Initial development of a free-surface wall jet at moderate Reynolds number

2017 ◽  
Vol 826 ◽  
pp. 235-269 ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Wall Jet ◽  
Ambient Fluid ◽  
Initial Development ◽  
Core Flow ◽  
Moderate Reynolds Number ◽  
Surface Jet ◽  
Infinite Wall ◽  
Steady Laminar

The steady laminar flow of a moderately inertial wall jet is examined theoretically near the exit of a channel. The free-surface jet emerges asymmetrically from the channel as it adheres to an infinite (upper) wall subject to a pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse cubic power of the Reynolds number. The flow field is obtained by matching the inviscid rotational core flow separately with the free-surface and the two wall layers. The upstream influence is examined as well as the break in the symmetry between the two wall layers. The wall jet exhibits a contraction near the channel exit that is independent of inertia, and eventually expands for any Reynolds number. Unlike the flow of a wall jet emerging into the same ambient fluid, the free-surface jet experiences a limited weakening in shear stress along the infinite wall, suggesting the possibility of separation for a jet with relatively low inertia. Significant shearing and elongation ensue at the exit, accompanied by flattening of the velocity profile near the upper wall.

Effect of Wall Movement on a Jet Depositing on a Moving Wall at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Yahia Hussain ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Core Region ◽  
Relaxation Length ◽  
Moving Wall ◽  
The Core ◽  
Wall Movement ◽  
Moderate Reynolds Number ◽  
Surface Jet

The steady flow of a moderately inertial jet depositing on a moving wall, is examined theoretically near channel exit. The free surface jet emerges from a channel and adheres to a wall, which may move in the same or opposite direction to the acting channel pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow field is obtained as a composite expansion by matching the flow in the boundary layer regions near the free surface, with the flow in the core region. The influence of inertia and wall velocity on the shape of the free surface, the velocity and stress is emphasized. It is found that the viscous relaxation length is essentially uninfluenced by the velocity of a forward moving wall. In contrast, it diminishes rapidly with the velocity of a backward moving wall.

Flow of Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Abul Kalam Azad ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Boundary Conditions ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wall Jet ◽  
Channel Exit ◽  
Moderate Reynolds Number ◽  
Layer Region

The wall jet flow near channel exit at moderate Reynolds Number, emerging from a two-dimensional channel, is examined theoretically in this study. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface, flow in the outer layer region and the flow in the core region. The fluid is assumed to be Newtonian and it is found that the jet contracts downstream from the channel exit. The influence of inertia on the shape of free surface, the velocity and stress is emphasized and the higher order boundary layer is explored. To leading order, the problem is similar to the case of the free jet (Tillett) [1] with different boundary conditions. A similarity solution can be carried out using a similarity variable problem which is then solved as an initial-value problem, where the equation is integrated subject to the boundary conditions and a guessed value of the slope at the origin. The slope is adjusted until reasonable matching is achieved between the solution and the asymptotic form at large θ. The level of contraction is essentially independent of inertia, but the contraction moves further downstream with increasing Reynolds number. The present work provides the correct conditions near exit, which are required to determine the jet structure further downstream. If the jet becomes thin far downstream, a boundary layer formulation can be used with the presently predicted boundary conditions for steady and possibly transient flows.

Free-surface jet flow of a shear-thinning power-law fluid near the channel exit

2014 ◽  
Vol 748 ◽  
pp. 580-617 ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Free Surface ◽  
Power Law ◽  
Shear Thinning ◽  
Viscous Sublayer ◽  
Jet Flow ◽  
Power Law Fluid ◽  
Downstream Distance ◽  
Moderate Reynolds Number ◽  
Sublayer Thickness ◽  
Surface Jet

AbstractThe jet flow of a shear-thinning power-law fluid is examined theoretically as it emerges from a channel at moderate Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer near the free surface, with the outer layer extending to the jet centreline. An inner thin viscous sublayer is introduced to smooth out the singularity in viscosity at the free surface, allowing the inner algebraically decaying solutions to be matched smoothly with the solution near the free surface. A Newtonian jet is found to contract more than a shear-thinning jet. While both the inner-layer thickness and the free-surface height are $O(\mathit{Re}^{-1/3})$, and grow with downstream distance, the sublayer thickness is smaller, $O(\mathit{Re}^{-(1+n)/3})$, growing with distance for $n < 0.5$, and decaying for $n > 0.5$. The relaxation downstream distance for the jet is found to grow logarithmically with $\mathit{Re}$.

