The main characteristics of compressible square vortex loop in the initial three-dimensional (3D) flow field of a supersonic underexpanded square jet are studied numerically for Ma = 1.4 at pressure ratio (jet flow pressure/ambient pressure) of 1.4. The governing equations of large eddy simulation (LES) for compressible flow have been employed and are solved numerically with the combination of high-order hybrid schemes.
The main flow structures of supersonic underexpanded square jets include the primary vortex loop (PVL), mixing layer (ML), oblique shock patterns (OS), Prandtl-Meyer expansion fans (PF), embedded shock (ES) and vortex-induced shock pair (VS1 and VS2), and some complicated phenomena, like the mixing layer instability, shock-vortex interaction etc., appear in the flow field (Fig. 1). Such a jet has the general flow characteristics of circular jets, however, owing to the different azimuthal curvature, it can also be viewed that there are some differences for the section of primary vortex loop along minor and major axes. The primary vortex loop in the major axis moves faster, while along the minor axis, the vortex loop moves further away from the jet center, therefore, the diameter of vortex core in the minor axis is larger than the major axis direction, then, the phenomeon of axis switching (the cross section rotates 45º) appears.
In addition, the overexpanded regions appear near the high curvature segment of the nozzle, and result in the formation of oblique shock wave planar surfaces (OS1, OS2, OS3 and OS4), and form the typical three-dimensional shock-cell structures upstream of the vortex loop, as shown in Fig. 2. These shock surfaces intersect each other at downstream, and form the intersection lines, e.g. OI1 - OI4, and I1 , I2.
Keywords: Supersonic jet, elliptic jet, compressible vortex loop, shock wave
Fig.1 The typical initial flow structures of square jet at t= 0.11ms. (ES: Embedded shock; MS: Mixing layer; PVL: Primary vortex loop; PF: Prandtl-Meyer expansion fan; OS: Oblique shock wave; VS1,VS2: Vortex-induced shock pair.)
Fig.2 The typical three-dimensional shock wave structures of the upstream of vortex loop.
Acknowledgement
This work was supported by the National Natural Science Foundation of China under Grant No. 11272156.
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