Modeling-of-Water-Pipeline-Filling-Events-Accounting-for-Air-Phase-Interactions

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/263965679 Modeling of Water Pipeline Filling Events Accounting for Air Phase Interactions Article  in  Journal of Hydraulic Engineering · September 2013 DOI: 10.1061/(ASCE)HY.1943-7900.0000757 CITATIONS READS 26 1,453 authors: Bernardo Trindade Jose G Vasconcelos Cornell University Auburn University 11 PUBLICATIONS   118 CITATIONS    117 PUBLICATIONS   1,026 CITATIONS    SEE PROFILE Some of the authors of this publication are also working on these related projects: Investigation of unsteady, two-phase flow conditions in stormwater systems View project Sediment-water flows in stormwater applications View project All content following this page was uploaded by Jose G Vasconcelos on 11 July 2014 The user has requested enhancement of the downloaded file SEE PROFILE Modeling of Water Pipeline Filling Events Accounting for Air Phase Interactions Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Bernardo C Trindade and Jose G Vasconcelos, A.M.ASCE Abstract: In order to avoid operational issues related to entrapped air in water transmission mains, water refilling procedures are often performed carefully to ensure no pockets remain in the conduits Numerical models may be a useful tool to simulate filling events and assess whether air pockets are adequately ventilated However, this flow simulation is not straightforward mainly because of the transition between free surface and pressurized flow regimes and the air pressurization that develops during the filling event This paper presents a numerical and experimental investigation on the filling of water mains considering air pressurization aiming toward the development of a modeling framework Two modeling alternatives to simulate the air phase were implemented, either assuming uniform air pressure in the air pocket or applying the Euler equations for discretized air phase calculations Results compare fairly well to experimental data collected during this investigation and to an actual pipeline filling event DOI: 10.1061/(ASCE)HY.1943-7900.0000757 © 2013 American Society of Civil Engineers CE Database subject headings: Water pipelines; Numerical models Author keywords: Water pipelines; Pipeline filling; Flow regime transition; Air pressurization; Numerical modeling Introduction Transmission mains are important components of water distribution systems and a relevant concern is the safety of operational procedures performed on those Among the operational procedures one includes what is referred to as pipeline priming, the refilling operations that often follow maintenance tasks that require total or partial emptying of the conduits During refilling procedures, the air phase initially present in the pipeline may become entrapped between masses of water in the form of air pockets Entrapped pockets may lead to pressure surges in the system and loss of conveyance when not properly expelled through air valves However, as will be shown, there is limited investigation on the development of numerical models to simulate pipeline priming, particularly involving the effects of entrapped air Similar to other applications that involve the transition between pressurized and free-surface flows (also referred to as mixed flows), there are certain characteristics on water pipeline filling events that pose challenges to the development of numerical models: • Pipeline filling events are characterized by the transition between free-surface and pressurized flow regimes, and while there are different approaches to simulate such transitions, current models are limited by difficulties in properly incorporating Hydraulics and Hydrology Engineer, Bechtel Corporation, 3300 Post Oak Blvd., Houston, TX 77056; formerly, Graduate Student, Dept of Civil Engineering, Auburn Univ., 238 Harbert Engineering Center, Auburn, AL 36849 E-mail: btrindad@bechtel.com Assistant Professor, Dept of Civil Engineering, Auburn Univ., 238 Harbert Engineering Center, Auburn, AL 36849 (corresponding author) E-mail: jvasconcelos@auburn.edu Note This manuscript was submitted on December 14, 2011; approved on March 15, 2013; published online on March 18, 2013 Discussion period open until February 1, 2014; separate discussions must be submitted for individual papers This paper is part of the Journal of Hydraulic Engineering, Vol 139, No 9, September 1, 2013 © ASCE, ISSN 0733-9429/2013/ 9-921-934/$25.00 the interaction between flow features (e.g., bores and depression waves) or because of issues such as postshock oscillations; • Pipeline filling is a two-phase, air-water flow problem, and models handling the two separate phases need to be appropriately linked The handling of the interface between air and water is particularly challenging; • Due to the formation of bores and the large discrepancy in the celerity magnitudes between different portions and phases of the flow, nonlinear numerical schemes should be used if bores are anticipated so that diffusion and oscillations at bores and shocks are minimized; • At certain regions of the flow, particularly in the vicinity of curved air-water interfaces, shallow water assumptions are not applicable due to strong vertical acceleration because the problem is intrinsically three-dimensional (Benjamin 1968); • Several different mechanisms may result in the entrapment of air pockets during filling events, yet because conditions leading to such entrapments are still not fully understood, these cannot be properly implemented in numerical models Related studies on the interference between air and water in closed conduits started as early as Kalinske and Bliss (1943), focusing on steady flows in which a hydraulic jump filled the conduit causing air entrainment through the jump The work presented an expression relating the amount of air entrained by the jump in terms of the Froude number of the free-surface portion of the flow upstream of the jump Recent experimental investigation on airwater interactions in water pipelines has led to advances on the understanding of the removal of air pockets by dragging, leading to expressions for the required water flow and velocity that will result in the removal of air bubbles and pockets from pipes Among such works one includes Little et al (2008), Pothof and Clemens (2010), and Pozos et al (2010) The removal of these pockets, however, would occur during the operation of these pipelines, and thus is different from the air ventilation process that takes place during pipeline priming Numerical simulation of the filling of water pipelines required the use of flow regime transition models because conduits start JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 921 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved empty and will be fully pressurized by the end of the event Such models simulate both flow