Numerical Solution Of Unsteady Flow Research Articles

Computational analysis of dual numerical solutions for unsteady flow of Cu-water nanofluids with the Cattaneo–Christov heat model

Computational analysis of dual numerical solutions for unsteady flow of Cu-water nanofluids with the Cattaneo–Christov heat model

Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating

We obtain similarity transformations to reduce a system of partial differential equations representing the unsteady fluid flow and heat transfer in a boundary layer with heat generation/absorption using Lie symmetry algebra. There exist seven Lie symmetries for this system of differential equations having three independent and three dependent variables. We use these Lie symmetries for the reduced-order modeling of the flow equations by constructing invariants corresponding to linear combinations of these Lie point symmetries. This procedure reduces one independent variable of the concerned fluid flow model when applied once. Double reductions are achieved by employing invariants twice that lead to ordinary differential equations with one independent and two dependent variables. Similarity transformations are constructed using these two sets of derived invariants corresponding to linear combinations of the Lie point symmetries. These similarity transformations have not been obtained earlier for this flow model. Moreover, the corresponding reduced systems of ordinary differential equations are different from those which exist in the literature for fluid flow and heat transfer that we have been dealing with. We obtain multiple similarity transformations which lead us to new classes of systems of ordinary differential equations. Accurate numerical solutions of these systems are obtained using the combination of an adaptive fourth-order Runge–Kutta method and shooting procedure. Effects of variation of unsteadiness parameter, Prandtl number and heat generation/absorption on fluid velocity, skin friction, surface temperature and heat flux are studied and presented with the help of tables and figures.

On the solution of a parabolic PDE involving a gas flow through a semi-infinite porous medium

Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, forming a porous matrix/pipe. The modeling of the gas flow through a porous media is quite valuable because of its importance in investigating the gas-solid processes.The present study is a valid contribution to the existing literature, by developing a nonstandard line method for the partial differential equation, in order to obtain a numerical solution of unsteady flow of gas through nano porous medium. Hence, the physical problem is modeled by a highly nonlinear ordinary differential equation detailed on a semi-finite domain and represents a guidance for several questions originating in the gas flow theory.The findings of this study offered a facile approach to improve an attractive issue related to materials science/chemistry, like synthesis of ZnO or TiO2 nanoparticles forming an ideal nano porous pipe with efficiency in industrial waste waters decontamination.

A Computational Study of The Effect of Blade Thickness on Performance of Vertical Axis Wind Turbine

Vertical axis wind turbine with straight blade is one of the modern vertical axis wind turbines for converting wind to electrical energy. Power production capability at low speed and turbulent winds and, low disturbing noise with good appearance, makes it suitable to use small scale of this type turbine in urban areas. In view of considering importance of blade aerodynamics in turbine performance, the flow over vertical axis wind turbine with straight blade is simulated by two dimensional computational fluid dynamics. In this regard, several conventional NACA series airfoils are chosen and the effect of airfoil thickness on turbine performance was studied. Blade geometry and grid generation were created in Gambit modeling software and, Fluent software which is based on finite volume method is used for solving the problem. For Numerical solution of unsteady flow around the airfoil, the Reynolds Averaged Navier-Stokes (RANS) have been used. The simulation results and comparison of power coefficient of vertical axis wind turbine in different thickness blades showed NACA 0012 airfoil has the best coefficient of performance in a range of tip speed ratio (λ>4). Such values are selected for tip speed ratio, so that the dynamic stall area of the blade to be prevented.

Numerical solutions of unsteady flows with low inlet Mach numbers

This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds, and to the human vocal tract. The flow is described by a system of Navier–Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor–corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the unsteadiness of the grid (motion of the grid), the basic system of conservation laws is considered in a changed form using the Arbitrary Lagrangian–Eulerian (ALE) method. The numerical solution has been carried out for a symmetric and a non-symmetric flow field in two computational domains. The numerical results for unsteady flows in the channel are presented for inlet Mach number M ∞ = 0.012 , Reynolds number R e = 5 × 1 0 3 and wall motion frequency 100 Hz. The authors present the numerical solution and simulations of flow fields in the channel, acquired from a program that has been developed exclusively for this purpose. The reason for using a numerical simulation was the lack of data from experimental results of flows through the glottal region, and the capability of such simulation to model the problem.

Numerical modeling of unsteady flow in steam turbine stage

This work deals with numerical solution of unsteady flow in turbine stage. We use models of compressible single-phase flow of air and two-phase flow of wet steam. Presented numerical methods are based on different stator-rotor matching algorithms, as well as different numerical schemes. Numerical results achieved by both methods and flow models are discussed.

Numerical solutions for unsteady flow past a semi-infinite inclined plate with temperature oscillations

A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temperature oscillations is presented in this work. The non-linear, coupled parabolic integro-partial differential equations governing flow and heat transfer have been solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The numerical values for the flow field, temperature, shearing stress, and heat transfer coefficients are presented in a graphical form. It is observed that the velocity and temperature profiles decrease as the frequency parameter increases.

Numerical solution of unsteady flow past a vertical cylinder with temperature oscillations

A finite-difference method is used to study the heat-transfer response of an incompressible, laminar, natural convection, unsteady flow along a semi-infinite vertical cylinder with temperature oscillations. The governing boundary layer equations are converted into a non-dimensional form. The dimensionless, unsteady, coupled and non-linear governing equations are solved by more accurate, unconditionally stable and fast converging implicit finite difference scheme of Crank-Nicolson method. Calculations have been carried out for a wide range of parameters to examine the results obtained. Transient effects of velocity and temperature are analysed. They found to be increase with time and after certain lapse of time attains temporal maximum and becomes steady. Velocity and temperature profiles decreases as the frequency parameter increases. Local and average skin-friction and Nusselt number are shown graphically.

The use of generalized eulerian–lagrangian formulations in composite materials processing

AbstractThe advantages of the Generalized Eulerian–Lagrangian (GEL) formulations in modeling and numerical solution of unsteady flow of fiber suspensions are discussed. This formulation offers the flexibility of selectively applying an Eulerian (Spatial), a Lagrangian (Material), and any combination of these two frames of reference in the same computational domain. This flexibility offered by the GEL formulation is exploited to exactly determine the shape and location of the free surfaces and moving boundaries in the numerical simulation of various manufacturing processes. The application of the GEL formulation to the solution for the flow field and fiber orientation in the unsteady flows of dilute and semiconcentrated fiber suspensions are presented. The flow field and fiber orientation predicted by this method agree well with the available theoretical and experimental results. © 1994 John Wiley & Sons, Inc.

Numerical solutions for unsteady flow in unconfined aquifers

AbstractTwo numerical methods for solving the problem of unsteady flow in unconfined aquifers are studied. They are an explicit finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into three schemes: vertical displacement approach, explicit scheme (FEM1), normal velocity approach, explicit scheme (FEM2), and vertical displacement approach, implicit scheme (FEM3). Results from the above methods are compared with experimental results from a sand box model. Various factors affecting the accuracy and numerical stability are investigated. Results indicate that, for a similar degree of accuracy, the FEM requires less computational effort than the explicit FDM. Amongst the three FEM schemes, FEM3 appears to be most attractive as it is the most stable and economical of the three schemes compared.

A numerical solution of unsteady flow in a two-dimensional square cavity

Two dimensional unsteady fluid flow in square cavity numerically analyzed from continuity and Navier-Stokes equations and recorded as computer-generated motion picture