Modelling of saline intrusion in a long sea outfall with two risers N.R. Shannon, P.A. Mackinnon & G.A. Hamill School of Civil Engineering, The Queen's University of Belfast, United Kingdom Abstract The quality of coastal waters is affected to a large degree by the dilution and dispersion of wastewater discharged through marine outfalls. Under intermittent or low flows, normal operation of these outfalls is often idubited by the occurrence of stratified flow and saline intrusion, a phenomenon which results in partial blockage of the system. Having established the validity of a numerical model to predict the main features of stratified flow in an outfall of simple geometry under laminar conditions, further tests were designed to prove its performance under more onerous conditions. The development, results and conclusions from these tests are reported in the current paper. Numerical and experimental tests were carried out using a scale model outfall discharging freshwater into ambient saline water. The tests used two risers in order to generate saline intrusion, where multi-port diffusers are persistently ingressed by saline water. The stratified flow within the long sea outfall was modelled in two dimensions under turbulent conditions, utilising a species model with two fluids (or species) physically interacting on a molecular level. The numerical data provided quantitative evidence of the fundamental mechanisms that take place when saline water enters the outfall diffuser. The comparisons of numerical and experimental results verified the capability of the numerical model to reproduce the main hydrodynamic processes that give rise to saline intrusion but also highlighted discrepancies in the more detailed aspects of the fluid behaviour.
1 Introduction 1.1 Saline intrusion in sea outfalls Submerged outfalls are widely used to discharge domestic and industrial wastewater to sea. These sea outfalls are designed to gve maximum dilution to the effluent as it leaves the outfall pipe. Thls is achieved by the use of a 'diffuser' section which, in its simplest form, incorporates of a series of vertical 'risers' placed in sequence to form a manifold. Wen pumping commences, the effluent moves along the outfall pipe soffit forming a saline wedge at the invert due to the buoyant nature of the effluent, which is primarily freshwater. Changes in pressure due to this buoyant discharge from the risers, along with interfacial entrainment, mean saline intrusion may also occur. This is where seawater is drawn into the seaward risers, mixes with the effluent as a result of turbulence, and is discharged through the central risers, as illustrated in Figure 1. The development of saline intrusion depends on various factors, including the geometric configuration of the outfall, the physical characteristics of the effluent and the receiving water, and the discharge pattern. The presence of a saline wedge in a sea outfall pipe or riser may greatly reduce the operating efficiency, as parts of the pipeline are effectively blocked, or reduced in cross-section. Once established, a salinc wedge is often difficult to displace, a process known as 'purging'. 1.2 Numerical modelling of saline intrusion When the first outfall diffusers were used in the 1950's to improve dilution and dispersion of effluent, the ensuing research related only to the initial dilution Diffuser section - Sea level 0 - --- --- -.Mixing and entrainment 7/ Saline wedge Figure 1 : Typical long sea outfall with saline intrusion /
of this effluent and the complex internal hydraulics were not considered. It was not until the 1970's that the problems relating to saline intrusion were effectively identified. Since then, further laboratory and field investigations have been carried out to predict the occurrence and extent of saline intrusion in long sea outfalls. With the increased availability of computers and the ability to investigate in greater detail using complex computational analysis techniques, a second approach was introduced and numerical models were developed. The first outfall model, whch was produced by Mort [l] and amended by Larsen and Burrows [2], was a one-dimensional numerical model which included the two fluids with different densities. Th~s numerical model was later enhanced by Guo and Sharp [3] by adding localised two-dimensional areas to improve the modelling of the fluid interaction and effects of buoyancy. However, the authors felt that the modelling of entrainment and mixing between the fluids was not adequate. Further improvements in computer resources and advances in numerical analysis have resulted in the development of new modelling techniques. Recent developments in numerical modelling have greatly increased the capability of the engineer to simulate complex hydraulic processes. Some of the latest techruques have the potential to produce a numerical model which is capable of predicting the complex flows and saline intrusion in marine outfalls. 2 Summary of previous work 2.1 Physical modelling Previous studies by Mackinnon et a1 [4,5] involved the development a model testing facility using a simphfied model outfall. The diffuser section of the outfall was constructed from a l lomm by l lomm square perspex duct whtch had four vertical risers, each one square in section with internal dimensions 50mm by 50mm. These risers were spaced at 450mm centres, and extended 350mm vertically from the diffuser centreline. For the tests in this document, the two outermost risers were sealed. The facilities available to perform tests comprised a saltwater flume, 19.5m long and u.75m wide, with a rectangular cross section. The maximum depth of water in the flume was 0.7m, giving a depth of water over the diffuser ports between 200mm and 270mm. During the experiments, velocity, density and pressure were used to quantify the flow characteristics. A Laser Doppler Anemometry (LDA) system used for velocity measurement. The square pipe section was chosen to overcome potential difficulties with the refraction of the beams. Twin wire probes were used in order to measure conductivity and establish the density at various locations inside the model. Pressure measurements were carried out using transducers fitted at selected positions withn the model.
