SPN7

Numerical investigations on the influence of hydraulic

boundary conditions on the efficiency of sewer flushing

Dr.-Ing. Joerg Schaffner

www.steinhardt.de

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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

Downstream water level

Sewer slope

Roughness

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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

Reference: Chow, 1959

- 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

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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: ShyEhy IrgIrg 0 3/4

22

hyr

vMSI

(Energy slope method)

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Results: Longitudinal slope

- 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.

05

101520253035404550

0 500 1000 1500 2000 2500

Length of sewer channel [m]

Shea

r str

ess

[N/m

²]

100 s 1 s 5 s 10 s 20 s 50 s 200 s 500 s 1000 s 1150 s

- 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.

Variation of longitudinal slope I = 0.25 - 2.25 ‰

I = 2.25 ‰

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Results: Longitudinal slope

0

500

1000

1500

2000

2500

3000

3500

0,25 0,50 1,00 1,25 1,50 1,75 2,00 2,25

Longitudinal slope I [‰]

Effe

ctiv

e flu

shin

g di

stan

ce [m

]

- 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.

Effective flushing distance- Location where:

< crit = 3 N/m²

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Results: Bottom roughness

00,5

11,5

22,5

33,5

44,5

0 1000 2000 3000 4000 5000 6000

Wave running time [s]

Shea

r str

ess

[N/m

²]

M = 0,01 M=0,0125 M=0,014 M=0,016 M = 0,02 M=0,025

Constant values:

- IS = 1 ‰- Hstor = 0.55 m- VFlush = 139.6 m³

Variation M = 0.01 - 0.025 s/m1/3 (very smooth concrete - medium sized gravel)

- 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.

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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.

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Results: Constant downstream water level

0

1

2

3

4

5

6

0 500 1000 1500 2000

Length of sewer channel [N/m²]

Shea

r str

ess

[N/m

²]

1 s 5 s 10 s 20 s 50 s 100 s 200 s 500 s 1000 s

0100200300400500600700800900

1000

0 0,01 0,05 0,1 0,15 0,2

Underwater level ho [m]

Effe

ctiv

e flu

shin

g di

stan

ce [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.

I = 1 ‰ M = 0.013 s/m1/3

h = 0.55 m V = 139.6 m³

h0 = 0.15 m