Numerical Simulation of Turbulence
International Combustion Engines
Turbulence in the core of the Earth
Advanced Power Generation
Professor J.E. Ffowcs Williams
Professor A.P. Dowling
Dr N. Peake
Research is aimed at understanding, predicting and eliminating instability in combustors. This area is of considerable practical importance because, to meet increasingly stringent chemical emission requirements, combustors need to operate close to instability. A number of different approaches to the problem are being developed, including detailed acoustic analyses with simple combustion models(A26,A37). Computational Fluid Dynamics(A9,A11,A54) and experiment. Advances in understanding the interaction between acoustic waves and combustion and how it leads to instability have been obtained(A25). The research involves extensive interactions and collaborations with other academics and with industry, and our work is sponsored by gas turbine manufacturers, EPSRC and the EU.
Active control not only provides a method of avoiding sound(A45), it also provides a new means of eliminating instability in gas turbines(A24) and has been shown to be feasible even at full-scale(A44). Both adaptive and robust controllers show exciting potential(A15). A new type of adaptive controller has been developed to eliminate combustion instabilities in collaboration with MIT(A30). Application has been made for a joint MIT/University of Cambridge patent.
Tyre noise is also a focus of research in the Department. Our work aims to provide a better understanding of the mechanisms governing tyre/road noise generation so that quiet tyres can be designed. We have shown that the geometry of the contact region between the tyre and the road can amplify this sound by as much as 20 dB. Numerical predictions for this amplification have been obtained and are in excellent agreement with measurements(A41). Insight into the physical mechanisms has been obtained through asymptotic analyses(A33). Close interaction with vehicle and tyre manufacturers is maintained through a DTI/DETR/EPSRC LINK project.
The interaction of sound and flow is a major theme(A28,A31). Unsteady vorticity can be a significant source of noise(A40). In other configurations, it can absorb acoustic energy(A26), a mechanism that we are currently seeking to exploit to provide a passive means of eliminating combustion instability. Helicopters in forward flight make a loud and characteristically impulsive sound. This is due to patches of supersonic flow near the blades, which occurs even through the blades themselves are subsonic. We are making use of CFD, with high-resolution shock capturing techniques, to calculate the flow field, placing particular emphasis on simple models that describe and explain the dynamic changes in the acoustic sources in flight. An extension of the acoustic analogy is used to predict the far field sound.
Our studies of unsteady heat transfer found experimental evidence for some predictable effects in turbulent pipe flow(A5), and various papers involving the stability of flow interaction with sound have been published during the year(A16,A42,A46).
Dr R.S. Cant
Professor K.N.C. Bray
Activity in Computational Combustion has centred on the three major topic areas of Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) simulation. Currently the group consists of five postdoctoral researchers and three PhD students. Close collaboration is being maintained with the CFD Laboratory (Professor WN Dawes) and with the Acoustics Laboratory (Professor AP Dowling).
DNS of turbulent flames is continuing to provide a great deal of useful insight and statistical data in support of modelling efforts(A12,A13). The technique involves the solution of the compressible reacting Navier-Stokes equations in three dimensions and time, without modelling of turbulence and with the largest possible range of length scales included in the problem. In computational terms this is very expensive and the work has made use of the Hitachi SR2201 supercomputer in Cambridge as well as the Cray T3E National Facility in Manchester. The group has recently carried out the largest premixed combustion DNS reported anywhere in the world to date(A38,A39). This work is supported mainly by EPSRC.
New developments have taken place in modelling turbulent names(A10,A23) and in the application of LES to turbulent combustion, using an approach based on the flame surface density(A34,A35). Support for this work has come from Alstom Power. This class of modelling is showing great promise for the future and further work is planned.
Modelling of industrial systems using RANS has continued, with applications to internal combustion engines(A48), accidental explosions in the oil and gas industry(A6,A8,A9), and lean premixed gas turbine combustors(A7,A11). The majority of the industrial combustion problems tackled involve significant unsteadiness of the flow together with complex geometrical features that are not easily handled using standard CFD. A good example is acoustically-coupled combustion instability in gas turbines, which is proving to be fruitful area for both fundamental and applied research. Sponsors for the RANS work include EPSRC, Ricardo Consulting Engineers, Shell Research and Rolls-Royce.
