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Mike 11 – Steep channels in PUB model
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Mike 11 – Steep channels in PUB model
Assumptions for Saint Venant Equations are:
• the bottom-slope is small• the wave lengths are large compared to the water depth
• hydrostatic pressure
• the flow is subcritical (Some terms is phased out for supercritical flow, see Mike 11
reference manual for details ).
Mike 11 solves Saint Venat Equation
+
=
+ (
) + ℎ + =0
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Mike 11 – Steep channels in PUB model
160.0 170.0 180.0 190.0 200.0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0 310.0 320.0 330.0 340.0 350.0
[m]
100.0
100.5
101.0
101.5
102.0
102.5
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
107.5
108.0
108.5
109.0
109.5
[meter] 1-1-2012 03:25:00
SIGLAP 600 - 0
2 5 4
2 5 9
2 6 0
2 6 7
2 7 9
2 8 0
2 9 4
2 9 9
3 0 0
3 1 9
3 2 0
3
3 9
3
4 0
3 4 3
3 4 4
3 4 7
3 4 8
3 5 0
3 5 1
3 5 3
3 5 4
3 5 7
3 5 8
3 6 1
3 6 2
3 6 4
3 6 5
3 6 8
3 6 9
3 7 4
4 3 1
4 4 1
Not optimal to apply Saint Venat Equation in short very steep sections.
• The bottom-slope of the section is not small, Saint Venant
assumption
• Stability of the simulation requires small time steps
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Mike 11 – Steep channels in PUB model
160.0 170.0 180.0 190.0 200.0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0 310.0 320.0 330.0 340.0 350.0
[m]
100.0
100.5
101.0
101.5
102.0
102.5
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
107.5
108.0
108.5
109.0
109.5
[meter] 1-1-2012 03:25:00
SIGLAP 600 - 0
2 5 4
2 5 9
2 6 0
2 6 7
2 7 9
2 8 0
2 9 4
2 9 9
3 0 0
3 1 9
3 2 0
3 3 9
3 4 0
3 4 3
3 4 4
3 4 7
3 4 8
3 5 0
3 5 1
3 5 3
3 5 4
3 5 7
3 5 8
3 6 1
3 6 2
3 6 4
3 6 5
3 6 8
3 6 9
3 7 4
4 3 1
4 4 1
The water level passes through critical depth
Sub critical flow conditions
Super critical flow conditions
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Mike 11 – Steep channels in PUB model
160.0 170.0 180.0 190.0 200.0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0 310.0 320.0 330.0 340.0 350.0
[m]
100.0
100.5
101.0
101.5
102.0
102.5
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
107.5
108.0
108.5
109.0
109.5
[meter] 1-1-2012 03:25:00
SIGLAP 600 - 0
2 5 4
2 5 9
2 6 0
2 6 7
2 7 9
2 8 0
2 9 4
2 9 9
3 0 0
3
1 9
3
2 0
3 3 9
3 4 0
3 4 3
3 4 4
3 4 7
3 4 8
3 5 0
3 5 1
3 5 3
3 5 4
3 5 7
3 5 8
3 6 1
3 6 2
3 6 4
3 6 5
3 6 8
3 6 9
3 7 4
4 3 1
4 4 1
Section model as one broad crested Weir:
• In most no limitation in the flow along the steep section
• So no back water effects
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Mike 11, Steep channels
1 30 .0 14 0.0 15 0. 0 1 60. 0 1 70 .0 1 80 .0 19 0.0 20 0. 0 2 10.0 2 20 .0 2 30 .0 24 0.0 25 0. 0 2 60.0 2 70 .0 2 80 .0 29 0.0 30 0. 0 3 10.0 3 20 .0 3 30 .0 34 0.0 35 0. 0
[m]
100.5
101.0
101.5
102.0
102.5
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
107.5
108.0
108.5
109.0
109.5
110.0
110.5
111.0
[meter] 1-1-2012 10:54:20
SIGLAP 600 - 0
2 5
4
2 5
9
2 6
0
2 6 7
2 7 9
2 8 0
2 9 4
2 9 9
3 0 0
3 1 9
3 2 0
3 3 9
3 7 4
4 3 1
4 4 1
H pointQ point
Broad crested M11 weir. Weir calculation separates between free and
sub merged flow conditions. In almost all cases the water level is fare
below the crest level, free overflow conditions and the solutions will be
“forced” to pass through critical depth at the weir.
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Mike 11 – Steep channels in PUB model
Mike 11 broad crested weir include inlet and outlet loss, see M11 reference
manual for details. Free overflow table is calculated on the basis of energy
equation and applying:
=
2 = 12
∆ = 0
M11 Broad crested weir calculation include the velocity head upstream on the
weir. Many standard weirs formula assumes zero upstream velocity head, which
may increase the water level too much.
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Mike 11 – Steep channels in PUB model
160. 0 170.0 180. 0 190.0 200. 0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0 310.0 320.0 330.0 340.0 350.0
[m]
100.0
100.5
101.0
101.5
102.0
102.5
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
107.5
108.0
108.5
109.0
109.5
[meter] 1-1-2012 03:25:00
SIGLAP 600 - 0
2 5 4
2 5 9
2 6 0
2 6 7
2 7 9
2 8 0
2 9 4
2 9 9
3 0 0
3 1
9
3 2
0
3 3 9
3 4 0
3 4 3
3 4 4
3 4 7
3 4 8
3 5 0
3 5 1
3 5 3
3 5 4
3 5 7
3 5 8
3 6 1
3 6 2
3 6 4
3 6 5
3 6 8
3 6 9
3 7 4
4 3 1
4 4 1
Backwater may occur in this section, so it is not correct to model this
section as one weir. Each of the small drops, is modeled with a broad
crested weir. Flow will often be submerged at these drops, but the broad
crested weir can handle this. Details of the submerged flow conditions
calculation is given in the Mike 11 reference manual
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Mike 11 – Steep channels in PUB model
Recommendations:
• Model steep section with one weir
• Model flat section as branch with broad crested weir at drops
This approach will increase stability of the model, reduce simulation timeand is a good modeling approach, within the limitation of a 1D model
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