Implementation of Strutures in the CMS: Part III, Culvert by Honghai Li, Alejandro Sanhez, Weiming Wu, and Christopher Reed PURPOSE: This Coastal and Hydraulis Engineering Tehnial Note (CHETN) desribes the mathematial formulation and numerial implementation of a ulvert in the Coastal Modeling System (CMS) operated through the Surfae-water Modeling System (SMS). A oastal appliation is provided to illustrate the implementation proedure at Poplar Island, MD. INTRODUCTION: Culverts are a ommon oastal engineering struture typially used in oastal wetlands to ontrol waste and storm water disharges, at as salinity barriers, optimally distribute freshwater, and manage sediment transport (Figure 1). In oastal appliations, the ulverts often onnet open water bodies of similar water surfae elevation to enhane flushing or ondut flow through levees or auseways. Sine ulverts are a signifiant omponent of hydrodynami and sediment transport ontrols in the oastal zone, it is important that the CMS simulates their effets. The implementation of ulverts in the CMS is based on equations developed by Bodhaine (1982). As a validation, the ulverts are applied for the hydrodynami alulations in a wetland appliation in Chesapeake Bay, Maryland. (a) Figure 1. (a) Cirular ulvert, and (b) retangular ulvert. (b) COASTAL MODELING SYSTEM: The CMS, developed by the Coastal Inlets Researh Program (CIRP), is an integrated suite of numerial models for simulating water surfae elevation, urrent, waves, sediment transport, and morphology hange in oastal and inlet appliations. It onsists of a hydrodynami and sediment transport model, CMS-Flow, and a spetral wave model, CMS-Wave (Buttolph et al. 2006; Sanhez et al. 2011a; Sanhez et al. 2011b; Lin et al. 2008). Both are desribed in Part I of this series (Li et al. 2013). Approved for publi release; distribution is unlimited.
MATHEMATICAL FORMULATION: Based on the ross-setional area, irular and retangular ulverts an be represented in the CMS (Figure 1). The flow through ulverts is determined using the pipe or open hannel flow equation. The CMS identifies the upstream and downstream ells oupied by the entrane and exit of eah ulvert and applies the same flow disharge as a soure or sink term in the ontinuity equation. The speially designed impliit sheme for weirs and tide gates is modified for representing the ulverts in the SIMPLEC algorithm (Wu 2012). Bodhaine (1982) desribed six types of (unidiretional) flow onditions through a ulvert that depends on the ulvert slope and the upstream and downstream water levels. A sketh of the typial flow onditions for the ulvert is shown in Figure 2. Considering the tidal flow in oastal zones, four types of flow onditions are grouped in the CMS and the equations desribed in the following an be applied for both irular and retangular ulverts. Figure 2. Sketh of ulvert flow. (1) The headwater and tailwater are higher than the ulvert top levels (height, D, plus invert elevations z b ), i.e. the ulvert inlet and outlet are submerged, and the ulvert flow is an orifie flow determined by Q A 2gh ( -h ) K = 1 2 L (1) where K L is the oeffiient of energy loss through the ulvert, K L Ki K f Ko, and K i is the entrane loss oeffiient, K f is the frition loss oeffiient, and K o is the outlet loss oeffiient. The frition loss (K f ) is determined by K f fl = (2) 4 R where f is the Dary-Weisbah frition oeffiient, L is the ulvert barrel length, and R is the hydrauli radius of the ulvert barrel. Crowe et al. (2005) and Bodhaine (1982) presented the methods for the determination of f, K i, and K o. (2) The headwater (h 1 ) is greater than 1.5D+z b1 and tailwater (h 2 ) is lower than D+z b2, and the ulvert inlet is submerged but the exit is unsubmerged. In this ase the ulvert may be partly or fully oupied by flow (Bodhaine 1982). Here, for simplifiation, a fully oupied ulvert is assumed and an orifie flow with free outflow is applied as 2
