Experimental investigation of turbulence and turbulent thermal diffusion in strongly inhomogeneous and anisotropic forced convection

TL;DR

The paper investigates turbulent transport of small non-inertial particles in strongly inhomogeneous and anisotropic forced convection at $Ra \approx 10^8$, using two oscillating-membrane turbulence generators and a steady grid to drive the flow. Velocity fields are measured with Particle Image Velocimetry, temperature is mapped with a 12-thermocouple array, and particle density is inferred from scattered light, enabling analysis of turbulent thermal diffusion in a highly structured flow. Results show that in regions with large horizontal mean temperature gradients, turbulent thermal diffusion drives large-scale particle clustering, with mean density peaking near the mean temperature minimum and described qualitatively by $\overline{n}(Y)/\overline{n}_0 = (\overline{T}(Y)/\overline{T}_0)^{-1} \exp\left(\int_0^Y \overline{U}_y / D_T \, dY'\right)$; the mean-flow topology exhibits a transition from a single-roll to a double-roll pattern with increasing $\Delta T$ and then back to a single-roll pattern at higher $\Delta T$, illustrating strong coupling between buoyancy, shear, and forcing. The study provides experimental support for turbulent thermal diffusion in strongly inhomogeneous, anisotropic convection and highlights potential stronger clustering for inertial particles, suggesting directions for future work with three-dimensional measurements and inertial effects.

Abstract

We investigate properties of turbulence and turbulent transport of non-inertial particles described in terms of turbulent thermal diffusion in strongly inhomogeneous and anisotropic convection forced by two similar turbulence generators with oscillating membrane and a steady grid in the air flow (with the Rayleigh number about $10^8$). Velocity field and spatial distribution of particles are measured using Particle Image Velocimetry system. The temperature distribution is measured in many locations using a temperature probe equipped with 12 E - thermocouples. In the forced convection, the gradients of the mean temperature field and the particle number density in the horizontal direction in the core flow are much stronger than in the vertical direction. The mean fluid velocity structure show transition between a single-roll pattern for isothermal turbulence to double-roll patterns with increase of the temperature difference between the bottom and upper walls of the chamber. For larger temperature differences, the mean fluid velocity structure returns to a single-roll pattern. In the turbulent regions with large mean temperature gradients, the dominant effect of the large-scale particle clustering is turbulent thermal diffusion, resulting in that the maximum of the mean particle number density is located in the regions with minimum of the mean temperature and vise versa. Deviations from this feature is observed in the regions with strong mean fluid velocities where the mean temperature gradients are small.

Figures (14)

• Figure 1: Experimental setup with the forced convective turbulence (left panel) produced by two turbulence generator with oscillating membrane and a steady grid: (1) digital CCD camera; (2) and (3) turbulence generator with oscillating membrane; (4) steady grid; (5) laser light sheet; (6) temperature probe equipped with 12 E - thermocouples; (7) heat exchanger at the bottom heated wall of the chamber; (8) heat exchanger at the top cooled wall of the chamber. Semi-exploding view of the experimental system, showing the different components assembly (right panel).
• Figure 2: Distributions of the mean velocity field $|\overline{U}|$ in the core flow: (a) for isothermal turbulence; and for forced convective turbulence at the temperature differences: (b)$\Delta T = 40$ K; (c)$\Delta T = 50$ K; and (d)$\Delta T = 60$ K between the bottom and upper walls of the chamber. The velocity is measured in cm/s and coordinates $Y$ and $Z$ are measured in cm.
• Figure 3: Distributions of the turbulent velocity $|u^{\rm (rms)}| = [\langle u_y^2 \rangle + \langle u_z^2 \rangle]^{1/2}$ in the core flow: (a) for isothermal turbulence; and for forced convective turbulence at the temperature differences: (b)$\Delta T = 40$ K between the bottom and upper walls of the chamber; (c)$\Delta T = 50$ K; and (d)$\Delta T = 60$ K. The velocity is measured in cm/s and coordinates $Y$ and $Z$ are normalized by $L_z=26$ cm.
• Figure 4: Distributions of the turbulent anisotropy $[\langle u_y^2 \rangle / \langle u_z^2 \rangle]^{1/2}$ in the core flow: (a) for isothermal turbulence; and for forced convective turbulence at the temperature differences: (b)$\Delta T = 40$ K between the bottom and upper walls of the chamber; (c)$\Delta T = 50$ K; and (d)$\Delta T = 60$ K. The velocity is measured in cm/s and coordinates $Y$ and $Z$ are normalized by $L_z=26$ cm.
• Figure 5: Distributions of the horizontal integral turbulent length scale $\ell_y$ in the core flow: (a) for isothermal turbulence; and for forced convective turbulence at the temperature differences: (b)$\Delta T = 40$ K between the bottom and upper walls of the chamber; (c)$\Delta T = 50$ K; and (d)$\Delta T = 60$ K. The integral turbulent length scale is measured in cm, and coordinates $Y$ and $Z$ are normalized by $L_z=26$ cm.