Showing papers on "Stream function published in 2005"
TL;DR: Numerical calculations of the 2-D steady incompressible driven cavity flow are presented and comparisons are made with benchmark solutions found in the literature.
Abstract: SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.
531 citations
TL;DR: This work presents a high-order modified immersed interface method for the 2D, unsteady, incompressible Navier-Stokes equations in stream function-vorticity formulation that employs an explicit fourth-order Runge-Kutta time integration scheme, and a nine-point, four-order compact discretization of the Poisson equation for computation of the stream function.
343 citations
TL;DR: In this paper, the peristaltic flow of Herschel-Bulkley fluid in an inclined tube is analyzed and the velocity distribution, the stream function and the volume flow rate are obtained.
Abstract: Peristaltic flow of Herschel–Bulkley fluid in an inclined tube is analyzed. The velocity distribution, the stream function and the volume flow rate are obtained. Also, when the yield stress ratio τ → 0 , and when the inclination parameter α = 0 and the fluid parameter n = 1 , the results agree with those of Jaffrin and Shapiro (Ann. Rev. Fluid Mech. 3 (1971) 13) for peristaltic transport of a Newtonian fluid in a horizontal tube. The effects of τ and n on the pressure drop and the mean flow are discussed through graphs. Furthermore, the results for the peristaltic transport of Bingham and power law fluids through a flexible tube are obtained and discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of Herschel–Bulkley fluid on the flow characteristics.
150 citations
TL;DR: In this article, the flow of an upper-convected Maxwell (UCM) fluid is studied theoretically above a rigid plate moving steadily in an otherwise quiescent fluid, and three different methods are used to solve the governing equation: (i) the perturbation method, (ii) the fourth-order Runge-Kutta method, and (iii) the finite difference method.
Abstract: The flow of an upper-convected Maxwell (UCM) fluid is studied theoretically above a rigid plate moving steadily in an otherwise quiescent fluid. It is assumed that the Reynolds number of the flow is high enough for boundary layer approximation to be valid. Assuming a laminar, two-dimensional flow above the plate, the concept of stream function coupled with the concept of similarity solution is utilized to reduce the governing equations into a single third-order ODE. It is concluded that the fluid's elasticity destroys similarity between velocity profiles; thus an attempt was made to find local similarity solutions. Three different methods will be used to solve the governing equation: (i) the perturbation method, (ii) the fourth-order Runge–Kutta method, and (iii) the finite-difference method. The velocity profiles obtained using the latter two methods are shown to be virtually the same at corresponding Deborah number. The velocity profiles obtained using perturbation method, in addition to being different from those of the other two methods, are dubious in that they imply some degree of reverse flow. The wall skin friction coefficient is predicted to decrease with an increase in the Deborah number for Sakiadis flow of a UCM fluid. This prediction is in direct contradiction with that reported in the literature for a second-grade fluid.
145 citations
TL;DR: In this article, a stream function-velocity formulation of the two-dimensional steady-state Navier-Stokes equations representing incompressible fluid flows in 2D domains is proposed.
132 citations
TL;DR: In this article, a theoretical formalism for nongeostrophic eddy transport in zonal-mean flows, using a transformed Eulerian-mean (TEM) approach in z coordinates, is discussed.
Abstract: A theoretical formalism for nongeostrophic eddy transport in zonal-mean flows, using a transformed Eulerian-mean (TEM) approach in z coordinates, is discussed. By using Andrews and McIntyre’s coordinate-independent definition of the “quasi-Stokes streamfunction,” it is argued that the surface boundary condition can be dealt with more readily than when the widely used quasigeostrophic definition is adopted. Along with the “residual mean circulation,” the concept of “residual eddy flux” arises naturally within the TEM framework, and it is argued that it is this residual eddy flux, and not the “raw” eddy flux, that might reasonably be expected to be downgradient. This distinction is shown to be especially important for Ertel potential vorticity (PV). The authors show how a closed set of transformed mean equations can be generated, and how the eddy forcing appears in the TEM momentum equations. Under adiabatic conditions, the “eddy drag” is just proportional to the residual eddy flux of PV along the mean isopycnals; in the diabatic layer close to the surface, it is more complicated, but becomes very simple for small Rossby number (without any assumption of small isopycnal slope).