regimes, and one may classify these models in two main types: shock-capturing and interfacetracking models Shock-capturing models apply a single set of equations to calculate both pressurized and free-surface flow regimes and require the use of a conceptual model to handle pressurized flows using free-surface flow equations These models are generally simpler to implement and provide seamless representation of the interaction between various flow features, but have the drawback of generating numerical oscillations at pipe-filling bore fronts that can be addressed by appropriate flux selection or numerical filtering technique (Vasconcelos et al 2009a) Interface-tracking models are more complex to implement because they require a set of equations for each flow regime and proper interaction between flow features is more complex to represent; however, the resolution of pressurization bores is exact (no diffusion) and there are no postshocks at pipe-filling bores With regards to air simulation, most models used a framework that is based on the ideal gas law, with fewer alternatives using a discretized framework To date, most one-dimensional, unsteady flow models that accounted for air pockets in pipelines are of the interface-tracking type and use the lumped inertia approach to simulate the water phase, while air is simulated using implementations of the ideal gas law Possibly the first such work was by Martin (1976), which presented a model to compute surges caused by the compression of air pockets at the end of an upward sloped pipeline Such models assume well-defined interfaces between air and a water phases, essentially a portion of the system that would be in pressurized water regime while the other would have the entire cross section occupied by air In some instances of these model applications, an orifice equation is added to the air formulation to account for air ventilation during the compression process This modeling approach further assumes uniform pressure head for the entire air mass, and is subsequently referred to as the uniform air pressure head (UAPH) model An example of other models that use the same principles of the UAPH model includes the work presented by Zhou et al (2002), which studied the compression of air pockets in the context of stormwater systems considering that the air ventilation at orifices may be choked Two other numerical modeling studies focused on the filling water mains and have also used the interface-tracking and lumpedinertia approaches Liou and Hunt (1996) proposed a simple alternative to simulate the pipeline filling characterized by flow regime transition, but have not included effects of air pressurization The model avoided the difficulties associated with the shock-fitting technique by assuming a vertical interface between air and water, implying in an instantaneous transition between dry pipe and pressurized flow upon inflow front arrival The second water main filling model using interface tracking was proposed by Izquierdo et al (1999) The model simulates the rapid startup of pipelines that are partially filled, so that the flow admission generates the entrapment of air pockets Air phase modeling uses the UAPH approach without ventilation for air pockets Fuertes et al (2000) tested that model against experimental data in order to validate the model with good agreement, but the tested inflow rate is possibly too large to be representative of pipeline priming operations As presented, these modeling studies that combine lumped inertia and UAPH approaches assume (1) well-defined interfaces separating air and water phases, (2) high inflow rates as consequence of the elevated driving pressure head, and (3) uniform pressure in the air pockets The first assumption may be invalid in cases in which air is not actually intruding into the pressurized flow, as discussed in Vasconcelos and Wright (2008) The second assumption usually does not hold if the filling is performed gradually However, the latter assumption may be applicable and is addressed in the present investigation Chaiko and Brinckman (2002) presented a comparative study of three modeling alternatives to simulate air-water interactions in a idealized pipe-filling problem The first model solves both phases by applying the method of characteristics (MOC) so that water characteristic lines need to be interpolated to match the grid during simulation, the second model simplifies air phase modeling by applying a type of UAPH model, and the third applied UAPH for the air phase and MOC for the water phase, however calculating only the unperturbed portion of the water flow so that the characteristic lines have constant slope and match the grid without the need of interpolation The researchers run tests for a vertical setup that consisted of a a cylinder with an air pocket on the upper part, which is compressed by the water phase due to an increase in the water pressure at the bottom of the cylinder It was found that the second model alternative captured all the relevant events as well as the first model, even though the second didn’t capture small oscillations due to the reflection of the pressure wave in the air, which has no major importance in most practical applications However, the geometry used in that study is idealized, and a question is how the obtained results are translated to a more complex setup in which initially stratified flow exists along with moving water pressurization interfaces Two studies are presented as instances of shock-capturing models to simulate rapid filling of closed conduits In the context of stormwater simulation, Arai and Yamamoto (2003) presented a model that performs flow regime transition calculation including a discretized air phase calculation approach The model applies the Saint-Venant equations for the water phase and the Preissmann slot to account for pressurization The model was implemented in a simple, quasi-horizontal geometry, and air was modeled with a set of discretized mass and momentum equations Model results compared well with experimental results and indicate the importance of accounting for air phase effects during simulation The conditions for air pocket entrapment were not focused in this study, and the linear numerical scheme applied in the study (four-point Preissmann scheme) is not appropriate to adequately capture bores when Courant numbers are very low; this is an issue that is further discussed subsequently The second study involved finite-volume models using numerical schemes based on approximate Riemann solvers that overcome problems with low Courant numbers applied in the context of pipeline filling A model based on the Saint-Venant equations was presented by Vasconcelos (2007) using the two-component pressure approach (TPA) (Vasconcelos et al 2006) This model was subsequently used in a study that involved the filling of an actual 4.4-km-long, 