Impinging jet flow and hydraulic jump on a rotating disk

2018 ◽  
Vol 839 ◽  
pp. 525-560 ◽  
Author(s):  
Yunpeng Wang ◽  
Roger E. Khayat
Keyword(s):  
Film Thickness ◽  
Hydraulic Jump ◽  
Free Surface Flow ◽  
Rotating Disk ◽  
Surface Flow ◽  
Thin Film Flow ◽  
Capillary Length ◽  
Rotating Speed ◽  
Stationary Disk ◽  
Low Viscosity

The free-surface flow formed by a circular jet impinging on a rotating disk is analysed theoretically. The study explores the effects of rotation and inertia on the thin-film flow. Both boundary-layer height and film thickness are found to diminish with rotation speed. A maximum film thickness develops in the supercritical region, which reflects the competition between the convective and centrifugal effects. Unlike the flow on a stationary disk, an increase in the wall shear stress along the radial direction is predicted, at a rate that strengthens with rotating speed. Our results corroborate well existing measurements. The location and height of the hydraulic jump are determined subject to the value of the thickness at the edge of the disk, which is established first for a stationary disk based on the capillary length, and then for a rotating disk using existing analyses and measurements in spin coating. The case of a stationary is revisited in an effort to predict the location and height of the jump uniquely. The formulated value of the height at the edge of the disk seems to give excellent results for a jet at moderately high flow rate (or low viscosity) where the jump structure is well identifiable in reality.

The role of gravity in the prediction of the circular hydraulic jump radius for high-viscosity liquids

2019 ◽  
Vol 862 ◽  
pp. 128-161 ◽  
Author(s):  
Yunpeng Wang ◽  
Roger E. Khayat
Keyword(s):  
Flow Rate ◽  
Hydraulic Jump ◽  
Free Surface Flow ◽  
High Viscosity ◽  
Surface Flow ◽  
Type I ◽  
Capillary Length ◽  
Flow Energy ◽  
Thin Film Equation ◽  
Downstream Flow

The free-surface flow formed by a circular jet impinging on a stationary disk is analysed theoretically. We develop a simple and coherent model to predict the location and height of the jump for high-viscosity liquids. The study explores the effect of gravity in the supercritical flow. The formulation reduces to a problem, involving only one parameter: $\unicode[STIX]{x1D6FC}=Re^{1/3}Fr^{2}$, where $Re$ and $Fr$ are the Reynolds and Froude numbers based on the flow rate and the jet radius. We show that the jump location coincides with the singularity in the thin-film equation when gravity is included, suggesting that the jump location can be determined without the knowledge of downstream flow conditions such as the jump height, the radius of the disk, which corroborates earlier observations in the case of type I circular hydraulic jumps. Consequently, there is no need for a boundary condition downstream to determine the jump radius. Our results corroborate well existing measurements and numerical simulation. Our predictions also confirm the constancy of the Froude number $Fr_{J}$ based on the jump radius and height as suggested by the measurements of Duchesne et al. (Europhys. Lett., vol. 107, 2014, 54002). We establish theoretically the conditions for $Fr_{J}$ to remain independent of the flow rate. The subcritical flow and the height of the hydraulic jump are sought subject to the thickness at the edge of the disk, comprising contributions based on the capillary length and minimum flow energy. The thickness at the edge of the disk appears to be negligibly small for high-viscosity liquids.

Free Surface Flow Profile and Fluctuations of a Circular Hydraulic Jump Formed by an Impinging Jet

1995 ◽  
Vol 117 (4) ◽  
pp. 677-682 ◽  
Author(s):  
J. W. Stevens
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Surface Profile ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Profile ◽  
Flow Depth ◽  
Supercritical Flow ◽  
Jump Size ◽  
Free Surface Profile

A fine wire probe was used to make quantitative measurements of the free surface profile and surface fluctuations around the hydraulic jump formed by a normally impinging free liquid jet. Representative magnitudes of both radial and axial fluctuations were presented for two nozzle sizes and several jet Reynolds numbers and subcritical flow depths. The results were compared to previous measurements of the supercritical flow depth and to theoretical predictions of the circular hydraulic jump size. The agreement appeared reasonable for the supercritical flow depth while the analytical expressions predicted a shorter hydraulic jump than that found by the measurements for the same supercritical flow conditions.

Thermal energy transport in thin film flow of nanofluid over a decelerating rotating disk

2021 ◽  
pp. 095440892110507
Author(s):  
Latif Ahmad ◽  
Jawad Ahmed ◽  
Awais Ahmed
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Film Thickness ◽  
Energy Transport ◽  
Film Flow ◽  
Rotating Disk ◽  
Brownian Diffusion ◽  
Thin Film Flow ◽  
Thickness Skin ◽  
Buongiorno Model

The thin film flow in nanotechnology is one of the most modern progresses in the study of thin films. This includes coating with nanocomposite materials, thus providing the materials improved mechanical properties due to a so-called size effect. The ultimate functional properties that can be gained are of high adherence, wear resistance, thermal conductivity, oxidation resistance, higher toughness and hardness. This article studies the transient motion of nanofluid thin film over a disk rotating with angular velocity inversely proportional to the time. The importance of Lorentz force arises due to the axial projection of magnetic flux is studied on thin film flow and heat transfer. Two active mechanisms of nanoparticles, namely thermophoresis and Brownian diffusion, are discussed using Buongiorno model. By adopting a similarity method, the velocity distribution thermal and concentration fields above the rotating disk are simulated numerically and assessed graphically. Numerical illustrations for nanofluid film thickness, skin friction and heat and mass transfer rates are depicted against the impacts of several influential parameters. Results highlight that film thickness reduces with unsteadiness and rotation parameters. The results also spectacle that the involvement of a magnetic beam reduces the velocity of nanofluid film. Further, it is observed that thermophoresis and Brownian motion effects make a better influence in enhancing the heat transfer rate.

scholarly journals Free Surface Flow and Film Thickness Induced by Blade Coating.

