Sprays will bring together the fundamental and applied material from all fields into one comprehensive source. Subject areas included in the reference are droplets, theoretical models and numerical simulations, phase Doppler particle analysis, applications, devices and more.
Design and Modeling of Mechanical Systems
Author: Mohamed Haddar
Publisher: Springer Science & Business Media
ISBN: 3642371434
Category : Technology & Engineering
Languages : en
Pages : 653
Book Description
The 5th International Congress on Design and Modeling of Mechanical Systems (CMSM) was held in Djerba, Tunisia on March 25-27, 2013 and followed four previous successful editions, which brought together international experts in the fields of design and modeling of mechanical systems, thus contributing to the exchange of information and skills and leading to a considerable progress in research among the participating teams. The fifth edition of the congress (CMSM ́2013), organized by the Unit of Mechanics, Modeling and Manufacturing (U2MP) of the National School of Engineers of Sfax, Tunisia, the Mechanical Engineering Laboratory (MBL) of the National School of Engineers of Monastir, Tunisia and the Mechanics Laboratory of Sousse (LMS) of the National School of Engineers of Sousse, Tunisia, saw a significant increase of the international participation. This edition brought together nearly 300 attendees who exposed their work on the following topics: mechatronics and robotics, dynamics of mechanical systems, fluid structure interaction and vibroacoustics, modeling and analysis of materials and structures, design and manufacturing of mechanical systems. This book is the proceedings of CMSM ́2013 and contains a careful selection of high quality contributions, which were exposed during various sessions of the congress. The original articles presented here provide an overview of recent research advancements accomplished in the field mechanical engineering.
Publisher: Springer Science & Business Media
ISBN: 3642371434
Category : Technology & Engineering
Languages : en
Pages : 653
Book Description
The 5th International Congress on Design and Modeling of Mechanical Systems (CMSM) was held in Djerba, Tunisia on March 25-27, 2013 and followed four previous successful editions, which brought together international experts in the fields of design and modeling of mechanical systems, thus contributing to the exchange of information and skills and leading to a considerable progress in research among the participating teams. The fifth edition of the congress (CMSM ́2013), organized by the Unit of Mechanics, Modeling and Manufacturing (U2MP) of the National School of Engineers of Sfax, Tunisia, the Mechanical Engineering Laboratory (MBL) of the National School of Engineers of Monastir, Tunisia and the Mechanics Laboratory of Sousse (LMS) of the National School of Engineers of Sousse, Tunisia, saw a significant increase of the international participation. This edition brought together nearly 300 attendees who exposed their work on the following topics: mechatronics and robotics, dynamics of mechanical systems, fluid structure interaction and vibroacoustics, modeling and analysis of materials and structures, design and manufacturing of mechanical systems. This book is the proceedings of CMSM ́2013 and contains a careful selection of high quality contributions, which were exposed during various sessions of the congress. The original articles presented here provide an overview of recent research advancements accomplished in the field mechanical engineering.
Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles
Author: Gino Sovran
Publisher: Springer Science & Business Media
ISBN: 1468484346
Category : Technology & Engineering
Languages : en
Pages : 381
Book Description
These Proceedings contain the papers and oral discussions presented at the Symposium on AERODYNAMIC DRAG MECHANISMS of Bluff Bodies and Road Vehides held at the General Motors Research Laboratories in Warren, Michigan, on September 27 and 28, 1976. This international, invitational Symposium was the twentieth in an annual series, each one having been in a different technical discipline. The Symposia provide a forum for areas of science and technology that are of timely interest to the Research Laboratories as weIl as the technical community at large, and in which personnel of the Laboratories are actively involved. The Symposia furnish an opportunity for the exchange of ideas and current knowledge between participating research specialists from educational, industrial arid governmental institutions and serve to stimulate future research activity. The present world-wide energy situation makes it highly desirable to reduce the force required to move road vehicles through the atmosphere. A significant amount of the total energy consumed for transportation is expended in overcoming the aerodynamic resistance to motion of these vehicles. Reductions in this aerodynamic drag can therefore have a large impact on ground transportation energy requirements. Although aerodynamic development work on road vehides has been performed for many years, it has not been widely reported or accompanied by much basic research.
