Project Report No. 594

An Experimental and Numerical Study of Long-throated Flumes

Final Report

By

William Herb and Matthew Hernick

University of Minnesota, St. Anthony Falls Laboratory

Prepared for:

Metropolitan Council Environmental Services

November, 2020

Minneapolis, Minnesota

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The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age or veteran status.

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Table of Contents Executive Summary..................................................................................................................................... 4

Acknowledgements .................................................................................................................................... 5

1. Literature Review ................................................................................................................................ 6

1.1 General Information on Long-Throated Flumes ................................................................................ 6

1.3 Long-Throated Flumes for Wastewater Applications ........................................................................ 9

1.4 Long-Throated Flume Theory (WinFlume and ISO 4359) ................................................................ 10

1.4 Analysis of Critical Depth Flumes using Computational Fluid Dynamics ......................................... 16

References ............................................................................................................................................ 17

2. Physical and Computational Models of a U-flume ............................................................................ 19

2.1 Introduction and Background ......................................................................................................... 19

2.2 Scaling and WinFlume ..................................................................................................................... 20

2.3 Physical Model ................................................................................................................................ 26

Physical Model Description ............................................................................................................... 26

Measurement and Procedure ........................................................................................................... 31

Physical model run procedure .......................................................................................................... 36

Physical Model Results and Discussion ............................................................................................. 37

2.4 CFD Analysis of the Physical Model ................................................................................................. 47

Boundary Conditions......................................................................................................................... 47

CFD Results ....................................................................................................................................... 50

2.5 Conclusions and Recommendations ............................................................................................... 55

References ............................................................................................................................................ 57

3. CFD Analysis of M025A ......................................................................................................................... 58

3.1 Introduction .................................................................................................................................... 58

3.2 Simulation of the as-designed M025A u-flume rating curve ........................................................... 60

3.3 Simulating the effect of high upstream pipe slope on the M025A rating curve. ............................. 61

3.4 Conclusions ..................................................................................................................................... 63

4. CFD Model Application to M200A/B ..................................................................................................... 64

4.1. Verification of ANSYS-Fluent Analysis Package .............................................................................. 64

4.2. CFD modeling of Dual U-flumes for M200A ................................................................................... 65

4.3. CFD Model of M200A w/ 1 flume ................................................................................................... 71

4.4. Model for Aeration/Misting at M200A/B ....................................................................................... 76

4.5. Conclusions .................................................................................................................................... 85

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Appendix 1. Measured Water Surface Profiles from the Physical Model ................................................. 86

Appendix 2. M200 Meter Vault Drawing .................................................................................................. 91

Executive Summary Section 1 summarizes information collected from published literature on long-throated flumes, including the ISO 4359 international standard and the theory behind the WinFlume modeling package. A key difference between long-throated (e.g. U-flumes) and short-throated flumes (e.g. Parshall flumes) is that the design of long-throated flumes allows the use of relatively simple mathematical expressions to predict the rating curve, whereas short-throated flumes require empirical rating curves. However, accurate modeling of the rating curve of a long-throated flume still requires some empirically-derived coefficients to consider boundary layer effects. The theory used to model the rating curves of long-throated flumes, e.g. using WinFlume or ISO 4359, has limitations at both low flows and high flows. Preliminary analysis of the rating curve for the U-flume designed for the physical model component of this study (Section 2) showed the WinFlume and ISO 4359 methods to give rating curves within 1% of each other.

Overall, the literature suggests that long-throated flumes have the advantage of greater design flexibility, and in some cases, lower installation costs compared to short-throated flumes. Some of the literature suggest a general movement from Parshall flumes to long-throated flumes, but no specific usage numbers were found. A potential disadvantage of U-flumes is increased fabrication cost, due to the complex shapes needed to for the upstream transition from a circular pipe to the U-shaped throat, however, newer fabrication technology (e.g. CNC machining) make custom, complex shapes more practical to manufacture. No information was found to compare the ability of long- and short-throated flumes to handle non-ideal upstream conditions.

Section 2 describes a physical and numerical modeling study of a U- flume design targeted for the M025A wastewater metering station. The study tested the ability of the software package WinFlume to predict the rating curve of a U-flume designed for M025A, using both a 1:2 scale physical model and a 3D computational fluid dynamics model. An experimental rating curve was developed over a range of scaled flows equivalent to the minimum and maximum flows at the M025A, and a range of tailwater levels were set for each flow rate, to test the tailwater limits of the flume design in comparison to WinFlume estimates. The results of the experimental study showed good agreement of the experimentally determined rating curve and the WinFlume predicted rating curve. For a given gauge depth, the measured and predicted gauge depths were within 1 to 2%, with the experimentally measured gauge depths consistently higher than the WinFlume predictions – this is within the estimated accuracy of WinFlume. The uncertainty of the experimental rating curve was about 1%. Experimentally, tailwater depth was found to affect the gauge measurement for tailwater depth above 80-95% of the gauge depth, a broader range than to the limiting tailwater values estimated by WinFlume (86-87%). 3D computational fluid dynamics model (CFD) results were also in good agreement with experimental results, with a 1-4% difference between the CFD and experimental rating curves. The CFD model is therefore a useful tool for examining the performance of U-flumes for cases not covered by WinFlume, such as non-ideal upstream conditions. Based on the results of the experimental and CFD studies, the

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WinFlume-generated rating curve for M025A is expected to be 3% accuracy or better over the typical flow range, assuming that the tailwater submergence is below 85%.

Section 3 summarizes the computational fluid dynamics (CFD) analysis of the u-flume installed at the M025A metering station. The first portion of this this study, looking at potential backwatering effects on the M025A u-flume from interceptor 8151, found that even with statistically rare (99th percentile) backwatering from interceptor 8151 flows, the submergence ratio (the ratio of the tailwater depth to gage depth) should not exceed 0.7 (70%). CFD analysis of the u-flume rating curve found that the accuracy should not be significantly affected for submergence ratios less than 0.95 for typical operating flows (4100 gpm) and 0.85 for very high flows (21000 gpm). As a result, backwatering effects are not expected to affect the performance of the M025A u-flume. In the second portion of the study, the effects of the surveyed upstream pipe invert slope on the as-built rating curve of the M025A u-flume were quantified for both the as-built u-flume and a proposed modified version with a raised throat. The CFD simulations suggest that the surveyed upstream pipe inverts cause the as-built u-flume to read 6 to 7% low. The composite accuracy of the CFD-generated rating curve points was estimated to be 4.5%, based on the CFD simulations and dye testing results. Raising the u-flume throat by 6” with an insert was projected to reduce the flow measurement error (compared to the WinFlume rating curve) from 7% to 3%.

Section 4 describes the computational fluid dynamics (CFD) analysis performed of several u-flume designs for retrofit in the M200 metering station, including a single u-flume and dual u-flumes with a custom transition to the downstream pipe. CFD analysis of a single u-flume design found that relatively smooth transition of the high-speed flow coming out of the u-flume into the 96” outlet pipe was achievable. The dual u-flume configuration requires relatively little modifications to the existing metering vault, while the single u-flume configuration would require costlier reconstruction of the meter vault and upstream pipes to eliminate the existing 5 ft. elevation drop inside the metering station. The dual u-flume analysis included 1) CFD modeling of the possible effect of the upstream splitter on the u-flume rating curve and 2) analysis of several custom transition channels to reduce misting and aeration downstream of the u-flumes. The upstream splitter was found to have minimal (<1%) impact on the u-flume rating curve up to 7000 gpm (per flume), and a moderate effect (~3%) at 14000 gpm. Several downstream transition designs for the dual u-flume configuration were analyzed. By designing the transition sections such that 1) the downstream water level matched the water level in the 96” outlet pipe, and 2) the high-speed flow from the transition had relatively little vertical momentum at the outlet, relatively smooth transition of the flow into the 96” outlet pipe was achieved.

Acknowledgements This study was funded by Metropolitan Council Environmental Services, under contract 16I046, with Dan Chouinard as Project Manager. The authors would like to acknowledge the extensive efforts of Erik Steen (St. Anthony Falls Lab) in the design and construction of the physical model used in this study.

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1. Literature Review

1.1 General Information on Long-Throated Flumes Long-throated flumes are a subset of venturi flumes, which measure flow in an open channel or gravity-flow pipe using a contraction through a control area (throat) to create critical flow, and a predictable relationship between flow rate and water depth at some point upstream of the critical flow point. Long-throated flumes are designed so that the throat section is sufficiently long to create parallel flow lines, which enables the rating curve to be predicted with analytical expressions. A diagram of a typical long-throated flume is given in Figure 1.1. In contrast, short-throated flumes such as the Parshall flume need to be experimentally calibrated, and therefore are tend to be used as a series of stock designs of different sizes.

Much of the work done in developing long-throated flumes was done by the US Bureau of Reclamation, with the primary application of measuring flow in open channels, particularly for irrigation systems (Clemmens 2001, USBR 2001, Wahl 2002). The advantages of long-throated flumes for irrigation applications include good ability to pass sediment and debris, low cost and ease of maintenance, and the ability to make accurate flow measurements with low head loss and with high submergence conditions (USBR 2001). These advantages of long-throated flumes for irrigation applications also make them suitable for wastewater applications.

There are several comprehensive resources available for designing long-throated flumes and for calculating the rating curve, including the ISO 4359 standard and the WinFlume software package. ISO 4359 (2013) is the international standard document describing the use of long-throated flumes. ISO 4359 includes theoretical information for determining the rating curve of long-throated flumes, including a general formulation and specific formulations for rectangular, trapezoidal, and U-shaped throat sections. Microsoft Excel spreadsheets are also included to calculate rating curves. WinFlume is a Windows package specifically for designing long-throated flumes (Wahl et al. 2000, 2002). The WinFlume tool allows the user to design a long-throated flume, calculate the rating curve, and determine the flow range over which accurate measurements can be expected. Options for the throat cross-sectional shape include rectangular, triangular, parabolic, trapezoidal, and U-flumes. The theoretical formulations used in ISO 4359 and WinFlume are detailed in the “Long-Throated Flume Theory” section of this report.

The theoretical formulations used in the WinFlume model are given in Clemmens et al. (2001). This report was preceded by Bos et al. (1984), Clemmens et al. (1987), and Clemmens et al. 1993. A main thrust of Clemmens et al. (2001) is to develop equations for prediction of the rating curves for various long-throated flume types, which form the theoretical basis for the WinFlume program. A substantial amount of practical design guidelines for long-throated flumes is also given, including the following:

• The overall head loss in a long-throated flume can be minimized by using an expansion section with an expansion rate of about 1:6. Very high expansion rates (>1:3) increase head loss due to flow separation, while more gradual expansions (1:10) increase frictional losses.

• Deposition of sediment upstream of the flume can be minimized by designing in a drop in the channel bottom elevation at the throat exit.

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• Scaling of flumes for laboratory studies is also discussed. Provided that viscous effects do not become important, Froude scaling should give good results. A guideline of scaling ratios between 1:4 and 4:1 is given.

Several water measurement manuals exist which include information on long-throated flumes. The USBR Water Measurement Manual (USBR 2001) is a relatively comprehensive source of information on flow measurement in open channels and piping. In the introduction of the newer version of the water measurement manual, the authors explain that information on Parshall flumes has been de-emphasized, and long-throated flumes are recommended for new installations, although it is noted that some states, by law, require Parshall flumes. The following advantages of long-throated flumes are given: 1) A rating curve can be calculated for any throat cross-section within ±2%, provided that critical flow is achieved in the throat. 2) Long-throated flumes can be custom fit to most channel geometries and optimized for the site to measure over a wide range of flows. 3) Long-throated flumes are amenable for use as portable devices. 4) The required head loss for long-throated flumes is relatively small. 5) Long-throated flumes have few problems with floating debris and sediment. 6) Long-throated flumes are usually the most economical structures for measuring flow. 7) Long-throated flumes can be designed and calibration by computer, and a rating curve can be generated based on post-construction dimensions.

Figure 1.1. Schematic diagram of a long-throated flume, showing many of the important dimensions. From Clemmens et al. (2001).

The USBR Water Measurement Manual includes a discussion of measuring flow in partially-full circular pipes, using long-throated flumes. Calibration coefficients are given for several long-throated flume types (rectangular, trapezoidal), based on the theory given in Clemmens et al. 1993 and Clemmens et al. 1987. The Isco Open Channel Flow Measurement Handbook (Grant and Dawson 2001) gives information on a number of weir and flume types. The Isco document has a short section on long-throated flumes, referencing the ISO 4359 document. The British rectangular flume is highlighted as a flume design commonly used in Europe, and is long-throated flume with a rectangular cross-section, a flat bottom, and side contractions. Siris is a manufacturer of these rectangular, long-throated flumes, which are

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described as being commonly used for metering wastewater treatment inflows (http://www.siris.co.uk/venturiflumes.html). The Palmer-Bowlus flume design falls somewhere between short- and long-throated flumes, behaving as a long-throated flume at low flow but become short-throated at high discharges (Dr. Bert Clemmens, 2016 personal communication). While Palmer-Bowlus flumes are, by design, easy to install in circular pipes, their high flow characteristics limit the measureable flow range (Grant and Dawson 2001). Kulin (1984) describes the application of Parshall and Palmer-Bowlus flumes for in-plant, open channel flow measurement of wastewater. This document summarizes a number of considerations for using Parshall and Palmer-Bowlus flumes for wastewater applications, including procedures for checking the calibration of the primary (flume) and secondary (depth measurement) flow measurement devices for cases where the flume rating curve uncertainty is higher than acceptable limits. Ackers et al. (1978) has extensive descriptions of the application of long- and short-throated flumes to flow measurement. For flow measurements in circular culverts and partially full pipes, U-flumes and trapezoidal flumes are recommended. A rather complete derivation of the rating curves for long-throated flumes is presented, where the discharge coefficient (Cd) is estimated based on displacement thickness. The variation of the boundary layer displacement thickness is given in the form of a chart, as in ISO 4359 (see Long-Throated Flume Theory Section and Figure 1.3).

Several studies have attempted to quantify the accuracy of WinFlume in predicting the rating curve of long-throated flumes. Ackers et al. (1978) gives several experimental data sets for the variation of the discharge coefficient (Cd) with flow rate, and estimates that the experimental rating curve is within 2% of the theoretical rating curve, based on ISO 4359 theory. Replogle et al. (1987) quantified flow measurement errors in long-throated flumes due to longitudinal leveling errors, up to ±30% error in head for ±3.7% error in level. This error was reduced to ±10% by moving the stilling well position to a point just downstream of the throat section, but keeping the pressure tap position upstream of the throat.

Several papers (Emamgholizadeh et al. 2009, Guan et al. 2014, Rady 2015) present design sensitivity studies that compare the rating curves of long-throated flumes over a range of design parameters for theoretical predictions and laboratory experiments. These papers do not give information on the accuracy of the reference flow measurement methods used for the experiments, so that the absolute accuracy of the rating curve data given is not known. Emamgholizadeh et al. (2009) compared WinFlume model results to experimental rating curve measurements for 0.25 m throat width, rectangular cross-section long-throated flumes with no width contraction, and found an average error of 10.6%. Guan et al. (2014) tested a series of trapezoidal long-throated flumes in a laboratory, to quantify the accuracy of the standard methods for estimating the rating curve for flumes with varying degrees of lateral and vertical contraction and contraction rates. Measurement errors of up to 9.6% were documented, with the highest errors associated with more abrupt lateral contractions (1:2), whereas the lowest errors were associated with intermediate contraction rates (1:3). Rady (2015) used WinFlume to model long-throated flumes with rectangular cross-sections, for a range of throat to channel width ratios, sill heights, and values of upstream and downstream pipe slope. The variability of the discharge coefficient was characterized as a function of the design parameters.

