Madeleine Coutanceau

Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow

A visualization method is used to obtain the main features of the hydrodynamic field for flow past a circular cylinder moving at a uniform speed in a direction perpendicular to its generating lines in a tank filled with a viscous liquid. Photographs are presented to show the particular fineness of the experimental technique. More especially, the closed wake and the velocity distribution behind the obstacle are investigated; the changes in the geometrical parameters describing the eddies with Reynolds number (5 Re

The early stage of development of the wake behind an impulsively started cylinder for 40 Re 4

The time development of the symmetrical standing zone of recirculation, which is formed in the early stage of the flow due to a circular cylinder impulsively set in motion perpendicular to its generators, has been studied using a flow visualization technique. The Reynolds numbers (based upon the diameter) range from 40 to 10 4 . Some new phenomena indicated in the flow patterns are revealed, and several different regimes are differentiated by a detailed analysis of the evolution of the main flow characteristics. A correlation with some theoretical results is established.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 10 3 and 10 4

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier-Stokes equations, while the experimental investigation is based on visualisation of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier-Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Influence of rotation on the near-wake development behind an impulsively started circular cylinder

The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers ( Re [les ] 1000). The rotating-to-translating-speed ratio α increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E 1 Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies E i ( i = 2,3,…) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter.

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.

Effect of finite boundaries on the slow laminar isothermal flow of a viscoelastic fluid around a spherical obstacle

Abstract This paper contains experimental and theoretical work on a non-viscomethric flow with constant strain for non-Newtonian fluids. An experimental investigation of the laminar isothermal flow of moderately concentrated aqueous solutions of polymers (polyethylene oxide) around a spherical obstacle, which moves along the axis of a cylinder at low Reynolds number, is carried out. The sphere is free from any attachment and falls under the action of gravity. By means of a vizualisation method, velocity distributions are accurately measured and their dependence upon the three dimensionless parameters We (Weissenberg number), Re (Reynolds number) and λ (sphere-cylinder diameter ratio) is studied. A remarkable difference between Newtonian and viscoelastic velocity fields is pointed out. The drag on the sphere is also determined. The effects of finite boundaries are analyzed for a range of sphere-cylinder diameter ratios greater than 0.25. In particular, it is shown that the wall proximity increases the effects due to the fluid elastic behavior, while, on the other hand, it reduces the inertial effect. In order to complete the experimental results, a theoretical analysis is developed for a Maxwell constitutive equation. The lower terms of an expansion in power series of Re and We and simplified boundary conditions are used. The numerical data conveniently represent the experimentally observed phenomena.

Cellular Stokes flow induced by rotation of a cylinder in a closed channel

The evolution of the cellular structure of the two-dimensional creeping flow induced by a rotating circular cylinder set in the centre of a rectangular channel is studied numerically and experimentally when the aspect ratio A increases from 1 to 7. In the calculations, depending on the value of A , either only series in terms of polar coordinates, or both matched polar and Cartesian coordinates series are employed to represent the stream function and an efficient least-squares method, very easy to program, is selected to satisfy some of the boundary conditions. For the experiments, a special technique which visualizes intermittently the paths of solid tracers during long times of exposure permits us to observe the fluid motion in the whole domain, even in the regions where the velocities are very small. An excellent measure of agreement between the numerical and experimental results is found. Thus it is clearly shown how, in the region beyond the rotating flow directly driven by the cylinder, the two main corner cells visualized at A = 1, develop with increasing A and then coalesce, to finally merge and give rise to a single central cell. This central cell develops in its turn, tending finally to the unbounded channel reference cell, after passing through a maximum length however. Owing to the very high precision of the calculations, many details of the flow development have been clearly shown, in particular the periodicity, with increasing A , of all the different phases, progressively inducing a succession of cells. The prediction that the angle of separation of the fluid boundaries of the cells tends towards the theoretical limit of 58.61° when the aspect ratio becomes large is also confirmed.

Viscous flow normal to a flat plate at moderate Reynolds numbers

An experimental and numerical investigation of the two-dimensional flow normal to a flat plate is described. In the experiments, the plate is started impulsively from rest in a channel for Reynolds numbers, based on the breadth of the plate, in the range 5 ≤ Re ≤ 20. Over this range of Re the flow remains symmetrical and stable and tends to a steady state but is shown to depend strongly on the ratio λ of the plate to channel breadth. The evolution of the experimental flow with time and Reynolds number is studied and the variation with λ in the range 0.05 ≤ λ ≤ 0.2 is investigated sufficiently to enable an estimate of properties of the flow as λ → 0 to be obtained for the steady-state flow. The numerical results are obtained for steady flow normal to a flat plate in an unbounded fluid for Reynolds numbers up to Re = 100. They supplement and extend results for this flow obtained for values of Re up to 20 by Hudson & Dennis (1985). The present solutions have been found using a vorticity-stream function formulation rather than the primitive-variable approach of Hudson & Dennis and provide an independent check on these results. A comparison of the theoretical results for Re ≤ 20 with the limit λ → 0 of the experimental results is, generally speaking, extremely satisfactory.

Wall effect on the bubble behaviour in highly viscous liquids

A theoretical and experimental study is carried out for the problem of the wall effect experienced by a fluid body moving with a constant speed along the axis of a vertical circular tube filled with a highly viscous liquid. In the theoretical study the body is limited to being either spherical or cylindrical and an optimization process with least squares is used to write the no-slip condition on the tube wall. Comparisons between the hydrodynamic and kinematic behaviour of a rigid, liquid and gaseous body are established. Furthermore, from an experimental investigation, based upon a fine visualization technique and rising-speed measurements, the respective limits of validity of the calculations have been found in the case of an air bubble. Information concerned especially with the shape of this bubble, and the hydrodynamic field that it generates, is given for the whole domain of the bubble and tube diameter ratio ranging from no wall influence to maximum wall influence.