Abstract
Based on the numerical and experimental visualization methods, the flow patterns around a uniformly moving plate located at an arbitrary angle of attack are studied. The study is based on the fundamental equations of continuity, momentum and stratifying substance transport for the cases of strong and weak stratified fluids, as well as potential and actually homogeneous ones. The visualization technique and computation codes were compiled bearing in mind conditions of internal waves, vortices, upstream, and downstream wakes registration, as well as the resolution of ligaments in the form of thin interfaces in schlieren flow images. The analysis was carried out in a unified mathematical formulation for a wide range of plate motion parameters, including slow diffusion-induced flows and fast transient vortex flows. The patterns of formation and subsequent evolution of the basic structural components, such as upstream disturbances, downstream wake, internal waves, vortices, and ligaments, are described both at start of motion and subsequent uniform movement of the plate. Calculations of forces acting on the obstacle in the flow were carried out to study effects of variations in fluid properties, flow conditions and plate parameters on the dynamic characteristics of the obstacle. The numerical and experimental results on the flow patterns around a plate are in a good agreement with each other for different flow regimes.
Highlights
The beginning of a new stage in the development of hydrodynamics is associated with the direct participation of outstanding mathematicians in solving the practically important problems
Different flow regimes are considered, such as creeping, wave and unsteady vortex ones, which are characterized by their individual sets of dominating structural flow components, including up-stream perturbations, internal waves, vortices, and ligaments
In the calculated and schlieren visualized patterns of stratified flows around a vertical plate, all the structural elements of the stratified flow are well manifested, including slowly evolving ones, such as fields of attached waves, upstream perturbations, and vortex wake past the obstacle, and rapidly changing ones, such as fine structural interfaces, and their sets: Vortices (Figure 8)
Summary
The beginning of a new stage in the development of hydrodynamics is associated with the direct participation of outstanding mathematicians in solving the practically important problems. The characteristics of the wake vortex structure, which depends on many parameters of the problem, including leading edge shape, angle of attack and velocity of the body, is studied by different methods in laboratory and numerical experiments. A significant scientific and practical interest lies in the study of a free 2D body motion with its angular position and velocity changing as a result of interaction with the formed flow Such kind of studies were carried out experimentally in [24], as well as analytically and numerically in [25] and [26] respectively. This review, being far from complete, shows that the study of the flow pattern around a plate, which depends on a large number of factors, including size, angular position, edge shape, surface quality, flow velocity of the body, stratification value, viscosity and density of the medium, etc., retains its scientific relevance and practical significance. The numerical results on stratified and homogeneous fluid flows around obstacles are qualitatively compared with the Schlieren visualization data in the laboratory experiments
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