Determining the structure of a laminar detachable current in an open cavity

Abstract

The paper reports a three-dimensional numerical solution to the test problem about a viscous incompressible liquid flow in the closed square-shaped cavity with a movable upper face. Disadvantages in a mathematical statement of the problem about a flow of fluid in a closed cavity have been identified. A finite element method was applied in order to investigate numerically the structure of a circulating detachable laminar movement of viscous incompressible fluid in an open cavity considering the external flow. The profiles of vorticity, the thickness of a boundary layer, the constituents of velocity components in different cross-sections of the cavity, in the boundary layer, as well as in the blending layer, have been given.Typically, studying laminar currents in cavities employs a model of the cavity with a movable wall. However, such a statement of the problem imposes a restriction on the flow pattern in the form of a straight line of the flow that connects the upper corners of the cavity, which results in the distorted structure of vorticity formation in the cavity in general. Within the framework of the current study, the problem statement that overcomes the specified disadvantage has been proposed. The movement of fluid in a cavity occurs due to the shear stress of the external flow in a channel above the cavity, which rules out the straightness of the flow line, which connects the cavity's corner points. Reliability of the reported results has been confirmed by comparing certain parameters to known experimental data by other authors. The study's scientific result in the form of the vorticity structure of a viscous incompressible laminar flow in an open cavity with a channel is interesting from a theoretical point of view. As regards the practical point of view, the identified structure of the flow makes it possible to define the conditions to control a flow in the cavity and, therefore, allows determining the conditions for optimizing the aerodynamic forces acting on a cavity. The applied aspect of the obtained scientific result is the possibility to employ it for a flow over industrial facilities: buildings, inter-carriage space in a railroad train, etc.