scholarly journals Longitudinal and transverse flow over a cavity containing a second immiscible fluid

2013 ◽  
Vol 717 ◽  
pp. 376-394 ◽  
Author(s):  
Clarissa Schönecker ◽  
Steffen Hardt
Keyword(s):  
Flow Field ◽  
Complex Analysis ◽  
Stokes Equations ◽  
Slip Length ◽  
Immiscible Fluid ◽  
Standard Case ◽  
Outer Flow ◽  
Reynolds Number Flow ◽  
Navier Slip ◽  
Flow Over A Cavity

AbstractAn analytical solution for the low-Reynolds-number flow field of a shear flow over a rectangular cavity containing a second immiscible fluid is derived. While flow of a single-phase fluid over a cavity is a standard case investigated in fluid dynamics, flow over a cavity that is filled with a second immiscible fluid has received little attention. The flow field inside the cavity is considered to define a boundary condition for the outer flow, which takes the form of a Navier slip condition with locally varying slip length. The slip-length function is determined heuristically from the related problem of lid-driven cavity flow. Based on the Stokes equations and complex analysis, it is then possible to derive a closed analytical expression for the flow field over the cavity for both the transverse and the longitudinal case. The result is a comparatively simple function, which displays the dependence of the flow field on the cavity geometry and the medium filling the cavity. The analytically computed expression agrees well with results obtained from a numerical solution of the Navier–Stokes equations.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Numerical Simulation of Flowfield around High Speed Trains Passing by each other at the same Speed

2011 ◽  
Vol 97-98 ◽  
pp. 698-701
Author(s):  
Ming Lu Zhang ◽  
Yi Ren Yang ◽  
Li Lu ◽  
Chen Guang Fan
Keyword(s):  
Numerical Simulation ◽  
Wind Tunnel ◽  
Flow Field ◽  
Point Source ◽  
High Speed ◽  
Stokes Equations ◽  
Field Structure ◽  
Vehicle Speed ◽  
Mesh Method ◽  
High Speed Trains

Large eddy simulation (LES) was made to solve the flow around two simplified CRH2 high speed trains passing by each other at the same speed base on the finite volume method and dynamic layering mesh method and three dimensional incompressible Navier-Stokes equations. Wind tunnel experimental method of resting train with relative flowing air and dynamic mesh method of moving train were compared. The results of numerical simulation show that the flow field structure around train is completely different between wind tunnel experiment and factual running. Two opposite moving couple of point source and point sink constitute the whole flow field structure during the high speed trains passing by each other. All of streamlines originate from point source (nose) and finish with the closer point sink (tail). The flow field structure around train is similar with different vehicle speed.

Small Reynolds Number Electro-Hydrodynamic Flow Around Drops and the Resulting Deformation

1979 ◽  
Vol 46 (3) ◽  
pp. 510-512 ◽  
Author(s):  
M. B. Stewart ◽  
F. A. Morrison
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Order Approximation ◽  
Creeping Flow ◽  
Small Reynolds Number ◽  
Zeroth Order ◽  
Regular Perturbation ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow

Low Reynolds number flow in and about a droplet is generated by an electric field. Because the creeping flow solution is a uniformly valid zeroth-order approximation, a regular perturbation in Reynolds number is used to account for the effects of convective acceleration. The flow field and resulting deformation are predicted.

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1996 ◽  
Author(s):  
Chunill Hah ◽  
Douglas C. Rabe ◽  
Thomas J. Sullivan ◽  
Aspi R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of 8 periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

scholarly journals Generalized slip condition over rough surfaces

2018 ◽  
Vol 858 ◽  
pp. 407-436 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Jacques Magnaudet ◽  
Alessandro Bottaro
Keyword(s):  
Boundary Condition ◽  
Rough Surface ◽  
Hexagonal Lattice ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Strain Rate Tensor ◽  
Outer Flow ◽  
Navier Slip ◽  
Roughness Amplitude

