Simultaneous velocity-temperature measurements in the heated wake of a cylinder with application to the modeling of turbulent passive scalars

The principal objective of this work is to study the sensitivity of (i) the turbulent Prandtl number ($Pr_T$), and (ii) the mechanical-to-thermal time-scale ratio ($r$) to differences in the scalar field's injection method within the same (hydrodynamic) flow. Both are recurring quantities employed in turbulence models, determined from experiments, and generally assumed to be (flow-dependent) constants. To this end, mixed velocity-temperature measurements were made in the heated wake of a circular cylinder. The passive scalar under consideration was temperature and the wake was heated by one of two ways: heating the cylinder itself, or by use of a mandoline placed downstream of the cylinder. For each case, the distributions of the turbulent Prandtl number and the mechanical-to-thermal time-scale ratio were compared. The experimental results demonstrate that both $Pr_{T}$ and $r$ differ for the two scalar injection methods (in addition to varying across the wake). Hence, both $Pr_{T}$ and $r$ not only depend on the type of flow, but on the scalar field injection method as well - a result that is generally not take into account when turbulent flows are modeled.