Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations

A spectral element method for fluid dynamics: Laminar flow in a channel expansion

▪ Abstract Predicting the motion of bubbles in dispersed flows is a key problem in fluid mechanics that has a bearing on a wide range of applications from oceanography to chemical engineering. In this review we synthesize the recent progress made in describing bubble motion in inhomogeneous flow. A trident approach consisting of experimental, analytical, and numerical work has given a clearer description of the hydrodynamic forces experienced by isolated bubbles moving either in inviscid flows or in slightly viscous laminar flows. A significant part of the paper is devoted to a discussion of drag, added-mass force, and shear-induced lift experienced by spheroidal bubbles moving in inertially dominated, time-dependent, rotational, nonuniform flows. The important influence of surfactants and shape distortion on bubble motion in a quiescent liquid is highlighted. Examples of bubble motion in inhomogeneous flows combining several of the effects mentioned above are discussed.

The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows

Nearly 40 years of theoretical development and practical experience has been incorporated in this book, which has won numerous awards as a scientific and technical publication in China. Now updated and fully translated into English, this volume is the first attempt in the field to unify the movement of sediment and boundary conditions. Going far beyond any book of its kind, it presents a synthetic analysis and thorough coverage of many schools of thought and provides practical survey of this discipline of the science. The authors introduce a synthesis of information gleaned from more than 800 papers spanning the fields of hydraulic engineering, mathematics, physics, geology, rheology, and chemistry, giving the reader a profound understanding of the present status and direction of the industry's research efforts. The volume includes chapters dedicated to rate phenomena and topics such as hyperconcentrated flows, effect of sediment existence on water flow, large-scale hydraulic construction on sediment-laden streams, and specialized research not available outside of China.

Mechanics of Sediment Transport

A numerical solution for steady incompressible flow over a two-dimensional backward-facing step is developed using a Galerkin-based finite element method. The Reynolds number for the simulations is 800. Computations are performed on an extended channel length to minimize the effect of the outflow boundary on the upstream recirculation zones. A thorough mesh refinement study is performed to validate the results. Extensive profile data at several channel locations are provided to allow future testing and evaluation of outflow boundary conditions.

A test problem for outflow boundary conditions—flow over a backward-facing step

Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083002839

Experimental and Theoretical Investigation of Backward-Facing Step Flow

Detailed information is provided in this paper on the physics of momentum transfer in bubble-driven liquid flows. Experimental information is obtained on the flow around bubbles and on the axisymmetric bubble-driven liquid flow inside liquid-filled cylinders located with their axes in the vertical direction. A laser-Doppler anemometer extended for particulate two-phase flows is employed for these measurements to yield local fluid velocity information as well as the rise velocity of bubbles. The bubble top radius and the bubble shape were also found from these measurements.Utilizing experimentally gained information and employing the basic equations for particulate two-phase flows, permits finite difference equations to be formulated that allow bubble-driven liquid flows to be computed. Results are presented for boundary conditions corresponding to those of the experimental studies. Comparisons of numerical and experimental results are shown to be in good agreement. This is taken as a justification to employ the developed computer programs to carry out parameter studies for bubble-driven liquid flow inside circular cylinders. Results of these studies are presented and discussed.

B. Schönung

Papers

Experimental and Theoretical Investigation of Backward-Facing Step Flow

Bubble-driven liquid flows

Experimental and theoretical investigations of backward-facing step flow