scholarly journals Construction of basic functions for problems of fluid oscillations in a tank

2019 ◽  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Surface ◽  
Singular Integral Equations ◽  
Spherical Shape ◽  
Free Liquid Surface ◽  
Surface Shape ◽  
Slight Rise ◽  
Oscillation Frequencies ◽  
The Impact

Considerable number of studies and publications is devoted to issues of dynamic behavior of liquids, the impact on the surface tension of a liquid in partially filled tanks in particular. The study of liquid vibrations in partially fluid-filled cylindrical containers with the presence of a free surface is an important technical task. The influence of the free surface curvature of the tank filler on the oscillation frequency is taken into account. It is assumed that the liquid is incompressible and inviscid, and its motion is irrotational. The method to solve a boundary value problem for determining fluid oscillations in a reservoir has been developed, and an integral presentation of an unknown velocity potential is proposed. The geometrical characteristics of the free liquid surface have been determined. It is taken into account that the free liquid surface deviates from the equilibrium position and assumes a spherical shape. A system of singular integral equations has been obtained for unknown values of the potential and flow. The method of boundary elements with constant approximation of an unknown density on the elements has been used to solve the system numerically. The oscillation frequencies for the zero harmonic are determined in accordance with the level of the free-surface elevation. It has been determined that the deviation of the free surface shape from the flat and even a slight rise in the free surface level leads to noticeable changes in the vibration frequencies. The vibrational modes obtained in the study mostly coincide with the modes for a flat free surface and can serve as the basic system of functions in the studies of free and forced fluid vibrations in tanks, as well as, in the study of the intrinsic and forced sloshing in the reservoirs provided surface tension is taken into account.

scholarly journals Splash jet generated by collision of two liquid wedges

2013 ◽  
Vol 737 ◽  
pp. 132-145 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Hodograph Method ◽  
Pressure Distributions ◽  
Wide Range ◽  
Self Similar Solution ◽  
Gravity Effects ◽  
Self Similar ◽  
The Impact ◽  
Analytical Expressions

AbstractA complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined.

Free Surface Effects on Normal Stress Measurements in Cone and Plate Flow

2007 ◽  
Vol 17 (3) ◽  
pp. 36494-1-36494-6 ◽  
Author(s):  
David C. Venerus
Keyword(s):  
Free Surface ◽  
Stress Field ◽  
Normal Stress ◽  
Spherical Shape ◽  
Normal Stress Difference ◽  
Surface Shape ◽  
Stress Difference ◽  
Stress Measurements ◽  
Free Surface Shape ◽  
Normal Stress Differences

Abstract The effects of free surface shape on normal stress difference measurements in cone and plate flow are investigated. The analysis shows that the stress field is significantly altered by deviations of the free surface from an ideal (spherical) shape. For the cone and partitioned plate technique, it is shown how modest deviation from a spherical free surface shape can lead to errors of roughly 10% in the measured normal stress differences.

scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

Low Reynolds Number Film Flow Down a Three-Dimensional Bumpy Surface

2005 ◽  
Vol 127 (6) ◽  
pp. 1122-1127 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Free Surface ◽  
Film Flow ◽  
Three Dimensional ◽  
Surface Shape ◽  
Maximal Flow ◽  
Free Surface Shape ◽  
Complex Boundary ◽  
First Time

The slow film flow down a doubly periodic bumpy surface is studied for the first time. Perturbations on the primary variables and the complex boundary conditions lead to a system of successive equations. The secondary flow and the free surface shape depend on the wavelength of the bumps and a surface tension-inclination parameter. There exists an optimum aspect ratio of the protuberances for maximal flow rate.

scholarly journals Bulging Modes of Circular Bottom Plates in Rigid Cylindrical Containers Filled with a Liquid

