ライブラリ登録: Guest
Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集
Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN 印刷: 1940-2503
ISSN オンライン: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2019026046
pages 387-400

EFFECTS OF DISCRETE CONTROLLERS ON THE STABILIZATION OF NATURAL CONVECTION INDUCED BY INTERNAL HEAT GENERATION IN A SHALLOW CAVITY

A. Mebrouki
Departement de Genie Mecanique, Faculte de Technologie, Universite Mustapha Ben Boulaid Batna, Algerie; Laboratoire d'Innovation en Construction, Eco-Conception et Genie Sismique, LICEGS, Universite Mustapha Ben Boulaid, Batna, Algerie
Alloui Zineddine
Departement de Genie Mecanique, Faculte de Technologie, Universite Mustapha Ben Boulaid Batna, Algerie; Laboratoire d'Innovation en Construction, Eco-Conception et Genie Sismique, LICEGS, Universite Mustapha Ben Boulaid, Batna, Algerie
Patrick Vasseur
Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. "Centre ville", Montréal, Québec H3C 3A7, Canada

要約

The stabilization of natural convection in a horizontal fluid layer with internal heat generation is studied numerically. The horizontal boundaries of the system are cooled isothermally. The system is stabilized using multiple sensors and discrete individually controlled actuators that modify the local intensity of the heating power. Discrete controllers of finite length and spacing are located on the horizontal boundaries of the system. The thermal sensors are positioned at a given vertical height of the fluid layer. Upon using a feedback proportional control, the heating power of the system is modulated in order to postpone the onset of motion or annihilate the intensity of convection. Two-dimensional numerical simulations of the full governing equations are carried out. The results are used to determine the influence of the governing parameters, such as the length and spacing of the actuators, positions of the thermal sensors, and control gain on the control of the system. A correlation equation is proposed to predict the critical length of the actuators, above which the no-motion state cannot be maintained in the layer, as a function of the Rayleigh number.

参考

  1. Abidin, N.H.Z., Mokhtar, N.F.M., Arbin, N., Said, J.M., and Arifin, N.M., Marangoni Convection in a Micropolar Fluid with Feedback Control, in Proc. of IEEE Symposium on Business, Engineering and Industrial Applications, Bandung, Indonesia, pp. 1-5, September 23-26,2012.

  2. Bachok, N., Arifin, N.M., and Ali, F.Md., Effects of Control on the Onset of Marangoni-Benard Convection with Uniform Internal Heat Generation, Matematika, vol. 24, pp. 23-29,2008.

  3. Bau, H.H., Control of Marangoni-Benard Convection, Int. J. Heat Mass Transf, vol. 42, pp. 1327-1341,1999.

  4. Benard, H., Les Tourbillons Cellulaires dans une Nappe Liquide, Rev. Gen. Sci. Pures Appl., vol. 11, pp. 1261-1271,1900.

  5. Goluskin, D. and Spiegel, E.A., Convection Driven by Internal Heating, Phys. Lett. A, vol. 377, pp. 83-92,2012.

  6. Howle, L.E., Active Control of Rayleigh-Benard Convection, Phys. Fluids, vol. 9, pp. 1861-1863,1997a.

  7. Howle, L.E., Control of Rayleigh-Benard Convection in a Small Aspect Ratio Container, Int. J. Heat Mass Transf., vol. 40, pp. 817-822,1997b.

  8. Howle, L.E., Linear Stability Analysis of Controlled Rayleigh-Benard Convection Using Shadowgraphic Measurement, Phys. Fluids, vol. 9, pp. 3111-3113,1997c.

  9. Khalid, I.K., Mokhtar, N.F.M., and Arifin, N.M., Rayleigh-Benard Convection in Micropolar Fluid with Feedback Control Effect, WorldAppl. Sci. J, vol. 21, pp. 112-118,2013.

  10. Khalid, I.K., Mokhtar, N.F.M., Hashim, I., Ibrahim, Z.B., and Gani, S.S.A., Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy, Adv. Math. Phys, vol. 2017, p. 2789024, 2017.

