Assessing the relationship between water level and combined sewer overflow with computational fluid...

11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008

S. Fach, R. Sitzenfrei and W. Rauch 1

Assessing the relationship between water level and combined sewer overflow with computational fluid dynamics

Stefan Fach*, Robert Sitzenfrei and Wolfgang Rauch

Unit of Environmental Engineering, Institute of Infrastructure

University of Innsbruck, Technikerstr. 13 A-6020 Innsbruck, Austria

*Corresponding author, e-mail: [email protected] ABSTRACT Nowadays it is state of the art to evaluate and optimize sewer systems with urban drainage models. Along with the increasing complexity of those models comes the growing need for data for both model input and calibration. Since spill flow data has the major impact on the calibration process of conceptual models - and with it on the reliability of the results - it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using conventional overflow equations and the water levels measured. However, these equations are only applicable to combined sewer overflow (CSO) structures, which weir constructions correspond with the standard weir layout. The objective of this work is to show an alternative approach to obtain spill flow discharge data without carrying out costly measurement campaigns. The idea is to determine the relation between water level and spill flow rate by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure especially concerning the weir construction. In a first step the simulation results were analyzed to identify flow conditions for discrete steady states. It will be shown how the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a conventional overflow equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in praxis. Furthermore the rating curves are compared with a conventional overflow equation by using historic water levels and hydrographs generated with a hydrodynamic model. KEYWORDS combined sewer overflow (CSO), spill flow, discharge equation for spillways, computational fluid dynamics (CFD), rating curves, calibration of hydrodynamic and conceptual models. INTRODUCTION The European Water Framework Directive (2000/60/EC, 2000) aims to achieve a good status of the water bodies. Urban drainage models are used for optimization and evaluation of sewer systems, to assess the impact of CSO discharge on the water course (RAUCH et al., 2002). The application of urban drainage models offers the advantage to consider the entire sewer system with all its interactions instead of measurement campaigns at discrete places.


2 S. Fach, R. Sitzenfrei and W. Rauch

The growing complexity of models results in a more and more increased data demand which causes difficulties in assessing the uniqueness of the input data and the reliability of model results (BECK, 1999; REICHERT, 2006). Nevertheless, in practice the necessary input data for model building often is not or only partially available, e.g. the spill flow hydrograph is calculated on basis of water levels in inflow or CSO basin. Obviously, only reliable models can lead to effective measures to improve water quality in urban areas. Due to the investment costs and lifespan of urban drainage constructions (GÜNTHERT and REICHERTER, 2001, DE TOFFOL et al., 2005), their design must be founded on realistic models, which desire accurate input data and calibration. In the recent past LEI and SCHILLING (1996), GRUM and AALDERINK (1999) and BERTRAND-KRAJEWSKI et al. (2002) have investigated kinds and scales of uncertainties on model results. For example the uncertainties of input data can even top the effect of optimization measures significantly (HOPPE and GRUENING, 2007). Urban drainage models are calibrated - depending on the type of model - often by comparing the discharge hydrographs or the discharge volumes and number of CSO events. On the one hand certain publications (e.g. RAUCH et al., 1998) or guidelines (e.g. ATV-DVWK-M 165, 2004) exist, concerning the required accuracy of rainfall data. On the other hand the available values presenting the stormwater overflow are often of poor quality. Due to immense effort the spill flow discharge in praxis is usually not measured, but the water level of the inflow instead. With this data the spill flow rate is calculated on basis of the conventional overflow equation which is only applicable in case of a standard weir. It is obvious that most CSO structures do not comply with these constraints and thus significant errors in spill flow data can occur by following this approach. Therefore an approach was chosen which uses CFD simulations to obtain more accurate rating curves for the relation between water level and spill flow rate. CFD simulations are state of the art to get basic information about the flow process, because differential equations describing transport processes are solved numerically. STOVIN and SAUL (1998), SCHUETZ et al. (2004) CULLIVAN et al. (2004) have used the CFD technique especially to investigate particle tracking in order to assess the separation efficiency. This paper is focused on the development of rating curves exemplarily for two CSO structures which were selected due to their non compliant geometry with a standard weir especially concerning the shape of the weir crest and the arrangement of the weir. METHODOLOGY The flow regime especially under stormwater conditions in two CSO structures were calculated for discrete time steps with CFD, in order to develop specific rating curves for the overflow process. The quality of the CFD results is determined by the simplifications and assumptions chosen in the model set-up. At the same time the mesh resolution also has a significant impact on the quality of the model results. Hence, there has to be a compromise between fineness of mesh resolution and computational calculation time. On the basis of sewer system and manhole plans, data sheets and photographs two CSO structures were designed as 3D models. Additionally, from all inlets and outlets the spot height of the sewer base and the section shape were known. The CFD models were calibrated on the surface roughness of a sewer segment of 10 m length. To get a better understanding of the flow process the relationship of rate of inflow and water level obtained from steady state simulations was analyzed.



