scholarly journals An Analytical Two-Dimensional Linearized Droplet Shape Model for Combined Tangential and Normal Body Forces

2020 ◽  
Vol 4 (3) ◽  
pp. 35 ◽  
Author(s):  
Margaritis Kostoglou ◽  
Thodoris D. Karapantsios
Keyword(s):  
Present Model ◽  
Two Dimensional ◽  
Shape Features ◽  
Droplet Spreading ◽  
Shape Model ◽  
Droplet Shape ◽  
Final Model ◽  
Droplet Behavior ◽  
Applied Forces ◽  
Range Of Values

In view of emerging research on forced wetting under complex applied forces, a simple model for a droplet shape evolution is developed here. In particular, the model refers to droplet spreading under quasisteady conditions. The corresponding linearized two-dimensional Young–Laplace equation is solved analytically resulting in a system of two equations that relates the droplet shape features to each other. Despite its simplicity, the final model produces a wealth of droplet behaviors when combined with the physical requirement that the contact angle should be within a particular range of values. Indicative results of the droplet behavior under several forces scenarios are examined here exhibiting why the present model is useful for designing experimental campaigns on forced spreading.

Droplet Impacting on a Hydrophobic Surface: Influence of Surface Wetting State on Droplet Behavior

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Abba Abdulhamid Abubakar ◽  
Bekir Sami Yilbas ◽  
Ghassan Hassan ◽  
Hussain Al-Qahtani ◽  
Haider Ali ◽  
...  
Keyword(s):  
Contact Angle ◽  
Hydrophobic Surface ◽  
Transition Time ◽  
Restitution Coefficient ◽  
Surface Wetting ◽  
Local Pressure ◽  
Droplet Spreading ◽  
Droplet Dynamics ◽  
Droplet Shape ◽  
Droplet Behavior

Abstract Water droplet impacting onto a hydrophobic surface is considered and the influence of the surface wetting state on the droplet dynamics is examined. Pressure variation in the impacting droplet is predicted numerically using the level set model. The droplet spreading and the retraction on the hydrophobic surface are assessed for various wetting states of the hydrophobic surface. Experiment is carried out to validate the predictions of the droplet shape and the restitution coefficient. It is found that predictions of impacting droplet shape and the restitution coefficient agree with those obtained from the experiment. The local pressure peaks formed in the droplet fluid, particularly in the retraction period, causes alteration of the droplet vertical height and the shape. Droplet spreading is influenced by the wetting state of the hydrophobic surface; hence, increasing contact angle of the hydrophobic surface lowers the spreading diameter of the droplet on the surface. The transition time of the droplet changes with the wetting state of the hydrophobic surface such that increasing droplet contact angle reduces the transition time of the droplet on the surface. The droplet remains almost round after the first bounding for large contact angle hydrophobic surface.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

Thermo-Elasto-Hydro-Dynamic Modeling of Hydrostatic Seals in Reactor Coolant Pumps

2005 ◽  
Author(s):  
Erwan Galenne ◽  
Isabelle Pierre-Danos
Keyword(s):  
Pressure Drop ◽  
Present Model ◽  
Operating Mode ◽  
Hysteretic Behavior ◽  
Two Dimensional ◽  
Critical Component ◽  
Dimensional Approach ◽  
Reactor Coolant ◽  
Energy Company ◽  
Injection Temperature

The French energy company EDF has experienced in the last years some problems in managing reactor coolant pumps (RCP) seals in operation. That’s why a thermo-elasto-hydrodynamical model of the seal has been developed. The present model is a steady two-dimensional approach so as to characterize the normal operating mode of the seal. Numerical results are successfully compared to experimental results of leak-flow rate. The influence of pressure drop and injection temperature is described. The influence of the conicity of the faceplates is underlined. The friction is introduced in the model in order to reproduce the hysteretic behavior of the seal. The development of this model leads to a better knowledge of the behavior of a critical component.

Numerical Investigation of a Liquid Droplet Impinging on a Heated Surface

2009 ◽  
Author(s):  
Andres Diaz ◽  
Alfonso Ortega ◽  
Ryan Anderson
Keyword(s):  
Heat Transfer ◽  
Numerical Investigation ◽  
Fundamental Problem ◽  
Water Drop ◽  
Liquid Droplet ◽  
Heated Surface ◽  
Heat Removal ◽  
Droplet Spreading ◽  
Droplet Shape ◽  
Spreading Dynamics