Q= A 2gh ( -h ) K 1 0 ' L + 10. (3) where K K K, and h 0 is the tailwater and is assumed to be D+z b2. L i f The headwater (h 1 ) is less than 1.5D+z b1 and the tailwater (h 2 ) is lower than D+z b2, and both the ulvert inlet and exit are unsubmerged. This is an open hannel flow ase, whih an be ritial or normal flow depending on the downstream water level and the ulvert slope. (3) For the ritial flow ase, the ulvert disharge an be determined by A Q A g B = (4) where A and B are the area and the top width of the flow at the ulvert opening, respetively, both being funtion of the flow depth ( h ) at the opening. (4) For the normal flow ase, the ulvert disharge is determined by 1 Q= A R S n 23 / 12 / where S is the hydrauli gradient. Considering the loal head loss, Equation (5) an be extended to the following form: 2gh ( -h ) Q= A K K gn L R 1 2 2 4/ 3 i + o+ 2 / where K i and K o are the loal head loss oeffiients at the ulvert entrane and exit, respetively. In this flow ase, the loal head loss oeffiients are assumed to be the same as K i and Ko in Equation (1). NUMERICAL IMPLEMENTATION: Figure 3 shows a sketh of a ulvert setup in the CMS. The ulverts an ross multiple land ells. The implementation requires the speifiations of the following parameters: upstream and downstream ells, the ulvert invert elevation (relative to the model datum), the ulvert type (irular or retangular) and assoiated sales, the length of the ulvert, the loal head loss oeffiients, the frition oeffiients, the outflow diretions at the entrane and exit ends, and a flap gate. For a irular ulvert, the diameter is speified, and for a retangular, the width and height are speified. The loal head loss oeffiients at the bay and sea sides may vary with tidal urrent diretion. For the ulvert with a flap gate, the flow is unidiretional from the upstream to the downstream. Thus, the identifiation of the upstream and downstream ells beomes more important for this ase. (5) (6) 3
Figure 3. Setup of ulvert in the CMS. The mass flux through ulverts is treated as a sink or soure in the ontinuity equation at the ulvert entrane and exit ells, respetively. There are two ways to treat the momentum flux through ulverts. The first method is to add the momentum flux as soure to the momentum equations at the ulvert entrane and exit ells, like the mass flux. For this method, the outflow diretions at both ells for tide urrent need to be speified. The seond method is to assume that the momentum flux is small and an be negleted in the momentum balane alulations. For a diret disharge of ulvert flow into bayside or seaside, the first method may be a better seletion. If an energy dissipater or stilling basin exists at the ulvert outlet, the seond method may apply. A speifiation of the outflow diretion between 0 o and 360 o orresponds to the first method and a diretion less than 0 o or larger than 360 o impliates the seond seletion. In order to enhane the numerial stability, the ulvert flow Equations (1), (3), (4), or (6) are expanded to a first-order Taylor series, and an impliit method is developed by inserting this Taylor series into the water level orretion (Wu 2012). INPUT SPECIFICATIONS: Multiple ulverts an be speified by identifying the paired entrane and exit ell IDs (the ell ounter on the flow grid) in the CMS. An advaned ard is designed, starting with CULVERT_BEGIN and ending with CULVERT_END. A desription of the ulvert parameters is shown in Table 1. In a demonstration ase, onsider the simulation with two ulverts as shown in Figure 3; A and B. Culvert A onsists of two ells with ID numbers, 4471 on the bay side and 4647 on the sea side, and a length of 480 m. Culvert B has two ells with ID numbers 5753 on the bay side and 5333 on the sea side, and a length of 530 m. In this ase, number ulvert = 2. The advaned ard is given in Figure 4 with red marked for ulvert A and blue for ulvert B. In the above speifiations, ulvert A has a retangular and ulvert B a irular ross setion. The outflow diretion of ulvert A on the bay side is 355 and 175 on the sea side. For ulvert B, the outflow diretion is 20 and 200, respetively, on the bay and sea sides. 4