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1.3 Long-Throated Flumes for Wastewater Applications Although the information in literature suggest that long-throated flumes are suitable for wastewater flow measurement, no data are given to suggest a trend towards increased usage of long-throated flumes. Hager (2010) discussed the application of short- and log-throated flumes to wastewater applications. Raised bottom sills are not recommended, to maximize sediment transport capability. The expression for the rating curve for a long-throated flume with a trapezoidal cross-section is derived, including an estimate of the effect of streamline curvature. A claimed disadvantage of long-throated flumes is the higher cost associated with the extra length of long-throated flumes compared to short-throated flumes. Boiten (2008) mentions both long- and short-throated flumes as suitable for sanitary flows, but no usage data are given.

Despite several statements indicating the usefulness of long-throated flumes in wastewater applications, there is little documentation of actual installations, and no apparent documentation of using U-flumes for metering for the purpose of revenue generation. References to long-throated flumes in wastewater fell into two categories, 1.) long-throated flumes in large rectangular or trapezoidal channels at wastewater treatment plants, and 2.) flumes for insertion into sewer pipes, having U-shaped or round-bottom approach sections with typically trapezoidal throat section, such as the Palmer-Bowlus geometry. No examples of flumes with U-shaped throat section were found. This may be due to the difficult of fabricating the converging section, which is summarized in text from the website of Flowmarque Limited, Oxfordshire, United Kingdom, “The U-shaped flume has compound curvature in the entrance transition and is therefore difficult to fabricate from sheet steel. [Flowmarque] does not offer U-shaped 4359 flumes but can supply flumes with trapezoidal throat sections for use in U-shaped drains in the form of the UV flume…” (http://www.flowmarque.com/Pages3_ISO_Flumes.htm) The “UV flume” referenced has a geometry which is simpler to construct but lacks a throat section, thus it is not a long-throated flume. A similar product, the Aqualyse Aqua-UV, is available from Groupe Aqualabo in France (http://www.aqualyse.fr/documentations/Fiche%20Aqua-UV.pdf). Newer fabrication technology (e.g. CNC machining foam/fiberglass) make custom, complex shapes more practical to manufacture, and may reduce the cost of manufacturing U-flumes.

Keller (2014) describes the design of a new long-throated flume to complement an existing long-throated flume for the purpose of measuring and controlling flow at a channel bifurcation near the Western Treatment Plant in Melbourne, Victoria, Australia. The channel shape was trapezoidal and flow rates ranged from 100 to 1600 ML/day (~25 to 425 MGD). Both flumes were studied in a 1:20 scale physical model and also with WinFlume. A comparison between the existing flume field rating curve and the models showed the field rating was 3% and 0.7% less than the WinFlume rating at low and high flow flow rates, respectively. The physical model rating was 8% and 3% less than the WinFlume rating, at low and high flows, respectively, which the author attributed to scale effects.

An abstract by Petrides et. al (2005) briefly describes the construction of a long-throated flume with a capacity of 100 to 700 MGD was at the Newtown Creek Wastewater Treatment Plant in Brooklyn, New York. The flume measures treated wastewater and is used for pacing of disinfection chemicals. The flume was designed using WinFlume software. The model was updated to account for as-built geometry. Tony Wahl (2016 personal email communication) at the US Bureau of Reclamation further described the Newtown Creek flume as 64 feet in width, with a rectangular throat and raised sill (ramp type design).

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1.4 Long-Throated Flume Theory (WinFlume and ISO 4359) The WinFlume program is windows package specifically for designing long-throated flumes. The rating curve calculations are based on the theory given in Clemmens et al. (2001). The limits on the applicability of this theory are also built into WinFlume, so that a number of design criteria are tested as the design process proceeds, including:

• Maintain user-specified freeboard in the approach channel at maximum flow. • Maintain a Froude number of 0.5 or less in the approach channel at maximum flow. • Maintain tailwater (submergence) conditions at or below allowable values • Operational flow range corresponding to a range of H1/L (upstream head/throat length)

between 0.07 < H1/L < 0.7, to maintain a rating curve accuracy within ±2%, or 0.05 < H1/L < 1.0 for 4% accuracy.

• Estimate the uncertainty in the measurement based on the head measurement method.

Clemmens et al. (2001) gives a comprehensive description of the use of flumes and weirs for flow measurement, with an emphasis on long-throated flumes, and is the main technical reference for the current version on WinFlume. A main thrust of this report is to develop equations for prediction of the rating curves for various long-throated flume types, which form the theoretical basis for the WinFlume program. The rating curve for a long-throated flume with a rectangular cross-section is given in the following form, based on conservation of mass and Bernoulli’s law:

(1) 1

2/1

32

32 hbgCCQ cvd

=

where Cd is the discharge coefficient, Cv is the velocity coefficient, g is the acceleration of gravity, bc is the bottom width of the throat section, and h1 is the water depth at the upstream measurement location. Other forms of Equation 1 are given for flumes with non-rectangular cross-sections, e.g. trapezoidal flumes and U-flumes.

The velocity coefficient takes into account the fact that the upstream water depth (h1) is measured, whereas the governing equations are derived based on the total upstream head (H1).

(2) u

v hHC

=

1

1

where the exponent u depends on the cross-sectional shape of the throat section. Clemmens at al. (2001) gives values of Cv in tabular form.

The discharge coefficient (Cd) takes into account wall friction, non-uniformities in the velocity distributions, and streamline curvature. Clemmens et al. (2001) first characterizes Cd as an empirical expression, in terms of the H1/L ratio, where L is the throat length (Figure 1.2). Friction losses at the wall boundary become more significant at lower values of H1/L, and limit the applicability of the expression for Cd to values of H1/L > 0.07 (for ±2% accuracy) or H1/L > 0.05 (for ±4% accuracy). At relatively high values of H1/L, the flow surface profile has more significant curvature, and Cd increases in a less predictable manner, limiting the predictability of Cd to H1/L < 0.7 (for ±2% accuracy) or H1/L < 1.0 (for ±4% accuracy).

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Figure 1.2. Variation of the discharge coefficient with H1/L (from Clemmons et al. 2001).

The WinFlume model does not use the empirical estimates of the discharge coefficient, but instead uses boundary layer theory to estimate head losses between the measurement point and the downstream end of the throat, described in Clemmens et al. (2001) section 6.5.1. Assuming that the boundary layer is tripped (initiated) at the upstream end of the throat, the transition of the boundary layer from laminar to turbulent is estimated, and the drag forces for the laminar and turbulent parts of the boundary layer, and the corresponding head loss, are estimated for each section of the flume based on:

(3) gR

LCH FL 2

2ν=∆

Where CF is the appropriate drag coefficient for turbulent or laminar conditions, R is the hydraulic radius, L is the length of the section, and ν is the mean velocity. The energy equation from the upstream head measurment to the critical flow point in the throat is then:

(4) 11 2H

BA

Hyc

cc ∆−−=

where yc is the critical depth, and Ac and Bc are the flow area and width of the free surface at the critical flow point, respectively. Note that this formulation for determining the head loss is different than the apporach used in ISO 4359, which uses a formulation based on displacement thickness.

Clemmens et al. (2001) gives additional corrections to the energy equation to take into account non-uniform flow across each cross section, which implies that the actual velocity head is not equal to the head based on mean velocity. For the approach channel, the ratio (α) of the actual velocity head to the

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mean velocity head is assumed to be 1.04, based on previous work. In the throat section, α is estimated based on the throat length, the water depth, and a drag coefficient, but is restricted to the range 1.0 < α < 1.04.

Compared to the emprical corrections discussed earlier, the theoretical corrections based on boundary layer theory give similar uncertainty in the final rating curve. Although the theoretical corrections should give more accurate rating curves at low flows, uncertainties in the actual surface roughness of a flume over time reduce the lower limit of the measureable flow range to H1/L=0.07.

Comparison of WinFlume to ISO 4359

ISO 4359 (2013) is the international standard document describing the use long-throated flumes. The general equations for the rating curve of a long-throated flume is given in a slightly different form from Clemmons et al. (2001):

(5) 2/3

2/32/12/3

*2*232

=

−=−=

=

e

ev

ee

eev

hH

C

hhbb

hbCgQ

δδ

where width and depth variables with the subscript “e” are effective dimensions and heads that take into account the displacement thickness of the boundary layer. The use of the effective dimensions eliminates the need for the Cv coefficient used in the Clemmens et al. (2001) formulations. The ISO 4359 document gives two methods for estimating the displacement thickness, δ*, taking into consideration

the Reynold’s number (υLu

) and the relative roughness, ks/L, where ks is the equivalent roughness of

the surface:

1) A simple method, where the effect of the boundary layer displacement is incorporated into a Cd coefficient, and δ*/L is assumed to be 0.003 for relatively smooth surfaces (105> L/ks > 4000) and Re > 3·105:

(6) 2/32/3

006.01006.01

−

−=

=

hL

bL

hh

bb

C eed

2) A detailed method, which attempts to fit the variability of the displacement thickness over a larger range of Re and L/ks (Figure 1.3). No equations for the detailed method are given in the ISO 4359 document, however, fits to the relationships given in Figure 1.3 are included in the spreadsheets that are included with the ISO document. The displacement thickness method is also described in Ackers et al. (1978). The spreadsheets calculate rating curves using both the simple and detailed methods.

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Figure 1.3. Relative displacement thickness δ*/L vs. Reynold’s number and relative surface roughness L/ks. Figure taken from ISO 4359; the data are originally from Harrison 1967.

To make a comparison between the ISO 4359 and WinFlume methodologies for calculating the rating curve of a long-throated flume, the rating curve was calculated for the U-flume designed for the physical model study component of this project, as summarized in Figure 1.4. The ISO 4359 rating curves were calculated using the Excel spreadsheet that is supplied with the ISO document, using both the “detailed” and “simple” ISO 4359 boundary layer methods. In both cases, the ISO calculations were within 1% of the WinFlume results.

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Figure 1.4. Calculated rating curves (flow vs. head) for the U-flume designed for the physical model component of this study. The percent difference between the curves is also given, scaled on the right axis. The throat is 0.30 m diameter x 0.928 m long, with no sill. The ISO 4359 rating curves were calculated using the Excel spreadsheet that is supplied with the ISO document. The upper and lower panels give results using the “detailed” and “simple” ISO 4359 boundary layer methods, respectively.

Other Accuracy Limitations of WinFlume and ISO 4359

Dabrowski and Polak (2012) point out the rating curve calculations used in ISO 4359 assumes that critical depth is achieved at the downstream end of the throat, whereas in reality, the stream wise position of critical depth can move substantially in as a function of the flow rate. For rectangular flumes, an analytic

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expression for the position of critical depth is derived. For Palmer-Bowlus flumes, they find a complex relationship between the critical depth position in the flume throat and flow rate, but suggest that a boundary layer calculation assuming that critical depth is achieved halfway down the length of the throat should reduce flow measurement error compared to the standard assumptions of ISO 4359 (Lcr/D=1).

Dufresne and Vazquez (2013, 2014, 2014b) published several studies that used computational fluid dynamics (CFD) to analyze stage-discharge relationships of long-throated flumes. These analyses focused on a particular design of long-throated flume with a rectangular cross section and no sill, proposed by Khafagi (1942). Dufresne and Vazquez (2013) use CFD to characterize a secondary discharge coefficient to correct the ISO 4359 formulation, to take into account curvature in the flow streamlines. Equations are given for the secondary discharge coefficient as a function of flume geometry, but are only valid for a specific flume geometry with curved walls in the converging section. Dufresne and Vazquez (2014) used CFD to analyze flow measurement errors in long-throated flumes associated with construction and installation problems, including significant adverse slopes, and depressions or bumps on the walls or floor of the throat. The open-source CFD package Open FOAM was used for the analysis, using Reynolds-average Navier-Stokes (RANS) techniques. The CFD model was verified against the data of Yeung (2007) – the model was found to reproduce the experimental discharge coefficients to an accuracy within the experimental scatter (about ±2%). Dufresne and Vazquez (2014b) analyze the location of critical depth and energy losses between the measurement section and the control section, using computational fluid dynamics (CFD). The limitations of using the boundary layer equations to estimate the discharge coefficient are discussed, and a methodology based on energy loss is proposed. Based on a CFD analyses (using ANSYS-FLUENT) of a long-throated flume with the exact geometry used by Yeung (2007), the following coefficients are estimated:

- A kinetic energy correction factor, which takes into account non-uniformity in the velocity distribution, and is found to vary between 1.01 and 1.16, upstream of the throat.

- A piezometric head correction factor, which corrects for non-hydrostatic pressure distributions due to curvature of the streamlines, and is found to vary between 0.88 and 1.02, in and slightly upstream of the throat.

- Energy loss terms upstream and downstream of the throat inlet.

The CFD-generated rating curve and the analytical rating curve corrected using the coefficients estimated from CFD are found to agree with the experimental results published by Yeung (2007) within the experimental scatter (~1%), except at the lowest discharge (2 l/s). Finally, Dufresne et al. (2014b) propose a procedure for calculating the rating curve of a long throated flume, however, the appropriate values of the coefficients were not generalized to other long-throated flume geometries.

Wahl et al. (2002) found that for width-contracted flumes with wide throat sections compared to the length, the flow disturbance created by the side wall contraction may not completely propagate across the channel before the flow exits the throat. Flume designs with a low length-to-width ratio (e.g. < 2) are more susceptible to submergence (tail water) effects – this information was incorporated into WinFlume.

Hager (2010) derives correction factors for streamline surface curvature, which limit the accuracy of long-throated flumes at high flows. As with the work of Dufresne and Vazquez, the surface curvature expressions are derived only for a specific geometry corresponding the flume design of Khafagi (1942).

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Noting the scarcity of experimental data to verify the methods used in ISO 4359, Yeung (2007) performed obtained experimental rating curve data for a rectangular, long-throated flume (the Khafagi design) with a throat width of 101 mm and a throat length of 300 mm. Tests of the long-throated flume were carried out in a recirculating flow system with an electromagnetic flow meter with a claimed accuracy of ± 0.2%. Yeung points out several potential deficiencies in the ISO 4359 model:

1) The model assumes that the boundary layer is initiated (tripped) at the leading edge of the throat. For flume designs with no sill, the boundary layer along the bottom surface may not be tripped.

2) Critical depth may be reached at an intermediate point in the throat, not at the downstream end (as assumed by ISO 4359).

3) The boundary layer assumptions used in the simplified ISO 4359 equations for Cv and Cd (Eqs. 5 and 6) are reasonable only for higher Reynold’s number (above 106), roughly corresponding to throat widths above 0.5 m.

Comparison of the experimental data to the ISO 4359 model were made in terms of the product Cd·Cv. For cases where the ratio of the upstream to downstream head (hu/hd) was at least 1.1, the ISO 4359 model matched the experimental results to about ±2%.