Previous studies, most of them experimental, reveal that the cooling effectiveness of a water drop impinging on a heated surface depends on the wall temperature, droplet shape and velocity. All previous studies focus on the behavior of a droplet falling in a quiescent environment, such as still air. Evidence in the literature also shows that gas assisted droplet sprays, in which a gas phase propels the droplets, are more efficient in heat removal than sprays consisting of droplets alone. It is conjectured that this is due to an increase in the maximum droplet spreading diameter upon impact, a thinner film, and consequently an increase in the overall heat transfer coefficient. Recent experiments in the author’s group [1, 2] show that the carrier gas jet strongly influences droplet spreading dynamics by imposing normal and shear forces on the liquid surface. The heat transfer is greatly augmented in the process, compared to a free falling droplet. To date, there has been no fundamental investigation of the physics of gas assisted spray cooling. To begin to understand the complicated process, this paper reports on a fundamental problem of a single liquid droplet that impinges on a heated surface. This paper contributes a numerical investigation of the problem using the volume of fluid (VOF) technique to capture droplet spreading dynamics and heat transfer in a single drop event. The fluid mechanics is investigated and compared to the experimental data. The greatest uncertainty in the simulation is in the specification of the contact angle of the advancing or receding liquid front, and in capturing the onset of the three-dimensional fingering phenomena.

Matrix Representation and Prediction of Three-Dimensional Cutting Forces

1977 ◽  
Vol 99 (4) ◽  
pp. 828-834 ◽  
Author(s):  
J. A. Kirk ◽  
D. K. Anand ◽  
C. McKindra
Keyword(s):  
Cutting Forces ◽  
Metal Cutting ◽  
Present Model ◽  
Cutting Tool ◽  
Matrix Representation ◽  
Three Dimensional ◽  
Experimental Results ◽  
Analytical Models ◽  
Two Dimensional ◽  
The Matrix

Matrix geometry techniques are applied to predicting three-dimensional cutting forces. In the present model a specific cutting plane is located and two-dimensional metal cutting theory is applied. Force predictions in this plane are then matrix transformed to three orthogonal forces acting on the cutting tool. Experimental results show the matrix model accurately predicts three-dimensional cutting forces in turning of long slender workpieces. Experimental results are also compared to other analytical models described in the literature.

Two-Dimensional Model for Wave-Induced Pore Pressure Accumulation in Marine Sediments

2013 ◽  
Author(s):  
Hongyi Zhao ◽  
Dong-Sheng Jeng ◽  
Huijie Zhang ◽  
Jisheng Zhang
Keyword(s):  
Pore Pressure ◽  
Marine Sediments ◽  
Wave Motion ◽  
Present Model ◽  
Two Dimensional ◽  
New Model ◽  
One Dimensional ◽  
Wave Cycle ◽  
Previous Solution ◽  
Wave Induced

In this paper, a two-dimensional (2D) porous model is established to investigate the predication of the wave-induced pore pressure accumulations in marine sediments. In the new model, the VARANS equation is used as the governing equation for the wave motion, while the Biot’s consolidation theory is used for porous seabed. The present model is verified with the previous experimental data [1] and provides a better prediction of pore pressure accumulation than the previous solution [2]. With the new model, a 2D liquefied zone is formed at the beginning of the process, and then gradually move down. After a certain wave cycle (for example, 30 wave cycles in the numerical example), the liquefaction zone will become one-dimensional (1D) and continuously move down and eventually approaches to a constant. Numerical results also conclude the maximum liquefaction depth increases as wave height increases and in shallow water.

Coherence Length in a Two-Dimensional Anisotropic Model of Superconductivity

1998 ◽  
Vol 12 (32) ◽  
pp. 3475-3483 ◽  
Author(s):  
L. Bujkiewicz ◽  
L. Jacak
Keyword(s):  
Coherence Length ◽  
Order Parameter ◽  
Cooper Pair ◽  
Mean Square ◽  
Two Dimensional ◽  
Anisotropic Model ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Range Of Values

The coherence length as a mean-square radius of a Cooper pair is calculated for various forms of the anisotropic order parameter. A wide range of values of this quantity is obtained and the smallest values are of the order of magnitude of a few lattice spacings.

The motion and stability of a vortex array above a pulsed surface

1993 ◽  
Vol 247 ◽  
pp. 231-245 ◽  
Author(s):  
E. Acton ◽  
M. R. Dhanak
Keyword(s):  
Flow Problem ◽  
Active Flow Control ◽  
Two Dimensional ◽  
Source Strength ◽  
Streamwise Direction ◽  
Infinite Array ◽  
Incompressible Flow Problem ◽  
Active Flow ◽  
Range Of Values ◽  
Uniform Stream

A model inviscid and incompressible flow problem is studied in which an infinite array of equi-spaced identical rectilinear line vortices moves in a uniform stream over a wall in which is embedded an equi-spaced array of discrete line sources of variable strength. It is shown that for a suitable choice of source spacing and strength, a flow that is periodic both in time and in the streamwise direction is possible. The flow is shown to be stable to small two-dimensional disturbances for a range of values of vortex height above the wall and source strength. The implications for the corresponding viscous problem and active flow control are discussed.

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