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Building Tomorrow’s SocietyB?tir la Société de DemainFredericton, CanadaJune 13 – June 16, 2018/ Juin 13 – Juin 16, 2018Experimental and Numerical Study of thermal buoyant offset jet Discharged into stagnant waterAlfaifi, Hassan1,2,3 and Mohammadian, Abdolmajid11 University of Ottawa, Canada2 King Abdulaziz City for Science and Technology (KACST), Saudi Arabia3 halfa103@uottawa.caAbstract: The aim of this paper is to study the behavior of the offset thermal jet in the mixing zone for the effluent of the industrial outfalls (e.g. desalination plants) on the near-field, experimentally and numerically. Several experiments of the thermal buoyant offset jet discharged horizontally into stagnant ambient water are conducted. The Particle Image Velocimetry (PIV) method is used to measure the time-history of the velocity distribution in the near-field mixing zone. The characteristics of the jet flow with different densimetric Froude numbers (Fd) compared with numerical results are presented in this study. Two different densimetric Froude numbers (Fd) (10 and 20) and difference density (Δρ) (5 and 10) are used. Three Reynolds-averaged Navier-Stokes (RANS) turbulence models; standard k-ε, realizable k-ε and buoyancy-modified k-ε models are applied in this study. The comparison between laboratory and numerical results for jet trajectory as well as with existing experimental and numerical data are presented. In general, a good agreement is observed between all numerical and experimental cases examined here, for both Froude numbers, where the realizable k-ε was shown to be the best among others.INTRODUCTION Cooling systems such as Multi-Stage Flash distillation system (MSF) of desalination plants produce hot water, known as reject water, which is discharged into the marine environment as a thermal buoyant jet, through a submerged outfall. Some parameters such as densimetric Froude number, pipe discharged diameter, density, and temperature can affect the jet behavior in order to achieve higher dilution, which is the main purpose of outfall facilities. Since most of hydraulic engineering practices happen in sensitive places of aquatic environment, investigation of the jet behavior and its impacts is essential. The outfall system is either made of diffusers with many ports or just one single pipe from which the effluent is discharged. The effluent can be denser or lighter than the receiving water. If the effluent density is less than the ambient water density, the jet behaves as a (positively) buoyant jet. This effluent may affect the surrounding water closer to the exit pipe by increasing the temperature. This might have another adverse impact on the marine ecosystem in the near-field area as well (Mabrook, 1994; Hashim and Hajjaj, 2005; Milione and Zeng, 2008; Lattemann and H?pner, 2008; Roberts et al., 2010). Therefore, it is important to study the characteristics of the near-field mixing zone to prevent any of adverse impacts caused by the outfall systems and to keep the marine environment clean and usable as a sustainable source of drinking water for future generations. A submerged outfall (offset, wall and inclined jets) is typically designed to achieve higher dilution for buoyant jets. An offset jet refers to a flow that is discharged above a horizontal solid wall offset with a certain distance which is parallel to the axis of the jet exit, as shown in Figure 1. Despite the fact that offset jets are currently in use worldwide, little research has been carried out on their properties. Therefore, more laboratory experiments are still required to study the near field flow and mixing characteristics of the thermal jets due to the complex nature of this phenomenon. Figure 1: An offset buoyant jet dischargedExperimental and numerical studies of negatively-buoyant jets have been conducted extensively (Bosanquet et al., 1961; Hoch and Jiji, 1981; Gu, 1996; Nasr and Lai, 1998; Kanna and Das, 2005; Shao and Law, 2009; Shao and Law, 2011; Agelin-Chaab and Tachie, 2011; Kheirkhah Gildeh et al, 2015a; Assoudi et al., 2015; Kheirkhah Gildeh et al, 2015b; Assoudi et al., 2016), while positive buoyant jets have been studied less and require further investigation. Some of these studies have been performed only using Particle Image Velocimetry system (PIV), or combined with planar Laser-Induced Fluorescence (LIF). Rawn and Palmer (1930) were pioneers in this field, where they made an