Dr P.A. Davidson
We are examining the behaviour of two-dimensional turbulence using direct numerical simulations (DNS). Particular emphasis is on the behaviour of the large scales, which are the hardest to compute accurately. We have shown that the periodic boundary conditions commonly used in DNS pollute the large-scale dynamics by imposing artificial long-range correlations. In order to produce simulations which are not heavily influenced by the artificial symmetry planes it is necessary to have a domain size which is at least 100 large eddy sizes. Typical DNS studies have a domain size of around 3 large eddy sizes. (Funded by FLUENT Inc.)
Dr N. Collings
The Engine Emissions Instrumentation and Control group (co-directed by Keith Glover, Professor of Control Engineering) has continued to make significant advances. Strong industrial support from the Ford Motor Company, and from the EPSRC, has enabled us to continue to employ first class facilities for IC engine research, and maintain a strong group. Our existing instrumentation for fast NOx measurement was used on a collaborative project with the University of Oxford. A new instrument has been under development for the measurement of CO2 emissions, which promises to be of value in understanding the exact detail of engine cold start, and exhaust gas recirculation transient behaviour. Work has continued in the area of catalyst after-treatment devices, especially their transient characteristics. A significant breakthrough occurred in our attempts to demonstrate the Homogeneous Charge Compression Ignition (HCCI) concept on conventional 4-stroke engines. We were able to reproduce the concept on a conventional engine where previously this had only been possible by using special fuels, or very high compression ratios. In principle, the development could lead to a high efficiency, low emissions operating point for part load operation of gasoline engines. Our activity in engine particle emissions is growing rapidly.
Dr T. Alboussière
Dr P.A. Davidson
The convection induced by thermal or solute buoyancy has continued to be investigated analytically and numerically for configurations related to crystal growth in the presence of a steady magnetic field. In the thermal diffusive case(A2) the problem is linear but when convective heat transfer becomes significant, a totally different velocity structure appears(A17,A43) with new boundary layers. Such studies show clearly the effect of applying a steady magnetic field on the expected convection velocity. In addition, some work has been done on the initial transient of solute incorporation during crystal growth(A32).
Experimental projects on magnetohydrodynamic turbulence have received funding from the EPSRC and the Leverhulme Trust. They relate to metallurgy and to the more and more frequent use of magnetic fields to control continuous casting. As a first step towards the study of turbulence, the study of a single vortex(A49,A50) provides a new insight of the action of steady magnetic fields when inertial effects are significant. Further studies on turbulence are planned, in particular its transition from a 3D state to a 2D state when the magnetic field is strong. Moreover, transition to turbulence and turbulent state of Hartmann layers predicted analytically(A3,A4) will be investigated experimentally. Contacts with Corus (previously British Steel) have been made on this point since heat transfer at the solid-liquid interface can be related to the behaviour of such boundary layers.
Dr P.A. Davidson
The earth's magnetic field is maintained against the forces of natural decay by turbulent motion within its core. Although the precise detail of how this is achieved is still unknown, it is thought by some that the small-scale eddies play an important rôle, teasing out the observed dipole magnetic field from a more intense azimuthal field which is trapped inside the earth's liquid core. We are examining the dynamics of these small-scale eddies, which are heavily influenced by Coriolis and Lorentz forces.
Professor J.B. Young
Several quite different aspects of particle transport and droplet formation in two-phase flows have provided recent research interest. In naturally nucleated droplet flows which occur in many industrial processes, vast numbers of submicrometre droplets form by the process of homogeneous nucleation. The interphase heat and mass transfer processes give rise to many interesting phenomena, particularly in supersonic flows where shock waves occur. A study of the interaction of shock waves with zones of homogeneous nucleation(A52) has shown that the droplet size distribution can be radically altered by the waves. Calculations of nucleating flows are computationally very expensive. Because this seriously restricts the scope of multi-dimensional calculations, an elegant new analytical method for predicting rapidly expanding nucleating flows has been developed(A53). With further work, fast and accurate calculations of three-dimensional nucleating flows should be feasible.
