Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
27
2-4
2000
Turbulent Flow and Heat Transfer Modeling in a Flat Channel with Regular Highly Rough Walls
159-199
V. S.
Travkin
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, California 90024-1597
Ivan
Catton
Morin, Martinelli, Gier Memorial Heat Transfer Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, University of California, Los Angeles, USA
Turbulent flow and heat transfer in a flat channel with highly rough walls is treated using porous media turbulent filtration theory. This approach yields the basis for a unified description of an enormous spectrum of roughness layer morphologies as well as a scalable treatment of diverse engineering and scientific issues. The focus of the current study is restricted to formulation of models of 2D and 3D regular roughness elements. The assigned regularity contributes to the simplification of the mathematical model as well as to closure modeling and numerical simulation. Some of the closure modeling elements were developed using experimental results. The results are then compared to theoretical and experimental studies of flow in channels with roughened walls, and with smooth walls by allowing the roughness elements to become vanishingly small. The results of simulation of different roughness element morphologies demonstrates the interdependency of the roughness layer morphology, the mathematical formulation of the problem and the transport characteristics.
Modified Reattaching Shear Layer Using a Stationary Cylinder
200-212
Bassam A/K
Abu-Hijleh
Department of Mechanical Engineering, Jordan University of Science & Technology, P.O. Box 3030, Irbid 22110 - JORDAN
The problem of an incompressible turbulent reattaching flow over a 2-D backward facing step with a cylinder mounted after the step was investigated numerically. The flow field was solved using the finite element numerical method with the RNG turbulence model. The effects of the cylinder diameter and position on the reattachment length, recirculation velocity, maximum axial velocity, and normalized maximum turbulent kinetic energy are reported and discussed. The cylinder could be used to modify the flow field.
Solidification with a Quasiequilibrium Mushy Zone: Exact Analytical Solution
213-222
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
The model of nonlinear equations for solidification in the presence of a quasiequilibrium mushy gone is solved analytically. Concentration, temperature fields, bulk fraction of the solid phase in the mushy zone, and the mushy region width are found theoretically.
Incipience of a Mushy Zone in Binary Melt Solidification Processes: General Theory
223-238
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
A theory of a mushy region emergence for binary alloys is developed based on the classical Stefan thermodiffusion problem. At the instant a concentration (constitutional) supercooling arises near a planar front of solidification, and, as a consequence, solid phase elements in the form of dendrites, grains, etc. grow ahead of a moving front, i.e. between pure solid and liquid phases a region of mixed solid phase and liquid phase (mushy zone) appears. If this is really the case, the Stefan thermodiffusion model becomes inapplicable. The time when the mushy region appears, and when the classical description of solidification becomes incorrect is found in the form of an integral equation.
Linear Analysis of Dynamic Instability of Solidification with a Quasiequilibrium Mushy Zone
239-247
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
Linear analysis of dynamic instability is carried out for a unidirectional solidification of binary melts in the presence of a mushy zone. An equation for the parameter characterizing a time behavior of perturbations is deduced. Regions of stability and instability corresponding to the "hard" and "soft" types of instability evolution are calculated for actual alloys.
Unsteady Flow in Nonlinear Fractured Reservoirs
248-269
S. A.
Plochoi
Ural State University, Ekaterinburg, Russia
V. S.
Nustrov
Ural State University, Ekaterinburg, Russia
V. V.
Podoplelov
Ural State University, Ekaterinburg, Russia
Yu. A.
Buyevich
CRSS, University of California, Santa Barbara, USA
A recently developed model is used to investigate flow problems concerning a fractured reservoir. The reservoir is modelled in two ways: 1) as macroscopically isotropic and subject to uniform overall compression; 2) as containing only flat fractures aligned in the horizontal plane which are under the action of a vertical overburden rock pressure. In both cases the reservoir can be elastically deformed as a result of the fractures contracting when the pressure drops in the fluid filling the fractures. The pressure field evolution is analyzed when either bottom-hole pressure or production rate is fixed. The processes of reservoir pressure depletion and recovery are also studied. The results obtained eliminate some limitations inherent in conventional approaches to fractured reservoir filtration and agree well with experimental evidence.
