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F4) A numerical approach to investigate solid transport characteristics in waste water drainage systems A.Öngören (1), B. Meier (2) (1) abdullah.oengoeren@geberit.com (2) boris.meier@geberit.com (1)(2) Geberit International AG, Technology Department, Basic Sanitary Technologies, Switzerland Abstract The accurate prediction of solid transport characteristics of wastewater drainage systems is an important issue of sanitary and construction field. Both geometrical constraints and material properties of solid body should be considered as influence parameters in the predictions for an accurate result. The solid transport in wastewater drainage systems has been thoroughly investigated experimentally in the literature and several semi-empirical prediction methods have been developed based on the collected data. These methods have been proved to be successful and have been used widely in the field to clarify some standard solid transport issues containing not too many complexities. The development of fluid dynamic simulation techniques in the past decade allows now making predictions of much complex geometries without any significant compromise in the geometry definition.

In this study, solid transport characteristics in several wastewater systems composed of different flushing devices and piping configurations is attempted to be predicted by means of a computational fluid dynamics method. Special attention is devoted to the study of dynamic coupling arising from fluid-solid body interaction and the examination of the mechanisms caused by such interactions in this modelling. The effects of including multiple solid bodies in the piping, the configuration of their distribution and the piping gradient on the transport characteristics are systematically investigated.

Keywords Wastewater drainage; Solid transport; CFD simulation. 1 Introduction The effectiveness of solid transport is one of the deciding parameters to be considered in designing wastewater drainage systems. Not only the geometrical constraints but also

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the material properties of solid body determine the effectiveness of a designed system. Furthermore, the transient behaviour of the flushing flow at the enterence of the main piping has a strong influence on the solid transport. The initial lift-off of the solid body from the pipe surface is prescribed by this unsteady flow action impinging upon the solid body. The unsteady nature of the entry flow and its influence on drainage system characteristics during a flushing action have been examined by a number of investigators in the literature. However, it is necessary here to mention the pioneer work of Wylie and Eaton [1] and Wylie [2] where the authors give exclusive information about the hydraulic capacities of drainage systems. A broad survey of the these studies and a thorough discussion of the recent developments in the field are given by Swaffield and Galowin in [3] and by Swaffield and Wise in [4]. Based on the information in the previous works these authors give a precise description of the flow mechanisms appearing under the unsteady conditions of wastewater discharge conduits. Furthermore, they provide a complete collection of parameters on which such flows may depend. Such knowledge is important because a comprehensive understanding of unsteady drainage flow mechnanisms is necessary in order to develop a method which can be utilised for the prediction of solid transport characteristics.

Although these issues have been investigated mostly experimentally in the literature, several semi-empirical prediction methods have also been developed based on the data collected in order to provide a basis for the design guidelines. By using the method of characteristics, Swaffield et al. [5,6] and Swaffield and Maxwell-Standing [7] have been able to develop a semi-emprical numerical method which can predict many features of unsteady flow behaviour quite accurately. These methods have been proved to be successful although they inherit a major drawback by requiring a significant simplification of the geometrical complexities which exist in actual systems. They are still used widely to predict and clarify drainage flow related problems.

The numerical prediction methods utilising the method of characteristics approach have been later modified to predict the solid transport characteristics in wastewater drainage systems. Swaffield et al. [8] have carried out extensive studies with the program they developed to explain the effects of drainage flow rate, slope of piping and drainage piping entry conditions on the solid transport phenomena. The authors utilise the data of Swaffield and Wakelin [9], Swaffield and Marriott [10] and Swaffield and Bokor [11] in developing the emprical relations required in their program for the influence parameters mentioned above.

The progress in the computer technology and fluid dynamic simulation (CFD) techniques in the past few decades allows now to predict the flow characteristics of much complex geometries without significant compromise in the geometrical definitions and in the description of the of boundary conditions. Although the use of CFD techniques is a common practice in other fields of engineering today, it is rarely used in sanitary equipment and wastewater applications. Only recently several studies including CFD flow simulations have been published by Öngören and Materna [12, 13] and by Chang et al. [14]. Öngören and Materna have presented flow simulation results on various wastewater drainage piping configurations in [12]. The same authors have examined the multi-phase flow mechanisms in a rainwater drainage system by means of CFD simulations in [13]. Chang et al. present simulations of air-water fluid patterns occurring during the discharge of water in a ventilated gravity drainage system in [14].

