Ta Phuoc Loc

NUMERICAL SOLUTION OF THE EARLY STAGE OF THE UNSTEADY VISCOUS FLOW AROUND A CIRCULAR CYLINDER: A COMPARISON WITH EXPERIMENTAL VISUALIZATION AND MEASUREMENTS

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3000 and 9500 are analysed numerically by direct integration of the Navier-Stokes equations - a fourth-order finite-difference scheme is used for the resolution of the stream- function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments. The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is discussed. The computed results were in good agreement qualitatively and quantitatively with experimental visualisation and measurements.

Vortex formation around an oscillating and translating airfoil at large incidences

The starting flows past a two-dimensional oscillating and translating airfoil are investigated by visualization experiments and numerical calculations. The airfoil, elliptic in cross-section, is set in motion impulsively and subjected simultaneously to a steady translation and a harmonic oscillation in pitch. The incidence of the airfoil is variable between 0° and 45° and the Reynolds number based on the chord length is between 1500 and 10000. The main object of the present study is to reveal some marked characteristics of the unsteady vortices produced from the oscillating airfoil set at large incidences in excess of the static stall angle. Another purpose is to examine, in some detail, the respective and combined effects of the major experimental parameters on the vortex wake development. It is shown that, in general, the dominant parameter of the flow is the reduced frequency not only when the airfoil oscillates at incidences close to the static stall angle but also at larger incidences. It is also demonstrated that, as the pitching frequency is increased, the patterns of the vortex wake are dependent on the product of the reduced frequency and the amplitude rather than on the frequency itself. It is noted that the combined effect of a high reduced frequency and a large amplitude can give rise to cyclic superposition of leading-edge vortices from which a gradually expanding standing vortex is developed on the upper surface.

Further experiments on vortex formation around an oscillating and translating airfoil at large incidences

The starting flows past a two-dimensional NACA 0012 airfoil translating and oscillating at large incidences are investigated by visualization experiments and numerical calculations. The airfoil model is set in motion impulsively and subjected simultaneously to a constant translation and harmonic oscillation in pitch. The evolution of the vortex wake is followed in a sequence of streamline visualizations and the wake pattern generated is analysed. The parameters varied in the visualization experiment are the Reynolds number ranging from 1500 to 10000, the reduced frequency from 0.1 to 1.0, the mean incidence 30° or 15° and the angular amplitude 15° or 7°. There are also two additional parameters of special interest: the airfoil cross-section and the pitching axis. The effects of these parameters are discussed in relation to the resultant wake patterns. Some comparison is made with the results of earlier experiments.

Large Eddy Simulation of Turbulent Flow past a Backward Facing Step with a new Mixed Scale SGS Model

In this paper, a computational fluid dynamic prediction method is proposed, based on the resolution of the full unsteady incompressible Navier-Stokes equations. An original numerical method is elaborated, corresponding to the threedimensionnal cartesian version of the PEGASE code for DNS and LES of incompressible flows. A new improved subgrid-scale model, the Mixed Scale Model, is proposed. This model is based on both the largest resolved scale gradients and the smallest resolved scale kinetic energy. The problem of turbulent flow past a backward facing step is used in the present study to evaluate the potentiality of LES for the prediction and the analysis of separated flows. Numerical results obtained by LES at a Reynolds number equal to 11 200 are compared with experimental data of Eaton & Johnston [3].

A numerical method for the three-dimensional unsteady incompressible Navier-Stokes equations

Abstract Computations of unsteady incompressible flows are carried out using the three-dimensional unsteady Navier-Stokes equations. Space discretization of the equations is achieved by a finite-difference method in a generalized coordinate system. To an explicit time discretization is added an implicit smoothing technique. The pressure equation is solved by minimizing a discrete norm of the velocity divergence. The method is applied to study the flow around an impulsively started circular cylinder.

Numerical simulation of unsteady compressible viscous flow NACA 0012 airfoil — vortex interaction

The numerical simulation of the compressible flow around a NACA 0012 airfoil has been undertaken using the unsteady Navier-Stokes and total energy equations. The resolution of the governing equations is based on a Roes approximate Riemann solver. Their space integration is performed by means of an upwind Total Variation Diminishing (TVD) scheme, developed by Harten and Yee. The time integration is performed by a linear conservative implicit form through the use of an Alternating Direction Implicit (ADI) formulation. The interaction between a vortex and a NACA 0012 airfoil has been studied. The Mach and Reynolds numbers considered are respectively equal to 0.6 and 22000. and the CFL number used is 20. The numerical results are then reviewed.

Two-dimensional Simulations with Subgrid Scale Models for Separated Flow

The PEGASE 1.1 Navier-Stokes solver [[6]] was modified to perform two-dimensional large-eddy simulations of flow behind a backward-facing step at Re h = 11200 based on the step height. Special attention was focused on the spatial discretization of subgrid-scale model terms and on the treatment of the convective term. Simulations with Smagorinsky model, stochastic backscatter model [[7]] and dynamic model ([[5]], [[8]]) were carried out and results are compared to experimental measurements of Eaton and Johnston [[2]]. Sensitivity of the results to both subgrid scale models and numerical parameters is investigated. Discrepancies between experiments and results obtained with subgrid-scale models are analysed.

An Efficient Numerical Algorithm for Velocity Vorticity 3D Unsteady Navier-Stokes Equations: Application to the Study of a Separated Flow Around a Finite Rectangular Plate

The 3D external viscous flow around a plate is predicted using the velocity-vorticity formulation of the Navier-Stokes equations. The problem is spatially discretized on a staggered grid using second order finite differences. We do not consider any hypothesis on the spatial nature of the flows. A second order Euler backward scheme is employed for the time marching. A decoupled algorithm is presented for the computation of the six components. One component of the velocity vector is calculted through the computation of one 3D elliptic equation. The others are explicitly determinated. Using an influence matrix technique, the method ensures the free-divergence constraint of the fields and the relation ω = ∇ × u.Flows at Re=100 are analysed and compared with the experiments.

Numerical simulation of the lift of a disk-slider

A numerical simulation is made of the phenomenon of the lift of a slider resting on a disk. The problem expressed in mathematical equations takes into account the molecular mean free path of the gas and the phenomena of impact and shocks. We assume that initially, because of the roughness of the disks surface, there is an infinitely narrow cushion of air beneath the slider. The results showing the sliders dynamic behaviour will be set out at the end of this paper.