302 Computational Methods in Multiphase Flo~, 2.2 Numerical modelling with laminar flow The preliminary numerical modelling involved the development of a twodimensional model using a commercially available software package. The package used the finite element method to solve the computational domain and included the capability of modelling the effects of buoyancy and multiple fluids, however, the model assumed laminar conditions. The same software was used in the current study, with the inclusion of turbulence. The details of these capabilities are discussed in more detail in section 4. 2.3 Limitations The results obtained using a laminar two-dimensional model of saline intrusion in a marine outfall with two risers showed moderate correlation with the general flow patterns observed in corresponding experimental tests. However, observations of turbulence within the flow indicated that some form of turbulence modelling was required if the flow was to be reproduced in its true form. 3 The model context 3.1 Computational Fluid Mechanics The use of Computational Fluid Dynamics (CFD) enables the governing equations of fluid flow in the outfall to be approximated when the flow field cannot be solved analytically. The first step in production of a numerical model of the outfall was defining the geometry of the outfall and receiving water body, known as the computational domain, as illustrated in Figure 2. The computational domain was then sub-divided into smaller units known as elements or control volumes to form a mesh. The preliminary mesh file was then imported into the software solution package. Part of this structured mesh was then refined resulting in an unstructured mesh of higher resolution in the dlfiser manifold and main outfall pipe regions. The algorithms used to solve the governing equations and to link elements are more complex in unstructured mesh simulations, however fewer elements are required in refining the mesh. This results in detailed information in the areas required, whle maintaining computational efficiency. 3.2 Boundary conditions The next stage in model cimaopment was the definition of the boundary conditions. In order to define these boundaries, the flow parameters for cells that were adjacent to them required special attention. The flow parameters within these cells were prescribed in order to simulate specific flow conditions. The boundary conditions used in the long sea outfall simulation were chosen to replicate those found in the physical model. The limits of the expanse of the
Conzputatioual Methods iil Multiphase Flow* 303 4 Extent of receiving water body F Manifold difiser section rc- - \ Water surface Figure 2: Computational domain of outfall model saline receiving water were modelled as 'hydrostatic pressure outlets' which, despite the name, allowed flow both in and out of the domain. These outlets were placed sufficiently far from the outfall diffuser manifold to have negligible effect on the discharge and the receiving water was therefore modelled as a continuum. The water surface was modelled using a 'symmetrical' boundary which gives zero flux of all parameters across it. The pipe walls and tank floor were replicated using wall shear factors, computed within the model using a specified surface roughness of 0.001mm to represent perspex. The inlet to the diffuser was described as a 'velocity inlet' with a freshwater velocity of 0.0165 mls in the X-direction. The turbulence characteristics were also defined as part of the velocity inlet boundary condition. These are discussed in Section 4.2. 3.3 Physical characteristics of the fluids The final stage of the pre-processing was to define the physical characteristics. In the long sea outfall, the physical parameters related mainly to the two fluids used in the simulation. The fluids were defined as a 'mixture set' of freshwater and saltwater with densities of 1003 kg/m3 and 101 8 kg/m3, and molecular weights of 18.0 and 19.6 kgkg m01 respectively. The molecular weight of the saltwater was an estimate as there is no true saltwater molecule. Both freshwater and saline water were defined as having a dynamic viscosity of 1.1 X 10" ~.s/m~. 4 The numerical modelling of fluid characteristics When the CFD problem had been fully defined, the solver was used to evaluate the unknown flow parameters. Integration was carried out for each cell using the truncated Taylor series to approximate flow processes such as convection and diffusion. The resulting finite difference equations were substituted into the