1.4 Analysis of Critical Depth Flumes using Computational Fluid Dynamics In addition to the CFD studies by Dufresne and Vazquez discussed above, a number of studies have used computational fluid dynamics (CFD) as a tool to analyze short- and long-throated flumes. Several CFD studies have focused on Parshall flumes (Davis and Deutsch 1980; Heiner 2009; Savage et al. 2014; Wright et al. 1994). Davis and Deutsch (1980) use an inviscid CFD model to assess the effect of channel slope, upstream velocity distortions, and flume geometry changes on flume performance. Heiner (2009) and Savage et al. (2014) used the Flow-3D package to assess the sensitivity of Parshall flumes to errors in the position of the head measurement and to variations in the wing-wall configuration. Wright et al. (1994) describes experiments and numerical models of boundary layer effects to develop corrections for the rating curve of Parshall flumes at low flow.

Hu et al. (2014) compared some characteristics Parshall, parabolic, and long-throated flumes using the Flow-3D package, for application to metering flow in u-shaped open channels. The described parabolic flume was a short-throated flume with a parabolic throat cross-section. The study concluded that the parabolic flume had substantially less head loss than both the Parshall and long-throated flumes, but no conclusions on the relative accuracy of the different flume designs was given.

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References Ackers, P., White, W.R., Perkins, J.A., and A.J.M. Harrison (1978). Weirs and flumes for flow measurement. Wiley. Boiten, W. (2008). Hydrometry: IHE Delft lecture note series. CRC Press. Bos, M.G., Replogle, J.A., and A.J. Clemmens, (1984). Flow Measuring Flumes for Open Channel Systems, John Wiley & Sons, New York, U.S.A. Clemmens, A.J., Replogle, J.A. and M.G. Bos, (1987). Flume: A Computer Model for Estimating Flow through Long-Throated Measuring Flumes, U.S. Department of Agriculture, ARS-57, Springfield, VA, U.S.A. Clemmens, A.J., Bos, M.G. and J.A. Replogle, (1993). FLUME: Design and Calibration of Long-Throated Measuring Flumes, ILRI, Publication 54, P.O. Box 45, 6700 AA Wageningen, The Netherlands.

Clemmens, A. J., Wahl, T. L., Bos, M. G., & Replogle, J. A. (2001). Water Measurement with Flumes and Weirs. Publication #58, International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands.

Dabrowski, W., & Polak, U. (2012). Improvements in Flow Rate Measurements by Flumes. Journal of Hydraulic Engineering, 138(8), 757-763.

Davis, R. W., & Deutsch, S. (1980). A numerical-experimental study of Parshall flumes. Journal of Hydraulic Research, 18(2), 135-152.

Dufresne, M., & Vazquez, J. (2014). Hydraulic influence of geometrical defects in Venturi flumes: shall we destroy and rebuild?. Journal of Applied Research in Water and Wastewater, 1(1), 38-42.

Dufresne, M., & Vazquez, J. (2014b). Head-discharge relationship of flumes: Energy loss versus boundary layer. Journal of Applied Research in Water and Wastewater, 1(2), 59-62.

Emamgholizadeh, S., Kazemassar, E., & Masodi, O. (2009). Comparison between the measured passing discharges through long throated flume and estimated discharge by Winflume software. ARPN Journal of Engineering and Applied Sciences, 4(5).

Guan, G., Liu, T., Wang, C., Chen, H., & Yao, X. (2014). Effect of side contraction on long-throated flume calibration. Transactions of the Chinese Society of Agricultural Engineering, 30(13), 1-9. (English abstract, Chinese manuscript).

Grant, D.M, and Dawson, B.D., 2001. Isco Open Channel Flow Measurement Handbook, 5th Edition, Isco Inc, Lincoln, NE.

Hager, W.H. (2010). Wastewater Hydraulics, 2nd Ed., Springer Verlag.

Harrison, A.J.M. (1967). Boundary-Layer Displacement Thickness on Flat Plates, Journal of the Hydraulics Division, 1967, Vol. 93, Issue 4, Pg. 79-91

Heiner, Bryan J., 2009. Parshall Flume Staff Gauge Location and Entrance Wingwall Discharge Calibration Corrections. M.S. Thesis, Civil and Environmental Engineering, Utah State University.

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Hu, H., Huang, J., Qian, Z., Huai, W., & Yu, G. (2014). Hydraulic analysis of parabolic flume for flow measurement. Flow Measurement and Instrumentation, 37, 54-64.

ISO 4359 (2013). Flow measurement structures — Rectangular, trapezoidal and U-shaped flumes. International Organization for Standardization, Geneva, Switzerland.

Jesson, M., Sterling, M. and D. Baker (2006). Application of ISO4359 for discharge calculation in a narrow flume. In Press, Flow measurement and instrumentation. (Abstract only).

Khafagi, A. (1942). Der Venturikanal (The Venturi flume). Versuchsanstalt für Wasserbau, Mitteilung 1. Leemann: Zürich [in German].

Keller, R. (2014) Physical Model Testing and Validation of Large Long-Throated Flumes. World

Kulin, G. (1984). Recommended Practice for the Use of Parshall Flumes and Palmer-Bowlus Flumes in Wastewater Treatment Plants. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/2-84/186.

Ludwig, R. G., and Parkhurst, J. D. (1974). Simplified application of Palmer-Bowlus flow meters. Journal (Water Pollution Control Federation), 2764-2769.

Petrides, T., Javaheri, J., and Gaba,. (2005) A. Design and Startup of a Long Throated Flume. (Abstract Only) Submitted to New York Water Environment Association (NYWEA) 78th Annual Meeting, New York City, February 2006. http://nywea.org/abstract/abstr-showall.cfm?MeetingID=8

Rady, R. M. (2015). Numerical Investigation of Flow Characteristics through Long-throated Flumes. International Journal of IT, Engineering and Applied Sciences Research (IJIEASR) 4 (9): 7-12.

Replogle, J. A., Fry, B. J., & Clemmens, A. J. (1987). Effects of nonlevel placement on accuracy of long-throated flumes. Journal of irrigation and drainage engineering, 113(4), 585-594.

Savage, B., Heiner, B., and Barfuss, S. (2014). Parshall flume discharge correction coefficients through modelling. Proceedings of the Institution of Civil Engineers - Water Management, 167(WM5): 279-287.

USBR (2001). Water Measurement Manual, 3rd Ed., U.S. Department of the Interior, Bureau of Reclamation, U.S. Government Printing Office, Washington, DC. USBR (2016). WinFlume web site.

http://www.usbr.gov/tsc/techreferences/computer%20software/software/winflume/index.html

Wahl, T. L., Clemmens, A. J., Replogle, J. A., & Bos, M. G. (2000). Win-Flume–Windows-based software for the design of long-throated measuring flumes. In Fourth Decennial National Irrigation Symposium, Phoenix, Arizona.

Wahl, T., Clemmens, A. J., Bos, M. G., & Replogle, J. A. (2002). Tools for design, calibration, construction and use of long-throated flumes and broad-crested weirs. Energy. Climate, Environment and Water-Issues and Opportunities for Irrigation and Drainage, 601.

Wahl, T. L. (2002). Performance limits of width-contracted flumes. In EWRI/IAHR Conference on Hydraulic Measurements and Experimental Methods, Estes Park, Colorado.

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Wright, S. J., Tullis, B. P., and T.M. Long, 1994. Recalibration of Parshall flumes at low discharges. Journal of Irrigation and Drainage Engineering, 120(2), 348-362.

Yeung H. (2007). An examination of BS3680 4C (ISO/DIS 4369) on the measurement of liquid flow in open channels-flumes, Flow Measurement and Instrumentation 18: 175-182.

2. Physical and Computational Models of a U-flume

2.1 Introduction and Background Metropolitan Council Environmental Services (MCES) commissioned this long-throated flume study to study the possible use of long-throated flumes (LTFs) to measure flow in open channel sanitary interceptor sewers, a role traditionally fulfilled by Parshall or Palmer-Bowlus flumes. However, the use of long-throated flumes may be advantageous in some situations. The U.S. Department of the Interior, Bureau of Reclamation has developed WinFlume software, a Windows-based program that performs a one-dimensional analysis of LTFs with outputs including a head vs. flow rating curve for custom flume geometries. WinFlume provides the ability to custom-design flumes for difficult applications, such as installations with high tailwater.

Prior to this study, there has been relatively little validation of WinFlume, and no validation of WinFlume for U-flumes designs. Therefore, a major thrust of the current project is to verify the accuracy of WinFlume for design of custom LTFs, specifically, flumes having a U-shaped throat (control section), through a comparison between a physical model, a WinFlume model, and a high-fidelity computational fluid dynamics (CFD) simulation, each with identical geometry. The basic geometry or parts of a long-throated flume are shown in Figure 2.1 below, which was taken from the WinFlume software.

Section 2.2 of this report introduces the flume geometry and WinFlume model, Section 2.3 is a summary of the physical modelling effort and comparison between the physical model results and WinFlume output, and Section 2.4 compares the high-fidelity computational model with the physical model.

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Figure 2.2. Flume Definition Sketch, from WinFlume, US Bureau of Reclamation (Wahl, Clemmens, Bos, and Replogle, 2001)

2.2 Scaling and WinFlume

Dimensions and Scaling

Physical models have been employed for many years in hydraulics research. A properly scaled model yields quantitative data which can be analyzed and applied to a larger prototype, that is, “full-scale” structure. For open channel flows such as those that are normal to sanitary sewers, Froude scaling is typically appropriate, as long as the flow remains well in the turbulent range as shown by the Reynolds number. The Froude number is a ratio of inertial to gravitational forces acting on water flowing through the flume. The Reynolds number is a ratio of inertial forces to viscous forces within the flow. When Froude scaling is applied, length dimensions scale directly and flow scales as shown in the following relationship:

where Q is flow rate and L is the length scale. After some analysis, St. Anthony Falls Laboratory (SAFL) initially proposed the construction of a physical model based on the preliminary U-shaped flume design for MCES meter M025A, with a preliminary scale of approximately 2:1, that is, one inch in the physical model is equal to two inches in the “full scale” prototype. Clemmens et al. (2001) recommends that physical models of flumes can be scaled down (or up) by up to a factor of 4, to keep the Reynold’s number and corresponding roughness and boundary layer effects in the same range.

At the start of the physical model project phase, MCES staff provided SAFL with an updated prototype scale WinFlume model “M025A - Revision 105” dated 10/27/2016. A new “model scale” WinFlume model was created by scaling down the M025A dimensions and formed the basis for design of the physical model.

As-built scaling

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Following completion of the physical model but before testing, flume dimensions were precisely measured using the overhead data carriage above the model, which is capable of scanning the model to a resolution of 1 mm. This is referred to as the as-built measurement, and was used to revise the WinFlume model and the CFD model. Figure 2.1 compares the prototype M025A geometry with the proposed and as-built physical (and WinFlume) model geometry. The as-built scale of model to prototype is 1:1.96, based on the average throat width relationship of 10.695 / 21.000 inches. This ratio was chosen to give a standard inlet pipe diameter (30 inches). At the prototype (full) scale, the Reynolds number varies from 1.8 x 10-5 to 3.6 x 10-5, while the Reynolds number of the scale model varies from 5.1 x 10-4 to 5.1 x 10-5 (Figure 2.1) at the low flow range. Reynolds numbers at model and prototype scales are high enough that nonlinear effects due to viscous forces will be negligible for the bulk flow.

It is important to note that, although it was initially derived by scaling a “prototype” design, identical geometry was used to compare results of the physical model, WinFlume model, and the CFD computer simulations.

WinFlume Model Description

The WinFlume software uses the long-throated flume theoretical formations developed by Clemmens, Wahl, Bos, and Replogle and published as Water Measurement with Flumes and Weirs (2001), to calculate a theoretical head for any given discharge or vice-versa, given the flume geometry and input parameters. Note that in this report, “head” refers to water level above the flume crest, shown as h1 in Figure 2.1., unless specifically noted.

A screen capture of the as-built WinFlume model is shown in Figure 2.2. Other relevant WinFlume parameters that are not shown on the screen include:

• Flume Construction Material Roughness Height: 0.000197 inches, “Glass [custom]” • Minimum Flow: 100 gallons per minute (gpm) • Maximum Flow: 3950 gpm • Tailwater calculation: normal depth (Mannings), actual tailbox geometry, n=0.013, S = 0.0004. • Head Measurement Method: Point gauge in stilling well, +/-0.003937 inches, 1 second intervals

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Table 2.1. Prototype and as-built model dimensions

Feature and dimension M025A PrototypePhysical Model As-

built NoteLength Scale P:M 1 0.509 1Length Scale M:P 1.957 1.964

U-Flume Features U-shaped throat width (inch) 21 10.695 Approach Length (inch) 42 21.398 Converging Length (inch) 66 33.319 Control Length (inch) 76 38.917 Expansion Length (inch) 42 21.425 2U-Flume Total Length (inch) 226 115.06

Drop through expansion (inch) 7 3.520 Drop end of expansion (inch) 7 3.625Total vertical drop at end (inch) 14 7.145

Upstream Pipe ID (inch) 58.5 29.95 3Downstream Pipe ID 72 36.00 4

h1 (inch) at Q (gpm) (WinFlume) 52.2" @21,000 gpm

Flow Scale (Froude) 1 0.185Velocity Scale (Froude) 1 0.714Actual Velocity in US Pipe (fps) 1.3 - 2.7 0.8 - 1.9

Qmin (gpm) 1000 115Qavg (gpm) 4100 767Qmax (gpm) 21000 3927

Note: Model Qmin = 200 gpm for calcs below. Re=(4*Vavg*R)/ νFroude # in US pipe @ Qmin 0.320 0.319Reynolds # in US pipe @ Qmin 1.8E+05 5.1E+04

Froude # in U-section @ Qmin 1 1Reynolds # in U-section @ Qmin 3.6E+05 5.4E+05

Notes:1. Scale based on throat width2. as measured. Slightly different in Winflume to get correct vertical drop3. 29.907" average rib diameter, 30.001" average valley diameter. 4. 36" channel with trapezoidal base

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Figure 2.2. WinFlume model screenshot for the as-built geometry.

WinFlume Output and Rating Equation

In addition to directly calculating head at any input flow, WinFlume will also calculate a best-fit rating equation, or rating curve, for use in estimating discharge at any head. For the parameters above, the curve-fit equation from 100 to 3,900 gpm is:

𝑄𝑄𝑓𝑓𝑓𝑓𝑓𝑓 = 27.1472 ∗ (ℎ1− 0.88869)1.52857

Table 2.2 is taken directly from WinFlume and lists the curve-fit discharge and percent difference for each theoretical discharge point. The fit is reasonable through much of the range, but noticeably not as good at the lowest flows, with errors of up to 1.6%. The rating curve was used to help in determining target discharges during the project, but the actual theoretical discharge calculations are more accurate, and thus best for comparison, and are used hereafter in this report.

The results of WinFlume theoretical calculations are presented alongside the physical model data in Section 2.3 of this report.

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Table 2.2. WinFlume theoretical and curve-fit discharge.

