Numerical investigation of natural convection in slope longitudinal air layer

Mathematics. Physics. Mechanics


Pivovarov D. E.

Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia



It is the numerical investigation of the natural convection flow pattern and heat transfer rate inside rectangular box heated from below and cooled from above with insulated sidewalls. The box is inclined from horizontal to vertical position and back round the shortest side. This is the longitudinal configuration of the inclined layer for which the transversal rolls are typical.
Direct numerical simulation (DNS) of Navier-Stokes equations for incompressible fluid is applied. The numerical method is based on a second-order central difference approximation in space and on integration for time by a third-order semi-implicit Runge–Kutta method. Spatial discretization retains some important properties of the Navier–Stokes equations, including energy conservation by the nonlinear and pressure-gradient terms. The scheme is supplied with a local error estimation and time-step control algorithm.
The hysteresis with subject to changing the inclination of the box has been confirmed. Different convection interactions have been detected. It is noted that there are oscillations of flow for some angles at high Rayleigh numbers. The comparison of regime diagram for spatial and plane flow showed the discrepancy in number of rolls and the borders of their number change.
The study is limited by laminar regime for incompressible fluid for which Boussinesq approximation is right. The observable fluid was air. The Rayleigh number is varied between 103 and 105 and the angle range from 0 up to 90°.
This is the study of spatial pattern and heat transfer rate of convection interactions in the longitudinal layer defined by the aspect ratios of the box. The diagram of the interactions regime was sketched.


Navier-Stokes equation, Boussinesq approximation, modeling, natural convection, bifurcations, hysteresis, slope layer


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