Skip to main content
Log in

Active Control of Thermal Convection in a Rectangular Loop by Changing its Spatial Orientation

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

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)

    Article  Google Scholar 

  • Zyuzgin, A.V., Putin, G.F., Kharisov, A.F.: Ground modeling of thermovibrational convection in real weightlessness. Fluid Dyn. 42(3), 354–361 (2007)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • Bratsun, D.A., De Wit, A.: Control of chemoconvective structures in a slab reactor. Techn. Phys. 53, 146–153 (2008)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Gershuni, G.Z., Lyubimov, D.V.: Thermal vibrational convection, p. 372. Wiley & Sons, New York (1998)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • Gaponenko, Y.u., Shevtsova, V.: Effects of vibrations on dynamics of miscible liquids. Acta Astronaut. 66, 174–182 (2010)

    Article  Google Scholar 

  • Gaponenko, Y.u., Shevtsova, V.: Shape of diffusive interface under periodic excitations at different gravity levels. Microgravity Sci. Technol. 28(4), 431–439 (2016)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Hu, H.Y., Wang, Z.H.: Dynamics of controlled mechanical systems with delayed feedback, p 294. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  • Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421–428 (1992)

    Article  Google Scholar 

  • Goldobin, D., Rosenblum, M., Pikovsky, A.: Controlling oscillator coherence by delayed feedback. Phys. Rev. Lett. 67, 061119 (2003)

    MATH  Google Scholar 

  • Welander, P.: On the oscillatory instability of a differentially heated fluid loop. J. Fluid Mech. 29, 17–30 (1967)

    Article  MATH  Google Scholar 

  • 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)

    Google Scholar 

  • Erhard, P., Müller, U.: Dynamical behavior of natural convection in a single-phase loop. J. Fluid Mech. 217, 487–518 (1990)

    Article  Google Scholar 

  • Singer, J., Bau, H.: Active control of convection. Phys. Fluids A 3, 2859–2865 (1991)

    Article  MATH  Google Scholar 

  • Wang, Y., Singer, J., Bau, H.: Controlling chaos in a thermal convection loop. J. Fluid Mech. 237, 479–498 (1992)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Remillieux, M., Zhao, H., Bau, H.: Suppression of rayleigh-bénard convection with proportional-derivative controller. Phys. Fluids 19, 017102–017111 (2007)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • Drozdov, S.M.: Experimental investigation of fluid convection in a closed toroidal channel. Fluid Dyn. 30(4), 503–509 (1993)

    Article  MathSciNet  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)

    Article  Google Scholar 

  • Lyubimov, D.V., Putin, G.F., Chernatynskii, V.: On convective motions in a Hele-Shaw cell. Sov. Phys. Dokl. 22, 360–362 (1977)

    Google Scholar 

  • Putin, G.F., Tkacheva, E.A.: Experimental investigation of supercritical convective motions in a Hele-Shaw cell. Fluid Dyn. 14(1), 1–5 (1979)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dmitry A. Bratsun.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-017-9573-6

Keywords

Navigation