Lagrangian-based investigation of multiphase flows by finite-time Lyapunov exponents

Abstract

Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors effectively. Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbulent cavitation under the framework of Navier-Stokes flow computations.For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream region after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the adverse pressure gradient is strong enough. It represents a barrier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FTLE field has the potential to identify the structures of multiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region. Nomenclature d eDiameter of nozzle exit d s Diameter of cross-section of propulsion system d t Diameter of nozzle throat E g Total energy of gas E w Total energy of water k eff Effective thermal conductivity, k eff = k + k t k g Thermal conductivity of gas k t Turbulent thermal conductivity k w Thermal conductivity of water m + , m − Source and sink terms in the cavitation model p 0 Stagnation pressure p a Ambient pressure p e Pressure at nozzle exit Q Vortex definition criterion, Q = 1/2(|Ω| 2 −|S| 2 ) SThe rate-of strain tensor t Time t 0 Initial time t ∞ Reference time scale t * Normalized time scale, t * = t/t ∞

Oscillation Flow Induced by Underwater Supersonic Gas Jets from a Rectangular Laval Nozzle

“…There are many explanations for the underling physics of the "back-attack" phenomenon. Shi et al [24], [25] have suggested that the "back-attack" can be a shockwave or jet expansion feedback phenomenon, while Tang et al [26] have described the "back-attack" is a backward flow generated due to the injected gas has difficulties approaching the downstream region after the necking/breaking process. These debatable explanations indicated the necessity to study the problem from the point of view of aerodynamics and fluid mechanics.…”

Study on three-dimensional expansion characteristics of four wall combustion-gas jets in confined liquid space

“…Numerically, Tang et al [16,17] revealed the phenomena of bulge, necking/breaking, and back-attack in the jets expansion processes by numerically simulating the process of jet expanding under water. A mathematical model was proposed by Cheng and Liu [18] for an exhaust gas bubbles in missiles launched in an underwater process through using different numerical methods to describe the gas flow field and water flow field, respectively.…”

Fluctuations of Lyapunov exponents in homogeneous and isotropic turbulence

“…Whereas the Lagrangian approach deals with dispersion of pairs of fluid particles, the Eulerian approach measures the evolution of two different flows with similar initial conditions. The study of Lagrangian chaos is widely applied in geophysical [4,[30][31][32][33][34][35][36] and astrophysical applications [37][38][39] as well as the study of engineering flows [40,41] and plasmas [42][43][44]. In these contexts, chaos is used to characterize mixing and transport properties as well as determining Lagrangian coherent structures (LCS) [45].…”