Matt de Stadler - Large Eddy Simulation of the near to intermediate wake of a heated sphere at Re = 10,000

Large Eddy Simulation of the near to intermediate wake of a heated sphere at Re = 10,000

Motivation: Scalar mixing is important for a large number of practical situations from industrial applications to the detection of underwater vehicles to mixing and transfer of energy and contaminants in the ocean and atmosphere. Despite the practical importance of this flow, the literature for scalar mixing in the wake of three-dimensional bluff bodies is rather limited. Here we investigate the near to intermediate wake of a heated sphere to demonstrate the ability of our immersed boundary method to provide accurate results for bluff body flows and to characterize the velocity and temperature fields in the near wake of a heated sphere.

Large eddy simulation was used to numerically simulate flow past a heated sphere at Re=10,000. A second order accurate in space and time, semi-implicit finite difference code is used with the immersed boundary to represent the sphere in a Cartesian domain; no wall model is used for LES. 106400 CPU hours on 800 processors were required for this study on Haise, an IBM iDataPlex at the NAVY DSRC. Good agreement with the DNS data of Rodriguez et. al. CF 2013 was observed for the mean velocity and fluctuations in the near wake.

Visualizations of the temperature and vorticity field show a link between the coherent structures in the velocity field and temperature fluctuations. The separated shear layer carries hot fluid away from the hot sphere and into the cold fluid. Mixing is enhanced by the Kelvin-Helmholtz shear instability which causes rollers to form which engulfs cold fluid into the hot region. The decay rates of the mean velocity, mean temperature, velocity fluctuation and temperature fluctuation showed the presence of different scaling rates in the near wake after the recirculation region and in the intermediate wake, 15 < x/D < 35. Similarity is observed for the mean temperature, fluctuating velocity and fluctuating temperature fields in the wake. The mean velocity is close to similar but the agreement is not as good as in the other cases. Radial profiles of the Reynolds stress, <u_x' u_r'> , exhibit similarity and so do the thermal fluxes <T' u_x'> and <T' u_r'>.

Important Conclusions: The thin separated shear layer plays a crucial role in transporting heat from the sphere surface to the wake and then later mixing it via Kelvin-Helmholtz instability. An intermediate region between the recirculating region and the classical far wake region was observed in agreement with the theoretical predictions of Nedic et. al. PRL 2013.

For further details on this work, see the 2014 International Journal of Heat and Fluid Flow paper by de Stadler, Rapaka, and Sarkar (accepted).


Movie showing the evolution of the temperature field behind a hot sphere at Re=10,000. Red indicates hot fluid and blue shows colder fluid.	Instantaneous contours of the temperature field (top) and spanwise vorticity &omega₂ (bottom) in an x-z plane. In the top image, darker color indicates hot fluid and white indicates cold fluid. Note the similar structure of the temperature and the vorticity fields.