Small droplets and particles interact with the turbulence in wall boundary layers and migrate to solid surfaces under the influence of turbophoresis, a newly-discovered transport mechanism causing particles to drift in the direction of decreasing turbulence levels. A new theory of particle deposition has been developed, the current area of interest being the effects of 'particle memory'. This refers to the fact that particle behaviour is sometimes controlled, not by local turbulence levels, but by the state of the fluid through which the particles have recently passed. It is of particular importance in the laminar sublayer close to solid surfaces. In non-isothermal boundary layers, thermophoresis is also an important mechanism for particle transport. A theoretical and experimental study funded by PowerGen has been established to investigate this phenomenon and its effect on the transport of small ash particles to turbine blades in coal-fired gas turbines.
Droplets and particles which are tens of micrometres in diameter pay little attention to the turbulence but have their own special problems. Calculations have traditionally used the 'Lagrangian tracking' approach which provides an efficient method for computing the particle velocity field but is rather less successful for particle concentration. Work to overcome this deficiency has resulted in a new Lagrangian method which allows the simultaneous calculation of particle velocity and concentration without significant computational overheads. Another project, funded jointly by Rolls-Royce and the Civil Aviation Authority, is investigating the effects on performance of the ingestion of tropical rain into aero-engines. Topics addressed include the deposition and movement of water on the blades and casing, and the breakup of droplets re-entrained into the flow from the trailing edges.
Professor J.B. Young
The global power generation industry is currently undergoing a technical revolution due to the widespread availability of natural gas, the rapid development of industrial gas turbines and the deregulation of electricity generation. Many new types of high efficiency power plant are currently under investigation by industry and university(A36). A collaboration between Cambridge and Rolls-Royce includes (i) a thermodynamic study of the cooling of gas turbine blades and the quantification of the cooling losses, (ii) an investigation of the possibilities of gas turbine cycles with water and steam injection, and (iii) a project to develop a computational model of the Rolls-Royce integrated-planar solid oxide fuel cell. The latter is particularly challenging, involving as it does brand new technology. Fuel cell/gas turbine systems are widely tipped as the most likely candidates to dominate the mid-range stationary power generation scene by 2020 and it is important that Cambridge should be involved in their development.
A1. Abu-Orf, G.M., Cant, R.S A turbulent reaction rate model for premixed turbulent combustion in spark-ignition engines. Combustion and Flame, 122, (3), 233-252 (August 2000).
A2. Alboussière, T., Garandet, J.P., Moreau, R. Asymptotic MHD convection and symmetries. ICTAM 2000: International Congress of Theoretical and Applied Mechanics, 20th IUTAM Congress, Chicago, USA (August/September 2000).
A3. Alboussière, T., Lingwood, R.J. A model for the turbulent Hartmann layer. Physics of Fluids, 12, (6), 1535-1543 (June 2000).
A4. Alboussière, T., Lingwood, R.J. Hartmann layers and turbulence. PAMIR 2000, Proceedings, 4th International PAMIR Conference on Magnetohydrodynamic at Dawn of Third Millennium, Presqu' île de Giens, France (September 2000).
A5. Barker, A.R., Ffowcs Williams, J.E. Transient measurements of the heat transfer coefficient in unsteady, turbulent pipe flow. International Journal of Heat and Mass Transfer, 43, (17), 3197-3207 (September 2000).
A6. Birkby, P., Cant, R.S. Unstructured adaptive methods for turbulent combustion. 8th International Conference on Numerical Combustion, Amelia Island Plantation, FL, USA (March 2000).
A7. Birkby, P., Cant, R.S., Dawes, W.N., Demargne, A.A.J., Dhanasekaran, P.C., Kellar, W.P., Rycroft, N.C., Savill, A.M., Eggels, R.L.G.M., Jennions, I.K. CFD analysis of a complete industrial lean premixed gas turbine combustor. ASME Turbo Expo 2000, 45th ASME International Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, Munich, Germany, ASME paper 2000-GT-0131 (May 2000).
A8. Birkby, P., Cant, R.S., Savill, A.M. The application of a Laminar flamelet model to confined explosion hazards. Flow Turbulence and Combustion, 63, (1-4), 361-377 (2000).
A9. Bray, K.N.C., Cant, R.S., Savill, A.M. The modelling of obstructed explosions. Proceedings, 3rd International Symposium on Scale Modelling, ISSM3, Nagoya, Japan (September 2000).
