scholarly journals 4. On the Equilibrium of Vapour at a Curved Surface of Liquid

1872 ◽  
Vol 7 ◽  
pp. 63-68 ◽  
Author(s):  
William Thomson
Keyword(s):  
Free Surface ◽  
Curved Surface ◽  
Solid Boundary ◽  
Closed Vessel ◽  
Bounding Surface ◽  
Capillary Tubes ◽  
Saturated Vapour ◽  
Different Levels

In a closed vessel containing only a liquid and its vapour, all at one temperature, the liquid rests, with its free surface raised or depressed in capillary tubes and in the neighbourhood of the solid boundary, in permanent equilibrium according to the same law of relation between curvature and pressure as in vessels open to the air. The permanence of this equilibrium implies physical equilibrium between the liquid and the vapour in contact with it at all parts of its surface. But the pressure of the vapour at different levels differs according to hydrostatic law. Hence the pressure of saturated vapour in contact with a liquid differs according to the curvature of the bounding surface, being less when the liquid is concave, and greater when it is convex.

Computation of Turbulent Flow in a Thin Liquid Layer of Fluid Involving a Hydraulic Jump

1991 ◽  
Vol 113 (3) ◽  
pp. 411-418 ◽  
Author(s):  
M. M. Rahman ◽  
A. Faghri ◽  
W. L. Hankey
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Grid Method ◽  
Optimization Procedure ◽  
Solid Boundary ◽  
Plane Flow ◽  
Recirculating Flow ◽  
Flow Configurations ◽  
Rapid Deceleration ◽  
Predictor Corrector

Numerically computed flow fields and free surface height distributions are presented for the flow of a thin layer of liquid adjacent to a solid horizontal surface that encounters a hydraulic jump. Two kinds of flow configurations are considered: two-dimensional plane flow and axisymmetric radial flow. The computations used a boundary-fitted moving grid method with a k-ε model for the closure of turbulence. The free surface height was determined by an optimization procedure which minimized the error in the pressure distribution on the free surface. It was also checked against an approximate procedure involving integration of the governing equations and use of the MacCormack predictor-corrector method. The computed film height also compared reasonably well with previous experiments. A region of recirculating flow as found to be present adjacent to the solid boundary near the location of the jump, which was caused by a rapid deceleration of the flow.

Evaluation of the Solid Boundary Treatment Methods in SPH

2018 ◽  
Vol 01 (02) ◽  
pp. 1840002 ◽  
Author(s):  
Shilong Liu ◽  
Ioan Nistor ◽  
Majid Mohammadian
Keyword(s):  
Free Surface ◽  
Free Water ◽  
Treatment Method ◽  
Free Surface Flows ◽  
Solid Boundary ◽  
Surface Flows ◽  
Boundary Treatment ◽  
Particle Hydrodynamics ◽  
Source Models ◽  
Definition Of

The smoothed particle hydrodynamics (SPH) method has been proved as a powerful algorithm for fluid mechanics, especially in the simulation of free surface flows with high speeds or drastic impacts. The solid boundary treatment method is important for the accuracy and stability of the numerical results, as the support domain of fluid particles is truncated near the vicinity of the boundary. This paper presents two commonly used methods for simulating a solid boundary in SPH simulations. Emphasis is placed on the description of the methods, definition of the boundary particles’ parameters, and discussion of their advantages and shortcomings. The classical dam break simulation is conducted using self-developed code and open source models such as DualSPHysics and PySPH in order to investigate the effects of the boundary methods. The results show that methods based on dynamic boundary particles can simulate the free water surface well with a good agreement with experimental results. The conclusions can also be used in research for boundary implementation methods for practical ocean and coastal engineering problems with free surface flows.

scholarly journals Early-time free-surface flow driven by a deforming boundary

2015 ◽  
Vol 767 ◽  
pp. 811-841 ◽  
Author(s):  
C. Frederik Brasz ◽  
Craig B. Arnold ◽  
Howard A. Stone ◽  
John R. Lister
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Liquid Layer ◽  
Early Time ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Solid Boundary ◽  
Jet Formation ◽  
Domain Perturbation ◽  
Quiescent Liquid

AbstractWhen a solid boundary deforms rapidly into a quiescent liquid layer, a flow is induced that can lead to jet formation. An asymptotic analytical solution is presented for this flow, driven by a solid boundary deforming with dimensionless vertical velocity $V_{b}(x,t)={\it\epsilon}(1+\cos x)\,f(t)$, where the amplitude ${\it\epsilon}$ is small relative to the wavelength and the time dependence $f(t)$ approaches 0 for large $t$. Initially, the flow is directed outwards from the crest of the deformation and slows with the slowing of the boundary motion. A domain-perturbation method is used to reveal that, when the boundary stops moving, nonlinear interactions with the free surface leave a remnant momentum directed back towards the crest, and this momentum can be a precursor to jet formation. This scenario arises in a laser-induced printing technique in which an expanding blister imparts momentum into a liquid film to form a jet. The analysis provides insight into the physics underlying the interaction between the deforming boundary and free surface, in particular, the dependence of the remnant flow on the thickness of the liquid layer and the deformation amplitude and wavelength. Numerical simulations are used to show the range of validity of the analytical results, and the domain-perturbation solution is extended to an axisymmetric domain with a Gaussian boundary deformation to compare with previous numerical simulations of blister-actuated laser-induced forward transfer.