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Although the CFD studies mentioned above delivers valuable results concerning the unsteady wastewater flows, they do not yet consider the dynamics of solid transport as coupled to these flows. In this study, a modified form of computational fluid dynamics technique is used in order to simulate the solid transport characteristics in several wastewater systems composed of different flushing devices and piping configurations. The simulations are carried out using solid bodies resembling a typical wastewater content which are fully coupled with the flow in the piping. The effects of solid body volume and piping gradient on the flow and transport behaviour are attempted to be systematically investigated. An evaluation of the validity of the present approach to carry out such work is the primary concern of this study.

2 Computational Fluid Dynamics Approach in Wastewater Drainage 2.1 CFD application for wastewater flows

A commercial general purpose computational fluid dynamics (CFD) program is used in this study to carry out simulations of wastewater drainage flow. The program principally solves the equations of motion for fluids, the so called Navier-Stokes equations, to obtain transient, three-dimensional solutions to multi-scale, multi-physics problem of wastewater drainage. The turbulent and unsteady nature of drainage flow is considered in the set-up of simulations by including the corresponding physical and numerical models in the calculation process. In addition, the multi-phase characteristics of the wastewater in the partially filled drainage system containing a large amount of air in the piping are taken into consideration by modelling the fluid motion as a free surface flow. A special technique developed to model the discontinuities of density, velocity and pressure at the water surface is used here to achieve an accurate calculation of free surface dynamics. The volume of fluid (VOF) method consisting of defining the volume of fluid function, a method to solve the resulting VOF transport equation and setting the boundary conditions at the free surface is employed for this purpose.

A numerical solution of the governing equations, resulting from the combination of all the physical models considered, involves approximating various terms with algebraic expressions and transferring the system of equations to a linear domain. The resulting equations are then solved to yield an approximate solution to the original problem. Detailed information about the formulation and the solution procedure of the technique used in this study is provided in reference 15.

2.2 Discretization of the test domain

The piping system is discretisized into a computational mesh which transfers the non-linear flow problem into a linear computational domain. A part of the discretisized domain is shown in Figure 1 to display the typical properties of a simulation grid. The mesh of the drainage piping used in this study consists of about 230´000 to 650´000 structured rectangular cells depending on the geometry of the simulated case. It should be noted that any valid numerical approximation approaches the original equations as the grid size is reduced. By carrying out several test runs with different grid sizes, it has

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been made sure that the computational domain is resolved by enough number of cells guarantying an accurate simulation.

Figure 1 – A sketch illustrating a part of the discretisized simulation domain. 2.3 Solid transport model The solid bodies drifting and floating in water in the drainage piping are modelled as general moving objects (GMO) which are dynamically coupled with the flow. In such a case both the moving object and fluid motion physically affect each other. The governing flow equations to be solved have to be modified in order to account for the physical changes caused by the body motion in the flow. A transient calculation procedure is required to correct the volume of fluid for the portion occupied by the moving body at each time step. An overall view of the transport phenomena as considered in this study is illustrated in Figure 2a. The moving solid bodies are assumed to possess six degrees of freedom (DOF), three translational and three rotational. The motion of the body can then be described by a system of six velocity components each corresponding to one degree of freedom of the body. All six velocity components are coupled with fluid flow. If there is any, the external forces and torques exerted on the body can be considered in the calculations. The external forces and torques are applied to the body’s mass center and about the mass center, respectively. The hydraulic, gravitational and non-inertial forces and torques are calculated automatically by the CFD program itself.

