Hydrodynamic Entrance Lengths for Incompressible Laminar Flow in Rectangular Ducts

1960 ◽  
Vol 27 (3) ◽  
pp. 403-409 ◽  
Author(s):  
L. S. Han
Keyword(s):  
Rectangular Channel ◽  
Theoretical Data ◽  
Mathematical Expression ◽  
Smooth Transition ◽  
Navier Stokes ◽  
Entrance Length ◽  
Entire Region ◽  
Navier Stokes Equation ◽  
Pressure Drops ◽  
Aspect Ratios

The problem of determining the hydrodynamic entrance length in a rectangular channel is solved by the method of linearizing the Navier-Stokes equation. The resulting equation is regarded as an equation to generate a mathematical expression for the axial velocity in the entire region, making smooth transition from a uniform profile to the fully developed one. From this expression, the entrance length, defined as where 99 per cent of the fully developed center-line velocity is attained, is calculated for channels of six aspect ratios. The pressure drops are also calculated and presented herein. A comparison is made with the limited amount of experimental and theoretical data.

Heat Transfer Enhancement for Turbulent Flow Through Blockages With Round and Elongated Holes in a Rectangular Channel

2007 ◽  
Vol 129 (11) ◽  
pp. 1611-1615 ◽  
Author(s):  
H. S. Ahn ◽  
S. W. Lee ◽  
S. C. Lau
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Rectangular Channel ◽  
Transfer Enhancement ◽  
Transfer Coefficients ◽  
Pressure Drops ◽  
Average Heat ◽  
Heat Transfer Coefficients ◽  
Aspect Ratios ◽  
Flow Through

Experiments were conducted to determine the average heat transfer coefficients on three wall segments between blockages with holes in a wide rectangular channel. Eight different configurations of the holes in the blockages—two diameters and four aspect ratios of the holes—were examined. The pressure drops across the blockages were also measured. The results showed that the elongated holes in the blockages in this study enhanced more heat transfer than the round holes, but they also caused larger pressure drops across the blockages.

Lateral Distributions of Depth-Averaged Velocity in Compound Channels with Submerged Vegetated Floodplains

2014 ◽  
Vol 641-642 ◽  
pp. 288-299
Author(s):  
Ming Wu Zhang ◽  
Chun Bo Jiang ◽  
He Qing Huang
Keyword(s):  
Experimental Data ◽  
Analytical Solution ◽  
Rectangular Channel ◽  
Navier Stokes ◽  
Compound Channel ◽  
Navier Stokes Equation ◽  
Compound Channels ◽  
Vegetated Floodplain ◽  
Vegetation Layer ◽  
Good Agreement

Lateral distributions of depth-averaged velocity in open compound channels with submerged vegetated floodplains are analyzed, based on an analytical solution to the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term included to account for the effects of vegetation. The cases of open channels are: rectangular channel with submerged vegetated corner, and compound channel with submerged vegetated floodplain. The present paper proposes a method for predicting lateral distribution of the depth-averaged velocity with submerged vegetated floodplains. The method is based on a two-layer approach where flow above and through the vegetation layer is described separately. An experiment in compound channel with submerged vegetated floodplain is carried out for the present research. The analytical solutions of the three cases are compared with experimental data. The corresponding analytical depth-averaged velocity distributions show good agreement with the experimental data.

Gaseous Flows in Rectangular Microchannels: Experimental Validation of a Second-Order Slip Flow Model

2003 ◽  
Author(s):  
Ste´phane Colin ◽  
Pierre Lalonde ◽  
Robert Caen
Keyword(s):  
Flow Model ◽  
Slip Flow ◽  
Second Order ◽  
Navier Stokes ◽  
Order Model ◽  
Navier Stokes Equation ◽  
Rectangular Microchannels ◽  
First Order ◽  
Aspect Ratios ◽  
Gaseous Flows

A precise analytical model for gaseous flows in microchannels is of great interest for various applications, as for example when these microchannels are parts of a complex fluidic microsystem. However, a decrease in the channel hydraulic diameter leads to an increase in the rarefaction effects. If the Knudsen number becomes higher than about 0.1, it is generally admitted that the Navier-Stokes equation, even with first-order slip flow boundary conditions, are no longer valid. In order to keep an analytical model for higher Knudsen numbers, a resolution of the Navier-Stokes equation with second-order boundary conditions has been proposed in rectangular microchannels. An experimental setup has been designed for the measurement of gaseous microflows under controlled temperature and pressure conditions. Data relative to nitrogen and helium flows through rectangular microchannels are presented and analyzed. The microchannels have been etched by DRIE in silicon and closed with Pyrex by anodic bounding. Their depths range from 4.5 to 0.5 μm, with aspect ratios from 1 to 9%. It is shown that for aspect ratios higher than 1%, a plane flow model is no longer accurate, and that the proposed rectangular model should be used. The different sources of uncertainty that could occur during the experiments are discussed. A method is proposed to eliminate the principal one, that is the uncertainty when measuring the dimensions of the microchannel cross-section. Theoretical and experimental mass flow rates are compared, and it is shown that in rectangular microchannels, the second-order model is valid up to about 0.25, whereas the first-order model is no longer accurate for Knudsen numbers higher than 0.05. The best fit has been found for a tangential momentum accommodation coefficient σ = 0.93 , both with helium and nitrogen. Perspectives of this work are also presented.

scholarly journals Assessing Machine Learning versus a Mathematical Model to Estimate the Transverse Shear Stress Distribution in a Rectangular Channel

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 596
Author(s):  
Babak Lashkar-Ara ◽  
Niloofar Kalantari ◽  
Zohreh Sheikh Khozani ◽  
Amir Mosavi
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Fuzzy Inference ◽  
Rectangular Channel ◽  
Tsallis Entropy ◽  
Shear Stress Distribution ◽  
Data Series ◽  
Shear Stresses ◽  
Inference System ◽  
Aspect Ratios

One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in the rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS) methods to assess the shear stress distribution (SSD) in the rectangular channel. To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse coordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 430
Author(s):  
Changyou Ding ◽  
Hong Lei ◽  
Hong Niu ◽  
Han Zhang ◽  
Bin Yang ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Mass Concentration ◽  
Distribution Curve ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Residence Time Distribution Curve ◽  
Tracer Solution ◽  
Time Distribution Curve

The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concentration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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