A Feature Tracking velocimetry technique applied to inclined negatively buoyant jets

We have applied a Feature Tracking Velocimetry (FTV) technique to measure displacements of particles on inclined negatively buoyant jets (INBJs), issuing from a circular sharp-edged orifice, in order to investigate, among the others, the symmetry properties of the velocity field on this phenomenon. Feature Tracking Velocimetry is less sensitive to the appearance and disappearance of particles and to high velocity gradients than classical Particle Image Velocimetry (PIV). The basic idea of Feature Tracking Velocimetry is to compare windows only where the motion detection may be successful, that is where there are high luminosity gradients. The Feature Tracking Velocimetry algorithm presented here is suitable in presence of different seeding densities, where other techniques produce significant errors, due to the nonhomogeneous seeding at the boundary of a flow. The Feature Tracking Velocimetry algorithm has been tested on laboratory experiments regarding simple jets (SJs) and inclined negatively buoyant jets released from a sharp-edged orifice. We present here velocity statistics, from the first to the fourth order, to study, among the others, the differences between simple jets and inclined negatively buoyant jets, and to investigate how the increase in buoyancy affects the inclined negatively buoyant jet behavior. We remark that, to the best of authors’ knowledge, this is the first attempt to investigate velocity statistics of an order higher than the second on Inclined Negatively Buoyant Jets. In Figure 1, the mean velocity field U, normalized by the maximum velocity at the outlet Umax, for an INBJ with Fr = 8, Re = 1000, and θ = 65° is shown; this allows to highlight the general features of INBJs. The jet axis is defined as the locus of maximum intensity velocity on sections orthogonal to the jet; on Figure 1 it is superimposed to the velocity field as a white line. An INBJ is driven by two forces acting in different directions, namely momentum and buoyancy: INBJs cover a very short initial distance, where they seem to be driven essentially by the initial momentum and maintain a width similar to the diameter of the orifice D while, after this distance, the onset of the Kelvin-Helmholtz billows causes the widening of INBJs. As the distance from the orifice increases, the buoyancy becomes more and more relevant, finally bending the jet downwards. After this point, where the INBJs reach their maximum height, they behave, in their descending branch, similarly to a plume. Figure 1 shows how this descending branch experiences a sudden widening at Y/D ≈ 10, due to the interaction between the upward branch and the downward one. As a matter of fact, the mean velocities in the upward branch tend to balance with the ones in the descending branch, preventing a larger widening of this last one. The analysis of mean velocity fields highlights the different behavior of Inclined Negatively Buoyant Jets with respect to Simple Jets, but only at a certain distance from the outlet. On the contrary, velocity second order statistic s already unveil the lack of axisymmetry at a very short distance from the jets’ origin. Moreover, the analysis of the second order statistics of the velocity highlights a dependence of the features of sharp-edged orifice jets on the densimetric Froude number. In Figure 2 we show the streamwise evolution of the non-dimensional spanwise velocity kurtosis Vr flat/Umax4 for two INBJs with Re = 1000, θ = 65° and different Fr (red asterisks 8, blue ones 15). The behavior of the spanwise component is opposite to the streamwise one: very low values close to the origin, highlighting a tailed distribution of Vr, which tend to grow until their maximum, at the s/D almost equal to the one of the jet maximum high, to eventually decrease and tend to oscillate around a value (approximately 1.5) which is much lower than the value of 3 typical of a Gaussian distribution. Hence, except for the peculiar maximum close to the jet maximum high, a strongly non Gaussian behavior characterizes the whole INBJ evolution. We can suppose that in the downward branch of INBJs the streamwise velocity components tend to a symmetrical Gaussian distribution (without reaching it), whilst the spanwise velocity components have a more heavy tailed distribution. Results show the role of buoyancy in modifying the inclined negatively buoyant jet features; moreover, it is highlighted that the asymmetry and non-Gaussianity of INBJs cannot be considered only a far field feature of this phenomenon, as it arises very close to the release point. This seems to be an outcome of the strong non-Gaussianity of the radial component of the velocity, as shown by the higher order statistics along the jet axis. This implies that the asymmetry and non-Gaussianity are key features of INBJs that cannot be neglected even in their near field, oppositely to what previously stated in literature.