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Issue 1, Volume 6,
January 2011
Special Issue:
Mathematical Fluid Dynamics - Part I
Editor:
Nikos Mastorakis
Title of the Paper: Asymptotic Solutions
and Unsymmetric Solutions of a Fifth Order Ordinary Differential Equation
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Authors: Chung-Hsien
Tsai, Shy-Jen Guo
Abstract: The objective of this paper is to construct the asymptotic solutions
and unsymmetric solutions of a fifth order model equation for steady
capillary-gravity waves over a smooth compact bump with the Froude number near
1 and the Bond number near 1/3.
Keywords: Steady
capillary-gravity wave, fifth order model equation, bump, Green’s function,
asymptotic solution, unsymmetric Solutions
Title of the Paper: Asymptotic Solutions
of a Fifth Order Ordinary Differential Equation
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Authors: Chung-Hsien
Tsai, Shy-Jen Guo
Abstract: The objective of this paper is to construct the asymptotic solutions
of a fifth order model equation for steady capillary-gravity waves over a
smooth compact bump with the Froude number near 1 and the Bond number near
1/3.
Keywords: Steady
capillary-gravity wave, fifth order model equation, bump, Green’s function,
asymptotic solution
Title of the Paper: Analytic Solutions
to a Boundary Layer Problem for Non-Newtonian Fluid Flow Driven by Power Law
Velocity Profile
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Authors: Gabriella
Bognar
Abstract: In this paper the similarity solutions of the Prandtl boundary layer
equations describing a non- Newtonian power law fluid past an impermeable flat
plate, driven by a power law velocity profile U = Bys (B > 0) have been
investigated. It is shown that there are analytical solutions for any n > 0, n
? 2 and any ?1/ 2 £s < 0 . We give a method for the determination of the power
series solutions to the momentum equation and we estimate the convergence
radius of the proposed solutions.
Keywords: Similarity
solution, power series solution, boundary value problem, non-Newtonian fluid
flow
Title of the Paper: Computer Modeling of
Planet Partial Fragmentation
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Authors: D. V. Voronin
Abstract: It is difficult to explain an origin of all celestial bodies of the
Solar system by smooth evolution of the protoplanet cloud. The alternative is
the hypothesis of the explosive origin of some bodies. The nuclear explosion
in active layer (particles of uranium and thorium oxides, weighed in liquid
iron at a planer core) might take place at collision of the protoplanet with
an asteroid. Subsequent fragmentation of the planet in conditions of
gravitation is numerically simulated. It was found that the structure and
composition of fragments may be determined by the cumulative jet, going from a
planetary core to its surface for small enough initial velocity of protoplanet
rotation. The origin of Io may be so explained, for example. Separation of the
great mass of the stone-silicate shell of the planet and the generation of
satellites like the Moon occurs at the great enough velocity of rotation.
Keywords: Numerical
simulations, active layer, celestial bodies, explosion, cumulative jet, planet
rotation
Title of the Paper: A Combined Space
Discrete Algorithm with a Taylor Series by Time for Solution of the
Non-Stationary CFD Problems
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Authors: Ivan V.
Kazachkov
Abstract: The first order by time partial differential equation (PDE) is used
as models in applications such as fluid flow, heat transfer, solid
deformation, electromagnetic waves, and many others. In this paper we propose
the new numerical method to solve a class of the initial-boundary value
problems for the PDE using any known space discrete numerical schemes and a
Taylor series expansion by time. Derivatives by time are got from the outgoing
PDE and its further differentiation (for second and higher order derivatives
by time). By numerical solution of the PDE and PDE arrays normally a second
order discretization by space is applied while a first order by time is
sometimes satisfactory too. Nevertheless, in a number of different problems,
discretization both by temporal and by spatial variables is needed of highest
orders, which complicates the numerical solution, in some cases dramatically.
Therefore it is difficult to apply the same numerical methods for the solution
of some PDE arrays if their parameters are varying in a wide range so that in
some of them different numerical schemes by time fit the best for precise
numerical solution. The Taylor series based solution strategy for the
non-stationary PDE in CFD simulations has been proposed here that attempts to
optimise the computation time and fidelity of the numerical solution. The
proposed strategy allows solving the non-stationary PDE with any order of
accuracy by time in the frame of one algorithm on a single processor, as well
as on a parallel cluster system. A number of examples considered in this paper
have shown applicability of the method and its efficiency.