A macroscopic boundary condition to be used when a fluid flows over a rough surface is derived. It provides the slip velocity $\boldsymbol{u}_{S}$ on an equivalent (smooth) surface in the form $\boldsymbol{u}_{S}=\unicode[STIX]{x1D716}{\mathcal{L}}\boldsymbol{ : }{\mathcal{E}}$, where the dimensionless parameter $\unicode[STIX]{x1D716}$ is a measure of the roughness amplitude, ${\mathcal{E}}$ denotes the strain-rate tensor associated with the outer flow in the vicinity of the surface and ${\mathcal{L}}$ is a third-order slip tensor arising from the microscopic geometry characterizing the rough surface. This boundary condition represents the tensorial generalization of the classical Navier slip condition. We derive this condition, in the limit of small microscopic Reynolds numbers, using a multi-scale technique that yields a closed system of equations, the solution of which allows the slip tensor to be univocally calculated, once the roughness geometry is specified. We validate this generalized slip condition by considering the flow about a rough sphere, the surface of which is covered with a hexagonal lattice of cylindrical protrusions. Comparisons with direct numerical simulations performed in both laminar and turbulent regimes allow us to assess the validity and limitations of this condition and of the mathematical model underlying the determination of the slip tensor ${\mathcal{L}}$.

Numerical investigation of supercritical Taylor-vortex flow for a wide gap

1984 ◽  
Vol 138 ◽  
pp. 21-52 ◽  
Author(s):  
H. Fasel ◽  
O. Booz
Keyword(s):  
Flow Field ◽  
Vortex Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Plane Boundary ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Wide Gap

For a wide gap (R1/R2= 0.5) and large aspect ratiosL/d, axisymmetric Taylor-vortex flow has been observed in experiments up to very high supercritical Taylor (or Reynolds) numbers. This axisymmetric Taylor-vortex flow was investigated numerically by solving the Navier–Stokes equations using a very accurate (fourth-order in space) implicit finite-difference method. The high-order accuracy of the numerical method, in combination with large numbers of grid points used in the calculations, yielded accurate and reliable results for large supercritical Taylor numbers of up to 100Tac(or 10Rec). Prior to this study numerical solutions were reported up to only 16Tac. The emphasis of the present paper is placed upon displaying and elaborating the details of the flow field for large supercritical Taylor numbers. The flow field undergoes drastic changes as the Taylor number is increased from just supercritical to 100Tac. Spectral analysis (with respect toz) of the flow variables indicates that the number of harmonics contributing substantially to the total solution increases sharply when the Taylor number is raised. The number of relevant harmonics is already unexpectedly high at moderate supercriticalTa. For larger Taylor numbers, the evolution of a jetlike or shocklike flow structure can be observed. In the axial plane, boundary layers develop along the inner and outer cylinder walls while the flow in the core region of the Taylor cells behaves in an increasingly inviscid manner.

The Derivation and Application of Fundamental Solutions for Unsteady Stokes Equations

2015 ◽  
Vol 31 (6) ◽  
pp. 683-691 ◽  
Author(s):  
C-H. Hsiao ◽  
D.-L. Young
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Mass Source ◽  
Reynolds Number Flow ◽  
Singularity Method ◽  
Vector Calculus ◽  
Unsteady Stokes Flow ◽  
Number Flow ◽  
Unsteady Stokes Equations

AbstractIn this paper, two formulations in explicit form to derive the fundamental solutions for two and three dimensional unsteady unbounded Stokes flows due to a mass source and a point force are presented, based on the vector calculus method and also the Hörmander’s method. The mathematical derivation process for the fundamental solutions is detailed. The steady fundamental solutions of Stokes equations can be obtained from the unsteady fundamental solutions by the integral process. As an application, we adopt fundamental solutions: an unsteady Stokeslet and an unsteady potential dipole to validate a simple case that a sphere translates in Stokes or low-Reynolds-number flow by using the singularity method instead by the traditional method which in general limits to the assumption of oscillating flow. It is concluded that this study is able to extend the unsteady Stokes flow theory to more general transient motions by making use of the fundamental solutions of the linearly unsteady Stokes equations.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

Analytical Modelling of Laminar Developing Flow Between Hydrophobic Surfaces with Different Slip-Velocities

2021 ◽  
Author(s):  
Sankar Vijay ◽  
Jaimon Cletus ◽  
Arun MG ◽  
Ranjith S Kumar
Keyword(s):  
Velocity Profile ◽  
Slip Length ◽  
Central Line ◽  
Momentum Equation ◽  
Layer Growth ◽  
Parallel Plates ◽  
Entrance Length ◽  
Navier Slip ◽  
Free Region ◽  
Separation Of Variable

Abstract Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modelled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more towards the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls are found to be entirely different and they merge at the entrance length and is noticed to be off-setted from the geometric centre-line. The effect of slip-length on the entrance length is analysed and an empirical correlation is deduced.

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