Flow Measurements in Tidal Spillways

Transcription

1 Fourt LACCEI International Latin American and Caribbean Conference for Engineering and Tecnology (LACCET 006) Breaking Frontiers and Barriers in Engineering: Education, Researc and Practice 1-3 June 006, Mayagüez, Puerto Rico. Flo Measurements in Tidal Spillays Panagiotis D. Scarlatos, Dr.-Eng. Cair & Professor, Department of Civil Engineering Florida Atlantic University, Boca Raton, Florida, U.S.A. Abstract Fres ater flos in coastal and estuarine environments may create ecological problems due to reduction in salinity levels. Terefore, accurate measures of regulated fresater discarges are important for an effective management of coastal aters. Traditionally flo rates troug spillays are estimated, depending on te gate opening, eiter as orifice-type flo or flo over a eir. Hoever, for fully open gates under lo-ead and tidally-effected conditions estimates based on te traditional formulas are inaccurate. Tis paper summarizes te state-of-te-art of flo troug spillays. A ne formula for estimation of flo rate in tidally-affected spillays is presented. Te formula as developed by applying dimensional analysis and π-teorem and as calibrated and verified by using field data from different coastal spillays in Souteast Florida. Keyords Coastal aters, Dimensional analysis, Flo measurements, Modeling, Spillays 1. Introduction Te exponential antropogenic grot in soutern Florida necessitated te development of ater controls in order to maintain adequate fres ater supplies for te rapidly groing population along te loer east coast, to sustain agricultural activities and to restore and protect te Everglades National Park and oter delicate etland ecosystems. Te agency in carge of te regional ater controls is te Sout Florida Water Management District (SFWMD) ic orks in cooperation it te U.S. Army Corps of Engineers and oter federal, state and local agencies. Te SFWMD operates and maintains over four undred ydraulic structures including spillays, eirs, culverts and pump stations. Approximately one undred and tenty of te ydraulic structures are gated spillays and about one-fift of tem are coastal spillays tat discarge excess runoff ater directly into te environmentally sensitive area of Biscayne Bay, sout of te Miami-Dade metropolitan area. Over te past years serious concerns ave been raised regarding te large fluctuations of salinity levels in Biscayne Bay caused by te fresater releases. Salinity variations can ave a negative impact on te quality and biodiversity of te native environment. Tus, for an effective and efficient management of te regional ater resources system tere is a substantial need for accurate estimates of te fresater discarges. Water managers at te SFWMD estimate flos at gated spillays using an in-ouse developed program knon as FLOW tat is based on instantaneous upstream and donstream ater stages obtained from operational control information. Te equations used in te FLOW model are basic orifice and eir type

2 discarge formulas tat ere developed by te U.S. Army Corp of Engineers in te early sixties by using data from small-scale pysical models, as ell as field observations from inland spillays (U.S. Army Corps of Engineers, 1963). Flo calculations, based on existing formulas for orifice-flo (free and/or submerged) and for free flo over a eir, provide adequately accurate predictions of te discarges. Hoever, for te case ere te gate is fully open and discarge occurs under submerged flo conditions te estimates are inaccurate. Te inaccuracy in flo estimations orsens during extreme events (e.g., urricanes) and/or at structures directly affected by tides. Te reason for tis inaccuracy is tat te flo is controlled in a very complex ay by a variety of parameters involving ater properties, flo regime, structure and canal geometry, as ell as oter occurring factors suc as floating debris, gate leaking, etc. A detailed description of te flo regime in te near-te-gate zone is extremely complicated. Vortices of all scales are continuously being generated, cascaded and dissipated in a very dynamic manner. Hoever, for practical purposes te simulation of tose localized turbulent effects is unnecessary since te net flo can be calculated by utilizing a number of bulk and easily measurable, in real-time, parameters. Notably, tese parameters can be engaged in an empirical rater tan a pysically-based model. For tat purpose te Buckingam Teorem (π-teorem) can be employed so tat a regression type formula is establised (Ansar and Raymond, 005). Tis study summarizes te state-of-te-art of metods related to flo estimation over spillays, and extends te ork of Ansar and Raymond (005) by applying a ider range of pysical and geometric parameters to te predictive formula. Te approac utilizes dimensional analysis and π-teorem for te derivation of a general formula. Ten te formula is calibrated troug regression analysis by using field measurements and oter data obtained from six coastal spillays in souteast Florida.. Formulas for Flo Estimation Troug Gated Spillays Depending on te gate operating conditions and te ater elevation on eiter side of te spillay flo at coastal spillays is classified into five different flo categories (Ansar and Raymond, 005), (Tillis and Sain, 1998). More specifically tose categories are (Figure 1): Submerged orifice-flo (partially opened gate) Free orifice-flo (partially opened gate i.e. gate is in te ater) Submerged eir-flo (fully opened gate) Free eir-flo (fully opened gate i.e. gate is out of te ater) Submerged tidally-affected eir-flo (fully opened gate) Figure 1: Classification of Flo Troug Gated Spillays (Tillis and Sain, 1998)

