Showing papers on "Incompressible flow published in 1989"
TL;DR: In this article, the appearance of chaotic particle trajectories in steady, laminar, incompressible flow through a twisted pipe of circular cross-section is demonstrated using standard dynamical systems diagnostics and a model flow based on Dean's perturbation solutions.
Abstract: The appearance of chaotic particle trajectories in steady, laminar, incompressible flow through a twisted pipe of circular cross-section is demonstrated using standard dynamical systems diagnostics and a model flow based on Dean's perturbation solutions. A study is performed to determine the parameters that control fluid stirring in this mixing device that has no moving parts. Insight into the chaotic dynamics are provided by a simple one-dimensional map of the pipe boundary onto itself. The results of numerical experiments illustrating the stretching of material lines, stirring of blobs of material, and the three-dimensional trajectories of fluid particles are presented. Finally, enhanced longitudinal particle dispersal due to the coupling between chaos in the transverse direction and the non-uniform longitudinal transport of particles is shown.
275 citations
TL;DR: In this paper, a numerical study is presented for unsteady laminar flow past a NACA 0015 airfoil that is pitched, at a nominally constant rate, from zero incidence to a very high angle of attack.
Abstract: A numerical study is presented for unsteady laminar flow past a NACA 0015 airfoil that is pitched, at a nominally constant rate, from zero incidence to a very high angle of attack. The flowfield simulation is obtained by solving the full two-dimensional compressible Navier-Stokes equations on a moving grid employing an implicit approximate-factorization algorithm. An evaluation of the accuracy of the computed solutions is presented, and the numerical results are shown to be of sufficient quality to merit physical interpretation. The highly unsteady flowfield structure is described and is found to be in qualitative agreement with available experimental observations. A discussion is provided for the effects of pitch rate and pitch axis location on the induced vortical structures and on the airfoil aerodynamic forces.
236 citations
TL;DR: An automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady-state incompressible Navier-Stokes equations.
216 citations
TL;DR: In this article, direct numerical simulations of the unsteady incompressible Navier-Stokes equations have been performed in order to investigate the behavior of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow.
Abstract: Direct numerical simulations of the unsteady incompressible Navier-Stokes equations have been performed in order to investigate the behavior of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow. For all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are found to be approximately aligned with the scalar flux vector itself. The simulation results are used to obtain dimensionless model coefficients as a function of the turbulence Reynolds and Peclet numbers.
142 citations
TL;DR: In this paper, the Navier-Stokes equations for incompressible fluids are used to model the steady and unsteady flows past a circular cylinder, which is assumed to be two-dimensional.
128 citations
TL;DR: An implicit procedure to solve steadystate Navier-Stokes equations with multigrid relaxation scheme to solve the scalar matrices resulting from the finite-volume formulation is developed.
Abstract: APRESSURE-BASED implicit procedure to solve steadystate Navier-Stokes equations is developed. A multistep pressure correction procedure with an implicit density treatment is used to establish the pressure and velocity fields. A multigrid relaxation scheme is used to solve the scalar matrices resulting from the finite-volume formulation. The algorithm is valid for all Mach number flows ranging from incompressible to supersonic flow regimes.
115 citations
TL;DR: The influence matrix method of enforcing incompressibility in pseudospectral simulations of fluid dynamics, as described by Kleiser and Schumann for channel flow, is generalized to other geometries as mentioned in this paper.
112 citations
TL;DR: In this article, the authors examined the three-dimensional flow structure of an incompressible viscous fluid in a square cubic cavity and obtained numerical solutions by directly integrating the Navier-Stokes equations.
109 citations
TL;DR: Peristaltic pumping by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid in which are distributed identical rigid spherical particles, is investigated theoretically and it is observed that the mean flow reversal is strongly dependent on the particle concentration and the presence of particles in the fluid favors the reversal flow.
Abstract: Peristaltic pumping by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid in which are distributed identical rigid spherical particles, is investigated theoretically. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The results show that the fluid phase mean axial velocity decreases with increase in the particle concentration. The phenomenon of reflux (the mean flow reversal) is discussed. A reversal of velocity in the neighborhood of the centerline occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid. It is further observed that the mean flow reversal is strongly dependent on the particle concentration and the presence of particles in the fluid favors the reversal flow. A motivation of the present analysis has been the hope that such a theory of two-phase flow process is very useful in understanding the role of peristaltic muscular contraction in transporting bio-fluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixtures by peristalsis.
