Generation of Upper Trailing Counter-Rotating Vortices of a Sonic Jet in a Supersonic Crossflow

Abstract

Direct numerical simulations were conducted to investigate physical structures of a transverse sonic air jet injected into a supersonic air crossflow at a Mach number of 2.7. Simulations were run for two different jet-to-crossflow momentum flux ratios (J) of 1.85 and 5.5. The main averaged flow features around the transverse jet, such as major counter rotating vortices (CRVs) and trailing CRVs (TCRVs) were captured. The major CRVs form in the lateral portion of the jet plume and absorb other induced trailing vortices downstream of the jet plume. Upper trailing CRVs form above the major CRVs downstream of the jet barrel shock. The streamline analysis indicates that the upper trailing CRVs are related to the Mach disk. As the streamlines penetrate the lateral side of Mach disk where a strong shear condition exists, the baroclinic torque induces upper vorticities in the opposite rotating direction against the major CRVs. Downstream of the Mach disk, the baroclinic vorticity production along the streamlines tends to approach zero, which means no more torque is pumped into the farfield and the upper TCRVs are merged into the major CRVs by their suction. Keywords: supersonic flow; transverse jet; direct numerical simulation; counter rotating vortices; upper trailing counter rotating vortices Nomenclature J =jet-to-crossflow momentum flux ratio BVP = baroclinic vorticity production CRV = counter rotating vortices DNS =direct numerical simulation JISC =jet interaction with supersonic crossflow LES =large eddy simulation STBL =supersonic turbulent boundary layer TCRV =trailing counter rotating vortices

Formation of surface trailing counter-rotating vortex pairs downstream of a sonic jet in a supersonic cross-flow

“…In addition, a variant of the standard total variation diminishing scheme is used for shock capturing (Yee et al 1999). To better resolve the steep gradient in flowfield around the injected jet, we used a hybrid scheme which combines the entropy splitting central scheme with a central-upwind WENO-CU4 scheme, which is developed following the procedure of the WENO-CU6 (Hu et al 2010) and given in our recent work (Sun & Hu 2018). The two schemes are combined using the Ducros sensor (Ducros et al 1999) as the hybriding function.…”

“…The two schemes are combined using the Ducros sensor (Ducros et al 1999) as the hybriding function. This hybrid scheme was well described in the paper (Sun & Hu 2018) and for brevity omitted here.…”

“…The jet centre is 75mm downstream of the inlet with an orifice diameter of D=2mm. The same computation domain was used in our previous work (Sun & Hu 2018) and more details could be referred. Table 2.…”

“…A fine mesh of 2305×279×271 grid points is used for the current simulations. The grid stretching scheme was described in our previous work (Sun & Hu 2018) and for brevity the description is omitted. To capture the wall bounded flow, the grids are clustered near the wall in the region y=0 to 0.6δ i uniformly and then stretched smoothly out.…”

“…In our previous work (Wang et al 2013;Zhang et al 2016), a hybrid RANS/LES methods were validated and used to study 3D jet mixing and the effect of micro-ramp on jet mixing in a supersonic crossflow. Recently, we conducted direct numerical simulations to study transverse jet in supersonic flows and focused on the upper trailing CVP (TCVP) which is located above the major CVP (Sun & Hu 2018). The main conclusion was that the upper trailing CVPs are related to baroclinic effects caused by the deflecting Mach disk.…”