Currently, the Q criterion, theΔ criterion and the λci criterion are
representative among the most widely used vortex identification criteria. These criteria
can be categorized as eigenvalue-based criteria since they are exclusively determined by
the eigenvalues or invariants of the velocity gradient tensor. However, these criteria are
not always satisfactory and suffer from several defects, such as inadequacy of identifying
the rotational axis and contamination by shearing. Recently, a novel concept of Liutex
(previously named Rortex), including the scalar, vector and tensor form, was proposed to
overcome the issues associated with the eigenvalue-based criteria. In the present paper,
the comparison of Liutex and two eigenvalue-based criteria, namely the λ ci criterion and
the QD criterion, a modification of the Q criterion, is performed to assess these methods
for compressible flows. According to the analysis of the deviatoric part of the velocity
gradient tensor, all the scalar, vector and tensor forms of Liutex are valid for compressible
flows without any modification, while two eigenvalue-based criteria, though applicable
to compressible flows, will tend to be severely contaminated by shearing as for
incompressible flows. Vortical structures induced by supersonic microramp vortex
generator (MVG) at Mach 2.5 are examined to confirm the validity and superiority of
Liutex for compressible flows.
Keywords: Compressible flows, Liutex/Rortex, Vortex identification, Vortex
structures, Turbulence.