Numerical analysis for the mixed Navier-Stokes and Darcy Problem with the Beavers-Joseph interface condition

2014 ◽  
Vol 31 (4) ◽  
pp. 1009-1030 ◽  
Author(s):  
Liyun Zuo ◽  
Yanren Hou
Keyword(s):  
Numerical Analysis ◽  
Interface Condition ◽  
Navier Stokes ◽  
Darcy Problem

The numerical analysis of bifurcation problems with application to fluid mechanics

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 39-131 ◽  
Author(s):  
K. A. Cliffe ◽  
A. Spence ◽  
S. J. Tavener
Keyword(s):  
Numerical Analysis ◽  
Fluid Mechanics ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Finite Difference Methods ◽  
Singularity Theory ◽  
Mixed Finite Element Method ◽  
Convergence Theory ◽  
Navier Stokes ◽  
Bifurcation Problems

In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.

scholarly journals Experimental and Numerical Investigation of Self-Burial Mechanism of Pipeline with Spoiler under Steady Flow Conditions

2019 ◽  
Vol 7 (12) ◽  
pp. 456 ◽  
Author(s):  
Woo-Dong Lee ◽  
Hyo-Jae Jo ◽  
Han-Sol Kim ◽  
Min-Jun Kang ◽  
Kwang-Hyo Jung ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Steady Flow ◽  
Pressure Field ◽  
Dynamic Pressure ◽  
The Self ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Projected Area ◽  
Experimental Values ◽  
Subsea Pipelines

Herein, hydraulic model experiments and numerical simulations were performed to understand the self-burial mechanism of subsea pipelines with spoilers under steady flow conditions. First, scour characteristics and self-burial functions according to the spoiler length-to-pipe diameter ratio (S/D) were investigated through hydraulic experiments. Further, the Navier–Stokes solver was verified. The experimental values of the velocity at the bottom of the pipeline with a spoiler and the pressure on the sand foundation where the pipeline rested were represented with the degree of conformity. Scour characteristics of a sand foundation were investigated from the numerical analysis results of the velocity and vorticity surrounding the pipelines with spoilers. The compilation of results from the hydraulic experiment and numerical analysis showed that the projected area increased when a spoiler was attached to the subsea pipes. This consequently increased the velocity of fluid leaving the top and bottom of the pipe, and high vorticity was formed within and above the sand foundation. This aggravated scouring at the pipe base and increased the top and bottom asymmetry of the dynamic pressure field, which developed a downward force on the pipeline. These two primary effects acting simultaneously under steady flow conditions explained the self-burial of pipelines with a spoiler attachment.

Variation of Hydraulic Performance by Impeller Trimming of a Mixed-Flow Pump

2015 ◽  
Author(s):  
Hyeonmo Yang ◽  
Sung Kim ◽  
Kyoung-Yong Lee ◽  
Young-Seok Choi ◽  
Jin-Hyuk Kim
Keyword(s):  
Numerical Analysis ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Total Efficiency ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Ansys Cfx ◽  
Total Head ◽  
Flow Pump

One of the best examples of wasted energy is the selection of oversized pumps versus the rated conditions. Oversized pumps are forced to operate at reduced flows, far from their highest efficiency point. An unnecessarily large impeller will produce more flow than required, wasting energy. In the industrial field, trimming the impeller diameter is used more than changing the rotation speed to reduce the head of a pump. In this paper, the impeller trimming method of a mixed-flow pump is defined, and the variation in pump performance by reduction of the impeller diameter was predicted based on computational fluid dynamics. The impeller was trimmed to the same meridional ratio of the hub and shroud, and was compared in five cases. Numerical analysis was performed, including the inlet and outlet pipes in configurations of the mixed-flow pump to be tested. The commercial CFD code, ANSYS CFX-14.5, was used for the numerical analysis, and a three-dimensional Reynolds-averaged Navier-Stokes equations with a shear stress transport turbulence model were used to analyze incompressible turbulence flow. The performance parameters for evaluating the trimmed pump impellers were defined as the total efficiency and total head at the designed flow rate. The numerical and experimental results for the trimmed pump impellers were compared and discussed in this work.

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