1997 ◽  
Vol 4 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Marco Amabili
Keyword(s):  
Free Surface ◽  
Liquid Surface ◽  
Dynamic Pressure ◽  
Ritz Method ◽  
Free Vibrations ◽  
Free Liquid Surface ◽  
Mode Shapes ◽  
Bottom Plate ◽  
Free Surface Waves ◽  
Theoretical Approaches

In this article the free vibrations of the bottom plate of an otherwise rigid circular cylindrical tank filled with liquid are studied, considering only the bulging modes (when the amplitude of the plate displacement is predominant with respect to that of the free surface). The tank axis is vertical, thus the free liquid surface is orthogonal to the tank axis. The liquid is assumed to be inviscid, and the contribution of the free surface waves to the dynamic pressure on the free liquid surface is neglected. Wet and dry mode shapes of the plate are assumed to be the same, so that the natural frequencies are obtained by using the nondimensionalized added virtual mass incremental (NA VMI) factors and the modal properties of dry plates. This simplifies computations compared to other existing theoretical approaches. NAVMI factors express the nondimensionalized ratio between the reference kinetic energy of the liquid and that of the plate and have the advantage that, due to their nondimensional form, they can be computed once and for all. Numerical results for simply supported and clamped bottom plates, as well as for supported plates with an elastic moment edge constraint are given. For more accurate results, and to exceed the limits of the assumed modes approach, the Rayleigh-Ritz method is applied and results are compared to those obtained by using the NAVMI factors and other existing methods in the literature.

The Impact of Liquid Surface Tension on Fabric Drying Efficiency

2012 ◽  
Vol 441 ◽  
pp. 613-618 ◽  
Author(s):  
Ji Li Tu ◽  
Chun Jie Qian ◽  
Hua Yun Ge ◽  
Ji Ping Wang ◽  
Jin Qiang Liu
Keyword(s):  
Surface Tension ◽  
Water Retention ◽  
Liquid Surface ◽  
Lower Surface ◽  
Liquid Surface Tension ◽  
Lower Surface Tension ◽  
Dehydration Processes ◽  
Drying Efficiency ◽  
The Impact ◽  
The Relationship

This study presents an experimental investigation of the relationship between liquid surface tension and fabrics water retention in dehydration processes such as centrifuging, line drying and heat drying. Selected surfactants were used to prepare wash baths with different surface tension, and dehydrating experiments of cotton fabric after immersion in above bath were conducted. The results showed that lower surface tension is beneficial to reducing fabrics water retention by centrifuging and improving line drying efficiency and heat drying efficiency. It was assumed that water with low surface tension is easy to drop down or separate from fabric, thus improving the de-watering and drying efficiency.

Numerical Simulation of Electrostatic Atomization in Spindle Mode

2010 ◽  
Author(s):  
Mohammad Passandideh Fard ◽  
Mohammad Reza Mahpeykar ◽  
Sajad Pooyan ◽  
Mortaza Rahimzadeh
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Stable State ◽  
Surface Shape ◽  
Liquid Jet ◽  
Perfect Conductor ◽  
Electric Force ◽  
Electrostatic Atomization ◽  
Liquid Free Surface

The behavior of a liquid jet in an electrostatic field is numerically simulated. The simulations performed correspond to a transient liquid jet leaving a capillary tube maintained at a high electric potential. The surface profile of the deforming jet is defined using the VOF scheme and the advection of the liquid free surface is performed using Youngs’ algorithm. Surface tension force is treated as a body force acting on the free surface using continuum surface force (CSF) method. To calculate the effect of the electric field on the shape of the free surface, the electrostatic potential is solved first. Next, the surface density of the electric charge and the electric field intensity are computed, and then the electric force is calculated. Liquid is assumed to be a perfect conductor, thus the electric force only acts on the liquid free surface and is treated similar to surface tension using the CSF method. To verify the simulation results, a simplified case of electrowetting phenomenon is simulated and free surface shape in stable state is compared with experimental results. Then the electrostatic atomization in spindle mode is simulated and the ability of the developed code to simulate this process is demonstrated.

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