Abstract: An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.
Abstract: A theoretical investigation on the effects of both
steady-state and dynamic deformations of the foils on the dynamic
performance characteristics of a self-acting air foil journal bearing
operating under small harmonic vibrations is proposed. To take into
account the dynamic deformations of foils, the perturbation method is
used for determining the gas-film stiffness and damping coefficients
for given values of excitation frequency, compressibility number, and
compliance factor of the bump foil. The nonlinear stationary
Reynolds’ equation is solved by means of the Galerkins’ finite
element formulation while the finite differences method are used to
solve the first order complex dynamic equations resulting from the
perturbation of the nonlinear transient compressible Reynolds’
equation. The stiffness of a bump is uniformly distributed throughout
the bearing surface (generation I bearing). It was found that the
dynamic properties of the compliant finite length journal bearing are
significantly affected by the compliance of foils especially whenthe
dynamic deformation of foils is considered in addition to the static
one by applying the principle of superposition.
Abstract: Steady incompressible couple stress fluid flow through two dimensional symmetric channel with stenosis is investigated. The flow consisting of a core region to be a couple stress fluid and a peripheral layer of plasma (Newtonian fluid). Assuming the stenosis to be mild, the equations governing the flow of the proposed model are solved using the slip boundary condition and closed form expressions for the flow characteristics (the dimensionless resistance to flow and wall shear stress at the maximum height of stenosis) are derived. The effects of various parameters on these flow variables have been studied. It is observed that the resistance to flow as well as the wall shear stress increase with the height of stenosis, viscosity ratio and Darcy number. However, the trend is reversed as the slip and the couple stress parameter increase.
Abstract: A filtering problem of almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain is studied. In this work general approaches to the solution of twodimensional filtering problems in ananisotropic, inhomogeneous and multilayered medium are developed, and on the basis of the obtained results mathematical models are constructed (according to Ollendorff method) for studying the certain engineering and technical problem of filtering the almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain. For some of the formulated mathematical problems with additional requirements for the structure of the porous inhomogeneous medium, namely, its isotropy, spatial periodicity of its permeability coefficient, solution algorithms are proposed. Continuation of the current work titled ”On one mathematical model for filtration of weakly compressible chemical compound in the porous heterogeneous 3D medium. Part II: Determination of the reference directions of anisotropy and permeabilities on these directions” will be prepared in the shortest terms by the authors.
Abstract: A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain. Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Numerical results have been found to be in good agreement with computational and experimental results available in the literature.
Abstract: The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not distributed uniformly throughout the domain. Unlike conventional approaches which assume globally similar values of RBF shape parameters, the presented ASP technique suggests that shape parameter be calculated exclusively for each data point (or node) based on the distribution of data points within its own influence domain. This will ensure interpolation accuracy while still maintaining well conditioned system of equations for RBF weights. Performance and accuracy of ASP technique has been tested by evaluating derivatives and laplacian of a known function using RBF in Finite difference mode (RBFFD), with and without the use of adaptivity in shape parameters. Application of adaptive shape parameters (ASP) for solution of incompressible Navier Strokes equations has been presented by solving lid driven cavity flow problem on mesh-free domain using RBF-FD. The results have been compared for fixed and adaptive shape parameters. Improved accuracy has been achieved with the use of ASP in RBF-FD especially at regions where larger gradients of field variables exist.
Abstract: The mixing of two or more liquids is very common in many industrial applications from automotive to food processing. CFD simulations of these processes require comparison with test results. In many cases it is practically impossible. Therefore, comparison provides with scalable tests. So, parameterization of the problem is sufficient to capture the performance of the mixer.
However, the influence of geometrical and thermo-physical parameters on the mixing is not well understood.
In this work influence of geometrical and thermal parameters was studied. It was shown that for full developed turbulent flows (Re > 104), Pet»const and concentration of secondary fluid ~ F(r/l).
In other words, the mixing is practically independent of total flow rate and scale for a given geometry and ratio of flow rates of mixing flows. This statement was proved in present work for different geometries and mixtures such as EGR and water-urea mixture.
Present study has been shown that the best way to improve the mixing is to establish geometry with the lowest Pet number possible by intensifying the turbulence in the domain. This is achievable by using step geometry, impinging flow EGR on a wall, or EGR jets, with a strong change in the flow direction, or using swirler like flow in the domain or combination all of these factors. All of these results are applicable to any mixtures of no compressible fluids.
Abstract: The ongoing effort to develop an in-house
compressible solver with multi-disciplinary physics is presented in
this paper. Basic compressible solver combined with IBM technique
provides us an effective numerical tool able to tackle the physics
phenomena and especially physic phenomena involved in Solid
Rocket Motors (SRMs). Main principles are introduced step by step
describing its implementation. This paper sheds light on the whole
potentiality of our proposed numerical model and we strongly believe
a way to introduce multi-physics mechanisms strongly coupled is
opened to ablation in nozzle, fluid/structure interaction and burning
propellant surface with time.
Abstract: In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.
Abstract: In this paper, we study the pulsatile flow of blood through stenotic arteries. The inner layer of arterial walls is modeled as a porous medium and human blood is assumed as an incompressible fluid. A numerical algorithm based on the finite element method is developed to simulate the blood flow through both the lumen region and the porous wall. The algorithm is then applied to study the flow behaviour and to investigate the significance of the non-Newtonian effect.
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: The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.
