Axisymmetric Unsteady Droplet Vaporization and Gas Temperature Distribution

1989 ◽  
Vol 111 (2) ◽  
pp. 487-494 ◽  
Author(s):  
S. K. Lee ◽  
T. J. Chung
Keyword(s):  
Gas Phase ◽  
Gas Temperature ◽  
The Finite Element Method ◽  
Grid Spacing ◽  
Droplet Model ◽  
Time Step ◽  
Two Phase ◽  
Droplet Vaporization ◽  
Droplet Liquid ◽  
Injection Pulse

Droplet vaporization and temperature distributions of axisymmetric unsteady sprays are investigated. The so-called discrete droplet model of two-phase flows, often known as the Eulerian–Lagrangian method, is used. Calculations are carried out with Eulerian coordinates using finite elements for the gas phase and the method of characteristics using the second-order Runge–Kutta scheme for the droplet liquid phase. The sensitivity of the numerical results to changes in time step, injection pulse time, grid spacing, and number of droplet characteristics is examined. Through a simple example, it is shown that applications of the finite element method to more complicated problems appear to be promising.

Calculation of Two-Phase Flow in Gas Turbine Combustors

1995 ◽  
Vol 117 (4) ◽  
pp. 695-703 ◽  
Author(s):  
A. K. Tolpadi
Keyword(s):  
Gas Turbine ◽  
Gas Phase ◽  
High Power ◽  
Liquid Droplet ◽  
Frame Of Reference ◽  
Curvilinear Coordinates ◽  
Combustion Model ◽  
Gas Temperature ◽  
Two Phase ◽  
Phase Calculation

A method is presented for computing steady two-phase turbulent combusting flow in a gas turbine combustor. The gas phase equations are solved in an Eulerian frame of reference. The two-phase calculations are performed by using a liquid droplet spray combustion model and treating the motion of the evaporating fuel droplets in a Lagrangian frame of reference. The numerical algorithm employs nonorthogonal curvilinear coordinates, a multigrid iterative solution procedure, the standard k-ε turbulence model, and a combustion model comprising an assumed shape probability density function and the conserved scalar formulation. The trajectory computation of the fuel provides the source terms for all the gas phase equations. This two-phase model was applied to a real piece of combustion hardware in the form of a modern GE/SNECMA single annular CFM56 turbofan engine combustor. For the purposes of comparison, calculations were also performed by treating the fuel as a single gaseous phase. The effect on the solution of two extreme situations of the fuel as a gas and initially as a liquid was examined. The distribution of the velocity field and the conserved scalar within the combustor, as well as the distribution of the temperature field in the reaction zone and in the exhaust, were all predicted with the combustor operating both at high-power and low-power (ground idle) conditions. The calculated exit gas temperature was compared with test rig measurements. Under both low and high-power conditions, the temperature appeared to show an improved agreement with the measured data when the calculations were performed with the spray model as compared to a single-phase calculation.

A Review of Droplet Dynamics and Vaporization Modeling for Engineering Calculations

1994 ◽  
Author(s):  
F. Peng ◽  
S. K. Aggarwal
Keyword(s):  
Gas Phase ◽  
Laboratory Experiments ◽  
Physical Processes ◽  
Two Phase ◽  
Droplet Motion ◽  
Droplet Dynamics ◽  
Droplet Vaporization ◽  
Drag And Lift ◽  
Made In ◽  
Flow Nonuniformity

The present paper reviews the methodologies for representing the droplet motion and vaporization history in two-phase flow computations. The focus is on the use of droplet models that are realistic in terms of their efficient implementation in comprehensive spray simulations, representation of important physical processes, and applicability under a broad range of conditions. The methodologies available at present to simulate droplet motion in complex two-phase flows may be broadly classified into two categories. First one is based on the modified BBO equation. This approach is more comprehensive, but requires modifications and/or correlations at higher droplet Reynolds number. Second approach aims at developing correlations, using detailed numerical simulations or laboratory experiments, for the effects of flow nonuniformity and droplet relative acceleration on the instantaneous drag and lift coefficients. Recent advances made in the droplet vaporization models are also discussed. The advanced vaporization models include the effects of transient liquid heating, gas-phase convection, and variable thermophysical properties. All of these models are discussed, and recommendations are made for their inclusion in comprehensive two-phase computations.

