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Measured multiple flow states in turbulent thermal convection with aspect ratio 10

Yi-Zhen Li, Jun-Jie Huo, Xin Chen, Heng-Dong Xi

TL;DR

This study demonstrates that turbulent Rayleigh–Bénard convection in a large-aspect-ratio cell (Γ = 10) exhibits robust multistability, forming horizontally stacked rolls (3–7) with six-roll states predominating. The number of rolls and the flow structure depend on Ra and Pr, with a notable transition to plume-dominated regimes at high Pr (67.3) that alters the Reynolds-number scaling from Re ∼ Ra^{0.58} Pr^{-0.97} to a higher Ra exponent (~0.72). Within individual rolls, horizontal and vertical Reynolds components show opposite trends as roll size changes, consistent with mass conservation, and the ratio Re_w,roll/Re_u,roll scales as Γ_roll^{-0.61}. By applying localized sidewall heating, the study demonstrates access to rarely observed double- and triple-roll states, supporting a potential-well picture of state selection and revealing that more rolls enhance vertical transport and heat transfer, while boundary effects and 3D geometry shape the observed roll counts relative to 2D simulations. These findings highlight how large-scale flow organization governs transport properties in turbulent convection and point to the need for fully resolved 3D experiments and simulations to unravel state selection and transition mechanisms.

Abstract

We report an experimental investigation of turbulent Rayleigh-Benard convection in a rectangular cell of large aspect ratio ($Γ= 10$) over the Rayleigh number range $5.4\times10^7 \le Ra \le 7.2\times10^9$ and Prandtl number range $4.3 \le Pr \le 67.3$. Planar particle image velocimetry measurements show that the flow self organises into several horizontally stacked convection rolls, and repeated experiments under identical parameters (both $Ra$ and $Pr$) reveal that the number of rolls varies within the range of 3 to 7 with 6 being the most probable, which demonstrates the presence of multiple flow states. When $Pr$ is increased to 67.3, the number of roll like structures increases significantly, indicating a structural transition from a roll dominated to a plume dominated flow. This transition is reflected in the global momentum transport, for $Pr \leq 18.3$ the Reynolds number scales as $Re \sim Ra^{0.58}Pr^{-0.97}$, whereas the scaling is changed to $Re \sim Ra^{0.72}$ when $Pr$ reaches 67.3. Within individual rolls, we further examine the Reynolds numbers based on horizontal and vertical velocity components, $Re_{u,\text{roll}}$ and $Re_{w,\text{roll}}$, and find that the former increases while the latter decreases with roll size (quantified as the aspect ratio of the roll $Γ_\text{roll}$) due to continuity constraints, with their ratio following $Re_{w,\text{roll}}/Re_{u,\text{roll}} \sim Γ_\text{roll}^{-0.61}$. We impose different initial flow conditions (roll structures) with controlled perturbations, and demonstrate that the initial condition can influence the final turbulent state. We show that the number of horizontally stacked rolls regulates the global transport, larger number of rolls induces greater vertical momentum and heat transfer.

Measured multiple flow states in turbulent thermal convection with aspect ratio 10

TL;DR

This study demonstrates that turbulent Rayleigh–Bénard convection in a large-aspect-ratio cell (Γ = 10) exhibits robust multistability, forming horizontally stacked rolls (3–7) with six-roll states predominating. The number of rolls and the flow structure depend on Ra and Pr, with a notable transition to plume-dominated regimes at high Pr (67.3) that alters the Reynolds-number scaling from Re ∼ Ra^{0.58} Pr^{-0.97} to a higher Ra exponent (~0.72). Within individual rolls, horizontal and vertical Reynolds components show opposite trends as roll size changes, consistent with mass conservation, and the ratio Re_w,roll/Re_u,roll scales as Γ_roll^{-0.61}. By applying localized sidewall heating, the study demonstrates access to rarely observed double- and triple-roll states, supporting a potential-well picture of state selection and revealing that more rolls enhance vertical transport and heat transfer, while boundary effects and 3D geometry shape the observed roll counts relative to 2D simulations. These findings highlight how large-scale flow organization governs transport properties in turbulent convection and point to the need for fully resolved 3D experiments and simulations to unravel state selection and transition mechanisms.

Abstract

We report an experimental investigation of turbulent Rayleigh-Benard convection in a rectangular cell of large aspect ratio () over the Rayleigh number range and Prandtl number range . Planar particle image velocimetry measurements show that the flow self organises into several horizontally stacked convection rolls, and repeated experiments under identical parameters (both and ) reveal that the number of rolls varies within the range of 3 to 7 with 6 being the most probable, which demonstrates the presence of multiple flow states. When is increased to 67.3, the number of roll like structures increases significantly, indicating a structural transition from a roll dominated to a plume dominated flow. This transition is reflected in the global momentum transport, for the Reynolds number scales as , whereas the scaling is changed to when reaches 67.3. Within individual rolls, we further examine the Reynolds numbers based on horizontal and vertical velocity components, and , and find that the former increases while the latter decreases with roll size (quantified as the aspect ratio of the roll ) due to continuity constraints, with their ratio following . We impose different initial flow conditions (roll structures) with controlled perturbations, and demonstrate that the initial condition can influence the final turbulent state. We show that the number of horizontally stacked rolls regulates the global transport, larger number of rolls induces greater vertical momentum and heat transfer.
Paper Structure (7 sections, 10 figures, 2 tables)

This paper contains 7 sections, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Experimental Set-up
  3. Results and discussions
  4. Typical flow structure
  5. Reynolds number
  6. The flow control and the heat transfer
  7. Conclusions

Figures (10)

  • Figure 1: Schematic of the convection cell. The blue and red plates represent the top and bottom plates, respectively. Two cameras are arranged in a parallel configuration and are used to measure the flow field.
  • Figure 2: (a) Long time (three hours) averaged velocity field at $Ra = 3.5 \times 10^8, Pr = 9.9$. The color map represents the magnitude of the in-plane velocity $(u^2 + w^2)^{1/2}$. (b) Horizontal velocity $u$ (black line) and its absolute value $\left\lvert u \right\rvert$ (blue line) along the line $z = 1 \text{cm}$. Green dots mark the positions of local minimum in $\left\lvert u \right\rvert$, corresponding to roll boundaries. (c) Space-time plot of horizontal velocity $u$ along $z = 1 \text{cm}$.
  • Figure 3: (a) Space-time plot of horizontal velocity $u$ along $z = 1 \text{cm}$ for $Ra = 3.5 \times 10^8, Pr = 9.9$. Vertical dashed lines indicate the times at which short-time-averaged velocity fields are extracted. (b, c) Velocity fields averaged over one turnover time $t_E$, showing (b) a four-roll state and (c) a five-roll state. Color represents the in-plane velocity magnitude $(u^2 + w^2)^{1/2}$
  • Figure 4: Short time averaged flow field at $Ra = 7.2 \times 10^9, Pr = 9.9$. (a) Five-roll state. (b) Triple-roll state.
  • Figure 5: Multiple flow states at different $Pr$ numbers. (a) shows the seven-roll state and six-roll state at $Ra = 2.05 \times 10^8$, $Pr=18.3$, respectively. (b) shows the roll-like flow structures at $Ra = 1.63 \times 10^8$, $Pr=67.3$.
  • ...and 5 more figures