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

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

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

In this article, a reduced-order modeling approach, suitable for active control of fluid dynamical systems, based on proper orthogonal decomposition (POD) is presented. The rationale behind the reduced-order modeling is that numerical simulation of Navier–Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. The possibility of obtaining reduced-order models that reduce the computational complexity associated with the Navier–Stokes equations is examined while capturing the essential dynamics by using the POD. The POD allows the extraction of a reduced set of basis functions, perhaps just a few, from a computational or experimental database through an eigenvalue analysis. The solution is then obtained as a linear combination of this reduced set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations (PDEs). It is used here in active control of fluid flows governed by the Navier–Stokes equations. In particular, flow over a backward-facing step is considered. Reduced-order models/low-dimensional dynamical models for this system are obtained using POD basis functions (global) from the finite element discretizations of the Navier–Stokes equations. Their effectiveness in flow control applications is shown on a recirculation control problem using blowing on the channel boundary. Implementational issues are discussed and numerical experiments are presented. Copyright © 2000 John Wiley & Sons, Ltd.

A reduced-order approach for optimal control of fluids using proper orthogonal decomposition

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

B. F. Armaly

Papers

Experimental and Theoretical Investigation of Backward-Facing Step Flow

Experimental and theoretical investigations of backward-facing step flow