Particle-to-fluid heat transfer in particle-laden turbulence

Preferential concentration of inertial particles by turbulence is a well-recognized phenomenon. This study investigates how this phenomenon impacts the mean heat transfer between the fluid phase and the particle phase. Using direct numerical simulations of homogeneous and isotropic turbulent flows coupled with Lagrangian point particle tracking, we explore this phenomenon over a wide range of input parameters. Among the nine independent dimensionless numbers defining this problem, we show that the particle Stokes number, defined based on a large-eddy time, and an identified number called the heat-mixing parameter have the most significant effect on particle-to-gas heat transfer, while variation in other nondimensional numbers can be ignored. An investigation of regimes with significant particle mass loading suggests that the mean heat transfer from particles to gas is hardly affected by momentum two-way coupling. Using our numerical results, we propose an algebraic reduced-order model for heat transfer in particle-laden turbulence.

Figure 1

Correction factor $\phi$ as a function of (a) total number of particles $N_p$, (b) nondimensional heat flux $\mathcal{S}$, (c) particle-to-gas heat capacity ratio $\chi$, and (d) Reynolds number $\text{Re}$ and ${\text{Re}}_{\lambda }$.

Figure 2

Correction factor $\phi$ as a function of (a) Stokes number ${\text{St}}_l$ and ${\text{St}}_{\eta }$ and (b) heat-mixing parameter ${\sigma }_l$.

Figure 3

Variation of $\phi$ as a function of (a) Reynolds number when the Stokes number and heat-mixing parameter are kept constant, where the subscripts $\eta$ and $l$ refer to normalizing by Kolmogorov and large-eddy turnover times, respectively, ${\text{St}}_l={\tau }_p/{\tau }_l,{\text{St}}_{\eta }={\tau }_p/{\tau }_{\eta },{\sigma }_l={\tau }_{th}/{\tau }_l$, and ${\sigma }_{\eta }={\tau }_{th}/{\tau }_{\eta }$, and (b) heat-mixing parameter ${\sigma }_l$ and Stokes number ${\text{St}}_l$.

Figure 4

Particle distribution and normalized fluid temperature deviation $T_g-{\langle T_g\rangle }_{\rho }$ contours for different combinations of ${\text{St}}_{\eta }$ and ${\sigma }_l$ in one slice of the domain.

Figure 5

(a) Particle-to-gas heat-transfer model schematics and (b) collapse of ${{\sigma }_l}^p/\phi -{{\sigma }_l}^p$ versus ${\text{St}}_l$ for different values of ${\sigma }_l$, with $p=0.95$.