  11. Kulacki, F.A. and Goldstein, R.J., Thermal Convection in a Horizontal Fluid Layer with Uniform Volumetric Energy Sources, J. FluidMech., vol. 55, pp. 271-287,1972.

  12. Kulacki, F.A. and Nagle, M.E., Natural Convection in Horizontal Fluid Layer with Volumetric Energy Sources, J. Heat Transf, vol. 97, pp. 204-211,1975.

  13. Mamou, M., Robillard, L., and Vasseur, P., Thermoconvective Instability in a Horizontal Porous Cavity Saturated with Cold Water, Int. J. Heat Mass Transf., vol. 42, pp. 4487-4500,1999.

  14. Marimbordes, T., Ould El Moctar, A., and Peerhossaini, H., Active Control of Natural Convection in a Fluid Layer with Volume Heat Dissipation, Int. J. Heat Mass Transf, vol. 45, pp. 667-678,2002.

  15. Mokhtar, N.F.M. and Khalid, I.K., Stabilization of Convective Instability in Micropolar Fluid Model by Feedback Control Strategy Subjected to Internal Heat Source, Int. J. Math. Models Meth. Appl. Sci., vol. 10, pp. 27-33, 2016.

  16. Mokhtar, N.F.M., Khalid, I.K., and Arifin, N.M., Effect of Internal Heat Generation on Benard-Marangoni Convection in Micropolar Fluid with Feedback Control, J. Phys. Conf. Ser., vol. 435,2012. DOI: 10.1088/1742-6596/435/1/012029.

  17. Mokhtar, N.F.M., Khalid, I.K., and Gani, S.S.A., Natural Convection in a Nanofluid Layer with Feedback Control Strategy, Int. J. Manag. Appl. Sci., vol. 5, pp. 30-35,2017a.

  18. Mokhtar, N.F.M., Khalid, I.K., Siri, Z., Ibrahim, Z.B., and Gani, S.S.A., Control Strategy on the Double-Diffusive Convection in a Nanofluid Layer with Internal Heat Generation, Phys. Fluids, vol. 29, p. 107105,2017b.

  19. Or, A.C., Cortelezzi, L., and Speyer, J.L., Robust Feedback Control of Rayleigh-Benard Convection, J. Fluid Mech., vol. 437, pp. 175-202,2001.

  20. Or, A.C. and Kelly, R.E., Feedback Control of Weakly Nonlinear Rayleigh-Benard-Marangoni Convection, J. Fluid Mech., vol. 440, pp. 27-47,2001.

  21. Or, A.C. and Speyer, J.L., Gain-Scheduled Controller for the Suppression of Convection at High Rayleigh Number, Phys. Rev. E, vol. 71, p. 046302,2005.

  22. Or, A.C. and Speyer, J.L., Robust Control for Convection Suppression in a Fluid Layer: The Effects of Boundary Properties, Actuator Lag, and Major Parameter Uncertainties, Phys. Rev. E, vol. 73, p. 046307,2006.

  23. Peaceman, D.W. and Rachford, H.H., The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Indust. Appl. Math, vol. 3, pp. 28-41,1955.

  24. Pearson, J.R.A., On Convective Cells Induced by Surface Tension, J. Fluid Mech., vol. 4, pp. 489-500,1958.

  25. Perekattu, G.K. and Balaji, C., On the Onset of Natural Convection in Differentially Heated Shallow Fluid Layers with Internal Heat Generation, Int. J. Heat Mass Transf., vol. 52, pp. 4254-4263,2009.

  26. Rayleigh, L., On Convective Currents in a Horizontal Layer of Fluid when the Higher Temperature is on the Underside, Philos. Mag, vol. 32, pp. 529-546,1916.

  27. Remillieux, M.C., Zhao, H., and Bau, H., Suppression of Rayleigh-Benard Convection with Proportional-Derivative Controller, Phys. Fluids, vol. 19, p. 017102,2007.