Abstract: The paper presents a numerical investigation on the
rapid gas decompression in pure nitrogen which is made by using the
one-dimensional (1D) and three-dimensional (3D) mathematical
models of transient compressible non-isothermal fluid flow in pipes.
A 1D transient mathematical model of compressible thermal multicomponent
fluid mixture flow in pipes is presented. The set of the
mass, momentum and enthalpy conservation equations for gas phase
is solved in the model. Thermo-physical properties of multicomponent
gas mixture are calculated by solving the Equation of
State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is
chosen. This model is successfully validated on the experimental data
[1] and shows a good agreement with measurements. A 3D transient
mathematical model of compressible thermal single-component gas
flow in pipes, which is built by using the CFD Fluent code (ANSYS),
is presented in the paper. The set of unsteady Reynolds-averaged
conservation equations for gas phase is solved. Thermo-physical
properties of single-component gas are calculated by solving the Real
Gas Equation of State (EOS) model. The simplest case of gas
decompression in pure nitrogen is simulated using both 1D and 3D
models. The ability of both models to simulate the process of rapid
decompression with a high order of agreement with each other is
tested. Both, 1D and 3D numerical results show a good agreement
between each other. The numerical investigation shows that 3D CFD
model is very helpful in order to validate 1D simulation results if the
experimental data is absent or limited.
Abstract: The paper presents a one-dimensional transient
mathematical model of compressible non-isothermal multicomponent
fluid mixture flow in a pipe. The set of the mass,
momentum and enthalpy conservation equations for gas phase is
solved in the model. Thermo-physical properties of multi-component
gas mixture are calculated by solving the Equation of State (EOS)
model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas
mixture viscosity is calculated on the basis of the Lee-Gonzales-
Eakin (LGE) correlation. Numerical analysis of rapid gas
decompression process in rich and base natural gases is made on the
basis of the proposed mathematical model. The model is successfully
validated on the experimental data [1]. The proposed mathematical
model shows a very good agreement with the experimental data [1] in
a wide range of pressure values and predicts the decompression in
rich and base gas mixtures much better than analytical and
mathematical models, which are available from the open source
literature.
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: The simulation of extrusion process is studied widely
in order to both increase products and improve quality, with broad
application in wire coating. The annular tube-tooling extrusion was
set up by a model that is termed as Navier-Stokes equation in
addition to a rheological model of differential form based on singlemode
exponential Phan-Thien/Tanner constitutive equation in a twodimensional
cylindrical coordinate system for predicting the
contraction point of the polymer melt beyond the die. Numerical
solutions are sought through semi-implicit Taylor-Galerkin pressurecorrection
finite element scheme. The investigation was focused on
incompressible creeping flow with long relaxation time in terms of
Weissenberg numbers up to 200. The isothermal case was considered
with surface tension effect on free surface in extrudate flow and no
slip at die wall. The Stream Line Upwind Petrov-Galerkin has been
proposed to stabilize solution. The structure of mesh after die exit
was adjusted following prediction of both top and bottom free
surfaces so as to keep the location of contraction point around one
unit length which is close to experimental results. The simulation of
extrusion process is studied widely in order to both increase products
and improve quality, with broad application in wire coating. The
annular tube-tooling extrusion was set up by a model that is termed
as Navier-Stokes equation in addition to a rheological model of
differential form based on single-mode exponential Phan-
Thien/Tanner constitutive equation in a two-dimensional cylindrical
coordinate system for predicting the contraction point of the polymer
melt beyond the die. Numerical solutions are sought through semiimplicit
Taylor-Galerkin pressure-correction finite element scheme.
The investigation was focused on incompressible creeping flow with
long relaxation time in terms of Weissenberg numbers up to 200. The
isothermal case was considered with surface tension effect on free
surface in extrudate flow and no slip at die wall. The Stream Line
Upwind Petrov-Galerkin has been proposed to stabilize solution. The
structure of mesh after die exit was adjusted following prediction of
both top and bottom free surfaces so as to keep the location of
contraction point around one unit length which is close to
experimental results.
Abstract: The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.
Abstract: In this paper, the dam-reservoir interaction is
analyzed using a finite element approach. The fluid is assumed to be
incompressible, irrotational and inviscid. The assumed boundary
conditions are that the interface of the dam and reservoir is vertical
and the bottom of reservoir is rigid and horizontal. The governing
equation for these boundary conditions is implemented in the
developed finite element code considering the horizontal and vertical
earthquake components. The weighted residual standard Galerkin
finite element technique with 8-node elements is used to discretize
the equation that produces a symmetric matrix equation for the damreservoir
system. A new boundary condition is proposed for
truncating surface of unbounded fluid domain to show the energy
dissipation in the reservoir, through radiation in the infinite upstream
direction. The Sommerfeld-s and perfect damping boundary
conditions are also implemented for a truncated boundary to compare
with the proposed far end boundary. The results are compared with
an analytical solution to demonstrate the accuracy of the proposed
formulation and other truncated boundary conditions in modeling the
hydrodynamic response of an infinite reservoir.
Abstract: The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.
Abstract: In this paper presents the mathematical model of
hydrothermal processes in thermal power plant with different wind
direction scenarios in the water reservoir, which is solved by the
Navier - Stokes and temperature equations for an incompressible
fluid in a stratified medium. Numerical algorithm based on the
method of splitting by physical parameters. Three dimensional
Poisson equation is solved with Fourier method by combination of
tridiagonal matrix method (Thomas algorithm).