Conditions for the Rupture of a Lubricating Film. Part I: Theoretical Model

1970 ◽  
Vol 92 (3) ◽  
pp. 451-456 ◽  
Author(s):  
J. C. Coyne ◽  
H. G. Elrod
Keyword(s):  
Thin Liquid Film ◽  
Tangential Velocity ◽  
Two Dimensional ◽  
Newtonian Flow ◽  
Moving Plate ◽  
Vapor Interface ◽  
Stagnation Points ◽  
Lubricating Film ◽  
Principal Assumption ◽  
Good Agreement

The shape of the film-vapor interface is found for a thin liquid film separating from a stationary surface and being swept away on an opposing moving surface. The analysis is for two-dimensional Newtonian flow, and includes the effects of gravity, inertia, and surface tension. The principal assumption is that of a quadratic tangential velocity distribution across the film. The solution shows that the entire separation phenomenon is completed in a distance of about one plate clearance from the stagnation point. Stagnation points occur on the vapor-liquid interface at the separation point and at a film height of 3h∞ (three times the film height on the moving plate far downstream). For a fixed separation height, the asymptotic film thickness h∞ is shown as a function of three dimensionless parameters. The results are in good agreement with published experimental data.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

scholarly journals Development of Two-Dimensional Non-Hydrostatic Wave Model Based on Central-Upwind Scheme

2020 ◽  
Vol 8 (7) ◽  
pp. 505
Author(s):  
Gangfeng Wu ◽  
Ying-Tien Lin ◽  
Ping Dong ◽  
Kefeng Zhang
Keyword(s):  
Hydrostatic Pressure ◽  
Large Scale ◽  
Wave Model ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Practical Engineering ◽  
Hydrostatic Model ◽  
Good Agreement ◽  
Biconjugate Gradient

In this study, a two-dimensional depth-integrated non-hydrostatic wave model is developed. The model solves the governing equations with hydrostatic and non-hydrostatic pressure separately. The velocities under hydrostatic pressure conditions are firstly obtained and then modified using the biconjugate gradient stabilized method. The hydrostatic front approximation (HFA) method is used to deal with the wave breaking issue, and after the wave breaks, the non-hydrostatic model is transformed into the hydrostatic shallow water model, where the non-hydrostatic pressure and vertical velocity are set to zero. Several analytical solutions and laboratory experiments are used to verify the accuracy and robustness of the developed model. In general, the numerical simulations are in good agreement with the theoretical or experimental results, which indicates that the model is able to simulate large-scale wave motions in practical engineering applications.

scholarly journals A space structural mechanics model of silicene

2020 ◽  
Vol 234 (1-2) ◽  
pp. 3-10
Author(s):  
Mohsen Motamedi
Keyword(s):  
Natural Frequencies ◽  
Strain Curve ◽  
Structural Mechanics ◽  
Dynamics Simulation ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Stress Strain Curve ◽  
Beam Elements ◽  
Mechanics Model ◽  
Good Agreement

The two-dimensional nanostructures such as graphene, silicene, germanene, and stanene have attracted a lot of attention in recent years. Many studies have been done on graphene, but other two-dimensional structures have not yet been studied extensively. In this work, a molecular dynamics simulation of silicene was done and stress–strain curve of silicene was obtained. Then, the mechanical properties of silicene were investigated using the proposed structural molecular mechanics method. First, using the relations governing the force field and the Lifson–Wershel potential function and structural mechanics relations, the coefficients for the BEAM elements was determined, and a structural mechanics model for silicene was proposed. Then, a silicene sheet with 65 Å × 65 Å was modeled, and Young’s modulus of silicene was obtained. In addition, the natural frequencies and mode shapes of silicene were calculated using finite element method. The results are in good agreement with reports by other papers.

scholarly journals Distance mapping applied to four well-known planetary nebulae and a nova shell

2020 ◽  
Vol 492 (3) ◽  
pp. 4097-4111 ◽  
Author(s):  
Sebastian Gómez-Gordillo ◽  
Stavros Akras ◽  
Denise R Gonçalves ◽  
Wolfgang Steffen
Keyword(s):  
Supernova Remnants ◽  
Tangential Velocity ◽  
Planetary Nebulae ◽  
Mapping Technique ◽  
Shape Models ◽  
Data Release ◽  
Astrophysical Objects ◽  
Kinematic Models ◽  
Distance Mapping ◽  
Good Agreement

ABSTRACT Accurate distance estimates of astrophysical objects such as planetary nebulae (PNe), and nova and supernova remnants, among others, allow us to constrain their physical characteristics, such as size, mass, luminosity, and age. An innovative technique based on the expansion parallax method, the so-called distance mapping technique (DMT), provides distance maps of expanding nebulae as well as an estimation of their distances. The DMT combines the tangential velocity vectors obtained from 3D morpho-kinematic models and the observed proper motion vectors to estimate the distance. We applied the DMT to four PNe (NGC 6702, NGC 6543, NGC 6302, and BD+30 3639) and one nova remnant (GK Persei) and derived new distances in good agreement with previous studies. New simple morpho-kinematic shape models were generated for NGC 6543, NGC 6302, and NGC 6702, whereas for BD+30 3639 and GK Persei published models were used. We demonstrate that the DMT is a useful tool to obtain distance values of PNe, in addition to revealing kinematically peculiar regions within the nebulae. Distances are also derived from the trigonometric Gaia parallaxes. The effect of the non-negligible parallax offset in the second Gaia data release is also discussed.

Numerical Investigation of EHD Conduction Pumping of Liquid Film With Phase-Change

2007 ◽  
Author(s):  
Miad Yazdani ◽  
Jamal Seyed-Yagoobi
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Phase Change ◽  
Flow System ◽  
Thin Liquid Film ◽  
Finite Thickness ◽  
Constant Heat Flux ◽  
Two Dimensional ◽  
Enhanced Heat Transfer ◽  
Constant Heat

Electrohydrodynamic (EHD) conduction pumping is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes, generated by the process of dissociation of the neutral electrolytic species and recombination of the generated ions. This paper numerically investigates the EHD conduction pumping of a thin liquid film in the presence of phase change. The flow system comprises a liquid film flowing over a two-dimensional flat plate while the vapor phase extended far beyond the interface to result in almost motionless vapor. The channel is separated into four different sections: the entrance, electrode, evaporation, and downstream sections. The entrance, electrode and downstream regions are adiabatic while a constant heat flux is applied in the evaporation side. The concept of EHD conduction pumping of liquid film in the presence of phase change is demonstrated in this paper. The enhanced heat transfer due to conduction pumping is evaluated.

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