مدل سازی و بررسی آزمایشی جت های گازی شناور افقی تزریق شده به مایع محیط یکنواخت راکد Modelling and experimental investigation of horizontal buoyant gas jets injected into stagnant uniform ambient liquid

۱٫ Introduction Turbulent buoyant jets form a complex multiphase system, which have a great interest in many environment and industrial applications. A buoyant jet is formed when a continuous stream of low-density fluid with large momentum originating from a nozzle enters into a liquid medium with bigger density. Depending on the initial jet momentum and the density difference between the two fluids, the jet breaks up into a train of bubbles, either immediately at the nozzle exit or at some distance downstream. Three general groups of factors govern the buoyant jet behavior they are: (i) jet parameters, (ii) environmental parameters and (iii) geometrical factors. The first group includes the initial jet velocity, the turbulence level, the jet mass, momentum and the density deficit between the jet and the ambient fluid. The second group of variables includes the ambient fluid parameters, such as turbulence level, currents, and density stratification. These factors usually begin to influence the jet behavior at some distance from the orifice. Finally, the geometrical factors include the depth of submergence of the jet, the jet shape, its orientation and proximity to solid boundaries or to the free surface. The considerable research activity in the area of buoyant jets over the past 50 years has resulted in different experimental studies and a number of different models that mathematically describe the jet flow path. Different experimental investigations have been conducted in the past few decades on the turbulent jets and the results provided support for the mathematical modeling approach (Liang et al., 2016; Taib, 2015; Harby 2012; Francis et al., 2014). The mathematical models based on the jet behavior existing in the literature can be classified mainly into three different categories: integral models, length-scale models, and models that use a combination of both length-scales and integral techniques. Integral models which are based on the conservation equations of mass, momentum and buoyancy fluxes are the most common ones; they are widely used in engineering practice for the prediction of the characteristics for these buoyant jet discharges (Ficher et al., 1979). Most of these models consider only the mean mass and momentum fluxes in the set of conservation equations. Hence, they can be referred to as first-order integral models. However, few experimental data and calculations on the buoyant jet with large density variations can be found in the literature. Most of the researches were carried out for small density variation when the Boussinesq approximation is valid and the jet is discharged vertically (Harby et al., 2014a). There is still very little experimental data and calculations to understand well these flows (Harby et al., 2014b). Crapper and Baines 1977 suggested that the upper bound of applicability of the Boussinesq approximation is that the initial fractional density difference ρ۰/ρa is 0.05. In general, one can say that the Boussinesq approximation is valid for small initial fractional density difference, ρ۰/ρa 1. The non-Boussinesq plume was studied by a number of researchers (Woods, 1997; Carlotti and Hunt, 2005). Xiao et al. 2009 studied and developed a nonBoussinesq integral model for horizontal buoyant round jets with a modified entrainment hypothesis. The system of conservation equations of the integral model was solved to obtain numerical solutions in the transition region from jet-like to plume-like. They concluded that for a strongly buoyant jet the Boussinesq approximation is violated which will over-predict the mass entrainment and under-estimate the buoyancy effect. This study reveals that the Boussinesq approximation is valid when the density variation is less than 10% being the entrainment assumption a key requirement for the integral model. The entrainment rate of a turbulent jet is defined as the ambient fluid that is mixed across the jet edge and becomes incorporated into the body of the jet. The agents of entrainment are turbulent eddies forming a mixing layer between the jet and its surroundings. This process has the effect of increasing the total jet mass flux (Houf et al., 1956). The first to incorporate the entrainment approach into a general jet model was Fan and Brook (1969) which used the Eulerian integral method, in which the flow passed through a fixed control volume, and integrated the equations of motion over that control volume. Other ones, who have used this approach, are: Muellenhoff et al. (1985), Wood (1993), Chu and Lee (1996) and Jirka (2004). Morton 1965 concluded that there was an average entrainment into the jet-like flow that was proportional to the mean centerline velocity. List et