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Figure 2 – Sketches illustrating (a) a general view of a solid body in a drainage pipe; (b) solid body as a six DOF system and (c) forces acting on the surface of simulated body. A sketch of a body moving in a six DOF system is illustrated in Figure 2(b). Multiple moving objects with independent motion possibilities can exist simultaneously in each simulation. Moreover, the program allows the solid bodies to collide with each other or with the boundary walls freely. The collisions can be perfectly elastic, partially elastic or completely plastic depending on the value of restitution coefficient assumed for the bodies. The program considers the friction between the colliding bodies as well by defining a Coulomb’s friction coefficient. The program tracks and displays the spatial position of each solid body in time. Additionally, it calculates the mass center velocity, angular velocity in the body system, the resultant hydraulic force and torque and the combined kinetic energy of the translation and rotational motion and lists them as an output. 3 Description of Simulated Drainage System and Flow Conditions 3.1 Piping geometry A detailed view of the wastewater drainage piping used as the test object in this study is shown in Figure 3. The piping is composed of a 30 cm horizontal entry pipe and a 50 cm vertical downpipe. At the downstream of the downpipe the 5 m long main pipe is located. Three standard elbows connect the pipe pieces with each other. A special precaution has not been given to the selection of the elbow geometry because it is assumed that it has a minimal effect on the flow characteristics when the piping is only partially filled as in the case of this study. All piping is made of dimension DN100 polyethylene piping considering that this size is one of the most used dimensions for inside building drainage applications.

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Figure 3 – Sketch illustrating the simulated wastewater drainage piping In order to enable a comprehensive and fast parametrical study, the appliance is not directly contained in the simulations. Instead, an appropriate boundary condition is defined and applied at the appliance entry which accounts for all relevant effects stemming from the use of such equipment. The main pipe is adjusted to the gradients, 0, 1/100 and 1/20 during the simulations in order to investigate the pipe slope on solid transport. A cylindrical object having a diameter of 3 cm and measuring 10 cm long is used as solid body to represent the household waste. The solid body material is defined slightly denser than water as ρs=1.01ρw where ρs and ρw are solid and water densities, respectively. With this definition the solid objects can behave as both sliding bodies on the wall and floating bodies on the water surface. Up to three identical solid objects are placed at the entrance of the main pipe, either serially aligned along the bottom line of the main pipe or parallel to each at the same longitudinal location at the entrance of the main pipe. In all cases the bodies are assumed to be stationary at the beginning of the simulation. The bodies can collide with each other and with the pipe walls elastically by having a coefficient of restitution 1 but they loose energy through a mechanical friction process added by implementing a friction factor of fm=0.2 for the collisions. 3.2 Boundary conditions for the simulations The appliance is not directly contained in the simulations as mentioned in the previous section above. However, the deficiency arising from this negligence is compensated by applying the measured transient flow characteristics at the inlet of the piping. Two different types of transient boundary conditions are used in the simulations. In the first case, a quasi-transient flow rate is applied at the inlet boundary where the flushing water rate increases linearly from 0 to Qmax=2.5 lt/s in 0.5 second. In the following 2 seconds, the flow remains at a constant level of Q=2.5lt/s. During the following 1 second the

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flushing is reduced again linearly to zero level. A total of 6 lt water is flushed out during this process. The curve corresponding to this boundary condition is given in Figure 4.

Figure 4 – Quasi-transient flow rate applied at the inlet boundary The second type of boundary condition replicates the actual flushing of a typical cistern. Here, the transient flow is initiated by a steep increase in the flow rate and reaches to its maximum in a period less than 0.5 second. Thereafter, the flow rate decreases slowly but gradually for the next 4.5 seconds during the main flushing period. The flow rate reduces to zero level during the last 2 seconds of flushing. These features are displayed in Figure 5 which corresponds to the flow rate curve of a cistern measured on a real

Figure 5 – Transient flow rate representing an actual 6 lt flushing applied at the inlet boundary. appliance. These features may vary slightly for different appliances however it has been proved thoroughly during the course of this study that such differences does not effect the occurrence of the flow mechanisms discussed in this study. 4 Results 4.1 Basic flow mechanisms in a drainage pipe during a typical flushing action The transient characteristics of the flow in the drainage pipe without the solid waste for a 6 liter flushing is shown in Figure 6. Here the pipe gradient is 1/100. As observed in this figure, the flow reaches to the observation location first around 1.2 seconds. After

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the appearance of the flow tongue in this cross-section, the flow rises rapidly to a maximum depth in a time less than 1 second indicating that a relatively thick water front has been build up just at the downstream of the main pipe entry. This initial flow build up is particularly important to start an effective solid transport in the vicinity of waste objects. The flow becomes thinner at the observation location thereafter, even the peak period of flushing still continues. The filling ratio of the pipe is relatively low as

Figure 6 – Time variation of the flow profile across the main pipe having a slope of 1/100 at a location 0.5m away from main pipe entry. observed in the pictures of Figure 6. It is less than 25% of the pipe cross-section. This is due to the oversize of DN100 pipe for a single 6 liter flushing. The low water level is expected to impose harder flow conditions for the solid transport.