Construction of the 3D CFD models Initially, 3D models of two real world CSO structures were built in AUTOCAD 2007, in order to define the geometrical boundary conditions. Each construction was created from a detailed 2D sketch in association with a data sheet including spot heights of all relevant points within the structure, e.g. along the weir crest or the dry weather flow channel. Because the shape of the weir sill has a strong influence on the stormwater overflow process, it was very well defined. Due to the negligible effect of small installations on the overall flow conditions small gates, building connections, steep ladders and banisters were disregarded in the 3D model. For the further use each 3D model was embedded into a rectangular solid form. For the processing in the CFD software both constructions were exported from AUTOCAD 2007 as stereolithography-files and afterwards imported in the CFD software Flow3D®. Due to this conversion surfaces of 3D objects are approximated by triangles. For each triangle a normal vector is used to indicate whether its area is faced to the surface or to the solid volume. Depending on the simulation run for each CSO structure two different mesh resolutions were used. The mesh resolution of the coarser model ranges between 1 cm and 4 cm for CSO structure A, 8 cm and 16 cm for CSO structure B respectively. The resolution of the fine mesh is the factor two to the coarse one.

Figure 1. CFD model for CSO structure A (left side) and CSO structure B (right side) The CFD modelling was done with the software Flow3D® in which the Reynolds-averaged Navier-Stokes equation is solved numerically. For all simulations a Newtonian fluid and a turbulence model based on the Renormalization-Group (RNG) method was chosen. As in Flow3D® combined wastewater is not available as fluid, water at 20°C was taken simplistically. The significant boundary conditions (BC) are generally determined by inflow and outflow. Hence, the sides with inlets were defined as inflow BC, the software expected a specified inflow water level and/or inflow velocity at these areas (Figure 1). Correspondingly, sides with outlets or spill flows were defined as free outflow BC. The ceiling of each CSO structure was characterized as wall, which has no impact on the flow process, and all other sides were determined as symmetry, which is given by default. Calibration of the 3D CFD models The CFD-models were calibrated on the surface roughness. For that purpose each inlet of the two CSO structures was analysed separately with a sewer segment of 10 m length and a slope corresponding to the mean slope of the real world structure. The discharge in the sewer segment was simulated for four different part-full flow states with steady inflow BC. Therefore the water level at the inlet, or rather the inflow velocity of each sewer segment was

