Session LP: Multiphase Flows V

Theoretical and numerical study of air layer drag reduction in two-phase Couette-Poiseuille flow

The objective of the present study is to predict and understand the air layer drag reduction (ALDR) phenomenon. Recent experiments (Elbing et al. 2008) have shown net drag reductions if air is injected beyond a critical rate next to the wall. The analysis is performed on a two-phase Couette-Poiseuille flow configuration, which mimics the far downstream region of boundary layer flow on a flat plate. Both theoretical and numerical approaches are employed to investigate the stability and mechanisms of ALDR. The linear stability of air-liquid interface is investigated by solving the Orr-Sommerfeld equations. From the stability analysis, the stability of the interface is reduced as the liquid free-stream velocity, Froude number and velocity gradients at the interface are increased, while the stability is enhanced as the gas flow rate and surface tension are increased. The Critical gas flow rates from stability theory are compared with experimental results, showing good agreement. Direct numerical simulations with a Refiend Level Set Grid technique has been performed to investigate the evolution of the interface, the turbulence interaction and nonlinear mechanisms of ALDR. It is observed that the Weber number has significant impact on the characteristics of the interface development.   

Time-resolved simulations and experiments of liquid jet break-up

High-speed, high-resolution experimental visualization of the break-up of a liquid jet by a gaseous cross-flow has recently become possible due to advances in video camera technology. These visualizations can now be contrasted to high fidelity CFD simulations which are also just becoming possible due to continuing growth of computational capabilities. Such a contrast is expected to go beyond traditional comparisons of time-averaged quantities and focuses on dynamics. For example, comparisons of the characteristic break-up frequency and of the spatial instantaneous features of the jet may serve as validation of the computational model and to yield insight into the physics of the dynamic interplay between the disturbances induced by the injection device and Kelvin-Helmholtz / Rayleigh-Taylor instabilities at the interface. A state-of-the-art second-order coupled Level Set and Volume Of Fluid method (CLSVOF) that can capture liquid-gas interface dynamics is used for the study. High-speed videos of non-turbulent liquid injection in laminar crossflow are used to validate the time- and grid-converged capability of the code to capture upwind wave structures caused by the centrifugal acceleration of the deflected liquid. The extension to increasing air crossflow is also discussed with focus on the column break-up mechanism.   

Large-eddy simulation of particle-laden flow over a backward-facing step using a spectral multidomain method

We present an investigation into the particle-laden flow in a dump-combustor configuration. An accurate prediction of particle dispersion within the combustors is necessary for improved design of spray combustion. The instantaneous local particle concentration and turbulent mixing provide insights into the physio-chemical processes that would be encountered in a reacting scenario. The principal difficulty in prediction of particle transport in the dilute flow regime, lies in the accurate description of the underlying complex, turbulent gas flow field featuring reattaching shear layers. Here, we present large-eddy simulations (LESs) of a particle-laden flow over an unconfined and confined backward-facing step at Reynolds numbers of 5000 and 28,000, respectively, using a spectral multidomain LES methodology. The LES captures the carrier flow accurately, while being computationally affordable. One-way coupled equations are considered and particles with different Stokes numbers are studied. The inlet turbulence is modeled using a novel stochastic model that reproduces the second order moments of the fully developed flow upstream of the step. The effects of the turbulent recirculating flow behind the step on particle dispersion are investigated in detail.   

Immersed Boundary and VOF Coupling Method for Bubble-Particle Interaction Problems

A new approach for the direct numerical simulation of three-phase flows is described. The method permits the simulation of the flow induced by a large population of bubbles and particles in a gas-liquid-solid system. Implementation of moving rigid surfaces is based on an immersed boundary method (IBM) of the body-force type, also developed by the present authors. In this method, the inter-phase momentum exchange is calculated by the distributed interaction force field shared by both the Eulerian (fluid) and Lagrangian (particles) frameworks. The gas-liquid interfaces are captured by the volume of fluid (VOF) method including surface tension. To assess its validity, the present method is applied to the piercing of the free surface of a liquid by a rising cylinder. Further applicability of the method is demonstrated in a 3-D situation, in which a rising bubble interacts with many settling particles.   

Experimental and numerical investigation of multiphase flow in disordered media

We present laboratory scale experiments and network simulations to investigate the influence of capillary, gravitational and viscous forces on multiphase flow in disordered microscopic media. Two-dimensional experiments, which are performed in a vertical glass bead pack to understand microscopic behavior, demonstrate the existence of small scale instability that is analyzed with the theory of invasion percolation. Numerical simulations based on pore networks are carried out to help investigate the possibility of developing effective conservation laws at the macroscopic scale.   