Figure 7 – Time variation of the flow profile across the main pipe having a slope of 1/20 at a location 0.5m away from main pipe entry.

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The flow behaviour in a drainage piping possessing a slope of 1/20 is displayed in Figure 7. Similar flow mechanisms are observed as compared to the previous case however the time required for the build up of the water front at the observation location seems to be slightly less. Moreover, the time period in which the water front forms is longer in this case meaning that it allows the development of a larger wave occupying a spatially larger volume in the pipe. These features suggest that a better solid transport characteristic can be achieved with this piping geometry. 4.2 Single solid body motion in a drainage pipe during a typical 6 liter flushing A series of pictures given in Figure 8 depicts some of the dominating characteristics of solid body motion in the drainage piping examined in this study. The solid body observed in the pictures is initially located downstream of the elbow on the inlet side of the main pipe. The body is considered to be at rest on the pipe bottom at the beginning of the simulation. As the water reaches and impinges upon the body, it is immediately

Figure 8 – The various dynamical mechanisms of solid body motion during a flushing action in a piping with a zero slope. lifted off the pipe bottom and starts to drift in the pipe inside the water front (Figure 8a). During the early period of flushing, it remains contained in the water front and it is drifted with about the same velocity as its surrounding (Figure 8b). In later periods of the flushing the body moves energetically, switching between drifting and floating motions. Such switching behaviour can be attributed partly to the touching of the body with the pipe bottom which causes a sudden stop of the body and starts a turning motion (Figure 8c) and partly to the strong coupling of the body with the highly turbulent flow behind the elbow. During this period of movement, the body is occasionally pushed out of the water surface as well (Figure 8d). After the settlement of turbulent activities, the body mainly floats in the water proceeding downstream. It should be noted that the thick water front is now distributed over a longer distance although it still possesses an appreciably larger depth on the front side (Figure 8e). The body sinks to the bottom gradually as the water level further decreases and the energy contained in the flow is distributed over a larger volume. The body may momentarily sit on the pipe bottom towards the end of this period which causes a local

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clogging and a raise in the flow depth so that the body is pushed forward again by the water accumulated behind it as seen in Figure 8f. 4.3 Multi-body motion in a drainage pipe during a typical 6 liter flushing In Figure 9, various dynamical mechanisms describing the motion of three identical solid bodies as they are flushed out in the examined drainage piping. The bodies interact both with each other and with the flow during this event. The bodies are placed initially 1.5 diameters away from each other and located just downstream of the elbow in-line with bottom line of the main pipe near the entry (Figure 9a). The bodies start drifting on the pipe bottom one after the other one following the impingement of the flow on the

Figure 9 – Various dynamical mechanisms of multi-solid body motion during a flushing action in a piping with a zero slope. first one located at the most upstream. The flow depth increases because of the clogging by the bodies which in turn help the bodies to lift off the pipe surface (Figure 9b). The bodies are then carried downstream as they float in the water front (Figure 9c). The bodies can move against each other by excessive turbulent activities in the pipe so that a

Figure 10 – The various dynamical mechanisms of multi-body motion during a flushing action in a piping with a zero slope.