3 .1 Broad-crested eirs Free flo conditions Flo over a fully open spillay structure is ydraulically similar to flo over a broad-crested eir. A general classification of broad crested eirs as related to te upstream ydraulic ead and teir lengt in te direction of flo as provided by Jain (001). For subcritical upstream flo conditions, te discarge over a broad-crested eir is estimated by te ell-knon general formula n Q = C BH ere B is te top idt, H is te upstream ydraulic ead, C is a correction coefficient, and n = 3/. Te coefficient C depends on a number of variables including te displacement tickness of te boundary layer (Rouse, 1950), te eir eigt (Hang and Hougtalen, 1996), and te eir lengt and configuration of te upstream crest corners (Kosrojerdi and Kavianpour, 00). Te correction coefficient requires calibration from field measurements. Te coefficient C can also be approximated as: C = C d C v ere C d is a correction coefficient tat accounts for local friction losses, flo curvature and nonuniform flo distribution, and C v is a correction coefficient tat accounts for te velocity ead (U.S. Bureau of Reclamation, 001). Te U.S. Army Corps of Engineers provided extensive design criteria for different types of spillays (i.e., sarp-crest, ogee, spillay cutes, and morning glory spillays). Tose criteria include design caracteristics of te spillay as ell as carts for selection of discarge coefficients (U.S. Army Corps of Engineers, 1987).. Broad-crested eirs - Submerged flo conditions. Under submerged flo conditions te governing equation for eir discarge is, (U.S. Army Corps of Engineers, 1963): Q = CsB g(h ) ere is te tailater ead. Te coefficient C s is commonly expressed as a function of te ratio H t /H as, (Tillis and Sain, 1998): C s = α H β ere α and β ere experimental coefficients. Anoter approac used by te USGS for submerged flo is given by te equation (Collins, 1977), Q = C so C BH H ere C is te discarge coefficient under free flo conditions, and C so is an additional flo correction factor. Leliavsky (1965) expressed te discarge for submerged flo conditions as: Q = CB g(h ) CB g(h )

