The radial spread of a liquid jet over a horizontal plane

1964 ◽  
Vol 20 (3) ◽  
pp. 481-499 ◽  
Author(s):  
E. J. Watson
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Thin Layer ◽  
Hydraulic Jump ◽  
Horizontal Plane ◽  
Boundary Layer Theory ◽  
Liquid Jet ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Radial Spread

When a smooth jet of water falls vertically on to a horizontal plane, it spreads out radially in a thin layer bounded by a circular hydraulic jump, outside which the depth is much greater. The motion in the layer is studied here by means of boundary-layer theory, both for laminar and for turbulent flow, and relations are obtained for the radius of the hydraulic jump. These relations are compared with experimental results. The analogous problems of two-dimensional flow are also treated.

Positive Solutions of the Falkner–Skan Equation Arising in the Boundary Layer Theory

2008 ◽  
Vol 51 (3) ◽  
pp. 386-398 ◽  
Author(s):  
K. Q. Lan ◽  
G. C. Yang
Keyword(s):  
Boundary Layer ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Viscous Incompressible Fluid ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
New Techniques ◽  
Numerical Result ◽  
Two Dimensional Flow ◽  
Equivalence Result

AbstractThe well-known Falkner–Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to λπ/2, where λ ∈ ℝ is a parameter involved in the equation. It is known that there exists λ* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each λ ≥ λ* and has no positive solutions for λ < λ*. The known numerical result shows λ* = –0.1988. In this paper, λ* ∈ [–0.4,–0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner–Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner–Skan equation.

The response of a turbulent boundary layer to lateral divergence

1979 ◽  
Vol 94 (2) ◽  
pp. 243-268 ◽  
Author(s):  
A. J. Smits ◽  
J. A. Eaton ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Structural Parameters ◽  
Axial Flow ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Transition Section ◽  
Two Dimensional Flow ◽  
Made In

Measurements have been made in the flow over an axisymmetric cylinder-flare body, in which the boundary layer developed in axial flow over a circular cylinder before diverging over a conical flare. The lateral divergence, and the concave curvature in the transition section between the cylinder and the flare, both tend to destabilize the turbulence. Well downstream of the transition section, the changes in turbulence structure are still significant and can be attributed to lateral divergence alone. The results confirm that lateral divergence alters the structural parameters in much the same way as longitudinal curvature, and can be allowed for by similar empirical formulae. The interaction between curvature and divergence effects in the transition section leads to qualitative differences between the behaviour of the present flow, in which the turbulence intensity is increased everywhere, and the results of Smits, Young & Bradshaw (1979) for a two-dimensional flow with the same curvature but no divergence, in which an unexpected collapse of the turbulence occurred downstream of the curved region.

Measurement of Recovery Factors and Friction Coefficients for Supersonic Flow of Air in a Tube: 2—Results Based on a Two-Dimensional Flow Model for Entrance Region

1952 ◽  
Vol 19 (2) ◽  
pp. 185-194
Author(s):  
J. Kaye ◽  
T. Y. Toong ◽  
R. H. Shoulberg
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Variable Mass ◽  
Entrance Region ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Change Of State ◽  
Two Dimensional Flow

Abstract The first part of a program to obtain reliable data on the rate of heat transfer to air moving at supersonic speeds in a tube has been devoted to measurements made on adiabatic supersonic flow of air in a tube. The details of these measurements have been described in a previous paper. The calculated quantities such as the local apparent friction coefficient, recovery factor, Mach number, and so forth, were obtained from the simple one-dimensional flow model for which the properties of the stream are uniform at any section, and boundary-layer effects are ignored. The analysis of some of the same data given in the previous paper is undertaken here with the aid of a simplified two-dimensional flow model. The supersonic flow in the tube is divided into a supersonic core of variable mass with the fluid remaining in the core undergoing a reversible adiabatic change of state, and a laminar boundary layer of variable mass. The compressible laminar boundary layer increases in thickness in the direction of flow, and then undergoes a transition to a turbulent boundary layer. The two-dimensional flow model is limited here to the region where a laminar boundary layer appears to be present in the entrance region of the tube. The results of the analysis based on the two-dimensional flow model indicate that where the flow in the tube boundary layer appears to be laminar, the measured pressures and temperatures in the tube for adiabatic supersonic flow of air could have been predicted, with sufficient accuracy for engineering problems, from measured data for supersonic flow of air over a flat plate with a laminar boundary layer, and with zero pressure gradient.

Calculation of Diffuser Efficiency for Two-Dimensional Flow

1947 ◽  
Vol 14 (3) ◽  
pp. A213-A216
Author(s):  
R. C. Binder
Keyword(s):  
Boundary Layer ◽  
Incompressible Flow ◽  
Potential Flow ◽  
Layer Growth ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Check Calculation ◽  
Two Dimensional Flow ◽  
Boundary Layer Growth ◽  
Potential Velocity

Abstract A method is presented for calculating the efficiency of a diffuser for two-dimensional, steady, incompressible flow without separation. The method involves a combination of organized boundary-layer data and frictionless potential-flow relations. The potential velocity and pressure are found after the boundary-layer growth is determined by a trial-and-check calculation.

