Multidimensional Fluid Transients by Latticework

1980 ◽  
Vol 102 (2) ◽  
pp. 203-209 ◽  
Author(s):  
E. B. Wylie ◽  
V. L. Streeter
Keyword(s):  
Transient Flow ◽  
Three Dimensional ◽  
Low Velocity ◽  
Flow Equations ◽  
Flow Problems ◽  
Fluid Transients ◽  
Physical Response ◽  
The One ◽  
Line Elements ◽  
The Continuum

An evaluation of a discretized method of analysis for low-velocity two and three-dimensional transient fluid-flow problems is presented. The method assumes the continuum can be represented by a latticework of flow elements and that the physical response in the continuum can be determined by solving the one-dimensional transient flow equations in the line elements. The approach is explained, and validated by presenting comparisons between numerical and analytical hydrodynamic solutions.

scholarly journals Two and Three-Dimensional Fluid Transients

1968 ◽  
Vol 90 (4) ◽  
pp. 501-509 ◽  
Author(s):  
V. L. Streeter ◽  
E. B. Wylie
Keyword(s):  
Transient Flow ◽  
Three Dimensional ◽  
Low Velocity ◽  
Irregular Boundary ◽  
Flow Equations ◽  
Flow Problems ◽  
Fluid Transients ◽  
The One ◽  
Irregular Boundary Conditions ◽  
The Continuum

The paper presents an approach for the analysis of low-velocity two and three-dimensional transient fluid-flow problems. The method assumes the continuum can be represented by a latticework of piping elements and that motion in the continuum can be described by solving the one-dimensional transient flow equations in the piping elements. The approach offers the advantage of being able to handle unusual and irregular boundary conditions, fixed or moveable, but restricted to the limitation of low Mach number. Undesirable grid characteristics are identified and comparisons with known hydrodynamic solutions are presented.

Linearized Two-Dimensional Fluid Transients

1984 ◽  
Vol 106 (2) ◽  
pp. 227-232 ◽  
Author(s):  
E. B. Wylie
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Low Velocity ◽  
Flow Problems ◽  
Spatial Dimensions ◽  
Dimensional Space Time ◽  
Fluid Transients ◽  
Explicit Procedure ◽  
The One

A numerical analysis of low-velocity two-dimensional transient fluid flow problems is presented. The method is similar in concept to the one-dimensional method of characteristics, but does not follow the traditional characteristics theory for two spatial dimensions. Distinct paths are defined in the three-dimensional space-time domain along which compatibility equations are integrated. The explicit procedure is explained, and validated by comparisons with analytical solutions.

scholarly journals HEAT TRANSPORT IN A THREE-DIMENSIONAL SLAB GEOMETRY AND THE TEMPERATURE PROFILE OF INGEN-HAUSZ'S EXPERIMENT

2013 ◽  
Vol 27 (13) ◽  
pp. 1350057 ◽  
Author(s):  
SHILADITYA ACHARYA ◽  
KRISHNENDU MUKHERJEE
Keyword(s):  
Temperature Profile ◽  
Three Dimensional ◽  
Initial State ◽  
Slab Geometry ◽  
Similar Nature ◽  
One Dimensional ◽  
Different Temperatures ◽  
Dimensional Version ◽  
The One ◽  
The Continuum

We study the transport of heat in a three-dimensional, harmonic crystal of slab geometry whose boundaries and the intermediate surfaces are connected to stochastic, white noise heat baths at different temperatures. Heat baths at the intermediate surfaces are required to fix the initial state of the slab in respect of its surroundings. We allow the flow of energy fluxes between the intermediate surfaces and the attached baths and impose conditions that relate the widths of Gaussian noises of the intermediate baths. The radiated heat obeys Newton's law of cooling when intermediate baths collectively constitute the environment surrounding the slab. We show that Fourier's law holds in the continuum limit. We obtain an exponentially falling temperature profile from high to low temperature end of the slab and this very nature of the profile was already confirmed by Ingen-Hausz's experiment. Temperature profile of similar nature is also obtained in the one-dimensional version of this model.