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collision between them is highly possible. Such collisions cause often strong transient changes in the flow which can end up with local damming of water. In Figures 9d to 9f the spreading of the solid bodies as a result of these transient activities is observed. The bodies are also placed parallel to each other near the main pipe entry to create a severer degree of blockage for the flow. The positioning of the bodies having such a configuration is sketched in the caption of Figure 10. The main characteristics of body motion in cases of zero and 1/100 slopes are also summarised in the four pictures displayed in Figure 10. The main characteristics are observed to be similar to the previous case of in-line body distribution, however a stronger clogging of the flow is observed in the vicinity of both slopes for this type of initial body distribution. Moreover, the clogging-damming events occur more often in these cases. A comparison of the pictures of figures 9 and 10 indicates that the flow becomes more turbulent in the latter cases because of higher body-body body-flow interactions. Conclusions This paper investigates the applicability of a commercially available computational method (CFD) in predicting the solid transport characteristics in wastewater drainage systems. A detailed description of the method as applied in this study is provided and the results are discussed. The technique used is proved to be very successful especially in capturing the transient behaviour of solid body dynamics. The method is efficient and accurate in predicting the coupled motion of the solid bodies with the flow. It is possible to carry out simulations of the solid transport phenomena with multiple bodies. The results indicate all the dominant features of the flow and the solid body dynamics. References [1] Wylie RS and Eaton HN – Capacities of stacks in sanitary drainage systems for buildings, US Department of Commerce, National Bureau of Standards, Monograph 31, Washington D.C., July 1961 [2] Wylie RS – Investigation of the hydraulics of horizontal drains in plumbing systems, US Department of Commerce, National Bureau of Standards, Monograph 86, Washington D.C., Dec. 1964 [3] Swaffield, J.A. and Galowin, L.S., The engineering design of building drainage systems, Ashgate Publishing, Hampshire, UK, 1992. [4] Swaffield JA and Wise AFE – Water, Sanitary and Waste Services for Buildings, Fifth Ed., Butterworth-Heinemann Ltd, London, UK, 2002. [5] Swaffield JA, Bridge S and Galowin LS – Wave attenuation in long drainage pipes, a numerical solution to the unsteady partially filled pipe flow equations, Drainage and Water Supply Seminar, CIB W062, Sept. 21-Sept 23, Berlin, Germany, 1981. [6] Swaffield JA, Bridge S and Galowin LS – Numerical analysis of wave attenuation in building drainage systems, Water Supply and Drainage Meeting, CIB W062, Aug 31-Sept 3, Zürich, Switzerland, 1982. [7] Swaffield JA and Maxwell-Standing K – Improvements in the application of the numerical method of characteristics to predict attenuation in unsteady partially filled pipeflow, Journal of Research, NBS, Vol. 91 No. 3, May-June 1986

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[8] Swaffield JA, Goulding RW and Crerar SA – Solid transport interaction in partially filled pipeflow, Water Supply and Drainage for Buildings, CIB W062, Sept. 12-14, Edinburg, UK, 1988. [9] Swaffield JA and Wakelin RHM – An analysis of the transport of waste solids in internal drainage systems, Seminar Drainage and Water Supply for Buildings, CIB W062, Mai 24-25, Oslo, Norway, 1977. [10] Swaffield JA and Marriott BST – An investigation of the effect of reduced volume w.c. flush on the transport of solids in above ground discharge systems, Seminar Water Supply and Drainage for Buildings, CIB W062, Oct. 10-11, Glasgow, UK, 1978. [11] Swaffield JA and Bokor SD – Application of laboratory test techniques to building drainage design, Drainage and Water Supply for Buildings Seminar, CIB W062, June 3-4, Middlesex, UK, 1980. [12] Öngören A and Materna R – Investigation of the effect of swept entry configuration on the air entrainment and self-siphoning behaviour in gravity drainage systems, 31th Symposium of Water Supply and Drainage for Buildings, CIB W062, September 19-21, Brussels, Belgium, 2005. [13] Öngören A and Materna R – Multi-phase flow characteristics of a siphonic roof drainage system under part load conditions, 32nd Symposium of Water Supply and Drainage for Buildings, CIB W062, Sept. 18-20, Taipei, Taiwan, 2006. [14] Chang W.R., Cheng C.L. and Wang J.T. – Simulation of multi-physics flow patterns in a single-drainpipe of gravity drainage systems -A preliminary CFD study, 32nd Int. Symp. on Water Supply and Drainage for Buildings, CIB W062, Sept 18-20, Taipei, Taiwan, 2006. [15] Flow-3D User Manual, Chapter 3 - Theory, Flow Science Inc., Santa Fe, USA, 2005. 5 Presentation of Authors Dr. Abdullah Öngören is the head of Basic Sanitary Technologies Department at Geberit International A.G. (Switzerland), where he is widely involved in research and development of sanitary products, and rain and waste water drainage systems. He is specialized in flow induced vibration and noise and CFD applications in sanitary equipment and systems. Boris Meier works at Basic Sanitary Technologies Department of Geberit International A.G (Switzerland). His main focuses are simulation and optimization of sanitary products using CAE (CFD and FEM) methods. He is involved in a wide range of structure mechanical analysis of sanitary products and systems using computational methods.