Order Boundary Layer Research Articles

The Singularity at Boundary Layer Separation Due to Mass Injection

A boundary layer analysis of separation due to uniformly distributed mass injection from a flat plate in a uniform external stream is reconsidered. The calculation is predicated upon the existence of a point of zero wall shear which numerical calculations based on first order boundary layer equations seem to imply. As a result of performing the analysis in terms of the stream function $\psi ( {x,y} )$ rather than Crocco variables $\tau ( {x,u} )$, it is possible to show directly that the boundary layer thickness becomes indefinitely large in a logarithmic fashion as the separation line is approached. Results for the wall shear distribution near separation are obtained in a form considerably more concise than that found in the past. An examination of the structure of the singularity at blowoff' implies that classical boundary layer theory fails to provide a meaningful description of the flow near points of very small shear. It is suggested that a pressure interaction analysis which has been used for a similarity blowoff calculation would provide a more meaningful description of the flow.

Second Order Boundary Layer Solutions on a Curved Surface

Solutions of the second order longitudinal curvature boundary layer equations near the stagnation point of a two-dimensional circular cylinder are presented. Four cases corresponding to 1 first order locally similar solutions, 2 first order nonsimilar solutions, 3 second order locally similar solutions, and 4 second order nonsimilar solutions are considered. For each of the four cases, results for four different altitudes are given. The only second order effect considered is longitudinal curvature. Based on the numerical results, it is concluded that similarity and curvature assumptions can alter the skin friction calculations significantly. The heat transfer calculations are much less sensitive to the various assumptions, at least for the cases studied in this paper.

VELOCITY AND SHEAR STRESS IN WAVE BOUNDARY LAYERS

The critical force for the entrainment of sediment on the ocean floor is the maximum, instantaneous shear force. A numerical estimate for the stress is made from the third approximation of a second order boundary layer theory for oscillating laminar flow. The analytical derivation satisfies both the case of flow in an oscillating water tunnel and the case of a progressive (Airy) wave, where the shear distribution depends on the form of the velocity distribution in the boundary layer. Solution for the velocity is on the basis of iteration in an infinite series, where the convective terms are numerically evaluated from lower order solutions. For the boundary shear, the phase lead is found to be less than predicted by linear theory, and although the correction at the third approximation is small compared to lower approximations, the modified vertical distribution provides a basis for the correction of shear measurements, obtained by indirect means, to the boundary value.

Self-similar solutions of the second order boundary layer of an incompressible fluid with heat transfer

Self-similar solutions of the second-order incompressible boundary-layer equations, containing terms due to longitudinal curvature, transverse curvature, external vorticity, displacement speed and stagnation enthalpy gradients have been studied. Numerical as well as several closed form solutions are presented for both the skin friction and heat transfer rate at the wall.

Time dependent shear stress and temperature distribution over an insulated flat plate moving at hypersonic speed

The laminar two-dimensional flow over a stepwise accelerated flat plate moving with hypersonic speed at zero angle of attack is analysed. The governing equations in the self-similar form are linearized and solved numerically for small times. The solutions obtained are the deviations of the velocity and the temperature profiles from those of steady state. The presented results may be used to find the first order boundary layer induced pressure on the plate.

Laminar incompressible flow past a circulation- controlled circular lifting rotor

Prandtl first order boundary layer equations for two dimensional laminar incompressible flow past circulation controlled circular lifting rotor

Comments on ''approximate solution of second- order boundary-layer equations.''

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KINETIC ENERGY GENERATION AND DISSIPATION IN THE LARGE-SCALE ATMOSPHERIC CIRCULATION

The kinetic energy budget and dissipation are studied in their various partitionings, using daily aerological (wind and geopotential) data from the network over North America for six months. The total kinetic energy dissipation is partitioned into vertical mean flow and shear flow and also into planetary boundary layer and free atmosphere. Furthermore, the dissipations in the vertical mean flow and shear flow are partitioned separately into components contributed by the boundary layer and free atmosphere. Two important terms in the total kinetic energy equation in determining the total dissipation are the generation and outflow. TWO important terms in the mean flow kinetic energy equation in determining the mean flow dissipation are the conversion between the vertical shear and mean flows and the outflow. The mean flow and shear flow dissipations seem to have numerical values of the same order of magnitude. The evaluated boundary layer dissipation and free atmosphere dissipation indicate that the latter is at least as important as the former. It is also shown that the mean flow dissipation is mainly contributed from the free atmosphere while the shear flow dissipation is contributed fromthe boundary layer and free atmosphere in the same order of magnitude. The evaluated dissipation values and related kinetic energy parameters are presented and examined in detail. Of special interest in this study is the direct evaluation of the kinetic energy generation due to the work done by the horizontal pressure force. Daily variation of the generation at different pressure levels seems to suggest three different modes of the generation cycle in the upper, mid, and lower troposphere. Clear vertical profiles of the generation from the surface to the 100-mb. level are obtained; it is shown that strong generation takes place in the upper and lower troposphere while the generation in the mid troposphere is very weak. It is also suggested that there may be an approximate balance of the kinetic energy generation and dissipation in the boundary layer.