Flow topology and bifurcations of buoyancy and mixed convection in an elongated channel with an abrupt section variation

Hybrid forced-buoyancy convection in a channel with a backward facing step

“…the scaling trend of the frequency spectrum (Kraichnan [43] ). Assuming the so-called Kolmogorov length scale ( ζ , known to be dependent on the Rayleigh and Reynolds number as indicated, e.g., in [30] ) as the typical mesh size, we have verified that the (-5/3) scaling trend predicted by Kolmogorov [ 44 , 45 ] is independent from the mesh in terms of velocity amplitude and related frequency distribution. Using this set of criteria, the required number of points has been found to range between a minimum of 400 and a maximum of 2800 in the horizontal direction (and a minimum of 40 and a maximum of 300 in the vertical direction) depending on the considered conditions (with the corresponding computational time required to run a complete simulation using four 3.4 GHz CPUs in parallel being 30 min, 4 h, 1 day, 3 days and 7 days for the cases with mesh 400 × 40, 800 × 80, 1200 × 120, 20 0 0 × 200 and 2800 × 300, respectively).…”

“…Conveniently, the relative importance of forced and buoyancy convection can be estimated a priori using a third characteristic parameter, namely, the aforementioned Richardson number, which for the sake of consistency with Lappa and Inam [29] and Inam and Lappa [30] here is introduced as:…”

“…An extensive verification of the present algorithm has already been provided in Inam and Lappa [30] where relevant arguments were also elaborated for mesh requirements. For the sake of…”

“…We wish also to recall that the present computational algorithm was validated in [30] through correlation with relevant test cases and benchmarks. Moreover, different fixed inclinations of the dominant temperature gradient with respect to vertical gravity were assumed in order to verify the ability of the solver to reproduce correctly the dynamics of the natural convection originating from the hot surfaces with horizontal or vertical orientation.…”

“…Furthermore, the ability of the algorithm to capture properly Hopf bifurcation was tested against the stability analysis by Mizushima and Adachi [48] . Finally, the properties of hybrid forced-buoyancy flow in the FFS configuration for various representative conditions were determined using different computational platforms (OpenFoam, Ansys Fluent and the code by Lappa [49] ) and compared in terms of non-dimensional angular frequency of the emerging oscillatory flow and/or time-averaged value of the Nusselt number (see again [30] ).…”