1998 ◽  
Vol 64 (620) ◽  
pp. 1079-1087
Author(s):  
Makoto KOUMURA ◽  
Eiji HASAGAWA ◽  
Masaomi OKAMOTO ◽  
Hisayoshi MATSUFUJI
Keyword(s):  
Free Surface ◽  
Film Thickness ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Blade Coating

scholarly journals CFD Software Applications for Transcritical Free Surface Flow

2009 ◽  
Author(s):  
Saira F. Pineda ◽  
Armando J. Blanco ◽  
Luis Rojas-Solo´rzano
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Stokes Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Commercial Software ◽  
Flow Equations ◽  
Software Packages ◽  
Commercial Package ◽  
Benchmark Solutions

Open flow channel is very common in engineering applications. Traditional approaches solve shallow-water flow equations, known as Saint-Venant equations, when one or two dimension solutions can be adequate for obtaining most of the important flow characteristics. However, complex situations can require solving Navier-Stokes equations. The arrival of high performance computers and commercial software packages offers new possibilities in the field of numerical hydraulics. However, commercial software packages should be tested on some specific cases; so that these can be used with confidence. In this paper we solve several cases of free surface flow that consider subcritical, supercritical, critical, oscillatory depth profiles and hydraulic jumps using a commercial package, CFX™. Most of these cases are proposed as benchmark solutions for non-prismatic cross section, non-uniform bed slope and transition between subcritical and supercritical flow. Other cases as Hydraulic jump consist of experimental data of hydraulics jumps for incident flow with Froude numbers up to 4.23. Both types of cases allow us to perform the verification and validation of the commercial package used. Results obtained with CFX™ show excellent agreement with analytical solutions, for subcritical, supercritical, transitional and hydraulic jump cases. Special care with grid selection and entrance boundary condition is crucial to simulate with accuracy these types of flows. In particular, when a proper structured mesh is used, quality results are highly improved. Finally, results show to be insensitive to entrance turbulence conditions.

Hydraulic jump in circular pipes

1999 ◽  
Vol 26 (3) ◽  
pp. 368-373 ◽  
Author(s):  
Helmut Stahl ◽  
Willi H Hager
Keyword(s):  
Pipe Flow ◽  
Hydraulic Jump ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Main Flow ◽  
Hydraulic Jumps ◽  
Circular Pipes ◽  
Conduit Diameter ◽  
Sequent Depth ◽  
Downstream Flow

Hydraulic jumps in conduits containing free surface flow have received practically no attention. This project was conducted to investigate experimentally the main features of such jumps and to obtain limits for conduit choking. The sequent depth ratio is determined in terms of the approach Froude number based on the conventional momentum approach. The lengths of the surface recirculation and aeration zones are also considered. Two different appearances of jumps are discussed and it is demonstrated that jumps with a small approach depth differ from those with a depth larger than about 30% of the conduit diameter. A choking condition is proposed for which conduits are subjected to full pipe downstream flow. Photographs are used to describe the main flow pattern. The results of this study are readily applicable for design.Key words: aeration, conduit choking, hydraulic jump, pipe flow, sequent depths.

Analysis of Polygonal Vortex Flows in a Cylinder with a Rotating Bottom

2021 ◽  
Vol 11 (3) ◽  
pp. 1348
Author(s):  
A. Rashkovan ◽  
S.D. Amar ◽  
U. Bieder ◽  
G. Ziskind
Keyword(s):  
Experimental Studies ◽  
Free Surface Flow ◽  
Careful Analysis ◽  
Numerical Approach ◽  
Surface Flow ◽  
Initial Water ◽  
Eddy Simulation ◽  
Disk Rotation ◽  
Inner Radius ◽  
Liquid Flows

The present paper provides a physically sound numerical modeling of liquid flows experimentally observed inside a vertical circular cylinder with a stationary envelope, rotating bottom and open top. In these flows, the resulting vortex depth may be such that the rotating bottom disk becomes partially exposed, and rather peculiar polygon shapes appear. The parameters and features of this work are chosen based on a careful analysis of the literature. Accordingly, the cylinder inner radius is 145 mm and the initial water height is 60 mm. The experiments with bottom disk rotation frequencies of 3.0, 3.4, 4.0 and 4.6 Hz are simulated. The chosen frequency range encompasses the regions of ellipse and triangle shapes as observed in the experimental studies reported in the literature. The free surface flow is expected to be turbulent, with the Reynolds number of O(105). The Large Eddy Simulation (LES) is adopted as the numerical approach, with a localized dynamic Subgrid-Scale Stresses (SGS) model including an energy equation. Since the flow obviously requires a surface tracking or capturing method, a volume-of-fluid (VOF) approach has been chosen based on the findings, where this method provided stable shapes in the ranges of parameters found in the corresponding experiments. Expected ellipse and triangle shapes are revealed and analyzed. A detailed character of the numerical results allows for an in-depth discussion and analysis of the mechanisms and features which accompany the characteristic shapes and their alterations. As a result, a unique insight into the polygon flow structures is provided.

scholarly journals Laminar free-surface flow into a vertical cylinder

1975 ◽  
Vol 3 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Thomas G. Smith ◽  
J.O. Wilkes
Keyword(s):  
Free Surface ◽  
Vertical Cylinder ◽  
Free Surface Flow ◽  
Surface Flow
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