Laboratory for Flow Instabilities and Dynamics

Linear and nonlinear Dynamics of two-phase flows

Background

Two-phase flows describe the interaction of fluids that have different aggregate states (e.g. liquid and gaseous) and occur in a variety of technical applications. These include, for example, fluid mixing or atomization by means of nozzles or the separation of fluids in industrial cyclones. In contrast to single-phase flows, these flows exhibit significantly more complex dynamics.

This is due to the fact that two fluids with different viscosities and densities interact with each other. In addition, the fluid phases are separated from each other by an interface, so that a interface is always ensured, along which surface tension acts.

The interaction of different fluids and surface tension sometimes has a strong influence on the formation or modification of known hydrodynamic instabilities, for example in shear layers (Kelvin-Helmholtz instability), baroclinic stratifications (Rayleigh-Taylor instability) or wake flows (von Kármán instability). In addition, surface tension enables the emergence of new instabilities (e.g. Plateau-Rayleigh instability). The interaction of different instability mechanisms can be seen in the accompanying figure, in which an oscillating water jet bursts and decays into ligaments and droplets.

In this project, the complex linear and nonlinear dynamics of two-phase flows will be modeled and analyzed. An important goal is to extend existing modeling methods from single-phase flows to two-phase flows.

Methods

For the investigation of two-phase fluid dynamics, Direct Numerical Simulation (DNS), to capture the nonlinear dynamics, and Linear Stability Analysis (LSA), to capture the linear dynamics, are mainly used in this project. In addition, well-known modal decompositions, such as Dynamic Mode Decomposition (DMD), are used for data analysis.

The DNS investigations are conducted using the Basilisk code, which allows for an accurate and robust simulation of two-phase flows, using the Volume-Of-Fluid method and Height-Function based interfacial curvature calculation.

Methods in the area of linear stability analysis are much less developed and established for two-phase flows, compared to single-phase flows. Thus, in the past, mainly local (one-dimensional) stability analysis has been used, which has limited explanatory power for general flow configurations. Global analysis, which is the quasi-standard for single-phase flows, has hardly been applied so far and consequently is not very widespread.

Therefore, an important aspect is the development of a global stability analysis code for two-phase flows. For this purpose, the employed DNS code is linearized and linear global modes are calculated by means of matrix-free time integration of the linearized solver and an Arnoldi method. On the one hand, this methodology exploits the efficiency and robustness of existing numerical methods for nonlinear flows. On the other hand, it allows for the computation of complex three-dimensional flows with the same memory requirements as the corresponding DNS.

Results

The methods developed are applied here as an example to a generic two-phase swirl flow. Corresponding configurations occur, for example, as cavitating vortex ropes in hydroturbines. The so-called Grabowski-Berger vortex is investigated using DNS and global LSA, which is already well studied for single-phase flows.

In the two-phase flow, where the internal fluid has lower viscosity, an increased destabilization of the flow is observed, so that the coherent structures emerge at lower swirl numbers than in the single-phase case. The LSA reliably identifies the structure and frequency of the dominant primary instability. Above this, prominent nonlinear dynamics is evident in the DNS, which is not observed at appropriate swirl numbers in the single-phase case.