Experimental And Computational Investigations Of Underexpanded Jets From Elliptical Sonic Nozzles

Abstract

Three dimensional nozzles and jet flows have attracted the attention of many researchers due to their potential application to many practical devices. Rectangular nozzles are considered for short/vertical take off and landing aircrafts for achieving powered lift. Axisymmetric nozzles with lobes, tabs or slots and elliptical nozzles are considered for noise reduction in aircrafts and mixing augmentation in airbreathing rockets. Interaction of supersonic jets with solid surface, as in the case of retro and ullage rockets in launch vehicles and interaction of multiple jets as in the case of launch vehicles with multiple booster rockets/multiple nozzle engines are of practical importance. Design of rockets and aircrafts employing these nozzles needs the understanding of the structure and behaviour of the complex three dimensional supersonic jets issuing from these nozzles. The problem is so complex that different investigators have addressed only some specific aspects of the problem and there is much more to be done to fully understand these flows. For example, in the case of rectangular nozzle with semi circular ends (known as elliptical nozzle), the investigations have been limited to a single nozzle of aspect ratio 3,0 and pressure ratio (ratio of the total pressure to ambient pressure) 3.0. Further, the measurements were made in the far field subsonic region beyond a distance of 20 times the equivalent nozzle radius (RJ.

For the present study, the elliptical sonic nozzle of the type mentioned above was chosen, as it offered simplicity for manufacturing and carrying out computations, but has all the complex features associated with the three dimensional jets. A systematic study to understand the mean flow structure and the effect of important governing parameters like ratio and pressure ratio on the flow development process of the jet issuing from Navier-Stokes equations.

The experimental study revealed many interesting flow features. It was found that the Underexpanded jet issuing from elliptical sonic nozzle spreads rapidly in the minor axis plane while it maintains almost constant width or contracts in the major axis plane. However, the gross spreading of this jet is much higher compared to the axisymmetric jet. The higher spreading rates experienced in the minor axis plane compared to the major axis plane of this 'et, results in the jet width in the minor axis plane to become higher than that in the major axis plane. The longitudinal location, where this occurs is called the axis switching location. This kind of axis switching phenomenon is known to exist for subsonic elliptical jets. However, for the present supersonic jets, the axis switching locations are much closer to the nozzle exit compared to the subsonic cases reported. It was further found that this location strongly depends on the pressure and aspect ratios. A critical pressure ratio was found to exist for each nozzle at which the axis switching location is the farthest. Above the critical pressure ratio, the axis switching location was observed to move upstream with the increase in the pressure ratio and is controlled by the complex interactions of shock and expansion waves near the nozzle exit. Below the critical pressure ratio, the axis switching location moves upstream with the decrease in pressure ratio and is controlled by some kind of instability in the minor axis plane.

The shock structure present in the underexpanded jet from an elliptical nozzle was also observed to depend on both pressure and aspect ratios. For some aspect ratios and pressure ratios, the shock pattern observed in both the major and minor axis planes are similar to that of an axisymmetric jet, where the incident barrel shock and the Mach reflection (from the edges of the Mach disk) are present. But for all other cases, this shock continues to be seen only in the major axis plane. Whereas, in the minor axis plane, the incident shock is absent in the shock pattern.

Detailed measurement in the jet cross sectional planes, for the case of aspect ratio 2.0 nozzle, shows that the cross sectional shape changes along the length and it becomes almost a circle at the axis switching location. Further downstream, the jet spreads rapidly in the minor axis plane whereas no significant change in the width of the jet in the major axis plane is observed. Far downstream, the jet boundary appears like a distorted ellipse with its major and minor dimensions lying respectively in the minor and major axis planes of the nozzle. The elongated shape of the jet cross sections at locations downstream of the axis switching point gives the impression that the entire flow in the major axis plane is turned towards the minor axis plane. This effect appears to be predominant at high pressure ratios.

The computed near field shock structure in the planes of symmetry, pitot pressure distributions, cross sectional shape of the jet and the spreading pattern agree very well with the experimental results. In addition to this, the present computational method gives the detailed near field flow structure including the azimuthal extent of the incident shock, cross flow details and distributions of flow variables. It is shown that the present inviscid methodology can also predict the axis switching point accurately if it occurs before the formation of the Mach disk and it demonstrates that the jet growth phenomenon in the near field, atleast, is mainly controlled by the inviscid flow process. The computed results have shown that changes in the jet cross sectional shape in the near field is caused mainly by the interaction of compression and expansion waves with each other and with the constant pressure boundary. The inviscid method seems to be able to capture the complicated secondary cross flow structure (indicating presence of longitudinal vortices) of the elliptical jet.

The complex mean flow structure in the near field region of the jet issuing from elliptical nozzles and the effect of nozzle aspect ratio and pressure ratio on the structure are brought out clearly in the present study. The mechanism governing the spreading and the axis switching characteristics are also brought out. Thus the present experimental and computational investigations give a comprehensive understanding of the mean flow structure of the underexpanded jets issuing from elliptical nozzles. Further studies are required to understand the other aspects of the elliptical jets as well as other three-dimensional jets. Some of these studies are identified for future work.