WinFlume warnings

WinFlume gave several warnings, which are explained briefly in Table 2.2. Further explanation for each warning is copied below, from pages 34 and 35 of the WinFlume User’s Manual (Wahl, 2001). While the warnings are important to note, it may not be possible to design a flume which entirely avoids warnings

h1 Q Q_fit D=Q_fit-Q (D/Q)*100% h1 Q Q_fit D=Q_fit-Q (D/Q)*100%Sill Curve Fit Sill Curve Fit

Referenced Theoretical Equation Referenced Theoretical EquationHead at Gage Discharge Discharge Difference Difference Warn- Head at Gage Discharge Discharge Difference Difference Warn-

inches gpm gpm gpm % ings inches gpm gpm gpm % ings3.21 100 98 -1.64 -1.64 23 20.173 2500 2502 1.72 0.07

3.962 150 151 1.04 0.69 23 20.425 2550 2552 1.97 0.084.61 200 202 2.31 1.15 23 20.676 2600 2602 2.21 0.09

5.192 250 253 2.69 1.07 23 20.925 2650 2652 2.45 0.09 125.73 300 303 2.50 0.83 23 21.173 2700 2703 2.68 0.1 12

6.235 350 352 2.00 0.57 23 21.418 2750 2753 2.89 0.11 126.714 400 401 1.36 0.34 23 21.662 2800 2803 3.10 0.11 127.173 450 451 0.73 0.16 21.905 2850 2853 3.29 0.12 127.616 500 500 0.21 0.04 22.146 2900 2903 3.47 0.12 128.045 550 550 -0.21 -0.04 22.386 2950 2954 3.64 0.12 12

8.46 600 599 -0.75 -0.12 22.624 3000 3004 3.78 0.13 128.864 650 649 -1.26 -0.19 22.86 3050 3054 3.91 0.13 12,239.257 700 698 -1.71 -0.24 23.096 3100 3104 4.03 0.13 12,239.641 750 748 -2.09 -0.28 23.329 3150 3154 4.12 0.13 12,23

10.017 800 798 -2.42 -0.3 23.562 3200 3204 4.19 0.13 12,2310.386 850 847 -2.70 -0.32 23.793 3250 3254 4.23 0.13 12,2310.747 900 897 -2.93 -0.33 24.023 3300 3304 4.25 0.13 12,2311.102 950 947 -3.11 -0.33 24.251 3350 3354 4.24 0.13 12,2311.451 1000 997 -3.25 -0.33 24.478 3400 3404 4.21 0.12 12,2311.794 1050 1047 -3.36 -0.32 24.702 3450 3454 3.74 0.11 12,2312.131 1100 1097 -3.43 -0.31 24.927 3500 3504 3.64 0.1 12,2312.464 1150 1147 -3.47 -0.3 25.15 3550 3554 3.50 0.1 12,2312.791 1200 1197 -3.47 -0.29 25.372 3600 3603 3.33 0.09 12,2313.115 1250 1247 -3.45 -0.28 25.593 3650 3653 3.12 0.09 12,2313.434 1300 1297 -3.41 -0.26 25.812 3700 3703 2.86 0.08 12,2313.748 1350 1347 -3.33 -0.25 26.031 3750 3753 2.56 0.07 12,2314.059 1400 1397 -3.24 -0.23 26.248 3800 3802 2.22 0.06 12,2314.367 1450 1447 -3.13 -0.22 26.464 3850 3852 1.83 0.05 12,23

14.67 1500 1497 -2.99 -0.2 26.678 3900 3901 1.38 0.04 6,12,2314.971 1550 1547 -2.84 -0.18 Equation: Q_fit = K1 * (h1 + K2) ^ u15.268 1600 1597 -2.67 -0.17 Parameters: K1 = 27.147215.562 1650 1648 -2.49 -0.15 K2 = -0.8886915.853 1700 1698 -2.29 -0.13 u = 1.5285716.141 1750 1748 -2.08 -0.12 Coefficient of determination: 0.9999834816.426 1800 1798 -1.87 -0.1 NOTE: This equation is only valid for h1 >= 0.88869 in16.709 1850 1848 -1.64 -0.0916.989 1900 1899 -1.40 -0.07 Theoretical discharge (Q) is determined by the WinFlume model, using17.266 1950 1949 -1.15 -0.06 hydraulic theory and empirical relationships determined from laboratory17.541 2000 1999 -0.91 -0.05 testing. It is the most accurate estimate of discharge. Curve fit discharge17.814 2050 2049 -0.65 -0.03 (Q_fit) is computed with the equation above, which was fitted to the18.084 2100 2100 -0.39 -0.02 theoretical discharge values. The 'difference' columns show the difference18.352 2150 2150 -0.13 -0.01 between the flow rates computed from the simplified equation and those18.618 2200 2200 0.14 0.01 obtained from the theoretical WinFlume model.18.882 2250 2250 0.41 0.0219.144 2300 2301 0.68 0.03 Summary of Warning Messages19.404 2350 2351 0.94 0.04 6 - Upstream energy head / control section length exceeds 0.7.19.662 2400 2401 1.21 0.05 12 - Gage is too close to converging section and/or throat.19.918 2450 2451 1.47 0.06 23 - Converging section may be too long (side contraction is too flat).

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at all discharges, while satisfying site constraints, e.g. length and available head drop. The same warnings were present in the prototype M025A WinFlume model at similar flows.

6 - Upstream energy head / control section length exceeds 0.7 - The ratio H1/L should be in the range of 0.07 to 0.7 to obtain the most accurate flow measurement. This error message is generally associated with the upper end of the discharge range of the structure. To eliminate this error, either increase the control section length or widen the control section (especially the top width) to reduce H1 at maximum flow.

Warning 6 occurs because at the very highest flows (21,000 gpm), upstream energy head exceeds 0.7 times the length of the control (U-shaped) section. Clemmens et. al. (2001) reports that outside of the range of 0.07 < H1/L<0.7, rating table error increases slowly from about +/- 2% at H1/L = 0.7 to about +/- 4% at H1/L = 1.0. However, the mean flow rate at M025A is 4100 gpm (Table 2.1), and the flow has exceeded 8000 gpm only a few times since 2001.

12 - Gage is too close to converging section and/or throat - The gaging- or head-measurement station should be located sufficiently far upstream from the structure to avoid the area of water surface drawdown, yet it should be close enough for the energy loss between the gaging station and the structure to be negligible. To meet these requirements, the gaging station should be located at a distance between two and three times H1max from the leading edge of the sill or at H1max from the beginning of the converging transition, whichever is greater. To eliminate this error, increase the approach channel length on the flume bottom profile drawing.

Warning 12 notes that the approach length is shorter than optimal at middle and high flows. In the current M025A U-flume design, the distance L’, from the gauge to the throat leading edge, is 108 in. For the design maximum flow (21000 gpm), 3· H1max is 160.7 in., and L’/H1max=0.67. However, flows can be as high as 11100 gpm while maintaining L’/H1>=3, so the design rule should be maintained for all but the most extreme flows. One possible effect is water surface drawdown at the measuring point, which would result in an apparent lower head measurement. It is difficult to ascertain if this occurred in the physical model. Compared to a flume with a rectangular cross-section, the upstream portion of the converging section of the U-flume has relatively little change in cross-sectional area and therefore relatively minor effects on the velocity and drawdown. Extending the approach length could result in higher friction and higher construction cost.

23 - Converging section length may be too long (side contraction is too flat) - When viewed in plan, flumes that are primarily side-contracted should have a contraction angle from the approach channel to the control section that is in the range of 2.5:1 to 4.5:1 (longitudinal to lateral distance). WinFlume checks to see that this condition is met at two elevations, the invert of the control section and the level of the approach channel water surface. If the transition is too long, there will be excessive friction loss between the gaging station location and the control section, and the structure may be more expensive to construct. To eliminate this error, reduce the length of the converging section. In unusual circumstances it may be impossible to eliminate all of the errors related to converging section length (10, 11, 22, and 23). In these cases, a converging transition that is too gradual (errors 11 and 23) is better than a converging transition that is too abrupt (errors 10 and 22).

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Warning 23 indicates the converging section may be too long at low and high flows, possibly resulting in excess friction (head loss), which would result in an apparent higher head measurement. WinFlume subtracts the approach surface width from control section width and divides by the contraction length to see if it’s between 2.5 and 4.5. One reason this warning may be displayed is that the contraction is checked at the invert of the control section, which in this case is the continuous flume centerline, and is not contracted for a circular approach and U-shaped throat geometry, unlike a rectangular or trapezoidal bottom geometry. WinFlume does not know the details of the converging section shape. In the present design, the flat sidewalls of the converging section converge at a rate of 3.5:1, placing it squarely in the recommended range.

2.3 Physical Model

Physical Model Description Figures 2.3, 2.4, and 2.5 show the physical model constructed for this project. The physical model consists of the following parts listed from upstream to downstream:

● Water supply piping. Water was drawn from the SAFL supply channel via and intake and pumped through a 40-horsepower centrifugal pump through 12-inch diameter PVC supply piping. Flow rate was controlled by means of the pump’s Variable Frequency Drive (VFD) and an inline knife valve.

● Orifice flow measurement. Refer to the Instrumentation and Measurement subsection for more information.

● Headbox. A headbox was constructed of lumber and plywood. A weir was positioned in the headbox to dissipate large scale turbulence before entering the approach pipe.

● Flow straightener. A tube bundle type flow straightener consisting of 3-inch diameter tubes each 30 inches long was inserted into the pipe to condition the flow as it exited the headbox. Screens with approximately ½-inch openings were placed on both ends of the straightener.

● Upstream pipe. The approach consisted of nominal 30-inch diameter dual-wall HDPE pipe, laid level and secured in place. The length of pipe between the flow straightener and the head measurement location was 303 inches, about 10.1 pipe diameters. Three sections of pipe were joined to make the full length. The outer wall of this plastic pipe is corrugated, but the interior is relatively smooth. The corrugation pattern, however, does slightly transfer to the interior of the pipe, with a pitch length between structures of 4 inches. As measured inside the pipe, the difference between average “ribs”, with smaller inner diameter, and “valleys” was about 2.4 mm or 3/32 inch. Diameters were measured with a caliper at nine rib and nine valley locations, horizontally and vertically. The average inner diameter was 760.8 mm (29.954 inches), as noted in Table 2.3.

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Table 2.2. Approach pipe inner diameter

mm inch Total Average Inner Diameter (ID) 760.8 29.954 Average ID at "Rib", or constricted 759.6 29.907 Average ID at "Valley" 762.0 30.001

This variation in diameter prompted some concern about effect on head. A pair of WinFlume models, identical except for pipe diameter of 29.91 and 30.00 inches, was used to compare estimated head elevations over the range of model flows. A maximum difference of 0.005 inches, approximately 0.02% was observed between models, which is negligible compared to the magnitude of the expected accuracy.

● Head measurement location. This is the location in the upstream pipe where all head measurements took place, and is noted as the Gauging Station in Figure 2.1. It was located at the approach length distance upstream (21.398 inches) of the beginning of the converging transition, as recommended by WinFlume. Refer to the Instrumentation and Measurement subsection for more information on head measurement.

● Converging transition. The intent of the transition is to smoothly guide streamlines from the circular pipe section to the U-shaped throat section. To accomplish the U-to-circle transition, the lower portion of the U (half circle) and a portion of the vertical leg of the U was expanded to meet the lower half of the upstream pipe. The lower portion was fabricated from shaped dense foam, sanded and sealed with multiple coats of smooth epoxy. Above this, the vertical walls of the U-shape were extended to the full 30-inch width of the upstream pipe. The vertical portion was fabricated from clear acrylic panels. A portion of the black polyethylene pipe was cut to fit between the vertical walls to guide streamlines in cases of higher flow. There is a cut out in the top to allow water surface scans. The converging transition is shown in Figure 2.4.

● Both the upstream pipe and downstream channel were installed at zero slope. The downstream level was controlled by the control gate, so that the downstream slope had no influence on the tailwater conditions. The upstream flow rate is established by the pump, and the depth upstream of the flume is established by backwatering effect of the flume itself, so that the flume measurements are not sensitive to the slope of the upstream pipe (this slope is not a specified parameter in the WinFlume model).

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Figure 2.2. Physical model, looking upstream at U-shaped flume section

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Figure 2.4. Flume section, looking downstream. Left: completed flume. Right: Epoxy coated dense foam base during construction.

● U-shaped control or throat section. This is the measurement section of the flume, in which the flow transitions from sub-critical to supercritical flow, passing through the critical depth. The lower curved surface was fabricated monolithically with the converging and diverging sections from epoxy-coated foam. The clear vertical walls were supported by metal bracing at the top to minimize deflection when the section was full of water, but still allow an unobstructed overhead view and scan.

● Diverging transition section. An expansion of the U-shape control section at 1:6 in all dimensions to meet a flat face, truncated at about 21.5 inches with a vertical drop to the downstream channel. The converging, control, and diverging sections are illustrated in Figure 2.4 and Figure 2.5.

● Downstream channel. A 36-inch wide epoxy coated plywood and stud wall channel, with 11 inch by 11 inch chamfered lower corners forming a trapezoidal lower section that was 14 inches wide at the base. This shape was chosen to approximate the lower half of a pipe, while leaving the top open to allow an overhead water surface scan, and providing good geometry (vertical walls) for operation of the adjustable weir. The downstream channel floor was level at 3.625 inches lower than the invert of the downstream end of the diverging transition per the WinFlume design.

● Adjustable height weir. The weir was hinged on the bottom and operated by an inclined screw and handwheel. The weir was used to set the tailwater elevation and to raise the tailwater in order to detect the point of submergence at any given flow rate.

● Tailbox and drains routed to the weigh tanks on a lower laboratory level.

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Figure 2.5. U-shaped flume section. Flow is from left to right.

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Measurement and Procedure

Instrumentation

In order to assess the flume’s rating curve for comparison to the WinFlume model, accurate measurements of A.) discharge, or water flow; and, B.) water depth, or head were required. Measurements of secondary importance were C.) tailwater elevation, to assess submergence, and D.) water surface profile for comparison to the predicted or computed water surface. The measurement techniques and estimated accuracies are presented below.

A1. Discharge: Orifice Meter

An orifice-type flow meter was used to continuously measure and record inflow during testing. Three different square-edged concentric round orifice plates were used. Pressure at D and D/2 pressure taps was installed was monitored by a Rosemount® 3051 differential pressure transducer. Instantaneous differential pressure was averaged, converted to a flow rate, and recorded every 10 seconds on the data acquisition PC. Orifice dimensions and flow relationships listed in Table 2.4 were developed using a method from the Flow Measurement Engineering Handbook, 2nd Edition, by R.W. Miller, 1989.

Table 2.4. Orifice meter relationships

Nom. Dia. (inch)

Actual Dia. (inch)

Beta ratio (d/D)

Runs Used Orifice Flow Equation (Q gpm, dP inches)

Base Wtr Temp. (F)

Coefficient Accuracy +/- (%)

6.5 6.501 0.547 5-11,5a 𝑄𝑄 = 2.5 + 151.8194(𝑑𝑑𝑑𝑑)0.5 35 0.6

4.5 4.500 0.379 12-15 𝑄𝑄 = 0.8 + 69.5628(𝑑𝑑𝑑𝑑)0.5 38 0.6

9.2 9.196 0.773 16-18,10a 𝑄𝑄 = 7.37 + 362.1170(𝑑𝑑𝑑𝑑)0.5 35 0.8 (β)

The orifice equations have a slight temperature dependence, but water temperatures only varied a few degrees, yielding very minor differences on the order of 0.03%. Piping upstream of the orifice location consists of two in-plane elbows followed by approximately 35 diameters of straight upstream pipe. This is sufficient straight length for all of the orifice plates used, such that the predicted accuracy of the method is +/- 0.6 - 0.8%, per Table 9.54 in the Flow Engineering Measurement Handbook.

