On the Instability of Plane Poiseuille Flow of Two Immiscible Fluids Using the Energy Gradient Theory

2014 ◽  
Vol 30 (3) ◽  
pp. 299-305 ◽  
Author(s):  
I. Farahbakhsh ◽  
S. S. Nourazar ◽  
H. Ghassemi ◽  
H.-S. Dou ◽  
A. Nazari-Golshan
Keyword(s):  
Experimental Data ◽  
Viscosity Ratio ◽  
Reynolds Numbers ◽  
Immiscible Fluids ◽  
Gradient Theory ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
Lower Viscosity ◽  
High Reynolds ◽  
Comparison Of The Results

ABSTRACTIn the present study, the instability of laminar flow of two immiscible fluids is investigated. The theory of energy gradient is employed for the analysis. The distributions of energy gradient for various viscosity ratios, i.e., ratios of lower viscosity to higher one, are obtained and the results for the onset of instability are compared with the available experimental data. The comparison of the results shows excellent agreement with the existing experimental data. It will be also demonstrated that as the viscosity ratio decreases the flow becomes more stable even at high Reynolds numbers.

Study of flow instability in a centrifugal fan based on energy gradient theory

2016 ◽  
Vol 30 (2) ◽  
pp. 507-517 ◽  
Author(s):  
Meina Xiao ◽  
Qing Xiao ◽  
Hua-Shu Dou ◽  
Xiaoyang Ma ◽  
Yongning Chen ◽  
...  
Keyword(s):  
Flow Instability ◽  
Gradient Theory ◽  
Centrifugal Fan ◽  
Energy Gradient Theory ◽  
Energy Gradient

scholarly journals Analysis of vortex breakdown in an enclosed cylinder based on the energy gradient theory

2018 ◽  
Vol 71 ◽  
pp. 66-76
Author(s):  
Meina Xiao ◽  
Hua-Shu Dou ◽  
Chuanyu Wu ◽  
Zuchao Zhu ◽  
Xifeng Zhao ◽  
...  
Keyword(s):  
Vortex Breakdown ◽  
Gradient Theory ◽  
Energy Gradient Theory ◽  
Energy Gradient

ENERGY SPECTRUM OF DISTURBANCE AT TURBULENT TRANSITION VIA ENERGY GRADIENT METHOD

2012 ◽  
Vol 19 ◽  
pp. 293-303 ◽  
Author(s):  
HUA-SHU DOU ◽  
BOO CHEONG KHOO
Keyword(s):  
Energy Spectrum ◽  
Flow Instability ◽  
Three Dimensional ◽  
Wave Number ◽  
Gradient Theory ◽  
Turbulent Transition ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
The Difference ◽  
2D And 3D

The energy gradient theory for flow instability and turbulent transition was proposed in our previous work. The theoretical result obtained accords well with some experimental data for pipe and channel flows in the literature. In the present study, the energy gradient theory is extended to examine the effect of disturbance frequency on turbulent transition. Then, the energy spectrum of disturbance at the turbulent transition is obtained, which scales with the wave number by an exponent of –2. This scaling is near to the K41 law of –5/3 for the full developed isentropic homogenous turbulence. The difference for the two energy spectra may be due to the intermittency of turbulence at the transition state. The intermittence causes the distribution of the energy spectrum to take on a steeper gradient (tending to –2 from –5/3). Finally, the flow instability leading to turbulent transition can be classified as two-dimensional (2D) or three-dimensional (3D) in terms of the wave number and the Re. It is found that there is an optimum wave number which separates the 2D and 3D transitions and at which the disturbance energy at transition is minimum.

