Unsteady Heat Transfer From a Spherical Particle in Turbulent and Oscillating Ambient Flows

Direct Numerical Simulation based on pseudospectral methodology is used to study the effect of freestream turbulence and freestream oscillation on the heat transfer from a sphere. The sphere Reynolds number is in the range 63 to 400, and the ratio of sphere diameter to Kolmogorov scale ranges from 1.08 to 8. The objective is to obtain the unsteady heat transfer from the sphere at finite sphere Reynolds number Re and Prandtl number Pr in presence of a time-dependent ambient flow from the DNS, and compare that with the analytical expression valid for vanishing thermal advection. Results from three sets of simulations are presented: (1) Only turbulent velocity field is applied in the inflow, while the inflow temperature condition is held constant; (2) turbulent temperature condition is applied at the inflow, and the velocity is held constant; and (3) both turbulent velocity and temperature fields are applied in the inflow. These simulations allow us to isolate the role of freestream temperature and velocity fluctuations on Nusselt number. We show that the freestream turbulence has a very little effect on the time-averaged Nusselt number, but the instantaneous Nusselt number can vary by a factor of two over time. The unsteady thermal effects are small for small particle size, but not so when particle size is larger than the Kolmogorov scale. It is observed that the analytical expression of the thermal added-mass force significantly over-predicts the unsteady thermal effects. The thermal history effect is shown to be insignificant. The DNS result can be predicted, at best, by the quasi-steady result. The difference is maximum when both the ambient velocity and temperature are turbulent. We also examine various approximations of the ambient velocity and temperature as seen by the particle that can give a better estimate for the thermal added-mass effect. We then present results on the unsteady heat transfer in presence of an oscillating freestream velocity and temperature, considered separately. It is shown that analytical form of the thermal added-mass predicts an order of magnitude higher values than that obtained in the DNS, supporting the results on ambient turbulent condition. We further show that a pure oscillating ambient velocity also has a thermal added-mass effect.