Lagrangian Refined Kolmogorov Similarity Hypothesis for Gradient Time-evolution in Turbulent Flows

We study the time evolution of velocity and pressure gradients in isotropic turbulence, by quantifying their decorrelation time scales as one follows fluid particles in the flow. The Lagrangian analysis uses data in a public database generated using direct numerical simulation of the Naiver-Stokes equations, at a Reynolds number 430. It is confirmed that when averaging over the entire domain, correlation functions decay on timescales on the order of the mean Kolmogorov turnover time scale, computed from the globally averaged rate of dissipation and viscosity. However, when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales. Remarkably, excellent collapse of the auto-correlation functions is recovered when using the `local Kolmogorov time-scale' defined using the locally averaged, rather than the global, dissipation-rate. This provides new evidence for the validity of Kolmogorov's Refined Similarity Hypothesis, but from a Lagrangian viewpoint that provides a natural frame to describe the dynamical time evolution of turbulence.Comment: 4 Pages, 4 figure

Study on coalescence dynamics of unequal-sized microbubbles captive on solid substrate

The dynamics of bubble coalescence are of importance for a number of industrial processes, in which the size inequality of the parent bubbles plays a significant role in mass transport, topological change and overall motion. In this study, coalescence of unequal-sized microbubbles captive on a solid substrate was observed from cross-section view using synchrotron high-speed imaging technique and a microfluidic gas generation device. The bridging neck growth and surface wave propagation at the early stage of coalescence were investigated by experimental and numerical methods. The results show that theoretical half-power-law of neck growth rate is still valid when viscous effect is neglected. However, the inertial-capillary time scale is associated with the initial radius of the smaller parent microbubble. The surface wave propagation rate on the larger parent microbubble is proportional to the inertial-capillary time scale

Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence

The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depend on the joint action of the self-streching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (i) Gaussian, (ii) Multifractal and (iii) Minimal Turnover Lagrangian Map (MTLM) incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effects. However, we show that the local effects appear to be the most important ones: by assuming that the pressure Hessian is local in space, an expression in terms of the Hessian of the second invariant Q of the velocity gradient tensor can be obtained. This term is found to be well correlated with the true pressure Hessian both in terms of eigenvalue magnitudes and eigenvector alignments.Comment: 10 pages, 4 figures, minor changes, final version, published in Phys. Fluid

Spatial and Temporal Scaling of Unequal Microbubble Coalescence

We numerically study coalescence of air microbubbles in water, with density ratio 833 and viscosity ratio 50.5, using lattice Boltzmann method. The focus is on the effects of size inequality of parent bubbles on the interfacial dynamics and coalescence time. Twelve cases, varying the size ratio of large to small parent bubble from 5.33 to 1, are systematically investigated. The “coalescence preference,” coalesced bubble closer to the larger parent bubble, is well observed and the captured power-law relation between the preferential relative distance χ and size inequality γ, math formula, is consistent to the recent experimental observations. Meanwhile, the coalescence time also exhibits power-law scaling as math formula, indicating that unequal bubbles coalesce faster than equal bubbles. Such a temporal scaling of coalescence on size inequality is believed to be the first-time observation as the fast coalescence of microbubbles is generally hard to be recorded through laboratory experimentation

Understanding Microbubble Coalescence Using High-Speed Imaging and Lattice Boltzmann Method Simulation

poster abstractMicrobubble coalescence is one of the important research areas of bubble dynamics. The purpose of this research is to seek deeper understanding and relative mathematical relation on microbubble coalescence. To fulfill that, we conducted both experiments and simulations. For the part of experiment, we fabricated a microfluidic gas generator with better performance leading corresponding fluidic chemical reaction. After that we utilized ultrafast synchrotron X-ray imaging facility at the Advanced Photon Source of Argonne National Laboratory to capture the gas generating and microbubble merging phenomena using high speed imaging. These experiments show how the microbubbles with the same ratio contact and merge in the reaction channel and different concentration of reactants. As for the part of simulation, we lead the simulation basing on lattice Boltzmann method to simulate microbubble coalescence in water with unequal diameter ratio. Focuses are on the effects of size inequality of parent bubbles on the coalescence geometry and time. The “coalescence preference” of coalesced bubble closer to the larger parent bubble is well captured. A power-law relation between the preferential relative distance and size inequality is consistent to the recent experimental observations. Meanwhile, the coalescence time also exhibits power-law scaling, indicating that unequal bubbles coalesce faster than equal bubbles