Table 1. Speifiations of ulvert parameters in the CMS. Input Format Note Number of Culvert [ard=number_culverts] [name=numulvert, type=integer] Number of ulvert strutures Cell ID Type of Culvert Culvert with Flap Gate [ard=cells] [name=idulvert, type=integer] [ard=type] [name=culverttype, type=har] [ard=flap_gate] [name=culvertflap, type=har] A pair of ell IDs for eah ulvert. The first one is the ell ID on the bay side of the ulvert and the seond one on the sea side Type of ulvert CIR: irular ulvert BOX: retangular ulvert Flap gate OFF: without gate ON: with flap gate Radius of Culvert [ard=radius] [name=radius, type=float] Radius of irular ulvert Width of Culvert [ard=width] [name=width, type=float] Width of retangular ulvert Height of Culvert [ard=height] [name=height, type=float] Height of retangular ulvert Length of Culvert [ard=length] [name=length, type=float] Length of ulvert barrel Dary Frition Fator [ard=darcy_friction_factor] [name=culvertfri, type=float] Dary-Weisbah frition oeffiient for the ulvert fully oupied by flow Manning (n) [ard=manning_coefficient] Manning frition oeffiient for the ulvert [name=culvertmann, type=float] partly oupied by flow Invert Elevation of Culvert Entry Head Loss Exit Head Loss Outflow Angle [ard=invert_elevation] [name=culvertelevbay/culvertelevsea, type=float] [ard=entry_head_losses] [name=culvertheadlossentry, type=float] [ard=exit_head_losses] [name=culvertheadlossexit, type=float] [ard=outflow_angles] [name=angleculvertbay/angleculvertsea, type=float] A pair of invert elevations on the bay side and the sea side of ulvert A pair of loal flow entrane head loss at the bay side and the sea side A pair of loal flow exit head loss at the bay side and the sea side A pair of outflow diretions of ulvert on the bay side and the sea side (ounterlokwise from positive x-axis) CULVERT STRUCTURES AT POPLAR ISLAND, MD: Poplar Island is loated in Chesapeake Bay, MD, to the south of the Baltimore Harbor (Figure 5). The island had a size of more than 1000 ares in the mid-1800 s but, it has been shrinking sine then due to ontinuous shoreline erosion. The island restoration projet started in the 1990s, whih used dredged materials from the Chesapeake Bay navigation hannels to rebuild the island. As shown in Figure 5, Poplar Island has been onstruted into a number of wetland ells. Separated numerial models were built to evaluate irulation for individual ells. This example of the ulvert implementation in the CMS fouses on Cell-3D beause a number of ulverts were built for water exhange between the ell and the bay. Figure 6 shows the loations of four ulverts for the Cell-3D in the CMS domain and Figure 7 the ulvert speifiations in a SMS/CMS advaned ard. As shown in Figure 7, the parameters for the 4 ulverts are shaded by different olors. A full list of the parameters is displayed for the first ulvert and only different parameters are for the other ulverts, suh as the ulvert ell IDs and the lengths of ulvert barrel. 5
ERDC/CHL CHETN-IV-95 Figure 4. Culvert Speifiations in the SMS/CMS. Figure 5. Poplar Island, MD and onstruted wetland ells. 6
Figure 6. Four Culverts in the CMS domain. Figure 7. Culvert Speifiations in a SMS/CMS advaned ard. DISCUSSION: A previous numerial modeling study of Cell-3D (Sanhez and Brown, personal ommuniation, June 9, 2008) showed general hydrodynami features around the wetland ell. The original CMS setup did not have the implementation of ulvert strutures. In this appliation the same CMS model was adopted, ulvert strutures onfigured in the system, and a 50-day simulation was onduted. The alulated irulation pattern is similar to the distribution of urrent magnitudes by the previous simulation, and strong urrents our near the tidal inlet. Figure 8 is a snapshot of the urrent field from the CMS simulation during an ebb and flood tide. The implementation of 7
ulverts indues the urrent speeds of 20-30 m/s at the entranes and exits of the ulverts on the wetland ell side and sea side. The field data were olleted inside the wetland ell. Figures 9 and 10 show the loations of four survey stations and the omparisons between the alulated and measured water levels and urrents. A Priniple Component Analysis was performed to obtain the flood and ebb diretions. Station 1 is loated near a ulvert and shows strong flood dominane with a peak urrent speed up to 20 m/s. Current speeds are signifiantly redued as tidal water reahes inside the wetland ell, indiating weak flushing at those loations. The hydrodynami features are well reprodued by the model with the introdution of the ulvert strutures. Figure 8. Snapshot of the Current Field during an Ebb and Flood Tide. Figure 9. Water Levels at the Four Survey Stations. 8