INLET

OUTLET SPILL FLOW

INLETINLET

OUTLET

SPILL FLOW



set according to the part-full pipe flow charts in combination with the WALLINGFORD and BARR (2006) charts in which flow-rate, pipe diameter and hydraulic gradient are graphically related. The surface roughness of all sewer segments was varied as long as the water level at the outlet did not coincide with the water level given at the inlet. One result of the calibration was the little influence of the surface roughness on the flow behaviour. Due to this effect the surface roughness adjusted for the sewer segment was applied accordingly for the entire CSO structure. Assessing relationship between inflow rate and water level The aim of this work was to develop rating curves for discrete steady state flows in order to describe the overflow process more precise. In a first step the CFD simulations were analysed concerning the relation between rate of inflow and corresponding water level for several steady states. The steady state was proved by balancing all inflows and outflows. Thereby it is possible to control to what extent storage and emptying processes are completed at each single time step regarded. Furthermore, overflow events could be identified due to a change of the gradient of the volume - time curve. The position of water levels collected for analysis corresponded to the position of the sonic depth finder installed in the CSO structure. Additionally, water levels at three to four spots evenly distributed along the weir crest were investigated due to the varying height of the weir along its length. Initially, both CSO structures were modelled with the coarse mesh in order to cut down total simulation time and to get an understanding for the specific flow behaviour of each construction. The final simulations were conducted with the fine mesh model. Due to specific flow behaviour the methodology was adopted and modified for each of the CSO structures. Simplistically, the velocity part related to gravitation was neglected in the cell based analysis. The maximum error due to this method was below 1 %. The simulation results are illustrated in Figure 2.

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er le

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m] weir height

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filling period 0.00.51.01.52.02.53.0

0 5 10 15 20 25inflow rate [m³/s]

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vel [

m]

weir height

cross section outlet

filling/emptyingperiod

Figure 2. Relation between inflow and water level for CSO structure A (left side) and for CSO

structure B (right side) The simulation results revealed for CSO structure A an extremely sensitive response of flow conditions and water levels in the range of the side weir height to an increasing inflow velocity. Precisely, a marginal rise of inflow velocity causes a disproportionately increase of water level. The reason for this effect is an increase of the vertical flow against the construction wall which causes circulation flow. If the water level is below the weir crest the relation of discharge rate and water level is nearly the same in inlet, CSO chamber and outlet. The constriction due to the weir construction in CSO structure A has no real impact on the flow regime, particularly as the slope of the chamber is larger than that of the incoming sewer base. Due to the circulation flow the starting water level was close to the ceiling of the CSO chamber in steady state. By reducing the rate of inflow incrementally the water level desired could be adjusted. Thereby it was possible to achieve simulation results based on a steady state flow for filling and emptying period, like one can see in the left side of Figure 2.



Because CSO structure B consists of two inlets, the corresponding rates of inflow were defined as part-full flow conditions with the same water level. The flow conditions proved to be less sensitive on a change of inflow velocity. Therefore discrete water levels in CSO structure B were modelled by an increase of inflow velocity and corresponding inlet water level. The relation between water level and inflow for CSO structure B is shown in right side of Figure 2. RATING CURVES OF THE OVERFLOW PROCESS In a second step the results of the CFD simulations for discrete steady state flow conditions were analyzed concerning the rate of overflow and the head over spillway. Due to the aim to develop rating curves, which are easy applicable in every day practice, the rating curves are developed on basis of the standard weir equation presented in Formula 1 (AKAN and HOUGHTALEN, 2003). Therein the coefficient of discharge kw mainly depends on the shape of the weir crest and the angle of incidence. In compliance with the German guideline on the hydraulic dimensioning of CSO installations ATV-A 111 E (1994) the coefficient of discharge was set to 0.5. To take into account the more complex flow regime of side weirs, the coefficient of discharge was reduced by the factor 0.95 according to SCHMIDT (1957). The effective weir length L is identical with the crest geometry given in the real world CSO structure. By it the weir length for CSO structure A is 3.1 m and for CSO structure B 8.1 m, respectively.

