Hydraulic jump on the surface of a cone

Zhou, Guangzhao; Prosperetti, Andréa

doi:10.1017/jfm.2022.777

Cited by 4 publications

(18 citation statements)

References 82 publications

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“…The agreement with the oil data is quite good. That with the water data is less so, although our results are in very close agreement with those of Rojas et al (2010) and Zhou & Prosperetti (2022). We may also note that Hansen et al (1997) stated that the radius of the jump was oscillating for Q greater than approximately 15 cm 3 s −1 (Fr > 1.5) so that the experimental data reported are mean values.…”

Section: Validation Against Numerical Modelssupporting

confidence: 86%

“…We may also note that Hansen et al (1997) stated that the radius of the jump was oscillating for Q greater than approximately 15 cm 3 s −1 (Fr > 1.5) so that the experimental data reported are mean values. Zhou & Prosperetti (2022) noted that the unsteadiness mentioned by Hansen et al (1997) was not observed in their simulation. We also recall that Rojas et al (2010) had to impose the thickness at the edge of the disk as measured by Hansen et al (1997).…”

Section: Validation Against Numerical Modelsmentioning

confidence: 90%

“…The comparison of the free-surface profiles based on our approach and experiment is shown in figure 6. We also included the prediction from the Navier-Stokes numerical solution of Zhou & Prosperetti (2022). As in the numerical simulation of Wang & Khayat (2021), the steady state was reached through the evolution of the transient flow.…”

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

“…As in the numerical simulation of Wang & Khayat (2021), the steady state was reached through the evolution of the transient flow. Zhou & Prosperetti (2022) reported that the computational domain was initially full of a gas medium with density and viscosity three orders of magnitude smaller than those of the liquid. The jet was injected from the inlet with a uniform velocity profile.…”

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

“…Indeed, recalling from figures 8(a) and 8(b) that r J ∼ Fr 7/10 and h max ∼ Fr 4/25 , we deduce that Fr J ∼ Fr 0.06 , confirming the quasi Fr independence. Figure 9 shows the dependence of the jump location on the Froude number (flow rate), where comparison is carried out against the measurements of Hansen et al (1997), the spectral inertial-lubrication solution of Rojas et al (2010) as well as the Navier-Stokes solution of Zhou & Prosperetti (2022) for water and silicone oil. We have included our results using the same log-log ranges used by Rojas et al (2010) in their figure 2 and Zhou & Prosperetti (2022) in their figure 3.…”

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

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A coherent composite approach for the continuous circular hydraulic jump and vortex structure

2023

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We examine the structure of the continuous circular hydraulic jump and recirculation for a jet impinging on a disk. We use a composite mean-field thin-film approach consisting of subdividing the flow domain into three regions of increasing gravity strength: a developing boundary layer near impact, an intermediate supercritical viscous layer and a region comprising the jump and subcritical flow. Unlike existing models, the approach does not require any empirically or numerically adjusted boundary conditions. We demonstrate that the stress or corner singularity for a film draining at the edge is equivalent to an infinite slope of the film surface, which we impose as the downstream boundary condition. The model is validated against existing experiment and numerical simulation of the boundary-layer and Navier–Stokes equations. We find that the flow in the supercritical region remains insensitive to the change in gravity level but is greatly affected by viscosity. The existence of the jump is not necessarily commensurate with the presence of recirculation, which is strongly dependent on the upstream curvature and steepness of the jump.

