Formulations of longitudinal dispersion coefficient
Download
1 / 22

Formulations of Longitudinal Dispersion Coefficient - PowerPoint PPT Presentation


  • 96 Views
  • Uploaded on

A Review:. Formulations of Longitudinal Dispersion Coefficient. Outline. Introduction and Applications Historical background New Formulations Conclusions. Longitudinal ADVECTION + Vertical or Lateral DIFFUSION =. Dispersion Coefficient (K). DISPERSION. River Mixing Processes.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Formulations of Longitudinal Dispersion Coefficient' - yelena


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Formulations of longitudinal dispersion coefficient

A Review:

Formulations ofLongitudinal Dispersion Coefficient


Outline
Outline

  • Introduction and Applications

  • Historical background

  • New Formulations

  • Conclusions


Longitudinal advection vertical or lateral diffusion
Longitudinal ADVECTION+Vertical or Lateral DIFFUSION=

Dispersion Coefficient (K)

DISPERSION



Practical applications
Practical Applications

  • Pollution Forecasting

  • Temperature Variations in a River

  • River Water Quality Control

  • Re-aeration in Water Bodies

  • Salt Intrusion in Tidal Estuaries


Historical background
Historical Background

  • Taylor (1953 & 1954)

  • Elder (1959)

  • Fischer (1966 & 1975)

  • Liu (1977)

  • Iwasa and Aya (1991)

  • Taylor (1953 & 1954)

  • Elder (1959)

  • Fischer (1966 & 1975)

  • Liu (1977)

  • Iwasa and Aya (1991)

Laminar flow in a tube of radius a

Turbulent flow in a pipe of radius a


Comparison of formulae
Comparison of Formulae

Discrepancy Ratio

Accuracy



New formulation

Seo & Cheong (1998)

New Formulation

  • Dimensional Analysis:

    Factors influencing dispersion


Seo cheong 1998
Seo & Cheong (1998)

Buckingham PI Theorem


Simplifications
Simplifications

  • Neglect irregularities

  • Flow is fully turbulent

Reduced equation:


Regression analysis
Regression Analysis

Nonlinear Multi-Regression Equation

Linear Multiple Form


Final equation
Final Equation:

Experimental data:

  • 59 streams, 26 states in US

  • 35 used to model equation

  • 24 used for verification


Seo cheong 19981
Seo & Cheong (1998)

Accuracy: 79%

Limitation:


Deng et al 2002
Deng et al. (2002)

  • Lateral Dispersion Coefficient

  • Velocity Deviation Parameter

  • Channel Shape Equation

  • Local Flow Depth

  • Channel Sinuosity



Conclusions
Conclusions

  • Analytical solution by Taylor (1954) available for regular cross sections.

  • Natural streams need empirical means with field data.

  • Liu’s equation (1977) offers the best prediction followed by Iwasa & Aya (1991).


Conclusions1
Conclusions

  • Seo and Cheong’s new equation (1998) with field data from 59 streams across 26 states in the US.

  • Deng et al. (2002) incorporated the effect of vertical and transverse irregularities.


References
References

  • Seo, I. W., and Cheong, T. S. (1998). “Predicting Longitudinal Dispersion Coefficient in Natural Streams.” J. Hydr. Engrg., ASCE, 124(1), 25-32.

  • Liu, H. (1977). “Predicting dispersion coefficient of streams.” J. Envir. Engrg. Div., ASCE, 103(1), 59-69.

  • Deng, Z.-Q., Bengtsson, L., Singh, V. P., and Adrian, D. D (2002). “Longitudinal Dispersion Coefficient in Single-Channel Streams”, J. Hydr. Engrg., ASCE, 128(10), 901-916.