Figure 10. Currents at the Four Survey Stations. Positive indiates the flood and negative the ebb diretions. SUMMARY: Culvert strutures were inorporated into the CMS and the implementation proedure was desribed in this note. The appliation of the algorithms in the CMS was demonstrated and hydrodynami results were validated via the omparisons with the measurements and the alulated results from a previous CMS study. ADDITIONAL INFORMATION: This CHETN was prepared as part of the CIRP and was written by Dr. Honghai Li (Honghai.Li@usae.army.mil, voie: 601-634-2840, fax: 601-634-3080), Alejandro Sanhez of the US Army Engineer Researh and Development Center (ERDC), Coastal and Hydraulis Laboratory (CHL), Dr. Weiming Wu of University of Mississippi, and Dr. Christopher W. Reed of URS. The CIRP Program Manager, Dr. Julie D. Rosati (Julie.D.Rosati@ usae.army.mil), the assistant Program Manager, Dr. Zeki Demirbilek, and the Chief of the Coastal Engineering Branh at CHL, Dr. Jeffrey P. Waters, reviewed this CHETN. Files for the study may be obtained by ontating the author. This CHETN should be ited as follows: Li, H., A. Sanhez, W. Wu, and C. W. Reed. 2012. Implementation of strutures in the CMS: Part III, Culvert. Coastal and Hydraulis Engineering Tehnial Note ERDC/CHL CHETN-IV-95. Viksburg, MS: US Army Engineer Researh and Development Center. An eletroni opy of this CHETN and I/O files for the example are available from: http://hl.wes.army.mil/library/publiations/hetn/ REFERENCES Bodhaine, G.L. 1982. Measurement of peak disharge at ulverts by indiret methods, Tehniques of Water Resoures Investigations of the United States Geologial Survey, Book 3, Chapter A3, US Geologial Survey, Washington. 9
Buttolph, A. M., C. W. Reed, N. C. Kraus, N. Ono, M. Larson, B. Camenen, H. Hanson, T. Wamsley, and A. K. Zundel. 2006. Two-dimensional depth-averaged irulation model CMS-M2D: Version 3.0, Report 2, sediment transport and morphology hange. Coastal and Hydraulis Laboratory Tehnial Report ERDC/CHL-TR-06-7. Viksburg, MS: US Army Engineer Researh and Development Center. Crowe, C.T., D. F. Elger, and J. A. Roberson. 2005. Engineering Fluid Mehanis, Jon Wiley & Sons, In. Li, H., A. Sanhez, W. Wu, and C. W. Reed, 2013. Implementation of strutures in the CMS: Part I, Rubble Mound. Coastal and Hydraulis Engineering Tehnial Note ERDC/CHL CHETN-IV-93. Viksburg, MS: US Army Engineer Researh and Development Center. Lin, L., Z. Demirbilek, and H. Mase. 2011. Reent apabilities of CMS-Wave: A oastal wave model for inlets and navigation projets. Journal of Coastal Researh, Speial Issue, 59, 7-14. Lin, L., Z. Demirbilek, H. Mase, J. Zheng, and F. Yamada. 2008. CMS-Wave: A nearshore spetral wave proesses model for oastal inlets and navigation projets. Coastal and Hydraulis Laboratory Tehnial Report ERDC/CHL-TR-08-13. Viksburg, MS: US Army Engineer Researh and Development Center. Sanhez, A., W. Wu, T. M. Bek, H. Li, J. Rosati III, R. Thomas, J. D. Rosati, Z. Demirbilek, M. Brown, and C. W. Reed. 2011a. Verifiation and validation of the Coastal Modeling System, Report 3: Hydrodynamis. Coastal and Hydraulis Laboratory Tehnial Report ERDC/CHL-TR-11-10. Viksburg, MS: US Army Engineer Researh and Development Center. Sanhez, A., W. Wu, T. M. Bek, H. Li, J. D. Rosati, Z. Demirbilek, and M. Brown. 2011b. Verifiation and validation of the Coastal Modeling System, Report 4: Sediment transport and morphology hange. Coastal and Hydraulis Laboratory Tehnial Report ERDC/CHL-TR-11-10. Viksburg, MS: US Army Engineer Researh and Development Center. Wu, W. 2012. Implementation of strutures in the impliit CMS2D model. An Interim Report to Coastal Inlets Researh Program, ERDC, USACE. NOTE: The ontents of this tehnial note are not to be used for advertising, publiation, or promotional purposes. Citation of trade names does not onstitute an offiial endorsement or approval of the use of suh produts. 10