Numerical Investigation of Flow Instability in Centrifugal Pump Based on Energy Gradient Method

2016 ◽  
Author(s):  
Lulu Zheng ◽  
Hua-Shu Dou ◽  
Xiaoping Chen ◽  
Zuchao Zhu ◽  
Baoling Cui
Keyword(s):  
Flow Rate ◽  
Flow Instability ◽  
Flow Stability ◽  
Gradient Theory ◽  
Small Flow Rate ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
Centre Region ◽  
Small Flow ◽  
Gradient Function

Simulation of turbulent flow in a pump is carried out with the RANS equations and the RNG k-epsilon turbulence model. Numerical simulation has been compared with the experimental data. The results show that separating vortex is firstly produced at the pressure side of the impeller passage near the tongue. Then it spreads to the inlet and outlet of the impeller passages and moved to the centre region of impeller passages from the boundaries. Finally, it almost occupies all the impeller passages and multiple vortices exist in impeller passages at small flow rate. It is found that the tongue has large effect on the flow in the impeller passage approaching to it. The impeller passage near the tongue is easily tending to be unstable comparing with others passages. The energy gradient theory is used to analyze the flow stability in the impeller. The region with larger value of energy gradient function K means the bigger turbulence intensity and poor flow stability. At small flow rate the regions with large value of K are enlarged and are mainly located at both sides of blade pressure and suction surfaces where the flow is easily tending to be unstable.

Drag Coefficients of Viscous Spheres at Intermediate and High Reynolds Numbers

2001 ◽  
Vol 123 (4) ◽  
pp. 841-849 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Efstathios E. Michaelides
Keyword(s):  
Drag Coefficient ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Computational Domain ◽  
High Reynolds

A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [ORe−1/2] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

scholarly journals Modeling of Particle Deposition in a Two-Fluid Flow Environment

2021 ◽  
Vol 39 (3) ◽  
pp. 1001-1014
Author(s):  
Yap Yit Fatt ◽  
Afshin Goharzadeh
Keyword(s):  
Fluid Flow ◽  
Particle Deposition ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rising Bubble ◽  
Lower Viscosity ◽  
Two Fluid

Particle deposition occurs in many engineering multiphase flows. A model for particle deposition in two-fluid flow is presented in this article. The two immiscible fluids with one carrying particles are model using incompressible Navier-Stokes equations. Particles are assumed to deposit onto surfaces as a first order reaction. The evolving interfaces: fluid-fluid interface and fluid-deposit front, are captured using the level-set method. A finite volume method is employed to solve the governing conservation equations. Model verifications are made against limiting cases with known solutions. The model is then used to investigate particle deposition in a stratified two-fluid flow and a cavity with a rising bubble. For a stratified two-fluid flow, deposition occurs more rapidly for a higher Damkholer number but a lower viscosity ratio (fluid without particle to that with particles). For a cavity with a rising bubble, deposition is faster for a higher Damkholer number and a higher initial particle concentration, but is less affected by viscosity ratio.

Hydrodynamics and Heat Convection From a Disk Facing a Uniform Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
Abdullah Abbas Kendoush
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Pressure Distribution ◽  
Dynamical Behavior ◽  
Circular Disk ◽  
Reynolds Numbers ◽  
Inviscid Flows ◽  
High Reynolds Numbers ◽  
Axis Of Symmetry ◽  
High Reynolds

Exact solutions of the equations of momentum and energy of a circular disk in a uniform incompressible flow directed along its axis of symmetry are obtained. Laminar, irrotational and inviscid flows were assumed. The solutions for the pressure distribution, drag coefficient and convective heat transfer of the disk are presented in explicit forms. Some peculiar fluid-dynamical behavior of the pressure distribution at low and high Reynolds numbers are revealed. The derived equations were agreeable with other numerical and analytical solutions and experimental data.

scholarly journals Stability of boundary layer flow based on energy gradient theory

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840003
Author(s):  
Hua-Shu Dou ◽  
Wenqian Xu ◽  
Boo Cheong Khoo
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Flow Instability ◽  
Mechanical Energy ◽  
Navier Stokes ◽  
Gradient Theory ◽  
External Edge ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
Gradient Function

The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier–Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

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