scholarly journals An Analytical Model With a Critical Richardson Number Closure for Sediment-Stratified Open Channel Flow

2018 ◽  
Vol 123 (9) ◽  
pp. 6922-6944 ◽  
Author(s):  
Shih-Nan Chen ◽  
Chiou-Jiu Chen
Keyword(s):  
Analytical Model ◽  
Channel Flow ◽  
Richardson Number ◽  
Open Channel ◽  
Open Channel Flow ◽  
Critical Richardson Number

scholarly journals Evolution of thermally stratified turbulent open channel flow after removal of the heat source

2019 ◽  
Vol 876 ◽  
pp. 356-412
Author(s):  
Michael P. Kirkpatrick ◽  
N. Williamson ◽  
S. W. Armfield ◽  
V. Zecevic
Keyword(s):  
Reynolds Number ◽  
Heat Source ◽  
Channel Flow ◽  
Central Region ◽  
Richardson Number ◽  
Open Channel ◽  
Open Channel Flow ◽  
Radiative Heating ◽  
Initial State ◽  
Near Surface

Evolution of thermally stratified open channel flow after removal of a volumetric heat source is investigated using direct numerical simulation. The heat source models radiative heating from above and varies with height due to progressive absorption. After removal of the heat source the initial stable stratification breaks down and the channel approaches a fully mixed isothermal state. The initial state consists of three distinct regions: a near-wall region where stratification plays only a minor role, a central region where stratification has a significant effect on flow dynamics and a near-surface region where buoyancy effects dominate. We find that a state of local energetic equilibrium observed in the central region of the channel in the initial state persists until the late stages of the destratification process. In this region local turbulence parameters such as eddy diffusivity $k_{h}$ and flux Richardson number $R_{f}$ are found to be functions only of the Prandtl number $Pr$ and a mixed parameter ${\mathcal{Q}}$, which is equal to the ratio of the local buoyancy Reynolds number $Re_{b}$ and the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. Close to the top and bottom boundaries turbulence is also affected by $Re_{\unicode[STIX]{x1D70F}}$ and vertical position $z$. In the initial heated equilibrium state the laminar surface layer is stabilised by the heat source, which acts as a potential energy sink. Removal of the heat source allows Kelvin–Helmholtz-like shear instabilities to form that lead to a rapid transition to turbulence and significantly enhance the mixing process. The destratifying flow is found to be governed by bulk parameters $Re_{\unicode[STIX]{x1D70F}}$, $Pr$ and the friction Richardson number $Ri_{\unicode[STIX]{x1D70F}}$. The overall destratification rate ${\mathcal{D}}$ is found to be a function of $Ri_{\unicode[STIX]{x1D70F}}$ and $Pr$.

A new analytical model for dip modified velocity distribution in fully developed turbulent open channel flow

2019 ◽  
Vol 46 (8) ◽  
pp. 657-668 ◽  
Author(s):  
Minakshee Mahananda ◽  
Prashanth Reddy Hanmaiahgari ◽  
Chandra Shekhar Prasad Ojha ◽  
Ram Balachandar
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Channel Flow ◽  
Correction Factor ◽  
Open Channel ◽  
Open Channel Flow ◽  
Channel Flows ◽  
Superior Performance ◽  
Open Channel Flows ◽  
Proposed Model

This paper presents a new analytical model to predict the streamwise time-averaged velocity profile affected by the dip phenomenon in open channel flows. The novel approach of the present study is that the Finley wake law has been used instead of Coles’ wake law for the outer layer. To validate the new analytical model, six high quality experiments were conducted in a hydraulically rough bed open channel flow by considering variations of aspect ratio, defined as the ratio of the width of the channel to the depth of flow, from 2 to 4. In these controlled experiments, the time-averaged velocities were measured using a Nortek Vectrino-plus acoustic Doppler velocimeter. In addition, 14 sets of available experimental data, including five field experiments conducted across the globe were also used to test the performance of the proposed model. The proposed model, the Finley-dip-modified-log-wake law (FDMLWL), was used to develop a semiempirical equation to compute the dip position as a function of the dip correction factor and the wake parameter. In addition, using the experimental data and FDMLWL, an empirical equation was developed to compute the dip correction factor for hydraulically smooth open channel flows. The comparison of the FDMLWL model with the experimental data belonging to hydraulically smooth, transition, and rough regimes has consistently indicated better representation of the velocity dip phenomenon. The FDMLWL model has also been compared with other analytical models available in the literature and the superior performance of the proposed model is further observed. Finally, based on the satisfactory validation between experimental data and FDMLWL, it is inferred that the proposed model is better suited for modeling zero velocity gradient at the boundary layer edge, as in open channel flows with dip phenomenon.

MODELING THE ORGANIC REMOVAL AND OXYGEN CONSUMPTION BY BIOFILMS IN AN OPEN-CHANNEL FLOW

1994 ◽  
Vol 30 (2) ◽  
pp. 53-61 ◽  
Author(s):  
Shiyu Li ◽  
Guang Hao Chen
Keyword(s):  
Water Quality ◽  
Oxygen Consumption ◽  
River Water ◽  
Channel Flow ◽  
Diffusion Layer ◽  
Open Channel ◽  
Open Channel Flow ◽  
River Water Quality ◽  
Monod Kinetics ◽  
Organic Removal

A mathematical model is proposed to predict the removal of dissolved organic substances and the consumption of dissolved oxygen by attached biofilms in an open-channel flow. The model combines the biofilm equations with the conventional Streeter–Phelps type equations of river water quality by considering the mass transfer of organics and oxygen in the river water through the diffusion layer into the biofilm. It is assumed that the diffusion and reaction within the biofilm are of steady-state, and follow Monod kinetics. The model is solved numerically with a trial-and-error method. The simulation results of the model for an ideal case of river flow and biofilm show that the organic removal rate and oxygen consumption rate caused by the biofilm are greater than that by suspended biomass. The effects of diffusion layer thickness, flow velocity, and biofilm thickness on the change of river water quality are discussed.

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