A study of four previously published computational criteria for identifying vortices in high-pressure flows has led to the selection of one of them as the best. This development can be expected to contribute to understanding of high-pressure flows, which occur in diverse settings, including diesel, gas turbine, and rocket engines and the atmospheres of Jupiter and other large gaseous planets.
Information on the atmospheres of gaseous planets consists mainly of visual and thermal images of the flows over the planets. Also, validation of recently proposed computational models of high-pressure flows entails comparison with measurements, which are mainly of visual nature. Heretofore, the interpretation of images of high-pressure flows to identify vortices has been based on experience with low-pressure flows. However, high-pressure flows have features distinct from those of low-pressure flows, particularly in regions of high pressure gradient magnitude caused by dynamic turbulent effects and by thermodynamic mixing of chemical species. Therefore, interpretations based on low-pressure behavior may lead to misidentification of vortices and other flow structures in high-pressure flows. The study reported here was performed in recognition of the need for one or more quantitative criteria for identifying coherent flow structures — especially vortices — from previously generated flow-field data, to complement or supersede the determination of flow structures by visual inspection of instantaneous fields or flow animations. The focus in the study was on correlating visible images of flow features with various quantities computed from flow-field data.
The quantities involved in the four criteria considered in the study are the following:
- The discriminant of the deformation tensor;
- The second invariant of the deformation tensor;
- The intermediate eigenvalue of the symmetric tensor representing the sum of the square power of the strainrate tensor and the square power of the rotation tensor; and
- The magnitude of the vorticity vector.
The criteria associated with the first three quantities are those inside a vortex core, the discriminant is positive, the second invariant is positive, and the intermediate eigenvalue is negative, respectively. The fourth criterion — taking magnitude of the vorticity as an indication of vortical activity — might intuitively seem to be a good choice, but it is subjective rather than objective because it entails subjective selection of a threshold magnitude value for isolating flow structures of interest in high-vorticity regions.
These criteria were tested by use of a database generated in direct numerical simulations of high-pressure, binary-speciesmixing flows undergoing transitions to turbulence. The quantities involved in the criteria were computed from the database, isosurfaces of these quantities were plotted, and plots were assessed with respect to utility in demarcating flow structures. Of the four criteria, that based on the second invariant was found to yield the most realistic plots of flow structures and to capture structures in all regions of the flow.
The figure presents plots of the second invariant isosurfaces showing vortical features from four of the simulations. The diversity of the features is noticeable and has been interpreted as boding well for the extraction of vortical features from visual data and enabling appropriate comparisons between experimental and computationally simulated flows.