1d d2dm d lli fb d1d and 2d modelling of bends and ... · right-angled bend (4 angled bend 1d 1d...

1D d 2D M d lli f B d1D and 2D Modelling of Bends and Hydraulic Structuresand Hydraulic Structures

Bill Syme

F LF LForm LossesForm LossesE di i t d h t d t h i l itEnergy dissipated as heat due to changes in velocity magnitude and direction

Pronounced at o ou ced atBends

Flow constrictions (structures)

Form loss coefficientProportion of dynamic head (V2/2g) lost

V = 1m/s; Dynamic Head = 0.05m

V = 4m/s; Dynamic Head = 0.82m

2

RightRight--Angled BendAngled Bend( 4

RightRight Angled BendAngled Bend1D 1D vsvs 2D2D

(3

3

( (

(

1 2

3

1 2 AA

Water Surface Profiles (V = 2m/s)0.5

Water Surface Profiles (V = 2m/s)0.5

0.3

0.4m

)1D Model

0.3

0.4m

)

Coarse 2D Model

1D Model

0.1

0.2

Wat

er L

evel

(m

A0.1

0.2

Wat

er L

evel

(m

-0.1

0

-0.1

0

3

0 50 100 150 200 250 300 350 400 450Distance (m)

0 50 100 150 200 250 300 350 400 450Distance (m)

33333333323

.223

.23.223.23.223.2

23.23.2

23.2

232323232323232323RiverRiver23.223.223.223.223.223.223.223.223.2

23.423.423.423.423.423.423.423.423.4

2323.

23.2323.2323.

23.

23.

23.223.223.223.223.223.223.223.223.223

.423

.423

.423.4

23.423.4

23.4

23.4

23.4

3.43.43.43.43.43.43.43.43.4

23.6

23.6

23.623.6

23.623.6

23.6

23.623.6

RiverRiverBendsBends

2323.423.42323.42323.423.423.4

23.6

23.6

23.6

23.6

23.6

23.6

23.6

23.6

23.6

23.623.623.623.623.623.623.623.623.64 m/s

23.823.823.823.823.823.823.823.823.8

242424242424242424

20 m deep

0.4m

24.424.424.424.424.424.424.424.424.4

2222222223.43 43 43.43 43.43 43 43 4666666666

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

23.8

242424242424242424

4242442442424240.4m superelevation at bend

24.224.224.224.224.224.224.224.224.2

22 422 422 4222222222222

22.6

22.6

22.622.6

22.622.6

22.6

22.6

22.622

.822

.822

.822

.822

.822

.822

.822

.822

.823232323232323232323.2

23.2

23.223.2

23.223.2

23.2

23.2

23.223

.423

.423

.423.4

23.423.4

23.4

23.4

23.4

23.6

23.6

23.6

23.6

23.6

23.6

23.6

23.6

23.6222222222

4

2D vs 3D?2D vs 3D?2D vs 3D?2D vs 3D?

2D 3D2D 3D

23 cm23 cm23 cm23 cm23 cm23 cm23 cm23 cm23 cm 30 cm30 cm30 cm30 cm30 cm30 cm30 cm30 cm30 cm

5

5

5

Bends Bends -- ConclusionsConclusions1D d 2D A h1D d 2D A h1D and 2D Approaches1D and 2D Approaches

1DApply extra losses by

Form loss coefficient, or

Increasing Manning’s nIncreasing Manning s n

Do not model superelevation

2DForm losses inherent / Models superelevation

HoweverAre model elements too coarse to simulate all losses?

Are there losses in the vertical plane? (Helicoidal circulations)

Additional form losses may be required

6

Hydraulic StructuresHydraulic StructuresHydraulic StructuresHydraulic StructuresHydraulic Structures

Bridges and Embankments

Large Culvertsa g u

Hydraulics is Complex (3D)y p ( )1D: Traditional Approach

2D: Looks impressive but is it accurate?2D: Looks impressive, but is it accurate?

1D/2D: Best of both?

7

1D: Traditional Approach1D: Traditional Approach//Uses Contraction/Expansion LossesUses Contraction/Expansion Losses

8

( (( ( 1 1 2 3 4 2 3 ((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((((((((0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s 2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s 0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s

2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m 2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m

2.9 m/s2.9 m/s2.9 m/s

Water Surface Profiles - Outlet Controlled

2.9

3

2.7

2.8

2.9

vel (

m)

1D Model

2.4

2.5

2.6

Wat

er L

ev

Upstreamof Culvert

Downstreamof Culvert

2.2

2.3

2.4

0 50 100 150 200 250 300

9

0 50 00 50 00 50 300Distance (m)

2D: Looks impressive, but is it accurate?2D: Looks impressive, but is it accurate?p ,p ,

??

