Impulsive Motion in a Particle-Fluid Suspension Including Particulate Volume, Density, and Migration Effects

1974 ◽  
Vol 41 (1) ◽  
pp. 35-41 ◽  
Author(s):  
P. R. Di Giovanni ◽  
S. L. Lee
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Lift Force ◽  
Interaction Force ◽  
Volume Density ◽  
Solid Particles ◽  
Impulsive Motion ◽  
Viscous Boundary Layer ◽  
Small Times ◽  
Particulate Volume

Based on expansions for small and large times, velocity and particulate volume distributions are obtained from the approximate continuum representation of a suspension of uniformly distributed small spherical solid particles for flow induced by impulsive motion of an infinite flat plate. Included in the analysis are major effects of the fractional particulate volume, which is assumed to vary due to the inclusion of the particle slip-shear lift force, as well as a generalized drag interaction force. For both small and large times, the lift force results in an accumulation of particles near the wall. Motion in the horizontal direction is determined in terms of modified similarity variables for large and small times indicating an increase or decrease in the viscous boundary layer for small times depending on the fractional volume of particles, and an increase or decrease for large times depending on whether the particles are lighter or heavier than the fluid. To the zeroth order, the skin friction on the wall is shown to increase or decrease for small times depending on whether the ambient fractional particulate volume is greater or less than 1/4. For large times the friction increases for heavy particles and decreases for light particles. Finally, by using the modified Rayleigh’s method, an estimate is made for boundary-layer flow past a semi-infinite flat plate.

Deposition of solid particles in laminar boundary layer on a flat plate

2009 ◽  
Vol 47 (6) ◽  
pp. 892-901 ◽  
Author(s):  
A. I. Kartushinsky ◽  
I. A. Krupensky ◽  
S. V. Tisler ◽  
M. T. Hussainov ◽  
I. N. Shcheglov
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Solid Particles

scholarly journals Karakteristik Wake Area Akibat Efek Penggunaan Vortex Generator di Belakang Wing Airfoil Naca 43018

2019 ◽  
Vol 4 (1) ◽  
pp. 55-63
Author(s):  
Setyo Hariyadi S.P ◽  
Wawan Aries Widodo
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Drag Force ◽  
Lift Force ◽  
Vortex Generator ◽  
Leading Edge ◽  
O 15 ◽  
O 19 ◽  
Wing Airfoil

Pada aliran yang melintasi suatu airfoil terdapat fenomena separasi, yakni ketika momentum aliran sudah tidak mampu lagi mengatasi adverse pressure gradien. Selanjutnya separasi ini akan diikuti dengan timbulnya daerah wake pada daerah di belakang airfoil yang mengakibatkan naiknya drag force dan menurunnya lift force. Untuk mengurangi hal tersebut maka vortex generator diletakkan pada sisi atas airfoil untuk mempercepat terbentuknya turbulent boundary layer sehingga dapat menunda separasi dan memperkecil daerah wake. Efektivitas dari vortex generator dipengaruhi oleh penempatan, ketinggian, dan interval antar vortex generator. Untuk mendapatkan hasil yang optimal, drag yang dihasilkan oleh vortex generator itu sendiri harus dikurangi. Untuk itu profil dari vortex generator yang digunakan harus sedemikian rupa sehingga drag yang dihasilkan dapat dikurangi tanpa menurunkan performasi dari airfoil tersebut. Oleh karena itu, penelitian ini dilakukan untuk melihat pengaruh penambahan vortex generator terhadap unjuk kerja airfoil melalui metode eksperimen. Tujuan penelitian ini adalah membandingkan karakteristik aliran fluida plain wing dan dengan penambahan vortex generator. Profil vortex generator yang digunakan adalah flat plate vortex generator dengan konfigurasi straight dan ditempatkan pada x/c = 10% dan 20% arah chord line dari leading edge. Variasi yang digunakan adalah bilangan Reynolds (Re), sudut serang (α) dan peletakan vortex generator pada airfoil. Kecepatan freestream yang digunakan yaitu kecepatan 12 m/s atau Re = 7,65 x 105 dan kecepatan 17 m/s atau Re = 9 x 105, dan pada sudut serang (α) 0o, 3 o, 6 o, 9 o, 12 o, 15 o, 19 o, dan 20 o. Hasil penelitian ini menunjukkan bahwa terjadi peningkatan performansi dari airfoil NACA 43018 dengan penambahan vortex generator dibandingkan dengan tanpa vortex generator. Adanya vortex generator, mempercepat perubahan dari aliran laminar ke turbulen. Separasi dapat tertunda dengan adanya vortex generator.