governing equations, which were then solved iteratively. Tlus was done in three steps: approximation of the unknown flow parameters; substitution of these approximations into the governing fluid flow equations to generate dlscrete algebraic equations; and, finally, solution of the algebraic equations. 4.1 Species modelling The long sea outfall was modelled using the species model with the two fluids (or species) specified as non-reacting. This method was found to provide the most accurate flow simulation. The software (FLUENT [6]) modelled the multifluid flow by introducing a further conservation equation, the conservation of species equation. This results in the formation of a set of governing equations for each fluid species with each element. These equations contain an additional term which specifies the fraction, by mass, of the species occupying the element to which the equation relates. The sum of the mass fractions for each cell is equal to unity. The mixing of the fluids was defined by additional terms in the transport equations. These terms are the diffusive mass flux due to convection and diffusion for laminar and turbulent condltions. These terms are given by eqns (1) and (2) for laminar and turbulent flux respectively. dm J,, =-pd,-. dx where P species density DI user defined laminar diffusion coefficient D, turbulent diffusion coefficient defined using the turbulent Schmidt number m mass fraction of species X distance CLt turbulence intensity Sc, turbulent Schmidt number The turbulent Schmidt number is defined by eqn (3). This value remained constant at 0.7. P D, Sc, =-. (3) P t
4.2 Turbulence modelling Specification of the flow characteristics was also required and this included the definition of turbulence. The two parameters used to describe turbulence were characteristic length and turbulent eddy intensity. The turbulent eddies were limited to the dimensions of the outfall pipe so 0. l lm was initially used as the characteristic length. The turbulence intensity parameter, p,, was found using experimental measurements w ith the main outfall pipe and eqn (4). where - U average velocity 1 typical dimension v kinematic viscosity The k-e model was used to model turbulence within the numerical model. The basis of this model is that kinetic energy, k, is decomposed into mean and turbulent kinetic energy. Likewise the deformation rate, e, of the fluid element is also decomposed. Applying this to the Reynolds momentum equations, two governing equations can be found which relate to the mean and fluctuating turbulent kinetic energy. The general form of the k-e model equations is given below Rate of + Transport = Transport of + Rate of - Rate of change of of k or E by k or E by production dissipation k or E convection turbulent of k or E by ofkor~ difhsion mean flow The k-e model equations rely on a relationship between kinematic turbulent viscosity, v', and eddy length scale, L,, devised by Prandtl and Kolmogorov, where the kinetic energy acts as a velocity scale. 5 Results In order to enable the validation of the numerical results it was necessary to compare them with the results of the experimental programme. The following section describes flow characteristics observed visually. The recorded data are superimposed on the results presented from the numerical model. 5.1 Experimental flow conditions Observation of discharge showed that a saline wedge formed within the outfall pipe when the flow commenced. The freshwater discharge occupied the top third
306 Cornputatiotzal Methods irl Multiphase Flow of the outfall pipe and reached the first of the two risers after one and a half minutes. The freshwater also progressed further along the outfall to the second (seaward) riser, again occupying the top third of the pipe. The freshwater reached approximately one third of the distance up the seaward riser before being forced back by secondary intrusion. The discharge from the landward riser remained segregated close to the base of the riser, with freshwater discharged from approximately two thirds of the cross-section on the landward side, and the intruded seawater being discharged on the seaward side. The two fluids became mixed towards the riser port. Once the saline wedge was formed, it remained static and was not eroded by the turbulent mixing visible at the interface of the fluids. This was the case in both the outfall and the riser. The saline wedge extended into the opaque pipe at a distance of lm from the landward riser. 5.2 Numerical results Due to the brief nature of this paper the results are presented at one time during the simulation period. After 960 seconds the numerical model had reached a reasonably steady state. Figure 3 illustrates the velocity profiles at this time. The cross-sectional velocity profiles in the risers of both models display the onset of saline intrusion. This is characterised by a discharge from the first riser, shown by a positive velocity, and intrusion in the second riser shown by the negative velocity in the second riser. The scale of the intrusions are similar in both models. Extent of saline wedge physical numerical Saline intrusion / Even iistribution Increased at invert -0 06-0.03 0 0.03 0 06 0 09-0 06-0 03 0 0.03 0.06 0.09 Figure 3: Velocity profiles at cross-sections after 960 seconds