A10. Bray, K.N.C., Champion, M., Libby, P.A. Premixed flames in stagnating turbulence. Part IV, a new theory for the Reynolds stresses and Reynolds fluxes applied to impinging flows. Combustion and Flame, 120, (1-2), 1-18 (January 2000).
A11. Brookes, S.J., Cant, R.S., Dupère, I.D.J., Dowling, A.P. Computational modelling of self-excited combustion instabilities. ASME Turbo Expo 2000, 45th ASME International Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, Munich, Germany, ASME paper 2000-GT-0104 (May 2000). Published in: Transactions of the ASME, Journal of Engineering for Gas Turbines and Power, 123, (2), 322-326 (April 2001).
A12. Cant, R.S. Direct numerical simulation of premixed turbulent flames. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 357, (1764), 3583-3604 (December 1999).
A13. Cant, R.S. Premixed turbulent combustion: DNS into modelling. Invited Plenary Lecture. 8th International Conference on Numerical Combustion, Amelia Island Plantation, FL, USA (March 2000).
A14. Cant, R.S. Simulation and modelling of turbulent premixed flames. Invited Lecture. GAMM 2000, Gesellschaft für Angewandte Mathematik und Mechanik, Annual Conference, Göttingen, Germany (April 2000).
A15. Chu, Y.C., Dowling, A.P., Glover, K., Evesque, S.M.N. Algorithms for feedback control of combustion oscillations. Proceedings, 38th IEEE Conference on Decision and Control, Pheonix, AZ, USA, 3, 2863-2868 (December 1999).
A16. Cooper, A., Peake, N. Trapped acoustic modes in aeroengine intakes with swirling flow. Journal of Fluid Mechanics, 419, 151-175 (September 2000).
A17. Cowley, M.D., Maclean, D.J., Alboussière, T. Natural convection in rectangular enclosures of arbitrary orientation with magnetic field vertical - problem revisited. PAMIR 2000, Proceedings, 4th International PAMIR Conference Magnetohydrodynamic at Dawn of Third Millennium, Presqu' île de Giens, France (September 2000).
A18. Davidson, P.A. An energy criterion for the linear stability of conservative flows. Journal of Fluid Mechanics, 402, 329-348 (January 2000).
A19. Davidson, P.A. MHD turbulence and the geodynamo. PAMIR 2000, Proceedings, 4th International PAMIR Conference Magnetohydrodynamic at Dawn of Third Millennium, Presqu' île de Giens, France (September 2000).
A20. Davidson, P.A. Overcoming instabilities in aluminium reduction cells - a route to cheaper aluminium. Materials Science and Technology, 16, (5), 475-479 (May 2000).
A21. Davidson, P.A. Was Loitsiansky correct? A review of the arguments. Journal of Turbulence, 1, 006 (August 2000). Electronic journal only, see http://www.iop.org/EJ/.
A22. Davidson, P.A., He, X., Lowe, A.J. Flow transitions in vacuum-arc remelting. Materials Science and Technology, 16, (6), 699-711 (June 2000).
A23. Domingo, P., Bray, K.N.C. Laminar flamelet expressions for pressure fluctuation terms in second moment models of premixed turbulent combustion. Combustion and Flame, 121, (4), 555-574 (June 2000).
A24. Dowling., A.P Active control of instabilities of gas turbines. NATO RTO Applied Vehicle Technology Panel Symposium, Active Control Technology for Enhanced Performance Operational Capabilities of Military Aircraft, Land Vehicles and Sea Vehicles, Braunschweig, Germany (May 2000). Published as: NATO RTO Meeting Proceedings 51 (NATO RTO, 2001). CD Rom ISBN 928370018X.
A25. Dowling, A.P. The 1999 Lanchester Lecture - Vortices, sound and flames - a damaging combination. Aeronautical Journal, 104, (1033), 105-116 (March 2000).
A26. Dowling, A.P., Hubbard, S. Instability in lean premixed combustors. Proceedings of the Institution of Mechanical Engineers Part A, Journal of Power and Energy, 214, (A4), 317-332 (2000).