Keywords: Non-stationary,
First Order by Time; Navier-Stokes Equations; Taylor Series; Numerical;
Fractional Derivative
Issue 2, Volume 6,
April 2011
Special Issue:
Mathematical Fluid Dynamics - Part II
Editor:
Nikos Mastorakis
Title of the Paper: The Mathematical
Models for Penetration of a Liquid Jets into a Pool
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Authors: Ivan V.
Kazachkov
Abstract: The peculiarities of a jet penetrating the liquid pool of different
density were examined by means of the non-linear and linear mathematical
models derived including bending instability. Based on experimental
observations reported in the literature for a number of situations, the
penetration behaviour was assumed to govern the buoyancy-dominated regime. A
new analytical solution of the one-dimensional non-linear model was obtained
for the jet penetration in this condition, as function of Froude number,
jet/ambient fluid density ratio and other parameters. The solution was
analysed for a number of limit cases. Analytical solution of the non-linear
second-order equation obtained can be of interest for other researchers as the
mathematical result.
Keywords: Jet,
Penetration, Pool of Liquid, Non-linear, Analytical Solution, Bifurcation,
Bending
Title of the Paper: High Velocity Motion
of a Wing in Compressible Fluid Near a Surface
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Authors: M. N. Smirnova,
A. V. Zvyaguin
Abstract: The two-dimensional problems of thin body motion in fluid parallel
to the boundary at a distance, comparable with the length of the body, are
regarded. In particular, resistance and lift forces in thin body motion
parallel to free surface and parallel to rigid surface are determined and
compared with existing solutions for resistance and lift forces in case of an
infinite space. The solution is determined under the assumption of fluid being
ideal and compressible. The Chaplygin-Zhukovsky hypothesis of
rear-edge-limited solution is taken into consideration. In case of moving near
free surface the solution is obtained for a problem of infinite span wing. The
solution allows determining drag and lift forces in the limiting cases. It was
shown that on Mach number tending to unity both forces infinitely increase.
For relatively thin fluid layer above the moving wing the resistance force
depends on the distance to the free surface, inclination and Mach number,
while for relatively thick fluid layer the force depends on wing length,
inclination angle and Mach number as well. In case of moving near rigid
surface the solution of a problem is reduced to the Fredholm equation, which
is solved numerically. The generalization of Zhukovski solution was obtained,
which provides the lift force dependence on the altitude of the flight. The
behavior of the lift force is very peculiar: it increases on decreasing
altitude above the rigid surface. The screen effect becomes essential on
moving wing altitude being smaller than the wing’s length. The effect was
detected experimentally before and gave birth to construction of a special
flying vehicle named “ecranoplan”. It is shown in the paper that the lift
force could increase several orders of magnitude. This effect could be used in
developing flying high-speed vehicles, which could be used in the territories
of smooth surface: steppes, deserts, lakes, swamps, etc.
Keywords: Wing,
compressible fluid, analytical function, Fredholm equation, Dirichlet problem,
lift and resistance forces
Title of the Paper: PIV Velocity and
Pressure Measurements of the Unsteady Flow Field behind Two Automobile Outside
Rear View Mirrors
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Authors: Bahram
Khalighi, Richard Lee
Abstract: The unsteady flow fields behind two different automobile outside
side rear view mirrors were examined experimentally in order to obtain a
comprehensive data base for the validation of the ongoing computational
investigation effort to predict the aero-acoustic noise due to the outside
rear view mirrors. This study is part of a larger scheme to predict the
aero-acoustic noise due to various external components in vehicles. To aid
with the characterization of this complex flow field, mean and unsteady
surface pressure measurements were undertaken in the wake of two mirror
models. Velocity measurements with particle image velocimetry were also
conducted to develop the mean velocity field of the wake. Two full-scale
mirror models with distinctive geometrical features were investigated.
Keywords: Outside mirror
flow. wake behind automobile mirrors, PIV
Title of the Paper: Large Eddy
Simulation of Pressure Distribution of Fluid Flow Over Ridges of Circular,
Parabolic and Rectangular Shapes
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Authors: A. J.
