scholarly journals Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 87 ◽  
Author(s):  
Domenica Mirauda ◽  
Maria Grazia Russo
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Cross Section ◽  
Open Channel ◽  
Shear Stress Distribution ◽  
Open Channels ◽  
Channel Cross Section ◽  
Small Scale ◽  
Large Set ◽  
Bed Shear Stress

The evaluation of bed shear stress distribution is fundamental to predicting the transport of sediments and pollutants in rivers and to designing successful stable open channels. Such distribution cannot be determined easily as it depends on the velocity field, the shape of the cross section, and the bed roughness conditions. In recent years, information theory has been proven to be reliable for estimating shear stress along the wetted perimeter of open channels. The entropy models require the knowledge of the shear stress maximum and mean values to calculate the Lagrange multipliers, which are necessary to the resolution of the shear stress probability distribution function. This paper proposes a new formulation which stems from the maximization of the Tsallis entropy and simplifies the calculation of the Lagrange coefficients in order to estimate the bed shear stress distribution in open-channel flows. This formulation introduces a relationship between the dimensionless mean shear stress and the entropic parameter which is based on the ratio between the observed mean and maximum velocity of an open-channel cross section. The validity of the derived expression was tested on a large set of literature laboratory measurements in rectangular cross sections having different bed and sidewall roughness conditions as well as various water discharges and flow depths. A detailed error analysis showed good agreement with the experimental data, which allowed linking the small-scale dynamic processes to the large-scale kinematic ones.

scholarly journals Entropy-Based Shear Stress Distribution in Open Channel for all types of Flow using Experimental Data

2021 ◽  
Author(s):  
Hae Seong Jeon ◽  
Ji Min Kim ◽  
Yeon Moon Choo
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Turbulent Flow ◽  
Correlation Coefficient ◽  
Open Channel ◽  
Shear Stress Distribution ◽  
Entropy Theory ◽  
Tractive Force ◽  
Design Standards ◽  
Wide Range

Abstract Korea’s river design standards set general design standards for river and river-related projects in Korea, which systematize the technologies and methods involved in river-related projects. This includes measurement methods for parts necessary for river design, but do not include information on shear stress. Shear Stress is to one of the factors necessary for river design and operation. Shear stress is one of the most important hydraulic factors used in the fields of water especially for artificial channel design. Shear stress is calculated from the frictional force caused by viscosity and fluctuating fluid velocity. Current methods are based on past calculations, but factors such as boundary shear stress or energy gradient are difficult to actually measure or estimate. The point velocity throughout the entire cross section is needed to calculate the velocity gradient. In other words, the current Korea’s river design standards use tractive force, critical tractive force instead of shear stress because it is more difficult to calculate the shear stress in the current method. However, it is difficult to calculate the exact value due to the limitations of the formula to obtain the river factor called the tractive force. In addition, tractive force has limitations that use empirically identified base value for use in practice. This paper focuses on the modeling of shear stress distribution in open channel turbulent flow using entropy theory. In addition, this study suggests shear stress distribution formula, which can be easily used in practice after calculating the river-specific factor T. and that the part of the tractive force and critical tractive force in the Korea’s river design standards should be modified by the shear stress obtained by the proposed shear stress distribution method. The present study therefore focuses on the modeling of shear stress distribution in open channel turbulent flow using entropy theory. The shear stress distribution model is tested using a wide range of forty-two experimental runs collected from the literature. Then, an error analysis is performed to further evaluate the accuracy of the proposed model. The results revealed a correlation coefficient of approximately 0.95–0.99, indicating that the proposed method can estimate shear stress distribution accurately. Based on this, the results of the distribution of shear stress after calculating the river-specific factors show a correlation coefficient of about 0.86 to 0.98, which suggests that the equation can be applied in practice.

P5631The impact of plaque type on strut embedment/protrusion and shear stress distribution in bioresorbable scaffold

2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
E Tenekecioglu ◽  
R Torii ◽  
Y Katagiri ◽  
J Dijkstra ◽  
R Modolo ◽  
...  
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Cross Section ◽  
Vessel Wall ◽  
Shear Stress Distribution ◽  
Local Flow ◽  
Bioresorbable Scaffold ◽  
Plaque Type ◽  
The Impact ◽  
Section Level

Abstract Background and aim Scaffold design and plaque characteristics influence implantation outcomes and local flow dynamics in treated coronary segments. Our aim is to assess the impact of strut embedment/protrusion of bioresorbable scaffold on local shear stress distribution in different atherosclerotic plaque types. Method Fifteen Absorb everolimus-eluting Bioresorbable Vascular Scaffolds were implanted in human epicardial coronary arteries. Optical coherence tomography (OCT) was performed post-scaffold implantation and strut embedment/protrusion were analyzed using a dedicated software. OCT data was fused with angiography to reconstruct three-dimensional coronary anatomy. Blood flow simulation was performed and wall shear stress (WSS) was estimated in each scaffolded surface and the relationship between strut embedment/protrusion and WSS was evaluated. Results There were 9083 struts analysed. Ninety-seven percent of the struts (n=8840) were well apposed and 243 (3%) were malapposed. At cross-section level (n=1289), strut embedment was significantly increased in fibroatheromatous plaques (76±48μm) and decreased in fibro-calcific plaques (35±52 μm). Compatible with strut embedment, WSS was significantly higher in lipid-rich fibroatheromatous plaques (1.50±0.81Pa), whereas significantly decreased in fibro-calcified plaques (1.05±0.91Pa). After categorization of WSS as low (<1.0 Pa) and normal/high WSS (≥1.0 Pa), the percent of low-WSS in the plaque subgroups were 30.1%, 31.1%, 25.4% and 36.2% for non-diseased vessel wall, fibrous plaque, fibro-atheromatous plaque and fibro-calcific plaque, respectively (p-overall<0.001). Table 1. Cross-section level Embedment/Protrusion and WSS according to the plaque type Plaque type Embedment depth (μm) Protrusion distance (μm) WSS (Pa) Non-atherosclerotic intimal thickening/normal vessel wall (n=2275) 47±34*Δ¥ 123±34¶Ξπ 1.44±0.9解 Fibrous (n=4191) 53±40*#& 118±38¶Ψ‡ 1.24±0.78αθ∞ Fibroatheromatous (n=2027) 76±48#ΦΔ 94.6±46Ω†Ψπ 1.50±0.81Σ§α Fibro-calcific (n=590) 35±52&Φ¥ 139±50‡†Ξ 1.05±0.91∞£Σ For embedment: *p=0.09, #p<0.001, &p<0.001, Φp<0.0001, Δp<0.0001, ¥p<0.0001. For protrusion: ¶p=0.74, Ξp<0.0001, πp<0.0001, Ψp<0.0001, ‡p<0.0001, †p<0.0001. For WSS: θp<0.001, §p=0.06, £p<0.0001, αp<0.0001, ∞p<0.0001, Ωp<0.0001. n=total strut number in each plaque type, p-values come from mixed-effects regression analysis. Conclusion The composition of the underlying plaque influences strut embedment which seems to have effect on WSS. The struts deeply embedded in lipid-rich fibroatheromas plaques resulted in higher WSS compared to the other plaque types.

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