4 Te recommended value for te empirical coefficient is 0.57 < C < Experimentally as been son tat te sape of te upstream corner of a eir can also ave an effect on te discarge for bot free and submerged flo conditions. Using a combination of momentum teory and dimensional analysis, Skogerboe and Hyatt (1967) investigated te effects of submergence on flo measuring flumes. Te expression tat tey proposed is: Q = C ( H) 1 n1 n [ ( logs + C )] ere H = H is te ead difference, S = /H is te submergence, and n 1, n are experimental exponents. Te values for te exponents ere given as n 1 =1.5, and 1.0 < n < 1.5. Te same autors suggested a similar formula for submerged subcritical flos over embankments (Skogerboe and Hyatt, 1967a). For long crested eirs, it is proven tat submerged flo, Q s, causes a reduction in discarge as compared to free flo conditions, Q, by te folloing ratio, (Irrigation Researc and Training Center, 00), Qs Q = 1 H Te above equation is knon as te Villemonte relationsip (Florida Department of Transportation, 1999). Generally, Mossa et al. (003) suggested tat for a general study of flo over a spillay te Froude, Reynolds, and Weber numbers, as ell as te relative rougness may be necessary to be considered for discarge estimations..3 Spillay gate flos in tidal environments Flo over a partially constructed barrage under tidal conditions as investigated by Halliell (1967). In is study, flos ere discretized into four categories: flood tide free flo (critical flo dept over te crest), flood tide submerged flo, ebb tide free flo and ebb tide submerged flo. Te velocity, U, over te barrage as assumed to depend on seven parameters, i.e. U = f(h, B,g, A,T, A ere g is te gravitational acceleration, A is te tidal amplitude, T is te tidal period, A t is te area of te confined ater body, and t is te time in te cycle. If only te maximum velocity itin te cycle is considered, ten te parameter, t, is dropped from consideration. On anoter study, Ansar and Raymond (005) assumed tat te discarge at a tidal gate is a function of eigt parameters, i.e., Q = f i, t) ( H,P,B,g,µ,ρ, A,T) Were P is te eir eigt, µ is te dynamic viscosity, ρ is te ater density, A is te tidal amplitude and T is te tidal period. By using π-teorem and dimensional analysis tey derived B Q 3 g P = λ T A gp ξ 6 10 H P W ζ

5 Tis regression type model improved te flo predictions as compared to tose obtained by te U.S. Army Corps of Engineers formulas (1963). Hoever, still tere as a discrepancy in te prediction of maximum and minimum flos (Ansar and Raymond, 005)..4 Special conditions affecting flo estimations over spillays Te flo over a spillay gate can be also be affected by a number of localized conditions suc as: (a) cannel constriction and skeness (Fiuzat and Skogerboe, 1984), (b) density stratification due to salinity or suspended sediments (Denton, 1987), and (c) air entrainment during gate operations (Emiroglu and Baylar, 003). An extensive literature revie regarding flo over spillays, eirs and embankments indicated tat altoug tere is a pletora of information regarding free flo conditions, tere is only a miniscule amount of information regarding submerged flos under tidal effects (Scarlatos, 005). 3. Metodology for Flo Estimation Troug Coastal Spillays 3.1 Application of te π-teorem Flo troug coastal spillays depends on a number of natural and artificial quantities of varying degree of importance. Tese quantities can be generally related to te properties of te transported ater, te caracteristics of te flo field, and te geometric design of te spillay structure. An extensive list of dimensional variables tat can be potentially involved in te description of flo troug coastal gates is discussed in te folloing sections. Tose variables ere particularly selected based on literature revie, field observations, and as-built blueprints for structures S-13, S-0F, S-0G, S-1, S-1A, and S Water Properties Variables. Te predominant variables related to fluid properties tat can affect te discarge are te folloing: density of fres ater (ρ f ), density of saline ater (ρ s ), density of transported solids (ρ t ), concentration of transported solids (C), dynamic viscosity of ater (µ), surface tension (σ) and gravitational acceleration (g). Regarding tose fluid-related variables, te densities of fres ater, saline ater and transported solids are important to caracterize any stratification effects and identify te possible formation of a alocline or lutocline interface. Salt ater intrusion (saline edge) troug te gates and sedimentation effects (soaling or scouring) if ignored, can cause inaccuracies to discarge calculations. Te amount of transported solids is also significant because in ig concentrations it can even cange te Netonian beavior of te ater to tat of a pseudo-plastic or Bingam fluid (Meta et al., 1991). Surface tension is of minor importance, ile gravitation acceleration is te driving force of te entire penomenon and tus te most important of all te parameters involved Flo Caracteristics Variables. Te most important variables tat control te flo regime are te folloing: upstream ydraulic ead (H), donstream (tail-ater) ydraulic ead (), flo discarge (Q), tidal amplitude (A), tidal period (T), time itin te tidal period (t) and location of saline interface (H i ). Regarding tose flo-related variables, under submerged flo conditions discarge is controlled by bot te upstream and tail-ater ydraulic eads. Tese eads are measured in reference to te crest of te eir. Tidal effects are caracterized by te tidal amplitude and tidal period. Te tidal amplitude is measured in reference to te MSL (Mean Sea Level). Consideration of te time itin te tidal period is necessary for flo estimations and te period can be divided into tree time segments representing te ebb, flood and slack tides. Discarge troug a spillay is enanced during ebb retarded during flood and unaffected during slack tide since tere is not any tidal current affecting te discarge. Tidal effects during slack tide are implicitly accounted for troug te tail-ater elevation (ig or lo ater). In case of saline edge te elevation of its interface

