# Analysis of Vorticity and Velocity Fields of Jets from Gas Injector Using PIV
## 1 Introduction  
The ever-increasing concerns about the expected growth of future energy demand are driving the search for new and alternative energy sources [1]. In this framework, hydrogen consists of a middle term option to boost the decarbonization of the so-called hard-to-abate sectors [2]. Of these, the road transport sector represents a test bench for studying hydrogen implementation and resulting performance. Here, hydrogen can be used in two main ways: via injection in internal combustion engines (H2-ICEs) or forcing an electrochemical reaction into a fuel cell (FC). Despite its potential, the physical properties that make hydrogen an attractive energy carrier also present several challenges for its application, from the very low density, which requires sophisticated manufacturing techniques [3, 4], to the wide flammability range that combined with the low minimum ignition energy make the hydrogen prone to explosive phenomena [5]. Because of the risks associated with the utilization of this fuel, an increasing number of articles propose the use of substitute orsurrogate fuels for those investigations that do not involve the experimental reproduction of reacting phenomena [6; 7; 8]. Helium, which is the second lightest element with the closest molecular mass weight to that of hydrogen, is already considered the best candidate to mimic the mixing properties. The literature offers a large number of studies involving the use of helium; from the simulation of hydrogen gas leaks in enclosed spaces [9; 10] to its application in the aerospace sector. [PERSON] et al. in [11] performed a numerical investigation for evaluating helium as a hydrogen substitute in supersonic mixing conditions. The results demonstrated how helium returns a qualitative understanding of the global mixing parameters, with a good agreement in terms of jet penetration while underestimating the dispersion, leading to an overall loss of about 10% in the mixing efficiency compared to H2. Other investigations exploit the use of advanced optical techniques like schlieren photography [12] and PIV [13] to bring additional margins for the understanding of the underlying phenomena that play a key role in the flow-field distribution. The schlieren photography exploits the inhomogeneities in gas density caused by temperature differences or by the presence of a species with different physical properties. Other methods were developed to extent the visualizable scale-flow [14], the analysis of the concentration of specific species [15] (i.e., rainbow schlieren reflectometry, RSD), or to make possible the study of the local heat transfer pattern [16]. Recent articles have studied hybrid solutions in which the turbulent flow field serves as tracer particles [17]. In contrast to the schlieren technique which provides qualitative results, the PIV is a quantitative optical technique capable of providing a detailed analysis of the flow-field under investigation [18; 19; 20; 21; 22]. The high precision of the results of this technique makes it suitable for the development of fluid dynamics codes (CFD) [23; 24]. Considering the purpose of the present study, the PIV technique has been chosen to carry out a detailed analysis on helium jet structure. The first gaseous jet model to be proposed is the one of [PERSON] in 1962 [25]. According to this model, if the injector features a round nozzle, the gaseous jet is assumed to have a conical shape with an almost axial symmetric head vortex. The model proposed by [PERSON] was one of the first to suggest that most of the air is dragged inside a structure from the back of the head, thus in the so-called steady state region. [PERSON] et al. in [26] used the schlieren method to record the injection process of hydrogen by using an outward opening injector. The study revealed that the self-similarity factor (S), defined as the ratio between radial penetration to the axial penetration, results always larger than 1 in the initial stage.