126 citations
TL;DR: In this paper, the steady-state free convection inside a cavity made of two horizontal straight walls and two vertical bent-wavy walls and filled with a fluid-saturated porous medium is numerically investigated.
116 citations
TL;DR: In this article, a mesh-free radial basis function collocation method was proposed for solving heat transfer and fluid flow problems in incompressible Newtonian Bussinesq fluid.
Abstract: This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady natural convection benchmark with Prandtl number Pr = 0.71, and Rayleigh numbers Ra = 103, 104, 105, 106. Multiquadrics radial basis functions are used. The three methods are assessed in terms of streamfunction extreme, cavity Nusselt number, and mid-plane velocity components. Best performance is achieved with the modified approach. keyword: radial basis function collocation method, heat transfer, fluid flow, natural convection.
96 citations
TL;DR: In this article, a pure stream function formulation for the numerical simulation of the Navier-Stokes equations is introduced, which is based on the Laplacian of the stream function.
79 citations
TL;DR: In this paper, the Navier-Stokes equations are solved in stream-function/vorticity formulation using an improved overset grid method while using a very high spectral accuracy compact scheme to represent the convection process.
72 citations
TL;DR: A new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the stream function from experimental data in 2D turbulent systems is presented.
Abstract: Multifractal or multiaffine analysis is a promising new branch of methods in nonlinear physics for the study of turbulent flows and turbulentlike systems. In this Letter we present a new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the stream function from experimental data in 2D turbulent systems. The essence of MSSM relies in relating statistical properties associated with the energy cascade in flows with geometrical properties. MSSM is a valuable tool to process sparse collections of data and to obtain instant estimates of the velocity field. We show an application of MSSM to oceanography as a way to obtain the current field from sea surface temperature satellite images; we validate the result with independent dynamical information obtained from sea level measurements.
TL;DR: In this paper, the Navier-Stokes and continuity equations are expressed in the stream function and vorticity formulation and are rewritten in an orthogonal system of curvilinear co-ordinates.
TL;DR: In this paper, the Boundary Element Method (BEM) is used for modeling 2D unsteady laminar flow using stream function-vorticity formulation of the Navier-Stokes equations.
Abstract: The paper deals with the Boundary Element Method (BEM) for modelling 2D unsteady laminar flow using stream function‐vorticity formulation of the Navier‐Stokes equations. The numerical algorithm for solving a general parabolic diffusion‐convection equation is based on linear mixed elements and a multidomain model also known as subdomain technique. Robustness, accuracy and economy of the developed numerical algorithm is shown on a standard case of steady backward facing step flow and a periodic flow past a circular cylinder test case.
TL;DR: In this paper, the flow has been divided into three regions, Region I is the region inside the porous sphere in which the flow is governed by Brinkman equation with the effective viscosity different from that of the clear fluid, Region II and III clear fluid flows and Stokes and Oseen solutions are respectively valid.
Abstract: low of an incompressible viscous fluid past a porous sphere has been discussed. The flow has been divided in three regions. The Region-I is the region inside the porous sphere in which the flow is governed by Brinkman equation with the effective viscosity different from that of the clear fluid. In Regions II and III clear fluid flows and Stokes and Oseen solutions are respectively valid. In all the three regions Stokes stream function is expressed in powers of Reynolds number. Stream function of Region II is matched with that of Region I at the surface of the sphere by the conditions suggested by Ochao-Tapia and Whitaker and it is matched with that of Oseen’s solutions far away from the sphere. It is found that the drag on the sphere reduces significantly when it is porous and it decreases with the increase of permeability of the medium.
TL;DR: Based on the flow field calculations, it is estimated that the coffee-stain phenomenon should be expected even for uniform evaporation flux throughout the cylindrical surface, provided that the contact lines remain anchored.
