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

Wang, W.; Baayoun, Abdelkader; Khayat, Roger E.

doi:10.1017/jfm.2023.374

Cited by 4 publications

(38 citation statements)

References 60 publications

(319 reference statements)

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“…Comparison was made against the spectral inertial-lubrication model of Rojas et al (2010), the numerical solution of the boundary-layer equations of Fernandez-Feria et al (2019), the Navier-Stokes solution of Zhou & Prosperetti (2022) as well as existing mean-field models (Kasimov 2008;Dhar, Das & Das 2020). Overall, agreement with our numerical predictions was surprisingly close; the reader is particularly referred to the validation § 4 of Wang et al (2023).…”

Section: Introductionmentioning

confidence: 54%

“…As indicated in the experimental work of Duchesne et al (2014), the edge film thickness also follows a weak power-law dependence on the flow rate. Although we have extensively validated our approach (Wang et al 2023) for a film freely draining at the disk edge, we further verify our model against the numerical solution of the Navier-Stokes equations of Askarizadeh et al (2019Askarizadeh et al ( , 2020 when an obstacle is placed at the disk edge. We also examine the influence of the obstacle height on the jump and vortex structure.…”

Section: Introductionmentioning

confidence: 88%

“…This assumption was adopted initially by Watson (1964), and has been commonly used in existing theories (Bush & Aristoff 2003;Prince et al 2012Prince et al , 2014Wang & Khayat 2018. Readers are referred to Wang et al (2023) for a complete discussion.…”

Section: The Physical Domain and Problem Statementmentioning

confidence: 99%

“…In a recent study (Wang, Baayoun & Khayat 2023), we proposed a theoretical treatment to simulate the circular hydraulic jump and recirculation for a jet impinging on a disk. We formulated a composite mean-field thin-film approach, which consists of subdividing the flow domain into three regions of increasing gravity strength: a developing boundary layer near impact, an intermediate supercritical viscous layer leading up to the edge of the jump and a region comprising the jump and subcritical flow.…”

Section: Introductionmentioning

confidence: 99%

“…Type IIb exhibits a tiered structure, which is referred to as a 'double-jump' by Bush et al (2006). The aim of the present study is to use our recent formulation and solution procedure (Wang et al 2023) to examine the different features of the type 0 and type Ia circular hydraulic jumps and elucidate the flow structure in each case.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 88%

Section: The Physical Domain and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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The interplay between gravity and centrifugal forces in the continuous circular hydraulic jump

Baayoun,

Khayat

2024

Physics of Fluids

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The flow of a thin film over a rotating disk is crucial in many industrial applications, such as spin coating and jet cooling. Accurate prediction of hydrodynamic features is essential for optimizing these processes. In this study, we examine the vertical downward impingement of a circular Newtonian liquid jet on a horizontally rotating disk, focusing on two distinct regimes based on the rotation level. For a stationary disk and low rotation speed, a continuous hydraulic jump is formed, while increased rotation speed leads to the transformation of the jump into a hump. A composite mean-field thin-film approach is utilized to analyze the flow dynamics in different regions of the domain. The effects of gravity and rotation are considered by developing a model to capture the continuous jump and vortex structure. The influence of rotation on the laminar boundary layer near impingement is found to be negligible. Specific conditions for gravity and rotation are established to differentiate between the jump and hump regimes. The model is validated for both regimes against existing experiment. In the jump regime, the flow transitions from predominantly azimuthal near the disk to predominantly radial toward the free surface, while in the hump regime, the flow maintains an azimuthal character around the hump. The vortex associated with the jump diminishes with increasing rotation speed, indicating the occurrence of a type-0 jump on a rotating disk. For small gravity, the vortex does not form in conjunction with the jump at any rotation level. In the case of small rotation, large gravity, and large disk size, the film exhibits a hydraulic jump near impingement followed by a sharp rise in thickness near the edge of the disk.

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Understanding Embolus Transport And Source To Destination Mapping Of Thromboemboli In Hemodynamics Driven By Left Ventricular Assist Device

Majee,

Sahni,

Pal

et al. 2024

Preprint

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Left Ventricular Assist Devices (LVADs) are a key treatment option for patients with advanced heart failure, but they carry a significant risk of thromboembolic complications. While improved LVAD design, and systemic anticoagulation regimen, have helped mitigate thromboembolic risks, ischemic stroke due to adverse thromboembolic events remains a major concern with current LVAD therapies. Improved understanding of embolic events, and embolus movement to the brain, is critical to develop techniques to minimize risks of occlusive embolic events such as a stroke after LVAD implantation. Here, we address this need, and devise a quantitative in silico framework to characterize thromboembolus transport and distrbution in hemodynamics driven by an operating LVAD. We conduct systematic numerical experiments to quantify the source-to-destination transport patterns of thromboemboli as a function of: LVAD outflow graft anastomosis, LVAD operating pulse modulation, thromboembolus sizes, and origin locations of emboli. Additionally, we demonstrate how the resulting embolus distribution patterns compare and correlate with descriptors based solely on hemodynamic patterns such as helicity, vorticity, and wall shear stress. Using the concepts of size-dependent embolus-hemodynamics interactions, and two jet flow model for hemodynamics under LVAD operation as established in our prior works, we gain valuable insights on departure of thromboembolus distribution from flow distribution, and establish that our in silico model can generate deep insights into embolus dynamics which is not otherwise available from standard of care imaging and clinical data.

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

Cited by 4 publications

References 60 publications

The characteristics of the circular hydraulic jump and vortex structure

The characteristics of the circular hydraulic jump and vortex structure

The interplay between gravity and centrifugal forces in the continuous circular hydraulic jump

Understanding Embolus Transport And Source To Destination Mapping Of Thromboemboli In Hemodynamics Driven By Left Ventricular Assist Device

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