Towards numerical simulation of bubbly flows in complex geometries

We are developing the LES capability for bubbly flows in complex geometries using unstructured grids and an Euler--Lagrangian methodology. Two Lagrangian bubble models are considered:\ (i) the bubbles are treated as a dispersed phase in the carrier fluid, and individual bubbles are point particles governed by an equation for bubble motion and (ii) the force coupling method by \mbox{Maxey$\!$ \textit{et al.}}\ \mbox{[\textit{Fluid Dyn.\ Res.}, \textbf{32} (1997), 143-156]}. The evolution of the bubble radius (assuming spherical bubbles) is governed by the Rayleigh--Plesset equation and integrated using a Runge--Kutta integrator with adaptive time-stepping. The talk will discuss numerical issues and contrast results between the two methodologies. Numerical results ranging from the motion of individual bubbles in channels and around bodies to drag reduction by bubbles in turbulent channel flow will be presented.   

Diffuse-interface modeling of phase segregation in van der Waals fluids

We simulate phase separation in a van der Waals fluid that is deeply quenched into the unstable range of its phase diagram. Our theoretical approach follows the diffuse-interface model, where convection induced by phase change is accounted for via a Korteweg force, expressing the tendency of the demixing system to minimize its free energy. Spinodal decomposition patterns for critical and off-critical van der Waals fluids are studied numerically, revealing the scaling laws of the typical length scale and composition of single-phase microdomains, together with their dependence on the Reynolds number. Unlike phase separation of viscous binary mixtures, here local equilibrium is reached almost immediately after single-phase domains start to form. In addition, as predicted by scaling laws, such domains grow in time like $t^{2/3}$. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon. For a binary mixture of van der Waals fluids, we show simulations of Marangoni migration during phase separation in a temperature gradient. Our results reproduce the large-scale unidirectional convection observed in recent experiments.   

The Effect of Water Compressibility on a Rigid Body Movement in Two Phase Flow

The motion of a rigid body in a tube full of water-filled, initiated by a sudden release of highly pressurized air is simulated presuming the flow field as a two dimensional one. The effects of water compressibility on the body movement are investigated, comparing results based on the Fluent VOF model where water is treated as an incompressible medium with those from the presently developed VOF scheme. The present model considers compressibility of both air and water. The Fluent results show that the body moves farther and at higher speeds than the present ones. As time proceeds, the relative difference of speed and displacement between the two results drops substantially, after acoustic waves in water traverse and return the full length of the tube several times. To estimate instantaneous accelerations, however, requires implementation of the water compressibility effect as discrepancies between them do not decrease even after several pressure wave cycles. This work was supported by a research fund granted from Agency for Defense Development, South Korea.   

Two Phase Compressible Flow Fields in One Dimensional and Eulerian Grid Framework

Numerical investigation for two phase compressible flow fields of air-water in one dimensional tube are performed in the fixed Eulerian grid framework. Using an equation of states of Tait's type for a multiphase cell, the two phase compressible flow is modeled as equivalent single phase which is discretized using the Roe`s approximate Riemann solver, while the phase interface is captured via volume fractions of each phase. The most common problem found in the computational approaches in compressible multiphase flow is occurrence of the pressure oscillation at the phase interface. In order to suppress that phenomenon, tried are two approaches; a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The results show that the direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. This work was supported by a research fund granted from Agency for Defense Development, South Korea   

A moving mesh interface tracking method for multiphase flows with topological changes

A moving mesh interface tracking (MMIT) method with local mesh adaptations on tetrahedral elements was developed to simulate incompressible, immiscible multiphase flows with large deformation and topological changes. The interface is represented by triangle elements, and moves with the fluid velocity. The boundary conditions across the interface are implemented directly without any smoothing of the fluids' properties as the interface is zero thickness. Mesh adaptations including smoothing, coarsening and refining are applied locally to achieve computing efficiency as well as to maintain good mesh quality. In order to handle the challenges such as interface breakup and merging, mesh separation and mesh combination are employed. These two schemes are based on the conversion of elements in one liquid phase to anther fluid by changing the fluid properties of the cells in the separation or combination region. The newly created interface is usually ragged, so a local projection method is applied to smooth the interface. Simulations of droplet oscillations and droplet-pair collisions show that the method is accurate in simulating two-phase flow, and that the method has the potential to perform detailed investigations of liquid particles breakup and coalescence.