Nonlinear diffusive surface waves in porous media

1997 ◽  
Vol 347 ◽  
pp. 119-139 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
JIANGANG WEN
Keyword(s):  
Experimental Data ◽  
Porous Medium ◽  
Surface Wave ◽  
Water Waves ◽  
General Equation ◽  
Numerical Solutions ◽  
Boussinesq Equations ◽  
Surface Wave Propagation ◽  
Damping Rate ◽  
Order Of Magnitude

A fully nonlinear, diffusive, and weakly dispersive wave equation is derived for describing gravity surface wave propagation in a shallow porous medium. Darcy's flow is assumed in a homogeneous and isotropic porous medium. In deriving the general equation, the depth of the porous medium is assumed to be small in comparison with the horizontal length scale, i.e. O(μ2) =O(h0/L)2[Lt ]1. The order of magnitude of accuracy of the general equation is O(μ4). Simplified governing equations are also obtained for the situation where the magnitude of the free-surface fluctuations is also small, O(ε)=O(a/h0)[Lt ]1, and is of the same order of magnitude as O(μ2). The resulting equation is of O(μ4, ε2) and is equivalent to the Boussinesq equations for water waves. Because of the dissipative nature of the porous medium flow, the damping rate of the surface wave is of the same order magnitude as the wavenumber. The tide-induced groundwater fluctuations are investigated by using the newly derived equation. Perturbation solutions as well as numerical solutions are obtained. These solutions compare very well with experimental data. The interactions between a solitary wave and a rectangular porous breakwater are then examined by solving the Boussinesq equations and the newly derived equations together. Numerical solutions for transmitted waves for different porous breakwaters are obtained and compared with experimental data. Excellent agreement is observed.

On the generation of surface waves by turbulent shear flows

1960 ◽  
Vol 7 (3) ◽  
pp. 469-478 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Energy Transfer ◽  
Surface Wave ◽  
Water Waves ◽  
Pressure Fluctuations ◽  
Normal Pressure ◽  
Turbulent Shear ◽  
Turbulent Wind ◽  
Stage Of Development ◽  
Surface Displacements ◽  
Order Of Magnitude

The model proposed by Phillips (1957) for the generation of water waves by the random fluctluations of normal pressure already present in a turbulent wind is generalized to include energy transfer associated with the interaction between surface wave and mean air flow (Miles 1957). It is found that this energy transfer may increase by an order of magnitude the surface displacements produced by a given distribution of pressure fluctuations in the principal stage of development.

Film Boiling Heat Transfer From a Sphere and a Horizontal Cylinder Embedded in a Liquid-Saturated Porous Medium

1988 ◽  
Vol 110 (4a) ◽  
pp. 961-967 ◽  
Author(s):  
J. Orozco ◽  
R. Stellman ◽  
M. Gutjahr
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Porous Medium ◽  
Theoretical Model ◽  
Layer Thickness ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
Vapor Layer

This paper analyses both theoretically and experimentally the problem of film boiling from a body embedded in a liquid-saturated porous medium. Two body geometries are investigated thoroughly: a horizontal cylinder and a sphere. The theoretical model relies on the Brinkman-extended flow model to describe the flow field inside the thin vapor layer occupying the neighborhood near the heated surface. The theoretical model also includes an improved formulation of the effective conductivity in the vicinity of the heater as a function of the vapor layer thickness and the geometry of the porous medium material. Solutions are obtained for the vapor layer thickness and the local Nusselt number as a function of angular position. Numerical solutions are also obtained for the overall heat transfer rates from the surface to the fluid for a given vapor superheat. Experimental data for a 12.70 mm stainless steel cylindrical heater embedded in a 3-mm glass particle porous medium were obtained under steady—state operation. The experimental data obtained are compared with the theoretical analysis. The comparison shows that there is a good agreement between theory and experiments. The theoretical model is also compared with the experimental data obtained by other investigators for a spherical geometry. Excellent results are obtained in such comparison.

