Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Regression and Dimensional Analysis for Modeling Two‐Phase Flow

Numerical models describing multiphase flow phenomena are typically used to predict the displacement of water during the infiltration of nonaqueous phase liquids (NAPLs) into a groundwater system. In this paper, the applicability of regression and dimensional analysis to develop simple tools to bypass these time consuming numerical simulations is assessed. In particular, the infiltration of NAPL through a vertical, homogeneous soil column initially saturated with water is quantified. Two output variables defining the extent of infiltration were considered – the elevation of the NAPL front and the volume of NAPL which had entered the system. Dimensional analysis was initially performed to identify dimensionless terms associated with the underlying relations between these two output variables and the input variables (independent variables and system parameters). Artificial neural network techniques were then employed to develop regression equations for approximating the input–output relationships over a given domain. Application of these equations illustrated the interrelationships among capillary, buoyancy, and viscous forces driving the NAPL infiltration process.     

Computation of Gas–Dynamic Parameters and Heat Transfer in Supersonic Turbulent Separated Flows near Backward–Facing Steps

Computation results of plane turbulent flows in the vicinity of backward–facing steps with leeward–face angles = 8, 25, and 45° for Mach numbers M_infin = 3 and 4 are presented. The averaged Navier—Stokes equations supplemented by the Wilcox model of turbulence are used as a mathematical model. The boundary–layer equations were also used for the case of an attached flow ( = 8°). The computed and experimental distributions of surface pressure and skin friction, the velocity and pressure fields, and the heat–transfer coefficients are compared.     

Modeling Kinetic Interphase Mass Transfer for Two-Phase Flow in Porous Media Including Fluid–Fluid Interfacial Area

Interphase mass transfer in porous media takes place across fluid–fluid interfaces. At the field scale, this is almost always a kinetic process and its rate is highly dependent on the amount of fluid–fluid interfacial area. Having no means to determine the interfacial area, modelers usually either neglect kinetics of mass transfer and assume local equilibrium between phases or they estimate interfacial area using lumped parameter approaches (in DNAPL pool dissolution) or a dual domain approach (for air sparging). However, none of these approaches include a physical determination of interfacial area or accounts for its role for interphase mass transfer. In this work, we propose a new formulation of two-phase flow with interphase mass transfer, which is based on thermodynamic principles. This approach comprises a mass balance for each component in each phase and a mass balance for specific interfacial area. The system is closed by a relationship among capillary pressure, interfacial area, and saturation. We compare our approach to an equilibrium model by showing simulation results for an air–water system. We show that the new approach is capable of modeling kinetic interphase mass exchange for a two-phase system and that mass transfer correlates with the specific interfacial area. By non-dimensionalization of the equations and variation of Peclet and Damköhler number, we make statements about when kinetic interphase mass transfer has to be taken into account by using the new physically based kinetic approach and when the equilibrium model is a reasonable simplification.     

A Continuous–Discontinuous Approach to Simulate Heat Transfer in Fractured Media

A macroscopic framework to model heat transfer in materials and composites, subjected to physical degradation, is proposed. The framework employs the partition of unity concept and captures the change from conduction-dominated transfer in the initial continuum state to convection and radiation-dominated transfer in the damaged state. The underlying model can be directly linked to a mechanical cohesive zone model, governing the initiation and subsequent growth and coalescence of micro-cracks. The methodology proved to be applicable for quasi-static, periodic, and transient problems.     

Explicit Rate–Time Solutions for Modeling Matrix–Fracture Flow of Single Phase Gas in Dual-Porosity Media

One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255, 1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil). However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose, the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions. Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator.     

Modeling and simulation of severe slugging in air–water pipeline–riser systems

A mathematical model, numerical simulations and stability and flow regime maps corresponding to severe slugging in pipeline–riser systems, are presented. In the simulations air and water were used as flowing fluids. The mathematical model considers continuity equations for liquid and gas phases, with a simplified momentum equation for the mixture, neglecting inertia. A drift-flux model, evaluated for the local conditions in the riser, is used as a closure law. The developed model predicts the location of the liquid accumulation front in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. The numerical procedure is convergent for different nodalizations. A comparison is made with experimental results corresponding to a catenary riser, showing very good results for slugging cycle and stability and flow regime maps.     

Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations

We consider the nonlinear elliptic system

Behavior of Nonaqueous Phase Liquids in Fractured Porous Media under Two‐Phase Flow Conditions

After dense nonaqueous phase liquids (DNAPLs) travel downward through the subsurface, they typically come to rest on fractured bedrock or tight clay layers, which become additional pathways for DNAPL migration. DNAPLs trapped in fractures are continuous sources of groundwater contamination. To decide whether they can be left in place to dissolve or volatilize, or must be removed with active treatment, the movement of DNAPLs in fractured media must be understood at a fundamental level. This work presents numerical simulations of the movements of DNAPLs in naturally fractured media under twophase flow conditions. The flow is modeled using a multiphase network flow model, used to develop predictive capabilities for DNAPL flow in fractures. Capillary pressure–saturation–relative permeability curves are developed for twophase flow in fractures. Comparisons are made between the behavior in crystalline, almost impermeable rocks (e.g. granite) and more permeable rocks like sandstone, to understand the effects of the rock matrix on the displacement of the DNAPLs in the fracture. For capillarydominated flow, displacements occur as a sequence of jumps, as the invading phase overcomes the capillary pressure at downgradient apertures. Preferential channels for the displacement of nonaqueous phase are formed due to high fracture aperture in some regions.     

Kinetic Formulation for Systems of Two¶Conservation Laws and Elastodynamics

For scalar conservation laws, the kinetic formulation makes it possible to generate all the entropies from a simple kernel. We show how this concept replaces and simplifies greatly the concept of Young measures, avoiding the difficulties encountered when working in L ^p . The general construction of the two kinetic functions that generate the entropies of 2 × 2 strictly hyperbolic systems is also developed here. We show that it amounts to building a “universal” entropy, i.e., one that can be truncated by a “kinetic value” along Riemann invariants. For elastodynamics, this construction can be completed and specialized using the additional Galilean invariance. This allows a full characterization of convex entropies. It yields a kinetic formulation consisting of two semi-kinetic equations which, as usual, are equivalent to the infinite family of all the entropy inequalities. Accepted May 29, 2000?Published online November 16, 2000     

Heat transfer and fluid dynamics of air–water two-phase flow in micro-channels

Heat transfer, pressure drop, and void fraction were simultaneously measured for upward heated air–water non-boiling two-phase flow in 0.51 mm ID tube to investigate thermo–hydro dynamic characteristics of two-phase flow in micro-channels. At low liquid superficial velocity j_l frictional pressure drop agreed with Mishima–Hibiki’s correlation, whereas agreed with Chisholm–Laird’s correlation at relatively high j_l. Void fraction was lower than the homogeneous model and conventional empirical correlations. To interpret the decrease of void fraction with decrease of tube diameter, a relation among the void fraction, pressure gradient and tube diameter was derived. Heat transfer coefficient fairly agreed with the data for 1.03 and 2.01 mm ID tubes when j_l was relatively high. But it became lower than that for larger diameter tubes when j_l was low. Analogy between heat transfer and frictional pressure drop was proved to hold roughly for the two-phase flow in micro-channel. But satisfactory relation was not obtained under the condition of low liquid superficial velocity.     

Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed \(L^2\)-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger–Korteweg-de Vries systems.     

Unsteady Radiative–Convective Heat Transfer in a Flow Emitting‐Absorbing and Scattering Medium around an Ablating Plate

A conjugate problem of radiative–convective heat transfer in a turbulent hightemperature gasdisperse flow around a thermally thin ablating plate is considered. The plate experiences intense radiative heating by an external source, which is a blackbody. The temperature fields and the distributions of heat fluxes along the plate under unsteady conditions are calculated. The data gained make it possible to examine the effect of the Stark number and phasetransition heat in the plate material on the time evolution of the thermal state of the boundarylayer medium and the plate itself being heated by a hightemperature radiation source.     

Complex Attractors and Patterns in Reaction–Diffusion Systems

We consider semiflows generated by initial boundary value problems for reaction–diffusion systems. In these systems, reaction terms satisfy general conditions, which admit a transparent chemical interpretation. It is shown that the semiflows generated by these initial boundary value problems exhibit a complicated large time behavior. Any structurally stable finite dimensional dynamics (up to an orbital topological equivalence) can be realized by these semiflows by a choice of appropriate external sources and diffusion coefficients (nonlinear terms are fixed). Results can be applied to the morphogenesis and pattern formation problems.     

Integrated Carbon Sequestration–Geothermal Heat Recovery: Performance Comparison Between Open and Close Systems

Transport in Porous Media - In this paper, the lateral boundaries for a theoretical homogeneous, isotropic, horizontal, 3-dimensional sedimentary hot aquifer were prescribed by either unhindered...