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Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.


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TL;DR: The results of an experimental study of stability, receptivity and transition of the flat-plate laminar boundary layer at Mach 3 are discussed in this paper, with a relatively low free-stream disturbance level (∼0.1%), spectra, growth rates and amplitude distributions of naturally occurring boundary layer waves were measured using hot wires.
Abstract: The results of an experimental study of stability, receptivity and transition of the flat-plate laminar boundary layer at Mach 3 are discussed. With a relatively low free-stream disturbance level (∼0.1%), spectra, growth rates and amplitude distributions of naturally occurring boundary layer waves were measured using hot wires. Physical (mass-flux) amplitudes in the boundary layer and free stream are reported and provide stability and receptivity results against which predictions can be directly compared. Comparisons are made between measurements of growth rates of unstable high-frequency waves and theoretical predictions based on a non-parallel, mode-averaging stability theory and receptivity assumptions; good agreement is found. In contrast, it was found that linear stability theory does not account for the measured growth of low-frequency disturbances. A detailed investigation of the disturbance fields in the free stream and on the nozzle walls provides the basis for a discussion of the source and the development of the measured boundary layer waves. Attention is drawn to the close matching in streamwise wavelengths for instability waves and the free-stream acoustic disturbances. It was also found that a calibration of the hot wire in the free stream yields a double-peak boundary layer disturbance amplitude distribution, as has been found by previous investigators, which is not consistent with the predictions of linear stability theory. This double peak was found to be an experimental anomaly which resulted from assumptions that are frequently made in the free-stream calibration procedure. A single-peak amplitude distribution across the boundary layer was established only when the hot-wire voltage was calibrated against the mean boundary layer profile. Finally, the late stages of transition, at a higher Reynolds number with a higher free-stream disturbance level, were explored. Calibrated amplitude levels are provided at locations where nonlinearities are first detected and where the mean boundary layer profile is first observed to depart from the laminar similarity solution. A qualitative discussion of the character of ensuing nonlinearities is also included.

33 citations

Journal ArticleDOI
TL;DR: In this paper, a thin, flat plate moving slowly and horizontally through a linearly stratified salt-water mixture has, in addition, a boundary layer over the plate whose thickness increases upstream from the back of the plate.
Abstract: The existence of a ‘wake’ upstream of an obstacle moving slowly through a stratified fluid has been known for some time. The present study shows that a thin, flat plate moving slowly and horizontally through a linearly stratified salt-water mixture has, in addition, a boundary layer over the plate whose thickness increases upstream from the back of the plate.The theory assumes that the ratio of diffusivity to viscosity is small, and that the plate moves so slowly that inertia forces are negligible; under these conditions, a similarity solution is derived describing the boundary layer over the plate. The study also shows that salt diffusion is important in a second, thinner boundary layer whose thickness increases from the front of the plate.In the experiment, a plate was towed through a tank of linearly stratified salt water. From streak photographs of the boundary layer over the plate, it was possible to confirm quantitatively the similarity solution and to infer at very slow velocities the presence of the thin diffusion boundary layer.

33 citations

Journal ArticleDOI
TL;DR: In this paper, a cold, thin film of liquid impinging on an isothermal hot, horizontal surface is modelled as a two-dimensional jet of prescribed uniform velocity, film thickness and temperature.

33 citations

Journal ArticleDOI
C. Sozou1
TL;DR: In this paper, the authors considered the flow field induced in an incompressible viscous conducting fluid, occupying the interior of a right circular cone, by an electric current source situated at the vertex of the cone.
Abstract: In this paper we consider the flow field induced in an incompressible viscous conducting fluid, occupying the interior of a right circular cone, by an electriccurrent source situated at the vertex of the cone. We assume that the velocity field is small and its effect on the electromagnetic field is negligible. A similarity solution is obtained for the non-linear problem. This solution is an adaptation of Slezkin's solution for the momentum transfer through a viscous jet and, apart from the numerical solution of a Riccati type of equation, is exact. In particular, we investigate the case when the half angle of the cone is ½π and the fluid occupies the whole space on one side of an infinite plane. We also consider the corresponding inviscid flow problem that was recently investigated by another author and suggest that the solution obtained is not physically realistic.

33 citations

Journal ArticleDOI
TL;DR: An analytical expression of the Sherwood number is developed from first principles for combined flow of pressure driven and electroosmotic flow in this paper, which is useful for efficient design of microfluidic devices and flow through porous media.

33 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850