scholarly journals Length Parameter for Scaling Abutment Scour Depth

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3508
Author(s):  
Puer Xu ◽  
Niansheng Cheng ◽  
Maoxing Wei
Keyword(s):  
Large Scale ◽  
Scour Depth ◽  
Length Scale ◽  
Bed Shear Stress ◽  
Combined Effects ◽  
Flow Depth ◽  
Vortex System ◽  
Bridge Abutment ◽  
Abutment Scour ◽  
Scale Turbulence

Flow constriction caused by bridge abutment increases bed shear stress and thus enhances local scour. For scaling the maximum scour depth at the abutment, either abutment length or flow depth has been empirically used in previous studies. By performing a step-by-step analysis, this study proposes a new length scale, which is able to represent combined effects of abutment length, approach flow depth and channel width. Physically, the new length scale describes the maximum possible dimension of the associated vortex system (or large-scale turbulence). Six series of data compiled from the published literature were used in the analysis. The results indicate that the new length scale helps improve the agreement of predictions with the experimental data.

scholarly journals Scaling of Scour Depth at Bridge Pier Based on Characteristic Dimension of Large-Scale Vortex

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2458 ◽  
Author(s):  
Nian-Sheng Cheng ◽  
Maoxing Wei
Keyword(s):  
Large Scale ◽  
Horseshoe Vortex ◽  
Bridge Pier ◽  
Theoretical Formula ◽  
Scour Depth ◽  
Flow Depth ◽  
Flow Conditions ◽  
Hydraulic Radius ◽  
Vortex System ◽  
Large Scale Vortex

By examining the variations in the dimensions of a horseshoe vortex system in front of a pier, the present study proposes a new length scale, called pier hydraulic radius, for the scaling of the maximum scour depth at a bridge pier. It is shown that, in comparison with other length scales, the pier hydraulic radius is more effective for quantifying combined effects of pier width and flow depth on the local scour for both low and high flow conditions. A theoretical formula is finally derived, which agrees well with experimental data reported in the literature.

scholarly journals Combined effects of homogenization and singular perturbations: Quantitative estimates

2021 ◽  
pp. 1-34
Author(s):  
Weisheng Niu ◽  
Zhongwei Shen
Keyword(s):  
Large Scale ◽  
Convergence Rates ◽  
Elliptic Systems ◽  
Small Scale ◽  
Length Scale ◽  
Combined Effects ◽  
Periodic Homogenization ◽  
Quantitative Estimates ◽  
Lipschitz Estimate ◽  
Scale Estimate

We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ε of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ε and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ε and κ.

Clear-Water Scour around Bridge Abutments under Backwater Conditions

1996 ◽  
Vol 1523 (1) ◽  
pp. 196-202 ◽  
Author(s):  
Terry W. Sturm ◽  
Aftab Sadiq
Keyword(s):  
Flow Distribution ◽  
Scour Depth ◽  
Clear Water ◽  
Bridge Abutments ◽  
Bridge Abutment ◽  
Rectangular Channels ◽  
Contraction Ratio ◽  
Bridge Approach ◽  
Contraction Scour ◽  
Abutment Scour

An experimental study was conducted of the depth of clear-water scour around the end of a square-edged bridge abutment terminating in the floodplain of a compound channel. The study's purpose was to improve current techniques of abutment scour prediction, which are based primarily on laboratory studies in rectangular channels. It is indicated that a discharge contraction ratio arising from a theoretical contraction scour analysis for equilibrium conditions can be used for explaining the effect of flow distribution on the local abutment scour depth in the case where significant backwater occurs from bridge contraction. The use of reference values of approach flow depth and velocity in the floodplain for undisturbed conditions without the bridge is shown to collapse experimental results for scour depth in both the case of a contraction with negligible backwater, and the case of a contraction with significant backwater in the bridge approach section.

scholarly journals Role of large-scale advection and small-scale turbulence on vertical migration of gyrotactic swimmers

2019 ◽  
Vol 4 (12) ◽  
Author(s):  
C. Marchioli ◽  
H. Bhatia ◽  
G. Sardina ◽  
L. Brandt ◽  
A. Soldati
Keyword(s):  
Vertical Migration ◽  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence

Evaluation of Selected Pier-Scour Equations Using Field Data

1996 ◽  
Vol 1523 (1) ◽  
pp. 186-195 ◽  
Author(s):  
Mark N. Landers ◽  
David S. Mueller
Keyword(s):  
Field Measurements ◽  
Bridge Piers ◽  
Critical Ratio ◽  
Scour Depth ◽  
Flow Depth ◽  
Clear Water ◽  
Pier Scour ◽  
Logarithmic Space ◽  
State Highway ◽  
Federal Highway

Field measurements of channel scour at bridges are needed to improve the understanding of scour processes and the ability to accurately predict scour depths. An extensive data base of pier-scour measurements has been developed over the last several years in cooperative studies between state highway departments, the Federal Highway Administration, and the U.S. Geological Survey. Selected scour processes and scour design equations are evaluated using 139 measurements of local scour in live-bed and clear-water conditions. Pier-scour measurements were made at 44 bridges around 90 bridge piers in 12 states. The influence of pier width on scour depth is linear in logarithmic space. The maximum observed ratio of pier width to scour depth is 2.1 for piers aligned to the flow. Flow depth and scour depth were found to have a relation that is linear in logarithmic space and that is not bounded by some critical ratio of flow depth to pier width. Comparisons of computed and observed scour depths indicate that none of the selected equations accurately estimate the depth of scour for all of the measured conditions. Some of the equations performed well as conservative design equations; however, they overpredict many observed scour depths by large amounts. Some equations fit the data well for observed scour depths less than about 3 m (9.8 ft), but significantly underpredict larger observed scour depths.

