Three-dimensional Viscous Incompressible Flows Research Articles

The Numerical Modeling of Coupled Motions of a Moored Floating Body in Waves

Nonlinear interactions between water waves and a moored floating body are investigated using the virtual boundary force (VBF) method. The paper first introduces an in-house three-dimensional viscous incompressible flow model (NEWTANK), which is used to simulate wave-floating structure interaction by using the VBF method. Then the coupling procedure between the mooring line model and the floater model is described. Some validation cases of the developed model, including the motions of a free-floating box in two different water waves, are presented. The present numerical results will be compared with the available experimental data and other numerical results from the published literature. After that, the validity of the mooring line in the numerical model is simulated by simulating the motions of a floating box in still water. Finally, the verified model is applied to analyze the wave-induced motions of a catenary moored floating structure, investigating the motion responses and mooring forces responses. The numerical results agree well with the experimental measurements on the whole. This indicates that the present numerical model can correctly capture the main features of the wave-moored floating structure interaction.

Flow along an attachment line controlled by a near-wall body force

The problems of the control of steady three-dimensional viscous incompressible flows modeling the gas flow in the vicinity of the attachment line on the leading edge of a swept wing are considered. It is assumed that the control is realized by means of the body force action approximating the action of a periodic sequence of plasma actuators mounted perpendicular to the leading edge. The corresponding boundary value problems for the system of Navier–Stokes equations are numerically solved using the Fourier method along the longitudinal coordinate and second-order difference approximation in the vertical coordinate. An important role played by the control-induced pressure gradient is shown.

A stable and accurate projection method on a locally refined staggered mesh

In this paper, a robust projection method on a locally refined mesh is proposed for two- and three-dimensional viscous incompressible flows. The proposed method is robust not only when the interface between two meshes is located in a smooth flow region but also when the interface is located in a flow region with large gradients and/or strong unsteadiness. In numerical simulations, a locally refined mesh saves many grid points in regions of relatively small gradients compared with a uniform mesh. For efficiency and ease of implementation, we consider a two-level blocked structure, for which both of the coarse and fine meshes are uniform Cartesian ones individually. Unfortunately, the introduction of the two-level blocked mesh results in an important but difficult issue: coupling of the coarse and fine meshes. In this paper, by properly addressing the issue of the coupling, we propose a stable and accurate projection method on a locally refined staggered mesh for both two- and three-dimensional viscous incompressible flows. The proposed projection method is based on two principles: the linear interpolation technique and the consistent discretization of both sides of the pressure Poisson equation. The proposed algorithm is straightforward owing to the linear interpolation technique, is stable and accurate, is easy to extend from two- to three-dimensional flows, and is valid even when flows with large gradients cross the interface between the two meshes. The resulting pressure Poisson equation is non-symmetric on a locally refined mesh. The numerical results for a series of exact solutions for 2D and 3D viscous incompressible flows verify the stability and accuracy of the proposed projection method. The method is also applied to some challenging problems, including turbulent flows around particles, flows induced by impulsively started/stopped particles, and flows induced by particles near solid walls, to test the stability and accuracy. Copyright © 2010 John Wiley & Sons, Ltd.

Oscillatory Stokes flow in a cylindrical container

We study the three-dimensional viscous incompressible flow generated in a cylindrical container, of radius R , by the sinusoidally oscillatory motion of the top lid, of frequency Ω . This study generalises the one in Shankar [1997a. Three-dimensional eddy structure in a cylindrical container, J. Fluid Mech. 342, 97–118] where inertial effects were not included. For sufficiently small velocities, the motion will be governed by the linearised Navier–Stokes equation. The solution is constructed as a sum of vector eigenfunctions that satisfy the no-slip conditions on the lateral wall. The eigenvalues are found as the roots of the relation, 4 k 2 J m - 1 ( α ) J m ( k ) J m + 1 ( α ) + k α J m ( α ) ( J m - 1 ( k ) - J m + 1 ( k ) ) ( J m - 1 ( α ) - J m + 1 ( α ) ) - 4 m 2 J m ( k ) J m 2 ( α ) = 0 where m and k are the azimuthal and vertical mode numbers and α = k 2 - i Re with Re being the oscillatory Reynolds number Ω R 2 / ν . J m is the Bessel function of the first kind of order m . For the flow generated by the sinusoidal motion of the lid, only the first non-axisymmetric mode m = 1 is excited. Roots of the above equation with m = 1 are calculated and the coefficients in the finite sum representations for the velocity fields are determined so as to satisfy the no-slip conditions on the top and bottom lids in a least squares sense. Detailed studies for a cylinder depth of 1 and an Re of 10 are made and these reveal interesting streamline patterns that include heteroclinic cycle type structures at the top lid (apart from the usual one at the bottom), saddle and closed stagnation lines, especially when the lid reverses its direction of motion.