10

2D: No2D: No Contraction/Expansion Losses?Contraction/Expansion Losses?2D: No 2D: No Contraction/Expansion Losses?Contraction/Expansion Losses?

11

Modify 2D Cells to represent

l tculvert


2 9

3

1D Model

2.7

2.8

2.9

el (m

)

2D Model (Culvert as 2D Cells)

2.4

2.5

2.6

Wat

er L

eve

Upstreamof Culvert


2.2

2.3

2.4

0 50 100 150 200 250 300

12

0 50 100 150 200 250 300Distance (m)

So 2D isn’t perfect!So 2D isn’t perfect!What are our options?What are our options?

Don’t use 2D!

Adapt 2D Solution

Insert 1D SolutionInsert 1D Solution

13

2D Scheme Modifications2D Scheme Modifications

Partially block cell sidesCell Obvert Partially block cell sidesCell Obvert

Deck FLC

Form LossForm Loss Coefficient

14

2D Layered Adjustments2D Layered AdjustmentsBlockage = 0%

FLC = 0

Bl k 100%

Blockage = 50%FLC = 0.5

Blockage = 100%FLC = 0.8

Blockage = 5%Form Loss Coeff = 0.1

15

“Calibrating” a “Calibrating” a 2D2D Sol tionSol tion2D 2D SolutionSolution

F lFor example, if we apply a 0.2 FLC,


3

0.2 FLC, ie. add 0.2*V2/2genergy loss

Water Surface Profiles - Outlet Controlled - Adjusted Form Losses

3

2 7

2.8

2.9m

)1D Model


energy loss

2 7

2.8

2.9m

)1D Model


2.5

2.6

2.7

Wat

er L

evel

(m

Upstreamof Culvert


2.5

2.6

2.7

Wat

er L

evel

(m

Upstreamof Culvert


2.2

2.3

2.4

0 50 100 150 200 250 3002.2

2.3

2.4

0 50 100 150 200 250 3000 50 100 150 200 250 300Distance (m)

0 50 100 150 200 250 300Distance (m)

“Calibrating”gBox Culverts

((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((

Culvert as 1D Element


3


3


3

1

Reduce Outlet Loss Coefficient by

2.7

2.8

2.9l (

m)

1D Model

2.7

2.8

2.9 (m

)1D Model


2.7

2.8

2.9 (m

)1D Model


2D Model (Culvert as 1D Element)

Coefficient by 0.2

2 4

2.5

2.6

Wat

er L

evel

Upstreamof Culvert


2 4

2.5

2.6

Wat

er L

evel

Upstreamof Culvert


2 4

2.5

2.6

Wat

er L

evel

Upstreamof Culvert


2.2

2.3

2.4

0 50 100 150 200 250 3002.2

2.3

2.4

0 50 100 150 200 250 3002.2

2.3

2.4

0 50 100 150 200 250 300

17 17

0 50 100 150 200 250 300Distance (m)

0 50 100 150 200 250 300Distance (m)

0 50 100 150 200 250 300Distance (m)

Box M dif 2D C llBl k 2D C llBox Culverts ( (( ( 1 1 2 3 4 2 3 ((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((((((((

0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s0.7 m/s 2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s2.9 m/s 0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s0.8 m/s

2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.42 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.86 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m2.88 m 2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m2.30 m

Modify 2D Cells to represent culvert

((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((

Block 2D Cells and insert1D elementculvert1D element


2 9

3


2 9

3

1D Model


2 9

3

1D Model


3

1D Model

2.7

2.8

2.9el

(m)

1D Model

2.7

2.8

2.9el

(m)

1D Model


2.7

2.8

2.9ve

l (m

)2D Model (Culvert as 2D Cells)

2D Model (Culvert as 1D Element)

2.7

2.8

2.9el

(m)

2D Model (Culvert as 2D Cells)2D Model (Culvert as 1D Element)2D (1D Culvert & Momentum)

2 4

2.5

2.6

Wat

er L

eve

Upstreamof Culvert


2 4

2.5

2.6

Wat

er L

eve

Upstreamof Culvert


2.4

2.5

2.6

Wat

er L

ev

Upstreamof Culvert


2 4

2.5

2.6

Wat

er L

eve

Upstreamof Culvert


2.2

2.3

2.4

0 50 100 150 200 250 3002.2

2.3

2.4

0 50 100 150 200 250 300

2.2

2.3

0 50 100 150 200 250 3002.2

2.3

2.4

0 50 100 150 200 250 300

18

0 50 100 150 200 250 300Distance (m)

0 50 100 150 200 250 300Distance (m)Distance (m)

0 50 100 150 200 250 300Distance (m)

Modelling Culverts ConclusionsModelling Culverts - ConclusionsCulvert as 2D Cell(s)

