Slipping free jet flow near channel exit at moderate Reynolds number for large slip length

2016 ◽  
Vol 793 ◽  
pp. 667-708 ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Reynolds Number ◽  
Layer Thickness ◽  
Slip Length ◽  
Rapid Change ◽  
Perturbation Parameter ◽  
Free Jet ◽  
Channel Exit ◽  
Moderate Reynolds Number ◽  
Order Of Magnitude ◽  
Free Jet Flow

The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. The ratio of the slip length to the channel width $S$ is assumed to be of order one, one order of magnitude larger than the perturbation parameter ${\it\varepsilon}=Re^{-1/2}$, $Re$ being the 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 of the free surface, with the outer layer extending to the jet centreline. The inner-layer thickness grows like $\sqrt{x/Re\,S}$. A slipping jet is found to contract like $x/Re$ very near and far from the channel exit, but does not have a definite behaviour in between compared to $(x/Re)^{1/3}$ for an adhering jet, $x$ being the distance from the channel exit. Eventually, the jet reaches uniform conditions far downstream. As in the case of entry flow, there is a rapid departure in flow behaviour for a slipping jet from the $S=0$ limit. This rapid change is notably observed in the drop of boundary-layer thickness, increase in exit and relaxation lengths as well as in jet width with slip length. Finally, the connections with microchannel and hydrophobic flows are highlighted.

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.

scholarly journals Effects of flexibility on the aerodynamic performance of flapping wings

2011 ◽  
Vol 689 ◽  
pp. 32-74 ◽  
Author(s):  
C.-K. Kang ◽  
H. Aono ◽  
C. E. S. Cesnik ◽  
W. Shyy
Keyword(s):  
Reynolds Number ◽  
Density Ratio ◽  
Flapping Wings ◽  
Mass Force ◽  
Propulsive Force ◽  
Propulsive Efficiency ◽  
Reduced Frequency ◽  
Moving Body ◽  
Order Of Magnitude ◽  
Direct Guidance

AbstractEffects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of $O(1{0}^{3} \ensuremath{-} 1{0}^{4} )$ and the reduced frequency of $O(1)$, the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing-tip deformation parameter ($\gamma $) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for micro air vehicle design and performance analysis.

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.

Models of the scalar spectrum for turbulent advection

1978 ◽  
Vol 88 (3) ◽  
pp. 541-562 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Temperature Fluctuations ◽  
Limited Extent ◽  
Temperature Spectrum ◽  
One Dimensional ◽  
Moderate Reynolds Number ◽  
Temperature Spectra ◽  
High Reynolds

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

Moderate Reynolds Number Mixing in a T-Channel

2010 ◽  
Author(s):  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Large Body ◽  
Experimental Studies ◽  
Numerical Work ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Particle Imaging ◽  
Experimental Trials

An experimental investigation of water flow in a T-shaped channel with rectangular cross section (20 × 20 mm inlet ID and 20 × 40 mm outlet ID) has been conducted for a Reynolds number Re range of 56 to 422, based on inlet diameter. Dynamical conditions and the T-channel geometry of the current study are applicable to the microscale. This study supports a large body of numerical work, and resolution and the interrogation region are extended beyond previous experimental studies. Laser induced fluorescence (LIF) and particle imaging velocimetry (PIV) are used to characterize flow behaviors over the broad range of Re where realistic T-channels operate. Scalar structures previously unresolved in the literature are presented. Special attention is paid to the unsteady flow regimes that develop at moderate Re, which significantly impact mixing but are not yet well characterized or understood. An unsteady symmetric topology, which develops at higher Re and negatively impacts mixing, is presented, and mechanisms behind the wide range of mixing qualities predicted for this regime are explained. An optimal Re operating range is identified based on multiple experimental trials.

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