A2. Discharge: Weigh Tanks

The SAFL weigh tanks were also used to measure the flow rate for most tests. Water flowing out of the U-flume was routed by gravity to the weigh tanks. Water was directed by pneumatically operated valves into one of two large cylindrical tanks, each hung on a 40,000 lb scale, as illustrated in Figure 2.6. A gravimetric flow rate was determined in lb/second by dividing the net weight of water in one tank by the time required to fill the tank. This was converted to a volumetric rate in cubic feet per second or gallons per minute by dividing the lb/sec rate by the density of water at the measured temperature. Errors associated with opening and closing tank valves were minimized by taking a series of weight measurements while keeping running time with a stop watch. A minimum of four tanks (left, right, left,

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right), but typically 6 or 8 tanks per flow rate was used. Estimated uncertainty in flow rate measured in the weigh tanks was +/- 0.6% to 1.2% of the flow rate.

Where both methods were used to measure flow, the rate generally registered slightly higher in the weigh tanks than the orifice meter; the maximum difference was less than 0.9%.

Table 2.5. Physical model discharge measurements. Note that the orange highlighted rows correspond with the CFD model flows

B. Head measurement

Two methods of head measurement were used; 1. An ultrasonic sensor mounted to the top of the approach pipe, and 2. A manually-read point gauge in a 6-inch diameter stilling well.

B1. Head: Ultrasonic sensor

Target Flow Rate (gpm) Run #

Q orifice (gpm)

Std. Dev. (gpm)

Std. Dev. As %

Orifice accuracy (1)

Combined uncert. +/- % (2)

Q weigh tank (gpm)

Uncert. (gpm)

Extra flow uncert. (gpm) (3)

Combined uncert. % +/-(2)

Difference as % of Orifice

115 Run 15 115.9 2.1 1.8% 0.6% 3.8% (4)187 Run 12 188.1 1.5 0.8% 0.6% 2.0% 189.7 1.0 1.0 1.2% -0.9%443 Run 13 443.7 1.6 0.4% 0.6% 1.4% 447.2 2.6 0.9 0.7% -0.8%767 Run 14 767.7 2.2 0.3% 0.6% 1.3% 770.8 4.2 1.0 0.6% -0.4%767 Run 11 769.8 3.9 0.5% 0.6% 1.6% 772.8 4.2 0.7 0.6% -0.4%767 Run 5a 770.0 3.9 0.5% 0.6% 1.6% (4)

1171 Run 8 1172.6 4.0 0.3% 0.6% 1.4% 1170.3 6.1 0.2 0.5% 0.2%1631 Run 9 1636.5 5.3 0.3% 0.6% 1.4% 1641.6 9.0 0.7 0.6% -0.3%2141 Run 18 2136.3 7.6 0.4% 0.8% 1.8% (4)2141 Run 6 2141.6 5.9 0.3% 0.6% 1.3% 2148.8 26.8 0.0 1.2% -0.3%2695 Run 10a 2693.7 9.7 0.4% 0.8% 1.8% (4)2695 Run 10 2693.7 6.3 0.2% 0.6% 1.3% (4)3291 Run 17 3287.3 9.6 0.3% 0.8% 1.7% 3301.9 19.2 0.9 0.6% -0.4%3927 Run 16 3927.4 10.6 0.3% 0.8% 1.7% 3933.3 24.1 1.0 0.6% -0.1%

Notes1. Engineering Flow Measurement Handbook, Table 9.542. Uncertainty at 95% confidence interval3. Estimated as 25% of measured base flows from other experiment drains4. No Data

Figure 2.6. Early sketch of SAFL weigh tanks

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An ultrasonic distance measuring sensor (Massa Products Corporation model M-300) was located over the center of the upstream pipe at the head measurement point specified by WinFlume, which was the “approach length” upstream of beginning of the converging section.

The ultrasonic sensor uses the travel time of reflected sound waves to determine the distance from the sensor to the water surface. The distance calculation depends on the speed of sound in air, which in turn depends on the temperature of the air through which the sensor waves travel. Although the ultrasonic device has an integrated temperature sensor, accuracy may be improved by using an additional external air temperature sensor. This was considered but rejected because the improvement in accuracy would be uncertain and relatively minor in relation to the additional effort. Instead, distance errors were minimized by reducing the distance measured. To accomplish this, the ultrasonic sensor was mounted on a vertically-moving point gauge (with 0.1 mm scale divisions) so that at each flow rate the sensor could be adjusted to the optimum range of 6-8 inches, slightly above the minimum range of four inches. For the highest flows, where the water surface was near the top of the pipe, an aluminum extension was added to the mount in order to raise the sensor and maintain the optimum measurement range.

The ultrasonic sensor reading was an input to the data acquisition software, which continuously calculated the water surface elevation. The manufacturer’s stated resolution is 0.01 inches, with an accuracy of 0.1% of target range. For a 6-inch target range, this would be 0.006 inches + 0.01 inches = 0.016 inches or about 0.4 mm. However, actual measurements varied somewhat, with standard deviations ranging from 0.012 inches to 0.25 inches, approximately 0.3% to 1.0% of the measured head at lowest and highest flows, respectively. Although the sensor is temperature compensated, variations in temperature of the air gap to the water surface are a likely source of error. The relatively close distance (6-8”) of the transducer to the water surface minimized this temperature effect, but the relatively small spot size of the measurement (1-2”) likely increased the standard deviation of the measurement, due to small waves on the water surface.

Measuring head directly in the pipe with an ultrasonic sensor had the advantage of real-time display of any changes, a continuous data record, and similarity with how head is likely to be measured in a field application. Disadvantages include the susceptibility to surface disturbances and lower total accuracy than a stilling well system. Data was recorded every 10 seconds. WinFlume does not provide an expected uncertainty for ultrasonic measurements.

B2. Head: Point Gauge and Stilling Well

This time-tested head measurement technique was used in conjunction with the ultrasonic measurements above. A clear 6-inch diameter stilling well was connected via ½-inch flexible tubing to a ½ inch hole in the invert of the approach pipe at the WinFlume-designated measurement point, directly below the ultrasonic location. The purpose of the stilling well was to provide damping of water surface disturbances to allow a better reading. The point gauge was a manually-read Lory Type C laboratory point gauge with a Vernier scale and precision of 0.1 mm. The measurement rod was J-shaped, with a sharp point oriented upward. To make a reading, the point was slowly raised until it visually just broke the water surface. At each measurement time, three readings were taken in quick succession and averaged. Three sets of three readings were typically taken at each flow rate. WinFlume lists the

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expected uncertainty of the “Point gage in stilling well” head measurement method as 0.003937 inches (0.1 mm). In practice, standard deviations of repeated measurements ranged from 0.011 to 0.20 inches.

Uncertainty for this experiment was calculated as the square root of the sum of squares of expected read error (0.1mm), estimated zero set error (0.5mm), and the observed standard deviation at each flow rate. An expanded uncertainty, approximately based on a 95% confidence interval, was found by multiplying the base uncertainty by a factor of 2.

Due to the better precision, the manual point gauge was chosen as the primary head measurement.

Datum

The invert (lowest point, on the centerline) of the downstream most edge of the U-shaped throat section was set as the “zero” elevation of the flume vertical datum. Both instruments were initially referenced to the vertical datum by physical measurements to the overhead data carriage. It became apparent that there were slight differences between the head measurements, so a vertical correction was then developed for each method to bring the ultrasonic, stilling well, and water surface scan measurements into alignment with the direct measurement. The flume was sealed and ponded with water to approximately ten inches depth. Ultrasonic headwater and tailwater measurements, repeated manual (stilling well) head measurements, and a water surface scan with the overhead data carriage were taken concurrently and compared to repeated direct measurements of the water depth at the datum point.

C. Tailwater elevation

The tailwater level was measured by an ultrasonic sensor mounted in a 4-inch diameter stilling well, using an adjustable mount identical to the headwater ultrasonic mount. The stilling well was connected to the downstream channel by ½ inch tubing at a location 72 inches downstream of the diverging transition, and approximately 48 to 72 inches upstream of the adjustable weir, depending on depth. Although flow in the downstream channel was quite turbulent, especially at higher discharges, this location appeared to be reasonable for the purposes of tailwater measurement.

D. Water surface profile

An ultrasonic sensor on the overhead measurement carriage was used to scan the centerline water surface through the throat and downstream sections at a spatial resolution of 1 cm in the streamwise direction and 1 mm vertically. This surface profile may be compared to CFD or WinFlume results. Water surface scans are shown in Appendix 1.

E. Other measurements

Water temperature was measured by a thermistor located in the downstream channel and recorded by the data acquisition software.

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Target Discharge

Expected minimum, average, and maximum flow rates were provided by MCES for the prototype and adjusted to the model using Froude scaling as described in a previous section. A set of target discharges was then selected to cover the flow range at an approximately even spacing. Five target discharges were selected for physical and computational (CFD) modeling. Five additional target discharges were selected for physical modeling only. The target discharges are summarized in the Figure 2.7 below. Note that the equivalent prototype discharges listed for Qmin, Qavg, and Qmax about 1% higher than the numbers originally provided as listed in Figure 2.1. This is because the model-scale target discharges were fixed in to begin CFD modeling before the as-built scale was calculated, based on as-built measurements of the average throat width of the physical model.

Figure 2.7. Target discharges for physical and CFD models

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Physical model run procedure The following operation and measurement procedure was used to collect data for each discharge point.

1. Check equipment and data computer. 2. Operate pump and gate valves to achieve steady discharge at the target rate as measured by the

orifice plate. 3. Adjust tailwater weir so that tailwater approximates predicted WinFlume tailwater (free

discharge condition). 4. Position ultrasonic head measurement sensors 6-8 inches from water surface. Purge lines to

stilling wells as needed to eliminate air bubbles. 5. Start data recording when flow rate and tailwater is achieved. The following data is recorded

every 10 seconds: Timestamp, orifice plate differential pressure and calculated flow, calculated headwater level, calculated tailwater level, and water temperature.

6. Measure upstream head with point gauge and record. Repeat at least twice over the course of the discharge point.

7. Perform gravimetric (weigh tank) flow measurements. 8. Scan centerline water surface with ultrasonic sensor mounted on the overhead data carriage. 9. Take still photos and notes as needed to document flow conditions. 10. Once free discharge data are complete, proceed to document the maximum submergence level.

A. Start overhead video; B. While keeping a continuous record of flume head and tailwater elevations with the ultrasonic level sensors, slowly raise the weir to raise the tailwater until the flume is clearly submerged; C. Stop video; D. Lower weir to restore free discharge.

11. Stop data recording. 12. Increase (or reduce) flow to next target discharge point.

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The photographs in Figure 2.8 are representative of the physical model in operation. The discharge is 1.71 cfs (767 gpm), representative of the estimated average M025A flow.

Figure 2.8. Side and top views of physical model during Run 11, 767 gpm (1.7 cfs).

Physical Model Results and Discussion A total of 21 physical model runs representing ten target discharges were completed. Runs 1-5, 6a, and 7 were discarded due to instrument malfunctions or bad data. Viable runs are listed in Table 2.6. Several runs were completed as replicates of the same discharge, for example, Run 11 and 14, and others were intended to capture missing data, for example Run 18 provided submergence data that Run 6, at the same discharge rate, lacked.

Table 2.3.4 also compares measured head (water level) and discharge to WinFlume-calculated theoretical head (h1). At all measured discharges, the measured head is greater than theoretical

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WinFlume head, by 0.8% to 1.9%. Orange shaded rows indicate runs that are common to WinFlume, physical measurements, and CFD.

Table 2.6. Summary of physical and WinFlume water level head and flow data.

Figure 2.9 is a graphical comparison of the WinFlume theoretical head and physical model measured head, represented by dashed and solid lines, respectively. The differences between theoretical and measured water surface as a percent of theoretical head (h1), and the estimated uncertainty of head measurements at each discharge, as a percent of the measured head, are represented in Figure 2.10. Both Figures 2.9 and 2.10 give WinFlume data for two roughness values: 0.000197 (glass) and 0.011 (gelcoat), representing a lower and upper bound on the actual roughness in the model. In the middle range of discharges, the percentage difference between theoretical and measured head exceeds the estimated uncertainty of the measurements, however, the head discrepancy is less for the higher roughness value (0.011). Again, the WinFlume head is less than the measured head at all discharges.

Target Flow Rate (gpm) Run #

Measured Discharge (gpm) (1)

Measured Head (inch) (2)

Measured Head Uncertainty (inch) (3)

WinFlume Theoretical Head h1 (inch)

WinFlume Head Uncertainty (inch )

WinFlume minus Measured (inch)

WinFlume minus Measured, as % of WinFlume

115 Run 15 115.9 3.490 0.046 3.464 0.066 -0.026 -0.8%187 Run 12 188.1 4.515 0.090 4.462 0.085 -0.053 -1.2%443 Run 13 443.7 7.178 0.092 7.116 0.136 -0.062 -0.9%767 Run 14 767.7 9.898 0.147 9.775 0.187 -0.123 -1.3%767 Run 11 769.8 9.911 0.125 9.791 0.187 -0.120 -1.2%767 Run 5a 770.0 9.916 0.087 9.793 0.187 -0.123 -1.3%

1171 Run 8 1172.6 12.805 0.050 12.612 0.241 -0.193 -1.5%1631 Run 9 1636.5 15.757 0.106 15.483 0.296 -0.274 -1.8%2141 Run 18 2136.3 18.614 0.189 18.279 0.349 -0.335 -1.8%2141 Run 6 2141.6 18.646 0.120 18.307 0.350 -0.339 -1.9%2695 Run 10a 2693.7 21.518 0.075 21.141 0.404 -0.377 -1.8%2695 Run 10 2693.7 21.536 0.178 21.141 0.404 -0.395 -1.9%3291 Run 17 3287.3 24.308 0.273 23.964 0.458 -0.344 -1.4%3927 Run 16 3927.4 27.094 0.403 26.796 0.512 -0.298 -1.1%

Notes:1. Orifice2. Point gauge in stilling well3. Uncertainty is inches +/- at 95% Confidence interval. WinFlume +/- 1.91%Head Uncertainty =sqrt(std dev^2+zero err^2 + read err^2)*2, where zero err=±0.5 mm, read err = ±0.1 mm

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Figure 2.9. Comparison of measured physical model head and WinFlume theoretical head for two values of assumed surface roughness in the WinFlume model. At the higher roughness, the WinFlume data are truncated at high flows due to an error in WinFlume (approach water level exceeds 0.9 times the pipe diameter).

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Figure 2.10. Head differences and uncertainty, for roughness=0.000197 (glass) and 0.011 (gel coat).