6 is important since it can cause reverse flo and salt ater intrusion, resulting not only in inaccurate flo estimations but also undesirable environmental conditions Structural Design Variables. Before discussing te structural design variables, it is important to outline te particular features of te coastal spillays under consideration. Te structures can be generally grouped into to main groups (a) tose it an elevated rectangular spillay structure (Figure ), and (b) tose it a lo-elevation gradually-rising spillay design (Figure 3). Spillays S-13 and S-1-A belong to te former group ile spillays S-0F, S-0G, S-1 and S- belong to te latter design group. In addition, it sould be noted tat on te top of te spillay tere is a eir located directly under te gate. It is anticipated tat tose to structural designs to create different flo patterns. Furtermore, it is expected tat for te elevated rectangular spillay design flo caracteristics ould be different under ig and lo upstream ead. Under ig ead conditions te massive spillay structure ould control te flo ile for lo ead conditions flo may be controlled only by te top eir. In te proceedings for clarification purposes te entire structure ill be called spillay and tat includes bot te base structure and te small eir on te top, ile te top eir under te gate ill be called as eir. Based on te above observations te structural design parameters are defined as follos: spillay eigt (P ), spillay crest lengt (L ), top eir eigt (P), top eir lengt (L), spillay gate opening idt (b), maximum gate opening (D), spillay skin rougness (k s ), angle of upstream spillay ing-all (φ), idt of upstream cannel (B) and eccentricity of operating gate (ε). Te spillay eigt is measured from te top of te canal bottom to te eir crest, ile te spillay lengt is measured longitudinally over te entire spillay structure excluding te lengt of any protective upstream and donstream riprap. Te eir eigt is measured from te top of te massive spillay structure to its crest, ile te eir lengt is measured longitudinally over its crest. Te spillay opening is te total idt en all gates are opened. Te skin rougness accounts bot for te spillay surface (concrete) as ell as te protective riprap. Te angle of te upstream ing-alls is affecting te flo by streamlining te ater toards te gate. Flo calculations can also be affected by te eccentricity of te structure and te location of te operating gate(s) in reference to te axis of te upstream canal. Tis is important since some structures ave to or tree gates tat may not operate all at te same time. Finally, te idt of te upstream canal is included since it is indicative of te flo convergence from te ide canal into te gates Formation of Dimensionless Groups. Considering te specifics of te 1 variables listed in te preceding paragraps, and accounting for te specifics of te local conditions te parameters can be combined troug te Buckingam Teorem into te folloing teoretical expression: β Q QL A = α g(h )Hb νb(h ) T gp Q 3 ksgl A P H P ere te coefficient α and te exponents β, γ, δ, ε, ζ, η and θ are to be estimated numerically. Tose constants must be evaluated under tree tidal flo conditions i.e. ebb, flood and slack tide. For slack tide te exponent γ sould be set equal to zero. Also, for smoot flo regime δ = 0, ile for roug flo regime β = 0. Te dependent variables tat need to be provided as input for te teoretical expression are te upstream ead, tail-ater ead, tidal amplitude, and te gate opening idt if all gates are not operational. All of te oter quantities are constant. Any oter potentially contributing factors (i.e., salinity, suspended solids, surface tension, eccentricity, etc,) are lumped itin te coefficient, α, unless existing data indicate te need to express tem explicitly. γ T δ ε ζ η b B ϑ