Spatial and Temporal Scaling of Unequal Microbubble Coalescence

poster abstractWe numerically study coalescence of air microbubble in water, with density ratio 833 and viscosity ratio 50.5, using lattice Boltzmann method (LBM). Focuses are on the effects of size inequality of parent bubbles on the coalescence geometry and time and underlying dynamics of unequal microbubble coalescence. Twelve cases, varying the size ratio of large to small parent bubble γ from 5.33 to 1, are systematically investigated. The “coalescence preference” of coalesced bubble closer to the larger parent bubble is well captured. A power-law relation between the preferential relative distance χ and size inequality γ as χ ∼ γ−2.079 is consistent to the recent experimental observations. Meanwhile, the coalescence time also exhibits power-law scaling as T ∼ γ−0.7, implying that unequal bubbles coalesce faster than equal bubbles. Such a time scaling of coalescence on size inequality is believed the first-time observation as the fast coalescence of microbubbles is generally hard to be recorded through laboratory experimentation

Lattice Boltzmann equation simulations of turbulence, mixing, and combustion

We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions are developed. Simulations of initially non-premixed mixtures yield scalar probability distribution functions that are in good agreement with numerical data obtained from Navier-Stokes (NS) equation based computation. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. The second study involves direct numerical simulation (DNS) and large-eddy simulation (LES) of decaying homogenous isotropic turbulence (HIT) with and without frame rotation. Three categories of simulations are performed: (i) LBE-DNS in both inertial and rotating frames; (ii) LBE-LES in inertial frame; (iii) Comparison of the LBE-LES vs. NS-LES. The LBE-DNS results of the decay exponents for kinetic energy k and dissipation rate ε, and the low wave-number scaling of the energy spectrum agree well with established classical results. The LBE-DNS also captures rotating turbulence physics. The LBE-LES accurately captures low-wave number scaling, energy decay and large scale structures. The comparisons indicate that the LBE-LES simulations preserve flow structures somewhat more accurately than the NS-LES counterpart. In the third study, we numerically investigate the near-field mixing features in low aspect-ratio (AR) rectangular turbulent jets (RTJ) using the LBE method. We use D3Q19 multiple-relaxation-time (MRT) LBE incorporating a subgrid Smagorinsky model for LES. Simulations of four jets which characterized by AR, exit velocity, and Reynolds number are performed. The investigated near-field behaviors include: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) Spanwise and lateral profiles of MSV; (3) Half-velocity width development and MSV contours; and (4) Streamwise turbulence intensity distribution and spanwise profiles of streamwise turbulence intensity. The computations are compared against experimental data and the agreement is good. We capture both unique features of RTJ: the saddle-back spanwise profile of MSV and axis-switching of long axis from spanwise to lateral direction. Overall, this work serves to establish the feasibility of the LBE method as a viable tool for computing mixing, combustion, and turbulence

VOLUMETRIC LATTICE BOLTZMANN SIMULATION FOR BLOOD FLOW IN AORTA ARTERY PUMPED THROUGH AORTIC HEART VALVE

poster abstractComplicated moving boundaries pose a major challenge in compu-tational fluid dynamics for complex flows, especially in the biomechan-ics of both blood flow in the cardiovascular system and air flow in the respiratory system where the compliant nature of the vessels can have significant effects on the flow rate and wall shear stress. We develop an innovative approach to treat arbitrarily moving boundaries in Lat-tice Boltzmann Method (LBM) using a volumetric lattice Boltzmann representation, which distributes particles in fluid lattice cells. A volu-metric bounce-back procedure is applied in the streaming step while momentum exchange between the fluid and moving solid boundary are accounted for in the collision step. Additional boundary-induced migra-tion is introduced to conserve fluid mass as the boundary moves across fluid cells. We use the volumetric LBM to simulate blood flow in aorta pumped from heart focusing on the flow rate, flow structure, pressure distribution within the aorta for different heart pumping con-ditions. For validation, the volumetric LBM is compared with Navier-Stokes computation and good agreements are achieved. We study the flow dynamics within the aorta in the cardiac cycle (systole and diasto-le) through alternatively opening and closing the inlet boundary to mimic the heart pumping mechanism