Péclet-number dependence of small-scale anisotropy of passive scalar fluctuations under a uniform mean gradient in isotropic turbulence

Scalars in bubbly turbulence

“…Let λ u and λ θ be the Taylor-microscale of the velocity and the temperature, respectively [12]. For the single phase turbulent thermal mixing layer, the Taylor Reynolds number is Re λu = u 0 λ u /ν = 130 and the Péclet numbers based on both microscales are Pe λu = u 0 λ u /κ = 870 and Pe λ θ = u 0 λ θ /κ = 520 [12].…”

“…Let λ u and λ θ be the Taylor-microscale of the velocity and the temperature, respectively [12]. For the single phase turbulent thermal mixing layer, the Taylor Reynolds number is Re λu = u 0 λ u /ν = 130 and the Péclet numbers based on both microscales are Pe λu = u 0 λ u /κ = 870 and Pe λ θ = u 0 λ θ /κ = 520 [12]. Re λu is the typical Reynolds number that is used for characterising the inertial effect when compared to viscous effect for grid-turbulence (freely decaying turbulence) [9], unlike other bounded turbulent flows which use the length of the size domain as the length scale.…”

“…Extending this notion to scalar field in grid-turbulence, to compare the inertial effect to the diffusive effect of the scalar, we use the Péclet number that based on the microscales. One traditional choice of such microscale is λ u [95] but recent numerical simulations uncover that the small-scale anisotropy of the scalar field depends on the Péclet number based on λ θ [12]. For the millimetric bubble sizes and velocities, the bubbles are detected by a circular Hough transform and tracked (see Table 4.1 in the Appendix).…”

“…Together (u 0 , u rms , T rms , η, η θ , λ u , λ θ , L u , L θ ) are the control parameters for a single-phase turbulent flow. By dimensional analysis, some dimensionless numbers can be formed to represent the physical system, namely Re = u 0 L u /ν, Pe = u 0 L θ /κ, Re λu = u rms λ u /ν, Pe λu = u rms λ u /κ, Pe λ θ = u rms λ θ /κ [12] and the Prandtl number Pr = ν/κ. In particular, in room temperature, water has Pr ≈ 7, and air has Pr ≈ 0.7.…”

“…Second, we estimate the scalar microscale λ θ = 6κ T 2 / θ , which also assumes isotropy. Third, motivated by recent work [12] that shows the Péclet number based on the scalar microscale can characterise the degree of small-scale anisotropy of passive scalar fluctuations, we also calculate such Péclet number P e λ θ = u 0 λ θ /κ, where κ is the thermal diffusivity of the working liquid. The commonly used Péclet number based on the Taylor microscale of the velocity P e λu = u 0 λ u /κ is also calculated [95].…”