An experimental investigation of the stability of the circular hydraulic jump (original) (raw)
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1981
The circular hydraulic jump commonly forms on a horizontal plate struck by a vertical jet of liquid. New observations of this phenomenon are described. A previously unreported instability of the jump is examined. This is shown to arise when the local Reynolds number R, just ahead of the jump exceeds a critical value of 147. Prior to this instability, the flow behind the jump contains a closed eddy, the length of which decreases to zero as R, increases towards its critical value. Physical explanations for this flow structure and instability are proposed. Accurate measurements of liquid depths were made using a light-absorption technique, in which a laser was shone through water containing a strong dye. Liquid depths ahead of and behind the jump were so determined and depth profiles of the jump in the stable regime were obtained. As the outer depth was increased, the jump closed in on the jet and eventually disappeared: this extinction of the jump is also investigated.
A numerical study of the transition in the circular hydraulic jump
Physics Letters A, 1999
We performed axisymmetric r-z simulations to clarify the structure formation of the circular hydraulic jump. The transition from a type I to a type II jump, which was induced by changing the depth of the fluid far away from the jet in the laboratory experiment, was investigated numerically. We found that the transition is associated with a rise in pressure beneath the surface immediately after the hydraulic jump. This result shows that the hydrostatic assumption used in most of the theoretical studies may not be appropriate for the formation of a type II jump. q 1999 Elsevier Science B.V. All rights reserved.
2014
— oblique and normal impingement of a circular liquid jet with a horizontal target gives rise to hydraulic jumps of unique shapes. Hydrodynamics of this phenomenon have been experimentally investigated in the present work. An obliquely inclined and normal circular water jet, impinging on a flat horizontal surface, confers a series of hydraulic jump profiles, pertaining to different jet inclinations and jet velocities. The present work attempts to find a geometric and hydrodynamic characterization of the spatial patterns formed as a consequence of such noncircular and circular hydraulic jump profiles. The aim of the present study is to elucidate the mechanisms of the formation of certain irregular and non-intuitive shapes of hydraulic jump profiles, originated as a consequence of oblique and normal impingement of single circular liquid
On the circular hydraulic jump
American Journal of Physics, 1999
We study both experimentally and theoretically the classical problem of the circular hydraulic jump. By means of elementary hydrodynamics we investigate the scaling laws governing the position of the hydraulic jump and compare our predictions with experimental data. The results of our simple model are in good agreement with the experiments and with more elaborate approaches. The problem can be effectively used for educational purposes, being appropriate both for experimental investigations and for theoretical application of many fluid mechanics concepts.
The influence of surface tension on the circular hydraulic jump
Journal of Fluid Mechanics, 2003
We present the results of a combined theoretical and experimental investigation of the influence of surface tension σ on the laminar circular hydraulic jump. An expression is deduced for the magnitude of the radial curvature force per unit length along a circular jump, F c = −σ (s − R)/R j , where R j is the jump radius, and s and R are, respectively, the arclength along the jump surface and radial distance between the nearest points at the nose and tail of the jump at which the surface is horizontal. This curvature force is dynamically significant when 2σ/(ρgR j H) becomes appreciable, where H is the jump height, ρ the fluid density and g the acceleration due to gravity. The theory of viscous hydraulic jumps (Watson 1964) is extended through inclusion of the curvature force, and yields a new prediction for the radius of circular hydraulic jumps. Our experimental investigation demonstrates that the surface tension correction is generally small in laboratory settings, but appreciable for jumps of small radius and height.
Numerical Study of Circular Hydraulic Jump Using Volume-of-Fluid Method
Journal of Fluids Engineering, 2011
When a vertical liquid jet impacts on a solid and horizontal surface, the liquid starts spreading radially on the surface, until a sudden increase in the fluid height occurs and a circular hydraulic jump (CHJ), easily seen in the kitchen sink, is formed. In this study, the formation of CHJ is numerically simulated by solving the flow governing equations, continuity and momentum equations, along with an equation to track the free surface advection using the volume-of-fluid (VOF) method and Youngs’ algorithm. The numerical model is found to be capable of simulating the jump formation and its different types. Extensive comparisons are performed between the model results and those of the available experiments and modified Watson’s theory. The model is shown to accurately predict the jump location and its behavior. Also a parametric study for the effects of different parameters including volumetric flow rate, downstream height, viscosity and gravity on the jump radius, and its characteri...
Instabilities and elastic recoil of the two-fluid circular hydraulic jump
Experiments in Fluids, 2014
The two-fluid circular hydraulic jump, also called ''rinsing flow,'' is a common process where a jet of one liquid impinges upon a layer of a second liquid. We present an experimental analysis of rinsing flows using a high-speed camera and model fluids to decouple the effect of shear-thinning and elasticity. Varying the rheology of the coating fluid produced several types of instabilities at both the air-liquid interface and liquid-liquid interface. Layered ''stepped jumps'' and ''crowning'' on the rim of the jumps were both suppressed by fluid elasticity, while Saffman-Taylor fingering patterns showed strong dependence on both shear-thinning and normal stresses. In addition, the hydraulic jump evolution was quantitatively determined using a laser triangulation technique, and ''recoil'' of the jump front resulting from fluid elasticity was observed. Our work shows that the non-Newtonian two-fluid circular hydraulic jump is very complex, and the instabilities that arise also introduce additional complications when developing theoretical models.
Circular Hydraulic Jumps Triggered by Boundary Layer Separation
Journal of Colloid and Interface Science, 2001
When a high-flow-rate circular jet impinges vertically on a horizontal plane, it flows out radially and then undergoes a distinctive hydraulic jump on the plane because of boundary layer separation induced by hydrostatic back pressure. The jump radius is shown to be 0.37 a Re 1/3 −1/8 , where = (ga 3 /ν 2 ) Re −7/3 is a modified Froude number, Re = (Q/aν) is the jet Reynolds number, a is the jet radius, and Q the liquid flow rate, which is favorably compared to experimental data in the limit of small . When exceeds 3.0 × 10 −4 at low flow rates, the jump radius decreases below a minimum in the film depth and our experiments detect a different jump mechanism that may be triggered by capillary pressure rather than hydrostatic pressure. C 2001 Academic Press
Circular hydraulic jumps: where does surface tension matter?
Journal of Fluid Mechanics, 2022
Recently, an unusual scaling law has been observed in circular hydraulic jumps and has been attributed to a supposed missing term in the local energy balance of the flow (Bhagat et al., J. Fluid Mech., vol. 851, 2018, R5). In this paper, we show that – though the experimental observation is valuable and interesting – this interpretation is presumably not the right one. When transposed to the case of an axial sheet formed by two impinging liquid jets, the assumed principle leads in fact to a velocity distribution in contradiction with the present knowledge for this kind of flow. We show here how to correct this approach by maintaining consistency with surface tension thermodynamics: for Savart–Taylor sheets, when adequately corrected, we recover the well-known 1/r1/r1/r liquid thickness with a constant and uniform velocity dictated by Bernoulli's principle. In the case of circular hydraulic jumps, we propose here a simple approach based on Watson's description of the flow in the ...
The Impingement of a Normal Liquid Jet on a Horizontal Surface
Spanish Journal of Agricultural …, 2009
In this study, the impingement of a vertical liquid jet on a solid horizontal surface which leads to the formation of a circular hydraulic jump (CHJ) is numerically simulated by using the Volume-of-Fluid (VOF) method. The results show that increasing the volumetric flow rate will increase the radius of the jump which is confirmed by the experimental observations. Also, the numerical results are compared with the CHJ observed in experiments and that of the theory.