Abstract: An analytical solution to the problem of potential flow inside an evaporating line is obtained. The line is shaped as a half-cylinder lying on a substrate, and evaporates with either pinned or depinned contact lines. The solution is provided through the technique of separation of variables in the velocity potential and stream function formulations. Based on the flow field calculations, it is estimated that the coffee-stain phenomenon should be expected even for uniform evaporation flux throughout the cylindrical surface, provided that the contact lines remain anchored. A simple expression for the velocity potential is also suggested, which reproduces the local velocity vector with excellent accuracy. The vertically averaged velocity is calculated also for other contact line values, revealing for any value an outward liquid flow for pinned lines as opposed to inward flow for depinned lines.
TL;DR: In this paper, mass transfer at the shell side of an in-line hollow fiber array subjected to cross-flow is simulated by applying the domain decomposition method combined with orthogonal grid generation.
TL;DR: In this article, an analytical solution for axisymmetric creeping flows around a spherical particle near a wall, when the unperturbed flow velocity varies as polynomial with the coordinates, is presented with a 10−16 precision.
Abstract: Analytical solutions are presented for axisymmetric creeping flows around a spherical particle near a wall, when the unperturbed flow velocity varies as polynomial with the coordinates. The perturbed fluid velocity and pressure are calculated directly with the method of bipolar coordinates. They are obtained with a 10−16 precision, even for small gaps of the order of 10−6 sphere radius. For a constant unperturbed flow, the problem is equivalent to that of a sphere moving perpendicularly to a wall in a fluid at rest. An alternative indirect solution for the fluid velocity and pressure is obtained in this case from the solution of Brenner [Chem. Eng. Sci. 16, 242 (1961)] and Maude [Brit. J. Appl. Phys. 12, 293 (1961)] for the stream function. For a small gap between the sphere and the wall, the values of the pressure are compatible with the ones from the lubrication approximation but are systematically larger; this may be important for applications. Calculations are also performed when the unperturbed flow ...
TL;DR: In this article, the heat transfer coefficient of free convection boundary layer flows from vertical surfaces adjacent to fluid saturated porous media is calculated without knowing the solution of the corresponding boundary value problem.
TL;DR: In this paper, natural convection in air in a convergent channel with the two principal flat plates at uniform heat flux with finite thickness and thermal conductivity was numerically investigated.
TL;DR: In this paper, a regular perturbation method is introduced to investigate the influence of two-dimensional roughness on laminar flow in microchannels between two parallel plates, and the relative roughness can be determined as the maximal value of the product between the normalised roughness functions and a small parameter.
Abstract: The regular perturbation method is introduced to investigate the influence of two-dimensional roughness on laminar flow in microchannels between two parallel plates. By superimposing a series of harmonic functions with identical dimensional amplitude as well as the same fundamental wave number, the wall roughness functions are obtained and the relative roughness can be determined as the maximal value of the product between the normalised roughness functions and a small parameter. Through modifying the fundamental wave number, the dimensionless roughness spacing is changed. Under this roughness model, the equations with respect to the disturbance stream function are obtained and analyzed numerically
TL;DR: In this article, a control volume based finite element method (CVFEM) is used to solve the full vorticity transport equation together with the stream function, concentration and energy equations.
TL;DR: In this article, a numerical method based on the stream function formulation of the Navier-Stokes equations to simulate two-dimensional planes or axisymmetric viscous flows is proposed.
Abstract: This work concerns the development of a numerical method based on the stream function formulation of the Navier–Stokes equations to simulate two-dimensional—plane or axisymmetric—viscous flows. The main features of the proposed method are: the use of the high order finite-difference compact method for the discretization of the stream function equation, the implicit pseudo-transient Newton–Krylov-multigrid matrix free method for the stationary stream function equation and the fourth order Runge–Kutta method for the integration of non-stationary flows. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, the average Nusselt numbers of concentric and vertically eccentric spheres with specified isothermal boundary conditions were calculated systematically for several different eccentricities and a range of Rayleigh numbers to determine the average number which are affected by the micropolar parameters on the flow and temperature fields.
TL;DR: In this article, a method is reported for calculating unsteady aerodynamics of hovering and flapping airfoil for two-dimensional flow via the following improved methodologies: (a) a correct formulation of the problem using stream function (ψ) and vorticity (ω) as dependent variables; (b) calculating loads and moment by a new method to solve the governing pressure Poisson equation (PPE) in a truncated part of the computational domain on a nonstaggered grid; (c) accurate solution using high accuracy compact difference scheme for the
Abstract: A method is reported here for calculating unsteady aerodynamics of hovering and flapping airfoil for two-dimensional flow via the following improved methodologies: (a) a correct formulation of the problem using stream function (ψ) and vorticity (ω) as dependent variables; (b) calculating loads and moment by a new method to solve the governing pressure Poisson equation (PPE) in a truncated part of the computational domain on a nonstaggered grid; (c) accurate solution using high accuracy compact difference scheme for the vorticity transport equation (VTE) and (d) accelerating the computations by using a high-order filter after each time step of integration. These have been used to solve Navier–Stokes equation for flow past flapping and hovering NACA 0014 and 0015 airfoils at typical Reynolds numbers relevant to the study of unsteady aerodynamics of micro air vehicle (MAV) and insect/bird flight.
TL;DR: In this paper, the authors studied the effect of the secondary flow induced by buoyancy forces and the presence of the double step expansion on the heat and mass transfer mechanism in an inclined duct.
Abstract: The present paper deals with the study of heat and mass transfer by mixed convection in an inclined duct preceded with a double step expansion. The control volume based finite element method was used to solve the set of non-dimensional equations for the vorticity, stream function, energy and species conservation. Numerical simulations are carried out for different combinations of the Lewis number, thermal and mass diffusion Grashof numbers for different inclinations. Streamlines, temperature and concentration distributions are presented and discussed. The results show the effect of the secondary flow induced by buoyancy forces and the presence of the double step expansion on the heat and mass transfer mechanism. It is found that the recirculation vortices induced by the expansion can be present along the channel and the flow structure can be wavy. For the vertical orientation, asymmetric fields are observed for the different simulated cases.
TL;DR: In this article, the authors investigated the Stokes flow through a circular tube with a thin orifice inside and derived the streamline pattern and pressure distribution from the results of the analysis.
Abstract: Axisymmetric Stokes flow through a circular tube with a thin orifice inside is investigated. At far upstream and downstream from the orifice, the Hagen–Poiseuille flow exists in the tube. The problem is investigated by considering Stokes equation analytically using a complex eigenfunction. Flow properties such as stream function and pressure distribution are determined. From the results, the streamline pattern and pressure distribution are drawn. The excess pressure drop due to the orifice and the force exerted on the orifice are calculated as functions of the radius of the orifice.
TL;DR: In this article, the temporal evolution of perturbations in stratified flow with inhomogeneous shear is examined analytically by an extension of the non-modal approach to flows with inhomeous shear and conditions at which these nonmodal effects may be strong enough to stabilize the Rayleigh-Taylor instability are presented.
Abstract: The temporal evolution of perturbations in stratified flow with inhomogeneous shear is examined analytically by an extension of the nonmodal approach to flows with inhomogeneous shear. The solutions of the equations that govern the linear evolution and the weak nonlinear evolution of perturbations of the stream function for stratified flow with monotonic inhomogeneous shear are obtained. It is shown that stabilization of perturbations arises from nonmodal effects due to flow shear. Conditions at which these nonmodal effects may be strong enough to stabilize the Rayleigh-Taylor instability are presented. These analytical results are also compared to numerical simulations of the governing equations performed by Benilov, Naulin, and Rasmussen.
TL;DR: In this article, a fourth order semi compact finite difference scheme has been developed to solve unsteady incompressible Navier-Stokes equations in stream function and vorticity formulation, the governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle non-regular domains.
Abstract: A fourth order semi compact finite difference scheme has been developed to solve unsteady incompressible Navier-Stokes equations in stream function and vorticity formulation. The governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle non-regular domains. Two test problems are utilized to explore the efficiency of the scheme. It is found that the solutions obtained with the present scheme are in good agreement with the analytical results or with the existing results depending on the availability.
TL;DR: The well-known Reid-Harris expansions and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square.
Abstract: The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptotically.