Influence of Particle Mass Fraction over the Turbulent Behaviour of an Incompressible Particle-Laden Flow
The presence of spherical solid particles immersed in an incompressible turbulent flow was numerically investigated from the perspective of the particle mass fraction (PMF or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semanti...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/da99ca31357948f187a345b0c87b60a4 |
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| Sumario: | The presence of spherical solid particles immersed in an incompressible turbulent flow was numerically investigated from the perspective of the particle mass fraction (PMF or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula>), a measure of the particle-to-fluid mass ratio. Although a number of different changes have been reported to be obtained by the presence of solid particles in incompressible turbulent flows, the present study reports the findings of varying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula> in the the turbulent behaviour of the flow, including aspects such as: turbulent statistics, skin-friction coefficient, and the general dynamics of a particle-laden flow. For this purpose, a particle-laden turbulent channel flow transporting solid particles at three different friction Reynolds numbers, namely <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo><mn>180</mn></mrow></semantics></math></inline-formula>, 365, and 950, with a fixed particle volume fraction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>v</mi></msub><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, was employed as conceptual flow model and simulated using large eddy simulations. The value adopted for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>v</mi></msub></semantics></math></inline-formula> allowed the use of a two-way coupling approach between the particles and the flow or carrier phase. Three different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula> were explored in this work <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ϕ</mi><mi>m</mi></msub><mo>≈</mo><mn>1</mn><mo>,</mo><mn>2.96</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>12.4</mn></mrow></semantics></math></inline-formula>. Assessment of the effect of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula> was performed by examining changes of mean velocity profiles, velocity fluctuation profiles, and a number of other relevant turbulence statistics. Our results show that attenuation of turbulence activity of the carrier phase is attained, and that such attenuation increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula> at fixed Reynolds numbers and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>v</mi></msub></semantics></math></inline-formula>. For the smallest Reynolds number case considered, flows carrying particles with higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula> exhibited lower energy requirements to sustain constant fluid mass flow rate conditions. By examining the flow velocity field, as well as instantaneous velocity components contours, it is shown that the attenuation acts even on the largest scales of the flow dynamics, and not only at the smaller levels. These findings reinforce the concept of a selective stabilising effect induced by the solid particles, particularly enhanced by high values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mi>m</mi></msub></semantics></math></inline-formula>, which could eventually be exploited for improvement of energetic efficiency of piping or equivalent particles transport systems. |
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