Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2233-2248 ◽  
Author(s):  
Dominique Legendre ◽  
Catherine Colin ◽  
Typhaine Coquard
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Added Mass ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Mass Force ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Linear Shear

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reynolds numbers (0.01≤ Re b , Re α ≤2000) and shear rate (0≤ Sr ≤5). The drag and lift forces are computed successively for the following situations: an immobile bubble in a linear shear flow; a bubble sliding on the wall in a fluid at rest; and a bubble sliding in a linear shear flow. The added-mass force is studied by considering an unsteady motion relative to the wall or a time-dependent radius.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

The evolution of thermocline waves from an oscillatory disturbance

1993 ◽  
Vol 254 ◽  
pp. 401-416 ◽  
Author(s):  
D. Nicolaou ◽  
R. Liu ◽  
T. N. Stevenson
Keyword(s):  
Finite Difference ◽  
Shear Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Ray Theory ◽  
Navier Stokes Equations ◽  
Linear Shear ◽  
Wave Shapes ◽  
The Way

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

scholarly journals Energy cascade and scaling in supersonic isothermal turbulence

2013 ◽  
Vol 729 ◽  
Author(s):  
Alexei G. Kritsuk ◽  
Rick Wagner ◽  
Michael L. Norman
Keyword(s):  
Fourth Order ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Order Relation ◽  
Energy Cascade ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Terrestrial Environments

AbstractSupersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier–Stokes equations (Galtier & Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-fifths law exist describing fifth- and fourth-order correlations, but only the fourth-order relation remains ‘universal’ in a wide range of Mach numbers from incompressible to highly compressible regimes. A new approximate relation valid in the strongly supersonic regime is derived and verified. We also briefly discuss the origin of bottleneck bumps in simulations of compressible turbulence.

The interaction of a diffusing line vortex and an aligned shear flow

1985 ◽  
Vol 399 (1817) ◽  
pp. 367-375 ◽  
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Kinematic Viscosity ◽  
Stokes Equations ◽  
Radial Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Line Vortex ◽  
Linear Shear

An exact solution of the Navier─Stokes equations of incompressible flow, which represents the interaction of a diffusing line vortex and a linear shear flow aligned so that initially the streamlines in the shear flow are parallel to the line vortex, is presented. If Γ is the circulation of the line vortex and v the kinematic viscosity then, when Re ═ Γ/2π v is large, the vorticity of the shear flow is expelled from the circular cylinder 0 < r ≪ ( vt ) 1/2 Re 1/3 , where r is the distance from the axis of the diffusing line vortex and t the time since initiation of the flow. At larger radii a peak vorticity 0.903Ω Re 1/3 is found at a radial distance 1.26( vt )1/2 Re 1/3 , where Ω is the initial uniform vorticity in the shear flow. The vortex filament is embedded in a growing cylinder from which vorticity has been expelled, the cylinder itself being bounded by an annular region of thickness of order Re 1/3 ( vt ) 1/2 in which the vorticity is of order Ω Re 1/3 .

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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