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= 2D Structure Modelling Theory =
The theory behind the modelling of energy losses and affluxes of hydraulic structures is presented in the following webinars by Bill Syme and Greg Collecutt (TUFLOW Developers).
These webinars by Bill Syme and Greg Collecutt (the TUFLOW Developers) discus the theory behind the energy losses and affluxes modelling associated with hydraulic structures.
 
*<u>[https://www.tuflow.com/library/webinars/#structures Webinar Link: Modelling Energy Losses at Structures]</u><br>
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Piers are usually smaller than the 2D cell size in real-world flood models. Although flexible mesh solver or quadtree refinement can be applied to reduce the local cell size around the pier, it also comes with an expensive computational cost that could significantly increase the simulation time. More practically, the backwater effect of piers can be modelled as sub-grid form losses.
 
Pier form loss coefficients can be derived from information in publications such as <u>[https://www.fhwa.dot.gov/engineering/hydraulics/library_arc.cfm?pub_number=1&id=5 ''Hydraulics of Bridge Waterways'' (Bradly, 1978)] or [https://austroads.com.au/publications/bridges/agbt08 ''Guide to Bridge Technology Part 8: Hydraulic Design of Waterway Structures'' (AUSTROADS, 20192018)]</u>. Energy loss estimated from bridge piers or other obstructions, vertical or horizontal, that do not cause upstream controlled flow regimes like pressure flow, are dependent on the ratio of the obstruction's area perpendicular to the flow direction to the gross flow area of the bridge opening, the shape of the piers or obstruction, and the angularity of the piers/obstruction to the flow direction. For example, using Hydraulics of Bridge Waterways (Bradly, 1978) the approach is:
<ol>
<li>Calculate the ratio of the water area occupied by piers to the gross water area of the constriction (both based on the normal water surface) and the angularity of the piers. These inputs are used to calculate "J" in the FHA documentation.</li>
<li>Use the Figure 74.10 ''Incremental Backwater Coefficient for Piers'' data to calculate Kp. <br>
[[File:incremental_backwater_coefficient_2018_pier_losses.png]]
[[File:FHA_Kp_arrow_crop.png|400px]]
<br>
'''NOTE''': the pier form loss coefficients in Hydraulics of Bridge Waterways are derived based on the cross-sectional averaged velocity through the bridge opening in the absence of piers. It's not necessary to specify a blockage value if a pier form loss coefficient estimated from this method is used.
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*If the hB/T ratio is less than 2 or greater than 6, use a peak form loss coefficient of 0.42 (minimum) or 0.20 (maximum), respectively.
 
'''NOTE''': This form loss value should not be confused with the value of 1.56 used in the pressure flow approached adopted in <u>[[1D_Bridges | TUFLOW 1D "B" and "BB" bridge]]</u>. TUFLOW 1D bridge pressure flow approach is based on the section 4.13.2 "All Girders in Contact with Flow (Case II)" of ''Guide to Bridge Technology Part 8: Hydraulic Design of Waterway Structures'' (AUSTROADS, 20192018). The original hydraulic experiment conducted by <u>[https://hdl.handle.net/10217/39009 Liu et al (1957)]</u> in a laboratory flume with a pair of bridge abutments and a deck. The flow conditions were similar to orifice flow due to the high blockage ratio caused by the abutments and the deck. When modelling bridges in 2D, the contraction/expansion losses caused by the abutments would be handled explicitly by the 2D solver, so a value 1.56 can lead to duplication of the contraction/expansion losses caused by the bridge abutments.<br>
<br>
 
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Four flow constriction layers are represented in a 2d_lfcsh layer. The lower three layers represents the pier, the bridge deck and the rails. Each layer has its own attributes to specify the blockage and the form loss coefficient. The top (fourth) layer assumes the flow is unimpeded, representative of flow over the top of a bridge. Within the same shape, the invert of the bed, and thickness of each layer can vary in 3D.
 