scholarly journals Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation

2013 ◽  
Vol 719 ◽  
pp. 230-267 ◽  
Author(s):  
Senthilkumaran Radhakrishnan ◽  
Josette Bellan
Keyword(s):  
Gas Phase ◽  
Single Phase ◽  
Independent Solution ◽  
Phase Flow ◽  
Grid Spacing ◽  
Single Phase Flow ◽  
Two Phase ◽  
Eddy Simulation ◽  
Filter Width ◽  
Spacing Ratio

AbstractPredictions from conventional large-eddy simulation (LES) are known to be grid-spacing and spatial-discretization-order dependent. In a previous article (Radhakrishnan & Bellan, J. Fluid Mech., vol. 697, 2012a, pp. 399–435), we reformulated LES for compressible single-phase flow by explicitly filtering the nonlinear terms in the governing equations so as to render the solution grid-spacing and discretization-order independent. Having shown in Radhakrishnan & Bellan (2012a) that the reformulated LES, which we call EFLES, yields grid-spacing-independent and discretization-order-independent solutions for compressible single-phase flow, we explore here the potential of EFLES for evaporating two-phase flow where the small scales have an additional origin compared to single-phase flow. Thus, we created a database through direct numerical simulation (DNS) that when filtered serves as a template for comparisons with both conventional LES and EFLES. Both conventional LES and EFLES are conducted with two gas-phase SGS models; the drop-field SGS model is the same in all these simulations. For EFLES, we also compared simulations performed with the same SGS model for the gas phase but two different drop-field SGS models. Moreover, to elucidate the influence of explicit filtering versus gas-phase SGS modelling, EFLES with two drop-field SGS models but no gas-phase SGS models were conducted. The results from all these simulations were compared to those from DNS and from the filtered DNS (FDNS). Similar to the single-phase flow findings, the conventional LES method yields solutions which are both grid-spacing and spatial-discretization-order dependent. The EFLES solutions are found to be grid-spacing independent for sufficiently large filter-width to grid-spacing ratio, although for the highest discretization order this ratio is larger in the two-phase flow compared to the single-phase flow. For a sufficiently fine grid, the results are also discretization-order independent. The absence of a gas-phase SGS model leads to build-up of energy near the filter cut-off indicating that while explicit filtering removes energy above the filter width, it does not provide the correct dissipation at the scales smaller than this width. A wider viewpoint leads to the conclusion that although the minimum filter-width to grid-spacing ratio necessary to obtain the unique grid-independent solution might be different for various discretization-order schemes, the grid-independent solution thus obtained is also discretization-order independent.

Numerical modeling of the influence of bubbles on flow and heat transfer in the descending gas-liquid flow in a pipe

2012 ◽  
Vol 9 (1) ◽  
pp. 131-135
Author(s):  
M.A. Pakhomov
Keyword(s):  
Heat Transfer ◽  
Gas Phase ◽  
Liquid Flow ◽  
Bubble Diameter ◽  
Gas Content ◽  
Two Phase ◽  
Eulerian Description ◽  
Flow And Heat Transfer ◽  
Gas Liquid Flow ◽  
The Mathematical Model

The paper presents the results of modeling the dynamics of flow, friction and heat transfer in a descending gas-liquid flow in the pipe. The mathematical model is based on the use of the Eulerian description for both phases. The effect of a change in the degree of dispersion of the gas phase at the input, flow rate, initial liquid temperature and its friction and heat transfer rate in a two-phase flow. Addition of the gas phase causes an increase in heat transfer and friction on the wall, and these effects become more noticeable with increasing gas content and bubble diameter.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Effect of Particle Residence Time on Particle Dispersion in a Plane Mixing Layer

1993 ◽  
Vol 115 (4) ◽  
pp. 751-759 ◽  
Author(s):  
Tsuneaki Ishima ◽  
Koichi Hishida ◽  
Masanobu Maeda
Keyword(s):  
Gas Phase ◽  
Residence Time ◽  
Time Scale ◽  
Characteristic Time ◽  
Mixing Layer ◽  
Particle Dispersion ◽  
Laser Doppler Velocimeter ◽  
Characteristic Time Scale ◽  
Two Phase ◽  
Particle Residence Time

A particle dispersion has been experimentally investigated in a two-dimensional mixing layer with a large relative velocity between particle and gas-phase in order to clarify the effect of particle residence time on particle dispersion. Spherical glass particles 42, 72, and 135 μm in diameter were loaded directly into the origin of the shear layer. Particle number density and the velocities of both particle and gas phase were measured by a laser Doppler velocimeter with modified signal processing for two-phase flow. The results confirmed that the characteristic time scale of the coherent eddy apparently became equivalent to a shorter characteristic time scale due to a less residence time. The particle dispersion coefficients were well correlated to the extended Stokes number defined as the ratio of the particle relaxation time to the substantial eddy characteristic time scale which was evaluated by taking account of the particle residence time.