350-mm-diameter water transmission main operated by an environmental sanitation company of the federal district, Brazil (CAESB) (Vasconcelos 2007) Field measurements of inflow rates and pressure heads indicated that the model was able to capture the general trend of the filling Yet some discrepancies between the pressure measurement and predictions were attributed to the inability of the numerical model to incorporate limited ventilation conditions and consequently effects of air pressurization to the flow Objectives This paper aims to obtain further insight on air-water interactions during water pipeline filling operations, with the overarching objective of developing a numerical framework that may be used to simulate a priori filling operations in pipelines and detect operational issues related to the entrapment of air pockets To achieve 922 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved this objective, two numerical models were proposed that differ in the strategy in which air is modeled Both alternatives use the variation of the TPA model presented by Vasconcelos et al (2009b) to describe the water phase Air phase modeling is performed either by using a discretized framework that applies the Euler equation or by using a type of UAPH model Another objective was to assess the benefits of using a discretized framework to simulate the air phase Associated with the numerical development, an experimental program was conducted using a scale model apparatus that incorporates essential features of a water pipeline filling problem Key parameters in the problem were systematically varied, including inflow rate, pipeline slope, and ventilation degree Experimental measurements included pressure, pressurization interface trajectories, and inflow rates Both modeling alternatives for the air phase were compared to experimental data and to the field data of an actual water main filling event presented by Vasconcelos (2007) Methodology Numerical Model Certain flow features of the water main pipeline filling problem were determinant in the model’s formulation so that it could describe the filling process adequately With regard to the water phase, these features include: • Mixed flows: Handled by applying the TPA model variation from Vasconcelos and Wright (2009); • Postshock oscillations at pipe-filling bore fronts: Use of a numerical filtering scheme (Vasconcelos et al 2009a, b); • Air pocket entrapment and pressurization: Used either the Euler equations or UAPH model; • Free-surface and pipe-filling bores: Use of the approximate Riemann solver presented by Roe (Macchione and Morelli 2003); and • Solution stationarity: Use approach presented by Sanders and Bradford (2011) The air phase in the model is represented by a well-defined air pocket that is not significantly fractured This pocket shrinks due to  hair ¼0 ≠0 compression by the water phase that gradually occupies the lowest points in the pipeline profile Air is displaced and escapes through ventilation orifices located at selected locations According to Tran (2011), for such flow conditions the air compression process may be considered isothermal and this assumption is used in both model approaches used to simulate the air phase The air phase is calculated as if the only atmospheric connections occur at ventilation points, which are treated as orifices for simplicity Ideal ventilation with negligible air phase pressure head is assumed to exist prior to the formation of an entrapped air pocket, as will be discussed subsequently When a pocket forms, it is delimited by a ventilation orifice and a flow regime transition interface, either abrupt (pipefilling bore) or gradual In the proposed model, an air pocket is caused by the closure of a downstream valve or by the development of a pressurization interface as water fills the lowest points of the pipeline Fig presents a sketch of a typical application, whereas Fig presents the overall structure of the proposed model Water Phase Modeling The TPA model, used in the water phase simulation, modifies the Saint-Venant equations, enabling them to simulate both pressurized flows and free-surface flow regimes This model has been improved in the past years and the alternative used in this paper was presented in Vasconcelos and Wright (2009) This alternative has a term that accounts for air phase pressure head, so the modified Saint-Venant equations are in divergence format ∂U ∂FðUÞ ỵ ẳS t x where  Uẳ  FUị ẳ Q  ; Q Q2  SUị ẳ A A þ gAðhc þ hs Þ þ gApipe hair  gAðS0 − Sf Þ → Free-surface flow without entrapped air pocket or pressurized flow → Free-surface flow with entrapped air pocket → Free-surface flow D 3sinðθÞ − sin3 ðθÞ − 3θcosðθÞ > > → Free-surfaceflow > > > >D : Pressurizedflow 5ị where U ẳ ½A; QŠT is the vector of the conserved variables; A = flow cross-sectional area; Q = flow rate; FðUÞ = vector with the flux of conserved variables; g = acceleration of gravity; hc = distance between the free surface and the centroid of the flow cross section (limited to D=2); hs = surcharge head; hair = extra head due ð1Þ  ; ð2Þ ð3Þ to entrapped air pocket pressurization; θ = angle formed by freesurface flow width and the pipe centerline; D = pipeline diameter; Apipe = cross-sectional area (0.25πD2 ); and a = celerity the acoustic waves in the pressurized flow The numerical solution used in the implementation of the water phase model used the finite-volume method and the approximate Riemann solver of Roe, as presented in Macchione and Morelli (2003) This choice was motivated by the significant discrepancy in the celerity values between the free-surface and pressurized flows, and between air and water flows This discrepancy may be of the order of or orders of magnitude and yields an extremely low Courant number for the free-surface water flow Nonlinear schemes such as the Roe scheme are known to provide accurate bore predictions even in very low Courant number conditions For dry bed regions of the flow, it was assumed that the flow depth would start as a minimum water depth of mm In such cases, the model would then predict the existence of a nonphysical JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 923 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved flow of this thin layer down the pipeline slope To deal with this problem, the approach presented in Sanders and Bradford (2011) was used In this formulation, in order keep a minimum water layer with no motion and at the same time keep the stationarity of the solution, two criteria were followed in order to perform flow calculations at interior finite-volume cells: one is based on the ratio between friction forces and the other based on the minimum submerged area of the cell After computing these criteria to all cells in the domain, only the cells in which at least one of the two criteria is met have the flow variables calculated Details of these formulations are