A numerical study of scalar dispersion downstream of a wall-mounted cube using direct simulations and algebraic flux models

Research highlights: → The computed DNS statistics indicate that a gradient-transport scheme can be applied to the vertical and spanwise scalar flux components. → The streamwise scalar flux is characterized by a counter-gradient transport mechanism in the wake region close to the obstacle. → The wake profiles of scalar fluctuations and the shape of probability density functions do not suggest a significant flapping movement of the scalar plume. → The evaluation of scalar dispersion models must include a careful assessment of the computed mean velocity field and Reynolds stress tensor. → Algebraic models provide an improved prediction of the mean concentration field as compared to the standard eddy-diffusivity model. -- Abstract: The dispersion of a passive scalar downstream of a wall-mounted cube is examined using direct numerical simulations and turbulence models applied to the Reynolds equations. The scalar is released from a circular source located on top of the obstacle, which is immersed in a developing boundary-layer flow. Direct simulations are performed to give insight into the mixing process and to provide a reference database for turbulence closures. Algebraic flux models are evaluated against the standard eddy-diffusivity representation. Coherent structures periodically released from the cube top are responsible for a counter-diffusion mechanism appearing in the streamwise scalar flux. Alternating vortex pairs form from the lateral edges of the cube, but the intensity profiles and probability density functions of scalar fluctuations suggest that they do not cause a significant flapping movement of the scalar plume. The gradient-transport scheme is consistent with the vertical and spanwise scalar flux components. From the comparative study with our direct simulations, we further stress that Reynolds stress predictions must be carefully evaluated along with scalar flux closures in order to establish the reliability of Reynolds-averaged computations. However, the analysis also shows that algebraic closures provide a significant improvement which cannot be achieved with the standard eddy-diffusivity model.