Abdurakipov S.S.   Kozinkin L.A.   Tokarev M.P.   Dulin V.M.   Markovich D.M.  

Analysis of spiral structures in swirling jets from time-resolved tomographic PIV data

Reporter: Abdurakipov S.S.

Swirling jet flows are widespread in a number of industrial devices: open burners, combustion chambers, mixers, etc. From a practical point of view, the imposed swirl can essentially enhance mixing processes in devices that utilise jet flow configurations. In par-ticular, swirl is often used for stabilization of flames. However, even for non-reacting swirling jets, substantially different flow regimes can be observed, depending on the swirl rate and on the manner in which the swirl is applied [1]. While vortex rings, resulted from growth of Kelvin–Helmholtz instability, prevails mixing layer of non-swirling and weakly swirling jets, a superposition of spiral convective instability modes determines the dynam-ics of jets at low and moderate swirl rates. A further increase in the swirl rate leads to the vortex breakdown (VB), which has been observed in different states: spiral, bubble, and conical, where the latter two can be either symmetric or asymmetric. Strong helical struc-tures become dominant in the shear layer of the jet with a sufficiently high swirl rate. Re-markable, that flow structure of strongly swirling jets with bubble-type VB and precession of the vortex core (PVC) manifests some common features, even for rather different nozzle geometries. Since the flow is absolutely unstable to a self-excited/globally unstable to a helical mode [1]. This coherent structure (co-rotating counter-winding spiral) dominates dynamics of the flow.

This work is devoted to analysis of the structure and dynamics of the most unstable spiral modes in low-swirl jet before the permanent VB and in high-swirl jet with the pro-nounced VB and PVC. We used the advantages of the time-resolved tomographic Particle Image Velocimetry (PIV) method, local linear stability analysis and statistical tools: Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) to obtain comprehensive information about spiral structures that dominated the swirling flows.
POD and DMD are efficient statistical tools for fluid mechanics [2] to extract coher-ent structures in turbulent flows. Application of the methods to a large set of instantaneous velocity fields allows to significantly reduce the dimensionality of the problem. POD pro-vides a set of temporal and spatial basis functions (eigenmodes), which contain the largest amount of turbulent kinetic energy in the considered domain of the flow. DMD extracts the set of eigenmodes, which correspond to characteristic frequencies of the flow. A time-resolved tomographic PIV with acquisition rate up to 4 kHz was used for the measurements of 2 000 instantaneous velocity fields in jet flows. The velocity sets were processed by the snapshot POD and DMD algorithms [2]. Profiles of the mean flow velocity were tested by a linear stability analysis, realized on the basis of Chebyshev pseudo-spectral collocation method. The PIV measurements were performed in a hydrodynamic loop described in de-tails in [3]. A nozzle with exit diameter d = 15 mm was used for organization of low- and high-swirl jets with an intermittently appearing VB and with a pronounced VB, respective-ly. The Reynolds number based on nozzle diameter and bulk velocity was Re = 5 000. The swirl rates based on the geometry of the swirler embedded in the nozzle were S = 0.41 (low swirl) and S = 1.0 (high swirl).
Analysis of the POD and DMD eigenmodes, estimated for the 3D time-resolved PIV measurements in the high-swirl jet, revealed that they correspond to the precession of the jet’s vortex core and a couple of secondary spiral vortices formed in the inner (around recirculation zone) and outer mixing layers of the jet. Fig. 1 (a) (presented in doc-file) shows 3D spatial structure of the spiral modes in the high-swirl jet. The structure was reconstructed on the basis of two the most powerful POD modes and visualized by isosurfaces of λci-criterion [2]. Ac-cording to the spatial Fourier analysis and linear stability analysis, these spiral structures were associated with an absolute unstable energetic helical mode with azimuthal wave-number |m| = 1. The specified mode oscillated with the frequency of 7 Hz. These secondary vortices with opposite sign of helicity are left-handed spirals (sense of winding opposite to the mean flow rotation) and are similar to the vortex structures reported in [2]. On the con-trary, a set of convectively unstable low-energy modes |m| = 0, 1, 2 was found in different regions of the low- swirl jet. As can be seen in Fig. 1 (b) (presented in doc-file), the spiral mode |m| = 2 takes place in outer mixing layer, the mode |m| = 1 dominates in jet’s vortex core near nozzle exit. A superposition of |m| = 1 with axisymmetric mode m = 0 was detected for a stagnation re-gion, where the axial velocity reached its minimum. The modes in the vortex core and in the outer mixing layer have different signs of helicity. Thus, the results, obtained from the 3D time-resolved PIV data, confirm the previous conclusions about types of spiral insta-bility modes in low- and high- swirl jets.

1. Oberleithner K., Paschereit C.O., Seele R., Wygnanski I. Formation of turbulent vortex breakdown: intermittency, criticality, and global instability // AIAA Journal. 2012. Vol. 50. No. 7. P. 1437-1452.
2. Markovich D.M., Abdurakipov S.S., Chikishev L.M., Dulin V.M., Hanjalic K. Comparative analysis of low- and high-swirl confined flames and jets by Proper Orthogonal and Dynamic Mode Decompositions // Physics of Fluids. 2014. Vol. 26. P. 22.
3. Alekseenko M.V., Bilsky A.V., Dulin V.M., Kozinkin L.A., Markovich D.M., Tokarev M.P. Diagnostics of jet flows by using tomographic Particle Image Velocimetry // Optoelectronics, Instrumentation and Data Processing. 2014. Vol. 50. No. 5. P. 457-565.

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