omitted for brevity, but may be found in the previously mentioned paper Two source terms were considered for the water phase modeling, one accounting for pipe wall friction and the other accounting for pipe slope Both calculations followed the approach presented in Sanders and Bradford (2011) For the pipe wall friction source term, a semi-implicit formulation based on Manning’s equation was used, while for the pipe slope a formulation that preserves stationarity of the solution was used The upstream boundary condition for the water phase refers to all that is inside the dashed box in Fig It is based on an iterative solution that ensures that local continuity and linear momentum at the pipeline inlet are satisfied, regardless of the flow regime at that location The local continuity equation for the reservoir is dH res ¼ Qrec − Qin dt ð6Þ where Hres = reservoir water level; Qrec = flow rate admitted into the reservoir from the recirculation system; and Qin = flow rate that enters the upstream end of the pipe The calculation of the updated flow velocity at the upstream boundary cell (unỵ1 ) uses an ordinary differential equation representing the linear momentum conservation, which in turn is derived from a lumped inertia approach:   g un2 jun2 j n Hres K eq ỵ t Δx 2g   un2 jun2 j un2 n n ẵwdepth ỵ max0; hs ỵ hair ị f 2x 2x  u1nỵ1 ẳ un1 ð7Þ where wdepth = local water depth; n = time step index; K eq = overall local loss coefficient in the inlet; and f = friction head loss in the short pipe portion inside the boundary condition right after the inlet After the velocity in the cell is obtained, Froude number is calculated with the current wdepth in order to assess if the flow is subcritical If this is the case, wdepth nỵ1 is updated according to the Hartree MOC for free-surface flows as shown in Sturm (2001) If flow depth at the inlet is less than the pipe diameter D, then the surcharge head hs is set to zero while hair may be nonzero if there is any entrapped pocket On the other hand, if wlevel nỵ1 > D, flow at inlet is pressurized, hair is set to zero, and hs is recalculated to match the piezometric head at the upstream end, calculated with the energy equation With the depth and the head updated, the flow area Anỵ1 is updated and a new flow rate is then calculated with unỵ1 and Anỵ1 1 The downstream boundary condition used to compare the model with the experiments can be either a fully opened or closed gate valve For the case in which the valve is fully opened, the approach called transmissive condition presented in Toro (2001) is used For the case in which the downstream boundary condition is a closed valve, the boundary condition is calculated enforcing the relevant characteristic equation and zero velocity at the downstream end: wlevel nỵ1 No ẳ cr K ị g r unỵ1 No ẳ 8ị where K r = constant factor that depends on the flow conditions in the previous time step (Sturm 2001) If wlevel nỵ1 > D, the flow depth at the downstream end becomes pressurized In such a case, wlevel nỵ1 No is set to the value of the pipe diameter, hs is set as the extra head of the cross section minus D, and hair is set to zero Air Phase Modeling In the proposed model, air is initially considered as a continuous layer over the water layer (stratified water in free-surface flow mode) During the simulation, air is handled in one of the two following manners: At the first stage of the filling, when the air within a given pipe consists of an entire layer that is connected to atmosphere at the ventilation orifice and at its lowest point within the pipe (ideal ventilation), it is assumed that the air pressure in the entire layer is approximately atmospheric, and air velocity is assumed negligible This condition persists until a pocket is formed at the lowest point during the filling process At the second stage, once an air pocket is formed, the connection to the atmosphere at its lowest point is lost Air phase pressure is expected to develop during the filling process, requiring calculations with either one of the two proposed air Fig Representation of the proposed model key components 924 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Fig Flowchart for the model calculation procedures JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 925 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved phase models to determine its pressure and influence in the water flow An algorithm was developed to track air pocket volume and start and end nodes as it shrinks in order to simulate its behavior with either of the two models For this, the mechanism considered for air pocket formation is the isolation of an air mass due to the development of a flow regime transition interface or a closed downstream valve As mentioned, it is assumed that during a pipeline filling event this air pocket will be delimited by a ventilation orifice and a flow regime transition interface This interface will move mainly toward the air pocket ventilation point, compressing the air pocket and forcing its elimination through the ventilation orifice, as is sketched in Fig The model alternative that uses the UAPH model assumes (1) uniform pressure in the whole air phase, (2) the validity of the ideal gas law, and (3) isothermal air flow This model may be expressed as ρn V np ẳ nỵ1 V pnỵ1 M nair ẳ M nỵ1 air 9ị where M air = mass of air within the pocket with volume V p ; and ρ = specific mass of air In order to consider the air escape or admission, an extra term was added to Eq (9), yielding n V np ẳ nỵ1 V pnỵ1 þ M air nþ1 out ð10Þ where Mair out = air mass that escapes through the ventilation orifice in that instant, calculated as presented in Eq (19) presented subsequently The second alternative to model the air phase uses a discretized framework, applying a one-dimensional isothermal form of the Euler equation: U FUị ỵ ẳS t x   Uẳ ; u  u ; FUị ẳ u2 ỵ p  11ị  Sd1 SUị ẳ Sd2 ỵ Sf a  12ị with the pressure p defined as p ẳ ρα2 ð13Þ where U = vector of conserved variables; F = vector of the conserved variables fluxes; S = vector of source terms; α = celerity of the acoustic waves in the air; and Sd1;i , Sd2;i , and Sf a = source terms Applying the Lax-Friedrichs scheme (LxF) as presented in Toro (2001) to Eq (12), one has the following expressions to update the conserved variables: niỵ1 ỵ ni1 t ẵuịniỵ1 uịni1 ỵ tSd1;i 2x uịniỵ1 ỵ uịni1 uịnỵ1 ẳ i   un þ uni−1 ρn − ρni−1 Δt − þ α2 iþ1 ẵuịniỵ1 uịni1 iỵ1 2x 2x nỵ1 ẳ i ỵ tSd2;i ỵ Sf a ị 14ị The choice for the LxF scheme was based on its simplicity and the lack of shocks in the air phase flow In pipeline filling problems, the mechanism causing the motion of the air phase is the displacement of air in the cross section caused by changes in the water flow depth underneath the air pocket This effect is accounted for in the source terms Sd , as presented in Toro (2009):      Aair Aair Sd1 ỵ uair ẳ 15ị u Sd2 x A t where Aair ¼ ðπ=4ÞD2 − A and is calculated only in free-surface flow cells An explicit implementation of source terms Sd led to instability of the numerical solution, so a semi-implicit approach was applied in this paper The air phase is first calculated without considering changes in Aair , returning a preliminary solution ˇ ρuŠ, ˇ which then needs to be adjusted with a correction facU ẳ ẵ; tor so that a definitive solution is achieved The definitive solution and correction factor ϕ are represented by     ρ Uẳ ẳ 16ị u u with   1 nỵ1 Aair nỵ1 Aair ni Aair nỵ1 iỵ1 Aair i1 n i ẳ 1ỵ n þ ui Ai Δt 2Δx ð17Þ The solution of Sd source terms presented some oscillations at the region of the strongest free-surface flow gradients, at the vicinity of the pressurization front Two approaches were used together to minimize these oscillations The first one was to limit ϕ to the range ẳ ẵ1.0050.995 The second was the application of an oscillation filter in the air phase internal nodes, following Vasconcelos et al (2009a) with ϵ ¼ 0.05 This approach resulted in a good balance between pressure accuracy, presenting an average continuity error of less than 4% for the air phase in the comparison with the experimental cases and 1% in the comparison with the field measurements The likely source of the continuity error for the Euler equation model are the orifice boundary condition and the limitation of the correction factor ϕ [Eq (16)] to a certain value, which distorts the actual required air compression due to pocket vertical shrinking However undesirable, air continuity errors did not seem to have an major impact in the overall results, as the comparison between numerical models and experiment indicate The other source term added to the simulation of the air phase flows was the friction between the air phase and the pipe walls, as described in Arai and Yamamoto (2003): Sf a ¼ f a Pa ua jua j 8gAair ð18Þ where Pa = perimeter of the air flow For the UAPH model, the boundary condition used at the uppermost point in the pipeline reach (where the ventilation valve was located) was a discharging orifice The orifice is represented by an equation similar to one presented in Zhou et al (2002): s nỵ1 atm nỵ1 M air out ẳ tCd Aorif nỵ1 ð19Þ α ρatm where Cd = discharge coefficient that is assumed as Cd ¼ 0.65; and Aorif = orifice area Eq (19) was coupled with Eq (10) to yield s nỵ1 atm n n nỵ1 nỵ1 nỵ1 20ị V p ẳ V p ỵ ΔtCd Aorif ρ α ρatm For the Euler equation model, two boundary conditions are required At the lower point of the pipe where the water pressurization front is displacing the air, a reflexive boundary condition 926 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Fig Sketch of the experimental apparatus used in the investigation (Toro 2001) was used At the uppermost point, the ventilation orifice boundary condition for the Euler equation approach is similar to the UAPH model in the sense that both apply a continuity equation along with the orifice equation The continuity equation for this boundary condition is nỵ1 nỵ1 nỵ1 tAnỵ1 ẳ Anỵ1 n1 ị ỵ M air nỵ1 out air u1 air Δxðρ1 ð21Þ where M air out = air mass discharged through the ventilation orifice, calculated using Eq (19) Eq (21) is solved for unỵ1 using the Riemann invariants for the isothermal, one-dimensional, primitive version of the Euler equation (Pulliam 1981): uair1 ¼ uair2 − αðlog ρ2 − log ρ1 Þ ð22Þ On both models, calculations are stopped when the pocket has evacuated 95% of its original volume When this condition is reached, the average head of the air pocket is assigned to its cells, remaining constant until the end of the simulation This was motivated to avert calculation instabilities caused by increasingly smaller air pocket volumes, and follows the strategy used in Zhou et al (2002) Experimental Program An experimental investigation was conducted to gather insights on the characteristics of the pipeline filling problem with limited ventilation, and to validate the proposed numerical model The apparatus was inspired in the one presented in Trajkovic et al (1999), yet with modifications that limited ventilation conditions Experimental Apparatus Setup A sketch of the experimental apparatus is presented in Fig The experimental apparatus included a clear PVC pipeline with length L ¼ 10.96 m and diameter D ¼ 101.6 mm with adjustable slope At the upstream end, a 0.66-m3 capacity water reservoir supplied flow to the pipeline through a 50-mm ball valve; at the downstream end flow discharged freely through a 101.6-mm knife gate valve into a 0.62-m3 reservoir, and flow was subsequently recirculated with pumps Right after the inlet control valve, a T-junction was installed in the pipe so that different caps with ventilation orifices could be installed Initial steady flow conditions were such that free-surface flows exist at the whole pipeline because the downstream gate was fully opened A sudden closure maneuver (within 0.3 s) of the knife gate valve at the downstream end of the pipeline blocked the downstream ventilation, triggered a backward-moving pressurizing interface, and resulted in the entrapment of an air pocket These air pockets became pressurized as water accumulated at the downstream end of the pipe pushed the air mass through the ventilation orifice in the beginning of the pipe Two pressure transducers, Meggit-Endevco 8510B-5, were installed at the upstream end of the pipe (xà ¼ x=L ¼ 1, measured from the downstream end) and at an intermediate point xà ¼ 0.39 Transducer results were calibrated each experimental run with the aid of four digital manometers, with of 3.5-m H2 O maximum pressure head and 0.3% accuracy Flow rates were measured with a Nortek MicroADV positioned in the recirculation system and confirmed by a paddlewheel flow meter Experimental Procedure The experiment procedure consisted of the following steps: With the desired slope set in the pipeline, the pumps were started; valves near the pump were throttled enough to provide the selected steady flow rate to the system The desired ventilation orifice was installed When the water level at the upstream reservoir and pipeline attained steady levels, readings were perfromed at all manometers, as well the upstream reservoir head The data logging was started for the pressure transducers, the MicroADV, and manometer at the upstream reservoir The downstream knife gate valve was rapidly maneuvered and closed, entrapping an air pocket and creating a backwardmoving pressurization front Digital cameras (30 frames per second) recorded the whole pipe filling process, one of them tracking the bore and another one tracking the pressurization interface When the pressurization interface approached the ventilation orifice, it was rapidly closed to avoid water spilling The pump was shut down and control valves closed so that pressure could attain hydrostatic conditions Manometer readings were performed and data logging was