23ww hg2Lk

32Q ⋅⋅⋅⋅⋅=

Formula 1

Qw flow rate [m³/s] kw coefficient of discharge [-] L effective length of weir [m] g acceleration due to gravity [m/s²] h height of water surface above weir crest [m]

In Figure 3 the relation between the head over spillway and the rate of overflow calculated with Formula 1 is shown. Due to an inconsistent height of the weir crest along its length the reference level of both CSO structures is set to their mean height. When the rate of overflow determined by CFD simulation is compared with the rate of overflow calculated on basis of Formula 1, both curves match satisfactorily for heads over spillway lower than 0.25 m. Due to the low water level above the platform beneath the side weir the effective weir length coincides with the given weir length. Therefore the flow over the platform has only insignificant influence on the total rate of overflow. Above this head the flow conditions in CSO structure A change significantly. This change is caused by the spill flow pipe which acts as a controlled outflow starting with this water level. For water levels higher than 0.25 m above the mean weir crest the rate of overflow would increase due to the additional spill flow over the platform, but this effect is superimposed by the impact of the spill flow pipe. If the head over spillway is lower than 0.25 m, the flow conditions in CSO structure B will be similar to those in CSO structure A. A discrepancy between the results based on Formula 1 and the CFD simulation results can be identified for heads over spillway between 0.25 m and 0.5 m. The reason for the underestimated rate of overflow by Formula 1 is the neglected effect



of flow velocities parallel to the side weir. If the head over spillway rises above 0.5 m, flow conditions in CSO structure B will also change like in CSO structure A. That means water levels above 0.5 m will cause the spill flow pipe to act as a controlled outflow. The discharge for controlled outflows is given by the following equation (AKAN and HOUGHTALEN, 2003). hg2akQ ooo ⋅⋅⋅⋅= Formula 2

Qo flow rate [m³/s] ko coefficient of discharge [-] ao area of the orifice [m²] g acceleration due to gravity [m/s²] h height of water surface above axis of outlet [m]

The coefficient of discharge ko can be assed in compliance to AKAN and HOUGHTALEN (2003) between 0.4 for ragged-edge and 0.6 for square-edge uniform entrance conditions, respectively. Although this equation is only correct for small orifices its combination with Formula 1 achieves an optimization of the relation between rate of overflow and head over spillway, as to be seen in Figure 3. Because it is not possible to assess the correct coefficient of discharge in advance, the rate of overflow is calculated with both coefficients to demonstrate the potential range for both CSO structures. Additionally, Figure 3 contains a third curve calculated with Formula 2 with a coefficient of discharge calibrated on the results of the CFD simulation. It can be seen from Figure 3 that this produces exact matching curves for CSO structure A, if the coefficient of discharge is equal to 0.25. Even for CSO structure B this methodology results in a better estimation of the rate of overflow, when the Formula 2 is used with a coefficient of discharge of 0.57. Due to the shape of the overflow curve the simplification by use of Formula 2 provides satisfactory results for water levels exceeding 1.0 m above the weir crest.

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over

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head

[m]

Qo(ko=0.6)

Qo(ko=0.57)Qo(ko=0.4)Qo(ko=0.25)top edge QwQCFD

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over

fall

head

[m]

Figure 3. Rating curves for CSO structure A (left side) and CSO structure B (right side) As a result it has to be concluded that the use of Formula 1 is limited to weir overflow events which are not influenced by the capacity of the spill flow pipe. Otherwise it is necessary to combine Formula 1 with Formula 2. In both CSO structures investigated in this work the spill flow pipe acts as a controlled outflow due to its limited flow capacity. From this point of view the wide spread practice to use Formula 1 solely is not allowable.