108 citations
01 Jan 1989
TL;DR: An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented and the results are compared with experimental data to verify the time accuracy of the algorithm.
Abstract: An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.
88 citations
09 Jan 1989
TL;DR: Artificial boundary conditions for the linearized incompressible Navier-Stokes equations were designed by approximating the symbol of the transparent operator in this paper, and the related initial boundary value problems were well posed in the same spaces as the original Cauchy problem.
Abstract: Artificial boundary conditions for the linearized incompressible Navier–Stokes equations are designed by approximating the symbol of the transparent operator. The related initial boundary value problems are well posed in the same spaces as the original Cauchy problem. Furthermore, error estimates for small viscosity are proved.
TL;DR: In this article, an incompressible fluid model of the Rayleigh-Taylor instability is generalized to include self-consistent diffuse boundaries, which can predict the scaling of the instability cutoff over an extended parameter range and its dependence on the heat conduction law.
Abstract: An incompressible fluid model of the ablative Rayleigh–Taylor instability [Phys. Fluids 29, 2067 (1986)] is generalized to include self‐consistent diffuse boundaries. With diffuse boundaries the incompressible model is found to be in excellent agreement with a number of previous stability studies of laser ablation. The present theory can predict the scaling of the instability cutoff over an extended parameter range and its dependence on the heat conduction law. It is found that more favorable stability behavior can be obtained both for weak and strong thermal diffusion. Furthermore a strong dependence of the stabilization mechanism on the functional form of the heat conductivity is indicated. Representative conditions for laser ablation are identified and discussed in detail.
TL;DR: The present paper relates the stretching properties of the flow to the resulting fractal dimension spectrum by exploiting the kinematic magnetic dynamo problem and recent experiments which demonstrate the possibility of measuring the fractaldimension of the gradient squared of convected passive scalars.
Abstract: The passive convection of vector fields and scalar functions by a prescribed incompressible fluid flow v(x,t) is considered for the case where v(x,t) is chaotic. By chaotic v(x,t) it is meant that typical nearby fluid elements diverge from each other exponentially in time. It is shown that in such cases, as time increases, a convected vector field and the gradient of a convected scalar will generally concentrate on a set which is fractal. The present paper relates the stretching properties of the flow to the resulting fractal dimension spectrum. Motivation for these considerations is provided by the kinematic magnetic dynamo problem (in the vector case) and (in the scalar case) by recent experiments which demonstrate the possibility of measuring the fractal dimension of the gradient squared of convected passive scalars.
TL;DR: In this paper, a more general Lagrangian description of turbulent velocity such as the Markov process with dependent increments, which recognizes the condition of incompressibility and the important phenomenon of intermittency, is presented.
Abstract: It is shown that the hypothesis of independent increments for velocity, which is widely used by many authors [e.g., A. M. Obukhov, Adv. Geophys. 6, 113 (1959)] in the Lagrangian description of turbulence, is inconsistent with the Navier–Stokes equations in a fundamental way. A more general Lagrangian description of turbulent velocity such as the Markov process with dependent increments, which recognizes the condition of incompressibility and the important phenomenon of intermittency, is proposed. A model of intermittent relative motion of fluid particles in turbulent flow is presented. The high‐order Lagrangian moments and the probability distribution are obtained. The distribution for the intermittent vorticity is also proposed.
TL;DR: In this article, the results of large eddy simulation (LES) of the Navier-Stokes equations are used to evaluate the validity of Taylor's hypothesis of frozen turbulence, which states that the time derivative of some instantaneous quantity is proportional to its derivative in the streamwise direction for incompressible plane channel flow.