Topological aspects of three-dimensional wakes behind rotary oscillating cylinders

The development of a three-dimensional viscous incompressible flow generated behind an infinitely long circular cylinder, impulsively started into rectilinear motion and rotationally oscillating, is studied computationally. The numerical scheme, an hybrid vortex method, is used to integrate the velocity–vorticity formulation of the Navier–Stokes equations. The Reynolds number considered is for which the flow becomes spontaneously three-dimensional. The numerical method is explained and its main points are developed. This scheme is then applied to solve some two-dimensional problems, both in order to validate the method and to compute a nominal two-dimensional flow, required to measure the impact of three-dimensionality. The three-dimensional flow past a steady cylinder is also compared to benchmark simulations. Once the flow has become fully three-dimensional, beyond the transient regime and saturation of instabilities, the cylinder begins a rotary oscillation around its axis. Two kinds of rotations are considered: constant amplitude and several frequencies, and constant frequency and various amplitudes. When amplitude and frequency are high enough, the whole flow comes back to its two-dimensional state. This result gives a justification for two-dimensional computations in the literature related to rotating cylinders. For the first super-harmonic frequency of the flow, a parametric study is performed in order to find the impact of the amplitude on the topology of the flow. A bifurcation is clearly identified. Finally, the mechanisms involved in the return to a two-dimensional state are explained: the interaction between transverse instabilities and von Kármán streets is quantified by means of a correlation analysis.

A numerical study of projection algorithms in the finite element simulation of three-dimensional viscous incompressible flow

A comparative study of two versions of the projection algorithm used either for time integration or as an iterative method to solve the three-dimensional incompressible Navier-Stokes equations is presented. It is also shown that these projection algorithms combined with the finite element method are particularly suited for the treatment of outflow boundary conditions in the context of external flows. This assertion is illustrated by means of some numerical examples in which five types of boundary conditions are compared. The scheme is applied to simulate the flow past a cylinder clamped on two fixed parallel solid walls

Instability of long-wave viscous flows

The asymptotics of the problem of stability of spatially periodic three-dimensional viscous incompressible flows are considered in the case in which one of the periods increases without bound, while the other two are fixed. This problem was solved for parallel flows ― with one nonzero velocity component depending on one space variable

Numerical Simulation of Three-Dimensional Viscous Flows using the Vector Potential Method

A method for solving three-dimensional viscous incompressible flows is presented. A complete set of the Navier-Stokes equation is transferred and expressed in terms of the vorticity, the scalar and the vector potential. In this formation, the velocity field satisfies the equation of continuity automatically. The vorticity transport equations discretized by the centred differences are solved by the rational Runge-Kutta (RRK) time integration scheme, and the Poisson equations are solved by the successive over-relaxatation (SOR) method. The numerical solutions of flows in a cubic cavity, in a square duct and in a rectangular duct with the aspect ratio of 2 are presented. Comparison of computed results with other calculations confirms the accuracy and reliability of the present approach.

A method for solving three-dimensional viscous incompressible flows over slender bodies

A marching iterative method for solving the three-dimensional incompressible and steady reduced Navier-Stokes equations in general orthogonal coordinate systems is described with the velocity and the pressure as dependent variables. The coupled set of the linearized finite-difference continuity and momentum equations are solved iteratively without any splitting or factorization errors. Each iteration consists of spatial marching from the upstream boundary to the downstream boundary. The discrete continuity and the two linearized crossflow momentum equations are satisfied at each marching step, even when the mainstream momentum equation is not converged. This solution procedure is equivalent to the solution of a single Poisson-like equation by the successive plane over relaxation method, while other available solution methods employ a Jacobi-type iterative scheme and therefore are less efficient. Several properties of the numerical method have been assessed through a series of tests performed on the laminar incompressible flow over prolate spheroids at intermediate incidence.

A method for solving three-dimensional viscous incompressible flows over slender bodies

A method for solving three-dimensional viscous incompressible flows over slender bodies

Numerical investigation of three-dimensional viscous incompressible flows in divergent curved channels and turbulent model study

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density- weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flows in divergent curved channels was carried out by means of parabolized computation method. The calculating results were used to analyze and investigate the aerodynamic performance of stator cascades in compressors preliminarily.