Templeman, M. G. Rasul
Abstract: This paper presents modeling and large eddy simulation of pressure
coefficient distribution of the flow of air over ridges of circular, parabolic
and rectangular shapes at different Reynolds numbers using computational fluid
dynamics (CFD) code FLUENT. The simulated results are compared and discussed
with the experimentally measured pressure distributions. The experiments were
done in an open circuit blower type wind tunnel. This study found that the
pressure coefficient distributions over the three ridges are not unique in
character at zero angle of attack for same Reynolds number and its magnitude
depends on the geometry of the ridges. The typical potential flow equations
are not applicable to predict the distance of pressure dissipation in the
downstream direction of the flow.
Keywords: CFD simulation,
ridges, pressure coefficient distribution
Title of the Paper: Linear and Weakly
Nonlinear Instability of Slightly Curved Shallow Mixing Layers
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Authors: Irina Eglite,
Andrei Kolyshkin
Abstract: The paper is devoted to linear and weakly nonlinear stability
analysis of shallow mixing layers. The radius of curvature is assumed to be
large. Linear stability problem is solved numerically using collocation method
based on Chebyshev polynomials. It is shown that for stably curved mixing
layers curvature has a stabilizing effect on the flow. Weakly nonlinear theory
is used to derive an amplitude evolution equation for the most unstable mode.
It is shown that the evolution equation in this case is the Ginzburg-Landau
equation with complex coefficients. Explicit formulas for the calculation of
the coefficients of the Ginzburg-Landau equation are derived. Numerical
algorithm for the computation of the coefficients is described in detail.
Keywords: Linear
stability, weakly nonlinear theory, method of multiple scales, Ginzburg-Landau
equation, collocation method
Issue 3, Volume 6,
July 2011
Special Issue:
Numerical Methods in Fluid Mechanics
Editor:
Nikos Mastorakis
Title of the Paper: Modeling of High
Velocity Flows with Chemical Reactions
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Authors: D. V. Voronin
Abstract: The numerical algorithm for the decision of non-stationary
two-dimensional problems of dynamics of compressible multi phase media is
developed on the base of the method of particles in cells. With the purpose of
elimination of non-physical fluctuations of the numerical decision inherent in
methods of this type, there are offered method of integration of the equation
of mass conservation and procedure of determination of pressure in nodes of
numerical grid. On the base of algorithm some examples of modeling were
executed: propagation of gas detonation with cellular structure in tube,
explosion in a planet interiors and bubble detonation.
Keywords: Modeling,
two-phase media, compressible flows, particle, detonation, explosion
Title of the Paper: Spray Injection and
Ignition in a Heated Chamber Modeling
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Authors: V. B. Betelin,
A. G. Kushnirenko, V. A. Nerchenko, V. F. Nikitin, N. N. Smirnov
Abstract: Computer simulation of liquid fuel jet injection into heated
atmosphere of combustion chamber, mixture formation, ignition and combustion
need adequate modeling of evaporation, which is extremely important for the
curved surfaces in the presence of strong heat and mass diffusion fluxes.
Combustion of most widely spread hydrocarbon fuels takes place in a gas-phase
regime. Thus, evaporation of fuel from the surface of droplets turns to be one
of the limiting factors of the process as well. The problems of fuel droplets
atomization, evaporation being the key factors for heterogeneous mixtures
reacting mixtures, the non-equilibrium effects in droplets atomization and
phase transitions will be taken into account in describing thermal and
mechanical interaction of droplets with streaming flows. In the present
lecture processes of non-equilibrium evaporation of small droplets will be
discussed. It will be demonstrated, that accounting for non-equilibrium
effects in evaporation for many types of widely used liquids is crucial for
droplets diameters less than 100 microns, while the surface tension effects
essentially manifest only for droplets below 0.1 micron. Investigating the
behavior of individual droplets in a heated air flow allowed to distinguish
two scenarios for droplet heating and evaporation. Small droplets undergo
successively heating, then cooling due to heat losses for evaporation, and
then rapid heating till the end of their life time. Larger droplets could
directly be heated up to a critical temperature and then evaporate rapidly.
Atomization of droplets interferes the heating and evaporation scenario.