A New Problem of Filtration Flows in Naturally Fractured Porous Reservoirs
270-288
V. S.
Nustrov
Ural State University, Ekaterinburg, Russia
V. V.
Podoplelov
Ural State University, Ekaterinburg, Russia
A problem of evolution of a region with closed fractures in oil formations is considered. There is an idea in special literature that this region can appear in naturally oil or gas beds when the filtrating liquid pressure decreases strongly. A nonlinear dependence of such systems on their stress state is well-known from numerous laboratory and field experiments. It is taken into account in the paper. A heat analogy of this specific Stefan problem is not known.
Dynamic Properties of Non-Dilute Magnetic Fluids
289-305
A. Yu.
Zubarev
Ural State University, Ekaterinburg, Russia
A. V.
Yushkov
Ural State University, Ekaterinburg, Russia
Functions of dynamic response to external magnetic field as well as rheological properties of moderately concentrated magnetic colloid consisting of identical spherical single-domain ferromagnetic particles have been derived by methods of statistical physics. Hydrodynamic and magnetodipole interactions between the particles were taken into account. The ferroparticle magnetic moment has been supposed to be constant in absolute value and to be frozen into the particle body. Our analysis has shown that the magnetodipole interaction increases both the functions of magnetic response and rheological parameters of the colloid as well as characteristic times of relaxation of both the colloid magnetization and hydrodynamic stress. We have studied some peculiarities of hydrodynamic behavior of the ferrocolloid in oscillating magnetic field. If the shear rate is large enough, the effective viscosity is nonmonotonic (with minimum) function of the field frequency w, the rotational effective viscosity is negative provided that this frequency is large enough. For the given w, the rotational viscosity is nonmonotonic function of the shear rate Ω. It is negative if Ω is small and positive if Ω. is large enough. The interparticle interaction increases the effective rotational viscosity in oscillating field.
Pseudopotential Study of Liquid Na-Cs and K-Cs Alloys
306-311
N. E.
Dubinin
Institute of Metallurgy of the Ural's Division of Russian Academy of Sciences, Ekaterinburg, Russia
T. V.
Trefilova
Institute of Metallurgy of the Ural's Division of Russian Academy of Sciences, Ekaterinburg, Russia
A. A.
Yuryev
Institute of Metallurgy of the Ural's Division of Russian Academy of Sciences, Ekaterinburg, Russia
N. A.
Vatolyn
Institute of Metallurgy of the Ural's Division of Russian Academy of Sciences, Ekaterinburg, Russia
We present a numerical calculations on the liquid Na-Cs and K-Cs alloys thermodynamics which are realized using modified by us local Animalu-Heine model pseudopotential. The advantage of this modification is that the dependency of the pseudopotential parameter A on alloy composition for each mixture's component is introduced. Good agreement with experimental data is achieved.
A Mathematical Model of Surface-Reaction Diffusion
312-319
A. O.
Ivanov
Department of Mathematical Physics, Ural State University Ekaterinburg, Russia
Yu. A.
Elfimov
Department of Mathematical Physics, Ural State University Ekaterinburg, Russia
Contact between two solid reagents, when the atoms of one of them exhibit high mobility over the surface of the other may result in a rapid surface diffusion penetration accompanied by a chemical reaction. In the case of reactions with participation of solid substances with low surface energy (tungsten, molybdenum and vanadium oxides) the diffusion was experimentally found to cease entirely when the visible boundary of the surface reaction moved through a certain, critical, not temperature dependent, distance. The article discusses a mathematical model of this phenomenon, constructed by subdividing the total reagent flux into the surface, intergranular and intragranular diffusion fluxes. The analytic solution was obtained on the assumption that the limiting factor of the process consists in slow motion of the front of chemical reaction into the grains of the substrate material. The model predicts stabilization of the surface concentration distribution of the reaction product. The analytic results were verified on the basis of experimental data for the CuO + MoO3 → CuMoO4 system. The temperature dependence of the characteristic time of stabilization of the length of the surface layer is described by the Arrhenius law, corresponding to the temperature variation of the chemical reaction constant.