Computational Methods in Multiphase Flow 307 By considering the main outfall pipe cross-sections, the size of the saline wedge and the form of the intruded flow can be examined. The profile measured in the physical model showed a wider saline wedge, with a narrower section of positive flow of greater velocity magnitude at the pipe soffit where the freshwater was concentrated. There was also less circulation within the wedge region, characterised by the negative velocity in the pipe invert. In the second profile, the numerical model shows the intruded flow being drawn to the main pipe invert by the greater magnitude of velocity in this region. There is also evidence of internal circulation within the outfall pipe between the risers in the numerical model, a feature which is not clear in the physical model. The density contour plot for this time, Figure 4, shows that a saline wedge has clearly formed in the pipe invert of the numerical model, indicated by the white regions. The dark region at the outfall soffit portrays the buoyant freshwater flow. It can also be seen that saline i~?+melon is in progress. The fluid discharged from h~t: first riser in the numerical model is well mixed on exiting from the riser, illustrated by the shaded area. This mixing results in the fluid which is drawn into the second riser is also being mixed, creating a 'trapped' region which cannot spread further than between the risers. Observation of the physical model suggests that, counter to this, a discrete layer of freshwater formed on the water surface, allowing mixing further afield. This discrepancy may be due to the effect of the hydrostatic boundaries at the limit of the water expanse The saline intrusion of mixed fluid in the numerical model led to the fluid within the outfall becoming less saline which would eventually lead to purging, unlike the physical model, which remained intruded with saltwater, illustrated by the white square areas which are predominant in the second riser.............,... I.. a....... Freshwater flow Figure 4: Density contours after 960 seconds
6 Conclusions It may be concluded from the study of a CFD model of saline intrusion in an outfall with two operational risers under turbulent conditions that the general hydraulic mechanisms have been recreated. However, comparisons between experimental and numerical results hrghlight sigmficant dwcrepancies between the models. These relate to the amount of mixing between the two fluids both within the manifold and in the ambient receiving water. Further studies using altered boundary conditions and a more detailed study into the modelling of turbulence would be required before this model would be viable as a tool for outfall design engineers. Work on both these aspects is currently under way. Acknowledgements The authors wish to acknowledge the contribution of the Engineering Physical Sciences Research Council in prwiding sponsorship for tlus research. References [l] Mort, R.B., The effect of wave action on long sea outfalls, University of Liverpool PhD thesis, 1989. [2] Larsen, T., Burrows, R. & Engedahl, L., Unsteady flow and saline intrusion in long sea outfalls, Water Science & Technology, Vol. 25, No. 9, pp. 225-234, 1992. [3] Guo, Z. R. & Sharp, J., Numerical model for sea outfall hydraulics, Journal of Hydraulic Engineering, Vol. 122, No. 2, pp. 82-89, 1996. [4] Mackinnon P.A., Shannon N.R. & Hamill G.A., Evaluation of a Two- Dimensional Model of Saline Intrusion in an Outfall with Two Risers, Proceedings 4& International Conference on Hydromechanics, Yokohama, Japan, Volume 11, pp. 753-758, 2000. [5] Mackinnon, P.A., Shannon, N.R., Hamill, G.A., & Doyle, B.M., An experimental investigation of saline intrusion in a long sea outfall, Proceedings 3"' International Conference on Advances in Fluid Mechanics, Montreal, Canada, pp. 33-423, 2000. [6] FLUENT UNS 'User Manual for Version 4.3. ' Fluent Europe, 1996.