WinFlume Measured Data Comparison (Discharge Comparison)

Measured Data Comparison is a built-in feature in WinFlume which allows the user to input pairs of measured head and discharge data for comparison to WinFlume’s own theoretical calculations. The theoretical discharge for each measured head value is compared to the measured discharge. Table 2.7 is taken from this comparison, and shows that in all cases the measured discharge for a given head was less than the theoretical discharge. This result corresponds to the previous comparison where WinFlume-calculated head is less than the measured head for a given measured flow. Discharge differences ranged from 1.4% to 2.9%, averaging 2.3%, and generally increased with head. Note that this WinFlume model featured a smooth wall (0.000197 inch roughness height). For the WinFlume model using as-built physical dimensions, a +/-1.91% uncertainty with 95% confidence interval was reported at Qmin and Qmax. For purposes of comparison, this was assumed to apply at each intermediate data point. Figure 2.11 compares the difference in discharge (measured minus theoretical) as a percent to the WinFlume uncertainty calculation, using the 0.000197 inch roughness and 0.011 roughness – note that the WinFlume-experimental discharge differences are less for the higher roughness value.

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Table 2.7. WinFlume measured vs. theoretical discharge comparison, for roughness=0.000197

Figure 2.11. Comparison of WinFlume stated uncertainty to difference between theoretical and measured flow, for roughness=0.000197 (glass) and 0.011 (gel coat).

Head at Gage, h1 inch

Measured Discharge, gpm

Theoretical Discharge, gpm

Discharge Difference, gpm

Discharge Difference, as % of theoretical Warnings

3.49 116 118 -1.7 -1.42 234.515 188 192 -4.3 -2.21 237.178 444 451 -6.9 -1.539.898 768 784 -16.4 -2.099.911 770 786 -16.0 -2.049.916 770 787 -16.5 -2.1

12.805 1173 1202 -29.6 -2.4615.757 1637 1684 -47.1 -2.818.614 2136 2199 -62.9 -2.8618.646 2142 2205 -63.7 -2.8921.518 2694 2770 -76.7 -2.77 1221.536 2694 2774 -80.4 -2.9 1224.308 3287 3363 -75.3 -2.24 12,23

Summary of Warning Messages12 - Gage is too close to converging section and/or throat.23 - Converging section may be too long (side contraction is too flat).Note - WinFlume did not calculate discharge for highest flow (3927 gpm)

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WinFlume roughness height sensitivity

The WinFlume user may specify the roughness height of the flume construction material in the “Flume Properties and Construction Data” dialog box. The roughness height factors in to the boundary layer calculations. A thicker boundary layer due to a rougher surface effectively reduces the effective flow area in the flume throat. Various references list roughness height for common materials, some of which are noted in Table 2.8.

Table 2.8. Roughness height from various sources, ranked small to large.

Within WinFlume, there are several pre-set options that may be chosen such as concrete-rough and concrete-smooth, or the user may enter a custom value. The M025A prototype WinFlume model from MCES listed the roughness height as “0.000197 inches, Glass [custom]”, representing a very smooth wall boundary condition. This value was retained for the WinFlume model with the as-built physical model dimensions, which is the basis for WinFlume – physical comparisons in this report, unless noted. This value is comparable to the “smooth plastic” listed in ISO 4359, as noted in Table 2.8.

A sensitivity analysis was done to observe the effect of differences in specified roughness height on the WinFlume model. Two additional roughness heights, 0.011024 inches (Fiberglass- gel coat), and 0.0590551 inches (Concrete-rough), were chosen for comparison to 0.000197 inches, (Glass [custom]). Table 2.9 lists a summary of the results of comparison at five target discharges.

Figure 2.12 is a representation of the variation in theoretical and measured head as compared to the “smooth” or “base” WinFlume case of 0.000197 inch roughness, on the basis of measured discharge. Assuming measurements and WinFlume outputs are completely correct, and that differences are only attributable to specified roughness height, the physical measurements are similar to the Fiberglass-gel coat roughness on lower discharges, and somewhere between the gel coat and concrete on higher discharges. The flume is somewhat more sensitive to roughness height at lower discharges. The river water used in the experiment contained a small proportion of particles and organic material, some of which adhered to the flume surface. It did not appear to form an appreciable layer, and no attempt was made to clean the flume between runs.

Roughness Ht (inch) Material Data Source Used for0.000118 Smooth plastic, PVC, perspex ISO 4359, Table 30.000197 Glass [custom] WinFlume (custom) base0.001181 Resin-bonded fiberglass, good ISO 4359, Table 30.002362 Resin-bonded fiberglass, normal ISO 4359, Table 30.0110 Fiberglass- gel coat WinFlume sensitivity0.0236 Concrete, thin film or sewage slime, good ISO 4359, Table 30.0591 Concrete- rough WinFlume sensitivity0.0591 Concrete, thin film or sewage slime, normal ISO 4359, Table 3

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Table 2.9. WinFlume roughness height comparison

Figure 2.12. WinFlume roughness height comparison

Modular Limit and Submergence

In long-throated flumes, critical flow depth is needed to disconnect the upstream water level, where the head (h1) is measured, from the tailwater, thus creating a single relationship between measured head and discharge. If the tailwater energy head (H2) is too large relative to the upstream energy head (H1), critical depth does not occur and the measured head (h1) is affected by downstream conditions. The maximum submergence ratio (defined as H2/H1) under which critical depth flow happens in the flume throat is defined as the modular limit.

Construction MaterialGlass [custom]

Fiberglass- gel coat

Concrete- rough

Physical - measured

Roughness Height (inch) 0.000197 0.0110236 0.059055Measured discharge (gpm) head (inch) head (inch) head (inch) head (inch)

188.1 4.462 4.511 4.555 4.515443.7 7.116 7.181 7.250 7.178770.0 9.793 9.874 9.969 9.916

2141.6 18.307 18.445 18.610 18.6463927.4 26.796 no data * no data * 27.094

* WinFlume: 17-FATAL: Approach channel water level exceeds 0.9 times diameter

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The technique used to determine the modular limit in the physical model consisted of slowly raising the tailwater level from an initial free discharge while monitoring headwater and tailwater levels with the ultrasonic sensors. The data was then reviewed to determine at what point the head measurement began to be affected by the tailwater. In other words, the point at which the flume became submerged and critical flow was lost. Figure 2.13 is an example of one such plot. The black lines with arrows represent the estimated points at which the maximum submergence was reached. In most cases, several sequences of tailwater raises and lowerings were done and the results averaged. Although this method compares water levels (h2/h1) and not energy head (H2/H1), calculations show that difference between these ratios are on the order of 0.01%.

Figure 2.13. Submergence plot example, Run 13, Q=444 gpm

The process of submerging and unsubmerging the flume is dynamic and not instantaneous. As shown in Figure 2.13, the tailwater (lower red line) was raised slowly and dropped quickly, leading to an unsteady flow condition. Maximum submergence estimates under these conditions (purple dashed line) were not reliable.

WinFlume can calculate the modular limit as well as the “allowable tailwater, h2” for any input discharge. Figure 2.14 shows that the observed sill-referenced tailwater depths (h2) are generally similar to the theoretical. Figure 2.15 compares the tailwater to headwater ratios (h2/h1). In the experimental data, maximum tailwater depths ranged from about 80 to 95% of headwater depths (sill-referenced). There is good agreement with WinFlume predicted values at 2136 gpm and 2694 gpm, but some deviation at higher and lower flows.

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Figure 2.14. Comparison of modular limit estimates

Figure 2.15. Comparison of headwater and tailwater energy and depth ratios

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Water surface profiles

The centerline water surface profile was scanned with the overhead measurement carriage at each discharge. An example of a water surface profile plot is shown as Figure 2.16. Additional water surface profiles are located in Appendix 1.

Figure 2.16. Water surface profile plot example

The water surface profiles were to determine the position of critical depth location within the throat. For each discharge, the critical depth was calculated based on as-built dimensions. At lower discharges where the critical depth was fully within the rounded bottom of the “U”, a critical depth formulation for semielliptical channels developed by Ali Vatankhah was used (Vatankhah, 2015). Table 2.10 lists the estimated location and relative position, normalized to the throat length, of the critical depth for five runs. This topic is explored further in relation to the CFD model.

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Table 2.10. Estimated critical depth location

2.4 CFD Analysis of the Physical Model A computational fluid dynamics (CFD) model was assembled for the ½ scale u-flume physical model. The model was based on the 2016, open-source version of CFD modeling software VSL3D developed at SAFL. The main characteristics of the VSL3D model software, which distinguish it from common commercial CFD models, include (i) second order accuracy; (ii) incorporation of Curvilinear Immersed Boundaries (CURVIB) method; and (iii) highly scalable parallel code that can employ up to 10,000 CPU’s. For this study, LES was employed to simulate turbulent flow, combined with the level set method for modeling the water free surface. The CFD model was 3-D, and included the entire extent of the physical model, starting at the outlet of the head box to the 30” diameter approach pipe. The dimensions of the flume represented in the CFD model, particularly the throat width, were based on the as-built dimensions of the physical model. The CFD model used a block of uniformly sized, rectangular fluid elements, with submersed boundary elements to define the walls of the inlet pipe, flume sections, and tailbox. The tailbox area of the model was lengthened from 10 feet to 22 feet, to improve model convergence and reduce the influence of the fixed downstream water level on turbulence near the outlet of the flume diverging section. The solid geometry used in the CFD simulations is show in Figure 2.17.

The CFD model used about 7 million nodes, corresponding to lateral and vertical resolutions of about 1.5 cm (0.6 inches), and a longitudinal (flow direction) resolution of 2.4 cm (0.96 inches) The simulations used the free-surface solver to calculated the water level distribution over the extent of the model, based on a specified flow rate. Typical simulated water surface levels through the U-flume are given in Figure 2.18 and Figure 2.19.

Boundary Conditions The flow rate was fixed for each simulation, specified at the upstream end of the 30” pipe. At the downstream end of the CFD model, the water level was fixed at a specified level – this water level was nominally set to the value predicted by WinFlume, based on the specified downstream pipe slope, diameter, and roughness. Flume submergence effects were examined by increasing the downstream water level in several increments.

Some difficulties were encountered in setting the upstream water level boundary condition. Initial model runs prescribed an initial water level, but allowed the model to adjust the upstream level as the simulation progressed. This approach led to model instability in some cases, which can be partially attributed to the inflow specification. When the inflow rate is specified as the upstream boundary

RunDischarge (gpm)

Calculated Critical Depth (inch)

Location (nearest 5 mm)

Relative position in throat (DS = 1.0)

12 188.1 3.27 1800 0.96 (1)13 443.7 5.12 1055 0.21 5a 770.0 7.01 1040 0.20 6 2141.6 12.72 1095 0.25 16 3927.4 18.47 1330 0.49

Notes1. Within ~1 mm of calc'd critical depth at 1060 (22%)

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condition, the model assumes a uniform velocity distribution over the inlet face. As the flow progresses downstream, the velocity field adjusts to the appropriate velocity profile, including the no-slip boundary and turbulent boundary layer. This transition from uniform flow to a realistic velocity profile can cause rather abrupt changes in the water level in the upstream end of the model (Figure 2.19). To alleviate this issue, the upstream water level was fixed, and several model runs were made at each flow rate, for several values of the inlet water level, to find an appropriate specified upstream water level, i.e. an inlet level leading to a converged solution with a level or slightly decreasing water surface elevation over the length of the inlet pipe. A simple calculation based on the Moody diagram suggests that there should be a head drop over the length of the inlet pipe of 1-2 mm. Obtaining an upstream boundary condition that does not affect the water level at the gauging site is a source of about ± 1% uncertainty in the CFD results.

Table 2.11. Summary of water levels at the gauging location (h1) of the scale-model flume, at the five simulated flow rates, for the CFD results and the measurements from the physical model. Since the CFD simulations and experimental runs were at slightly different flow rates, the experimental h1 data from Table 2.3.4 were interpolated to the CFD flow rates using polynomial fits.

Flow Rate, CFD (gpm)

Flow Rate, CFD (cfs)

h1, CFD (inches)

h1, experimental (inches)

h1 difference, CFD – Experiment (%)

187.0 0.42 4.600 4.515 1.88 443.7 0.99 7.320 7.178 1.98 766.6 1.71 9.980 9.889 0.92 2141.4 4.77 18.700 18.649 0.27 3926.9 8.75 26.883 27.092 -0.77

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Figure 2.17. The solid model geometry used in the CFD model to represent the inlet pipe, flume, and tailbox.

Figure 2.18. Shaded plot of the instantaneous free-surface flow through the U-flume, at a flow rate of 767 gpm (1.71 cfs, left panel) and 2141 gpm (4.77 cfs, right panel).

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Figure 2.19. Plot of the longitudinal variation of water depth, at a flow rate of 2141 gpm (4.77 cfs). The 0 point on the x-axis is the water level metering location.

CFD Results The primary output of the CFD simulations were data to generate a rating curve – the mean water level at the gauging location (21.3 inches upstream of the throat). These output data are summarized in Table 2.11, along with the corresponding flow/gauge depth data from the experiments. For a given flow rate, the CFD model predicted gauge water levels (h1) were slightly higher (2%) than the experimental values at the lower flow rates, transitioning to slightly lower (-0.7%) at the higher flow rates (Table 2.11). The differences in the CFD and experimental h1 values were similar in magnitude to the experimental uncertainty of the level measurement (Figure 2.20). Based on the shape of the rating curve, a certain error or uncertainty in the water level corresponds to a greater uncertainty in the flow rate. The errors in the h1 value given in Table 2.11, ranging from -0.7% to 1.98%, correspond to flow measurement errors ranging from -1.24% (at high flow) to 3.8% (at low flow).

The location of the critical depth point was also quantified for each run, using the same estimated critical depth used in the experimental analysis. Figure 2.21 summarizes the location of the critical depth point, normalized to the throat length – this normalized distance ranges from 0.23 to 0.95, depending on flow rate. The trends of the critical depth location over the flow range are quite similar for the CFD and experimental measurements.

A second result of the CFD modeling was to test the ability of the model to respond to submergence conditions (high tailwater). Three separate runs were made with varying tailwater level at 2141 gpm, with tailwater submergences (h2/h1) of 0.8, 0.9, and 0.95. The effect of submergence on the gauge level predicted by the CFD model is shown in Figure 2.22.

Additional plots are given in Figures 2.23-25, showing the CFD modeled velocity distributions in the U-flume at several flow rates.

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Figure 2.20. Gauge water depth vs. flow rate for the CFD and experimental results (upper panel) and difference in gauge water depth (h1 CFD-Exper.) in comparison to the uncertainty in the experimental measurements.

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Figure 2.21 Relative position of critical depth in the U-flume throat vs. flow rate, based on the CFD and experimental results. The y-axis gives the distance from the upstream edge of the throat, normalized to the throat length: 0=upstream edge, 1=downstream edge.

Figure 2.22. Simulated change in gauge depth vs. depth ratio (h2/h1) for a flow rate of 2141 gpm (4.77 cfs).

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Figure 2.23. Velocity magnitude distribution (in m/s) plotted along a vertical plane through the flume centerline, for a flow rate of 1.71 cfs (767 gpm). The simulated velocities include the entrained air above the water surface.

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Figure 2.24. Velocity magnitude distribution (in m/s) plotted along a vertical plane through the flume centerline, for a flow rate of 4.77 cfs (2141 gpm).

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Figure 2.25. Plot of water surface with the velocity magnitude superimposed, for a flow rate of 4.77 cfs (2141 gpm).