It is obvious that the application of Formula 1 and Formula 2 requires the coefficients to be set correctly. On the one hand the use of Formula 1 together with a coefficient of discharge accordingly to ATV-A 111 E (1994) and SCHMIDT (1957) produces proper results. On the other hand it is not possible to choose the coefficient of discharge for Formula 2 in advance, even if the geometry of the outlet is well known. For CSO structure A the coefficient calibrated on the CFD simulations is outside of the range in compliance to AKAN and HOUGHTALEN (2003). Thereby the CFD simulation is an adequate tool to determine the specific coefficients. COMPARISON OF PREVIOUS AND DEVELOPED METHODOLOGY In the previous chapter the significant difference of the wide spread application of Formula 1 and the enhanced relation between rate of overflow and head over spillway calibrated on CFD simulations could be demonstrated. In order to evaluate the impact using the wide spread or the enhanced methodology, the water levels measured in both CSO structures in the time period June 2006 – December 2007 were used to calculate the spill flow volume on basis of the rating curves. The total spill flow volume of CSO structure A was 380 m³ with Formula 1 and 417 m³ with the CFD calibrated rating curves, respectively. So the application of the enhanced methodology results in an increase of 10 % for the two overflow events. CSO structure B showed a slightly different behaviour. There the total spill flow volume of 18 events reduces by 7 % from 131,970 m³ calculated with Formula 1 to 122,480 m³ determined by the enhanced methodology. A reason for the insignificant difference between both methodologies is that in the time period regarded there were just less extreme rainfall events.

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]

Structure AStructure B

hwc

hwc,max

VCFD

Vf1

height above weir crest

maximum height above weir crestspill flow vol. with CFD rating curvespill flow vol. with formula 1

Figure 4. Hydrograph of CSO structure A (left side) and change of spill flow volume (right side) Because of this circumstance both methodologies were compared additionally by using generated hydrographs based on the assumption, that the drained area is connected directly to the CSO structure. Due to the aspect of comparability the connected area was defined in compliance with the former Austrian guideline ÖWAV-RB 19 (1987) by the controlled outflow. The left side of Figure 4 illustrated exemplarily a hydrograph, which was generated by the EPA Storm Water Management Model (SWMM) for one rain event. The maximum head over spillway is given by the position of the sonic depth finder in the CSO chamber. The right side of Figure 4 validates that the spill flow volume based on the enhanced methodology is decreasing with increasing maximum water levels. If the maximum of the hydrograph meets the maximum height above the weir crest, the difference in spill flow volume will be 67 % for CSO structure A and 43 % for CSO structure B respectively.



CONCLUSION AND OUTLOOK In this work it could be shown that the wide spread practice to determine the CSO spill flow discharge from sonic water depth measurements by using only Formula 1 can significantly differ from the discharge based on a CFD simulation, which is closer to reality. For minor heads over spillway the wide spread practice achieves satisfactory results. But this simplified approach does not meet the complex flow regime in case of extreme rainfall events. Due to the limited capacity of the spill flow pipe the discharge is then grossly overestimated. By analyzing the CFD results an enhanced approach was developed, which combines Formula 1 with Formula 2. The water level which indicates an impact of the capacity of the spill flow pipe depends on the specific geometry of the CSO structure and cannot be predicted reliably in general. In the same way it is not possible to assess the coefficient of discharge of Formula 2 without measurement campaigns or CFD simulations. To estimate the impact of the rating curves developed on basis of the CFD results the water levels measured in each CSO structure in the period 2006/07 were statistically evaluated to determine the spill flow volume. The spill flow volume for CSO structure A was increased by 10 % and for CSO structure B decreased by 7 %. Additional hydrographs generated with a hydrodynamic model were used to compare the enhanced approach with the wide spread practice for discrete water levels. If the maximum of the hydrograph meets the maximum height above the weir crest, the difference in spill flow volume will be 67 % for CSO structure A and 43 % for CSO structure B respectively. The work presented in this article should be regarded within the context that the overflow volume is generally used to calibrate conceptual sewer models. Because urban drainage models are calibrated usually on extreme rainfall events the impact of the calculated spill flow volume on the model results will even increase. It was demonstrated that the spill flow volume used for calibration can differ up to 43 % or even 67 % depending on the CSO structure for a single extreme rain event. With the developed rating curves deviating efficiencies of the total sewer system will be obtained. REFERENCES 2000/60/EC (2000): Directive of the European Parliament and of the Council establishing a framework for

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