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Section: Validation Against Numerical Modelssupporting

confidence: 86%

Section: Validation Against Numerical Modelsmentioning

confidence: 90%

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

Section: Validation Against Numerical Modelsmentioning

confidence: 99%

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A coherent composite approach for the continuous circular hydraulic jump and vortex structure

2023

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Volume oscillations slow down a rising Taylor bubble

Zhou,

Prosperetti

2024

J. Fluid Mech.

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A gas volume rising in a vertical tube is called a Taylor bubble when its equivalent spherical diameter is greater than the diameter of the tube. Continuity dictates that the rising velocity of such bullet-shaped bubbles must be such that the drainage flow in the liquid film separating the gas from the tube wall equals the rate at which space is vacated by the bubble tail on its rise. The numerical simulations presented here show that, if the volume of the bubble is made to execute small-amplitude oscillations, this drainage flow can be markedly decreased so that the bubble slows down so much as to very nearly stop. The mechanism is a subtle nonlinear interplay between the upward flow imposed by the bubble expansion and the inertia of the falling liquid. Two manners of excitation are considered. In the first one the liquid column above the bubble is forced to oscillate sinusoidally, e.g. by a piston. In the second one, an oscillating pressure is imposed on the top liquid surface. With the first arrangement the bubble slows down during its entire ascent by an amount depending on the oscillation frequency and amplitude. With the second one, for a given frequency, the bubble slows down only in the neighbourhood of a certain resonant depth at which the volume oscillations are maximized, but is little affected at deeper and shallower depths.

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The characteristics of the circular hydraulic jump and vortex structure

Wang,

Baayoun,

Khayat

2024

J. Fluid Mech.

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In an effort to capture the continuous hydraulic jump and flow structure for a jet impinging on a disk, we recently proposed a composite mean-field thin-film approach consisting of subdividing the flow domain into three distinct connected regions of increasing gravity strength (Wang et al., J. Fluid Mech., vol. 966, 2023, A15). In the present study, we further validate our approach, and examine the characteristics and structure of the circular jump and recirculation. The influence of the disk radius is found to be significant, especially in the subcritical region. Below a disk radius, the jump transits from type Ia to type 0 after the recirculation zone has faded. The supercritical flow and jump location are insensitive to the disk size, but the jump length and height as well as the vortex size are strongly affected, all decreasing with decreasing disk radius, exhibiting a maximum with the flow rate for a small disk. The jump is relatively steep with a strong recirculation zone for a high obstacle at the disk edge. Comparison against the Navier–Stokes solution of Askarizadeh et al. (Phys. Rev. Fluids, vol. 4, 2019, 114002; Intl J. Heat Mass Transfer, vol. 146, 2020, 118823) for the weak and intermediate surface tension suggests that the surface tension effect is unimportant for a high obstacle for a jump of type 0 or type Ia. The film thickness at the disk edge for a freely draining film is found to comprise, in addition to a static component (capillary length), a dynamic component: ${h_\infty }\sim {(Fr/{r_\infty })^{2/3}}$ that we establish by minimizing the Gibbs free energy at the disk edge, and, equivalently, is also the consequence of the flow becoming supercritical near the edge. By assuming negligible film slope and curvature at the leading edge of the jump and maximum height at the trailing edge, we show that the jump length is related to the jump radius as ${L_J}\sim Re{(F{r^2}/{r_J}^5)^{1/3}}$ . The vortex length follows the same behaviour. The energy loss and conjugate depth ratio exhibit a maximum with the flow rate, which we show to originate from the descending and ascending branches of the supercritical film thickness. The presence of the jump is not necessarily commensurate with that of a recirculation; the existence of the vortex closely depends on the upstream curvature and steepness of the jump. The surface separating the regions of existence/non-existence of the recirculation is given by the universal relation $R{e^{10/3}}F{r^2} = 9r_\infty ^9/50$ . The jump can be washed off the edge of the disk, particularly at low viscosity and small disk size. The flow in the supercritical region remains insensitive to the change in gravity level and disk size but is greatly affected by viscosity.

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Hydraulic jump on the surface of a cone

Cited by 4 publications

References 82 publications

A coherent composite approach for the continuous circular hydraulic jump and vortex structure

A coherent composite approach for the continuous circular hydraulic jump and vortex structure

Volume oscillations slow down a rising Taylor bubble

The characteristics of the circular hydraulic jump and vortex structure

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