scholarly journals Analysis of Erbium and Vanadium Diffusion in Porous Silicon Carbide

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Marina G. Mynbaeva ◽  
Evgeny L. Pankratov ◽  
Evgeniy N. Mokhov ◽  
Karim D. Mynbaev
Keyword(s):  
Experimental Data ◽  
Silicon Carbide ◽  
Porous Medium ◽  
Structure Modification ◽  
Satisfactory Description ◽  
Surface Diffusion Coefficient ◽  
Order Of Magnitude ◽  
Diffusion Rates ◽  
Porous Sic ◽  
And Diffusion

Experimental data on diffusion of erbium and vanadium in porous and nonporous silicon carbide at 1700 and 2200°C have been used for modelling diffusion in porous SiC. It is shown that the consideration of pore structure modification under annealing via vacancy redistribution allows for satisfactory description of dopant diffusion. As expected, important contribution to the diffusion in the porous medium is found to be made by the walls of the pores: in SiC, the vacancy surface diffusion coefficient on the walls appears to exceed that in the bulk of the material by an order of magnitude. When thermal treatment transforms pore channels into closed voids, pathways for accelerated diffusion cease to exist and diffusion rates in porous and nonporous SiC become similar.

scholarly journals EXTENDED BOUSSINESQ EQUATIONS FOR WAVES IN TWO POROUS LAYERS

2018 ◽  
pp. 92
Author(s):  
Changhoon Lee ◽  
Van Nghi Vu ◽  
Tae-Hwa Jung ◽  
Thanh Thu Huynh
Keyword(s):  
Experimental Data ◽  
Porous Layer ◽  
Analytical Solutions ◽  
Water Waves ◽  
Royal Society ◽  
Boussinesq Equations ◽  
Water Layer ◽  
Boussinesq Model ◽  
Porous Layers ◽  
Good Agreement

In this study we continue the work of Vu et al. (2018) [Coastal Eng. 139, 85-97] to develop an extended Boussinesq model that predicts the propagation of water waves in two porous layers. The first and second layer can be a water layer or a porous layer. The inertial and drag resistances are considered in the developed model. After being successfully validated against the analytical solutions, the model is used to simulate waves propagating over a submerged triangular porous bar. The numerical results show good agreement with the physical experimental data of Hsiao et al. (1998) [Proc. Royal Society of London A 458, 1291-1322].

EFFECT OF THE ROTATION ON WAVE MOTION THROUGH CYLINDRICAL BORE IN A MICROPOLAR POROUS MEDIUM

2011 ◽  
Vol 25 (20) ◽  
pp. 2713-2728 ◽  
Author(s):  
S. R. MAHMOUD ◽  
A. M. ABD-ALLA ◽  
M. A. EL-SHEIKH
Keyword(s):  
Porous Medium ◽  
Surface Wave ◽  
Phase Velocity ◽  
Frequency Equation ◽  
Wave Number ◽  
Velocity Versus ◽  
Cubic Symmetry ◽  
Surface Wave Propagation ◽  
Cylindrical Bore ◽  
Made In

In the present paper, we have studied the propagation of axial symmetric cylindrical surface waves through rotating cylindrical bore in a micropolar porous medium of infinite extent possessing cubic symmetry. The frequency equation for surface wave propagation in the micropolar porous medium has been derived and liquid filled bore are derived. The effect of the rotation on phase velocity of surface wave has been studied in detail. Radius of bore and other material parameters for empty and liquid filled bore are derived. A particular case of interest has been deduced. Numerical results have been obtained and illustrated graphically to understand the behavior of phase velocity versus wave number of a wave. The results have indicated that the effect of rotation on phase velocity is highly pronounced. Comparisons are made in the absence of rotation.

scholarly journals Surface wave propagation in a fluid-saturated incompressible porous medium