Numerical Simulation of Violent Impinging Jet Flows with Improved SPH Method

2016 ◽  
Vol 13 (04) ◽  
pp. 1641001 ◽  
Author(s):  
J. R. Shao ◽  
S. M. Li ◽  
M. B. Liu
Keyword(s):  
Free Surface ◽  
Pressure Field ◽  
Surface Condition ◽  
Time History ◽  
Impinging Jet ◽  
Jet Flows ◽  
Solid Boundary ◽  
Sph Method ◽  
Pressure Time ◽  
Kernel Gradient Correction

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for simulating violent water impinging jet flow problems. The presented SPH method involves three major modifications on the traditional SPH method, (1) The kernel gradient correction (KGC) and density correction are used to improve the computational accuracy and obtain smoothed pressure field, (2) a coupled dynamic solid boundary treatment (SBT) is used to remove the numerical oscillation near the solid boundary and ensure no penetration condition, (3) a free surface condition, which is obtained from the summation of kernel function and volume, is used to describe the water jet accurately. Different cases about violent impinging jet flows are simulated. The influences of impact velocity and angles are investigated. It is demonstrated that the presented SPH method has very good performance with accurate impinging jet patterns and pressure field distribution. It is also found that the pressure time histories of observation points are greatly influenced by the rarefaction wave from surrounding air. Closer distance from free surface can lead to quicker decay of the pressure time history.

scholarly journals Entropy Generation in Cu-Al2O3-H2O Hybrid Nanofluid Flow over a Curved Surface with Thermal Dissipation

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 941 ◽  
Author(s):  
Muhammad Idrees Afridi ◽  
Tawfeeq Abdullah Alkanhal ◽  
Muhammad Qasim ◽  
Iskander Tlili
Keyword(s):  
Differential Equations ◽  
Entropy Generation ◽  
Numerical Results ◽  
Curvilinear Coordinates ◽  
Curved Surface ◽  
Thermal Dissipation ◽  
Solid Boundary ◽  
Radius Of Curvature ◽  
Physical Parameters ◽  
Hybrid Nanofluid

Heat transfer and entropy generation in a hybrid nanoliquid flow caused by an elastic curved surface is investigated in the present article. To examine the effects of frictional heating on entropy generation, the energy dissipation function is included in the energy equation. The Tiwari and Dass model for nanofluid is used by taking water as a base fluid. A new class of nanofluid (hybrid nanofluid) with two kinds of nanoparticles, Copper (Cu) and Aluminum oxide (Al2O3), is considered. Curvilinear coordinates are used in the mathematical formulation due to the curved nature of the solid boundary. By utilizing similarity transformations, the modelled partial differential equations are converted into ordinary differential equations. Shooting and the Runge-Kutta-Fehlberg method (FRKM) have been used to solve the transformed set of non-linear differential equations. The expression for entropy generation is derived in curvilinear coordinates and computed by using the numerical results obtained from dimensionless momentum and energy equations. Comparisons of our numerical results and those published in the previous literature demonstrate excellent agreements, validating our numerical simulation. In addition, we have also conducted parametric studies and find that entropy generation and temperature suppress with increasing values of dimensionless radius of curvature. Furthermore, it is found that less entropy is generated in regular nanofluid as compare to hybrid nanofluid. To examine the influences of a set of embedding physical parameters on quantities of interest, different graphs are plotted and discussed.

Analysis of Variable Porosity, Thermal Dispersion, and Local Thermal Nonequilibrium on Free Surface Flows Through Porous Media

2004 ◽  
Vol 126 (3) ◽  
pp. 389-399 ◽  
Author(s):  
Bader Alazmi ◽  
Kambiz Vafai
Keyword(s):  
Porous Media ◽  
Free Surface ◽  
Free Surface Flows ◽  
Solid Boundary ◽  
Thermal Dispersion ◽  
Thermal Nonequilibrium ◽  
Surface Flows ◽  
Variable Porosity ◽  
Flows Through Porous Media ◽  
Local Thermal Nonequilibrium

Characteristics of momentum and energy transport for free surface flows through porous media are explored in this study. Effects of variable porosity and an impermeable boundary on the free surface front are analyzed. In addition, effects of thermal dispersion and local thermal nonequilibrium (LTNE) are also analyzed. Pertinent parameters such as porosity, Darcy number, inertia parameter, Reynolds number, particle diameter, and solid-to-fluid conductivity ratio are used to investigate the significance of the above mentioned effects. Results show that considering the effect of variable porosity is significant only in the neighborhood of the solid boundary. The range of parameters which enhance the dispersion and LTNE effects are prescribed. Finally, it is shown that adding the effect of thermal dispersion to LTNE increases the sensitivity of LTNE between the two phases.

Role of rigid boundary on the decay of turbulence generated by passive-grid for free surface flow

2020 ◽  
pp. 095440622094256 ◽  
Author(s):  
Pankaj Kumar Raushan ◽  
Santosh Kumar Singh ◽  
Koustuv Debnath
Keyword(s):  
Free Surface ◽  
Near Field ◽  
Flow Characteristics ◽  
Joint Probability ◽  
Mesh Size ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Solid Boundary ◽  
Joint Probability Distribution ◽  
Rigid Boundary

The present study aims to investigate the flow characteristics of grid-generated turbulence under the consideration of solid boundary in free surface flow. To understand the nature of isotropy and anisotropy in the flow, the turbulent intensity is evaluated at the downstream of the grid for different mesh sizes. The energy spectrums based on the Fast Fourier and marginal Hilbert–Huang transform are presented to understand the decay of energy in the associated spectral frequency domain. It is observed that the peak of energy associated with the Fourier spectrum decreases in the near-field region of the grid with the increase in mesh size of the grid. Further, to characterise the concentrated velocity fluctuations, the paper strives to analyse the joint probability distribution function and the local intermittency measure in the close and far stream of the grid. The autocorrelation functions and the magnitude of integral length scale of the stream-wise fluctuating velocity components are also presented at two different vertical levels from the solid boundary. The normalised Shannon entropy is also evaluated to characterise the degree of the orderness or disorderness in the flow due to the interaction of grid and rigid boundary.

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