An Analysis for Simulating Reservoir Performance Under Pressure Maintenance by Gas and/or Water Injection

1968 ◽  
Vol 8 (04) ◽  
pp. 331-340 ◽  
Author(s):  
K.H. Coats
Keyword(s):  
Gas Injection ◽  
Water Injection ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Gas Density ◽  
Flow Equations ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Three Phase ◽  
Compressibility Effects

Coats, K.H., Member AIME, The U. of Texas, Austin, Texas Abstract This paper describes a generalized analysis for calculating three-phase, three-dimensional flow in reservoirs. The analysis handles pressure maintenance type problems where fluid compressibility effects are negligible. A separate analysis for depletion type problems is described in another paper. The calculations consist of numerical, simultaneous solution of the three-flow equations using the iterative alternating direction technique of Douglas and Rachford. The mathematical details are fully described in the Appendix. The analysis is a computerized mathematical model that accounts for gravity, and capillary and viscous forces, and allows arbitrary reservoir heterogeneity, geometry, well locations and rates. A unique aspect of the analysis is the simultaneous solution of only as many difference equations in each grid block of the reservoir as there are mobile phases present. Thus, while the analysis handles phases present. Thus, while the analysis handles three-phase flow, the efficiency of the calculations (in a typical problem where three phases actually coexist only in a minor portion of the reservoir) is four to eight times greater than that of an analysis solving three equations in every block. The program may be applied to two-phase flow problems and to one-, two- or three-dimensional flow problems with negligible loss in efficiency, compared to programs specifically written for these sub cases. This paper also describes several applications of the analysis which illustrate some effects of gravitational and capillary forces in waterflooding of a heterogeneous reservoir. Another application indicates the utility of the program in simulating the fillup stage of water injection into a reservoir containing an initial free gas phase. Computer times and costs for the applications performed are given to indicate the current expense performed are given to indicate the current expense of three-dimensional, three-phase reservoir simulation. Introduction Under pressure maintenance by water and/or gas injection, fluid compressibility effects are generally negligible in producing operations. Although gas compressibility may be appreciable, the maintenance of pressure results in negligible time variation of gas density. In addition, the spatial variation of gas density is usually small in relation to the gas density itself. Producing schemes of pattern or flank waterflood and/or crestal gas injection, therefore, may be simulated with an analysis which presumes fluid incompressibility. presumes fluid incompressibility. The computing efficiency of a numerical model for simulating incompressible fluid flow is as much as 50 percent greater than that of a compressible flow model. Therefore, an analysis for numerically simulating three-dimensional flow of three incompressible, immiscible phases was developed and programmed. programmed. THE MODEL The equations describing three-phase, incompressible flow are the continuity equation and Darcy's law for each flowing phase. Combining these equations and introducing capillary pressures gives the three flow equations: ................ (1a) ............... (1b) SPEJ p. 331

Transonic and Supersonic Inviscid Flow Equations in 3-D Eccentric Nozzles

2002 ◽  
Author(s):  
Ali Reza Mazaheri ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Three Dimensional ◽  
Flow Simulation ◽  
Inviscid Flow ◽  
Analytic Solutions ◽  
Inviscid Flows ◽  
Flow Equations ◽  
The Stability ◽  
The One ◽  
Volume Method ◽  
Steady And Unsteady Flows

Three dimensional unsteady inviscid flows in convergent-divergent nozzles is of importance in understanding the stability of rockets and jet propulsion. A computer program for evaluating unsteady inviscid flow conditions in three-dimensional eccentric as well as concentric nozzles is developed. The program uses the cell-centered finite-volume method based on Roe’s approximate Riemann solver scheme. The flow simulation results in concentric circular nozzles are compared with the one-dimensional analytic solutions and the accuracy of the computation model is verified. The results for steady and unsteady flows through eccentric and concentric convergent-divergent nozzles are then presented. A range of exit to throat areas, pressure ratios, and inlet Mach number are considered.

