Heat flux at the transition from harmonic to chaotic flow in thermal convection

Journal Article · Tue Sep 01 04:00:00 EDT 1998 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.58.4016· OSTI ID:641624

Castillo, V M; Hoover, W G ^[1]

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1. Department of Applied Science, University of California at Davis--Livermore and Lawrence Livermore National Laboratory, Livermore, California 94551-7808 (United States)

Numerical simulations of the fully compressible Navier-Stokes equations are used to study the transition from simple-periodic {open_quotes}harmonic{close_quotes} thermal convection to chaotic thermal convection as the Rayleigh number Ra is increased. The simulations suggest that a sharp discontinuity in the relationship between the Nusselt number Nu (the ratio of the total heat flux to the Fourier heat flux) and the Rayleigh number is associated with this transition in flow morphology. This drop in the Nusselt number is also seen in the data reported in independent experiments involving the convection of two characteristically different fluids{emdash}liquid mercury [Phys. Rev. E {bold 56}, R1302 (1997)] (a nearly incompressible fluid with Prandtl number Pr=0.024) and gaseous helium [Phys. Rev. A {bold 36}, 5870 (1987)] (a compressible fluid with unit Pr). The harmonic flow generates a dual-maximum (quasiharmonic) temperature histogram, while the chaotic flow generates a single-maximum histogram at the center point in the simulated cell. This is consistent with the temperature distributions reported for the convecting mercury before and after the drop in Nu. Our simulations also suggest a hysteresis in the Nu-Ra curve linking the two distinctly different flow morphologies, heat fluxes, and temperature-fluctuation histograms at the same Rayleigh number. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 641624
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 58; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
BIFURCATION
CONVECTION
DYNAMICS
HEAT FLUX
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
NUSSELT NUMBER
TEMPERATURE DISTRIBUTION
TRANSITION FLOW
TURBULENCE
TURBULENT FLOW