Keywords: Combustion,
ignition, phase transition, heat flux, evaporation, non-equilibrium,
diffusion, mathematical simulation
Title of the Paper: On the Assessment of
an Unstructured Finite-Volume DES/LES Solver for Turbomachinery Applications
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Authors: Chiara
Bernardini, Mauro Carnevale, Simone Salvadori, Francesco Martelli
Abstract: Improvements in mean flow and performances simulation in
turbomachinery has brought research to focus more demanding topics like
turbulence effects on turbines. Although overall performances are well
predicted by Unsteady-RANS, other phenomena such as aerodynamic noise or
transition need more accurate prediction of turbulent flow features. Thus
different kinds of equation modeling other than URANS are needed to cope with
this issue. The success of Detached-Eddy Simulation and Large-Eddy Simulation
applications in reproducing physical behavior of flow turbulence is well
documented in literature. Despite that, LES simulations are still
computationally very expensive and their use for investigating industrial
configurations requires a careful assessment of both numerical and closure
modeling techniques. Moreover LES solvers are usually developed on a
structured mesh topology for sake of simplicity of high-order schemes
implementation. Application to complex geometries like those of turbomachinery
is therefore difficult. The present work addresses this issue considering the
feasibility of converting an operative in-house URANS solver, widely validated
for applicative purposes, into higher resolution DES and LES, in order to face
turbulence computation of turbomachinery technical cases. The solver presents
a 3D unstructured finite-volume formulation, which is kept in LES approach in
order to handle complex geometries and it is developed to perform unsteady
simulations on turbine stages. Preliminary assessment of the solver has been
performed to evaluate and improve the accuracy of the convective fluxes
discretization on an inviscid bump test case. First a DES-based approach has
been implemented, as it is less computationally challenging and numerically
demanding than LES. A square cylinder test case has been assessed and compared
with experiments. Then, a pure LES with a Smagorinsky sub-grid scale model has
been evaluated on the test case of incompressible periodic channel flow in
order to assess the capability of the solver to correctly sustain a time
developing turbulent field.
Keywords: DES, Inflow
Boundary, Numerical accuracy, Turbulent channel flow, Unstructured LES
Title of the Paper: Finite Element Model
for Wave Propagation Near Shore Based on Extended Boussinesq Equations
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Authors: L. Pinheiro, C.
J. Fortes, J. A. Santos, L. Fernandes, M. Walkley
Abstract: This paper describes the numerical model BOUSS-WMH (BOUSSinesq Wave
Model for Harbours), a finite element model for nonlinear wave propagation
near shore and into harbors. It is based upon an extended version of the
Boussinesq equations to which terms were added to generate regular or
irregular waves inside the numerical domain, absorb outgoing waves, partially
reflect waves at physical boundaries, control numerical instabilities and
reproduce energy dissipation due to bottom friction and wave breaking. The
paper focuses on the implementation of partial reflection, bottom friction and
wave breaking as well as on the model applications to experimental test cases.
Results are compared with physical model tests and another numerical model.
Keywords: Wave
Propagation, Boussinesq Equations, Harbours, Finite Elements
Title of the Paper: Droplet Simulation,
A Case Study: Evaporation
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Authors: Sadegh Torfi,
Seyed Mohammad Hosseini Nejad
Abstract: For heat and mass transfer simulation of single droplet in a
two-pieces solution with saturated solvent vapor environment, a numerical
model is developed by finite volume method and transient SIMPLEC algorithm. I
this study, dimensionless equations of motion, heat transfer and mass transfer
(based on mass ratio) are solved simultaneously. All the thermodynamic and
transitional solution properties have been considered as a function of
temperature and concentration. The numerical analysis results are presented
for mass transfer of lithium bromide solution droplet in 300K and initial
concentration of 50%. Verification of method is done by compare these
numerical results with analytical and numerical analysis of other studies.
Droplet Growth Chart, average temperature and concentration, variation of drag
coefficient diagrams, Nusselt number and flow line, temperature and
concentration and temperature distribution contours, penetration rate of mass
and the level of tangential velocity at droplet surface as the modeling
results are presented.
Keywords: Heat and Mass
Transfer, Finite volume, Droplet, Simulation, SIMPLEC Algorithm
Issue 4, Volume 6,
October 2011
Title of the Paper: Supersonic and
Hypersonic Flows on 2D Unstructured Context: Part I
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Authors: Edisson Sávio
De Góes Maciel
Abstract: In this work, numerical simulations involving supersonic and
hypersonic flows on an unstructured context are analyzed. The Van Leer and the
Radespiel and Kroll schemes are implemented on a finite volume formulation,
using unstructured spatial discretization. The algorithms are implemented in
their first and second order spatial accuracies. The second order spatial
accuracy is obtained by a linear reconstruction procedure based on the work of
Barth and Jespersen. Several non-linear limiters are studied, as well two
types of linear interpolation, based on the works of Frink, Parikh and
Pirzadeh and of Jacon and Knight. Two types of viscous calculation to the
laminar case are compared. They are programmed considering the works of Long,
Khan and Sharp and of Jacon and Knight. To the turbulent simulations, the
Wilcox and Rubesin model is employed. The ramp problem to the inviscid
simulations and the re-entry capsule problem to the hypersonic viscous
simulations are studied. The results have demonstrated that the Van Leer
algorithm yields the best results in terms of the prediction of the shock
angle of the oblique shock wave in the ramp problem and the best value of the
stagnation pressure at the configuration nose in the re-entry capsule problem.
