Abstract: Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.
Abstract: The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.
The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.
Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,
Abstract: The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system.
Abstract: A numerical investigation is performed for non Newtonian fluids flow between two concentric cylinders. The D2Q9 lattice Boltzmann model developed from the Bhatangar-Gross-Krook (LBGK) approximation is used to obtain the flow field for fluids obeying to the power-law model. The inner and outer cylinders rotate in the same and the opposite direction while the end walls are maintained at rest. The combined effects of the Reynolds number (Re) of the inner and outer cylinders, the radius ratio (η) as well as the power-law index (n) on the flow characteristics are analyzed for an annular space of a finite aspect ratio (Γ). Two flow modes are obtained: a primary mode (laminar stable regime) and a secondary mode (laminar unstable regime). The so obtained flow structures are different from one mode to another. The transition critical Reynolds number Rec from the primary to the secondary mode is analyzed for the co-courant and counter-courant flows. This critical value increases as n increases. The prediction of the swirling flow of non Newtonians fluids in axisymmetric geometries is shown in the present work.
Abstract: Numerical simulation performed to investigate the behavior of the high pressure hydrogen jetting of air. High pressure hydrogen (30–40 MPa) was injected to air at atmospheric pressure through 2mm orifice. Numerical simulations were performed with Kiva3V code with 2D axisymmetric geometry. Numerical simulations showed that auto ignition of high pressure hydrogen to air are possible due to molecular diffusion. Auto ignition was predicted at hydrogen-air contact surface due to mass and energy exchange between high temperature hydrogen and air heated by shock wave.
Abstract: This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.
Abstract: An explicit axisymmetrical FE methodology is
developed here to study the particle temperature arising in WC-Co
particle on an AISI 1045 steel substrate. Parameters of constitutive
Johnson-cook model were used for simulation. The results show that
particle velocity and kinetic energy have important role in
temperature arising of particles.
Abstract: High-velocity oxygen fuel (HVOF) thermal spraying
uses a combustion process to heat the gas flow and coating material.
A computational fluid dynamics (CFD) model has been developed to
predict gas dynamic behavior in a HVOF thermal spray gun in which
premixed oxygen and propane are burnt in a combustion chamber
linked to a parallel-sided nozzle. The CFD analysis is applied to
investigate axisymmetric, steady-state, turbulent, compressible,
chemically reacting, subsonic and supersonic flow inside and outside
the gun. The gas velocity, temperature, pressure and Mach number
distributions are presented for various locations inside and outside
the gun. The calculated results show that the most sensitive
parameters affecting the process are fuel-to-oxygen gas ratio and
total gas flow rate. Gas dynamic behavior along the centerline of the
gun depends on both total gas flow rate and fuel-to-oxygen gas ratio.
The numerical simulations show that the axial gas velocity and Mach
number distribution depend on both flow rate and ratio; the highest
velocity is achieved at the higher flow rate and most fuel-rich ratio.
In addition, the results reported in this paper illustrate that the
numerical simulation can be one of the most powerful and beneficial
tools for the HVOF system design, optimization and performance
analysis.
Abstract: Metal matrix composites (MMC) are generating
extensive interest in diverse fields like defense, aerospace, electronics
and automotive industries. In this present investigation, material
removal rate (MRR) modeling has been carried out using an
axisymmetric model of Al-SiC composite during electrical discharge
machining (EDM). A FEA model of single spark EDM was
developed to calculate the temperature distribution.Further, single
spark model was extended to simulate the second discharge. For
multi-discharge machining material removal was calculated by
calculating the number of pulses. Validation of model has been done
by comparing the experimental results obtained under the same
process parameters with the analytical results. A good agreement was
found between the experimental results and the theoretical value.
Abstract: In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.
Abstract: Einstein vacuum equations, that is a system of nonlinear
partial differential equations (PDEs) are derived from Weyl metric
by using relation between Einstein tensor and metric tensor. The
symmetries of Einstein vacuum equations for static axisymmetric
gravitational fields are obtained using the Lie classical method. We
have examined the optimal system of vector fields which is further
used to reduce nonlinear PDE to nonlinear ordinary differential
equation (ODE). Some exact solutions of Einstein vacuum equations
in general relativity are also obtained.
Abstract: The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
Abstract: Dynamic shear test on simulated phantom can be used
to validate magnetic resonance elastography (MRE) measurements.
Phantom gel has been usually utilized for the cell culture of cartilage
and soft tissue and also been used for mechanical property
characterization using imaging systems. The viscoelastic property of
the phantom would be important for dynamic experiments and
analyses. In this study, An axisymmetric FE model is presented for
determining the dynamic shear behaviour of brain simulated phantom
using ABAQUS. The main objective of this study was to investigate
the effect of excitation frequencies and boundary conditions on shear
modulus and shear viscosity in viscoelastic media.