The flow past a rapidly rotating circular cylinder

1957 ◽  
Vol 242 (1228) ◽  
pp. 108-115 ◽  
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Present Theory ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Rotating Circular Cylinder ◽  
Flow Past ◽  
Separating Flow ◽  
Two Dimensional Flow ◽  
Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

On Numerical Prediction of the Stability of Hypersonic Boundary-Layer Flow Over a Row of Microcavities

2003 ◽  
Author(s):  
Vassilios Theofilis ◽  
Michel O. Deville ◽  
Peter W. Duck ◽  
Alexander Fedorov
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Flow Instability ◽  
Viscous Sublayer ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Flow Stabilization ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow

This paper is concerned with the structure of steady two–dimensional flow inside the viscous sublayer in hypersonic boundary–layer flow over a flat surface in which microscopic cavities (‘microcavities’) are embedded. Such a so–called Ultra Absorptive Coating (UAC) has been predicted theoretically [1] and demonstrated experimentally [2] to stabilize passively hypersonic boundary–layer flow. In an effort to further quantify the physical mechanism leading to flow stabilization, this paper focuses on the nature of the basic flows developing in the configuration in question. Direct numerical simulations are performed, addressing firstly steady flow inside a singe microcavity, driven by a constant shear, and secondly a model of a UAC surface in which the two–dimensional boundary layer over a flat plate and a minimum nontrivial of two microcavities embedded in the wall are solved in a coupled manner. The influence of flow– and geometric parameters on the obtained solutions is illustrated. Based on the results obtained, the limitations of currently used theoretical methodologies for the description of flow instability are identified and suggestions for the improved prediction of the instability characteristics of UAC surfaces are discussed.

The Effect of a Wall Boundary Layer on Local Mass Transfer From a Cylinder in Crossflow

1984 ◽  
Vol 106 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. J. Goldstein ◽  
J. Karni
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Tunnel Wall ◽  
Wall Boundary Layer ◽  
Naphthalene Sublimation Technique ◽  
Displacement Thickness ◽  
Two Dimensional Flow

A naphthalene sublimation technique is used to determine the circumferential and longitudinal variations of mass transfer from a smooth circular cylinder in a crossflow of air. The effect of the three-dimensional secondary flows near the wall-attached ends of a cylinder is discussed. For a cylinder Reynolds number of 19000, local enhancement of the mass transfer over values in the center of the tunnel are observed up to a distance of 3.5 cylinder diameters from the tunnel wall. In a narrow span extending from the tunnel wall to about 0.066 cylinder diameters above it (about 0.75 of the mainstream boundary layer displacement thickness), increases of 90 to 700 percent over the two-dimensional flow mass transfer are measured on the front portion of the cylinder. Farther from the wall, local increases of up to 38 percent over the two-dimensional values are measured. In this region, increases of mass transfer in the rear portion of the cylinder, downstream of separation, are, in general, larger and cover a greater span than the increases in the front portion of the cylinder.

Study on Conditional Statistics in Two-Dimensional Liquid Jet With the Second-Order Chemical Reaction

2011 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Hiroki Yasuhara ◽  
Yasuhiko Sakai ◽  
Takashi Kubo ◽  
Kouji Nagata ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Chemical Reaction ◽  
Mixture Fraction ◽  
Spectroscopic Method ◽  
Second Order ◽  
Moment Closure ◽  
Liquid Jet ◽  
Two Dimensional ◽  
Conditional Moment ◽  
Conditional Moment Closure

It is important in engineering to elucidate the mechanism of a chemical reaction in turbulent flow. But there are still few studies on reacting turbulent flow in a liquid phase. In this study, the two-dimensional liquid jet with the second-order reaction (A+B←R) is investigated. The concentrations of the species R and the conserved scalar (which is the concentration of other species independent of the above chemical reaction) are measured simultaneously by the optical fiber probe based on light absorbtion spectroscopic method. The concentrations of species A and B are obtained from the conserved scalar theory. Regarding the velocity field, the streamwise velocity is measured by the hot-film anemometer. The moment closure methods are often used for the prediction of turbulent flow. But it is difficult to apply it to the reacting turbulent flow because of the high non-linearity of the reaction rate terms. It is commonly known that the values of concentrations depend strongly on the mixture fraction (which is a conserved scalar) defined as the normalized concentration of the species which is independent of reaction. Hence, Conditional moment closure (CMC) methods are useful for the prediction of the turbulent flow with chemical reactions. In this study, conditional scalar statistics are investigated by using the conditional moment closure methods and experimental data. It is shown that the conditional averages of concentration of reactant and product species approach the equilibrium limit (which correspond to the limiting case of the fast chemical reaction) in the downstream direction and the value of the conditional scalar (mixture fraction) dissipation decreases and its distribution varies in the downstream direction and comes to show the local minimum value near the point η = ξS (which is the stoichiometric value of the mixture fraction).

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

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