7 Tail-ater Gate Spillay Weir Water surface Flo Canal bottom Figure : Scematic configuration of Structures S-13 and S-1A Tail-ater Gate Weir Water surface Flo Riprap Spillay Canal bottom Figure 3: Scematic configuration of Structures S-0F, S-0G, S-1 and S- Te pysical significance of te individual terms in te above equation is identified as: Q = F r is te Froude number and sos te relative significance beteen inertia and g(h )Hb QL gravitational forces; = R e is te Reynolds number and sos te relative significance νb(h ) beteen inertia and viscous forces; altoug te bulk flo is turbulent tis term represents te effects of

8 A te laminar sub-layer in case of smoot or transitional flo conditions; sos te relative T gp significance of te vertical tidal fluctuating motion (rising/falling of te ater surface) versus te Q orizontal tidal propagation speed; sos te relative significance beteen inertia and frictional 3 k gl s T forces; A sos te relative significance of te tidal amplitude versus te tail-ater ead; te relative significance beteen te tail-ater and te eigt of te entire spillay structure; P sos H P sos te relative significance beteen te ead difference and te eigt of te eir; B b sos te relative significance beteen te gate opening idt and te average idt of te canal and can become important in case tat not all of te gates are operational. 4. Calibration and testing Te proposed curve as calibrated using data from four coastal spillay structures in souteastern Florida, U.S.A. Te actual flo rates ere estimated by using a combination of continuously recording Ultrasonic Velocity Meter (UVM) and data collected from an Acoustic Doppler Current Profiler (ADCP). All geometric data ere obtained from structural design blueprints ile te ater elevations and oter related data ere obtained from SFWMD records. Structure S-13 Structure S-1A Estimated Flo Rates [cfs] Estimated F lo R ates [cfs] Structure S-0F Structure S Estimated Flo Rates [cfs] Estimated F lo R ates [cfs] Figure 4: Flo Rate Simulation Results

