Journal of Hydraulic Engineering

Various concepts have been proposed or used in the development of Theological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold's concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non‐Newtonian fluid mechanics. Although the generality of Bagnold's model is still at issue, debris‐flow modelers in Japan have generally accepted Takahashi's formulas derived from Bagnold's model. Some efforts have recently been made by theoreticians in non‐Newtonian fluid mechanics to modify or improve Bagnold's concept or model. A viable rheological model should consist both of a rate‐independent part and a ratedependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris‐flow modeling. In fact, Bagnold's model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold's simplified assumption of constant grain concentration.

Theoretical velocity profile and theoretical pressure and concentration distributions for (steady) uniform debris flow in wide channels are derived from a generalized viscoplastic fluid (GVF) model without imposing Bagnold's assumption of constant grain concentration. Good agreement between the theoretical velocity profile and the experimental data of Japanese scientists strongly supports the validity of both the GVF model and the proposed method of solution from the model. It is shown that both Bingham and Bagnold versions (or submodels) of the GVF model can be used to simulate debris flow at the dynamic state. Although Bagnold's dilatant submodel appears to fit the Japanese data better than the Bingham submodel for flow of noncohesive grains, the choice between them is by no means clear‐cut. No matter which submodel is used, a full understanding of the major factors that affect the behavior of debris flows is essential prior to its application. This paper thus lays theoretical ground for extensive further studies of such factors.

A computer model of two-dimensional steady flow in a confined space is described in this paper. The simplest case of radial jet-forced flow within a circular cylinder with a single inlet and outlet is considered. The first stage in the numerical model consists of mapping the circular flow boundary onto a rectangle by means of a Schwarz-Christoffel transformation. As a result, two opposite sides of the rectangle represent the inlet and outlet. A potential uniform flow solution is then obtained for the flow in the rectangle and hence the cylinder. In the second stage of the flow simulation, discrete vortices are added at the inlet in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the potential uniform flow solution. The positions of the vorticese are updated using a finite-difference time-stepping scheme. Thus, a qualitative simulation of the complete flow is built up. The results show reasonable agreement with experimental observations.

The performance of the cross‐flow turbine, CFT, also known as the Banki turbine, was studied experimentally by varying the number of blades, the runner diameter, and the nozzle entry arc under flow/head variations. The results, as presented in this paper, show that the maximum efficiency of the CFT at any flow/head combination increases as the nozzle entry arc increases or the aspect ratio of the runner decreases. Equations have been suggested to obtain the optimum number of blades for maximum efficiency of the turbine and to find the specific speed of the CFT as a function of unit discharge and nozzle entry arc.

A new type of spiral‐flow dropshaft, composed of a vertical circular shaft with tangential inlet and outlet conduits and one or more continuous helicoidal ramps attached to the shaft wall, is described. Experimental results indicate that these helicoidal‐ramp dropshafts are superior to other types of dropshafts both in their energy‐dissipation and air‐handling characteristics. Additionally, the needs for energy‐dissipation and deaeration chambers at the bottoms of these structures are obviated. The friction factors of flows along the channels formed by the helicoidal ramps are somewhat higher than those of equivalent straightchannel flows. Prototype‐installation experience indicates that helicoidal‐ramp dropshafts are significantly cheaper than conventional ones in installations requiring low air discharges from and intensive energy dissipation in the dropshafts.

The following finite difference schemes are employed in an alternating direction-implicit format to approximate the linear form of the two-dimensional constituent transport equation: (1) Forward time centered space (FTCS); (2) forward time upwind space (FTUS); (3) spread time centered space (STCS); (4) spread time upwind space (STUS); and (5) flux-corrected transport (FCT). Several test problems for which analytical solutions are available are considered on a small (7 × 8) uniformly spaced computational grid. It is shown that the FCT scheme exhibits superior numerical properties. Additional tests on a (60 × 60) uniformly spaced grid confirm the small grid tests. Although all the small grid tests were performed on a Cray-I supercomputer, it is demonstrated that these tests may be duplicated on currently available mini- and microcomputers. Therefore, the engineer may screen new finite difference transport schemes on local mini- and microcomputers prior to incorporating these schemes in large grid prototype supercomputer simulations.