Statistical properties of thermally expandable particles in soft-turbulence Rayleigh-Bénard convection

Kim Alards, Rudie Kunnen, Herman Clercx, Federico Toschi (Corresponding author)

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Abstract

Abstract.: The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, τ T, and the thermal expansion coefficient of particles relative to that of the fluid, K= α p/ α f. In particular, the residence time is constant for small thermal response times, τ T≲ 1 , and increasing with τ T for larger thermal response times, τ T≳ 1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with τ T for larger response times, thus explaining the trends in the DNS data well. Graphical abstract: [Figure not available: see fulltext.].

Original languageEnglish
Article number126
Number of pages12
JournalEuropean Physical Journal E : Soft Matter
Volume42
Issue number9
DOIs
Publication statusPublished - 1 Sep 2019

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Convection
Turbulence
convection
Hot Temperature
turbulence
Fluids
Reaction Time
thermal boundary layer
fluids
Thermal expansion
Boundary layers
Direct numerical simulation
thermal expansion
direct numerical simulation
Buoyancy
coefficients
buoyancy
inertia
time constant
trends

Keywords

  • Topical issue: Flowing Matter, Problems and Applications

Cite this

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title = "Statistical properties of thermally expandable particles in soft-turbulence Rayleigh-B{\'e}nard convection",
abstract = "Abstract.: The dynamics of inertial particles in Rayleigh-B{\'e}nard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, τ T, and the thermal expansion coefficient of particles relative to that of the fluid, K= α p/ α f. In particular, the residence time is constant for small thermal response times, τ T≲ 1 , and increasing with τ T for larger thermal response times, τ T≳ 1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with τ T for larger response times, thus explaining the trends in the DNS data well. Graphical abstract: [Figure not available: see fulltext.].",
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AU - Alards, Kim

AU - Kunnen, Rudie

AU - Clercx, Herman

AU - Toschi, Federico

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Abstract.: The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, τ T, and the thermal expansion coefficient of particles relative to that of the fluid, K= α p/ α f. In particular, the residence time is constant for small thermal response times, τ T≲ 1 , and increasing with τ T for larger thermal response times, τ T≳ 1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with τ T for larger response times, thus explaining the trends in the DNS data well. Graphical abstract: [Figure not available: see fulltext.].

AB - Abstract.: The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, τ T, and the thermal expansion coefficient of particles relative to that of the fluid, K= α p/ α f. In particular, the residence time is constant for small thermal response times, τ T≲ 1 , and increasing with τ T for larger thermal response times, τ T≳ 1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with τ T for larger response times, thus explaining the trends in the DNS data well. Graphical abstract: [Figure not available: see fulltext.].

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