Effect of freestream isotropic turbulence on heat transfer from a sphere

We consider direct numerical simulation (DNS) based on pseudospectral methods to study the heat transfer around a stationary sphere held at a constant temperature and subject to an ambient turbulent velocity and temperature condition. The sphere Reynolds number is in the range of 63–400, and the sphere diameter (d) varies from one to eight times the Kolmogorov scale (η). The ambient turbulent field is isotropic, and the Taylor microscale Reynolds number Rλ varies from 38 to 240. Results from two sets of DNS are presented. In the first set, the ambient velocity field is turbulent, but the ambient temperature is held constant. In the second set of simulations, both the ambient velocity and the temperature fields are turbulent. These two sets of simulations allow us to isolate the role of freestream velocity fluctuations and temperature fluctuations in modifying the mean and time-dependent heat transfer from the sphere. The mean Nusselt number is observed to be independent of Rλ. It is shown that the freestream turbulence does not have any significant effect on the mean Nusselt number, and the available correlations for a steady and uniform ambient can predict the mean Nusselt number under the turbulent ambient condition. The instantaneous Nusselt number, however, can differ significantly from the mean, and can be negative in case of large temperature fluctuation in the far field. The instantaneous Nusselt number obtained from the DNS is analyzed and compared with the analytical expression for the unsteady thermal response of a sphere. It is shown that the thermal added-mass effect is small for d/η≈1 but introduces spurious oscillation at higher d. The thermal history effect is shown to be insignificant for all d/η. Properties of the thermal wake in the presence of the turbulent velocity and temperature fields are studied. The mean thermal wake is observed to be shorter in streamwise direction and wider in crossflow direction in a turbulent ambient than that in a steady and uniform ambient. The mean thermal wake is shown to behave like a self-preserving laminar wake. It is also shown that the fluctuation in the ambient temperature is damped out in the sphere wake, and the large variation observed in the instantaneous Nusselt number arises from the variation in the local heat transfer near the front stagnation area of the sphere rather than the wake.