Fish use of stage-specific fluvial habitats as refuge patches during a flood in a low-gradient Illinois stream

2005 ◽  
Vol 62 (7) ◽  
pp. 1540-1552 ◽  
Author(s):  
John S Schwartz ◽  
Edwin E Herricks
Keyword(s):  
Fish Habitat ◽  
Three Dimensional ◽  
Fish Density ◽  
Low Velocity ◽  
Habitat Classification ◽  
Point Bars ◽  
Ecological Importance ◽  
The One ◽  
Density And Biomass ◽  
Flow Stage

A stage-specific habitat classification scheme was developed emphasizing the ecological importance of habitat space as flow refugia for fish. Habitat units were based on planform and channel morphology and the resulting three-dimensional hydraulic patterns that form during floods. Fish were sampled in specific habitat patches using prepositioned areal electrofishing devices at two high-flow stages, near bankfull flow and one-half bankfull flow, during a flood. Fish were also sampled at baseflow immediately following the flood to compare changes in habitat use related to flow stage. During the bankfull stage, fish were found to use floodplain habitat units identified as vegetated point bars and concave-bank benches. During the one-half bank-full stage, fish density and biomass were greater in low-velocity habitat units identified as deflection eddies and expansion eddies than in the high-velocity habitat unit identified as the channel thalweg. Once flow returned to baseflow, fish density and biomass were greater in the main channel habitat units (pools, riffles, and glides) than in lateral habitat units identified as submerged point bars and lateral backwaters. This study provided a framework to quantify flow refugia in low-gradient streams, which is especially important in the restoration of anthropogenically disturbed watersheds that have lost habitat connectivity.

Dynamic Destruction of High Pressure Water to the Mining Floor Deformation

2011 ◽  
Vol 121-126 ◽  
pp. 3361-3365
Author(s):  
Wen Bin Sun ◽  
Wei Jia Guo ◽  
Jin Xiao Liu
Keyword(s):  
High Pressure ◽  
Transient Flow ◽  
Three Dimensional ◽  
Underground Water ◽  
Deep Well ◽  
Fracture Development ◽  
Destructive Action ◽  
Pressure Water ◽  
The One ◽  
The Impact

At present, the mines in our country gradually shift from the shallow mining to the deep mining, but the deep well floor is particularly serious hazard by high pressure underground water.This article considers the high pressure underground water as three-dimensional transient flow, sets up mechanical model by combining mechanical knowledge and to analyze the destructive action on floor from two aspects. On the one hand, researching the impact destruction of high pressure water at different positions of floor ; the other hand, to analyze mechanical function on fracture development from high pressure water.

Numerical Performances of Explicit Cartesian Methods for Compressible Moving-Boundary Flow Problems

2006 ◽  
Author(s):  
Kwen Hsu
Keyword(s):  
Moving Boundary ◽  
Transient Flow ◽  
Moving Boundaries ◽  
Piston Problem ◽  
Time Saving ◽  
Flow Problems ◽  
Grid Convergence ◽  
Background Mesh ◽  
Flow Evolution ◽  
The One

Cartesian method, which in some places is mentioned as Volume-Tracking Method, is one of the popular methods used in simulating transient flow problems involving complex moving boundaries. It has the advantage of being time-saving, efficient and robust for certain types of fluid-structure interaction problems. This method is featured by a Cartesian background Euler mesh discretizing the flow domain and a moving surface cutting through it. The most critical operation of this method is treating the cells cut by the moving boundaries accurately and stably. When the Cartesian methods are applied, the temporal discretization of the governing equations of the flow can be either implicit or explicit. For simulations cases in which time-accurately capturing wave propagation or flow evolution is essential, explicit approach still plays an important role among the researchers and currently available simulation codes. The current study is focused on the numerical performances of the explicit type of Cartesian methods when applied on the compressible flow cases. The accuracy of the simulation results, stability and grid-convergence problems resulted from a moving, impermeable boundary cutting through the background mesh are addressed. Example problems include the one-dimensional piston problem and the expanding sphere flow problems. In one case the sphere expands supersonically thus a spherical shock is generated. In another case it expands at a subsonic speed and works as a monople impulse noise source. To the best knowledge of the author, the problem of expanding-sphere generated acoustic impulse has not been reported anywhere else. Simple theoretical analyses are included and results of numerical experiments are reported.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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