Abstract: The results of large eddy simulation (LES) of the Navier–Stokes equations are used to evaluate the validity of Taylor’s hypothesis of frozen turbulence, which states that the time derivative of some instantaneous quantity is proportional to its derivative in the streamwise direction, for incompressible plane channel flow. Time and space derivatives in the streamwise direction of the velocity components are, in fact, found to be well correlated. Root‐mean‐square fluctuations of the terms in Taylor’s hypothesis also support the validity of this hypothesis above the buffer layer. The good agreement between LES and experimental results indicates that errors in the evaluation of derivatives in the streamwise direction are due mostly to insufficient resolution.
09 Jan 1989
TL;DR: The semi-implicit method for pressure-linked equations (SIMPLE) algorithm of Rhie and Chow is extended, and a SIMPLE-revised (SIMPLER) algorithm is formulated on nonstaggered curvilinear grids and a new algorithm, SIMPLM, is formulated.
Abstract: The semi-implicit method for pressure-linked equations (SIMPLE) algorithm of Rhie and Chow [6] for flow problems on nonstaggered curvilinear grids is extended, and a SIMPLE-revised (SIMPLER) algorithm is formulated on nonstaggered curvilinear grids. In addition, a new algorithm, SIMPLE-modified (SIMPLEM), is formulated. The performance of these three algorithms is examined through two test problems (driven flow in a cavity and flow in a sudden expansion). The integral form of the continuity equation is shown to be not satisfied in the SIMPLE formulation. In the SIMPLER formulation, the residuals of the momentum equation do not decrease to acceptably low values. The SIMPLEM algorithm shows reasonably good convergence behavior and is superior to both the SIMPLE and SIMPLER algorithms. On the basis of these comparisons, the SIMPLEM algorithm is recommended for use in nonstaggered curvilinear meshes.
IBM1
TL;DR: In this article, the Navier-Stokes equations are solved in primitive variables using a pseudospectral formulation, and a new method is developed to solve 2D time dependent incompressible viscous flows in an arbitrary geometry.
TL;DR: In this article, the solutions of the equations of fluid motion for compressible and incompressible flow in a concentric annular heat pipe have been analyzed and a similarity solution is presented that can predict the pressure losses in all the segments of the concentric heat pipe as well as conventional heat pipes.
Abstract: The solutions of the equations of fluid motion for compressible and incompressible flow in a concentric annular heat pipe have been analyzed In addition, a similarity solution is presented that can predict the pressure losses in all the segments of the concentric annular heat pipe as well as conventional heat pipes A theoretical analysis to predict the sonic limit for this new pipe is also presented
TL;DR: In this paper, a particle discretisation of the flow is used to conserve the total vorticity of the Navier-Stokes equations, and numerical results concerning the shear layer problem are presented and the influence of the Reynolds number on the numerical solution is explored.
09 Jan 1989
TL;DR: In this paper, a high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow, which can be applied to complex geometries more easilty than highly accurate spectral methods.
Abstract: A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.
TL;DR: In this paper, the existence of an inverse cascade is demonstrated for three-dimensional incompressible flow displaying the Anisotropic Kinetic Alpha (AKA) instability (Frisch, She & Sulem).
Abstract: The existence of an inverse cascade is demonstrated for three-dimensional incompressible flow displaying the Anisotropic Kinetic Alpha (AKA) instability (Frisch, She & Sulem). By means of full three-dimensional simulations of the Navier–Stokes equations, it is shown that flow stirred at small scales by an anisotropic force lacking parity-invariance (i.e. lacking any centre of symmetry) can generate strongly helical structures on larger scales. When there is a substantial range of linearly unstable modes, the most unstable ones emerge at first, but are eventually dominated by modes with the smallest wavenumbers. The key observation for the theory of this inverse cascade is that, in the presence of forcing, the small-scale Reynolds stresses will become dependent on the large-scale flow. Elimination of the small scales produces the nonlinear AKA equations for the large-scale flow. The latter have non-trivial one-dimensional solutions also displaying an inverse cascade, qualitatively similar to the one reported above. This cascade has been numerically simulated over a range of more than two decades. For a simple choice of the forcing, a steady state is eventually reached; it can be described analytically and presents interesting geometric features in the limit of very extended systems. The corresponding energy spectrum has a k −4 range. A number of other scaling relations are also derived. The multi-dimensional extension of the theory is briefly considered. The resulting large-scale structures are conjectured to correspond to solutions of the incompressible Euler equation.
