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Numerical investigations on the influence of hydraulic boundary conditions on the efficiency of sewer flushing Dr.-Ing. Joerg Schaffner. www.steinhardt.de. Downstream water level. Roughness. Sewer slope. Introduction. Recent investigations:

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slide1

Numerical investigations on the influence of hydraulicboundary conditions on the efficiency of sewer flushingDr.-Ing. Joerg Schaffner

www.steinhardt.de

slide2

Downstream water level

Roughness

Sewer slope

Introduction

  • Recent investigations:
  • - Focused on behaviour of flush waves on initially dry sewer/tank bottom
  • Simplified assumption does not match reality
  • Present investigation:
  • - Analysis of the influence of hydraulic boundary conditions on bottom shear stresses :
    • Longitudinal sewer slope and the bottom roughness
    • Initial downstream water levels caused by lateral inflows or Qdry
slide3

Reference: Chow, 1959

Sewer flushing

  • Impoundage dry-weather runoff to designed storage level
  • Fast lifting of the flushing shield
  • Development of a turbulent flush wave downstream
  • Pipes 600 - 3500 mm in diameter
  • Cleaning distance up to several kilometers in length
  • Flush wave acts hydraulically like a dam-break wave
  • Historical analytic equations are not suitable for sewer channels
  • Numerical modelling (1-D) is a good tool for fast and realistic results

Oldest formulation: Ritter (1892) dam-break wave

slide4

Numerical Modelling

  • 1 – D Numerical model EDWA
  • Developed by Technical University of Darmstadt / Germany with special regard to the calculation of flush waves
  • Full Saint – Venant equations - Finite Volume Method
  • Godunov-Upwind scheme with approximated HLL – Riemann solver
  • Basic geometry, numerical grid and initial conditions
  • Circular sewer 1600 mm diameter ( L = 2200 m)
  • Location of the flushing shield according to investigations
  • Grid distance in flow direction: ∆ x = 0.5 m
  • Upstream BC was a free standing water body with vt=0 = 0 m/s.
  • Downstream BC: Pressure boundary
  • Bottom shear stress:

(Energy slope method)

slide5

Results: Longitudinal slope

Variation of longitudinal slope I = 0.25 - 2.25 ‰

  • Bottom roughness:M = 0.013 s/m1/3 (constant)
  • Flushing volume:V = 139.6 m³ (constant)
  • Hstor = 0.31 m - 0.77 m
  • Adjustment of storage distance according to the slope in order to keep the flushing volume constant.

I = 2.25 ‰

  • High bottom shear stresses at the beginning with 46 N/m².
  • Then fast declination of the values.
  • At the end of the sewer channel crit = 3 N/m² still exceeded.
slide6

Results: Longitudinal slope

Effective flushing distance

- Location where:

 < crit = 3 N/m²

  • Linear rise of the effective flushing distances depending on the slope.
  • Difference from 101 m (I = 0.25 ‰) to 2992 m (I = 2.25 ‰).
  • Increase of 2992 %
  • Major influence of longitudinal slope on cleaning efficiency of flush waves.
  • Fortunately: Slope of sewer channel is usually well known and reliable value.
slide7

Results: Bottom roughness

Variation M = 0.01 - 0.025 s/m1/3

(very smooth concrete - medium sized gravel)

  • Constant values:
  • IS = 1 ‰
  • Hstor = 0.55 m
  • VFlush = 139.6 m³
  • Distribution of the shear stresses at the end of the sewer channel
  • Shear stresses increase with a higher M-value while the flow velocity drops.
  • M = 0.01 s/m1/3: wave running time t = 1446 s and max = 2.29 N/m².
  • M = 0.025 s/m1/3: wave running time t = 3538 s and max= 4.21 N/m².
slide8

Results: Bottom roughness

  • High influence of bottom roughness on:
    • Wave flow velocity
    • Water level development
    • Bottom shear stresses
    • On the necessary flushing volume (design volume).
  • Correct choice of the bottom roughness very difficult for the planning engineer when modelling a flush wave.
  • Bottom roughness is usually unknown new and existing sewer channels.
  • Existing sewer channels: - Measurement of sediments heights and characteristics.
  • New projects:
  • - No prior knowledge how and which sediments will develop.
  • - Trust in calibrated models based on sediment and wave measurements.
slide9

Results: Constant downstream water level

I = 1 ‰

M = 0.013 s/m1/3

h = 0.55 m

V = 139.6 m³

h0 = 0.15 m

  • Downstream water levels: Remaining dry-weather runoff a/o lateral inflows.
  • Deceleration of flush wave and reduction in cleaning efficiency.
  • Variation of downstream water levels between h0 = 0.01 – 0.2 m.
  •  drops fast due to flow resistance of DWL.
  •  < crit = 3 N/m² after 191 m running distance.
  • Reduction of effective flushing distance of 75 % by h0 = 0.10 m.
  • Strong effect of downstream water levels on the efficiency of the flush wave.
  • DWL very important when modeling flush waves for a practical applications.