Final Report Summary - T2T-VDG (Transition to turbulence in ventilated double glazing)
Turbulent flow is one of the most important forces in nature, controlling everything from the weather and the behavior of light to the behavior of individual atoms and molecules within chemical reactions or molecular assemblies embedded within materials. Turbulence is motion characterised by aperiodicity, diffusivity, undulation and dissipation. Turbulent (or chaotic) flow occurs when universal parameters that depend on the factors such as viscosity, momentum and dissipation, exceed specific values. These parameters can be used, therefore, to pinpoint (with a high degree of accuracy) where the transitions to turbulence occur. The identification of these transitions will, in turn, help us to solve one of the remaining unsolved problems in physics and mathematics.
Historically, attempts to computationally model turbulent flow and understand its origins, structure and evolution were based on statistical approaches. Since the details of the aperiodic velocity fields observed in experiments or in numerical simulations, are of little interest, one usually tries to characterise turbulent systems by their statistical and time averaged properties. Since it is widely accepted that the basic Navier–Stokes equations (NSE) of motion should provide the correct basis for the description of turbulent fluid flow it is regrettable that rather little information from the basic dynamic balances (provided by the NSEs) enters into the statistical analysis, or in numerical simulations attempting to probe the detailed structure of turbulence.
However, more recently, the sequence of bifurcation/deterministic, approach has emerged which derives its origins from nonlinear differential equations. This approach gained popularity due to the discovery of coherent solutions that are universal [Itano and Generalis PRL 102, 114501 (2009)] i.e. they exist in a variety of fluid flows, are manifold solutions within the turbulent regime and they have been obtained from first principles, without the presumption of favourable or pre-set conditions based on empirical laws. Therefore the sequence of bifurcation approach has the potential to overcome difficulties, if the appropriate (combined) tools are used. While numerical simulations based on selected techniques (c.f. difference methods) are certainly appropriate for certain regions of the bifurcation tree, these have to be combined with the elegant methods of stability theory and programmes that follow the fluid by providing information of the balanced NSE on moving frames that are following the fluid flow.
Pioneering numerical techniques, that have not been employed before concurrently, were proposed in this project. They can capture the transition to turbulence of shear flow and in the process offer the capability of proposing methods for the state of the art control of such transitions. The proposed methods can enhance the calculation of fluid flow by identifying the hierarchical bifurcation of the evolving states and can be captured in an engineering orientated software (computational) tool that will aid the real life implementation of these, otherwise, generalised but tried mathematical techniques. In this sense the predictive power of the underlying mathematical modelling techniques, upon which the engineering tool will be crucially dependent, will display their true potential. The novel methods can be used to pinpoint the transition of the flow from its laminar (basic) state to its fully developed (turbulent) state with pinpoint accuracy and for arbitrary geometrical configurations. The ensuing stability analysis is a unique attribute of this mathematically engineered software.
Our software, in brief, that unified a multitude of mathematical techniques, that compliment each other, bringing together Galerkin, spectral, finite element and analytical methods spanning across a variety of disciplines techniques, is able to oversee the development of the fluid flow throughout its evolution, from birth to turbulent arrival. It was the ultimate aim of this set of programmes to apply the resulting software to complex configurations applicable to a variety of every day engineering configurations. Simple geometries were considered at first to act as benchmarks and common ground for the two different state of the art software avenues at our disposal: the proprietary code already developed at Aston University and a suite of programmes developed this project. We intend to use the results of our studies for the design and industrial implementation of a new concept that is at the heart of European energy, environment and socioeconomic focus: ventilated double glazing.
In this project we analysed the linear stability of the secondary flow against the general type of three-dimensional disturbances in order to identify possible bifurcation points for the tertiary flow and from this we obtained the tertiary and higher order bifurcating flows that arise at the bifurcation points. Finally we analysed the stability of the tertiary flows obtained here so that we can identify possible bifurcation points for the quaternary and higher order flows via a numerical study. This step provided sequential ‘snapshots’ of the transitions to turbulence. It enabled us to capture states that are intermittent or lead to connection branches between the states that have been identified as secondary, tertiary and so on via the other two methods that are available to us. For higher order states this procedure will become more and more computationally time-consuming. Thus the linear stability analysis of higher order states was based on the established Newton-Raphson method for the nonlinear eigenvalue problem instead of solving full eigenvalue problem points. This will be done sequentially in the toolbox depending on the state of the bifurcation tree analysis.