Flow of Moving Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Rizwana Amin ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Equations Of Motion ◽  
Outer Region ◽  
Moving Wall ◽  
Moderate Reynolds Number ◽  
Boundary Layer Region ◽  
Asymptotic Development ◽  
Layer Region

The two-dimensional jet flow of a Newtonian fluid at moderate Reynolds Number emerging from a channel where the upper plate is moving is examined theoretically in this study. In this case, the equations of motion are reduced by expanding the flow field about the basic Couette flow. Inertia is assumed to be large enough, allowing asymptotic development in terms of the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow in the free surface and the moving wall. The influence of this boundary layer is investigated with the aid of the method of matched asymptotic expansions. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface and the flow both in the inner (boundary-layer) region and in the outer region of the core. The influence of wall velocity on the shape of the free surface, the velocity and stress is emphasized. The formulation allows for the determination of the steady state flow and free surface profiles analytically. The present work provides the conditions near exit, with the help of Higher-order boundary-layer effects (i.e. the cubic term of the inverse Reynolds number), to determine the jet structure further downstream.

Density distribution in the flow past a sphere descending in a salt-stratified fluid

2021 ◽  
Vol 927 ◽  
Author(s):  
Shinya Okino ◽  
Shinsaku Akiyama ◽  
Koki Takagi ◽  
Hideshi Hanazaki
Keyword(s):  
Reynolds Number ◽  
Density Distribution ◽  
Stratified Fluid ◽  
Buoyant Jet ◽  
Jet Formation ◽  
Initial Development ◽  
Density Distributions ◽  
Image Velocimetry ◽  
Moderate Reynolds Number ◽  
Short Time

The density distribution around a sphere descending in a salt-stratified fluid is measured by the laser-induced fluorescence (LIF) method. The corresponding velocity distribution is measured by particle image velocimetry (PIV), and numerical simulation is also performed to supplement the observations by LIF and PIV. In steady flow, LIF observes a thin and vertically long structure which corresponds to a buoyant jet. The bell-shaped structure, which appears under strong stratification and moderate Reynolds number (Froude number $Fr \lesssim 3$ , Reynolds number $50 \lesssim Re \lesssim 500$ ), is also identified. The measured density distributions in the salinity boundary layer and in the jet agree with the numerical simulations which use the Schmidt number of the fluorescent dye ( $Sc \sim 2000$ ). The initially unsteady process of the jet formation is also investigated. Under weak stratification, the LIF shows an initial development of an axisymmetric rear vortex as observed in homogeneous fluids. However, as time proceeds and the effect of stratification becomes significant, the vortex shrinks and disappears, while the jet extends vertically upward. Under strong stratification, a thin jet develops without generating a rear vortex, since the effect of stratification becomes significant in a short time before the vortex is generated.

Effects of Submergence on Low and Moderate Reynolds Number Free-Surface Flow Around a Matrix of Cubes

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Z. Ikram ◽  
E. J. Avital ◽  
J. J. R. Williams
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Immersed Boundary ◽  
Surface Boundary ◽  
Reynolds Number Flow ◽  
Eddy Simulation ◽  
Moderate Reynolds Number ◽  
Submergence Depth

The effect of reducing submergence depth at a low and moderate Reynolds number flow is investigated using large eddy simulation (LES) around a matrix of cubes. The submerged body is modeled using an immersed boundary method, while the free-surface is accounted for using a moving mesh. Results show that for reducing the submergence depth, the forces acting on the cube reduce as the force variation increased. Variation in depth is also found to influence the level of damping and redistribution of turbulence near the free-surface boundary. Both submergence depth and Reynolds number are also found to influence the dominant free-surface signature and shedding frequencies from the cube. In the interobstacle region (IOR), the variation of Reynolds number and submergence depth is found to have little effect.

Vortex shedding from a circular cylinder in moderate-Reynolds-number shear flow

1980 ◽  
Vol 101 (4) ◽  
pp. 721-735 ◽  
Author(s):  
Masaru Kiya ◽  
Hisataka Tamura ◽  
Mikio Arie
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Number Range ◽  
Uniform Shear ◽  
Reynolds Number Range ◽  
Moderate Reynolds Number ◽  
Shear Parameter

The frequency of vortex shedding from a circular cylinder in a uniform shear flow and the flow patterns around it were experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter and the approaching velocity at its centre, ranged from 35 to 1500. The shear parameter, which is the transverse velocity gradient of the shear flow non-dimensionalized by the above two quantities, was varied from 0 to 0·25. The critical Reynolds number beyond which vortex shedding from the cylinder occurred was found to be higher than that for a uniform stream and increased approximately linearly with increasing shear parameter when it was larger than about 0·06. In the Reynolds-number range 43 < Re < 220, the vortex shedding disappeared for sufficiently large shear parameters. Moreover, in the Reynolds-number range 100 < Re < 1000, the Strouhal number increased as the shear parameter increased beyond about 0·1.

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