Turbulent Sediment Transport Over a Flat Bottom Using Momentum Balance

1975 ◽  
Vol 42 (1) ◽  
pp. 38-44 ◽  
Author(s):  
D. A. Drew
Keyword(s):  
Settling Velocity ◽  
Sediment Concentration ◽  
Momentum Balance ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Asymptotic Results ◽  
Flat Bottom ◽  
Fluid Mixture ◽  
Linear Drag ◽  
Mixing Length Theory

The turbulent flow of a sediment-fluid mixture over a flat bottom is studied using momentum balance. The in-the-small forces included are gravity, buoyancy, and a linear drag. A turbulent average is applied and mixing length theory is used for the resulting Reynolds stresses. Assuming small concentrations and small still water settling velocity, the resulting velocity profile is logarithmic; the sediment concentration profile is relatively constant near the bottom, and drops off rapidly above a certain level predicted by the theory. Numerical and asymptotic results are discussed.

scholarly journals TIME-AVERAGED TURBULENT MIXING AND VERTICAL CONCENTRATION DISTRIBUTION OF HIGH-DENSITY SUSPENSIONS FORMED UNDER WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 20
Author(s):  
Bing Yan ◽  
Qing-He Zhang ◽  
Michael Lamb
Keyword(s):  
Turbulent Mixing ◽  
Concentration Distribution ◽  
Suspended Sediment Concentration ◽  
Sediment Concentration ◽  
High Density ◽  
Oscillating Flow ◽  
Mixing Length ◽  
Flow Data ◽  
The Stability ◽  
Mixing Length Theory

We analyzed oscillating flow data from U-tube experiments by Lamb et al. (2004) and found that the time-averaged turbulent kinetic energy (TKE) near bed decreased exponentially with height above the bed in high-density-suspension (HDS) flows under waves, and that the ratios of TKE distributions in the streamwise, cross-stream, and vertical dimensions were constant. Based on the finite-mixing-length theory, a semi-theoretical time-averaged suspended sediment concentration model for HDS was developed. To avoid the stability problems with the numerical solution, a simplified model was also formulated through combing the apparent Fickian diffusivity and the damping function. The comparison between the calculated results and measurements shows both models consider the effect of the sediment-induced stratification well.

scholarly journals ANALISIS KECEPATAN JATUH SEDIMEN PADA SUNGAI CIBEET, JAWA BARAT

2021 ◽  
Vol 5 (1) ◽  
pp. 45
Author(s):  
Kevin Wijaya Warsito ◽  
Wati Astriningsih Pranoto
Keyword(s):  
Conceptual Understanding ◽  
Settling Velocity ◽  
Soil Mechanics ◽  
River Estuary ◽  
Sediment Concentration ◽  
Water And Sediment ◽  
Sediment Research ◽  
Hydraulics Laboratory ◽  
The Relationship ◽  
Optimum Salinity

Cibeet River is one of the branch of the Citarum river in West Java province with a length of 101 km. Cibeet River is one of the rivers supplying water and sediment to the West Tarum irrigation channel or known as the Kalimalang. In this research, the sample used was in the form of mud taken at the Cibeet River Estuary. This research is focused on settling velocity which is a parameter for sedimentation in order to improve numerical modeling and conceptual understanding of sediment dynamics, especially mud. Sediment research is carried out in the Soil Mechanics laboratory and Hydraulics laboratory. Bottom withdrawal tube experiments were carried out using 5 types of salinity and 6 kinds of sediment concentrations. The purpose of the study was to obtain settling velocity and compare laboratory results with the Stokes law approach and compare the relationship between settling velocity with sediment concentration and salinity. The optimum salinity is obtained at 15 ‰, and the optimum sediment concentration at 4700 ppm with an average fall speed of 37,28 mm / s. The results from the laboratory are not in accordance with the Stokes law due to the influence of flocculation from the cohesive nature of the mud sediment, so that using the Stokes law approach cannot calculate the velocity of falling sediment on the mud. Keywords: concentration; salinity; sediment; settling velocity AbstrakSungai Cibeet merupakan salah satu anak sungai dari sungai Citarum di provinsi Jawa Barat dengan panjang 101 km. Sungai Cibeet merupakan salah satu sungai pemasok air dan sedimen ke saluran irigasi Tarum Barat atau dikenal sebagai Kalimalang. Pada penelitian ini, sampel yang digunakan berupa lumpur yang diambil di Muara Sungai Cibeet. Penelitian ini difokuskan pada kecepatan jatuh sedimen yang merupakan parameter untuk sedimentasi demi meningkatkan permodelan numerik dan pemahaman konsep dari dinamika sedimen terutama lumpur.  Penelitian ini dilakukan di laboratorium Mekanika Tanah dan laboratorium Hidrolika, memakai bottom withdrawal tube, dilakukan dengan menggunakan 5 macam jenis salinitas dan 6 macam konsentrasi sedimen.  Penelitian ini membandingkan antara hasil laboratorium dengan pendekatan yaitu hukum Stokes serta membandingkan hubungan antara konsentrasi sedimen dengan salinitas. Untuk salinitas didapat optimum pada saat 15‰, dan konsentrasi sedimen yang optimum pada saat 4700 ppm dengan kecepatan jatuh rata-rata 37,28 mm/s. Hasil dari laboratorium tidak sesuai dengan pendekatan hukum stokes dikarenakan adanya pengaruh flokulasi dari sifat sedimen lumpur yang kohesif, sehingga menggunakan pendekatan hukum stokes tidak bisa untuk menghitung kecepatan jatuh sedimen pada lumpur.

Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

2022 ◽  
Author(s):  
M Prasad
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Mathematical Representation ◽  
Mixing Length ◽  
Series Form ◽  
High Reynolds ◽  
Mixing Length Theory ◽  
Grain Roughness

Abstract Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

scholarly journals Turbulent Convection: A New Model

1991 ◽  
Vol 130 ◽  
pp. 27-32
Author(s):  
V. M. Canuto
Keyword(s):  
Observational Data ◽  
Turbulent Convection ◽  
Mixing Length ◽  
Convective Flux ◽  
New Model ◽  
Mixing Length Theory

AbstractWe use the latest models of turbulence to compute a new expression for the turbulent convective flux, Fc. The new values of Fc are up to ten times larger than those given by the mixing length theory, MLT. Astrophysical considerations indicate that the new model fares better with observational data than the MLT.

scholarly journals Test of a New Theory for Stellar Convection using Helioseismology

1993 ◽  
Vol 137 ◽  
pp. 63-65
Author(s):  
L. Paternó ◽  
R. Ventura ◽  
V.M. Canuto ◽  
I. Mazzitelli
Keyword(s):  
Reaction Rates ◽  
Turbulent Convection ◽  
Standard Theory ◽  
Evolutionary Models ◽  
Mixing Length ◽  
Surface Layers ◽  
Stellar Convection ◽  
The Standard Model ◽  
Convection Model ◽  
Mixing Length Theory

AbstractTwo evolutionary models of the Sun have been tested using helioseismological data. The two models use the same input micro-physics (nuclear reaction rates, opacity, equation of state) and the same numerical evolutionary code, but differ in the treatment of turbulent convection. The first model employs the standard mixing - length theory of convection, while the second one employs a new turbulent convection model which overcomes some basic inconsistencies of the standard theory of convection.The test rests on the calculation of p-mode eigenfrequencies and on the comparison with the helioseismological data.The comparison shows an overall improvement of the eigenfrequencies calculated with the new model with respect to those calculated with the standard model, although it appears that both models still suffer from inaccuracies especially in the treatment of the surface layers.

scholarly journals A Unified View of the Law of the Wall Using Mixing-Length Theory

1973 ◽  
Vol 24 (1) ◽  
pp. 55-70 ◽  
Author(s):  
V C Patel
Keyword(s):  
Friction Velocity ◽  
Critical Value ◽  
Wall Region ◽  
Pressure Gradients ◽  
Mixing Length ◽  
Stress Distributions ◽  
General Validity ◽  
Law Of The Wall ◽  
Unified View ◽  
Mixing Length Theory

SummaryIt is shown that, if the well-known mixing-length formula is regarded simply as a relationship between the velocity and the stress distributions in the wall region of a turbulent flow, then a truly universal distribution of mixing length is sufficient to describe the experimentally observed departures of the velocity distribution from the usual law of the wall as a result of severe pressure gradients and transverse surface curvature. Comparisons have been made with a wide variety of experimental data to demonstrate the general validity of the mixing-length model in describing the flow close to a smooth wall.An extension of the re-laminarisation criterion of Patel and Head, and some experimental evidence, suggest that the thick axisymmetric boundary layer on a slender cylinder placed axially in a uniform stream cannot be maintained in a fully turbulent state for values of the Reynolds number, based on friction velocity and cylinder radius, below a certain critical value.

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