experimental investigation of the diffusion of horizontal offset jets. Their study included 388 experimental observations of dilution at the surface for the offset jets of fresh water injected into sea water. Abraham (1963) studied jets injected horizontally into homogeneous denser ambient fluid, theoretically. Recently, Cuthbertson and Davies (2008) carried out a set of laboratory experiments to investigate the characteristic features of particle-laden, round, turbulent, buoyant jets discharged horizontally into stationary and coflowing receiving fluids using PIV system. Michas and Papanicolaou (2009) studied horizontal turbulent buoyant jets discharged in a homogeneous calm ambient fluid, experimentally. They evaluated the mixing characteristics such as trajectories, turbulence properties, and dilution factors. However, numerical simulations of buoyant offset jets still require further investigation. A numerical investigation has been carried out by Liu and Lam (2015) for round jet discharge horizontally with sediment particles. They applied Large Eddy Simulation (LES) for fluid phase comparison, while Lagrangian particle tracking was used to calculate the motion of sediment particles.This paper investigates the behaviors of the buoyant offset jets discharged into stagnant ambient water experimentally, using PIV system technique, and numerically. The numerical results of the centerline trajectory were compared with laboratory experimentsEXPERIMENTAL SETUP AND PROCEDURESIn this study, Particle image velocimetry (PIV) system was used to measure the time-history of the velocity distribution of the jet flow. The PIV system is an experimental technique in fluid mechanics which basically involves photographic recording of the motion of microscopic particles that follow the fluid. Image processing methods are then used to determine the particle motion, and hence the flow velocity, from the photographic recordings. PIV system has generally four main components; laser box, laser lens, high-speed CCD camera, and computer for synchronization between camera and lasers. Small tracer particles have to be added to the discharged flow to be able to follow the fluid paths.All experiments were conducted in a rectangular transparent glass tank with dimensions of 1.2 m length, 0.5 m width, and 0.5 m depth. Both the bottom and side walls of the tank were made of glass panels. Tap water was used for all experiments as an ambient water (tank water) with certain temperature (Ta) and density (ρa). A circular jet nozzle with an internal diameter (D) of 5.18 mm was attached horizontally to one end of the tank wall (at the center) with 10 cm distance from the bottom wall. The jet was parallel to and offset from the bottom of the tank. A buoyant jet with an initial velocity (U0), temperature (T0) and density (ρ0) was generated by discharging heated and fresh water into the tank through this nozzle. The nozzle was connected to a pipe that is equipped with valves to control the discharged water and a flow meter (rotameter) to determine the flow rate of the discharged water. The pipe was connected to a constant head tank with dimensions of 0.75 m length, 0.3 m width, and 0.3 m depth. This tank contained discharged water, which was located about 1.5 m above the discharged nozzle. The head tank had two separate storage tanks, one of which was used as a store for the surplus of the discharged water. The water was then returned from the store tank using a pump to make sure the water level was constant. To ensure that the water temperature in the pipe was equal to that of the heated water in the elevated tank, the pipe was covered and isolated by heat-insulating material. Also, there was another outlet located outside of the experimental tank with a distance of 10 cm upstream of the nozzle to check the temperature of the discharged water before running the experiments. Moreover, the nozzle outlet was equipped with a very thin sensor connected to a thermometer to check the flow temperature during the experiments. For brevity, only the results of three cases are shown in the table and figures.The same concept is applied in all experiments using hot water (low density) discharged into stationary water as a thermal buoyant offset jet. A summary of the experimental and numerical parameters, same parameter values were used in both, are given in Table 1.Table 1: Experimental and numerical parametersCaseD(mm)U0 (m/s)T0(°C)ρ0(kg/m3)Ta(°C)ρa(kg/m3)FdReΔρ15.180.1638.6992.7521.5997.891012225.125.180.2350.5988.0621.5997.8910.321629.835.180.4550.7987.7521.5997.8919.8424610.1NUMERICAL MODELOpenFOAM (OPEN Field Operation and Manipulation) CFD model with structured grid, was used to simulate the buoyant offset jet discharge in this study. OpenFOAM (a free and open-source package) is widely used for modelling and solving scientific problems, for example, positively and negatively buoyant jets (Kheirkhah Gildeh et al., 2015a and 2015b; Zhang et al., 2016). The model solves a set of Partial Differential Equations (PDEs) using the Finite Volume Method (FVM). The pisoFoam solver for incompressible fluid was developed to use in this study. Advection-diffusion equation for temperature was added to handle the transport and dispersion. Three different Reynolds-averaged Navier-Stokes (RANS) turbulence models were chosen to apply in this study due to their accuracy among other RANS turbulence models, as reported on the recent studies of Kheirkhah Gildeh et al. (2014, 2015a and 2015b). These models are; the standard k-ε, realizable k-ε and buoyancy-modified k-ε erning EquationsThe model uses three-dimensional RANS equations as the governing equations for incompressible fluids: Continuity Equations:[1]Momentum Equations:[2][3][4]where:[5]where , and are the components of the mean velocity in the , and direction, respectively, P is the fluid pressure, t is the time,is the modified gravity acceleration,is the acceleration of gravity, ρ is the fluid density, ρ0 is the effluent fluid density,is the effective kinematic viscosity of water (), andis the turbulent kinematic viscosity. The effect of the variable density (buoyancy) in the vertical direction (y-coordinate) is considered and added in Eq. (3). Temperature equation:[6]where:[7]where is the fluid temperature, is the heat transfer coefficient, is the Prandtl number, and is the turbulent Prandtl number. In this study, the and values are chosen to be 1.0 based on Kheirkhah Gildeh et al. (2015a). The details of the buoyancy-modified k-ε turbulence model are not described here for brevity, more details can be found in (Yan and Mohammadian, 2017). Boundary ConditionsThe boundary conditions for the buoyant offset jet discharged in a rectangular tank are discussed in this section. Figures 2 and 3 illustrate the schematic views of the numerical model with the coordinate systems and the domain dimensions, respectively.Figure 2: Schematic diagram of the computational domain with the coordinate systemsThe parameters used in the numerical model are similar to the ones in the experiments (see Table 1). The nozzle (outfall) boundary conditions are chosen based on Kheirkhah Gildeh et al. (2014), as , , , , . A zero-gradient boundary condition perpendicular to the outlet plane is defined for , and for the flow at the outlet boundary section. For the walls, boundary conditions defined as and no-slip condition was considered for this study. Thus, and are assumed to be standard wall function for the thermal buoyant jet. Finally, the symmetry boundary was modeled using zero gradient conditions. In the present study, only half of the buoyant offset jet domain is considered because of the symmetry nature of the problem. The dimensions of the computational domain (Figure 4) were chosen to simulate the present experiments. A refined mesh is considered in the near field area of the offset jet to better capture velocity and temperature characteristics for all simulations, as shown in Figure 3. (a) (b) Figure 3: a) The numerical model domain and boundary definition; b) fine grids mesh near the nozzle at the symmetry planeRESULTS AND DISCUSSIONSExperimental ObservationsWhen a horizontal offset buoyant jet discharged into a water body, the entrainment of the water affects the jet and causes a change in jet behavior. Within a short distance away from the nozzle exit, the jet flow is dominated by momentum force. Then, after a certain distance from the nozzle tip, the buoyancy force becomes larger and dominates the jet and enforces it to rise up to the water surface. The experiments in this paper were intended primarily to obtain some quantitative measurements of the trajectory behaviors of buoyant offset jets to be used for validation of the numerical simulations.In these experiments, development of the jet was recorded using a PIV system. Figure 4 shows three different jet flows of the average velocity superimposed on the velocity filed contours which extracted from