TL;DR: In this article, a pseudospectral matrix element (PSME) method employing the primitive variable formulation of the Navier-Stokes equations was used to simulate 3D time-dependent driven cavity flow at a Reynolds number of 3200 with an aspect ratio of 3 in the spanwise direction as well as 3D flow over a backward step.
TL;DR: In this article, it was shown that the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients.
Abstract: We prove that, for solutions to the two- and three-dimensional incompressible Navier-Stokes equations, the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed in three dimensions. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result, to the decay rate of the energy spectrum are discussed.
TL;DR: In this article, a new class of steady solutions of the axisymmetric Euler equations for an incompressible inviscid fluid is introduced, each solution represents a three-dimensional vortex flow whose azimuthal components of vorticity and velocity are nonzero inside a toroidal region determined by the solution.
Abstract: This work introduces a new class of steady solutions of the axisymmetric Euler equations for an incompressible inviscid fluid. Each solution represents a three-dimensional vortex flow whose azimuthal components of vorticity and velocity are nonzero inside a toroidal region determined by the solution. The governing free-boundary problem is solved by variational techniques. The underlying variational principle is formulated from the natural invariants associated with the evolution equations for axisymmetric flows, and involves a family of invariants that generalizes the standard angular impulse and helicity integrals. A direct method is employed to prove the existence of steady solutions in a bounded domain and steadily translating solutions in space. Qualitative properties of these vortices are discussed and concentrated vortex rings with large swirl are shown to constitute a desingularization of the classical circular vortex filament.
TL;DR: In this article, displacement theorems are presented for the solutions in spherical coordinates of the linear Navier-Stokes equations for time independent flow in an incompressible viscous fluid, allowing one to expand spherical solutions about a chosen center into spherical solutions centered elsewhere.
Abstract: Displacement theorems are presented for the solutions in spherical coordinates of the linear Navier–Stokes equations for time‐independent flow in an incompressible viscous fluid. The theorems allow one to expand spherical solutions about a chosen center into spherical solutions centered elsewhere.
TL;DR: The main finding is that time discretization errors, induced by the nondivergent splitting mode, scale with the order of the accuracy of the integration rule employed if a proper rotational form of the pressure boundary condition is used; otherwise a first-order accuracy in time similar to the classical splitting methods is achieved.
Abstract: A normal mode analysis is presented and numerical tests are performed to assess the effectiveness of a new time-splitting algorithm proposed recently in Karniadakiset al. (1990) for solving the incompressible Navier-Stokes equations. This new algorithm employs high-order explicit pressure boundary conditions and mixed explicit/implicit stiffly stable time-integration schemes, which can lead to arbitrarily high-order accuracy in time. In the current article we investigate both the time accuracy of the new scheme as well as the corresponding reduction in boundary-divergence errors for two model flow problems involving solid boundaries. The main finding is that time discretization errors, induced by the nondivergent splitting mode, scale with the order of the accuracy of the integration rule employed if a proper rotational form of the pressure boundary condition is used; otherwise a first-order accuracy in time similar to the classical splitting methods is achieved. In the former case the corresponding errors in divergence can be completely eliminated, while in the latter case they scale asO(vΔt)1/2.
01 Jan 1989
TL;DR: In this paper, a lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations, which is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.
Abstract: A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.
TL;DR: This paper examines mainly oscillatory behavior of a fluid-conveying collapsible tube using a two-dimensional flexible channel made of a pair of membranes using an explicit finite difference method.
Abstract: This paper examines mainly oscillatory behavior of a fluid-conveying collapsible tube using a two-dimensional flexible channel made of a pair of membranes. The equation of equilibrium of the membrane in a large deflection theory is coupled with the equations of continuity and momentum of an incompressible flow in a one-dimensional flow theory accounting for flow separation. An explicit finite difference method was used to solve the governing equations numerically. According to numerical results, the fluids in the inlet and outlet rigid channels have strong effects on the oscillation of the system. Depending on initial values for the numerical integration, there may exist both a stable static equilibrium and an oscillatory solution for the same parameter values, but only if the external pressure is sufficiently large.