The following table provides an overview for how to determine the blockage and form loss coefficient for each layer:. Note that this is just an overview and additional guidelines may need to be considered.<br>
{| style="text-align: left; margin-left: 0; " class="wikitable" width="80%"
!colspan="1" style="background-color:#005581; font-weight:bold; color:white;"| Layer
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| 1 || Pier layer || ~5% (can be omitted if included in FLC) || Estimate using <u>[[TUFLOW_2D_Hydraulic_Structures#Pier_Losses | Pier Losses]]</u> || Represents flow obstruction from piers beneath the bridge deck
|-
| 2 || Bridge deck || 100% || Use calibration data, if available, to determine FLC. <br> If no calibration is available, estimate using <u>[[TUFLOW_2D_Hydraulic_Structures#Bridge_Design_.28hB.2FT.29_vs_Form_Loss_Coefficient_Table | hB/T vs FLC]]</u> table || Full blockage, no flow through the deck
If using the <u>[[TUFLOW_2D_Hydraulic_Structures#Bridge_Design_.28hB.2FT.29_vs_Form_Loss_Coefficient_Table | hB/T vs FLC]]</u> table, it is recommended to enable the Method C Form Loss Approach
|-
| 3 || Bridge rails || 10% – 100% || Use calibration data, if available, to determine FLC. <br>
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*L2 FLC and L3 FLC should sum to the combined FLC
|Blockage and FLC depends on rail type <br> Sensitivity testing with 100% blockage is recommended due to potential for debris during flood
If using the <u>[[TUFLOW_2D_Hydraulic_Structures#Bridge_Design_.28hB.2FT.29_vs_Form_Loss_Coefficient_Table | hB/T vs FLC]]</u> table, it is recommended to enable the Method C Form Loss Approach
|-
| 4 || Above rails || 0% || 0 || Represents unimpeded overtopping flow
|}
<ol>
[[File:2d_lfcsh_attributes2d_lfcsh_attributes_02.png jpg| 500px 700px]]
</ol>
<br>
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2D BG Shape is similar to the Layered Flow Constriction, but has several updates to simplify the input based on the findings from the joint study with TMR <u>[https://tuflow.com/media/7554/2022-bridge-deck-afflux-modelling-benchmarking-of-cfd-and-swe-codes-to-real-world-data-collecutt-et-al-hwrs.pdf (Collecutt et al, 2022)]</u>.
 
The following table provides an overview of how to determine the blockage and form loss coefficient for each layer:. Note that this is just an overview and additional guidelines may need to be considered.<br>
{| style="text-align: left; margin-left: 0; " class="wikitable" width="80%"
!colspan="1" style="background-color:#005581; font-weight:bold; color:white;"| Layer
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<ol>
[[File:2d_bg_attributesBridge block.pngjpg | 700px 800px]]
</ol>
 
 
===Inflection Point===
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| Thick
| between zero and 1.5 times the cell size
| Half of totalTotal form loss of the bridge
| FLC/2 applied to all sides of the selected cells
| A cell is selected if the polyline intersects the cell crosshair. Caution should be taken when using a "thick" line, as changes in cell size can cause it to become a "wide" line. If this occurs, the FLC attribute shouldmay need to be recalculated to avoid overestimating or underestimating losses.
|-
| Wide
| larger than 1.5 times the cell size
| Total form loss divided by number of cellthe sidesbridge in<br>''(may theneed directionto ofbe flowrecalculated, <br>see notes)''
| FLC divided by number of cell sides in the direction of flow <br>
''(number of cell sides in the direction of flow is calculated as line width divided by cell size)''
| FLCPolygon appliedshapes toare allrecommended sidesif more than 3 rows of faces must be selected.. <br> cells
Caution should be taken when using a "wide" line. The cell size and alignment of the 2d_lfcsh line may result in selecting too many or too few cell faces in the direction of the flow. The FLC input may need to be recalculated to ensure FLC Applied multiplied by the number of cell sides in the direction of flow equates to the intended total form loss.
| Caution should be taken when using a "wide" line. Changes in cell size may require recalculating losses.
|-
!rowspan="1" | Polygon
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<br>
The following diagrams demonstrate how the input FLC is applied for the four geometry options for 2d_lfcsh and 2d_bg layers: <br>
[[File:2dlfcsh 2dbg combined v2.png|1200px]]
 
It is good modelling practice to check the <u>[[Check_Files_2d_lfcsh_uvpt | lfcsh_uvpt_check]]</u> and <u>[[Check Files 2d bg uvpt check | bg_uvpt_check]]</u> files to confirm the number of faces selected and the FLC values assigned. It is also strongly recommended to undertake a sensitivity analysis on the applied form losses in the model to check if it makes any difference to the results and/or double check against other methods (hand calculations, other software, CFD modelling), especially if the bridge is near an area of interest. If calibration data is available, this should be used to guide the form loss value specification.<br>
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== What FLC values should be used for 2d_bg bridge if hB/T is below 2 or above 6? ==
TMR has extended the CFD simulation to hB/T ratios of 1 to 10. PleaseRefer see the section 2D Bridge Structures into the <u>[https://docs.tuflow.com/classic-hpc/manual/latest/ latestTUFLOW TUFFLOWManual]</u> manual]for details.
 
If hB/T is outside this ratio:
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