2D solution models 70 to 80% of losses

Need 20 to 30% additional form losses

Culvert as 1D ElementOver predicts losses by 0 to 70%Over predicts losses by 0 to 70%

Small – 0% over prediction

Large – up to 70% over predictionLarge up to 70% over prediction

Reduce inlet / outlet losses of 1D element(s)

19 19

Embankments / Levees/(Weir Flow)

Cell sides set to 1m highCell sides set to 1m highCell sides set to 1m highfor 2D Model (Thin Weir)Cell sides set to 1m highfor 2D Model (Thin Weir)

Approach

Test submergence

Comparison Upstream Water Level HydrographsComparison Upstream Water Level HydrographsComparison Upstream Water Level Hydrographs

across cell side

BC Weir equation if unsubmerged

2

2.2

2.4

300

350

400

Unsubmerged Submerged

2

2.2

2.4

300

350

400


2

2.2

2.4

300

350

400


unsubmerged

No adjustment if submerged

Thin Weir Test1.4

1.6

1.8

Wat

er L

evel

(m)

150

200

250

Inflo

w (m

3 /s)

D/S Water Level

Inflow Hydrograph1.4

1.6

1.8

Wat

er L

evel

(m)

150

200

250

Inflo

w (m

3 /s)1D Model & Theory

D/S Water Level

Inflow Hydrograph1.4

1.6

1.8

Wat

er L

evel

(m)

150

200

250

Inflo

w (m

3 /s)1D Model & Theory

2D Model (Thin Weir)

D/S Water Level

Inflow Hydrograph

0.8

1

1.2

W

0

50

100

Weir Crest Level

0.8

1

1.2

W

0

50

100

y g p

Weir Crest Level

0.8

1

1.2

W

0

50

100

Inflow Hydrograph

Weir Crest Level

20

0:00 0:30 1:00 1:30 2:00 2:30 3:00 3:30

Time (hh:mm)0:00 0:30 1:00 1:30 2:00 2:30 3:00 3:30

Time (hh:mm)0:00 0:30 1:00 1:30 2:00 2:30 3:00 3:30

Time (hh:mm)

Oblique Weirs

Flow oblique to gridgrid

Weir at 45˚ test Unit Flow Across a Broad-Crested Weir - Upstream Controlled

3.50

Unit Flow Across a Broad-Crested Weir - Upstream Controlled

3.50

Unit Flow Across a Broad-Crested Weir - Upstream Controlled

3.50

2.50

3.002 /s

) BC Weir Formula2.50

3.002 /s

)BC Weir Formula

2D Model (Weir Coef = 1.0)

2.50

3.002 /s

)BC Weir Formula


2D M d l (W i C f 1 1)

Correct using weir coefficient

1.00

1.50

2.00

Uni

t Flo

w (m

1 00

1.50

2.00

Uni

t Flo

w (m

2 2D Model (Weir Coef 1.0)

1.00

1.50

2.00

Uni

t Flo

w (m


0.00

0.50

1.00

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 60.00

0.50

1.00

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 60.00

0.50

1.00

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6

21

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Upstream Head above Sill (m)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Upstream Head above Sill (m)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Upstream Head above Sill (m)

Real World Example

((((((((((((((((((

((((((((( ((((((((((((((((((

((((((((( ((((((((((((((((((

Bruce Hwy, Eudlo Creek, Qld – 1998

((((((((((((((((((((((((((((((((((((

Creek, Qld 1998

Bridge Piers and Bridge Piers and DeckDeckDeckDeck

Weir flow over leveesWeir flow over levees

((((((((((((((((((((((((((((((((((((

Nested 1D ElementsNested 1D Elements

PipesPipes

Weir flow over Weir flow over bridge deckbridge deck

22

Real-WorldlApplications2D S h d t2D Schemes need to:

Adjust cell: widths / flow areas / wetted perimeters

Set cell obverts (lids)Set cell obverts (lids)

Apply additional form losses

Handle unsubmerged weir flowHandle unsubmerged weir flow

Nested 1D Elements need to:

Reduce inlet/outlet loss coefficientsReduce inlet/outlet loss coefficients(to prevent over prediction of losses)

23 23

ConclusionsConclusions2D contracts and expands flow lines2D contracts and expands flow lines

Inherently models form losses

May not model 100% of lossesNeed ability to add form losses (calibrate)

Need momentum terms

Nesting 1D elementsUseful when the structure is small

May over predict lossesMay over predict losses

Need to reduce inlet / outlet losses (calibrate)

Check and UNDERSTAND your results

24 24

1d d2dm d lli fb d1d and 2d modelling of bends and ... · right-angled bend (4 angled bend 1d 1d...

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