2.5 Conclusions and Recommendations Based on results obtained from the U-flume physical model, WinFlume seems to estimate rating curves with an accuracy close to the values claimed. For a given flow rate, WinFlume predicted water levels at the gauging location (h1) within 0.8-1.9%. For a given gauge level measurement, the flow rate predicted by WinFlume differed from the experimental flow by 1.4-2.9%, which somewhat exceeded the estimated uncertainty (1.9%) given by WinFlume. However, given the uncertainty of the experimental measurements of flow rate (±1.3-2%) and depth (up to 2%), WinFlume may be predicting the rating curve within its estimated uncertainty.

Overall, we did not find that the WinFlume-experimental differences were systematically higher at lower flows or higher flows. As a result, it is difficult to identify the particular mechanisms leading to these differences (e.g. inadequate boundary layer theory at low flow, non-parallel streamlines at high flow). There is evidence that the location of critical depth in the flume throat varies substantially with flow rate, which could lead to errors in the equations WinFlume uses to estimate boundary layer effects (Dabrowski and Polak 2012). However, the expected direction of this error (less head loss for shorter boundary layers) is opposite the observed discrepancies (experimental head > theoretical head). Uncertainty in the surface roughness (Figure 2.10) may be a larger contributor to the WinFlume-

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experimental differences, and will likely be a source of uncertainty in the rating curves of field installations. Roughness measurements taken on the flume scale model surfaces were inconclusive, however, we believe the surface roughness were smoother than the 0.013 inch roughness attributed to gel coat, and were probably rougher than the 0.000197 attributed to glass. In addition, small separation zones were observed at the sharp break between the converging section and the throat – this likely added a small energy loss not accounted for in the WinFlume model.

Measurement of water level with a point gauge and stilling well setup was found to be more accurate and reliable than direct measurement with an ultrasonic transducer. Where ultrasonic devices are likely to be used in the field, the measurement accuracy will have an effect on the accuracy of the flow measurement, but are specific to the transducer being used. In the physical model study, we kept the ultrasonic transducer relatively close (about 6”) to the water surface to minimize air temperature effects, however, the resulting small measurement spot size probably lead to higher measurement fluctuations.

The experimental results for high tailwater (submergence) also are in line with the WinFlume estimates, but experimentally it was found that the limiting tailwater depth varied more over the flow range, from 80 to 95% of the upstream depth, than the WinFlume estimates, which were in the range of 86 to 87%.

Compared to WinFlume, the CFD model results suggest a similar, or slightly higher, level of error in flow rate and depth predictions (-0.7% to 2% for water level, -1.2% to 3.8% for flow rate). The CFD modeled gauge levels responded to high tailwater levels in a similar manner to the experimental results, and should be a useful tool for examining non-ideal upstream and/or downstream flow conditions. The CFD model also predicted the location of critical depth in the flume throat consistent with the experimental results.

Overall, the results of this portion of the study suggest that WinFlume is a useful tool for predicting the rating curves of long-throated flumes, and U-flumes in particular. The tool not only provides the ability to predict the rating curve of a custom flume, but also does a reasonable job of estimating the uncertainties of the rating curve.

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References

Clemmens, Albert J., Tony L. Wahl, Marinus G. Bos, and John A. Replogle, 2001, Water Measurement with Flumes and Weirs, ILRI Publication 58, International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands.

Dabrowski, W., & Polak, U. (2012). Improvements in Flow Rate Measurements by Flumes. Journal of Hydraulic Engineering, 138(8), 757-763.

ISO 4359 (2013). Flow measurement structures — Rectangular, trapezoidal and U-shaped flumes. International Organization for Standardization, Geneva, Switzerland.

Miller, R.W., 1989. Flow Measurement Engineering Handbook, 2nd Ed. McGraw-Hill.

University of Minnesota Characterization Facility (CharFac). Proximal Nanoprobe Tencor P10 Profilometer. http://www.charfac.umn.edu/instruments/tencor_p10_description.html, accessed 4/13/2017

Vatankhah, Ali. (2015). Technical Note. Critical and Normal Depths in Semiellipical Channels. J. Irrig. Drain Eng., 2015, 141(10). Am. Soc. Civil Engineers. DOI: 10.1061/(ASCE)IR.1943-4774.0000888.

Wahl, Tony L. WinFlume User's Manual. Software for Design and Calibration of Long-Throated Flumes and Broad-Crested Weirs for Open-Channel Water Flow Measurement. Version 1.05, September 2001. US Bureau of Reclamation Water Resources Research Laboratory, Denver, Colorado.

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3. CFD Analysis of M025A 3.1 Introduction This section summarizes the computational fluid dynamics (CFD) analysis of the u-flume installed at the M025A metering station. The original purpose of this analysis was to use CFD models to 1) check the rating curve predicted by WinFlume, including the sensitivity of the design to tailwater conditions. As the task progressed, an additional goal was added to assess the effect of locally high upstream pipe slopes on the as-built M025A rating curve and analyze a possible retrofit to reduce these impacts.

As with the CFD analysis of ½ scale prototype (Task 2), the CFD model of the full-scale M025A design was based on the 2016, open-source version of CFD modeling software VSL3D developed at SAFL. The flume geometry was based on an AutoCad geometry file supplied by MCES, and included the flume geometry contained in the metering vault, plus 98 ft. (30 m) of the 58.5” upstream pipe and 33 ft. (10 m) of the 72” downstream pipe. The CFD model used a block of uniformly sized, rectangular fluid elements, with submersed boundary elements to define the walls of the inlet pipe, flume sections, and outlet pipe. The solid geometry used in the CFD simulations is shown in Figure 3.1. The as-built design geometry of the 21” u-flume for M025A is given in Figure 3.2, along with a modified, raised-throat geometry discussed later in this report.

The CFD model used about 7 million nodes, corresponding to lateral and vertical resolutions of about 1.5 cm (0.6 inches), and a longitudinal (flow direction) resolution of 2.4 cm (0.96 inches) The simulations used the free-surface solver to calculate the water level distribution over the extent of the model, based on a specified flow rate.

The flow rate was fixed for each simulation, specified at the upstream end of the 58.5” pipe. At the downstream end of the CFD model, the water level was fixed at a specified level – this water level was nominally set to the value predicted by WinFlume, based on the specified downstream pipe slope, diameter, and roughness. Flume submergence effects were examined by increasing the downstream water level in several increments.

Some difficulties were encountered in setting the upstream water level boundary condition. Initial model runs prescribed an initial water level, but allowed the model to adjust the upstream level as the simulation progressed. This approach led to model instability. To alleviate this issue, the upstream water level was fixed, and several model runs were made at each flow rate, for several values of the inlet water level, to find an appropriate specified upstream water level, i.e. an inlet level leading to a converged solution with a level or slightly decreasing water surface elevation over the length of the inlet pipe. A simple calculation based on the Moody diagram suggests that there should be a head drop over the length of the inlet pipe of 1-2 mm. Obtaining an upstream boundary condition that does not affect the water level at the gauging site is a source of about ± 1% uncertainty in the CFD results.

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Figure 3.1. Typical geometry defining the solid walls of the u-flume model.

Figure 3.2. Dimensions (in inches) of the 21” throat width u-flume designs. The upper panel gives the original design, and the lower panel gives a proposed modification to raise the throat with a custom insert.

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3.2 Simulation of the as-designed M025A u-flume rating curve A series of simulations were performed using VSL3D to analyze the rating curve of the 21” M025A u-flume, including the effects of downstream submergence due to inflow from interceptor 8151 just downstream of M025A. A year-long flow record (6/1/2016 – 6/1/2017) for M025 and M35S (interceptor 8151) was analyzed to determine the upper end of interceptor 8151 flow rates compared to M025A, as a worst-case backwatering condition. The corresponding water level in the 72” pipe downstream of M025A was then calculated, assuming a slope of 0.04% and a Manning’s n of 0.013. This predicted tailwater level was then divided by the M025A gage level at the same flow rate to determine the submergence ratio from 500 to 6000 gpm flow rate through M025A.

The predicted submergence ratio for M025A is summarized in Figure 3.3, reaching a maximum of 73% at 6000 gpm. The highest observed flow rate through M025 for 6/1/2016 – 6/1/2017 was 5965 gpm, and the highest observed flow rate at M35S was 7094 gpm. The CFD simulation results for the effect of the submergence ratio on the M025A rating curve are summarized in Figure 3.4. At a typical flow rate of 4100 gpm, the tailwater submergence was predicted to have minimal effect on the gage level up to a submergence ratio of 0.95. At 21000 gpm, the effect of tailwater submergence became noticeable (>1 % error) at a submergence ratio of 0.85.

Figure 3.3. Predicted submergence of the M025A tailwater for 90th, 95th, and 99th percentile inflows from interceptor 8151.

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Figure 3.4. Simulated effect of downstream submergence on the rating curve error of the M025A u-flume at 4100 and 21000 gpm. The gage error references the simulated gage level for an 0.6 submergence ratio.

3.3 Simulating the effect of high upstream pipe slope on the M025A rating curve. This task was added to examine the effect of surveyed pipe slopes upstream of the M025A metering station on the as-built M025A u-flume (Figure 3.2, upper panel). The surveyed pipe invert elevations are illustrated in Figure 3.5. Over the last 20 feet of pipe upstream of M025A, the slope is about 1.7%. A VSL3D CFD model was set up with upstream pipe invert elevations matching those of the field survey and run for several flow rates. The irregularities in the upstream pipe slope produced irregularities in the water surface level upstream of the flume, particularly at lower flow (1500 gpm, Figure 3.6). The simulated water levels at the gage location are summarized in Table 3.1. At 4100 gpm, the -5.6% difference from the WinFlume curve is similar to results from the dye flow tests (6-8% low). At 8000 gpm, the CFD result is +5% off from the WinFlume rating curve, with the CFD water level higher than the WinFlume value for the 8000 gpm flow rate. This is consistent with the CFD results for the 1/2 scale physical model, where the differences between the experimentally measured rating curve and the CFD rating curve switched sign from low flow to high flow.

Based on the CFD runs and dye measurements, the as-built u-flume may be biased low in its flow reading. The accuracy of the CFD generated rating curve is estimated to be +- 6% at low flow (1500 gpm) and +-4% at high flow (4100 gpm). Based on the 1-year M025 flow record analyzed in the previous section, about 37% of the total flow volume is between 1000 and 3000 gpm, while 63% of the total flow is between 3000 and 6000 gpm. So, a composite accuracy of the CFD rating curve can be made using the low/high flow percentages to weight the low/high flow accuracies:

0.37*6% + .63*4% = 4.5% overall accuracy.

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An additional CFD simulation was performed for a proposed, modified M025A u-flume design with a throat insert to raise the throat invert 6” (Figure 3.2, lower panel), to reduce the effect of the high upstream pipe slope. At 1500 gpm, the water level at the gage point read about 1.9% low, corresponding to a 2.8% low flow reading compared to the WinFlume value. The bump in the water surface profile upstream of the flume was reduced, but not eliminated (Figure 3.6). This 2.8% difference can be compared to a difference of -7.3% for the as-built flume (Table 3.1).

Table 3.1. Simulated water level at the M025A gage for the as-built geometry and surveyed upstream pipe inverts.

Flow Rate (gpm)

Gage level, CFD (in)

Gage level, WinFlume (in)

% Difference, level

% Difference, flow

1500 10.37 10.80 -3.5 -7.3 4100 18.40 19.05 -3.4 -5.6 8000 29.42 28.547 3.1 5.0

Figure 3.5. Surveyed pipe invert elevation upstream of the M025A metering vault.

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Figure 3.6. Simulated water level for the M025A u-flume at 1500 gpm, for the as-built condition and for the proposed raised-throat retrofit.

3.4 Conclusions The first portion of this this study, looking at potential backwatering effects on the M025A u-flume from interceptor 8151, found that even with statistically infrequent (99% exceedance) backwatering from interceptor 8151, the submergence ratio (the ratio of the tailwater depth to gage depth) should not exceed 0.7 (70%). CFD analysis of the u-flume rating curve found that the accuracy should not be significantly affected for submergence ratios less than 0.95 for typical operating flows (4100 gpm) and 0.85 for very high flows (21000 gpm). As a result, backwatering effects are not expected to affect the performance of the M025A u-flume.

In the second portion of the study, the effects of the surveyed upstream pipe invert elevations on the as-built rating curve of the M025A u-flume were quantified for both the as-built u-flume and a proposed modified version with a raised throat. The CFD simulations suggest that the surveyed upstream pipe inverts cause the as-built u-flume to read 6 to 7% low. The composite accuracy of the CFD-generated rating curve points was estimated to be 4.5%, based on the CFD simulations and dye testing results. Raising the u-flume throat by 6” with an insert was projected to reduce the flow measurement error (compared to the WinFlume rating curve) from 7% to 3%.

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4. CFD Model Application to M200A/B 4.1. Verification of ANSYS-Fluent Analysis Package The ANSYS Fluent CFD package (V 17.0) was used for the analysis, as part of the transition away from the SAFL computing cluster and the VSL3D package, which has not been updated since 2016. To check that the simulation capabilities of Fluent are comparable to the VSL3D package, a simulation of the M025A u-flume (21” throat width) previously performed with VSL3D was repeated using Fluent. For both packages, the simulation was done using large eddy simulation (LES) and higher order correction terms in the solution. The Fluent model mesh is illustrated in Figure 4.1. Figure 4.2 shows the simulated water level along the centerline of the flume for a flow rate of 0.26 cms (4120 gpm). At the level gage location, the simulated water levels were 0.499 and 0.507 m (19.64 and 19.96 inches) for the Fluent and VSL3D solutions, respectively, a difference of 1.6%. The water level prediction by WinFlume for this case is 0.485 m (19.09 inches), so Fluent’s solution of 0.499 m has slightly better agreement (2.9%) with WinFlume than VSL3D’s solution of 0.507 (4.5%).

Figure 4.1. Detail of the Fluent model mesh for the M025A u-flume used to verify the Fluent modeling package.

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Figure 4.2. Streamwise water level profiles for flow through the M025A u-flume using the Fluent and VSL3D CFD packages.

4.2. CFD modeling of Dual U-flumes for M200A The purpose of this part of the study was to analyze the effect of the upstream piping configuration, including a flow splitter, on the rating curve of the proposed dual M200A u-flumes (36” throat width). The CFD model assembled for this task included the 36” u-flume, a 3 m long section of the transition section downstream of the flume, the approach channel in the meter box, a section of 72” RCP, the flow splitter, and a 20 m section of the 96” inflow RCP (Figure 4.3). For reference, an engineering drawing of the existing M200 meter vault is given in Appendix 2. Per MCES plans, the 96” inflow RCP section in the model had a slope of 0.052%, and has a horizontal orientation 0.9o away from normal to the meter vault orientation. The lined 72” RCP/CIPP between the meter vault and the splitter was assumed level. For most of the simulations, symmetry conditions were used on the 96” inflow pipe and splitter, to represent the case where both flumes are active. The converging section of the u-flume was designed with curved wing-walls (Figure 4.5) to minimize flow separation. As with the other CFD model runs, ANSYS-Fluent was used with LES (large eddy simulation), to capture the turbulence in and downstream of the splitter, and the volume-of-fluid model to simulate the air-water free surface. A 5 cm mesh was used, resulting in a model with about 2.6 million nodes.

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Figure 4.3. Illustration of the CFD model geometry for the symmetric flume.

Figure 4.4. Dimensions (in feet) of the proposed M200B u-flume, as shown in the WinFlume model.