Thermo-mechanical coupling particle simulation of three-dimensional large-scale non-isothermal problems

2017 ◽  
Vol 34 (5) ◽  
pp. 1551-1571 ◽  
Author(s):  
Ming Xia
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Simulation Method ◽  
Particle Simulation ◽  
Similarity Criteria ◽  
Particle Model ◽  
Length Scale ◽  
Content Type ◽  
Mechanical Coupling ◽  
Particle Simulation Method

Purpose The main purpose of this paper is to present a comprehensive upscale theory of the thermo-mechanical coupling particle simulation for three-dimensional (3D) large-scale non-isothermal problems, so that a small 3D length-scale particle model can exactly reproduce the same mechanical and thermal results with that of a large 3D length-scale one. Design/methodology/approach The objective is achieved by following the scaling methodology proposed by Feng and Owen (2014). Findings After four basic physical quantities and their similarity-ratios are chosen, the derived quantities and its similarity-ratios can be derived from its dimensions. As the proposed comprehensive 3D upscale theory contains five similarity criteria, it reveals the intrinsic relationship between the particle-simulation solution obtained from a small 3D length-scale (e.g. a laboratory length-scale) model and that obtained from a large 3D length-scale (e.g. a geological length-scale) one. The scale invariance of the 3D interaction law in the thermo-mechanical coupled particle model is examined. The proposed 3D upscale theory is tested through two typical examples. Finally, a practical application example of 3D transient heat flow in a solid with constant heat flux is given to illustrate the performance of the proposed 3D upscale theory in the thermo-mechanical coupling particle simulation of 3D large-scale non-isothermal problems. Both the benchmark tests and application example are provided to demonstrate the correctness and usefulness of the proposed 3D upscale theory for simulating 3D non-isothermal problems using the particle simulation method. Originality/value The paper provides some important theoretical guidance to modeling 3D large-scale non-isothermal problems at both the engineering length-scale (i.e. the meter-scale) and the geological length-scale (i.e. the kilometer-scale) using the particle simulation method directly.

Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method

2013 ◽  
Author(s):  
Scott Martin ◽  
Aleksandar Jemcov ◽  
Björn de Ruijter
Keyword(s):  
Turbulent Combustion ◽  
Large Scale ◽  
Reaction Rates ◽  
Moment Closure ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Conditional Moment ◽  
Progress Variable ◽  
Conditional Moment Closure ◽  
Scale Turbulence

Here the premixed Conditional Moment Closure (CMC) method is used to model the recent PIV and Raman turbulent, enclosed reacting methane jet data from DLR Stuttgart [1]. The experimental data has a rectangular test section at atmospheric pressure and temperature with a single inlet jet. A jet velocity of 90 m/s is used with an adiabatic flame temperature of 2,064 K. Contours of major species, temperature and velocities along with velocity rms values are provided. The conditional moment closure model has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes [2]. The simplified CMC model used here falls into the class of table lookup turbulent combustion models where the chemical kinetics are solved offline over a range of conditions and stored in a table that is accessed by the CFD code. Most table lookup models are based on the laminar 1-D flamelet equations, which assume the small scale turbulence does not affect the reaction rates, only the large scale turbulence has an effect on the reaction rates. The CMC model is derived from first principles to account for the effects of small scale turbulence on the reaction rates, as well as the effects of the large scale mixing, making it more versatile than other models. This is accomplished by conditioning the scalars with the reaction progress variable. By conditioning the scalars and accounting for the small scale mixing, the effects of turbulent fluctuations of the temperature on the reaction rates are more accurately modeled. The scalar dissipation is used to account for the effects of the small scale mixing on the reaction rates. The original premixed CMC model used a constant value of scalar dissipation, here the scalar dissipation is conditioned by the reaction progress variable. The steady RANS 3-D version of the open source CFD code OpenFOAM is used. Velocity, temperature and species are compared to the experimental data. Once validated, this CFD turbulent combustion model will have great utility for designing lean premixed gas turbine combustors.

A Novel Turbulent Aggregation Device for Flue Gas

2014 ◽  
Vol 955-959 ◽  
pp. 2425-2429 ◽  
Author(s):  
Yun Fei Li ◽  
Jian Guo Yang ◽  
Yan Yan Wang ◽  
Xiao Guo Wang
Keyword(s):  
Size Distribution ◽  
Flue Gas ◽  
Large Scale ◽  
Balance Model ◽  
Small Scale ◽  
Multiphase Model ◽  
Specific Performance ◽  
Particles Size Distribution ◽  
Scale Turbulence ◽  
Eulerian Multiphase Model

The purpose of this study is to construct a turbulent aggregation device which has specific performance for fine particle aggregation in flue gas. The device consists of two cylindrical pipes and an array of vanes. The pipes extending fully and normal to the gas stream induce large scale turbulence in the form of vortices, while the vanes downstream a certain distance from the pipes induce small one. The process of turbulent aggregation was numerically simulated by coupling the Eulerian multiphase model and population balance model together with a proposed aggregation kernel function taking the size and inertia of particles into account, and based on data of particles’ size distribution measured from the flue of one power plant. The results show that the large scale turbulence generated by pipes favours the aggregation of smaller particles (smaller than 1μm) notably, while the small scale turbulence benefits the aggregation of bigger particles (larger than 1μm) notably and enhances the uniformity of particle size distribution among different particle groups.

scholarly journals An overview of the effect of large-scale inhomogeneities on small-scale turbulence

2002 ◽  
Vol 14 (7) ◽  
pp. 2475 ◽  
Author(s):  
L. Danaila ◽  
F. Anselmet ◽  
R. A. Antonia
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence
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