ALBERT

Description: The stability of steady isothermal flow of one-dimensional Newtonian fibres is considered. Bifurcation theory yields a stable supercritical Hopf bifurcation, with frequency decreasing for increasing winder speeds near the critical winder speed. A new Chebyshev expansion procedure is used with time-marching to obtain accurate numerical solutions valid far from the critical point. Our numerical solution agrees well with our analytical solution near the critical winder speed, but differs significantly from those of previous numerical models. There is qualitative agreement with a previous isothermal experiment for oscillation amplitude but not for oscillation frequency. These comparisons are discussed. © 1984, Cambridge University Press 1984. All rights reserved.

Description: A class of compressible laminar boundary-layer flows subject to adverse pressure gradients of different magnitude is studied using a finite-element—differential method in which the assumed solutions are represented by classical cubic spline functions. The numerical integration process for the reduced initial-value problem has been carried out directly to at least one integration step upstream of the separation point, and very accurate numerical results have been obtained for a large number of integration steps extremely close to separation. The skin-friction and heat-transfer coefficients for nearly zero-heat-transfer, cooled-wall and heated-wall cases, computed under the assumption of constant Prandtl number Pr = 1.0 as well as Pr = 0.72, have clearly exhibited the same distinctive behaviour near separation. It is deduced that Buckmaster's series expansions for the solution near separation, derived on the assumptions of cooled wall and Pr — 1.0, are valid for all the cases considered. By matching the numerical results with Buckmaster's expansions, accurate distributions of skin friction and heat transfer have been obtained up to the separation point. Moreover, the importance of Prandtl number on the solution is evidenced from the numerical results presented. © 1984, Cambridge University Press 1984. All rights reserved.

Description: A linearized potential-flow analysis is presented for predicting the unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers. The unsteady aerodynamic model includes the effects of blade geometry, non-zero mean-pressure variation across the blade row, high-frequency blade motion, and shock motion within the framework of a linearized frequency-domain formulation. The unsteady equations are solved using an implicit least-squares finite-difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady flow field is determined by matching a solution determined on a rectilinear-type cascade mesh, which covers an extended blade-passage region, to a solution determined on a detailed polar-type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Results are presented for cascades of double-circular-arc and flat-plate blades to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, blade-vibration frequency and shock motion on unsteady response. © 1984, Cambridge University Press 1984. All rights reserved.

Description: This paper describes the results of experiments conducted on a circular jet simultaneously excited by two different acoustic tones. By varying the phase between two signals at harmonically related frequencies, control can be exercised on the process of harmonic generation-sometimes the process being virtually destroyed. This is shown to be so for both harmonic and subharmonic generation, but the latter is more difficult to control. © 1984, Cambridge University Press 1984. All rights reserved.

Description: We present experimental results on the modified Stokes force F exerted on a sphere in magnetic levitation whose position is kept fixed by an optical feedback system. A Newtonian liquid moves at a constant velocity U relative to the sphere. We consider the motion in two different situations. (i) When the sphere approaches a wall perpendicular to U, the increase in IFl due to lubrication agrees quantitatively with theoretical results such as those of Brenner (1961) and Maude (1961), obtained neglecting the unsteadiness of the flow field. (ii) In the complementary situation of a sphere moving along the axis of a cylindrical tube, our results expressed as a function of the eccentricity of the trajectory and of the ratio of the two radii confirm and extend previous theoretical analyses. They show in particular the existence of a minimum of |F| away from the axis of the cylinder and a sharp increase in | F| when the sphere approaches the sidewall. By comparing with the results for a sphere moving parallel to a flat wall, we analyse the effect of the curvature of the cylindrical tube. © 1984, Cambridge University Press. All rights reserved.

Description: The transition from diffusion-dominated to inertia-dominated behaviour in the transport of condensable heavy molecules carried in a continuum subsonic He jet that impinges on a solid surface is studied experimentally. The Stokes number S, or ratio between the heavy-molecule relaxation time and the fluid-dynamic time, is varied in the interval 0 ≲S ≲ 1 by changing the jet Mach number at a constant value of the Reynolds number. Although the heavy species departs considerably from equilibrium at all but the smallest values of S, the helium jet is always near equilibrium conditions. At values of S of order unity the observed rate of deposition at the stagnation point asymptotes to a value some six times greater than in the diffusion region (where S →0), implying that the process is governed by the large inertia of the heavy species, very much like in aerosol impactors. As a result, it is argued that the concept of pressure diffusion is unsuitable to explain the observed behaviour. An approximate theoretical description of the transport process is given for the region S ≪ 1 where the kinetic problem is amenable to a hydrodynamic treatment. Finally, the analogy with the inertia-dominated behaviour of aerosols is used to assess the relative merits of various aerodynamics schemes aiming at separating isotopes. © 1984, Cambridge University Press. All rights reserved.