Computing Rotational Relaxation on the Basis of Three-Dimensional Equations of Molecule Motion
320-330
A. I.
Yerofeyev
Central Aerohydrodynamic Institute, Moscow, Russia
Three-dimensional molecule motion equations of classical mechanics are solved to study rotational relaxation of nitrogen. The problem of relaxation is treated by the Monte Carlo method. The investigation is concerned with dependence of the process on interaction-potential parameters and initial conditions: (1) a type of a rotational energy distribution function and (2) rotational and translational temperatures.
Numerical Analysis of Multiphase Mixing - Comparison of First and Second Order Accurate Schemes
331-362
M.
Leskovar
"Jozef Stefan" Institute, Slovenia
Borut
Mavko
Reactor Engineering Division, "Jozef Stefan" Institute, Jamova 39, 1000 Ljubljana, SLOVENIA
Jure
Marn
University of Maribor, Slovenia
During a severe reactor accident following core meltdown when the molten fuel comes into contact with the coolant water a steam explosion may occur. The steam explosion can be divided into more stages. The first, premixing stage is important since it gives the initial conditions of the possible steam explosion and determines the maximum quantity of melt, which might be then involved into the explosion. To investigate the mixing process associated with the melt penetration a large number of premixing codes has been developed.
The purpose of this work is to analyze the influence of first and second order accurate numerical schemes on the premixing phase simulation results and to find out if a probabilistic treatment of some terms in the multiphase flow equations introduces any advantages. For performing this kind of analysis the simple premixing code ESE has been developed.
With ESE a number of premixing experiments performed at the Oxford University and at the QUEOS facility at Forschungszentrum Karlsruhe has been simulated using the first order accurate upwind method and the second order accurate high-resolution method. The performed analysis showed that the results obtained with the first and second accurate numerical schemes differ and that the probabilistic approach has an almost negligible effect on the simulation results.
Application of a New Turbulence Theory to Compressible 2-D Planar Flow through Small Gaps with Heat Transfer
363-385
R. A.
Morstadt
Science & Engineering, Thiokol Corp, Brigham City, Utah
A new turbulence model has been derived in a manner such that the first equation for the turbulence transport is consistent with the second equation for the relaxation rate. In addition an equation has been derived for the transport of the internal energy fluctuations. The Mu-Beta turbulence model has then been applied to compressible flow through a small gap with heat transfer using only three turbulent constants. These are the same constants that were used in the turbulent Couette flow problem. The model predicts the friction coefficient and the Nusselt number over a large range of Reynolds number. For the particular case of a hot gas over a cold wall, the predicted Nusselt number is less than the standard values usually given for fully developed turbulent flow. One possible explanation for this prediction is that the gas viscosity increases moving away from the cold wall due to the higher gas temperature. As a consequence, the Nusselt number is less than that for fully developed turbulent flow.
Hydromagnetic Flow and Heat Transfer of a Particulate Suspension Over a Non-Isothermal Surface with Variable Properties
386-402
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
A numerical study of steady, laminar, hydromagnetic, boundary-layer flow and heat transfer of a particulate suspension exhibiting finite particle volume fraction over a non-isothermal semi-infinite flat plate with variable properties is performed using a modified dusty-gas model. This modified model allows for particle-phase stresses, magnetic field and heat generation or absorption effects. The development of the displacement thicknesses and the skin-friction coefficients of both phases, as well as the wall particle-phase tangential velocity and the wall heat transfer coefficient are illustrated graphically for various parametric conditions. The results indicate that the presence of a transverse magnetic field causes the displacement thicknesses of both phases to decrease over the whole of the computational domain while the skin-friction coefficients of both phases and the wall heat transfer coefficient increase.