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Figure 4.5. Detail of the CFD model mesh for the u-flume throat and converging section, with curved wing-walls.

Results

Simulations were made for total (both flumes running) flow rates of 7000, 14000, and 28000 gpm (0.44, 0.88, 1.77 cms). For the symmetric half-model, the flow rates were specified as 3500, 7000, and 14000 gpm. The simulated water levels at the gage location (10 ft upstream of the throat entrance) are summarized in Table 4.1 in comparison to WinFlume predictions. At the two lower flows (3500 and 7000 gpm), the Fluent and WinFlume water levels are within 1%. At the highest flow (14000 gpm), there is larger disagreement (3.1%), with the Fluent water level prediction higher than the WinFlume prediction.

To help determine the cause of the 3.1% disparity at 14000 gpm, an additional CFD model was set up and run for the same u-flume with a straight, 40m long inflow pipe (no splitter). At 14000 gpm, the simulated was level was 0.790 m (2.591 ft), 2.3% from the WinFlume value. Comparing the results with and without the splitter suggests that the splitter causes about a 1% change in the u-flume rating curve at 14000 gpm.

The simulated velocity and water level and velocity fluctuations between the splitter and the u-flume are illustrated in Figure 4.6 – 4.8 for 14000 gpm flow rate. The water level and velocity fluctuations produced by the splitter dampened significantly by the time the flow reached the level gaging location. The root-mean-square air/water phase fluctuations shown in Figure 4.8 are related to, but not equal to, water level fluctuations.

The simulated velocity and water level and velocity fluctuations between the splitter and the u-flume are illustrated in Figure 4.9 – 4.11 for the case of 28000 gpm through a single flume. Again, the water level fluctuations produced by the splitter dampened significantly by the time the flow reached the level gaging location. The simulated water level, 3.73 ft, is 1.9% lower than the WinFlume value, 3.805 ft

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(Table 4.1). The reversal in the difference between the CFD and WInFlume results between low and high flow is consistent with the results from the CFD analysis of the u-flume physical model (Task 2B).

Table 4.1. U-flume gage water levels for WinFlume and Fluent models.

Flow Rate Upstream Geometry

Gage Water Level, WinFlume (ft)

Gage Water Level, CFD (ft)

% Difference, CFD - Winflume

3500 gpm per flume Splitter, symmetric

1.201 1.197 -0.33% 7000 gpm per flume 1.725 1.729 0.23% 14000 gpm per flume 2.532 2.611 3.1% 14000 gpm, one flume no splitter 2.532 2.591 2.3% 28000 gpm, one flume Splitter 3.805 3.730 -1.9%

Figure 4.6. Simulated velocity at the water surface in the u-flume and approach section for 14000 gpm.

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Figure 4.7. Simulated velocity and root-mean-square velocity fluctuations at cross-sections of the approach pipe, from the gage location to the splitter, for 14000 gpm. The velocity scale has been clipped to better show the velocity variability in water phase.

Figure 4.8. Simulated air/water phase and the root-mean-square fluctuations of the phase at cross-sections of the approach pipe, from the gage location to the splitter, for 14000 gpm.

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Figure 4.9. Simulated velocity at the water surface in the u-flume and approach section for 28000 gpm through one flume.

Figure 4.10. Simulated velocity and root-mean-square velocity fluctuations at cross-sections of the approach pipe, from the gage location to the splitter, for 28000 gpm through one flume. The velocity scale has been clipped to better show the velocity variability in the water phase.

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Figure 4.11. Simulated air/water phase and the root-mean-square fluctuations of the phase at cross-sections of the approach pipe, from the gage location to the splitter, for 28000 gpm through one flume.

4.3. CFD Model of M200A w/ 1 flume This portion of the study analyzed a single u-flume for retrofit into the M200 meter station. The task was originally intended to analyze a single 60” throat width u-flume retrofit for M200 without modifying the inverts of inflow and outflow 96” pipes. The single u-flume retrofit is expensive compared to the dual u-flume retrofit analyzed in Section 4.2 because it requires extensive meter vault and upstream interceptor reconstruction to align the pipe inverts. To place more emphasis on Section 4.2 (Task 4A), Task 4B was modified to analyze outflow from a 36” u-flume, configured as shown in Figure 4.21, as a preliminary step in analyzing the single u-flume retrofit option. The goal of the modified Task 4B was to analyze the design of the expansion section of the u-flume, to give the best energy dissipation of the high-speed flow exiting the u-flume into the 96” outlet pipe with minimal turbulence and aeration. Two different lengths of the expansion section were analyzed: the nominal 3 ft long expansion, and a 6 ft long expansion. The simulations were run at 0.63 cms flow rate (10000 gpm), using the large eddy simulation and volume of fluid options in Fluent to simulate turbulence and the water free surface. The shorter transition design was also run at 12500 gpm, to provide a better comparison to the dual u-flume results.

Figure 4.12. Dimensions (in feet) of the proposed M200B u-flume, as shown in the WinFlume model.

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Figure 4.13. Detail of the CFD mesh for the u-flume transitioning into the 96” outlet pipe.

Results

Figure 4.14 – 4.17 give the simulated mean water surface level and streamwise velocities for the 36” and 72” expansion designs at 10000 gpm. The water surface profiles are similar, but the 36” expansion gives a slightly more persistent jet along the invert of the 96” outlet pipe compared to the 72” expansion. Cross-sections of the water surface profiles for the two cases are similar, with slightly more fluctuation near the upstream end of the outlet pipe for the 36” expansion (Figures 4.16, 4.17). Additional results for the 36” long expansion at 12500 gpm are given in Figures 4.18, 4.19, and 4.20. The water level fluctuations in the outlet pipe given in Figure 4.20 may be compared to the fluctuations given in Figure 4.31 for the dual u-flume case. The root-mean-square fluctuations corresponding to the single flume results in Figure 4.20 was 0.81 cm, compared to 2.6 cm for the dual flume with transition design 4.

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Figure 4.14. Air/water phase (upper panel) and streamwise velocity (lower panel) along the flume centerline at 10000 gpm, for the 36” long expansion. For the phase plot, air=1, water=0.

Figure 4.15. Simulated streamwise velocity (left panel) and water surface level (right panel) at the expansion/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 10000 gpm (each flume), 36” long expansion.

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Figure 4.16. Air/water phase (upper panel) and streamwise velocity (lower panel) along the flume centerline at 10000 gpm, for the 72” long expansion.

Figure 4.17 Simulated streamwise velocity (left panel) and water surface level (right panel) at the expansion/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 10000 gpm (each flume), 36” long expansion.

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Figure 4.18. Air/water phase (upper panel) and streamwise velocity (lower panel) along the flume centerline at 12500 gpm, for the 36” long expansion.

Figure 4.19. Simulated streamwise velocity (left panel) and water surface level (right panel) at the expansion/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 12500 gpm (each flume), 36” long expansion.

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Figure 4.20. Streamwise water level profiles in the 96” outlet pipe for 20 time steps at 0.1 second intervals, for the 36” expansion section.

4.4. Model for Aeration/Misting at M200A/B The main goal of this portion of the study was to evaluate designs for a custom transition section for the M200 metering station, to transition the flow from the outlet of dual u-flumes to the single 96” pipe downstream. The current M200 metering station uses a pair of Parshall flumes. At the outlet of the flumes, there is a 5 ft step down to the invert level of the 96” downstream pipe. This drop produces substantial flow aeration, leading to a hazardous and corrosive environment within the metering station. The proposed solution evaluated in this study is to retrofit a custom transition section to the metering station that provide a smooth flow transition over the 5 ft drop in elevation (Figure 4.21), to be installed in conjunction with retrofitting the Parshall flumes with dual 36” u-flumes.

The ANSYS Fluent CFD package was used for the analysis. The model geometry included one u-flume, the upstream approach channel, the downstream transition, and a section of the 96” outlet pipe (Figure 4.21). To simulate the case of the flow split between the two u-flumes, only half of the downstream pipe was modeled, using a symmetry condition in the CFD model. For the case of routing the flow through one u-flume, the full width of the 96” outlet pipe was modeled. The Fluent model was run using the Large Eddy Simulation (LES) turbulence option, with a fixed upstream water level and flow rate and a pressure-based downstream boundary condition, and using the volume-of-fluid (VOF) method for simulating the air-water interface. The CFD had a typical resolution of 5 cm, resulting in models with about 400,000 nodes. A typical mesh is shown in Figure 4.22.

Four versions of the transition geometry were simulated (Figure 4.23). In all cases, the transition invert followed a constant downward slope from the u-flume outlet to a distance 1.5 m (4.9 ft) from the 96” outlet pipe. From that point, the invert was smoothly transitioned from the slope to horizontal with a constant radius curve. Viewed from above, the transition followed a smooth s-curve to transition over

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the 62” lateral offset (1.57 m), with the width of the transition smoothly tapering from the 36” flume width to the 15” exit width (Figure 4.21).

Figure 4.21. Geometry domain of the CFD model for transition flow study.

Figure 4.22. Detail of the CFD mesh for the u-flume and transition regions for transition design 4. The height of the transition in the model was kept to a minimum to reduce model size.

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Figure 4.23. Drawings of the four transition geometry versions run. Not to scale.

Most of the simulations using the transition model were run assuming both flumes were operating, at 12500 gpm each (0.79 cms), with the water level set equal to the u-flume gage level at the model inlet (for 12500 gpm), and the outlet water level in the 96” pipe set based on the total flow rate (25000 gpm) and assumed slope and roughness (0.005 and 0.012, respectively). For the case of a single operational flume, both the flume and outlet pipe water levels were set based on 25000 gpm.

Results

The CFD simulations were mainly used to characterize the flow in the 96” outlet pipe, including the magnitude of water level fluctuations on the surface, signs of aeration in the flow, and the characteristics of the jet produced by the transition outlet and recirculation. The volume-of-fluid model used in the Fluent simulations produces, as an output, the variation of the air-water phase over the modeling domain. The phase parameter (φ) varies from 0 to 1, where φ=0 represents all water, φ=1 represents all air, and the air-water interface is assumed to be at the surface with φ=0.5. The lack of a sharp transition from φ=0 to φ=1 (blurriness in plots of air-water phase parameter φ) suggests surface turbulence and aeration, and this can be used as one basis for comparing the different designs. However, φ was not used to directly quantify flow aeration and the amount of mist generated in the meter vault.

Transition design 1 was run at 6000 gpm per flume (12000 gpm total), and showed significant plunging and backflow at the exit of the transition (Figure 4.15), with the water surface level at the end of the transition significantly below the water level in the 96” outlet pipe.

Transition design 2, with the invert of the transition raised 15” above the outlet pipe invert, had a better match of the water level at the outlet of the transition and the outlet pipe water level at 12500 gpm per flume (Figure 4.25, 4.26). Note the tilt in the water level at the flow exits the transition, due to the upstream lateral curvature (Figure 4.26). This tilt was present for designs 1, 2, and 3.

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Transition design 3 kept the transition outlet 15” above the pipe invert, but moved the transitions away to 15” away from the pipe centerline in each direction (Figure 4.23), for structural reasons. This causes the high-speed flow from the transition to enter the 96” pipe at a shallower depth (Figure 4.23), and the simulation of design 3 suggest more turbulence and aeration in the 96” pipe (Figures 4.7, 4.8). It was hypothesized that the flow plunging at the entrance to the 96” pipe is caused by residual vertical momentum from the sloped transition. To alleviate this, transition design 4 adds a 30” long level section to the downstream end of the transition (Figure 4.23). Since the overall length of the transition is constrained by the meter vault, adding this level section also increased the slope of the transition from 0.20 to 0.26 (m/m). This design change improved the flow characteristics in the 96” pipe markedly (Figure 4.29, 4.30), with little or no flow plunging and backflow over the top. The water level fluctuations, were large for design 3 compared to 4 (Figure 4.31), with the overall root-mean-square fluctuations of 5.2 cm for design 3 and 2.6 cm for design 4.

The CFD model for design 4 was also run for the case of 28000 gpm through a single flume. For this case, the higher water level in the transition section caused a return of the plunging flow phenomena (Figures 4.32 and 4.33), suggesting that the transition section design cannot be optimized for both single- and dual-flume operation.

Figure 4.24. Simulated streamwise velocity (upper panel) and air-water phase and surface level (lower panel) along a vertical plane centered on the transition outlet, for transition design 1 at 6000 gpm (each flume). The water surface level corresponds to the air-water phase φ = 0.5.

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Figure 4.25. Simulated streamwise velocity (upper panel) and air-water phase and surface level (lower panel) along a vertical plane centered on the transition outlet, for transition design 2 at 12500 gpm (each flume).

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Figure 4.26. Simulated streamwise velocity (left panel) and water surface level (right panel) at the transition/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 12500 gpm (each flume), transition design 2.

Figure 4.27. Simulated streamwise velocity (upper panel) and air-water phase and surface level (lower panel) along a vertical plane centered on the transition outlet, for transition design 3 at 12500 gpm (each flume).

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Figure 4.28. Simulated streamwise velocity (left panel) and water surface level (right panel) at the transition/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 12500 gpm (each flume), transition design 3.

Figure 4.29. Simulated streamwise velocity (upper panel) and air-water phase and surface level (lower panel) along a vertical plane centered on the transition outlet, for transition design 4 at 12500 gpm (each flume).

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Figure 4.30. Simulated streamwise velocity (left panel) and water surface level (right panel) at the transition/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 12500 gpm (each flume), transition design 4.

Figure 4.31. Water level in the 96” outlet pipe for 20 time steps at 0.1 second intervals, for transition designs 3 and 4 at 12500 gpm.

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Figure 4.32. Air/water phase (water level) in the transition end and 96” outlet pipe for 25000 gpm through a single u-flume, with transition design 4.

Figure 4.33. Simulated streamwise velocity (left panel) and water surface level (right panel) at the transition/outlet pipe junction and outlet pipe cross-sections 2, 4, and 6 m downstream, for 25000 gpm (each flume), transition design 4.

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4.5. Conclusions This study explored two options for retrofitting the M200 metering station to improve measurement accuracy and reduce misting and aeration within the meter vault. The single u-flume option removes the upstream flow disturbance of the splitter and the downward step in elevation downstream of the flume, but requires relatively expensive reconstruction of the meter vault and neighboring piping. The second option, to retrofit the existing metering vault with dual u-flumes and custom downstream transitions, can be designed to provide relatively smooth downstream flow into the 96” outlet pipe at typical operating conditions, but with increased misting and aeration for atypical operation, such as single flume operation. However, the increased level of misting at atypical operation should still be substantially less than the existing meter vault. Transition design 4, with the 30” level section at the downstream end of the transition, appears to be the best design, because it reduces the vertical momentum of the flow as it enters the 96” outlet pipe, resulting in reduced turbulence and aeration. The CFD simulation results suggest that at typical operating conditions, the upstream splitter may cause flow metering inaccuracies on the order of 1% at flow rates of 28000 gpm split between two u-flumes. The differences between the CFD and WinFlume rating curves suggest that the accuracy of the dual u-flume configuration for M200 is within the individual accuracies of the WinFlume and CFD analyses, about 3% each.

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Appendix 1. Measured Water Surface Profiles from the Physical Model

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Appendix 2. M200 Meter Vault Drawing

Drawing of the exiting M200 meter vault, with side-by-side Parshall flumes.