In order to treat strongly heated, forced gas flows at low Reynolds numbers in vertical circular tubes, the k-ε turbulence model of Abe, Kondoh, and Nagano (1994), developed for forced turbulent flow between parallel plates with the constant property idealization, has been successfully applied. For thermal energy transport, the turbulent Prandtl number model of Kays and Crawford (1993) was adopted. The capability to handle these flows was assessed via calculations at the conditions of experiments by Shehata (1984), ranging from essentially turbulent to laminarizing due to the heating. Predictions forecast the development of turbulent transport quantities, Reynolds stress, and turbulent heat flux, as well as turbulent viscosity and turbulent kinetic energy. Overall agreement between the calculations and the measured velocity and temperature distributions is good, establishing confidence in the values of the forecast turbulence quantities—and the model which produced them. Most importantly, the model yields predictions which compare well with the measured wall heat transfer parameters and the pressure drop.
Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow * Zhang Hong-Na(张红娜) a)b) , Li Feng-Chen(李凤臣) a) † , Cao Yang(曹 阳) a) , Kunugi Tomoaki a)b) , and Yu Bo(宇 波) c)
A gas-liquid interface involves complex physics along with unknown phenomena related to thermodynamics, electromagnetics, hydrodynamics, and heat and mass transfer. Each phenomenon has various characteristic time and space scales, which makes detailed understanding of the interfacial phenomena very complex. Therefore, modeling the gasliquid interface is a key issue for numerical research on multiphase flow. Currently, the continuum surface force (CSF) model is popular in modeling the gas-liquid interface in multiphase flow. However, the CSF model cannot treat the various chemical and physical phenomena at the gas-liquid interface because it is derived based only on mechanical energy balance and it assumes that the interface has no thickness. From certain experimental observations, bubble coalescence/repulsion was found to be related to a contamination at the interface.The present study developed a new gas-liquid interfacial model based on thermodynamics via a mathematical approach, assuming that the interface has a finite thickness like a thin fluid membrane. In particular, free energy, including an electrostatic potential due to the contamination at the interface, is derived based on a lattice gas model. Free energy is incorporated into the conventional Navier-Stokes equation as new terms using Chapman-Enskog expansion based on the multiscale concept. Using the Navier-Stokes equation with the free energy terms, we derived a new governing equation of fluid motion that characterizes mesoscopic scale phenomena. Finally, the new governing equation was qualitatively evaluated by simulating an interaction between two microbubbles in two dimensions while also accounting for electrostatic force.
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