9 A single calibration curve applicable to all of te spillays as still not feasible since tere ere some significant differences among te various structures under consideration. Tose differences included design features of te structure (particularly te magnitude of te ratio of P/P ) and te number of te spillay gates (ranging from one to tree). Te equations ere fitted in terms of te unknon coefficient and te exponents by using data series of te discarge, Q, te eadater, H, and te tailater,. For tat purpose, te governing equation as ritten in terms of natural logaritms so tat a linear regression as applied. Te simulation results as compared to actual field measurements are son in Figure 4. As it can be seen te results are very promising, Hoever, calibration and verification of te proposed formulas is still an undergoing process and te accuracy is anticipated to be improved by using additional data as tey become available. 5. Conclusions Based on te researc and analysis conducted in tis study, te folloing conclusions can be dran: 1. Tere is a need for more accurate formulas for te estimation of flo rates over coastal spillays operating under submerged and tidally-affected systems.. A regression-type model based on dimensional analysis and π-teorem is very effective in producing accurate flo predictions. 3. A ide variety of parameters involving ater properties, flo caracteristics and structural design can ave a major effect on te flo rates simulation accuracy. References Ansar, M., Alexis, A., Damisse, E. (00) Atlas of Flo Computations at District Hydraulic Structures, Tecnical Report, Hydrology and Hydraulics Division, Sout Florida Water Management District, West Palm Beac, Florida. Ansar, M., Raymond J.H. (005) Tidal Flo Computations at a Coastal Prototype Spillay, Submitted to J. of Hydraulic Engineering, ASCE. Collins, D.L. (1977) Computation of Records of Streamflo at Control Structures, U.S. Geological Survey, Water Resources Investigation Report Denton, R.A. (1987) Locating and Identifying Hydraulic Controls for Layered Flo Troug an Obstruction, J. Hydraulic Researc, IAHR, 5(3): Emiroglu, E., Baylar, A. (003) Te Effect of Broad-Crested Weir Sape on Air Entrainment, J. Hydraulic Researc, IAHR, 41(6): Fiuzat, A.A., Skogerboe, G.V. (1984) Comparison of Open Cannel Constriction Ratings, J. Hydraulic Engineering, ASCE, 109(1): Huppert, H.E., Britter, R.E. (198) Separation of Hydraulic Flo Over Topograpy, J. Hydraulic Engineering, ASCE, 108(HY1): Halliell, A.R. (1967) Tidal Velocities Across a Partly-Completed Barrage, J. Hydraulic Engineering, 93(HY5): Hang, N.H.C., Hougtalen, R.J. (1996) Fundamentals of Hydraulic Engineering Systems, 3 rd Edition, Prentice Hall, Upper Saddle River, Ne Jersey. Irrigation Researc and Training Center (00) Long Crested Weir Design, Tecnical Report, California Polytecnic State University, San Luis Obispo, California. Jain, S.C. (001) Open-Cannel Flo, Jon Wiley & Sons, Ne York, Ne York. Kosrojerdi, A., Kavianpour, M.R. (00) Hydraulic Beavior of Straigt and Curved Broad Crested Weirs, Proc. Fift International Conference on Hydro-Science and Engineering, Warsa, Poland. Leliavsky, S. (1965) Irrigation Engineering: Sipons, Weirs and Locks, Capman & Hall, London,.K. Meta, A., Scarlatos, P.D. & Srinivas (1991) Preliminary Studies on Mixing and Entrainment of Fluid Mud, US Army COE, Report UFL/COEL-91/005, Gainesville, Florida.

10 Mossa, M., Petrillo, Canson, H. (003) Tailater Level Effects on Flo Conditions at an Abrupt Drop, J. Hydraulic Researc, IAHR, 41(1): Rouse, R. (Editor) (1950) Engineering Hydraulics, Jon Wiley & Sons, Ne York, Ne York. Scarlatos, P.D. (005) Tidal Hydraulics at Coastal Spillays, Tecnical Report, Sout Florida Water Management District, West Palm Beac, Florida. Skogerboe, G.V., Hyatt, L. (1967) Analysis of Submergence in Flo Measuring Flumes, J. Hydraulic Engineering, ASCE, 93(HY4): Skogerboe, G.V., Hyatt, L. (1967a) Subcritical Flo Over Higay Embankments, J. Hydraulic Engineering, ASCE, 93(HY6): Tillis, G.M., Sain, E.D. (1998) Determining Discarge-Coefficient Ratings for Selected Coastal Control Structures in Broard and Palm Beac Counties, Florida, U.S.G.S., Water-Resources Investigations Report , Tallaassee, Florida. U.S. Army Corps of Engineers (1963) Typical Spillay Structure for Central and Soutern Florida Water-Control Project: Hydraulic Model Investigation, Tecnical Report Vicksburg, Mississippi. U.S. Army Corps of Engineers (1987) Hydraulic Design Criteria Overflo Spillays Discarge Coefficients, Seet 1-1/5, Vicksburg, Mississippi. U.S. Bureau of Reclamation (001) Water Measurement Manual, Water Resources Tecnical Publication, U.S. Dept. of Interior & U.S.D.A., Agricultural Researc Service, Water Resources Researc Laboratory, Wasington, D.C. Autorization and Disclaimer Autors autorize LACCEI to publis te papers in te conference proceedings. Neiter LACCEI nor te editors are responsible eiter for te content or for te implications of at is expressed in te paper.