Abstract: Axisymmetric vibration of an infinite Pyrocomposite
circular hollow cylinder made of inner and outer pyroelectric layer of
6mm-class bonded together by a Linear Elastic Material with Voids
(LEMV) layer is studied. The exact frequency equation is obtained
for the traction free surfaces with continuity condition at the
interfaces. Numerical results in the form of data and dispersion
curves for the first and second mode of the axisymmetric vibration of
the cylinder BaTio3 / Adhesive / BaTio3 by taking the Adhesive layer
as an existing Carbon Fibre Reinforced Polymer (CFRP) are
compared with a hypothetical LEMV layer with and without voids
and as well with a pyroelectric hollow cylinder. The damping is
analyzed through the imaginary parts of the complex frequencies.
Abstract: The comparisons of two typical fluidic thrust vectoring exhaust nozzles including two-dimensional(2-D) nozzle and axisymmetric nozzle on aerodynamic characteristics was presented by numerical simulation. The results show: the thrust vector angles increased with the increasing secondary flow but decreased with the nozzle pressure ratio (NPR) increasing. With the same secondary flow and NPR, the thrust vector angles of 2-D nozzle were higher than the axisymmetric nozzle-s. So with the lower NPR and more secondary weight flow, the much higher thrust vector angle was caused by 2-D fluidic nozzle. And with the higher NPR and less secondary weight flow, there was not much difference in angular dimension between two nozzles.
Abstract: The Spalart and Allmaras turbulence model has been
implemented in a numerical code to study the compressible turbulent
flows, which the system of governing equations is solved with a
finite volume approach using a structured grid. The AUSM+ scheme
is used to calculate the inviscid fluxes. Different benchmark
problems have been computed to validate the implementation and
numerical results are shown. A special Attention is paid to wall jet
applications. In this study, the jet is submitted to various wall
boundary conditions (adiabatic or uniform heat flux) in forced
convection regime and both two-dimensional and axisymmetric wall
jets are considered. The comparison between the numerical results
and experimental data has given the validity of this turbulence model
to study the turbulent wall jets especially in engineering applications.
Abstract: Today, Hydroforming technology provides an
attractive alternative to conventional matched die forming, especially
for cost-sensitive, lower volume production, and for parts with
irregular contours. In this study the critical fluid pressures which lead
to rupture in the workpiece has been investigated by theoretical and
finite element methods. The axisymmetric analysis was developed to
investigate the tearing phenomenon in cylindrical Hydroforming
Deep Drawing (HDD). By use of obtained equations the effect of
anisotropy, drawing ratio, sheet thickness and strain hardening
exponent on tearing diagram were investigated.
Abstract: The plastic forming process of sheet plate takes an
important place in forming metals. The traditional techniques of tool
design for sheet forming operations used in industry are experimental
and expensive methods. Prediction of the forming results,
determination of the punching force, blank holder forces and the
thickness distribution of the sheet metal will decrease the production
cost and time of the material to be formed. In this paper, multi-stage
deep drawing simulation of an Industrial Part has been presented
with finite element method. The entire production steps with
additional operations such as intermediate annealing and springback
has been simulated by ABAQUS software under axisymmetric
conditions. The simulation results such as sheet thickness
distribution, Punch force and residual stresses have been extracted in
any stages and sheet thickness distribution was compared with
experimental results. It was found through comparison of results, the
FE model have proven to be in close agreement with those of
experiment.
Abstract: The aim of this work is to analyze a viscous flow in
the axisymmetric nozzle taken into account the mesh size both in the
free stream and into the boundary layer. The resolution of the Navier-
Stokes equations is realized by using the finite volume method to
determine the supersonic flow parameters at the exit of convergingdiverging
nozzle. The numerical technique uses the Flux Vector
Splitting method of Van Leer. Here, adequate time stepping
parameter, along with CFL coefficient and mesh size level is selected
to ensure numerical convergence. The effect of the boundary layer
thickness is significant at the exit of the nozzle. The best solution is
obtained with using a very fine grid, especially near the wall, where
we have a strong variation of velocity, temperature and shear stress.
This study enabled us to confirm that the determination of boundary
layer thickness can be obtained only if the size of the mesh is lower
than a certain value limits given by our calculations.
Abstract: The Stokes equation connected with the fluid flow
over the axisymmetric bodies in a cylindrical area is considered. The
equation is studied in a moving coordinate system with the
appropriate boundary conditions. Effective formulas for the velocity
components are obtained. The graphs of the velocity components and
velocity profile are plotted.