stopped The use of two cameras to track the inflow and pressurization front was particularly necessary in the cases in which interface breakdown (Vasconcelos and Wright 2005) occurred; otherwise just one camera tracking the pipe-filling bore front was used The described experimental program varied systematically the flow rates, ventilation orifice diameters, and pipeline slopes Table presents the ranges of the tested experiment variables, with a total of 36 conditions tested A minimum of two repetitions were Table Experimental Variables Variables Tested range Normalized range 2.53, 3.79, and 5.05 L=s 0.245, 0.368, and 0.490 0.5, 1, and 2% Not available 0.63, 0.95, 1.27, 0.0625, 0.09375, and 5.06 cm 0.125, 0.5 pffiffiffiffiffiffiffiffi à Note: Flow rate normalized by Q ¼ Q= gD and ventilation diameter by dà ¼ dorif =D Flow rate Slope Ventilation orifice diameter JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 927 J Hydraul Eng 2013.139:921-934 performed for each condition to ensure consistency of the data collected Results and Discussion Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved The experimental results are compared with the proposed numerical model using both approaches to simulate the air phase pressure The numerical model predictions are also compared with the field data collected by Vasconcelos (2007) during an actual refilling operation of a 4.4-km-long, 350-mm-diameter, ductile iron pipeline in Brasilia, Brazil, operated by the waterworks company CAESB Experimental Results Fig shows the pressure history close to the ventilation orifice for all tested cases in the experimental program with normalized orifice diameter dÃorif ¼ dorif =D smaller than or equal to 0.125 The transducer at that station was located at the pipe crown, so it measured air phase pressures for most of the filling processes As would be anticipated, higher pressurization levels were observed for smaller ventilation orifices, while the filling time was smaller for higher flow rates Air phase pressure head results were not significantly different for varying pipeline slopes On the other hand, there was a slight difference in the filling time between different pipeline slopes for a given ventilation orifice and flow rate This difference is attributed to the different initial water levels in the apparatus prior to the closing of the knife gate valve at the downstream end Also, as can be noticed in Fig 4, the smallest ventilation air phase pressure head kept increasing during the filling process, indicating steady flow for these cases was not attained Fig presents the pressure head hydrograph for xà ¼ 0.39 (measured at pipe crown) for experimental runs with dÃorif ≤ 0.125 There is a sudden step up in the pressure values the moment at Fig Measured air phase pressure heads for all tested conditions where dorif < 0.5 928 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Fig Pressure head variation at the pipe crown for xà ¼ 0.39 for all tested conditions where dÃorif < 0.5 which the flow regime transition interface reached that station As in the case of pressure measurements at the ventilation orifice, these pressures kept increasing due to the increase in the air pressure for the smallest ventilation case The magnitude of the jump in the pressure readings was an indication of the strength of the pipe-filling bore front, which increased for larger inflow rates and ventilation orifices The absence of this discontinuity was a sign of either gradual pressurization interface and/or the occurrence of interface breakdown feature due to the interaction between the backward-propagating pipe filling bore front and the depression wave generated at the pipeline inlet by the air pressurization The relevance of the interface breakdown feature is that its occurrence may pose difficulties to the application of pipeline filling models that use well-defined inflow interfaces as a modeling hypothesis To illustrate the impact of the interface breakdown feature to results, Fig presents two sets of trajectories of moving pressurization interfaces for normalized flow rates of Qà ¼ pffiffiffiffiffiffiffiffi Q= gD ¼ 0.245 and 0.490 and 2% slope, measured for all tested ventilation diameters All these interfaces start as pipe-filling bore fronts at xà ¼ as the gate valve is closed Such bores lasted until xà ≈ 0.28 when they encountered the depression wave originated from the upstream end of the pipe For both flow rates, an interface breakdown feature was noticed when the smallest ventilation orifice was used On occurrence of the feature, the pipe-filling bore became an open-channel bore that moved more slowly toward the ventilation orifice, leaving an air intrusion on its top Interestingly, as the backward-moving bores approached the ventilation orifice, there was an acceleration on their motion, regardless of whether interface breakdown occurred or not The cause for this change in bore velocity is not determined yet When interface breakdown occurred, interface measurements included both the position of the open-channel bore and the pressurization front The latter was a gradual transition, and JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 929 J Hydraul Eng 2013.139:921-934 was moderately slowed by the interface breakdown For the smallest ventilation (dÃorif ¼ 0.0625), on the other hand, the velocity of the pressurization bore was significantly reduced, with a much larger separation between the pressurization front and interface breakdown Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Comparison between Experimental Results and Numerical Model Predictions Fig Trajectory of moving bore for (a) Qà ¼ 0.245; (b) Qà ¼ 0.368 and pipeline slope = 2% immediately following the interface breakdown it was noticed that the pressurization front retreated Soon afterward, the pressurization front resumed the motion toward the ventilation orifice, trailing the open-channel bore Fig presents the trajectories for the condition Qà ¼ 0.245 and 1% slope for all four tested dÃorif The largest one (dÃorif ¼ 0.50) has not generated any sign of air pressurization, and the pipe-filling bore kept its shape as it propagated toward the ventilation point However, for dÃorif < 0.50, there was the occurrence of interface breakdown and the the trajectory of the pressurization fronts (thin lines) are plotted along the trajectories of the pressurization bores For the cases when dÃorif ¼ 0.125 and dÃorif ¼ 0.0938, the trajectory of the gradual pressurization front was approximately parallel to the backward-moving bore, which Fig Trajectory of moving bore (thick line) and pressurization interface (thin line) for Qà ¼ 0.245 and slope of 1% The comparison between experimental results and corresponding numerical predictions is presented in Figs and All calculations were performed assuming that the clear PVC pipeline Manning roughness coefficient was n ¼ 0.0085 