This research was disseminated via Journal publications in high impact factor journals, and conference dissemination, as outlined below. In addition, a book proposal for a research monograph on the subject is currently constructed, in order to outline the essential sequential steps for the construction of toolkit, with examples of the shear fluid flows examined.
The Fellow, Dr Takeshi Akinaga, engage with the UK Knowledge Transfer Network’s to transfer knowledge to relevant UK industry. The KTN’s focus on a range of themes, the fellow will work with the following KTN’s: Applied Maths - https://ktn.innovateuk.org/web/mathsktn(odnośnik otworzy się w nowym oknie); Modern Built Environment - https://ktn.innovateuk.org/web/modernbuiltktn(odnośnik otworzy się w nowym oknie); Space - https://ktn.innovateuk.org/web/space(odnośnik otworzy się w nowym oknie). Each KTN has a dedicated member of staff to organize industry related activities. The Fellow made contact with the lead to organize a series of practical seminars to transfer findings and relevant detail to a selected audience of industry groups.
During the duration of the project, therefore, the following contacts with industry were established:
• Contact with GTS (GLASS TECHNOLOGY SERVICES LTD) about techniques for the development of the next generation double glazing windows;
• SEAWATER GREENHOUSE Ltd, about the construction of environmentally friendly greenhouses in hot climates, via implementation of our computational results.
During the project the host Dr Sotos Generalis and the Marie Curie Fellow commenced active interactions with academic members of staff in the Mechanical, Chemical and Electrical Engineering groups. The interaction involved the formulation of the laminar state analytically (for laminar flow in complex curvilinear geometries) and numerically the establishment of transition diagrams en route to turbulence, with the multitude of applications discussed above. We have also started studying desalination in collaboration with Prof. Philip Davies of Aston University and Prof. Jamel Orfi of King Saud University, Saudi Arabia, exclusively based on the T2T-VDG developed software.
Training/workshops/conferences given/participated by the fellow:
• WORKSHOP APPLICATION OF MATHEMATICAL MODELS IN SCIENCE AND ENGINEERING 19 Mar 2013 (Transition to turbulence of flow in ventilated double glazing using a spectral method)
• Water Conference, Aston University, July 2014
• Cyprus EU Conference 5-6 November 2012: coherent turbulence (abstract, poster and a document in proceedings)
• ETC 12 conference in Lyon 1-4 September 2013 (paper in proceedings)
• Talk/Seminar at the University of Sheffield 22 October 2014
Throughout the project the Fellow provided sequential research methodology and skill transfer through the training and co-supervision of Aston postgraduate and research students and research fellows. This took place through lectures on the Masters programmes and through direct supervision of research students in FDG on new projects in shear flow with/without complex geometries. The Fellow introduced postgraduate and research students in the stability and transition of flow past bluff bodies, transfered knowledge in establishing bifurcation analysis via time marching techniques and introduce direct flow visualization in Masters programmes through programmed lectures and to research students directly through co-supervision.
Additionally the IIFellow trained the Fellows and Ph.D students at FDG on research methodology and lab skills via a series of lectures, seminars and individual and focused group discussion in four areas: (i) Research background study on turbulence theories; (ii) Planning and implement research project and lab measurement skills. The outstanding research achievements and personal experience and skills has put the IIF in the best position to train Aston’s postdoctoral fellows, Ph.D Master and Final Year undergraduate students. This procedure will create the scientific basis for transferring knowledge to young able scientists for the further development of the software that the host, Dr Sotos Generalis and the Fellow, Dr Akinaga developed. In this respect Dr Akinaga supervised the MSc on venlo-type greenhouses (as appended in the relevant section), with a successful defence of it by the postgraduate student. Dr Akinaga copiously assisted the student to develop software for the project, which was commented highly by the examiners during the viva voce of the MSc.
The Fellow and host implemented research knowledge transfer through the extensive network of the host and that of Bayreuth University. Knowledge on parallel computing implementation to fluid dynamical problems, insight gained by the identification of the bifurcation tree of T2T-VDG, the introduction of complex geometries and the concurrent study of a generalized type shear flow (through the interaction of flow present in T2T-VDG and that of volumetrically heated flow), created a knowledge package, in the form of software tool (named in the application as TAGF), that will be of enormous benefit to Europe in general. The intense collaboration fro Prof Dr Friedrich Busse on Taylor Couette flow is now being consolidated by the high impact journal publications, as stated on the on-line report.
