Heat transport regimes in an inclined channel

Abstract

In this paper we report measurements of the heat flux in a slightly tilted channel (angle less than 45°), filled with water, that connects two chambers: the hot in the lower part and the cold on the top. We show that different regimes develop depending on the angle and the applied power. We put in evidence a hard turbulent regime, a soft turbulent regime, a laminar regime, and an intermittent one. In the last regime, the flow oscillates between laminar and turbulent, which locks the temperature gradient to a constant value. We characterize those regimes thanks to the measurement of the axial gradient of temperature and to the measurement of the power. We model them giving descriptions in term of Nusselt and Rayleigh numbers. The soft turbulence to hard turbulence transition is interpreted as the birth of the inertial range of developed turbulence. This transition, which appears in several systems, is particularly clear here, thanks to its consequences on heat transport properties.

Turbulent convective heat transfer in an inclined tube filled with sodium

“…However, in the case of free convec tion of helium, the maximal heat flux exceeds by 4-5 times the heat flux in the vertical channel, while in the case of sodium, the flux increases by 11 times. An increase in the efficiency of heat transfer with the angle of inclination from the vertical increasing to 45°w as also observed when turbulent convection was studied in a channel connecting reservoirs with hot and cold water [13].…”

Buoyancy-induced turbulence in a tilted pipe

“…Increasing the Atwood number would allow non-Boussinesq effects, which are expected to induce top-down asymmetries within the pipe section, to be explored. Nevertheless we think the most urgent step should rather consider varying the pipe inclination, following the experimental investigations of Séon et al (2004) and Znaien et al (2011), or Riediger et al (2013 in the context of heat transport. It may be inferred from (4.1) and (4.2), (6.9) and (6.11) that ∂ z U, ∂ z C, u w and c w vary linearly with sin Θ for small inclination angles.…”

“…Subsequent measurements by Znaien, Moisy & Hulin (2011) revealed that, with large enough density contrasts and Reynolds numbers and small enough Θ, the mean velocity and all second-order moments including the variance of density fluctuations are stationary, although the mean density profile keeps on evolving. Last, Rayleigh-Bénard convection in a long inclined cell was recently considered by Riediger et al (2013) who, by recording the variations of the mean streamwise temperature gradient with the injected power, were able to identify several distinct flow regimes. In particular, they found 'hard' turbulence (for which the above 'ultimate' scaling holds) to occur for Θ 20 • at large enough Rayleigh numbers, followed by 'soft' turbulence (for which the Nusselt number varies as the square of the Rayleigh number) at larger Θ.…”

Turbulent heat transport regimes in a channel

“…In the past decade, scalar free convection in a tiltable channel appeared as an interesting model flow for evidencing the base mechanisms of convection [1][2][3][4][5][6][7][8][9][10][11]. Different regimes have been evidenced depending on the angle ψ between the channel axis and the vertical one, the Prandtl (or Schmidt) number ν/κ, or the amplitude of density differences.…”

“…In a similar way, the Soft Turbulence regime (Gr 2 ) should disappear for P r >> 1. Following Riedinger et al [8], we shall call the N u ∝ Gr 1/2 regime the Hard Turbulence one. We develop our arguments in the following section.…”