  28. Shiby, K., Pandey, M.C., Radhakrishna, K., and Bawa, A.S., Technology, Applications and Modelling of Ohmic Heating: A Review, J. Food Sci. Technol., vol. 51, pp. 2304-2317,2014.

  29. Shim, Y.M. and Hyun, J.M., Transient Confined Natural Convection with Internal Heat Generation, Int. J. Heat Fluid Flow, vol. 18, pp. 328-333,1996.

  30. Silva, V.L.M., Santos, L.M.N.B.F., and Silva, A.M.S., Ohmic Heating: An Emerging Concept in Organic Synthesis, Chem. Eur. J., vol. 23, pp. 7853-7865,2017.

  31. Singer, J. and Bau, H.H., Active Control Convection, Phys. Fluids, vol. 12, pp. 2859-2865,1991.

  32. Tang, J., Active Control of Rayleigh-Benard Convection, PhD, University of Pennsylvania, 1996.

  33. Tang, J. and Bau, H.H., Feedback Control Stabilization of the No-Motion State of a Fluid Confined in a Horizontal Porous Layer Heated from below, J. FluidMech, vol. 257, pp. 485-505,1993a.

  34. Tang, J. and Bau, H.H., Stabilization of the No-Motion State in Rayleigh-Benard Convection through the Use of Feedback Control, Phys. Rev. Lett., vol. 70, pp. 1795-1798,1993b.

  35. Tang, J. and Bau, H.H., Stabilization of the No-Motion State in of a Horizontal Fluid Layer Heated from below with Joule Heating, J. Heat Transf., vol. 117, pp. 329-333,1995.

  36. Tang, J. and Bau, H.H., Experiments on the Stabilization of the No-Motion State of a Fluid Layer Heated from below and Cooled from above, J. Fluid Mech, vol. 363, pp. 153-171,1998a.

  37. Tang, J. and Bau, H.H., Numerical Investigation of the Stabilization of the No-Motion State of a Fluid Layer Heated from below and Cooled from above, Phys. Fluids, vol. 10, pp. 1597-1610,1998b.

  38. Young, D., Iterative Solution of Large Linear Systems, New York: Academic Press, 1971.

  39. Yuji, T. and Yasushi, T., Effects of Heat Source Distribution on Natural Convection Induced by Internal Heating, Int. J. Heat Mass Transf., vol. 48, pp. 1164-1174,2005.


Articles with similar content:

LINEAR RESPONSE OF THE TEMPERATURE AND FLOW FIELDS IN A SQUARE ENCLOSURE TO IMPOSED WALL TEMPERATURE OSCILLATIONS
International Heat Transfer Conference 9, Vol.3, 1990, issue
Q. Xia , K. T. Yang
FEEDBACK CONTROL OF FLOWS IN A POROUS SQUARE ENCLOSURE HAVING NONUNIFORM INTERNAL HEATING
Journal of Porous Media, Vol.15, 2012, issue 8
Rozaini Roslan, Z. Mustafa, Habibis Saleh, Ishak Hashim
GEOMETRIC OPTIMIZATION FOR MAXIMUM HEAT TRANSFER DENSITY RATE FROM CYLINDERS ROTATING IN NATURAL CONVECTION
ICHMT DIGITAL LIBRARY ONLINE, Vol.0, 2012, issue
Josua Petrus Meyer, Logan Page , Tunde Bello-Ochende
Modified Reattaching Shear Layer Using a Stationary Cylinder
International Journal of Fluid Mechanics Research, Vol.27, 2000, issue 2-4
Bassam A/K Abu-Hijleh
Comparison Between Free and Rigid Boundaries Effects on Soret Driven Thermosolutal Convection in a Shallow Porous Enclosure
ICHMT DIGITAL LIBRARY ONLINE, Vol.2, 2004, issue
M. Bourich, Mohammed Hasnaoui, Abdelkhalk Amahmid, Mahmoud Mamou