A27. Dupère, I.D.J., Dowling, A.P. Absorption of sound near abrupt area expansions. AIAA Journal, 38, (2), 193-202 (February 2000).
A28. Evers, I., Peake, N. Noise generation by high-frequency gusts interacting with an airfoil in transonic flow. Journal of Fluid Mechanics, 411, 91-130 (May 2000).
A29. Evers, I., Peake, N. Steady and unsteady flow in a transonic cascade with shocks. 6th AIAA/CEAS Aeroacoustics Conference and Exhibit, Lahaina, Hawaii, USA, AIAA paper 2000-1990 (June 2000).
A30. Evesque, S.M.N., Dowling, A.P., Annaswamy, A.M. Adaptive algorithms for control of combustion. NATO RTO Applied Vehicle Technology Panel Symposium, Active Control Technology for Enhanced Performance Operational Capabilities of Military Aircraft, Land Vehicles and Sea Vehicles, Braunschweig, Germany (May 2000). Published as: NATO RTO Meeting Proceedings 51 (NATO RTO, 2001). CD Rom ISBN 928370018X.
A31. Ffowcs Williams, J.E., Möhring, W. Control action for stabilising free shear layers. Journal of Fluid Mechanics, 404, 27-46 (February 2000).
A32. Garandet, J.P., Corre, S., Kaddeche, S., Alboussière, T. The influence of convection on the duration of the initial solute transient in alloy crystal growth. Journal of Crystal Growth, 209, (4), 970-982 (February 2000).
A33. Graf, R.A.G., Kuo, C-Y., Dowling, A.P., Graham., W.R. Horn amplification at a tyre/road interface - Part I: Experiment and computation. INTERNOISE 99, Proceedings, 1999 International Congress on Noise Control Engineering, Fort Lauderdale, FL, USA (December 1999); Edited by J. Cushieri, S. Glegg, Y. Yong, 119-124 (Institute of Noise Control Engineering, Poughkeepsie, USA, 1999). ISBN 0962207233.
A34. Hawkes, E.R., Cant, R.S. A flame surface density approach to large eddy simulation of premixed turbulent combustion. 28th International Symposium on Combustion, Edinburgh (July/August 2000).
A35. Hawkes, E.R., Cant, R.S. Large eddy simulation of premixed turbulent combustion. 8th International Conference on Numerical Combustion, Amelia Island Plantation, FL, USA (March 2000).
A36. Horlock, J.H., Young, J.B., Manfrida, G. Exergy analysis of modern fossil fuel power plants. Transactions of the ASME, Journal of Engineering for Gas Turbines and Power, 122, (1), 1-7 (January 2000).
A37. Hubbard, S., Dowling, A.P. Acoustic resonances of an industrial gas turbine combustion system. ASME Turbo Expo 2000, 45th ASME International Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, Munich, Germany, ASME paper 2000-GT-0094 (May 2000).
A38. Jenkins, K.W., Cant, R.S. Direct numerical simulation for turbulent flame kernels. 8th International Conference on Numerical Combustion, Amelia Island Plantation, FL, USA (March 2000).
A39. Jenkins, K.W., Cant, R.S. Direct numerical simulation of turbulent flame kernels. Recent advances in DNS and LES: Proceedings, 2nd AFOSR Conference, New Brunswick, NJ, USA (June 1999); Edited by D. Knight, L. Sakell, 191-202. Fluid Mechanics and Its Applications 54 (Kluwer Academic, 1999). ISBN 0792360044.
A40. Kuo, C-Y., Dowling, A.P. Acoustics of a two-dimensional compact jet impinging normally onto a flat plate. Journal of Fluid Mechanics, 414, 251-284 (July 2000).
A41. Kuo, C-Y, Graf, R.A.G., Dowling, A.P., Graham, W.R. Horn amplification at a tyre/road interface - Part II: Ray theory and experiment. INTERNOISE 99, Proceedings, 1999 International Congress on Noise Control Engineering, Fort Lauderdale, FL, USA (December 1999); Edited by J. Cushieri, S. Glegg, Y. Yong, 125-130 (Institute of Noise Control Engineering, Poughkeepsie, USA, 1999). ISBN 0962207233.
A42. Lingwood, R.J., Peake, N. On the casual behaviour of flow over a compliant wall. Journal of Fluid Mechanics, 396, 319-344 (October 1999).
