Quasi-one-dimensional method of calculating an MHD generator on the boundary-layer approximation

1976 ◽  
Vol 9 (4) ◽  
pp. 615-620
Author(s):  
V. V. Breev ◽  
V. P. Panchenko
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Approximation ◽  
One Dimensional ◽  
Mhd Generator

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

A simple calculation method for estimating the flow velocity on the roof of a train running through a tunnel using an unsteady incompressible flow model

2019 ◽  
Vol 234 (7) ◽  
pp. 734-748
Author(s):  
Katsuhiro Kikuchi ◽  
Satoru Ozawa ◽  
Yuhei Noguchi ◽  
Shinya Mashimo ◽  
Takanobu Igawa
Keyword(s):  
Boundary Layer ◽  
Flow Velocity ◽  
Calculation Method ◽  
Model Experiment ◽  
Flow Model ◽  
Simple Calculation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Calculation Results ◽  
Tunnel System

Predicting the aerodynamic phenomena in a train-tunnel system is important for increasing the speed of railway trains. Among these phenomena, many studies have focused on the effects of pressure; however, only a few studies have examined the effects of flow velocity. When designing train roof equipment such as a pantograph and an aerodynamic braking unit, it is necessary to estimate the flow velocity while considering the influence of the boundary layer developed on the train roof. Until now, numerical simulations using a one-dimensional model have been utilized to predict the flow velocity around a train traveling through a tunnel; however, the influence of the boundary layer cannot be taken into consideration in these simulations. For this purpose, the authors have previously proposed a simple calculation method based on a steady incompressible tunnel flow model that can take into account the influence of the boundary layer, but this method could not incorporate the unsteadiness of the flow velocity. Therefore, in this study, the authors extend the previous simple calculation method such that it can be used for an unsteady incompressible tunnel flow. The authors compare the calculation results obtained from the extended method with the results of a model experiment and a field test to confirm its effectiveness.

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