Two-dimensional Horizontal Flow Research Articles

Clogging of granular materials in a horizontal hopper: Effect of outlet size, hopper angle, and driving velocity.

Due to the independence of the driving velocity and outlet size, it is possible to isolate geometrical and kinematic contributions to clogging in two-dimensional horizontal flow in a hopper driven by a conveyor belt. We experimentally investigate the geometric (outlet size and hopper angle) and kinematic effects (driving velocity) on the clogging in such a horizontal flow. Based on quantitative measurements and analysis of the avalanche size, blocking probability of a particle at the outlet, and other parameters, we show that the geometric factors can more effectively affect clogging. In addition, we find that the clogging tends to be alleviated with the increases of the driving velocity, suggesting a possible "fast is fast" behavior within a wide range of driving velocity. We borrow and modify a model from clogging in gravity-driven hoppers, which can accurately describe the shape of the clogging probability function in the conveyor belt driven flow, suggesting that these two systems could share some mechanisms for clogging.

A Dual Approach for Model Construction of Two-Dimensional Horizontal Flow

The two-dimensional horizontal flow model in the classical integration approach is integrated from the three-dimensional Navier-Stokes system of equations. Using the classical theory, the integral is taken directly from the bed to the free water surfaces. Consequently, the effects between the channel bed and free water surface, in the process of integration, was disappeared. However, with the proposed dual-process approach, the integral can be performed locally several times. The receiving equations thus allow to contain many physical phenomena which may be lost in the classical integral process. As a result, the derived model based on the proposed dual approach will be more complex and accurate than the classical one. In this paper, the authors perform twice integrals. The improved two-dimensional horizontal flow model was received from the dual approach which allows the calculation of flow parameters, which, having the unusual phenomena in the channel as solid objects, liquids containing other added ingredients, external forces, reversals, and so on.

Shore protection for the coast of Mousuni Island in West Bengal, India

The Mousuni Island in West Bengal, India is wide-open to Bay of Bengal. This island by virtue of its location is exposed to river flow as well as wave action. It is thus subjected to severe erosion along its south-western coastal stretch and also significantly affecting agriculture due to seawater inundation. This is due to the lower level of bund crest elevation combined with high water levels during coastal flooding. The most suitable method to arrest the shore erosion and salt water intrusion is to divert the flow gradually toward the deeper section of the channel. To meet this requirement, after carrying out a comprehensive profiling of the existing bund, bank connected series of spurs with locally available construction materials and unskilled labor are proposed. In order to design these spurs, the magnitude and direction of sediment movement along the stretch is estimated. The layout of protection measures is proposed based on a detailed analysis of site conditions and the environmental conditions. The tranquility inside the proposed coastal protecting structure is substantiated with a two-dimensional horizontal flow model. Furthermore, the behavior of the shorelines has been studied numerically with the proposed coastal protection measure. The detailed analysis of the results from the numerical model and the protection measure are discussed in this article.

Hysteretic upscaled constitutive relationships for vertically integrated porous media flow

Subsurface two-phase flow in porous media often takes place in reservoirs with a high ratio between the associated lateral and vertical extent and the lateral and vertical flow time scales. This allows for a two-scale approach with effective quantities for two-dimensional horizontal flow equations obtained from reconstructed hydrostatic vertical pressure and saturation distributions. Here, we derive explicit expressions for the two dimensional constitutive relationships for a play-type hysteretic Brooks---Corey capillary pressure function with a pore-size distribution index of 2 and quadratic relative permeabilities. We obtain an explicit hysteretic parametrization for the upscaled capillary pressure function and the upscaled relative permeabilities. The size of the hysteresis loop depends on the ratio between buoyancy and the entry pressure, i.e. it scales with the reservoir height and the ratio between drainage and imbibition capillary pressure. We find that the scaling for the relative permeability is non-monotonic and hysteresis vanishes for both small and large reservoirs.

Is the forward problem of ground water hydrology always well posed?