and the wave celerity assumed for the PVC pipe was 200 m=s Courant numbers of 0.80, 0.90, and 0.95 were tested and results are shown for the case Cr ¼ 0.80 Air phase pressure head predictions for dÃorif < 0.50 and 1.0% slope are compared with experimental results in Fig Both Euler and UAPH approach models showed good agreement with experimental data for most of the cases, especially for the lower flow rates (Qà ¼ 0.245 and Qà ¼ 0.368) At higher flow rates and smaller orifice sizes, air pressures were slightly overpredicted In a few of the numerical predictions there were strong, highfrequency oscillations on the air pressurization results as the pocket volume shrank to zero Results obtained at the intermediate point (xà ¼ 0.39) for slope of 0.5% are presented in Fig and indicate fair agreement between numerical and experimental results There is a tendency of pressure overprediction by the numerical model, which also anticipates the arrival of the pressurization front at the upstream end of the system In the chart with Qà ¼ 0.490, dÃorif ¼ 0.0625, there are two zones with oscillations, but these are due to the flow regime transition that results from the use of the shock-capturing TPA method Animation of the simulated results for this particular case show that the backward-moving bore front stops briefly close to xà ¼ 0.4 between tà ¼ 0.6 and tà ¼ 0.8, resuming its movement upstream later on During this, the oscillations are not detected in the simulation results A limitation of the numerical predictions was related to the prediction of the interface breakdown occurrences The proposed numerical model (both air phase model implementations) was able to predict the onset of the interface breakdown as the interaction of the depression wave and pipe-filling bore resulted in an open channel bore However, unlike the experiments, the predicted pressurization front does not retreat following the breakdown There was some overprediction of the pressure head in cases when interface breakdown occurred; results obtained with the Euler equation indicate the instant of the breakdown by a second smaller increase in pressure head at tà ≈ 0.2 This discrepancy, however, was not significant and has not compromised the general accuracy of the numerical model Observations during the experimental runs indicate that pressure increases at the upstream reservoir during the filling events Prior to the knife gate valve closure, the reservoir head was steady Considering that the inflow rate into the reservoir was constant, the increase in reservoir head following the knife gate valve maneuver indicates a drop in the inflow rate admitted into the pipeline inlet due to the almost instantaneous air pressurization Steeper reservoir pressure head increase is linked to stronger air pressurization and decrease in the flow admitted into the system, which resulted in the depression wave that trigged interface breakdown events The numerical model provides general agreement with experimental measurements Results, however, are not presented in this paper for brevity 930 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 7 Q*=0.245, dorif*=0.125 Q*=0.368, dorif*=0.125 Q*=0.490, dorif*=0.125 Q*=0.245, dorif*=0.09375 Q*=0.368, dorif*=0.09375 Q*=0.490, dorif*=0.09375 Q*=0.245, dorif*=0.0625 Q*=0.368, dorif*=0.0625 * hres =hres/D Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Q*=0.490, dorif*=0.0625 0 3 t*=t/(L/sqrt(gD)) Euler equation UAPH Exp rep Exp rep Fig Measured and predicted air phase pressure heads for all tested conditions where dorif < 0.5 and slope of 1% Both models yielded similarly accurate results when compared with experimental data despite the two considerably different approaches to simulate air phase Yet an aspect to be considered is the computational effort involved in each air phase modeling alternative In general, the simulation time using the Euler equation model was more than times larger than one required by the UAPH model approach for the comparison with the experimental results Not only due to the additional model complexity, the enforcement of the Courant condition for the air phase simulation used resulted in even smaller time steps as the celerity of the air phase was of the order of 300 m=s The criterion for computation end was the shrinkage of the pocket to a lower volume limit (5% of initial volume) Model Comparison with Actual Pipeline Filling Event The comparisons between the field data and the numerical predictions for the filling of CAESB ductile iron pipeline, whose profile is presented in Fig 10, are presented in Figs 11–13 This 350-mm-diameter transmission main has a pump station, and the filling process occurs in two steps In the first step, the initial 4.4-km extension line is filled by gravity, throttling the upstream butterfly valve so that the inflow rate is limited to Qà ¼ 0.18 In the second step, pumps are turned on and the remaining 2.8 km of the pipeline is filled The analysis presented in this paper focuses on simulation of the initial 1,700 m of the gravity filling The air valves positioned at x ¼ 400 m correspond to a couple of 50-mm spherical shutter air release valves The actual discharge area of these valves was not measured and was calibrated in the numerical model so that the observed air pressure at the discharge point was approximately similar to the measurements The pipeline friction losses were calculated using the Manning equation, and the assumed value for the Manning roughness was n ¼ 0.011 and for the celerity was 100 m=s While the anticipated celerity is probably much larger, the adopted value is adequate considering that the modeling is not focusing on transient pressure issues but instead on pipeline filling Moreover, the larger celerity helped reduce the computational effort for the simulation In these simulations, continuity error for the air phase calculation were limited to 1% The work by Vasconcelos (2007) applied the TPA model that did not incorporate effects of air pressurization to simulate pipeline filling Fig 11 presents a comparison of the pressure head hydrograph measured downstream from the pump station (x ≈ 380 m), and the sample frequency was s The field measurement signals an increase in the pressure head at approximately 200 s into the simulation and attains a stable level At approximately t > 1,100 s, the pressure begins to steadily rise again and will arrive at m when t > 2,700 s The results obtained with the traditional TPA model indicate a small pressure rise (corresponding to the water depth) until approximately t ¼ 2,300 s, when the pressure rapidly climbs achieving levels over 7.5 m after t ¼ 3,500 s The results obtained with both the proposed models better approximate the field measurements Pressure begins to climb at t ¼ 500 s and will arrive at 8.0 m for t ¼ 2,900 s (Euler equation model) The UAPH model presents fairly good agreement too, but at