Flows in large, self-similar tree networks and their control

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2074, 2006, Pages 2907-2926

  Franco, Walfre ^a,b   Sen, Mihir ^a   Yang, K T ^a  

^a University of Notre Dame   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Flow stability; Linear control; Relaminarization; Tree networks

Indexed keywords

EID: 33750335899     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2006.1705     Document Type: Article

References (33)

1. Alharbi, A. Y., Pence, D. V. & Cullion, R. N. 2004 Thermal characteristics of microscale fractal-like branching channels. ASME J. Heat Transfer 126, 744-752. (doi:10.1115/1.1795236)
2. Bejan, A. 2000 Shape and structure, from engineering to nature, 1st edn. New York, NY: Cambridge University Press.
3. Bejan, A. & Errera, M. R. 1997 Deterministic tree networks for fluid flow: geometry for minimal flow resistance between a volume and one point. Fractals 5, 685-695.
4. Bejan, A., Rocha, L. A. O. & Lorente, S. 2000 Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams. Int. J. Therm. Sci. 39, 949-960. (doi:10.1016/S1290-0729(00)01176-5)
5. Berne, R. M. & Levy, M. N. 1992 Cardiovascular physiology, 1st edn. St Louis, MO: Mosby.
6. Brenan, K. E., Campbell, S. L. & Peztold, L. R. 1996 Numerical solution of initial-value problems in differential-algebraic equations. Philadelphia, PA: Society for Industrial and Applied Mathematics.
7. Brion, L. M. & Mays, L. W. 1991 Methodology for optimal operation of pumping stations in water distribution systems. J. Hydraul. Eng. ASCE 117, 1551-1569.
8. Caputo, A. C. & Pelagagge, P. M. 2002 An inverse approach for piping networks monitoring. J. Loss Prev. Process Ind. 15, 497-505. (doi:10.1016/S0950-4230(02)00036-0)
9. Chen, Y. & Cheng, P. 2002 Heat transfer in fractal tree-like micro-channels for cooling of electronic chips. Int. J. Heat Mass Transfer 45, 2643-2648.
10. Cohn, D. L. 1954 Optimal systems: the vascular system. Bull. Math. Biophys. 16, 59-74.
11. Dager, R. & Zuazua, E. 2001 Controllability of tree shaped networks of vibrating strings. C. R. Acad. Sci., Ser. I Math. 332, 1087-1092.
12. Dai, L. 1989 Singular control systems. Berlin: Springer.
13. Fox, R. W. & McDonald, A. T. 1998 Introduction to fluid mechanics, 5th edn. New York, NY: Wiley.
14. Gafiychuk, V. V. & Lubashevsky, I. A. 2001 On the principles of the vascular network branching. J. Theor. Biol. 212, 1-9. (doi:10.1006/jtbi.2001. 2277)
15. Greenblatt, D. & Moss, E. A. 1999 Pipe-flow relaminarization by temporal acceleration. Phys. Fluids 11, 3478-3481. (doi:10.1063/1.870205)
16. Hu, Y. N., Koroleva, O. I. & Krstic, M. 2003 Nonlinear control of mine ventilation networks. Syst. Control Lett. 49, 239-254. (doi:10.1016/S0167- 6911(02)00336-5)
17. Iguchi, M. & Ohmi, M. 1982 Transition to turbulence in a pulsatile pipe-flow. 2. Characteristics of reversing flow accompanied by relaminarization. Bull. Jpn Soc. Mech. Eng. 25, 1529-1536.
18. Iida, O. & Nagano, Y. 1998 The relaminarization mechanisms of turbulent channel flow at low Reynolds numbers. Flow Turbul. Combust. 60, 193-213. (doi:10.1023/A:1009999606355)
19. Koroleva, O. I. & Krstic, M. 2005 Averaging analysis of periodically forced fluid networks. Automatica 41, 129-135. (doi:10.1016/S0005-1098(04)00251- 1)
20. Lorente, S., Wechsatol, W. & Bejan, A. 2002 Tree-shaped flow structures designed by minimizing path lengths. Int. J. Heat Mass Transfer 45, 3299-3312. (doi:10.1016/S0017-9310(02)00051-0)
21. Morillo, C. A. & Villar, J. C. 1997 Neurogenic syncope. Baillière's Clin. Neurol. 6, 357-380.
22. Murray, C. D. 1926 The physiological principle of minimal work in the vascular system, and the cost of blood volume. Proc. Natl Acad. Sci. USA 12, 207-214.
23. Narasimha, R. & Sreenivasan, K. R. 1979 Relaminarization of fluid flows. Adv. Appl. Mech. 19, 221-309.
24. Ohmi, M., Iguchi, M. & Urahata, I. 1982 Transition to turbulence in a pulsatile pipe flow. 1. Wave forms and distribution of pulsatile velocities near transition region. Bull. Jpn Soc. Mech. Eng. 25, 182-189.
25. Paraskevopoulos, P. N. 2002 Modern control engineering. New York, NY: Marcel Dekker.
26. Pedley, T. J. 2000 Blood flow in arteries and veins. In Perspectives of fluid dynamics ch.3, (ed. G. K. Batchelor, H. K. Moffatt & M. G. Worster) 1st edn., pp. 395-574. Cambridge, UK: Cambridge University Press.
27. Pence, D. V. 2002 Reduced pumping power and wall temperature in microchannel heat sinks with fractal-like branching channel networks. Microscale Thermophys. Eng. 6, 319-330. (doi:10. 1080/10893950290098359)
28. Reis, A. H., Miguel, A. F. & Aydin, M. 2004 Constructal theory of flow architecture of the lungs. Med. Phys. 31, 1135-1140. (doi:10.1118/1. 1705443)
29. Schmid-Schönbein, G. W. 1999 Biomechanics of microcirculatory blood perfusion. Annu. Rev. Biomed. Eng. 1, 73-102. (doi:10.1146/annurev.bioeng.1.1. 73)
30. Seebacher, F. 2000 Heat transfer in a microvascular network: the effect of heart rate on heating and cooling in reptiles (pogona barbata and varanus varius). J. Theor. Biol. 203, 97-109. (doi:10. 1006/jtbi.1999.1067)
31. Senn, S. M. & Poulikakos, D. 2004 Tree network channels as fluid distributors constructing double-staircase polymer electrolyte fuel cells. J. Appl. Phys. 96, 842-852. (doi:10.1063/1.1757028)
32. Wechsatol, W., Lorente, S. & Bejan, A. 2005 Tree-shaped networks with loops. Int. J. Heat Mass Transfer 48, 573-583. (doi:10.1016/j. ijheatmasstransfer.2004.08.020)
33. Yip, E. L. & Sincovec, R. F. 1981 Solvability, controllability, and observability of continuous descriptor systems. IEEE Trans. Autom. Control 26, 702-707. (doi:10.1109/TAC.1981.1102699)