spn7 numerical investigations on the influence of hydraulic boundary conditions on the efficiency of...
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SPN7
Numerical investigations on the
influence of hydraulic
boundary conditions on the
efficiency of sewer flushing
Dr.-Ing. Joerg Schaffner
Numerical investigations on the
influence of hydraulic
boundary conditions on the
efficiency of sewer flushing
Dr.-Ing. Joerg Schaffner
www.steinhardt.de
SPN7
Introduction 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 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 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 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.
0
5
10
15
20
25
30
35
40
45
50
0 500 1000 1500 2000 2500
Length of sewer channel [m]
Sh
ear
stre
ss [
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 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 [‰]
Eff
ecti
ve f
lush
ing
dis
tan
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 Results: Bottom roughness
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
0 1000 2000 3000 4000 5000 6000
Wave running time [s]
Sh
ear
stre
ss [
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 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 Results: Constant downstream water level
0
1
2
3
4
5
6
0 500 1000 1500 2000
Length of sewer channel [N/m²]
Sh
ear
stre
ss [
N/m
²]
1 s 5 s 10 s 20 s 50 s 100 s 200 s 500 s 1000 s
0
100
200
300
400
500
600
700
800
900
1000
0 0,01 0,05 0,1 0,15 0,2
Underwater level ho [m]
Eff
ecti
ve f
lush
ing
dis
tan
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