Abstract
The problem of the automatic control of the fluid flow in a rectangular convective loop heated from below is studied theoretically and experimentally. The control is performed by using a feedback subsystem which changes the convection regimes by introducing small discrete changes in the spatial orientation of the loop with respect to gravity. We focus on effects that arise when the feedback controller operates with an unavoidable time delay, which is cause by the thermal inertia of the medium. The mathematical model of the phenomenon is developed. The dynamic regimes of the convection in the thermosyphon loop under control are studied. It is shown that the proposed control method can successfully stabilize not only a no-motion state of the fluid, but also time-dependent modes of convection including the irregular fluid flow at high values of the Rayleigh number. It is shown that the excessive gain of the proportional feedback can result in oscillations in the loop orientation exciting the unsteady convection modes. The comparison of the experimental data obtained for dielectric oil and dodecane with theory is given, and their good agreement is demonstrated.
Similar content being viewed by others
References
Zyuzgin, A.V., Putin, G.F., Ivanova, N.G., Chudinov, A.V., Ivanov, A.I., Kalmykov, A.V., Polezhaev, V.I., Emelianov, V.: The heat convection of near critical fluid in the controlled microacceleration field under zero-gravity condition. Adv. Space Res. 32(2), 205–210 (2003)
Zyuzgin, A.V., Putin, G.F., Kharisov, A.F.: Ground modeling of thermovibrational convection in real weightlessness. Fluid Dyn. 42(3), 354–361 (2007)
McDermott, P.E., Chang, H.: On the global dynamics of an autothermal reactor stabilized by linear feedback control. Chem. Eng. Sci. 39(9), 1347–1356 (1984)
McDermott, P.E., Chang, H.C., Rinker, R.G.: Experimental investigation of controller-induced bifurcation in a Fixed-bed autothermal reactor. Chem. Eng. Sci. 40(8), 1355–1366 (1985)
Hwang, S.H., Chang, H.C.: A theoretical examination of closed-loop properties and tuning methods of single-loop pi controllers. Chem. Eng. Sci. 42(4), 1–21 (1987)
Bratsun, D.A., Shi, Y., Eckert, K., De Wit, A.: Control of chemo-hydrodynamic pattern formation by external localized cooling. Europhys. Lett. 69(5), 746–752 (2005)
Bratsun, D.A., De Wit, A.: Control of chemoconvective structures in a slab reactor. Techn. Phys. 53, 146–153 (2008)
Bratsun, D.: On Rayleigh-Benard mechanism of alignment of salt fingers in reactive immiscible two-layer systems. Microgravity Sci. Technol. 26(3), 12–35 (2014)
Gershuni, G.Z., Lyubimov, D.V.: Thermal vibrational convection, p. 372. Wiley & Sons, New York (1998)
Mialdun, A., Ryzhkov, I.I., Melnikov, D.E., Shevtsova, V.: Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment. Phys. Rev. Lett. 101, 084501 (2008)
Gaponenko, Y.u., Shevtsova, V.: Effects of vibrations on dynamics of miscible liquids. Acta Astronaut. 66, 174–182 (2010)
Gaponenko, Y.u., Shevtsova, V.: Shape of diffusive interface under periodic excitations at different gravity levels. Microgravity Sci. Technol. 28(4), 431–439 (2016)
Bratsun, D.A., Stepkina, O.S., Kostarev, K.G., Mizev, A.I., Mosheva, E.A.: Development of concentration-dependent diffusion instability in reactive miscible fluids under influence of constant or variable inertia. Microgravity Sci. Technol. 28(3), 575–585 (2016)
Bratsun, D.A., Teplov, V.: On the stability of the pulsed convective flow with small heavy particles. Eur. Phys. J. A. P 10, 219–230 (2000)
Bratsun, D.A.: Effect of unsteady forces on the stability of non-isothermal particulate flow under finite-frequency vibrations. Microgravity Sci. Technol. 21(Suppl. 1), 153–158 (2009)
Hu, H.Y., Wang, Z.H.: Dynamics of controlled mechanical systems with delayed feedback, p 294. Springer, Berlin (2002)
Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421–428 (1992)
Goldobin, D., Rosenblum, M., Pikovsky, A.: Controlling oscillator coherence by delayed feedback. Phys. Rev. Lett. 67, 061119 (2003)
Welander, P.: On the oscillatory instability of a differentially heated fluid loop. J. Fluid Mech. 29, 17–30 (1967)
Malkus, W.V.R.: Non-periodic convection at high and low Prandtl numbers. mém. Soc. Royale de Sci. de Liè,ge Ser. 6(4), 125–128 (1972)
Erhard, P., Müller, U.: Dynamical behavior of natural convection in a single-phase loop. J. Fluid Mech. 217, 487–518 (1990)
Singer, J., Bau, H.: Active control of convection. Phys. Fluids A 3, 2859–2865 (1991)
Wang, Y., Singer, J., Bau, H.: Controlling chaos in a thermal convection loop. J. Fluid Mech. 237, 479–498 (1992)
Tang, J., Bau, H.: Feedback control stabilization of the no-motion state of a fluid confined in a horizontal porous layer heated from below. J. Fluid Mech. 257, 485–505 (1993)
Remillieux, M., Zhao, H., Bau, H.: Suppression of rayleigh-bénard convection with proportional-derivative controller. Phys. Fluids 19, 017102–017111 (2007)
Getling, A.V.: Convective Motion concentration at the boundaries of a horizontal fluid layer with inhomogeneous unstable temperature gradient along the height. Fluid Dyn. 10(5), 745–750 (1975)
Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)
Drozdov, S.M.: Experimental investigation of fluid convection in a closed toroidal channel. Fluid Dyn. 30(4), 503–509 (1993)
Bratsun, D.A., Zyuzgin, A.V., Polovinkin, K.V., Putin, G.F.: Active control of fluid equilibrium in a thermosyphon. Techn. Phys. Let. 34(8), 650–652 (2008)
Bratsun, D., Krasnyakov, I., Zyuzgin, A.: Delay-induced oscillations in a thermal convection loop under negative feedback control with noise. Commun. Nonlinear Sci. Numer. Simul. 47, 109–126 (2017)
Bratsun, D., Volfson, D., Hasty, J., Tsimring, L.S.: Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. U.S.A. 102, 14593–14598 (2005)
Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)
Lyubimov, D.V., Putin, G.F., Chernatynskii, V.: On convective motions in a Hele-Shaw cell. Sov. Phys. Dokl. 22, 360–362 (1977)
Putin, G.F., Tkacheva, E.A.: Experimental investigation of supercritical convective motions in a Hele-Shaw cell. Fluid Dyn. 14(1), 1–5 (1979)
Author information
Authors and Affiliations
Corresponding author
Additional information
This article belongs to the Topical Collection: Non-Equilibrium Processes in Continuous Media under Microgravity
Guest Editor: Tatyana Lyubimova
The work was supported by the Ministry of Education and Science of Russia (grant No. 3.6990.2017/8.9).
Rights and permissions
About this article
Cite this article
Bratsun, D.A., Krasnyakov, I.V. & Zyuzgin, A.V. Active Control of Thermal Convection in a Rectangular Loop by Changing its Spatial Orientation. Microgravity Sci. Technol. 30, 43–52 (2018). https://doi.org/10.1007/s12217-017-9573-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12217-017-9573-6