Publisher: Springer Science & Business Media
ISBN: 1468484346
Category : Technology & Engineering
Languages : en
Pages : 381
Book Description
These Proceedings contain the papers and oral discussions presented at the Symposium on AERODYNAMIC DRAG MECHANISMS of Bluff Bodies and Road Vehides held at the General Motors Research Laboratories in Warren, Michigan, on September 27 and 28, 1976. This international, invitational Symposium was the twentieth in an annual series, each one having been in a different technical discipline. The Symposia provide a forum for areas of science and technology that are of timely interest to the Research Laboratories as weIl as the technical community at large, and in which personnel of the Laboratories are actively involved. The Symposia furnish an opportunity for the exchange of ideas and current knowledge between participating research specialists from educational, industrial arid governmental institutions and serve to stimulate future research activity. The present world-wide energy situation makes it highly desirable to reduce the force required to move road vehicles through the atmosphere. A significant amount of the total energy consumed for transportation is expended in overcoming the aerodynamic resistance to motion of these vehicles. Reductions in this aerodynamic drag can therefore have a large impact on ground transportation energy requirements. Although aerodynamic development work on road vehides has been performed for many years, it has not been widely reported or accompanied by much basic research.
Active Flow Control II
Author: Rudibert King
Publisher: Springer Science & Business Media
ISBN: 364211735X
Category : Technology & Engineering
Languages : en
Pages : 417
Book Description
The interest in the field of active flow control (AFC) is steadily increasing. In - cent years the number of conferences and special sessions devoted to AFC org- ized by various institutions around the world continuously rises. New advanced courses for AFC are offered by the American Institute of Aeronautics and Ast- nautics (AIAA), the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), the International Centre for Mechanical Sciences (CISM), the von Karman Institute for Fluid Dynamics (VKI), to name just a few. New books on AFC are published by prominent colleagues of our field and even a new periodical, the ‘International Journal of Flow Control’, appeared. Despite these many activities in AFC it was felt that a follow-up of the highly successful ‘ACTIVE FLOW CONTROL’ Conference held in Berlin in 2006 was appropriate. As in 2006, ‘ACTIVE FLOW CONTROL II’ consisted only of invited lectures. To sti- late multidisciplinary discussions between experimental, theoretical and numerical fluid dynamics, aerodynamics, turbomachinary, mathematics, control engineering, metrology and computer science parallel sessions were excluded. Unfortunately, not all of the presented papers made it into this volume. As the preparation and printing of a book takes time and as this volume should be available at the conf- ence, the Local Organizing Committee had to set up a very ambitious time sch- ule which could not be met by all contributors.
Publisher: Springer Science & Business Media
ISBN: 364211735X
Category : Technology & Engineering
Languages : en
Pages : 417
Book Description
The interest in the field of active flow control (AFC) is steadily increasing. In - cent years the number of conferences and special sessions devoted to AFC org- ized by various institutions around the world continuously rises. New advanced courses for AFC are offered by the American Institute of Aeronautics and Ast- nautics (AIAA), the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), the International Centre for Mechanical Sciences (CISM), the von Karman Institute for Fluid Dynamics (VKI), to name just a few. New books on AFC are published by prominent colleagues of our field and even a new periodical, the ‘International Journal of Flow Control’, appeared. Despite these many activities in AFC it was felt that a follow-up of the highly successful ‘ACTIVE FLOW CONTROL’ Conference held in Berlin in 2006 was appropriate. As in 2006, ‘ACTIVE FLOW CONTROL II’ consisted only of invited lectures. To sti- late multidisciplinary discussions between experimental, theoretical and numerical fluid dynamics, aerodynamics, turbomachinary, mathematics, control engineering, metrology and computer science parallel sessions were excluded. Unfortunately, not all of the presented papers made it into this volume. As the preparation and printing of a book takes time and as this volume should be available at the conf- ence, the Local Organizing Committee had to set up a very ambitious time sch- ule which could not be met by all contributors.