Complex aquifer systems are often modeled with quasi-three-dimensional models, which consider two-dimensional horizontal flow in the aquifers and one-dimensional vertical flow through aquitards. When the aquifer system consists of a phreatic aquifer and one or more semiconfined aquifers connected by aquitards, the discrete model consists of a nonlinear system of algebraic equations, because the transmissivity of the phreatic aquifer depends on the phreatic head. If the water extraction is very high, the phreatic aquifer can be depleted and the equations of the model must be modified accordingly. There are not simple and general criteria to state if the phreatic aquifer is depleted before solving the system of equations. Therefore, the iterative procedures (e.g., relaxation methods), used to find the solution to the forward problem, must handle these particular conditions and can suffer several problems of convergence. These problems can be caused by the choice of the initial head values or of the relaxation coefficient of the iterative algorithms; however, they can also be caused by the nonexistence or nonuniqueness of the solution to the system of nonlinear equations. The study of existence and uniqueness of the general problem is very difficult and, therefore, we consider a simplified problem, for which the discrete model can be handled analytically. The results of the numerical experiments show that the solution to the forward problem can be nonunique. Only for some cases it is possible to invoke physical arguments to eliminate tentative solutions.

The vertical component of the supergranular convection

Proper motion measurements of solar granulation made by local cross-correlation analysis of a 190 minute time series of white-light images reveal persistent flows with scales of 5-50 Mm. The two-dimensional horizontal flow shows mainly the horizontal supergranulation, and the divergence of the flow, of the 5-10 Mm mesogranulation. Time-averaged Doppler vertical velocities in the photospheric Fe I 5576 A and in the temperature minimum Mg I b2 5173 A lines are correlated with the flow divergence. The time-averaged chromospheric intensity in Mg I b2 is correlated with the flow divergence. Fourier spectrum and autocorrelation analyses of the flow divergence gives a measure of 6.6 Mm in the principal component and indicates little power at scales larger than 15 Mm.

Velocity and temperature measurement with thermistor anemometers in a thermally stratified rotating fluid

The implementation of a new scheme for a thermistor anemometer for the measurement of both velocity and temperature in a two-dimensional horizontal flow is described. The anemometer is composed of a cluster of four bead thermistors, consisting of a central heater bead and three surrounding sensor beads. Empirical relationships for the dependence of flow direction on sensor/heater spacing, fluid flow speed, and fluid, heater and sensor temperatures are presented which permit in situ calibration of large numbers of thermistor anemometers. Fabrication details, calibration procedures and results of measurements from a large number of anemometers under actual experimental conditions in a thermally stratified, rotating fluid flow are included.

Oceanic Velocity Gradients

Abstract This paper is a theoretical and experimental investigation of the nature of oceanic velocity gradients.Starting with the equations of motion, equations governing the dynamic behavior of velocity gradients alongwith a first integral are derived. These nine equations are partitioned differently than in a previous derivation by Carstoiu so as to simplify the physical interpretation. It is pointed out that solutions to the gradientequations overspecify the equations of motion. This leads to the development of compatibilityconditionsfor the solutions. These conditions generalize similar equations used in elasticity. The general gradientequations are applied to two-dimensional horizontal flow. This application demonstrates the role that thewind field and bottom topography can play in generating velocity gradients. Free solutions to the linearizedgradient equations are discussed. The solutions show that inertial gravitational waves can be present in thegradient fields. A summary of observations of veloc...

Buoyant convection from horizontal surfaces at const ant pressure

A two-dimensional horizontal flow is discussed, which is induced by other, buoyancy-driven flows elsewhere. It is an adaptation of the incompressible wall jet, which is driven by conditions a t the leading edge and has no streamwise pressure gradient. The relation of this flow to the classical buoyancy-driven boundary layers on inclined and horizontal surfaces is investigated, as well as its possible connexion with a two-dimensional buoyant plume driven by a line source of heat. Composite flows are constructed by patching various such solutions together. The composite flows exhibit$Gr^{\frac{1}{4}}$scaling (Grbeing the Grashof number).