Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
43
2
2016
Some Solutions of Simplified Open Channel Flow Equations
95-104
Sujit K.
Bose
S.N. Bose National Center for Basic Sciences, Salt Lake City, Kolkata 700098, India
Open channel flows of shallow depth in hydraulics are characteristically turbulent due to disturbances generated by bed friction and other causes. The governing equations of such flows based on Reynolds Averaged Navier − Stokes (RANS) equations have been developed in recent years in collaborative papers by Bose and Dey, and have found useful applications. In as much as the equations are of nonlinear evolution type, several types of solutions can exist. The present paper develops five types of solutions, based on the similarity method, localized solution method, and the method of separation of variables. The last two methods deliver two solutions in each case. The self-similar solution and the two localized solutions, reduce to solution of ODE's that are numerically presented. The two separation of variables solutions are obtained in explicit form.
Varying Magneto-Hemodynamics Flow in a Semi-Porous Vertical Channel with Heat Transfer: Numerical and Analytical Solutions
105-118
Y.
Abd Elmaboud
Mathematics Department, Faculty of Science and Arts, Khulais, University Of Jeddah Saudi Arabia; Mathematics Department, Faculty of Science, Al-Azhar University (Assiut Branch) Assiut, Egypt
An analysis has been achieved to discuss the natural convection behavior of a Newtonian fluid in a vertical semi-porous channel with varying magnetic field. The Navier-Stokes and the energy equations are reduced to a system of nonlinear PDE by using the similarity transformation. The variational iteration method (VIM) is introduced to obtain approximate solutions for velocity and temperature fields. The comparison between the analytical and numerical solutions is achieved. The analysis for the velocity and the heat transfer across the channel have been discussed for various values of the problem parameters.
Momentum and Mass Transfer Phenomena of Contaminated Bubble Swarms in Power-Law Liquids
119-140
Nanda
Kishore
Department of Chemical Engineering, Indian Institute of Technology Guwahati Assam781039, India
Venkata Swamy
Nalajala
Department of Chemical Engineering, Indian Institute of Technology Guwahati Assam781039, India
Computational fluid dynamics based approach is used to investigate the momentum and mass transfer behaviors of swarms of contaminated bubbles in surfactant-laden power-law liquids using a segregated approach. Effects of surface contamination and bubble holdup are incorporated in the solver through spherical stagnant cap model and free surface cell model, respectively. Extensive new results are obtained on streamline and vorticity patterns, drag coefficients, concentration contours and local and surface averaged Sherwood numbers of contaminated bubbles in the range of conditions as: Reynolds number, Re = 1 to 200; Schmidt number, Sc = 1 to 100; bubble holdup, Φ = 0.1 to 0.5; stagnant cap angle, α = 0 to 180° and power-law behavior index, n = 0.6 to 1. Some of the key findings indicate that the drag coefficients decrease with the decreasing power-law index and/or with the decreasing cap angle and/or with the decreasing bubble holdup and/or with the increasing Reynolds number. The concentration boundary layer become thinner with the decreasing cap angle and/or with the decreasing power-law index regardless the values of the Reynolds and/or Schmidt numbers. The rate of mass transfer is found to increase with the decreasing cap angle and/or with the decreasing power-law index and/or with the increasing bubble holdup and/or with the increasing Reynolds and Schmidt numbers.
Flow in a Channel with an Overlapping Constriction and Permeability
141-160
Muthu
P
National Institute of Technology Warangal
M.
Varunkumar
Department of Mathematics, National Institute of Technology Warangal-506004, Telangana, India
In this paper, we discuss the steady laminar flow of viscous incompressible fluid through a two dimensional non-uniform channel with an overlapping constriction and permeable walls. The fluid reabsorption through permeable walls is considered by taking flux as a function of axial distance. An approximate analytical method based on regular perturbation technique is applied to get the solution for velocity profiles, mean pressure drop, wall shear stress and streamlines, by assuming δ (ratio of inlet half-width to length of channel) as a small parameter. The effects of various parameters on the velocity profiles at different positions along the axis, the axial distribution of wall shear stress, mean pressure drop and streamlines are discussed and presented graphically. From the above discussions, the model may be considered for possible applications to flow in renal tubule.
Investigation on Influences of Bubble Location and Momentum Transfer Direction on Liquid Turbulence Modification for the Dilute Bubbly Flow
161-181
Mingjun
Pang
School of Mechanical Engineering, Changzhou University Changzhou 213016, China
Jinjia
Wei
School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P.R. China; Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong Uniersity, Xi'an, 710049,
P.R.China
Bo
Yu
Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum
Beijing 102249, China
It is very significant for the effective design and operation of bubbly equipments to understand deeply the liquid turbulence modulation mechanism by bubbles. In the present paper, detailed investigations on modulation of bubbles on the liquid turbulence, for the dilute bubbly flow with a low liquid-phase Reynolds number, were carried out with the developed Euler-Lagrange numerical method when bubbles always stayed in different turbulence layers for the horizontal and vertical channels, respectively. The velocity field of the liquid phase was solved with direct numerical simulation (DNS), and the bubble motion was followed with Newtonian motion equations. The present studies show that the liquid-phase turbulence modulation is tightly related to the bubble location and the momentum transfer direction between bubbles and liquid (i. e., the gravity direction); it should be noted that when bubbles are located in the turbulence buffer layer, the opposite phenomena happen to the liquid turbulence modulation by bubbles for the horizontal and vertical channels.
The Theory of Equivalence Measures and Stochastic Theory of Turbulence for Non-Isothermal Flow on the Flat Plate
182-187
Artur V.
Dmitrenko
Department of Thermal Physics, National Research Nuclear University "MEPhI", 31 Kashirskoe Shosse, Moscow, 115409, Russia; Department of Power Engineering, Moscow State University of Railway Engineering (MIIT),
9 Obraztsov St., Moscow, 127994, Russia
In accordance with a theory of equivalence measures, the systems of stochastic equations for energy, momentum and mass are applied to non-isothermal flows. The analytical dependencies for estimations of the critical Reynolds number and value of the critical point of regime change for non-isothermal and compressible flows are written. As an example, the classical flow of the Newtonian medium on the smooth flat plate is considered.