摘要:

Turbulence measurements with a high resolution laser Doppler anemometer in a channel flow with injection of a concentrated polyethylene oxide solution are reported. With polymer injection sufficient to yield a well mixed concentration of 10 ppm the total drag is reduced by 38%, but the sum of the Reynolds stress and the conventional molecular shear stress is only (2)/(3) of the force produced by the streamwise pressure gradient. Thus, the injected polymer solution has a significant effect on the turbulence and causes an additional retarding force equal to approximately (1)/(3) of the total drag.

ISSN:0031-9171    

DOI:10.1063/1.866278

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The slow decay of turbulent kinetic energy downstream of the grid is shown to contribute to the skewness of the velocity fluctuations. Estimates are given that show that energy decay has much stronger influence on the odd‐order moments than the even‐order moments.

ISSN:0031-9171    

DOI:10.1063/1.866279

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Measurements have been made of the velocity of a thin circular disk of radiusr, as it falls with its axis vertical, through a viscous liquid toward a horizontal plane boundary. The distance from the fixed plane to the bottom surface of the disk is denoted byh. Forh<0.032rthe results agree with the squeeze film expression from lubrication theory. Forh>3rthe results agree with the far‐field boundary effect formula derived by Brenner [J. Fluid Mech.12, 35 (1962)]. An empirical expression is proposed for intermediate values ofh. The squeeze film solutions for both a circular cylinder and a sphere approaching a plane are compared with the exact solutions for a cylinder [D. J. Jeffrey and Y. Onishi, Q. J. Mech. Appl. Math.34, 129 (1981)] and a sphere [H. Brenner, Chem. Eng. Sci.16, 242 (1961)] and empirical formulas are proposed for the departure from lubrication theory in these two cases.

ISSN:0031-9171    

DOI:10.1063/1.866280

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Motivated by a stretched version of the Taylor–Green initial‐value problem for the Euler and Navier–Stokes equations, nearly two‐dimensional incompressible flows are considered involving a single direction of slow spatial variation. A multiple‐scale formulation of the problem leads by contour averaging to a system that determines the slow development in space and time. It is shown that the latter system is equivalent to an axisymmetric problem with nonstandard connection between circulation, cylindrical radius, and angular velocity component. Special solutions of the system in the exact axisymmetric case suggest that near‐two‐dimensionality is lost in finite time.

ISSN:0031-9171    

DOI:10.1063/1.866281

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

New experimental results concerning the stability of convective patterns in Be´nard–Marangoni convection are presented. The hexagonal pattern usually seems to be the most stable. By means of a new thermal technique a predetermined pattern can be imposed and the evolution of a pattern of rolls thus created is observed. For small depths of the fluid layer, hexagons are very stable but they become less and less so as the depth of the layer increases, whereas the imposed rolls become more and more stable. This is linked to the relative importance of the driving mechanisms—surface tension or buoyancy forces—and may correspond to a change in the order of this nonequilibrium phase transition.

ISSN:0031-9171    

DOI:10.1063/1.866282

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A linear stability analysis of the base‐state convective flows, which occur in inclined particle settlers and which were studied in a companion paper by Shaqfeh and Acrivos [Phys. Fluids29, 3935 (1986)], is described. The analysis considers the spatial growth of small two‐dimensional disturbances over the entire range of the parameters &thgr; (the angle of inclination of the vessel), &ohgr;ˆ (the wave frequency),Rˆ (a stability Reynolds number), and &xgr;1/6(the parameter governing inertial effects in the base flow). Numerical solutions to the relevant Orr–Sommerfeld equations for the wave growth rates and other important quantities are presented over this entire range. It is shown that, for very large values ofRˆ, these solutions approach asymptotically those of a certain set of Rayleigh equations which are also derived and solved. The results demonstrate that the base flows become most unstable when &xgr;1/6≊O(1), primarily owing to the development of an inviscid instability. This instability is shown to have a number of interesting characteristics including the fact that (a) it is insensitive to the inclination of the vessel, and (b) it tends to destabilize higher frequencies. In addition, it is demonstrated that, although it is very unstable for &xgr;1/6≊O(1), the flow restabilizes as &xgr;1/6→∞, as predicted by Prasad [J. Fluid. Mech.150, 417 (1985)]. The analysis, therefore, bridges the gap between previous asymptotic results and, at the same time, resolves the existing paradox between the experimental observations of Schaflinger [Int. J. Multiphase Flow11, 189 (1985)] and theoretical predictions. Moreover, it provides a theoretical basis for predicting the vigorous instabilities which are witnessed in practice.

ISSN:0031-9171    

DOI:10.1063/1.866283

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The effects of variable viscosity on the surface wave mode of instability of a liquid film flowing down heated or cooled inclined surfaces are examined. Stability boundaries are presented using two models of viscosity variation with temperature. Both models yield qualitatively similar results. It is shown that heating destabilizes the flow, while cooling stabilizes it. For the case of heating the critical wavenumber &agr;cis always zero, while for the case of cooling &agr;ccan be nonzero. By variation of the governing nondimensional parameters, a reasonably complete picture is given when instability occurs first at finite wavelengths.

ISSN:0031-9171    

DOI:10.1063/1.866284

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Falling films on inclined planes display surface and shear instability modes, the latter being important at small angles &bgr; of inclination of the plane. These modes are analyzed with particular attention paid to the effects of surface tension. The results show that the critical Reynolds number of the shear mode is nonmonotonic in either the angle &bgr; or the surface‐tension parameter &zgr; but displays a local minimum at nonzero values of &bgr; and &zgr;. For large Reynolds number, an analysis shows that the shear mode is inviscidly stable, but that the surface mode is unstable.

ISSN:0031-9171    

DOI:10.1063/1.866285

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Flow of incompressible Newtonian liquid films is governed by the Navier–Stokes system with shear‐free, balanced‐normal‐stress, and kinematic boundary conditions at the free surface. This system is solved here for the evolution of finite‐amplitude two‐dimensional disturbances to otherwise steady flow down a vertical plate by means of a finite element method adapted for free boundary problems. When flow is specified to bespatiallyperiodic, fully developed steady flows that ensue approach time‐periodic states, i.e., waves, the finite amplitude of which depends upon their wavelength. The family of time‐periodic states connects to the steady, fully developed flow at a Hopf bifurcation that lies at a critical disturbance length, in agreement with the Orr–Sommerfeld analysis. Initial disturbances to flow down a plate offinitelengthgrow as they propagate downward. In all cases studied here, however, steady flow is eventually approached.

ISSN:0031-9171    

DOI:10.1063/1.866286

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A numerical method based on solution of the Orr–Sommerfeld equation is formulated to demonstrate the suppression of a two‐dimensional, Tollmien–Schlichting‐type, time‐harmonic instability wave in a developing channel flow by a downstream secondary wave created through alternating suction and blowing at the surface. An analytical expression is derived providing the amplitude and a second parameter (the width or the phase) of the downstream surface‐velocity distribution required to create a wave that will suppress the downstream continuation of the original disturbance.

ISSN:0031-9171    

DOI:10.1063/1.866287

出版商:AIP    

年代:1987

数据来源: AIP