A front-tracking method for the computations of multiphase flow

The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

https://ntrs.nasa.gov/api/citations/20030112277/downloads/20030112277.pdf

Algorithms for the fractional calculus: A selection of numerical methods

Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations, of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation of bubble pairs have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical methods used for direct numerical simulations of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, and then discuss studies of bubbles in periodic domains, along with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.

https://assets.cambridge.org/97805217/82401/frontmatter/9780521782401_frontmatter.pdf

Direct Numerical Simulations of Gas-Liquid Multiphase Flows

The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. DOI: 10.1115/1.4000563

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

A Volume of Fluid Based Method for Fluid Flows with Phase Change

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach

The quasi-static viscoelastic response of polymeric materialsis investigated utilizing constitutive models based on fractionalcalculus Time-based fractional calculus analysis techniques areemphasized Analytic solutions to quasi-static boundary value problemsin which the viscoelastic behavior is characterized by thefour-parameter fractional calculus-based solid model are given Varioussets of data from the literature are fit with existing and newfractional calculus-based constitutive equations

Samuel W. J. Welch

Papers

A Volume of Fluid Based Method for Fluid Flows with Phase Change

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach

Application of Time-Based Fractional Calculus Methods to Viscoelastic Creep and Stress Relaxation of Materials

Direct simulation of vapor bubble growth

Local simulation of two-phase flows including interface tracking with mass transfer