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The fluid temperature statistics along particle trajectories is crucial to under- stand the mechanisms of turbulent non-isothermal or reactive fluid-particle flow, especially for the Lagrangian model of non-isothermal particle-laden turbulent flow. In the present study, direct numerical simulations were utilized to generate temperature field statistics in particle-laden incompressible stationary homogeneous isotropic turbulent flows, which is focused on the effect of particle response time on the Lagrangian statistics of the particle and the fluid temperature seen by particles. It shows that, for the particles with τp/τk < 1, the ratio of the fluid intensity seen by particle to fluid temperature intensities deceased as τp/τk increased; while for larger particles (τp/τk > 1), the trend is inversed. For small parti- cles (τp/τk<5), the Lagrangian autocorrelation coefficient of the particle temperature RpT decreases as the particle inertia (τp/τk) increases. The trend is reversed for larger particles. The autocorrelation of fluid temperature along the particle path, RpfT, decreased as the particle inertia increased. And as the particle inertia increased, the autocorrelation coeffi- cient of the fluid temperature seen by particle decreased more rapidly than that of the particle temperature. The mean temperature gradient contributes to the correlation be- tween the particles velocity component and temperature fluctuations in the direction of the gradient. For the particles with τp/τk<1, the magnitude of the correlation coefficient in- creases as the particle inertia increases, while this value is independent of the particle time constant for larger particles.
The fluid temperature statistics along particle trajectories is crucial to under-stand the mechanisms of turbulent non-isothermal or reactive fluid-particle flow, especially for the Lagrangian model of non-isothermal particle-laden turbulent flow. In the present study, direct numerical simulations were utilized to generate temperature field statistics in particle-laden incompressible stationary homogeneous isotropic turbulent flows, which is focused on the effect of particle response time on the Lagrangian statistics of the particle and the fluid temperature seen by particles. It shows that for the particles with τp / τk <1, the ratio of the fluid intensity seen by particle to fluid temperature intensities deceased as τp / τk increased; while for larger particles (τp / τk> 1), the trend is inversed. For small parti- cles τp / τk <5), the Lagrangian autocorrelation coefficient of the particle temperature RpT decreases as the particle inertia (τp / τk) increases. The trend is reverse d for larger particles. The autocorrelation of fluid temperature along the particle path, RpfT, decreased as the particle inertia increased. And as the particle inertia increased, the autocorrelation coeffi- cient of the fluid temperature seen by particle decreased more rapidly than that of the particle temperature. The mean temperature gradient contributes to the correlation be- tween the particles velocity component and temperature fluctuations in the direction of the gradient. For the particles with τp / τk <1, the magnitude of the correlation coefficient in- creases as the particle inertia increases, while this value is independent of the particle time constant for larger particles.