The convective time step is the best choice to accelerate the convergence of
the numerical schemes, as reported by Maciel. In terms of turbulent results,
the Wilcox and Rubesin model yields good results, proving the good capacity of
this turbulence model in simulate high hypersonic flows. This paper is the
first part of this work and is related to the theory and inviscid solutions.
The second paper of this work is concerned with the laminar and turbulent
viscous results.
Keywords: Supersonic and
hypersonic flows, Unstructured discretization, Van Leer algorithm, Radespiel
and Kroll algorithm, Wilcox and Rubesin turbulence model, Euler and
Navier-Stokes equations, Two-dimensions
Title of the Paper: Supersonic and
Hypersonic Flows on 2D Unstructured Context: Part II
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Authors: Edisson Sávio
De Góes Maciel
Abstract: In this work, numerical simulations involving supersonic and
hypersonic flows on an unstructured context are analyzed. The Van Leer and the
Radespiel and Kroll schemes are implemented on a finite volume formulation,
using unstructured spatial discretization. The algorithms are implemented in
their first and second order spatial accuracies. The second order spatial
accuracy is obtained by a linear reconstruction procedure based on the work of
Barth and Jespersen. Several non-linear limiters are studied, as well two
types of linear interpolation, based on the works of Frink, Parikh and
Pirzadeh and of Jacon and Knight. Two types of viscous calculation to the
laminar case are compared. They are programmed considering the works of Long,
Khan and Sharp and of Jacon and Knight. To the turbulent simulations, the
Wilcox and Rubesin model is employed. The ramp problem for the inviscid
supersonic simulations and the re-entry capsule for the viscous hypersonic
simulations are considered. The results have demonstrated that the Van Leer
algorithm yields the best results in terms of the prediction of the wall
pressure distribution and the shock angle in the inviscid simulations and the
best value of the stagnation pressure at the configuration nose in the viscous
simulations. Moreover, the Van Leer algorithm in the SS case and using the
Wilcox and Rubesin turbulence model predicts the best value of the lift
aerodynamic coefficient. Hence, the Wilcox and Rubesin model yielded good
results, proving its good capacity to predict high hypersonic flows. This
paper is the second part of this work and is concerned with the laminar and
turbulent viscous results.
Keywords: Supersonic and
hypersonic flows, Unstructured discretization, Van Leer algorithm, Radespiel
and Kroll algorithm, Wilcox and Rubesin turbulence model, Euler and
Navier-Stokes equations, Two-dimensions
Title of the Paper: Fluid Flow in
Channels Between Two Gas Turbines and Heat Recovery Steam Generator – A
Theoretical Investigation
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Authors: H. Walter, C.
Dobias, F. Holzleithner
Abstract: The paper present the results of a study for a special configuration
of a combined cycle power plant. In this plant two gas turbines are installed
to feed one Heat Recovery Steam Generator (HRSG). The flue gas flow in the
channels between the two gas turbines and the HRSG was analyzed to get a more
homogenous flow distribution in front of the first heating surface of the HRSG
which is arranged downstream of the gas turbines. In the study a particular
attention was placed at the operation conditions where only one gas turbine is
in operation.
The results of the investigation have shown that the measures with a higher
possibility to get a homogenous flow distribution in front of the first tube
bank arranged downstream of the gas turbine have also a higher pressure loss
and in last consequence they are linked with a higher loss of gas turbine
power respectively a lower efficiency of the combined cycle. The study has
also shown that a larger merging area for the flue gas arranged between the
merging point of the two flue gas ducts and the entrance into the HRSG results
in a more even flow distribution.
Keywords: Numerical
simulation, Flue gas channel, Heat recovery steam generator, Channel
optimization, Flow distribution
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