A Developed Numerical Method for Turbulent Unsteady Fluid Flow in Two-Phase Systems with Moving Interface

2017 ◽  
Vol 14 (06) ◽  
pp. 1750063 ◽  
Author(s):  
A. M. Hegab ◽  
S. A. Gutub ◽  
A. Balabel
Keyword(s):  
Numerical Model ◽  
Gas Phase ◽  
Level Set ◽  
The Body ◽  
Phase System ◽  
Computational Domain ◽  
Two Phase ◽  
Moving Interface ◽  
Level Set Function ◽  
Gas System

This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents the surface and the body forces as boundary value conditions on the interface. The adapted approaches enable accurate modeling of fluid flows driven by either body or surface forces. The moving interface is tracked and captured using the level set function that initially defined for both fluids in the computational domain. To asses the developed numerical model and its versatility, a selection of different unsteady test cases including oscillation of a capillary wave, sloshing in a rectangular tank, the broken-dam problem involving different density fluids, simulation of air/water flow, and finally the moving interface between the solid and gas phases of solid rocket propellant combustion were examined. The latter case model allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady nonuniform regression of either liquid or the propellant solid surfaces. The propagation of the unsteady nonplanar regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The computational results demonstrate a remarkable capability of the developed numerical model to predict the dynamical characteristics of the liquid–gas and solid–gas flows, which is of great importance in many civilian and military industrial and engineering applications.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

Numerical Study of Bicomponent Droplet Vaporization in a High Pressure Environment

1996 ◽  
Author(s):  
J. Stengele ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Gas Phase ◽  
Numerical Study ◽  
Droplet Evaporation ◽  
Single Component ◽  
Vapor Concentration ◽  
Diffusion Limit ◽  
Evaporation Process ◽  
Droplet Vaporization

The understanding of multicomponent droplet evaporation in a high pressure and high temperature gas is of great importance for the design of modern gas turbine combustors, since the different volatilities of the droplet components affect strongly the vapor concentration and, therefore, the ignition and combustion process in the gas phase. Plenty of experimental and numerical research is already done to understand the droplet evaporation process. Until now, most numerical studies were carried out for single component droplets, but there is still lack of knowledge concerning evaporation of multicomponent droplets under supercritical pressures. In the study presented, the Diffusion Limit Model is applied to predict bicomponent droplet vaporization. The calculations are carried out for a stagnant droplet consisting of heptane and dodecane evaporating in a stagnant high pressure and high temperature nitrogen environment. Different temperature and pressure levels are analyzed in order to characterize their influence on the vaporization behavior. The model employed is fully transient in the liquid and the gas phase. It accounts for real gas effects, ambient gas solubility in the liquid phase, high pressure phase equilibrium and variable properties in the droplet and surrounding gas. It is found that for high gas temperatures (T = 2000 K) the evaporation time of the bicomponent droplet decreases with higher pressures, whereas for moderate gas temperatures (T = 800 K) the lifetime of the droplet first increases and then decreases when elevating the pressure. This is comparable to numerical results conducted with single component droplets. Generally, the droplet temperature increases with higher pressures reaching finally the critical mixture temperature of the fuel components. The numerical study shows also that the same tendencies of vapor concentration at the droplet surface and vapor mass flow are observed for different pressures. Additionally, there is almost no influence of the ambient pressure on fuel composition inside the droplet during the evaporation process.

Experimental Determination of Statistical Properties of Two-Phase Turbulent Motion

1960 ◽  
Vol 82 (3) ◽  
pp. 609-621 ◽  
Author(s):  
S. L. Soo ◽  
H. K. Ihrig ◽  
A. F. El Kouh
Keyword(s):  
Gas Phase ◽  
Tracer Diffusion ◽  
Statistical Properties ◽  
Solid Particles ◽  
Turbulent Motion ◽  
Two Phase ◽  
Gaseous State ◽  
Diffusion Technique ◽  
And Diffusion

Experimental methods for the determination of certain statistical properties of turbulent conveyance and diffusion of solid particles in a gaseous state are presented. Methods include a tracer-diffusion technique for the determination of gas-phase turbulent motion and a photo-optical technique for the determination of motion of solid particles. Results are discussed and compared with previous analytical results.

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