PIV data for Fd 10, 10.3 and 19.9. As we can see from the figure, all jet behaves different when the initial velocity increased even if the temperature or Fd are almost the same. Although case 2 and 3 have the same temperature and almost same difference in density, but the Fd in cases 3 is higher, the jet deviates far away from the nozzle as a result of the effect of the Fd. It can be observed from the experiments that when the jet goes farther into the ambient water, the time to reach the surface is increased, thus the dilution may increase (Roberts and Toms (1987). Therefore, studying the parameters that can be more sensitive on the behave of the jet trajectory and then the near-field mixing characteristics are needed. The jet trajectory behaviors are discussed in detail in the following section.(a)(b)Figure 4: The average velocity overlying on the velocity filed contours extracted from PIV data: (a) u = 0.16 m/s, = 10, = 5.1; (b) u = 0.23 m/s, = 10.3, = 9.8; (c) u = 0.45 m/s, = 19.8, = 10.1Figure 5: Comparison of the centerline trajectory from PIV data for cases 1, 2 and 3(a)(b)(c)Figure 6: Numerical results of the centerline trajectory: (a) u = 0.16 m/s, =10, =5.1; (b) u = 0.23 m/s, =10.3, =9.8; (c) u = 0.45 m/s, =19.8, =10.1Jet Trajectory Jet trajectory is a very important parameter in outfall system design as it identifies the path that jet goes through and where it reaches the water surface. The final dilution at the end of near-field is also a function of the jet path and ambient water characteristics (e.g. water depth especially for positively buoyant jets). Jet trajectory can be determined when the jet enters into a region known as the buoyant region or the free jet region (Huai et al., 2010). The PIV measurements for the average velocity vectors of the jet trajectory for the experimental results of for all cases are shown in Figure 5. The figure shows clearly a different behavior in jet trajectory in all experiments where their parameters are different. Experimental and Numerical Comparison The experimental results were used to examine the capability of three different turbulence models, standard k-ε, realizable k-ε and buoyancy-modified k-ε, in the same conditions. The numerical results of the jet centerline trajectory for all models comparing with all experiments are shown in Figure 6. The results show that all numerical results of all models were in a good agreement with the case 3, especially the realizable k-ε model which was the best among others. Also, a good match was observed between the numerical results of realizable k-ε model and other cases (1 and 2). As mentioned, one can clearly see from the figures that a better prediction is obtained using realizable k-ε than standard k-ε and buoyancy-modified k-ε turbulence models. In addition, standard k-ε and buoyancy-modified k-ε models for case 3 show a good prediction than other cases where the Fd and turbulences are increased. Therefore, the numerical results of the realizable k-ε model are in a good agreement with present experimental studies.CONCLOSIONSThis paper presented the results of an experimental and numerical study of thermal buoyant offset jets discharged into stagnant water. The main objective of this study was to obtain experimental data to be used for comparison with the numerical model results. The OpenFOAM software with structured grid was used to simulate thermal buoyant offset jet discharged in stagnant water. Three RANS turbulence models, standard k-ε, realizable k-ε and buoyancy-modified k-ε were applied to predict the behavior of these jets. The numerical results of the realizable k-ε model showed that the jet trajectory was in a good agreement with all experiments. Moreover, a good general agreement of jet trajectories is observed between all numerical models and the experimental case 3 examined here. Finally, the obtained results from standard k-ε in this study, have shown a better prediction for jet trajectory compared to the buoyancy-modified k-ε turbulence model. More investigation for the buoyant offset jet with different higher Froude numbers and various numerical models is currently in progress by the authors.AcknowledgementsHassan Alfaifi would like to thank King Abdulaziz City for Science and Technology (KACST) for their financial support.ReferencesAbraham, G. 1963. Jet Diffusion in Stagnant Ambient Fluid. PhD thesis. Amsterdam University of Applied Sciences. 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