Sadhana ◽  
2007 ◽  
Vol 32 (3) ◽  
pp. 155-166 ◽  
Author(s):  
Rajneesh Kumar ◽  
B. S. Hundal
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Wave Propagation

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Diagnostics of metal samples using the results of experimental and theoretical study of positively charged microparticles formed upon sample destruction

2018 ◽  
Vol 84 (10) ◽  
pp. 23-28
Author(s):  
D. A. Golentsov ◽  
A. G. Gulin ◽  
Vladimir A. Likhter ◽  
K. E. Ulybyshev
Keyword(s):  
Experimental Data ◽  
Early Stage ◽  
Experimental Studies ◽  
Material Model ◽  
Total Charge ◽  
Cross Sectional ◽  
Practical Applications ◽  
Mechanical And Electrical Properties ◽  
Order Of Magnitude ◽  
Using Data

Destruction of bodies is accompanied by formation of both large and microscopic fragments. Numerous experiments on the rupture of different samples show that those fragments carry a positive electric charge. his phenomenon is of interest from the viewpoint of its potential application to contactless diagnostics of the early stage of destruction of the elements in various technical devices. However, the lack of understanding the nature of this phenomenon restricts the possibility of its practical applications. Experimental studies were carried out using an apparatus that allowed direct measurements of the total charge of the microparticles formed upon sample rupture and determination of their size and quantity. The results of rupture tests of duralumin and electrical steel showed that the size of microparticles is several tens of microns, the particle charge per particle is on the order of 10–14 C, and their amount can be estimated as the ratio of the cross-sectional area of the sample at the point of discontinuity to the square of the microparticle size. A model of charge formation on the microparticles is developed proceeding from the experimental data and current concept of the electron gas in metals. The model makes it possible to determine the charge of the microparticle using data on the particle size and mechanical and electrical properties of the material. Model estimates of the total charge of particles show order-of-magnitude agreement with the experimental data.

Comparison of soot models for reacting sprays in diesel engine-like conditions

2021 ◽  
pp. 095440702110154
Author(s):  
Pavan Prakash Duvvuri ◽  
Rajesh Kumar Shrivastava ◽  
Sheshadri Sreedhara
Keyword(s):  
Experimental Data ◽  
Volume Fraction ◽  
Soot Volume Fraction ◽  
Modeling Framework ◽  
Aerosol Dynamics ◽  
Significant Difference ◽  
Polycyclic Aromatic ◽  
Order Of Magnitude ◽  
Detailed Kinetics ◽  
Soot Model

Stringent emission legislations and growing health concerns have contributed to the evolution of soot modeling in diesel engines from simple empirical relations to methods involving detailed kinetics and complex aerosol dynamics. In this paper, four different soot models have been evaluated for the high temperature, high pressure combusting dodecane spray cases of engine combustion network (ECN) spray A which mimics engine-relevant conditions. The soot models considered include an empirical, a multistep, a method of moments based, and a discrete sectional method soot model. Two experimental cases with ambient oxygen volume of 21% and 15% have been modeled. A good agreement between simulations and experiments for vapor penetration and heat release rate has been obtained. Quasi-steady soot volume fraction contours for the four soot models have been compared with experiments. Contours of the species and source terms involved in soot modeling have also been compared for a better understanding of soot processes. The empirical soot model results in higher magnitude and spread of soot due to a lack of modeling framework for oxidation through OH species. Among the four models studied, the multistep soot model has been observed to provide the most promising agreement with the experimental data in terms of distribution of soot and location of peak soot volume fraction. Due to a two-way coupling of soot models, the detailed models predict an upstream location for soot as compared to the multi-step soot model which is one way coupled. A significant difference (of an order of magnitude) in the concentration of PAH (polycyclic aromatic hydrocarbons) precursor between multistep and detailed soot models has been observed because of precursor consumption due to the coupling of detailed soot models with chemical kinetics. It is recommended that kinetic schemes, especially those concerning PAH, be validated with experimental data with a kinetics-coupled soot model.

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