A43. Maclean, D.J., Alboussière, T., Cowley, M.D. Buoyancy driven convection in a tall cavity with a uniform horizontal magnetic field. PAMIR 2000, 4th International PAMIR Conference on Magnetohydrodynamic at Dawn of Third Millennium, Presqu' île de Giens, France (September 2000).
A44. Moran, A.J., Steele, D., Dowling, A.P. Active control of combustion and its applications. NATO RTO Applied Vehicle Technology Panel Symposium, Active Control Technology for Enhanced Performance Operational Capabilities of Military Aircraft, Land Vehicles and Sea Vehicles, Braunschweig, Germany (May 2000). Published as: NATO RTO Meeting Proceedings 51 (NATO RTO, 2001). CD Rom ISBN 928370018X.
A45. Peake, N., Crighton, D.G. Active control of sound. Annual Review of Fluid Mechanics, volume 32; Edited by J.L. Lumley, M. Van Dyke, W.L. Reed, 137-164 (Annual Reviews Inc, 2000). ISBN 0824307321.
A46. Peake, N., Lingwood, R.J. A causal stability analysis of the boundary layer over a compliant wall. Laminar Turbulent Transition, Proceedings, IUTAM Symposium, Sedona, AZ, USA (September 1999); Edited by H.F. Fasel, W.S. Saric, 51-56 (Springer-Verlag, 1999). ISBN 3540679472.
A47. Prosser, R., Cant, R.S. Wavelet operators in combustion simulation. 8th International Conference on Numerical Combustion, Amelia Island Plantation, FL, USA (March 2000).
A48. Ranasinghe, D.J., Cant, R.S. A turbulent combustion model for a stratified charged spark ignited internal combustion engine. Multi-Dimensional Engine Modeling, Selected Papers, Society of Automotive Engineers 2000 World Congress, Detroit, MI, USA, SAE technical paper 2000-01-0275. SAE SP-1512 (March 2000). ISBN 0768005620.
A49. Sreenivasan, B., Alboussière, T. Evolution of a vortex in a magnetic field. European Journal of Mechanics B: Fluids, 19, (3), 403-421 (May/June 2000).
A50. Sreenivasan, B., Alboussière, T. Study of an isolated vortex subject to a uniform magnetic field. PAMIR 2000, 4th International PAMIR Conference on Magnetohydrodynamic at Dawn of Third Millennium, Presqu' île de Giens, France (September 2000).
A51. Sutela, C., Hands, T., Collings, N. Fast response CO2 sensor for automotive exhaust gas analysis. General Emissions, Selected Papers, Society of Automotive Engineers International Fuels and Lubricants Meeting and Exposition, Toronto, Canada, SAE Technical Paper 1999-01-3477. Society of Automotive Engineers SP-1477 (October 1999). ISBN 0768004853.
A52. White, A.J., Young, J.B. Homogeneous nucleation and shock wave interaction in condensing steam flows. Nucleation and Atmospheric Aerosols 2000: 15th International Conference, Rolla, MO, USA (August 2000); Edited by B.N. Hale, M. Kulmala, 888-891. AIP Conference Proceedings 534 (American Institute of Physics, 2000). ISBN 1563969580.
A53. Young, J.B., Huang, L. Analytical prediction of homogeneous nucleation in rapidly expanding pure vapours. Nucleation and Atmospheric Aerosols 2000: 15th International Conference, Rolla, MO, USA (August 2000); Edited by B.N. Hale, M. Kulmala, 884-887. AIP Conference Proceedings 534 (American Institute of Physics, 2000). ISBN 1563969580.
A54. Zhu, M., Dowling, A.P., Bray, K.N.C. Self-excited oscillations in combustors with spray atomisers. ASME Turbo Expo 2000, 45th ASME International Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, Munich, Germany, ASME paper 2000-GT-0108 (May 2000).
A55. Zikanov, O., Thess, A., Davidson, P.A., Ziegler, D.P. Nonlinear shallow water model of the interfacial instability in aluminium reduction cells. Proceedings, 3rd International Symposium on Electromagnetic Processing of Materials, Nagoya, Japan, 109-114 (April 2000).
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Last modified: September 2001