Description: The ionization relaxation and radiative cooling of weakly unsteady shock waves in krypton and xenon is examined. We find that, besides radiation energy loss, the shock-tube boundary layers and shock attenuation strongly influence the radiative-cooling region. Calculations taking these effects into account are in excellent agreement with experimental values of electron densities. The contribution of line radiation to total radiation energy loss is obtained, and amounts to about 54% at temperatures of 10000 K in krypton. For xenon, first comparisons indicate a similar result. © 1984, Cambridge University Press 1984. All rights reserved.

Description: The vortex loop observed in flow-visualization studies of boundary-layer transition has been investigated by mapping the instantaneous velocity and vorticity fields. All three velocity components have been measured with hot-film anemometers at numerous grid points in a measuring volume centred on the location where the vortex loop appears in flow-visualizaton studies. The instantaneous vorticity field has been computed from the velocity field, and the vortex loop is revealed in the longitudinal component of vorticity. The loop propagates downstream at approximately the primary disturbance wavespeed. The fluid in the outer part of the boundary layer travels faster, and flows over the loop. This forms the inflexional high-shear layer, which breaks down into the hairpin vortices. The magnitude of the vorticity in the high-shear layer is actually about three times larger than that in the loop. These two regions of vorticity are distinguished by the direction of the instantaneous vorticity vectors, i.e. the vectors in the high-shear layer run in the spanwise direction, while the vectors in the vortex loop run primarily in the downstream direction. This also explains why the loop cannot be detected with simple Əu/Əy measurements. © 1984, Cambridge University Press. All rights reserved.

Description: This paper we investigate some effects of a boundary forcing on 2-dimensional cellular patterns in instabilities above threshold. Boundary forcing is modelled as an inhomogeneous boundary condition on the slowly varying amplitude A, i.e. A = λ eiϕ0on boundaries. The relevant range is A—0(ε1/2), where e is the relative distance to the linear-instability threshold. A wavenumber-selection mechanism then occurs, resulting in a band of selected wavenumbers of width proportional to λ A. For large values of λε-1/2 it is shown that no stationary solution exists outside the band of Eckhaus-stable wavenumbers (Eckhaus 1965). For finite geometries of size L, a nonlinear analogue of 'quantization' of modes is investigated. The amplitude equation (equivalent to a space-dependent Ginzburg-Landau model) is analysed by an expansion in powers of exp (—L/£), where £ is the coherence length. The range A = 0(e) is also investigated. A correction to previous theories of wavenumber selection through boundaries (Cross, Daniels, Hohenberg & Siggia 1983a; Pomeau & Zaleski 1981) is calculated. The latter results are general and assume only the existence of a higher-order stationary amplitude equation, which is recast in a form consistent with its boundary conditions. © 1984, Cambridge University Press. All rights reserved.

Description: This paper reports an experimental study of a meandering water stream upon an inclined smooth hydrophobic surface. It was found that the sinuosity (ratio of the total stream length to the length of the projection of the stream on the line of maximum slope of the surface) increases with both increasing discharge rate and surface slope. It was observed that the meandering pattern is not always stable: once the discharge rate exceeds the upper critical value, the meandering pattern becomes unstable, whereas, when the discharge rate is smaller than the lower critical value, the water stream becomes discontinuous, and normally forms droplets, sliding successively down the sloping surface. It was found that, with increasing surface slope, the upper critical value decreases exponentially, while the lower critical value decreases only gradually. It was found that, when a system of stable meanders is formed on the surface, the meander loops are smoothly curved, swinging gradually from left-handed to right-handed deflections from the line of fastest descent, and vice versa, with an almpst constant amplitude and wavelength. The stable meandering pattern migrates gradually down the sloping surface. The observations showed that the central axis of the meandering stream does not coincide with the locus of the highest points of the stream, the highest points being displaced towards the outside of each bend: the cross-sectional profile of the stream is thus usually asymmetrical. It was found that the cross-sectional area of the stream varies cyclically, with one increase and one decrease associated with each bend of the stream. This cyclic variation is repeated many times along the length of the stream, with each point of maximum cross-sectional area located close to a bend. A secondary reversing spiral flow was observed in the stream, and it was found that the sense of rotation of the flow is reversed at each bend. A plausible mechanism of these stream meanders is proposed on the basis of the present results, involving the existence of hysteresis of the contact angle between water and Plexiglas, the presence of asymmetrical surface-tension forces on the stream, and the acceleration and deceleration of the stream as it swings from loop to loop. © 1984, Cambridge University Press. All rights reserved.