Chute Flow Research Articles

A numerical study of steady plane granular chute flows using the Jenkins–Savage model and its extension

AbstractThe granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour.We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom‐near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non‐linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non‐dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two‐point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins–Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.

Plane steady shear flow of a cohesionless granular material down an inclined plane. A model for flow avalanches Part II: numerical results

The granular flow model proposed by Jenkins and Savage., [2], and extended by us [1] is used here to construct numerical solutions of steady chute flows thought to be typical of such flows. We briefly state the equations and boundary conditions and present numerical solutions when the following model parameters of the Senkins and Savage model are varied: (a) the coefficient of restitution of the particles under binary collision, (b) the number of particles per layer, (c) the inclination angle of the chute, and (d) the basal and free surface boundary conditions. We demonstrate that the Jenkins and Savage model may yield physically questionable results, that those of its extension differ markedly from them and are physically more reasonable in certain cases, but yield equally questionable results in others. The results are apt to redefine research directions which granular flow modellers might want to pursue in the near future.

Jet noise suppressor nozzle

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Measurement of the velocity profile in liquid streams of large volumes using a laser Doppler velocimeter

The use of the laser Doppler velocimeter (LDVM) in fluid mechanics already has a solid past history and work on its development is proceeding rather intensively [1, 2], This method has been used successfully to measure various parameters of flows in channels or chutes of small size [3–6]. Fundamental difficulties due to possible local variations in the index of refraction along the path of the laser beam [7], in addition to technical difficulties, have not been eliminated for its use in other cases of practical importance, particularly in basins or reservoirs of large size. The aim of the present paper is the investigation of the velocity structure of streams in large volumes using an LDVM on the example of a turbulent submerged water jet. In order to estimate the effect of the thickness of the water layer on the applicability of the method we tested three schemes: based on direct [8] and back scattering [9] and a scheme with reflection of forward-scattered light from a mirror [10]. The results of the investigation of a submerged turbulent jet using an LDVM are presented.