Finally the Fellow was instrumental in assisting Dr Sotos Generalis to apply for a variety of research projects and all these applications are now pending review.
It is the aim of the host to actively ‘closely’ collaborate with the Fellow for many years to come for the benefit of science and industry in Europe and sequentially worldwide.
Historically, attempts to computationally model turbulent flow and understand its origins, structure and evolution were based on statistical approaches. Since the details of the aperiodic velocity fields observed in experiments or in numerical simulations, are of little interest, one usually tries to characterise turbulent systems by their statistical and time averaged properties. Since it is widely accepted that the basic Navier–Stokes equations (NSE) of motion should provide the correct basis for the description of turbulent fluid flow it is regrettable that rather little information from the basic dynamic balances (provided by the NSEs) enters into the statistical analysis, or in numerical simulations attempting to probe the detailed structure of turbulence.
However, more recently, the sequence of bifurcation/deterministic, approach has emerged which derives its origins from nonlinear differential equations. This approach gained popularity due to the discovery of coherent solutions that are universal [Itano and Generalis PRL 102, 114501 (2009)] i.e. they exist in a variety of fluid flows, are manifold solutions within the turbulent regime and they have been obtained from first principles, without the presumption of favourable or pre-set conditions based on empirical laws. Therefore the sequence of bifurcation approach has the potential to overcome difficulties, if the appropriate (combined) tools are used. While numerical simulations based on selected techniques (c.f. difference methods) are certainly appropriate for certain regions of the bifurcation tree, these have to be combined with the elegant methods of stability theory and programmes that follow the fluid by providing information of the balanced NSE on moving frames that are following the fluid flow.
Pioneering numerical techniques, that have not been employed before concurrently, were proposed in this project. They can capture the transition to turbulence of shear flow and in the process offer the capability of proposing methods for the state of the art control of such transitions. The proposed methods can enhance the calculation of fluid flow by identifying the hierarchical bifurcation of the evolving states and can be captured in an engineering orientated software (computational) tool that will aid the real life implementation of these, otherwise, generalised but tried mathematical techniques. In this sense the predictive power of the underlying mathematical modelling techniques, upon which the engineering tool will be crucially dependent, will display their true potential. The novel methods can be used to pinpoint the transition of the flow from its laminar (basic) state to its fully developed (turbulent) state with pinpoint accuracy and for arbitrary geometrical configurations. The ensuing stability analysis is a unique attribute of this mathematically engineered software.
Our software, in brief, that unified a multitude of mathematical techniques, that compliment each other, bringing together Galerkin, spectral, finite element and analytical methods spanning across a variety of disciplines techniques, is able to oversee the development of the fluid flow throughout its evolution, from birth to turbulent arrival. It was the ultimate aim of this set of programmes to apply the resulting software to complex configurations applicable to a variety of every day engineering configurations. Simple geometries were considered at first to act as benchmarks and common ground for the two different state of the art software avenues at our disposal: the proprietary code already developed at Aston University and a suite of programmes developed this project. We intend to use the results of our studies for the design and industrial implementation of a new concept that is at the heart of European energy, environment and socioeconomic focus: ventilated double glazing.
In this project we analysed the linear stability of the secondary flow against the general type of three-dimensional disturbances in order to identify possible bifurcation points for the tertiary flow and from this we obtained the tertiary and higher order bifurcating flows that arise at the bifurcation points. Finally we analysed the stability of the tertiary flows obtained here so that we can identify possible bifurcation points for the quaternary and higher order flows via a numerical study. This step provided sequential ‘snapshots’ of the transitions to turbulence. It enabled us to capture states that are intermittent or lead to connection branches between the states that have been identified as secondary, tertiary and so on via the other two methods that are available to us. For higher order states this procedure will become more and more computationally time-consuming. Thus the linear stability analysis of higher order states was based on the established Newton-Raphson method for the nonlinear eigenvalue problem instead of solving full eigenvalue problem points. This will be done sequentially in the toolbox depending on the state of the bifurcation tree analysis.
This research was disseminated via Journal publications in high impact factor journals, and conference dissemination, as outlined below. In addition, a book proposal for a research monograph on the subject is currently constructed, in order to outline the essential sequential steps for the construction of toolkit, with examples of the shear fluid flows examined.