t ¼ 1,700 s it begins to diverge from the solution obtained by the Euler equation and pressure will attain the 8.0 m only for t ¼ 3,500 s An analogous comparison, this time however focusing on the measured and predicted inflow rate admitted into the pipeline, is JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 931 J Hydraul Eng 2013.139:921-934 7 * * Q =0.245, dorif =0.125 * * Q =0.368, dorif =0.125 Q*=0.490, dorif*=0.125 Q*=0.245, dorif*=0.09375 Q*=0.368, dorif*=0.09375 hres*=hres/D Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved * * Q =0.490, dorif =0.09375 * * Q =0.245, dorif =0.0625 Q*=0.368, dorif*=0.0625 0 Q*=0.490, dorif*=0.0625 3 * t =t/(L/sqrt(gD)) Euler equation UAPH Exp rep Fig Measured and predicted pressures at the pipe crown for xà ¼ 0.39, dorif à < 0.5, and slope of 1% Fig 10 Pipeline profile used by Vasconcelos (2007) investigation presented in Fig 13 Flow measurements in the water main were performed with an electromagnetic flow meter, with a sampling frequency of The butterfly valve opening was gradual and took approximately The simulation performed with the traditional TPA model [presented in Vasconcelos (2007)] reproduced this gradual opening; the results presented in this paper have skipped this for simplicity, assuming the final opening right on the onset of simulation Flow measurement indicate an initial flow rate slightly above 40 L=s, which will start declining for t > 1,600 s, stabilizing in 29 L=s when t ¼ 2,700 s Assuming that the flow rate drop is caused by air pressurization (as in the case of the experiments performed in this study), there seems to be a slight inconsistency with the pressure measurements that indicate that pressure begins to climb when for t > 1,200 s The cause for this possible inconsistency is not determined The numerical predictions by the TPA model indicate that the flow rate drop will occur much later, whereas the proposed model indicates the flow rate drop occurring much sooner, as soon as air pressure begins to climb in the pipeline 932 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Fig 11 Field measurements and predicted heads at the upstream ventilation valve of the water main accurately predict the occurrence of flow regime transitions, pipefilling bores, interface breakdown, and interactions between flow features While the UAPH model presents itself as an alternative that has a much smaller computational effort, the results obtained with the model using the Euler equation better approached the field measurements Future versions of the proposed model frameworks will aim to improve its stability and reduce air phase continuity errors Moreover, future versions of this model will try to incorporate other mechanisms such as air pocket movement caused by drag and buoyancy forces Experimental results confirmed the importance that ventilation design has on the maximum pressures observed in a system A significant increase in the maximum pressure in the system along with a increase in the filling time was observed for the smallest ventilation orifices Experimental results established the relationship of stronger pipeline slopes with increased pipeline filling time Future developments for this problem should also address more complex pipeline geometries, including the formation of several air pockets at the same time and a wider range of boundary conditions anticipated in transmission mains Finally, as more insight is gained in the mechanisms for air pocket formation in closed conduits, these may be included in the formulation of numerical models for the pipeline filling flow problem Acknowledgments Fig 12 Field measurements and predicted heads at the downstream ventilation valve of the water main The authors thank the data provided by CAESB regarding the monitoring of the filling of the water main presented in this paper The support of Auburn University in conducting this research is also acknowledged Notation Fig 13 Field measurements and flow rates at the upstream ventilation valve of the water main Conclusions This paper presented two model framework alternatives for the simulation of the filling of a water main considering effects of air pressurization, together with experimental investigations on this problem using an experimental apparatus While different modeling alternatives to this or related problems have been proposed, some of the hypotheses used in these previous investigations may limit the applicability of these in cases when the filling is performed gradually and ventilation is limited Thus there is a need of a new formulation that considers these two constraints in the simulation In general, both numerical model alternatives were successful in capturing the general trend of the pressure head and flow rate variations for experimental and field data The model was also able to The following symbols are used in this paper: A = water flow cross sectional area; a = celerity the acoustic waves in the pressurized flow; Aair = air flow cross-sectional area ðπ=4ÞD2 − A; Aorif = orifice area; Cd = discharge coefficient, which is assumed as Cd ¼ 0.65; D = pipeline diameter; dorif = ventilation orifice diameter; dà = normalized ventilation diameter dorif =D; FðUÞ = vector with the flux of conserved variables; f = friction head loss in the short pipe portion inside the boundary condition right after the inlet; g = acceleration of gravity; hair = extra head due to entrapped air pocket pressurization; hc = distance between the free surface and the centroid of the flow cross section (limited to D=2); Hres = reservoir water level; hs = surcharge head; K eq = overall local loss coefficient in the inlet; Mair = mass of air within the pocket; M air out = air mass that escapes through the ventilation orifice; n = time step index; Pa = water flow wet perimeter; Q = water flow rate; Qin = water flow rate that enters the upstream end of the pipe; Qrec = water flow rate that is admitted into the reservoir from the recirculation system; pffiffiffiffiffiffiffiffi Qà = normalized flow rate Q= gD5 ; S = vector of source terms; Sdisp;i = source term that accounts for air displacement; JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013 / 933 J Hydraul Eng 2013.139:921-934 Downloaded from ascelibrary.org by Auburn University on 08/19/13 Copyright ASCE For personal use only; all rights reserved Sf = source term that accounts for shear stress between air and pipe walls; S1 = source term for a continuity equation; S2 = source term for a momentum equation; U = vector of the conserved variables; Uˇ = vector conserved variables prior to air displacement correction; u = flow velocity; V p = air pocket volume; wdepth = local water depth; α = celerity of the acoustic waves in the air; θ = angle formed by free surface flow width and the pipe centerline; ρ = specific mass of air; and ϕ = correction 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