The generation of Tollmien-Schlichting waves by free-stream turbulence

1996 ◽  
Vol 312 ◽  
pp. 341-371 ◽  
Author(s):  
P. W. Duck ◽  
A. I. Ruban ◽  
C. N. Zhikharev
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Stokes Equations ◽  
Leading Edge ◽  
Wave Generation ◽  
Generation Process ◽  
Viscous Boundary Layer ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting

The phenomenon of Tollmien-Schlichting wave generation in a boundary layer by free-stream turbulence is analysed theoretically by means of asymptotic solution of the Navier-Stokes equations at large Reynolds numbers (Re → ∞). For simplicity the basic flow is taken to be the Blasius boundary layer over a flat plate. Free-stream turbulence is taken to be uniform and thus may be represented by a superposition of vorticity waves. Interaction of these waves with the flat plate is investigated first. It is shown that apart from the conventional viscous boundary layer of thickness O(Re−1/2), a ‘vorticity deformation layer’ of thickness O(Re−1/4) forms along the flat-plate surface. Equations to describe the vorticity deformation process are derived, based on multiscale asymptotic techniques, and solved numerically. As a result it is shown that a strong singularity (in the form of a shock-like distribution in the wall vorticity) forms in the flow at some distance downstream of the leading edge, on the surface of the flat plate. This is likely to provoke abrupt transition in the boundary layer. With decreasing amplitude of free-stream turbulence perturbations, the singular point moves far away from the leading edge of the flat plate, and any roughness on the surface may cause Tollmien-Schlichting wave generation in the boundary layer. The theory describing the generation process is constructed on the basis of the ‘triple-deck’ concept of the boundary-layer interaction with the external inviscid flow. As a result, an explicit formula for the amplitude of Tollmien-Schlichting waves is obtained.

scholarly journals On the instability of hypersonic flow past a flat plate

1993 ◽  
Vol 247 ◽  
pp. 369-416 ◽  
Author(s):  
Nicholas D. Blackaby ◽  
Stephen J. Cowley ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Flat Plate ◽  
Leading Edge ◽  
Fluid Viscosity ◽  
Hypersonic Boundary Layer ◽  
Interaction Zone ◽  
Viscous Boundary Layer ◽  
Starting Point ◽  
Inviscid Instability

The instability of hypersonic boundary-layer flow over a flat plate is considered. The viscosity of the fluid is taken to be governed by Sutherland's formula, which gives a more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapman's approximate linear law. A Prandtl number of unity is assumed. Attention is focused on inviscid instability modes of viscous hypersonic boundary layers. One such mode, the ‘vorticity’ mode, is thought to be the fastest growing disturbance at high Mach numbers, M [Gt ] 1; in particular it is believed to have an asymptotically larger growth rate than any viscous instability. As a starting point we investigate the instability of the hypersonic boundary layer which exists far downstream from the leading edge of the plate. In this regime the shock that is attached to the leading edge of the plate plays no role, so that the basic boundary layer is non-interactive. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained if a Chapman viscosity law is assumed. In particular, we find that the growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O((log M)½). Next, the development of the vorticity mode as the wavenumber decreases is described. It is shown, inter alia, that when the wavenumber is reduced to O(M-3/2) from the O(1) initial, ‘vorticity-mode’ scaling, ‘acoustic’ modes emerge.Finally, the inviscid instability of the boundary layer near the leading-edge interaction zone is discussed. Particular attention is focused on the strong-interaction zone which occurs sufficiently close to the leading edge. We find that the vorticity mode in this regime is again unstable. The fastest growing mode is centred in the adjustment layer at the edge of the boundary layer where the temperature changes from its large, O(M2). value in the viscous boundary layer, to its O(1) free-stream value. The existence of the shock indirectly, but significantly, influences the instability problem by modifying the basic flow structure in this layer.

A note on the distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

1993 ◽  
Vol 248 ◽  
pp. 531-541 ◽  
Author(s):  
M. E. Goldstein ◽  
S. J. Leib
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Local Solution ◽  
Residual Velocity ◽  
Viscous Boundary Layer ◽  
Wall Boundary Layer ◽  
Viscous Boundary ◽  
Flat Plate Boundary Layer

The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib & Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.

Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

1992 ◽  
Vol 237 ◽  
pp. 231-260 ◽  
Author(s):  
M. E. Goldstein ◽  
S. J. Leib ◽  
S. J. Cowley
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Leading Edge ◽  
Uniform Flow ◽  
Viscous Boundary Layer ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Flat Plate Boundary Layer

We consider a nominally uniform flow over a semi-infinite flat plate. Our analysis shows how a small streamwise disturbance in the otherwise uniform flow ahead of the plate is amplified by leading-edge bluntness effects and eventually leads to a small-amplitude but nonlinear spanwise motion far downstream from the leading edge of the plate. This spanwise motion is then imposed on the viscous boundary-layer flow at the surface of the plate – causing an order-one change in its profile shape. This ultimately reduces the wall shear stress to zero – causing the boundary layer to undergo a localized separation, which may be characterized as a kind of bursting phenomenon that could be related to the turbulent bursts observed in some flat-plate boundary-layer experiments.

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