al. 1979 showed that the entrainment mechanism is the same in both jets and plumes and is dominated by almost periodic large-scale motions which engulf the ambient fluid. The unmixed fluid is transported well into the turbulent fluid and mixed by the action of small eddies. Abraham 1963 showed that the rate of expansion of a buoyant flow was independent of the type of flow (jet-like or plume-like) and with this alternative assumption proceeded to the solution. List and Imberger 1973; Jirka and Harleman 1979 were able to relate the two assumptions and derive the entrainment constants for the jet and the plume. Taylor (1958), Kotsovinos (1975) and Agrawal and Prasad (2004) suggested that for turbulent buoyant jets, the turbulent entrainment is usually parameterized by relating the inflow velocity to the mean flow in the jet body also they suggested that a substantial contribution to entrainment is made through nibbling of small scale vortices see also Mathew and Bassu (2002). Numerous experimental and numerical studies provided values of the entrainment rate for example Houf and Schaefer (2008), ElAmin et al. (2010) and El-Amin and Kanayama (2009) assumed that the local rate of entrainment consisted of two components; one was the component of entrainment due to jet momentum while the other one was the component of entrainment due to buoyancy. Also, they reported that the local rate of entrainment increases as the jet leaves the momentum-dominated region and enters a region where the effects of buoyancy become more pronounced. This non-similarity of the entrainment rate along the jet trajectory has been discussed by Carazzo et al. (2006). Other authors predicted the behavior of the buoyant jet by using integral equations formulated under the assumption of axial symmetry and self-similar transverse profiles (Fisher et al., 1979; Wood, 1993; Pantokratoras, 1998). Batchelor (1954) showed that a strong entrainment from the ambient will take place when the density ratio tends to unity (ρg/ρa→۱) while as the density ratio tends to zero (ρg/ρa→۰) the entrainment falls to zero and as the density ratio varies between the two limits there will be a smooth transition. The horizontal buoyant jets with large density variations have not received sufficient research before, and almost no experimental data could be found in the open literature. However, submerged horizontal gas jets in liquid exhibits different flow characteristics from gas-gas flow because bubble breakup occurs in two-phase flow and the unsteady motion of the gas-liquid interface has a strong influence on the momentum transfer and the buoyancy force. Hence, it remains a challenging issue to understand well these flows, to calculate the flow structures numerically, to verify the numerical models and to measure them experimentally. In their efforts to understand the characteristics of submerged gas jets, past researchers have relied on point measurements such as electro-resistivity probes to separate the liquid and gas phases for study (Mori et al., 1982; Ito et al., 1991). In these techniques, the probe is placed at the measurement point for some time and is then traversed in space. The sensing element can be a singular measurement point or be composed of several measuring points capable of simultaneous measurement at multiple spatial locations. In either case, the probe itself is intrusive and only permits timeaveraged whole-field measurements since the probe can only exist at one (or several) points in space at any given time. In such an unsteady and highly irregular flow field, a global measurement is preferred since instantaneous information can be obtained. An example of a global measurement is high-speed photography, which has been used in the past (McNallan and King 1982; Loth and Faeth 1989) to observe the interface, but the level of quantitative detail gathered from the recorded images was very low. In this study, an integral numerical model was developed to predict the behavior of a horizontal gas jet injected from straight tubes into water ambient under different operating conditions. Since a major goal of this work was to study the interface motion itself, the technological limitations imposed by traditional measurement techniques were unacceptable. Thus high-speed photography was used to record the position and motions of the entire gas jet and the digital images were analyzed to extract the interface position. Thus direct and instantaneous global measurements of the interface were taken. Recorded images are a projection of the density variations seen in the test section. The gas jet parameters were obtained performing first a time-average of the recorded images followed by a careful analysis of the processed data. The model equations and a solution procedure was coded with input and graphical output routines into a MATLAB program and finally compared with the experimental data.