Boundary Layer Flow of a Fluid-Particle Suspension Past a Flat Plate in the Presence of a Magnetic Field
403-418
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
John
Peddieson
Department of Mechanical Engineering, Tennessee Technological University, Cookeville, Tennessee, U.S.A.
The plane, steady, laminar, boundary-layer flow of a two-phase fluid/particle suspension in the presence of a variable transverse magnetic field is simulated using an extension of the dusty-gas model which includes dispersed-phase diffusivity and viscosity. Numerical calculations based on this model show that its predictions are quite different from those of the dusty-gas model.
Outflow Boundary Conditions for the Computational Analysis of Jet Noise
419-432
James N.
Scott
Department of Aeronautical & Aeronautical Engineering, The Ohio State University, Columbus, Ohio, U.S.A. and ICOMP, NASA Lewis Research Center, Cleveland, Ohio
R. R.
Mankbadi
NASA Lewis Research Center, Cleveland, Ohio, U.S.A.
M. E.
Hayder
ICOMP, NASA Lewis Research Center, Cleveland, Ohio, U.S.A.
S. I.
Hariharan
Department of Mathematical Sciences, The University of Akron, Akron, Ohio, U.S.A.; and ICOMP, NASA Lewis Research Center, Cleveland, Ohio, U.S.A.
Prediction of far field noise radiation from high speed jets depends upon the accurate computation of the unsteady jet flow features and preserving the wave-like character of such features. It is particularly critical that these features be preserved as the disturbances pass through the computational boundaries. The present effort is directed toward examining various formulations based on the method of characteristics for outflow boundaries. Small harmonic disturbances are introduced at the inflow and the computed results for the growth of the input disturbance are compared against that of linear stability theory using three different outflow boundary conditions in a Navier-Stokes code. Another issue of importance examined in this study is the influence of proximity of the outflow boundary (or length of the computational domain) relative to the jet diameter.
Gas Release Effect on Transient Homogeneous Bubbly Flow Parameters
433-446
Mohand
Kessal
Université M'hamed Bougara, Laboratoire de Génie Physique des Hydrocarbures
A one-dimensional homogeneous bubbly flow model is developed taking into account the gas release phenomena. In order to analyze its effect, the three conservation equations are solved numerically by a predictor-corrector finite difference scheme and also by an improved characteristic method. A good agreement is noticed in comparison with others authors experimental and computed results. Beside this, approximate models of gas release rate are performed and compared by studying the diffusion phenomena.
Analytical Solutions for Hydromagnetic Free Convection of a Participate Suspension from an Inclined Plate with Heat Absorption
447-467
H. M.
Ramadan
Kuwait Airways Corporation, Operations Department, Salmeya, Kuwait
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
Continuum equations governing steady, laminar, free convection flow of a particulate suspension over an infinite, permeable, inclined, and isothermal flat plate with magnetic field and fluid heat absorbing effects are developed. The equations account for particulate viscous effects which are absent from most two-phase fluid-particle models. Analytical solutions are developed for inviscid and viscous particle phase situations. Graphical results for the velocity and temperature profiles for both phases as well as their skin-friction coefficients and the Nusselt number are presented and discussed.
Transient Forced Convection due to a Positive Step Change on Thermal Wall Conditions
468-480
Mourad
Rebay
University of Reims Champagne-Ardenne GRESPI / Faculte des Sciences PB 1039, 51687 Reims, France
Jacques
Padet
Laboratoire de Thermomécanique - UTAP Moulin de la housse, Faculté des Sciences, Université de Reims Champagne Ardenne, B.P. 1039, 51687 Reims cedex 2, France
The thermal response of an incompressible laminar boundary layer over a semi-infinite plate due to a positive step change in either the plate temperature or the plate heat flux density is investigated. Some coordinate transformations are obtained with the differential method in the two cases of boundary conditions. Numerical solution of differential equations is obtained by a combination of two types of finite difference schemes. Temperature profiles, thermal boundary-layer thickness and convective heat coefficient are displayed graphically for air flow. Empirical relations for the transient duration as function of Prandtl number are given for the two cases of wall conditions, for Pr ranging from 0.71 to 100.