Introduction
Three-dimensional wall-jets have received attention due to their wide range of applications, such as film cooling or effluent discharges into hydrosphere. One of the main characteristics of these type of jets is high lateral to vertical spread ratio.
Viets and Sforza (1966) showed potential core will be dissipated as stream-wise distance increase. Sforza and Herbst (1970) found that at far enough distances, the expansion rate and velocity decay are independent of nozzle geometry. Rajaratnam and Pani (1974) showed that nozzle caused no major influence on jet behavior at far region, whereas, Davis and Winarto (1980) found that nozzle-to-wall distance affects the rate of velocity decay and the rate of velocity development in lateral plan. Launder and Rodi (1983) results showed stream-wise vortices are the primary contributors to secondary flows. Later, Eriksson et al. (1998) and Padmanabham and Lakshmana Gowda (1991), investigated the influence of presence of confining walls. Moreover, Agelin-Chaab and Tachie (2011) demonstrated the independency of expansion rate and decay rate of velocity from the Reynolds number.
In this research, application of LRR turbulence model have been studied. By calculating velocity field, results compared to experimental data, such as maximum velocity decay, velocity profiles and spread rates.
Methodology
The governing equations for three-dimensional wall-jet consist of the conservation of mass and momentum equations, as presented in Equations (1) and (2). The Launder–Reece–Rodi (LRR) turbulence model was employed in this study to address a research gap in the literature. Unlike two-equation models such as k-ϵ, this turbulence model is not based on the Boussinesq hypothesis. The numerical simulations were conducted using OpenFOAM, an open-source software, with appropriate boundary conditions and numerical algorithms, which are briefly discussed in Sections 2.2 and 2.3, respectively. Furthermore, additional details regarding the simulation configuration in OpenFOAM, including the discretization methods for different parameters, are also provided. It should be noted that a schematic representation of the computational domain is depicted in Figure 1.
Results and Discussion
In this research, the assessment of the LRR turbulence model in simulating a three-dimensional wall jet is discussed in Section 3. The jet discharges fluid from a circular nozzle into a rectangular domain with a quiescent ambient. Earlier studies has demonstrated that the presence of an impermeable wall near the nozzle exit affects the flow structure, causing it to develop asymmetrically which is shown in Figure 4.
To evaluate the accuracy of the LRR turbulence model in predicting the characteristics of the jet, some important parameters which computed numerically, compared with experimental data. These parameters are the decay rate of maximum velocity along the nozzle axis, the velocity distribution profiles in both vertical and lateral directions, and the half-width variations in the horizontal and vertical planes, which shows how much velocity spreads. As depicted in Figure 3, maximum velocity decay rate, which can be approximated by Equation (3), was found to be higher than the values reported in literature. However, despite this discrepancy, the general trend remains consistent with experimental data.
Figures 5 and 6, exhibit a strong correlation between the vertical and horizontal velocity profiles with measured data, indicating that the numerical model provides sufficient accuracy in prediction of velocity filed. To further analyzing of the spreading characteristics of the velocity field, the vertical and horizontal half-widths were plotted against the stream-wise distance from the nozzle exit. The results showed that the vertical spread rate agreed with the range of experimental data only for x/d > 20, whereas the lateral velocity spread, particularly in the range 10 < x/d < 40, demonstrates excellent agreement with experimental measurements data.
Overall, these findings confirm that the LRR turbulence model is a reliable model for predicting the flow behavior of three-dimensional wall jets discharged from a circular nozzle in a quiescent ambient.
Conclusion
In present research, three-dimensional wall-jet was simulated numerically. The LRR turbulence model was employed. To evaluate its performance in predicting the velocity flow field numerical results compared to experimental data. Results indicated rate of velocity decay was higher than the experimental measurements but qualitatively acceptable. The lateral and vertical velocity profiles were computed with high accuracy. Som. Moreover, lateral spreading rate, which is one of the most important parameters in studying three-dimensional wall jets, was predicted well within the range of previous studies.