Harmonic solutions for polygonal hydraulic jumps in thin fluid films

Rojas, Nicolás; Tirapegui, E.

doi:10.1017/jfm.2015.458

Cited by 12 publications

(4 citation statements)

References 50 publications

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“…Given Higuera's singularity, the film height at the edge is part of the solution of the shallow-water problem. Interestingly, other authors propose a regular terminal state directly obtained from a lubrication limit applied to the downstream portion of the jump such that the terminal film height represents a missing ingredient to a nearly constant value of the local Froude number found experimentally (Duchesne, Lebon & Limat 2014;Rojas & Tirapegui 2015; see references therein). Here the following deserves notation.…”

Section: Motivationmentioning

confidence: 99%

Developed liquid film passing a trailing edge under the action of gravity and capillarity

2018

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We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

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Section: Motivationmentioning

confidence: 99%

Developed liquid film passing a trailing edge under the action of gravity and capillarity

2018

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“…As the flow is assumed to be axisymmetric, polygonal jumps (Rojas & Tirapegui 2015) are not considered. In this case, we solve the axisymmetric version of the full Navier–Stokes equations in cylindrical coordinates (see Wang & Khayat 2021 for details), with the gas–liquid interface (i.e.…”

Section: Results and Validationmentioning

confidence: 99%

The transient spread of a circular liquid jet and hydraulic jump formation

2022

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The transient flow of a circular liquid jet impinging on a horizontal disk, and the hydraulic jump formation, are examined theoretically and numerically. The interplay between inertia and gravity is particularly emphasised. The flow is governed by the thin-film equations, which are solved along with a force balance across the jump. The unsteadiness of the flow is caused by a linearly accelerating jet from an initial to a final steady state. To validate the predicted boundary-layer flow evolution, an analytical development is conducted for small distance from impingement, and for small time. In addition, the predictions of the film profile and jump location are compared against numerical simulation for the transient flow, and are further validated against experiment for steady flow. The evolutions of the film thickness and the wall shear stress in the developing boundary-layer region are found to be similar to those reported for a fluid lying on a stretching surface. The flow responds to the jet acceleration quasi-steadily near impingement but exhibits a long-term transient behaviour near the jump. Analysis of the jump evolution is considered in the range 5 < Fr < 40 for the Froude number (based on the jet radius and velocity). For Fr < 10, the jump reaches the final state instantly when the jet acceleration ceases. At higher Froude number, the jump settles at a later time, exhibiting an overshoot in the thickness due to the dominance of inertia.

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“…He presented the region of stability in terms of Re and We numbers. Rojas and Tirapegui (2015) presented numerical and theoretical results of the circular and polygon hydraulic jumps derived from the inertial lubrication theory. Their results are in good agreement with the experimental results of Ellegard et al (1998).…”

Section: Introductionmentioning

confidence: 99%

The Effects of Target Plate Roughness on the Parameters of Circular Hydraulic Jumps: An Experimental Investigation

Soukhtanlou¹,

Teymourtash²,

Mahpeykar³

2018

JAFM

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When a vertical liquid jet impinges on a horizontal flat plate, at a certain distance from the location of impingement, the depth and velocity of the liquid change and a circular hydraulic jump is formed. The importance of this phenomenon in certain industries has motivated continued quest for more thorough knowledge of the parameters affecting it. Previous research has shown that physical parameters, such as flow rate, jet diameter and geometry of target plate, significantly affect the size and shape of hydraulic jumps. In this study, the effect of target plate roughness on the parameters of circular hydraulic jumps is experimentally investigated. The results show that adding roughness to the target plate leads to an increase in hydraulic jump radius. Furthermore, utilizing the results obtained from the experiments, an empirical law is proposed which determines the hydraulic jump radius and fluid height downstream of the jump position for a given surface roughness of target plate. One of the best-known models for the characterization of the behavior of circular hydraulic jumps is the Bush and Aristoff's model, which is presented as a curve for smooth surfaces. Since the effect of roughness of target plate surface is ignored in the Bush and Arisstof's model, the results obtained in this investigation are further used, for the first time, to improve this model for different degrees of surface roughness.

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Harmonic solutions for polygonal hydraulic jumps in thin fluid films

Cited by 12 publications

References 50 publications

Developed liquid film passing a trailing edge under the action of gravity and capillarity

Developed liquid film passing a trailing edge under the action of gravity and capillarity

The transient spread of a circular liquid jet and hydraulic jump formation

The Effects of Target Plate Roughness on the Parameters of Circular Hydraulic Jumps: An Experimental Investigation

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