Shyam N. Prasad

Experiments on headcut growth and migration in concentrated flows typical of upland areas

Experiments were conducted to examine soil erosion by headcut development and migration in concentrated flows typical of upland areas. In a laboratory channel, packed sandy loam to sandy clay loam soil beds with preformed headcuts were subjected to simulated rain followed by overland flow. The rainfall produced a well-developed surface seal that minimized surface soil detachment. During overland flow, soil erosion occurred exclusively at the headcut, and after a short period of time, a steady state condition was reached where the headcut migrated at a constant rate, the scour hole morphology remained unchanged, and sediment yield remained constant. A fourfold increase in flow discharge resulted in larger scour holes, yet aspect ratio was conserved. A sediment bed was deposited downstream of the migrating headcut, and its slope depended weakly on flow discharge.

On the influence of wall properties and Poiseuille flow in peristalsis.

The present study extends the two-dimensional analysis of peristaltic motion by Fung and Yih to include an elastic or viscoelastic wall, and a Poiseuille flow. This fluid-solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. The wall characteristics appear in their equations of motion, which are solved to represent boundary conditions of fluid motion. The influence of Poiseuille flow on pure peristalisis is also investigated. The phenomenon of the ‘mean flow reversal’ is found to exist both at the center and at the boundaries of the channel. When the walls of the channel are elastic, pure peristalsis involves flow reversal only at the center. This position may shift drastically to the boundaries, if viscous damping forces are considered.

Extension of the Heaslet‐Alksne Technique to arbitrary soil water diffusivities

Note: 28: 2793-2798 Reference EFLUM-ARTICLE-1992-002 Record created on 2005-09-08, modified on 2017-02-23

The usefulness of adjoint systems in solving nonconservative stability problems of elastic continua

Abstract The general linearized problem of stability of equilibrium of an elastic continuum subjected to follower-type surface tractions is formulated and it is indicated how an adjoint system may be constructed. It is proved that the two sets of eigenvalues of the original and adjoint systems are identical and that each member of the set is a stationary value for a variation of the displacement functions. These properties are then exploited to establish an approximate method of stability analysis which is shown to be more powerful than the commonly used Galerkin method. An illustrative example concludes the presentation.

Wave formation on a shallow layer of flowing grains

The phenomenon of longitudinal waves in shallow grain flows has been studied through laboratory experiments. The transport process of spherical particles on a metallic chute has been characterized for this purpose. The wave mode of material transport could be measured within selected combinations of flow parameters such as the angular inclination of the chute, the mean size of the grains and the mass flow rate. It has been observed that the moving particles tend to redistribute systematically in the direction of mean flow. As a result, nonlinear longitudinal waves evolve on the surface of the chute. Observations of the predominantly rolling mode of particle motion revealed significant particle dispersion away from the wavefronts. The frequency of inter-particle collisions was low in the dispersed flow regions but increased rapidly near the wavefronts to dissipate the excess kinetic energy, thus resulting in a large increase in the average volumetric solid fraction. In order to explain the appearance of discontinuities in the volumetric solid fraction, a theoretical model that preserves the overall balance of energy and allows a discontinuous periodic solution is examined here. The depth-averaged dispersed flow of the grains has been approximated by equations of motion similar to those of shallow fluid flow. The resistance to the rolling motion of the particles is expressed in terms of the hydrodynamic drag force. The theoretical model predicts the flow criterion for which the longitudinal waves would be self-sustaining.

Adjoint variational methods in nonconservative stability problems

Abstract A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.

Model for drying during fluidized-bed combustion of wet low-rank coals

Abstract An unsteady state heat conduction model with a convective boundary condition is proposed for the drying of low-rank, high-porosity coals, such as lignites, during fluidized-bed combustion. The drying front is assumed to be the receding surface of a wet core. The solution technique for this moving boundary problem is based on the heat balance integral approach with immobilization of the moving boundary by a change in space variable. The governing cubic equation describing the drying curve in dimensionless form may be solved easily by the Newton—Raphson method. The model predictions are compared with experimental data for Mississippi lignite with excellent agreement. A correlation for estimation of total drying time is proposed. The temperature profiles obtained may be used for the study of the coupled drying and devolatilization in fluidized-bed combustors. The profiles could also be of importance in the study of formation of fissures/cracks in lignites subjected to intense heating conditions encountered during fluidized-bed combustion.

Suspended sediment concentration profiles using conservation laws

The suspended sediment transport problem in open channels is studied from the conservation laws point-ofview. Beginning with equations describing the conservation of mass and momentum of both sediment and water, equations for suspended sediment concentrations in free surface flow are derived. Sediment shear and normal stresses are modeled in a manner similar to that of fluid turbulent stresses. Ordinary differential equations for concentration profiles in the viscous sublayer and in the logarithmic velocity region of a steady uniform flow are developed. Although analytical solutions of these equations were attempted, no closed form solution was found. Therefore, a numerical technique such as the fourth order Runge-Kutta method, is used to solve the concentration profile equations. For lack of data in the viscous sublayer, only the concentration profile for flow with the logarithmic velocity distribution is solved and compared to data.

On Papkovich-Fadle solutions of crack problems relating to an elastic strip

Abstract Papkovich-Fadle eigenfunctions are employed to study a class of crack problems of an elastic strip. A system of series relations is obtained which is reduced to a Fredholm integral equation of the second kind by the use of the generalized orthonormality of the eigenfunctions and the calculus of residues. Four types of crack configuration are considered. Based on the numerical solutions of the integral equations, stress intensity factor and crack energy for two types of edge cracks are reported. Some crack problems of the strip have been attempted by integral transforms which have been widely used in elasticity by Sneddon. It is not clear, however, how they may be used to tackle the problems considered here. The present approach is quite general and straightforward and, may be applied to a wide class of mixed boundary problems.

Series solution of the three-dimensional elasticity problem of a layer☆

Abstract Series solution in cylindrical co-ordinates of the traction boundary value problems of an infinite, elastic layer with body forces and arbitrary temperature distribution is presented. This is accomplished by means of certain Fourier expansions as well as a simultaneous expansion of two functions in a set of complex eigenfunctions. The solution is in close form which may be extended to displacement and some mixed boundary value problems of a layer. The axisymmetric problem of compression of a layer is reconsidered. The series solution obtained for this case is shown to be equivalent to the integral transform solution of Sneddon. The solutions of the following nonaxisymmetric problems of a layer subjected to forces parallel to the middle plane are also given here: 1. (i) Shear stresses distributed uniformly over a circle on the surfaces. 2. (ii) A concentrated force in the middle plane. 3. (iii) Concentrated forces on the surfaces. 4. (iv) Forces distributed over a line normal to the middle plane.