The Fellow, Dr Takeshi Akinaga, engage with the UK Knowledge Transfer Network’s to transfer knowledge to relevant UK industry. The KTN’s focus on a range of themes, the fellow will work with the following KTN’s: Applied Maths - https://ktn.innovateuk.org/web/mathsktn(odnośnik otworzy się w nowym oknie); Modern Built Environment - https://ktn.innovateuk.org/web/modernbuiltktn(odnośnik otworzy się w nowym oknie); Space - https://ktn.innovateuk.org/web/space(odnośnik otworzy się w nowym oknie). Each KTN has a dedicated member of staff to organize industry related activities. The Fellow made contact with the lead to organize a series of practical seminars to transfer findings and relevant detail to a selected audience of industry groups.
During the duration of the project, therefore, the following contacts with industry were established:
• Contact with GTS (GLASS TECHNOLOGY SERVICES LTD) about techniques for the development of the next generation double glazing windows;
• SEAWATER GREENHOUSE Ltd, about the construction of environmentally friendly greenhouses in hot climates, via implementation of our computational results.
During the project the host Dr Sotos Generalis and the Marie Curie Fellow commenced active interactions with academic members of staff in the Mechanical, Chemical and Electrical Engineering groups. The interaction involved the formulation of the laminar state analytically (for laminar flow in complex curvilinear geometries) and numerically the establishment of transition diagrams en route to turbulence, with the multitude of applications discussed above. We have also started studying desalination in collaboration with Prof. Philip Davies of Aston University and Prof. Jamel Orfi of King Saud University, Saudi Arabia, exclusively based on the T2T-VDG developed software.
Training/workshops/conferences given/participated by the fellow:
• WORKSHOP APPLICATION OF MATHEMATICAL MODELS IN SCIENCE AND ENGINEERING 19 Mar 2013 (Transition to turbulence of flow in ventilated double glazing using a spectral method)
• Water Conference, Aston University, July 2014
• Cyprus EU Conference 5-6 November 2012: coherent turbulence (abstract, poster and a document in proceedings)
• ETC 12 conference in Lyon 1-4 September 2013 (paper in proceedings)
• Talk/Seminar at the University of Sheffield 22 October 2014
Throughout the project the Fellow provided sequential research methodology and skill transfer through the training and co-supervision of Aston postgraduate and research students and research fellows. This took place through lectures on the Masters programmes and through direct supervision of research students in FDG on new projects in shear flow with/without complex geometries. The Fellow introduced postgraduate and research students in the stability and transition of flow past bluff bodies, transfered knowledge in establishing bifurcation analysis via time marching techniques and introduce direct flow visualization in Masters programmes through programmed lectures and to research students directly through co-supervision.
Additionally the IIFellow trained the Fellows and Ph.D students at FDG on research methodology and lab skills via a series of lectures, seminars and individual and focused group discussion in four areas: (i) Research background study on turbulence theories; (ii) Planning and implement research project and lab measurement skills. The outstanding research achievements and personal experience and skills has put the IIF in the best position to train Aston’s postdoctoral fellows, Ph.D Master and Final Year undergraduate students. This procedure will create the scientific basis for transferring knowledge to young able scientists for the further development of the software that the host, Dr Sotos Generalis and the Fellow, Dr Akinaga developed. In this respect Dr Akinaga supervised the MSc on venlo-type greenhouses (as appended in the relevant section), with a successful defence of it by the postgraduate student. Dr Akinaga copiously assisted the student to develop software for the project, which was commented highly by the examiners during the viva voce of the MSc.
The Fellow and host implemented research knowledge transfer through the extensive network of the host and that of Bayreuth University. Knowledge on parallel computing implementation to fluid dynamical problems, insight gained by the identification of the bifurcation tree of T2T-VDG, the introduction of complex geometries and the concurrent study of a generalized type shear flow (through the interaction of flow present in T2T-VDG and that of volumetrically heated flow), created a knowledge package, in the form of software tool (named in the application as TAGF), that will be of enormous benefit to Europe in general. The intense collaboration fro Prof Dr Friedrich Busse on Taylor Couette flow is now being consolidated by the high impact journal publications, as stated on the on-line report.
Finally the Fellow was instrumental in assisting Dr Sotos Generalis to apply for a variety of research projects and all these applications are now pending review.
It is the aim of the host to actively ‘closely’ collaborate with the Fellow for many years to come for the benefit of science and industry in Europe and sequentially worldwide.