### Abstract

Abstract We report the first experimental study of Lagrangian acceleration in turbulent Rayleigh-Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance a ^{2} was obtained for various values of the three control parameters: the Rayleigh number Ra (6× 10 ^{8} ≤ Ra ≤ 1× 10 ^{11}), the Prandtl number Pr (Pr= 4. 4, 5. 5 and 6.1) and the system size L (L= 19. 2 and 48. 6 cm). These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that a ^{2} in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg-Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant a of the acceleration variance in the micro-scale Reynolds number range 20 ≤ R _{λ} ≤ 120, which fills a gap in this constant in the lower R _{λ} end from the experimental side, and provides possible constraints for its high R _{λ} behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different Ra. It is found that the zero crossing time of acceleration correlation functions is at τ ≈ 2. 2 τ _{η} (τ _{η} is the Kolmogorov time scale) over the range of Ra(R _{λ}) spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time τ _{1/e} = (1. 12 ± 0. 05) τ _{η}, which is larger than (0. 73∼ 0. 80) τ _{η} found experimentally for other types of turbulent flows with larger R _{λ}.

Original language | English (US) |
---|---|

Pages (from-to) | 395-419 |

Number of pages | 25 |

Journal | Journal of Fluid Mechanics |

Volume | 692 |

DOIs | |

State | Published - Feb 10 2012 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Fluid Mechanics*,

*692*, 395-419. https://doi.org/10.1017/jfm.2011.520

}

*Journal of Fluid Mechanics*, vol. 692, pp. 395-419. https://doi.org/10.1017/jfm.2011.520

**Lagrangian acceleration measurements in convective thermal turbulence.** / Ni, Rui; Huang, Shi Di; Xia, Ke Qing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Lagrangian acceleration measurements in convective thermal turbulence

AU - Ni, Rui

AU - Huang, Shi Di

AU - Xia, Ke Qing

PY - 2012/2/10

Y1 - 2012/2/10

N2 - Abstract We report the first experimental study of Lagrangian acceleration in turbulent Rayleigh-Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance a 2 was obtained for various values of the three control parameters: the Rayleigh number Ra (6× 10 8 ≤ Ra ≤ 1× 10 11), the Prandtl number Pr (Pr= 4. 4, 5. 5 and 6.1) and the system size L (L= 19. 2 and 48. 6 cm). These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that a 2 in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg-Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant a of the acceleration variance in the micro-scale Reynolds number range 20 ≤ R λ ≤ 120, which fills a gap in this constant in the lower R λ end from the experimental side, and provides possible constraints for its high R λ behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different Ra. It is found that the zero crossing time of acceleration correlation functions is at τ ≈ 2. 2 τ η (τ η is the Kolmogorov time scale) over the range of Ra(R λ) spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time τ 1/e = (1. 12 ± 0. 05) τ η, which is larger than (0. 73∼ 0. 80) τ η found experimentally for other types of turbulent flows with larger R λ.

AB - Abstract We report the first experimental study of Lagrangian acceleration in turbulent Rayleigh-Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance a 2 was obtained for various values of the three control parameters: the Rayleigh number Ra (6× 10 8 ≤ Ra ≤ 1× 10 11), the Prandtl number Pr (Pr= 4. 4, 5. 5 and 6.1) and the system size L (L= 19. 2 and 48. 6 cm). These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that a 2 in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg-Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant a of the acceleration variance in the micro-scale Reynolds number range 20 ≤ R λ ≤ 120, which fills a gap in this constant in the lower R λ end from the experimental side, and provides possible constraints for its high R λ behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different Ra. It is found that the zero crossing time of acceleration correlation functions is at τ ≈ 2. 2 τ η (τ η is the Kolmogorov time scale) over the range of Ra(R λ) spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time τ 1/e = (1. 12 ± 0. 05) τ η, which is larger than (0. 73∼ 0. 80) τ η found experimentally for other types of turbulent flows with larger R λ.

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U2 - 10.1017/jfm.2011.520

DO - 10.1017/jfm.2011.520

M3 - Article

VL - 692

SP - 395

EP - 419

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -