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Showing papers on "Streamlines, streaklines, and pathlines published in 1995"


Journal ArticleDOI
TL;DR: In this paper, it is shown that the creation of vorticity is due primarily to the axial unsteady pressure gradient across mean flow streamlines at the surface, and that there is a transfer of energy from the pressure oscillations (acoustic field) to the rotational waves (vorticity field).
Abstract: Combustion stability computations are currently based on an irrotational model that allows slip flow at the burning surface. However, the no-slip boundary condition must be satisfied when gas motions are parallel to the combustion zone. Then waves of vorticity are created that distort the acoustic wave structure and modify the fluctuating normal velocity component upon which system stability is so strongly dependent. This flow problem is solved here in analytical form to bring the physical details into focus. Crocco's theorem shows that the creation of vorticity is due primarily to the axial unsteady pressure gradient across mean flow streamlines at the surface. Hence, there is a transfer of energy from the pressure oscillations (acoustic field) to the rotational waves (vorticity field). It is in this interaction that the incoming flow acquires the axial motion of the acoustic wave. Stability calculations based on this model yield the three-dimensional form of Culick's one-dimensional flow-turning correction and clarify its origin. However, continuity at the burning surface requires a correction to the radial velocity fluctuations. Incorporation of this new driving effect leads to a motor system that is significantly less stable than in the classical prediction (Standard Stability Prediction Program) for some configurations.

193 citations


Journal ArticleDOI
TL;DR: In this article, a semianalytic approach for modeling tracer motion in heterogeneous permeable media is presented, which is analytic along streamlines; the streamlines are derived from an underlying velocity field which is obtained numerically from a conventional fluid flow simulator.

140 citations


Journal ArticleDOI
TL;DR: In this paper, a stochastic-convective reactive (SCR) transport method is developed for one-dimensional steady transport in physically heterogeneous media with nonlinear degradation.
Abstract: A stochastic-convective reactive (SCR) transport method is developed for one-dimensional steady transport in physically heterogeneous media with nonlinear degradation. The method is free of perturbation amplitude limitations and circumvents the difficulty of scale dependence of phenomenological parameters by avoiding volume-averaged specifications of diffusive/dispersive fluxes. The transport system is conceptualized as an ensemble of independent convective-reactive streamlines, each characterized by a randomized convective velocity (or travel time). Dispersive effects are treated as a component of the randomness in the streamline velocity ensemble, so no explicit expression for hydrodynamic dispersive flux is written in the streamline transport equation. The expected value of the transport over the stream tube ensemble is obtained as an average of solutions to the reactive convection equation according to the stream tube (travel time) probability distribution function. In this way, transport with reaction can be expressed in terms of global-scale random variables, such as solute travel time and travel distance, which are integrals of the stochastic variables such as velocity. Derivations support the hypothesis that via the SCR the decay process can be factored out of the mechanical transport behavior (as reflected by movement of a passive tracer) and scaled independently. Solution strategies are presented for general linear and nonlinear kinetic reactions. Demonstration simulations show that for Fickian transport with nonlinear reactions the SCR and convection dispersion equation can give different results. Ginn et al. (this issue) extend the SCR solution to coupled nonlinear equations, to accommodate Michaelis-Menten biodegradation of solute with an accounting of microbial growth.

101 citations


Journal ArticleDOI
TL;DR: Rajagopalan et al. as discussed by the authors compare finite element simulations and detailed point-wise experimental velocity measurements for the international benchmark problem of a sphere sedimenting axially under gravity through a cylindrical tube of viscoelastic fluid.
Abstract: The first direct comparisons of finite element simulations and detailed point-wise experimental velocity measurements are presented for the international benchmark problem of a sphere sedimenting axially under gravity through a cylindrical tube of viscoelastic fluid. In addition to measurements and calculations of the viscoelastic correction to the drag force exerted by the fluid on the sphere, the non-invasive technique of laser Doppler velocimetry is used to probe the kinematics of the fluid over a wide range of Deborah numbers, 0.4≤De≤9, and dimensionless radius ratios, 0.12≤ a R ≤0.64 . These observations are augmented in Part 2 of this work (Rajagopalan et al., 1995) by digital video-imaging studies and fully-implicit time-dependent numerical simulations of the initial acceleration of the sphere from rest and the resulting overshoot in the velocity that arises from fluid viscoelasticity. Numerical simulations are reported for the upper-convected Maxwell (UCM) model, the Chilcott-Rallison model (each with a single relaxation time constant) and the multimode Phan-Thien-Tanner model. For the radius ratio of a R = 0.5 , flow simulations using the UCM model have been extended well above the commonly reported limit point of De = 1.6 through careful mesh refinement. The multimode simulations with a spectrum of time constants allow a quantitative description of the fluid rheology in both viscometric shear flows and transient extensional experiments. However, the range of computationally attainable De is limited by the inability to resolve intense stress boundary layers. Both experimental measurements and numerical calculations indicate the wall correction factor for the motion of a sphere through a viscoelastic fluid is a sensitive function of the radius ratio and the Deborah number. They also show that non-Newtonian effects in the strong extensional flow near the rear stagnation point result in the formation of a pronounced viscoelastic wake effect extending up to 30 sphere radii behind the sphere and corresponding to a downstream shift in the fluid streamlines. However there is no experimental indication of the formation of a negative wake or a flow instability in the wake, and the flow remains stable for all radius ratios and Deborah numbers investigated experimentally.

93 citations


Journal ArticleDOI
TL;DR: In this paper, a full numerical simulation based on spectral methods is used to investigate linearly accelerating and decelerating flows past a rigid sphere, and the authors find that the viscous force on the sphere decays in a power law manner after acceleration or deceleration ends, followed by rapid convergence at later times to the steady state.
Abstract: A full numerical simulation based on spectral methods is used to investigate linearly accelerating and decelerating flows past a rigid sphere. Although flow separation does not occur at Reynolds numbers below 20 for a steady flow, in the linearly decelerating flow separation is observed at much lower Reynolds numbers with complete detachment of vorticity possible in certain cases. The existence of a large recirculation region contributes to the result that a negative viscous force on the sphere is possible. The contribution of the pressure to the force includes a component that is well described by the inviscid added-mass term in both the accelerating and decelerating cases. The force on the sphere is found in general to initially decay in a power law manner after acceleration or deceleration ends followed by rapid convergence at later times to the steady state. For the cases examined this convergence is found to be exponential except for those in which the sphere is brought to rest in which case the convergence remains algebraic. This includes the special case of an infinite acceleration or deceleration where the free stream velocity is impulsively changed.

84 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054) was studied.
Abstract: A numerical study is conducted to understand the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054). The two side walls are maintained at uniform but different temperatures θh and θc (θh > θc), while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of the ADI (Alternating Direction Implicit) method, which incorporates upwind differencing for non-linear convective terms and the SLOR (Successive Line Over Relaxation) method are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Grashof number Gr ranging from 2 × 104 to 2 × 106, Marangoni number Ma from 0 to 105 and Hartmann number Ha from 0 to 100. The detailed flow structure and the associated heat transfer characteristics inside the cavity are presented. At large Ma, two counter-rotating cells are formed at the upper half and lower half of the enclosure. As Ha increases, the temperature field resembles that of a conduction type and the streamlines are elongated in nature in the horizontal direction. The upper cell is crowded and stretched along the free surface. The average Nusselt number increases with Ma but decreases with Ha.

71 citations


Proceedings ArticleDOI
29 Oct 1995
TL;DR: Flow volumes are extended for use in unsteady (time-dependent) flows and are the 3D analogs of streaklines, which present some solutions to the problems which occur in subdivision, rendering and system design.
Abstract: Flow volumes [1] are extended for use in unsteady (time-dependent) flows. The resulting unsteady flow volumes are the 3 dimensional analog of streaklines. There are few examples where methods other than particle tracing have been used to visualize time varying flows. Since particle paths can become convoluted in time there are additional considerations to be made when extending any visualization technique to unsteady flows. We will present some solutions to the problems which occur in subdivision, rendering, and system design. We will apply the unsteady flow volumes to a variety of field types including moving multi-zoned curvilinear grids.

67 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical study on the laminar natural convection flow of air in differentially heated, trapezoidal enclosures is presented, where the influence of the inclination angle on the flow and Nusselt number is discussed.
Abstract: Results are presented of a numerical study on the laminar natural convection flow of air in differentially heated, trapezoidal enclosures. Special attention is given to the applied solution method, using a coordinate-invariant formulation of the transport equations. For Rayleigh numbers between 104 and 108, results are presented for inclination angles of the isothermal walls from — 45° ( trapezoidal enclosure) to 0° ( square enclosure) The influence of the inclination angle on the flow and Nusselt number is discussed. Flow patterns and isotherms are shown to give greater understanding of the local heat transfer. The dependence of the averaged Nusselt number on the Rayleigh number is studied.

61 citations


Journal ArticleDOI
TL;DR: In this paper, a convergent numerical algorithm for the steady inertialess flow of an upper-convected Maxwell (UCM) fluid through a four-to-one abrupt axisymmetric contraction is presented.
Abstract: This paper reports the first convergent numerical algorithm for the steady inertialess flow of an Upper-Convected Maxwell (UCM) fluid through a four-to-one abrupt axisymmetric contraction. The Finite Volume Method (FVM) is adopted along with a stream function-vorticity approach in the Elastic Viscous Split Stress (EVSS) form with a first-order upwind approximation applied to the convective terms of the stress constitutive equation. A staggered volume discretization of the flow variables eliminates the stress singularity from the computational domain without loosing any flow physics. The volume integrals of the governing equations over the flow domain result in a system of nonlinear algebraic equations that are solved iteratively by a semi-implicit line-to-line method with a pseudo-trasient term added to the stress constitutive equation. Computations of an UCM fluid using this method are carried out to a much higher value of the Deborah number ( De ) than previous numerical simulations using the Finite Element Method (FEM). The solutions are found to be smooth, stable, and convergent with the finger stress tensor remaining posiitive-definite throughout the flow domain. Calculations are not performed above De = 6.25 because of the decreasing pseudo-time step constraint at higher elasticity. The finite volume algorithm approximates better solutions upon mesh refinement, demonstrates the smoothness and the mathematical well-posedness of this problem, and predicts a Newtonian-like flow structure near the singularity for an UCM fluid. Using this new method, the inertialess flow of an UCM fluid through 4:1 abrupt axisymmetric contraction, for the first time, produces larger corner vortices at higher values of De .

59 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied numerically thin accretion flows with finite thickness as well as those with vanishing thickness and showed that the governing equations become self-similar, involving no free parameters.
Abstract: The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated

52 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe the mixing of a scalar field under the action of diffusion and of a class of steady, bounded, three-dimensional flows, which can have chaotic streamlines.
Abstract: Results of numerical simulation of the advection‐diffusion equation at large Peclet number are reported, describing the mixing of a scalar field under the action of diffusion and of a class of steady, bounded, three‐dimensional flows, which can have chaotic streamlines. The time evolution of the variance of scalar field is calculated for different flow parameters and shown to undergo modulated exponential decay, with a decay rate which is a maximum for certain values of the flow parameters, corresponding to cases in which the streamlines are chaotic everywhere. If such global chaos is present, the decay rate tends to oscillate, whereas the presence of regular regions produces a more constant decay rate. Significantly different decay rates are obtained depending on the detailed properties of the chaotic streamlines. The relationship between the decay rate and the characteristic Lyapunov exponents of the flow is also investigated.

Journal ArticleDOI
TL;DR: In this article, the authors studied numerically thin accretion flows with finite thickness as well as those with vanishing thickness and showed that the governing equations become self-similar, involving no free parameters.
Abstract: The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated

Journal ArticleDOI
TL;DR: In this article, the same authors investigated coupled conduction and natural convection transport within a discretely heated cavity, where one vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity.

Journal ArticleDOI
TL;DR: In this article, the authors synthesize plasmapause position surveys into a description of the underlying global distribution of plasmasphere-like or core plasma densities unique to a steady state magnetosphere.
Abstract: Previous results of plasmapause position surveys have been synthesized into a description of the underlying global distribution of plasmasphere-like or core plasma densities unique to a steady state magnetosphere. Under these steady conditions, the boundary between high- and low-density regions is taken to represent the boundary between diurnal near-corotation and large-scale circulation streamlines that traverse the entire magnetosphere. Results indicate a boundary that has a pronounced bulge in the dusk sector that is rotated westward and markedly reduced in size at increased levels of geomagnetic activity (and presumably magnetospheric convection). The derived profile is empirical confirmation of an underlying 'tear drop' distribution of core plasma, which is valid only for prolonged steady conditions and is somewhat different from that associated with the simple superposition of sunward flow and corotation, both in its detailed shape and in its varying orientation. Variation away from the tear drop profile suggests that magnetospheric circulation departs from a uniform flow field, having a radial dependence with respect to the Earth that is qualitatively consistent with electrostatic shielding of the convection electric field and which is rotated westward at increased levels of geophysical activity.

Journal ArticleDOI
TL;DR: In this paper, a finite difference method was used to solve two-dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation and using the κ-e model for turbulence, in enclosures bounded by a massive wall.

Proceedings ArticleDOI
19 Jun 1995
TL;DR: In this paper, a conservative upwind residual distribution scheme for solving the steady Euler equations on unstructured meshes is presented, where the flux balance is decomposed locally into a set of eigenvectors, which are then upwinded along the directions of the steady characteristics of the Euler equation.
Abstract: Conservative upwind residual-distribution schemes for solving the Euler equations on unstructured meshes a.re presented. The method is truly multidimensional in the sense that no Riemann solver is invoked, and the geometry of the mesh plays no role in determining the upwinding directions. Instead, the flux balance is decomposed locally into a set of eigenvectors, which are then upwinded along the directions of the steady characteristics of the Euler equations. These are well-known to be the streamlines, as well as the Mach lines in supersonic flow. The decomposition corresponds to an optimal diagonalization of the steady Euler equations, which fully uncouple in supersonic flow, expressing the invariance of entropy and total enthalpy along the streamlines, and acoustic characteristics along the Mach lines. In subsonic flow, the latter two are no longer defined, as the acoustic sub-system takes on a purely elliptic character. Different discretizations for these equations are discussed. Results are presented, showing excellent resolu tion of stagnation regions, smooth and discontinuous flows.

Journal ArticleDOI
TL;DR: In this article, a mathematical framework is presented for three-dimensional shallow groundwater flow with variable density, which is based on the Dupuit-Forchheimer assumption, and the problem is posed in terms of a discharge potential that satisfies the same differential equation as the discharge potentials for single-density flow.
Abstract: A mathematical framework is presented for three-dimensional shallow groundwater flow with variable density. The formulation is based on the Dupuit-Forchheimer assumption. The problem is posed in terms of a discharge potential that satisfies the same differential equation as the discharge potentials for single-density flow. The freshwater head, defined as the pressure divided by the unit weight of fresh water plus the elevation head, may be computed as a function of position in three dimensions from the potential and a known density distribution. The density distribution may be approximated using the multiquadrics interpolator. It is explained how the change in density may be computed as a function of time. Discontinuities in the aquifer properties cause a jump in the normal component of flow for flow fields computed with the Dupuit-Forchheimer approximation. An interpretation of this jump is given by comparison with an exact formulation, which makes it possible to obtain the approximate streamlines as they cross discontinuities.

Journal Article
TL;DR: In this paper, a flow induced around a sphere with a non-uniform surface temperature in a rarefied gas is investigated using the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition.
Abstract: A flow induced around a sphere with a non-uniform surface temperature in a rarefied gas is investigated using the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition. With the aid of the accurate and efficient numerical method developed by the authors with Aoki, the behaviour of the gas (the velocity distribution function as well as macroscopic variables and force on the sphere) is clarified for the whole range of the Knudsen number. In addition, the solutions of the drag and thermal force (thermophoresis) problems of a spherical particle with an arbitrary thermal conductivity are obtained by appropriate superpositions of the present solution and those of a sphere with infinite thermal conductivity, obtained by the authors with Aoki. The resulting thermal force is compared with various experimental data.

Journal ArticleDOI
TL;DR: Passive tracers in steady-state three-dimensional (3-D) convective flows with infinite Prandtl number, which is relevant for the Earth's mantle, show a remarkable flow structure.
Abstract: Passive tracers in steady‐state three‐dimensional (3‐D) convective flows with infinite Prandtl number, which is relevant for the Earth’s mantle, show a remarkable flow structure Individual flowlines as shown by Poincare sections of the tracer paths lie on a two‐dimensional (2‐D) surface with distorted toroidal topology Furthermore, the space occupied by the convecting fluid is filled by a set of these toroidal surfaces nested one within another The small radius of the innermost toroidal surface approaches zero, defining a closed streamline whose location we have determined in specific cases using numerical solutions The outermost of the toroidal surfaces coincides with the upper and lower surfaces of the layer and with vertical symmetry planes which separate the flow between neighboring cells Both square and hexagonal convection planforms show a triangular cellular structure with triangles defined by (π/2,π/4,π/4) and (π/2,π/6,π/3), respectively The outer toroidal surface is closed by a horizontal flow line through the middle of the cell The numerical experiments suggest that streamlines are not generally closed in any small number of orbits Instead the toroidal surface appears to be progressively filled in by the trace of a single streamline which, in successive orbits, is displaced across the surface without returning to the same path This flow structure ensures that, while extreme shear strains can occur, particularly in the vicinity of the cell separatrices, mixing of the material only occurs in 2D Tracers initially on one toroidal surface remain on that surface indefinitely Like for 2‐D convective flow, time dependence of the solution appears to be a necessary prerequisite for thorough spatial mixing to occur

Journal ArticleDOI
TL;DR: Nonlinear phase portraits are employed to represent the streamlines of scalar flow images generated by particle tracing experiments and extended to the compression of vector field data by using orthogonal polynomials derived from the Taylor series model.

Journal ArticleDOI
TL;DR: In this paper, the authors used a simplified Phan-Thien-Tanner constitutive model with parameter values representative of polymer solutions to simulate viscoelastic flows for two planar problems, a 4:1 contraction flow and a mixing and separating flow.
Abstract: Consideration is given to a methodology for achieving highly elastic solutions of complex flows. Steady solutions are obtained through an unsteady finite element approach that employs a pressure-correction scheme. A simplified Phan-Thien-Tanner constitutive model is used with parameter values representative of polymer solutions to simulate viscoelastic flows for two planar problems, a 4:1 contraction flow and a mixing and separating flow. Highly elastic flows are studied for both problems. For mixing and separating flow, various bifurcations are investigated for Newtonian and viscoelastic fluids to reveal the effects of increasing inertia, elasticity and variation in geometric gap width. Good agreement with experimental observations is achieved.

Journal ArticleDOI
TL;DR: In this article, an asymptotic model of DiPrima & Stuart (1972b, 1975) describing steady Taylor vortex flow between eccentric cylinders was investigated under the assumption that the eccentricity E, the clearance ratio 6 and the Taylor vortex amplitude A satisfy E, 6 and A small.
Abstract: We investigate an asymptotic model of DiPrima & Stuart (1972b, 1975) describing steady Taylor vortex flow between eccentric cylinders, under the assumption that the eccentricity E, the clearance ratio 6 and the Taylor vortex amplitude A satisfy E, 6 and A small. By solving a boundary value problem for the radial eigenfunctions we numerically obtain the flow field of DiPrima & Stuart and investigate its topology, after correcting higher-order terms to ensure that the flow preserves volume. We find regions of chaotic streamlines at all eccentricities and discuss the reason for their existence. We make an analogy between the full model and a modulated vortex flow field which qualitatively displays the same behaviour. For large eccentricities, we examine the flow field and the topology of its streamlines, especially where the two-dimensional flow contains a separated region of recirculation. In this case Taylor vortices give rise to transport of fluid particles in and out of the separated region. We find that the onset of Taylor vortices encourages recirculation in the inflow plane, whilst discouraging it in the outflow plane.

Journal ArticleDOI
TL;DR: In this paper, the lowest-order mixed method is presented including its hybridization, which results in a sparse symmetric positive definite system of linear equations, which can be solved efficiently by the preconditioned conjugate gradient method.

Journal ArticleDOI
TL;DR: In this paper, an enthalpy formulation is used for the energy equation, with a porous medium approximation for the region undergoing phase change, and the governing equations are solved using primitive variables in the physical space.
Abstract: Solidification in an enclosed space is investigated, considering conduction in the mold wall. This gives rise to a conjugate, transient problem, with the flow in the liquid driven by thermal buoyancy. An enthalpy formulation is used for the energy equation, with a porous medium approximation for the region undergoing phase change. The governing equations are solved using primitive variables in the physical space. The control volume approach is employed to discretize the equations. The numerical simulation of the phase change process is discussed in detail. The mold is subjected to different thermal conditions at the outer surface, and the effect of these on the shape of the solid-liquid interface, rate of solid formation, and rate of heat transfer quantified. Streamlines, isotherms, and velocity profiles are also obtained. The conditions under which natural convection in the melt can be neglected are investigated. The effects of important design parameters such as the mold material and width, aspect ratio of the cavity, and heat removal rate from the mold are considered in detail. A comparison is made of the important characteristics between the conjugate and nonconjugate cases. The differences in the numerical simulation of these two cases are investigated. Of particular interest aremore » the temperature distributions that arise in the liquid, solid, and mold. It is shown that conjugate transport must be included for a realistic simulation of practical problems.« less

Journal ArticleDOI
TL;DR: In this article, the authors deal with the visualization of swirling decaying flow in an annular cell fitted with a tangential inlet, where a wall visualization method, the dot-paint method, allows the determination of the flow direction on both cylinders of the cell.
Abstract: This paper deals with the visualization of swirling decaying flow in an annular cell fitted with a tangential inlet. A wall visualization method, the so-called dot-paint method, allows the determination of the flow direction on both cylinders of the cell. This study showed the complex structure of the flow field just downstream of the inlet, where a recirculation zone exists, the effects of which are more sensitive on the inner cylinder. The flow structure can be considered as three-dimensional in the whole entrance section. The swirl number and the entrance length were estimated using the measured angle of the streamlines. Experimental correlations of these two parameters, taking into account the Reynolds number and the axial distance from the tangential inlet, are given.

Journal ArticleDOI
TL;DR: In this paper, the steady viscous flow and heat transfer past a circular cylinder were studied for some fluid saturated fibrous porous media. Numerical results were obtained according to the Darcy-Brinkman model by means of the finite element method.

Journal ArticleDOI
TL;DR: In this article, it was shown that the instability can be interpreted as a problem in local instability and a discussion of the appropriate boundary conditions for localized instability problems is also given, and direct numerical integration of the full quasigeostrophic equations is then undertaken to determine the ultimate fate of the explosive instability.
Abstract: In a previous paper the authors developed an asymptotic time-dependent theory for coherent structures on a marginally stable baroclinic flow. It was shown that solitary waves, as well as other more general disturbances of sufficient amplitude, could be explosively unstable and that the asymptotic theory provided no mechanism for equilibration. The asymptotic theory is reexamined and shows that the instability can be interpreted as a problem in local instability. A discussion of the appropriate boundary conditions for localized instability problems is also given. Direct numerical integration of the full quasigeostrophic equations is then undertaken to determine the ultimate fate of the explosive instability. The instability equilibrates as a locally steady, zonally uniform O(1) alteration of the original zonal flow that expands slowly in time. This region is connected to the original flow by narrow regions of strong meridional flow. The finite-amplitude region develops both closed streamlines and ...

Journal ArticleDOI
TL;DR: In this paper, the authors examined the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational flow and showed that a large amplitude, O(Re 1/3), distortion results when the monopole is forced at its resonant frequency.
Abstract: This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational flow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the flow will cause the monopole to distort. It is shown that a shear‐diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Re1/3 time scale, much faster than the Re decay time scale of an axisymmetric monopole. This separation of time scales leads to the quasisteady evolution of a monopole in a slowly varying flow. The asymptotic theory is verified by numerically computing the linear response of a Lamb monopole to a time‐periodic straining flow and it is shown that a large amplitude, O(Re1/3), distortion results when the monopole is forced at its resonant frequency.

Journal ArticleDOI
TL;DR: In this article, a finite difference method was proposed for solving incompressible flow problems in two dimensions, where the boundary values of vorticity, including those at singular points, are not required for computing the flow field inside the domain.

Proceedings ArticleDOI
29 Oct 1995
TL;DR: A specialized version of the Runge-Kutta method has been developed to speed up the integration of particle pathes and close-form solutions for calculating angular rotation rate and radius to construct streamribbons and streamtubes on unstructured grids are derived.
Abstract: The plotting of streamlines is an effective way of visualizing fluid motion in steady flows. Additional information about the flowfield, such as local rotation and expansion, can be shown by drawing in the form of a ribbon or tube. In this paper, we present efficient algorithms for the construction of streamlines, streamribbons and streamtubes on unstructured grids. A specialized version of the Runge-Kutta method has been developed to speed up the integration of particle pathes. We have also derived close-form solutions for calculating angular rotation rate and radius to construct streamribbons and streamtubes, respectively. According to our analysis and test results, these formulations are two to four times better in performance than previous numerical methods. As a large number of traces are calculated, the improved performance could be significant.