scholarly journals Induced dusty flow due to normal oscillation of wavy wall

2001 ◽  
Vol 26 (4) ◽  
pp. 199-223
Author(s):  
K. Kannan ◽  
V. Ramamurthy
Keyword(s):  
Boundary Layer ◽  
External Pressure ◽  
Boundary Layer Theory ◽  
Dust Particles ◽  
Large Reynolds Number ◽  
Wavy Wall ◽  
Regular Perturbation ◽  
Outer Flow ◽  
Normal Oscillation ◽  
Matching Process

A two-dimensional viscous dusty flow induced by normal oscillation of a wavy wall for moderately large Reynolds number is studied on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for outer flow and inner flow for various values of mass concentration of dust particles are drawn. The inner and outer solutions are matched by the matching process. An interested application of present result to mechanical engineering may be the possibility of the fluid and dust transportation without an external pressure.

scholarly journals Flow of a dusty fluid due to Wavy motion of a wall for moderately large Reynolds numbers

1989 ◽  
Vol 12 (3) ◽  
pp. 559-578 ◽  
Author(s):  
V. Ramamurthy ◽  
U. S. Rao
Keyword(s):  
Boundary Layer ◽  
Steady Flow ◽  
Transverse Velocity ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Dust Particles ◽  
Periodic Flow ◽  
Wavy Wall ◽  
Outer Flow ◽  
Dusty Fluid

The two-dimensional flow of a dusty fluid induced by sinusoidal wavy motion of an infinite wavy wall is considered for Reynolds numbers which are of magnitude greater than unity. While the velocity components of the fluid and the dust particles along the axial direction consist of a mean steady flow and a periodic flow, the transverse components of both the fluid and the dust consist only of a periodic flow. This is true both for the outer flow (the flow beyond the boundary layer) and the inner flow (boundary layer flow). It is found that the mean steady flow is proportional to the ratio4π2a2/L2(a/L<<1), where a and L are the amplitude and the wavelength of the wavy wall, respectively. Graphs of the velocity components, both for the outer flow and the inner flow for various values of mass - concentration of the dust particles are drawn. It is found that the steady flow velocities of the fluid and the dust particles approach to a constant value. Certain interesting results regarding the axial and the transverse velocity components are also discussed.

Effect of large bulk viscosity on large-Reynolds-number flows

2014 ◽  
Vol 751 ◽  
pp. 142-163 ◽  
Author(s):  
M. S. Cramer ◽  
F. Bahmani
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Bulk Viscosity ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Outer Flow ◽  
First Order ◽  
Large Bulk

AbstractWe examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).

A note on the laminar mixing of two uniform parallel semi-infinite streams

1972 ◽  
Vol 55 (1) ◽  
pp. 25-30 ◽  
Author(s):  
J. B. Klemp ◽  
Andreas Acrivos
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Fundamental Property ◽  
Higher Order ◽  
Boundary Layer Theory ◽  
Large Reynolds Number ◽  
Laminar Mixing ◽  
Parallel Streams ◽  
Classical Boundary

According to classical boundary-layer theory, when two uniform parallel streams are brought into contact at large Reynolds number (R) the location of the dividing streamline remains indeterminate to O(R−½) if both streams are subsonic and semi-infinite in extent. It is demonstrated here that this indeterminacy is a fundamental property of such a system which cannot be resolved, as Ting (1959) proposed, by balancing the pressure across the viscous mixing region to higher order in R.

On the rapid rotation of a massive sphere in a monatomic gas

1974 ◽  
Vol 64 (1) ◽  
pp. 17-31
Author(s):  
M. R. Foster
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Solid Sphere ◽  
Large Reynolds Number ◽  
Thin Boundary Layer ◽  
Order Unity ◽  
Outer Flow ◽  
Rapid Rotation ◽  
First Order ◽  
Monatomic Gas

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flowisboundary-layer driven. The parameter boundary between these two dissimilar steady states is σ =O(ε⅙).

Higher approximations in boundary-layer theory Part 1. General analysis

1962 ◽  
Vol 14 (2) ◽  
pp. 161-177 ◽  
Author(s):  
Milton Van Dyke
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Theory ◽  
Successive Approximations ◽  
Large Reynolds Number ◽  
Temperature Changes ◽  
Perturbation Problem ◽  
Systematic Scheme ◽  
Displacement Speed ◽  
Solid Bodies ◽  
Past Plane

Prandtl's boundary-layer theory is embedded as the first step in a systematic scheme of successive approximations for finding an asymptotic solution for viscous flow at large Reynolds number. The technique of inner and outer expansions is used to treat this singular-perturbation problem. Only analytic semi-infinite bodies free of separation are considered. The second approximation is analysed in detail for steady laminar flow past plane or axisymmetric solid bodies. Attention is restricted to low speeds and small temperature changes, so that the velocity field is that for an incompressible fluid, the temperature field being calculated subsequently. The additive effects are distinguished of longitudinal curvature, transverse curvature, external vorticity, external stagnation enthalpy gradient, and displacement speed. The effect of changing co-ordinates is examined, and the behaviour of the boundary-layer solution far downstream discussed. Application to specific problems will be made in subsequent papers.

INVERSE PROBLEMS OF BOUNDARY LAYER THEORY

2018 ◽  
Vol 49 (8) ◽  
pp. 793-807
Author(s):  
Vladimir Efimovich Kovalev
Keyword(s):  
Boundary Layer ◽  
Inverse Problems ◽  
Boundary Layer Theory
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