Wave formation on vertical falling liquid films

Алексеенко, С. В.; Nakoryakov, V. E.; Покусаев, Б. Г.

doi:10.1016/0301-9322(85)90082-5

Cited by 101 publications

(56 citation statements)

References 12 publications

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“…Kelly et al show that the energy transfer TANg to these waves is indeed through the disturbance shear stresses at the interface, while Smith uses a long-wavelength expansion to discuss the forces and flow patterns involved in creating instability. Additional contributions to the single-phase falling film problem have been made by Alekseenko et al (1985), Floryan et al (1987), Chin et al (1986 and Giovine et al (1991), among many others.…”

Section: Gravity-induced Instabilitymentioning

confidence: 99%

Classification of instabilities in parallel two-phase flow

Boomkamp

Miesen

1996

International Journal of Multiphase Flow

147

127

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Section: Gravity-induced Instabilitymentioning

confidence: 99%

Classification of instabilities in parallel two-phase flow

Boomkamp

Miesen

1996

International Journal of Multiphase Flow

147

127

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“…Although the depth-averaged equations are only of second order in time, they yield plausible results, at least qualitatively, but they remain fundamentally questionable because of the semi-parabolic assumption [14,15]. The parabolic approximation is widely used in the literature, and its validity was established experimentally by Aleksenko et al [17] for thin-ÿlm ow. However, it is generally argued that the parabolic approximation is valid at low or moderately-low Reynolds number, and provided the surface waves are far from the entry [18,19].…”

Section: Introductionmentioning

confidence: 97%

A spectral/finite‐difference approach for narrow‐channel flow with inertia

Siddique

Khayat

2003

Numerical Methods in Fluids

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SUMMARYA hybrid spectral=ÿnite-di erence scheme is proposed to determine the inertial ow inside narrow channels. The ow ÿeld is represented spectrally in the depthwise direction, which together with the Galerkin projection lead to a system of equations that are solved using a variable step ÿnite di erence discretization. The method is particularly e ective for non-linear ow, and its validity is here demonstrated for a ow with inertia. The problem is closely related to high-speed lubrication ow. The validity of the spectral representation is assessed by examining the convergence of the method, and comparing with the fully two-dimensional ÿnite-volume solution (FLUENT), and the widely used depth-averaging method from shallow-water theory. It is found that a low number of modes are usually su cient to secure convergence and accuracy. Good agreement is obtained between the low-order description and the ÿnite-volume solution at low to moderate modiÿed Reynolds number. The depth-averaging solution is unable to predict accurately (qualitatively and quantitatively) the high-inertia ow. The in uence of inertia is examined on the ow.

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“…From the literature, the steady-state proÿle based on the semi-parabolic proÿle is easily found to be Á s = 2:5x=Re [2]. The parabolic approximation is widely used in the literature, and its validity was established experimentally by Alekseenko et al [7]. However, it is generally argued that the parabolic approximation is valid at low or moderately low Reynolds number, and provided the waves are far from the entry [45; 46].…”

Section: Introductionmentioning

confidence: 99%

Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

Khayat

Kim

Delosquer

2004

Numerical Methods in Fluids

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SUMMARYThis study examines theoretically the development of early transients for axisymmetric ow of a thin ÿlm over a stationary cylindrical substrate of arbitrary shape. The uid is assumed to emerge from an annular tube as it is driven by a pressure gradient maintained inside the annulus, and/or by gravity in the axial direction. The interplay between inertia, annulus aspect ratio, substrate topography and gravity is particularly emphasized. Initial conditions are found to have a drastic e ect on the ensuing ow. The ow is governed by the thin-ÿlm equations of the 'boundary-layer' type, which are solved by expanding the ow ÿeld in terms of orthonormal modes in the radial direction. The formulation is validated upon comparison with the similarity solution of Watson (J. Fluid Mech 1964; 20:481) leading to an excellent agreement when only 2-3 modes are included. The wave and ow structure are examined for high and low inertia. It is found that low-inertia uids tend to accumulate near the annulus exit, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the di culty faced with coating high-viscosity uids. The annulus aspect is found to be in uential only when inertia is signiÿcant; there is less ow resistance for a ÿlm over a cylinder of smaller diameter. For high inertia, the free surface evolves similarly to two-dimensional ow. The substrate topography is found to have a signiÿcant e ect on transient behaviour, but this e ect depends strongly on inertia. It is observed that the ow of a high-inertia uid over a step-down exhibits the formation of a secondary wave that moves upstream of the primary wave. Gravity is found to help the ÿlm (coating) ow by halting or prohibiting the wave growth. The initial ÿlm proÿle and velocity distribution dictate whether the uid will ow downstream or accumulate near the annulus exit.

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Wave formation on vertical falling liquid films

Cited by 101 publications

References 12 publications

Classification of instabilities in parallel two-phase flow

Classification of instabilities in parallel two-phase flow

A spectral/finite‐difference approach for narrow‐channel flow with inertia

Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

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