Similarity Analysis of Condensing Flow in a Fluid-Driven Fracture

1988 ◽  
Vol 110 (3) ◽  
pp. 754-762 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson
Keyword(s):  
Single Phase ◽  
Dimensionless Parameter ◽  
Nuclear Explosion ◽  
Similarity Solutions ◽  
Pure Substance ◽  
Underground Nuclear Explosion ◽  
Governing Equations ◽  
Opening Displacement ◽  
One Dimensional ◽  
Fracture Length

Similarity solutions are derived for some fundamental problems of condensing flow in a hydraulically driven fracture. The governing equations describe one-dimensional homogeneous turbulent flow along a wedge-shaped hydraulic fracture in an elastic medium. The instantaneous fracture speed is determined as an analytical function of fracture length, material properties, process parameters, and a single eigenvalue, which is calculated by solving a system of ordinary differential equations for the variation of pressure, energy, velocity, and opening displacement along the fracture. Results are presented for abrupt condensation of a pure substance and for gradual condensation of air/water mixtures. The rate of condensation is controlled by the rate of heat transfer to the fracture wall, which depends upon a single dimensionless parameter. For small and large values of this parameter the present multiphase solutions are in agreement with previous solutions for single-phase flows of vapors and liquids. Although most of the results are presented in dimensionless form, some numerical examples are given for steam-driven fractures emanating from the cavity resulting from an underground nuclear explosion.

scholarly journals COMPUTATION OF ONE DIMENSIONAL ONE PHASE STEFAN PROBLEMS

2020 ◽  
Author(s):  
V.G. Naidu ◽  
P. Kanakadurga Devi
Keyword(s):  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Initial Time ◽  
Neumann Condition ◽  
Type Problem ◽  
Governing Equations ◽  
Accurate Analysis ◽  
One Dimensional ◽  
Stefan Problems

To design an efficient device or to calculate the performance of existing device requires an accurate analysis of parameters involved in the system. In this work, an efficient front tracking finite difference method is developed to solve one dimensional single phase moving boundary problem with Neumann condition. The basic difficulty apart from the need to find the moving boundary presented, that there is no domain for the first phase at initial time. This difficulty is handled by the age old principle of basic mathematics. Naturally, giving symbolic names to the unknowns by modelling the problem, governing equations are developed with the conditions of the Stefan type problem, solved it and compared the obtained solutions with existing results wherever possible.

Freezing Flow in a Subcooled Permeable Medium

1992 ◽  
Vol 114 (4) ◽  
pp. 1036-1041 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson
Keyword(s):  
Freezing Point ◽  
Freezing Temperature ◽  
Similarity Solutions ◽  
Inlet Temperature ◽  
Governing Equations ◽  
Phase Zone ◽  
Two Phase ◽  
Liquid Zone ◽  
One Dimensional ◽  
Order Of Magnitude

Analytical similarity solutions are derived for the problem of transient one-dimensional flow and freezing of a liquid in an initially dry permeable half-space. The structure of the flow consists of three regions: a liquid zone in which the temperature decreases to the freezing temperature, a central two-phase zone where the temperature is at the freezing point, and a leading gas-filled region in which the temperature is nearly undisturbed. The propagation velocity of this intrusion is determined as a function of the subcooling, latent heat, and other process parameters. As the inlet temperature approaches the freezing temperature, the governing equations admit a pair of solutions having propagation velocities that sometimes differ by more than an order of magnitude.

Geologic effects of the Rainier underground nuclear explosion : a summary progress report of U.S. Geological Survey investigations

1959 ◽  
Author(s):  
William H. Diment ◽  
V.R. Wilmarth ◽  
R.E. Wilcox ◽  
Alfred Clebsch ◽  
G.E. Manger ◽  
...  
Keyword(s):  
Nuclear Explosion ◽  
Progress Report ◽  
Geological Survey ◽  
Underground Nuclear Explosion

Design and Research of Flat Micro Heat Pipe with Glass Fiber Wick

2011 ◽  
Vol 483 ◽  
pp. 603-606
Author(s):  
Tian Han ◽  
Xiao Wei Liu ◽  
Chao Wang
Keyword(s):  
Glass Fiber ◽  
Heat Pipe ◽  
Experimental Testing ◽  
Governing Equations ◽  
Maximum Heat ◽  
One Dimensional ◽  
Micro Heat Pipe ◽  
Wick Structure

A kind of flat micro heat pipe with glass fiber wick structure is designed and fabricated. The structure of the wick is presented and also the excellence of the structure is described. For the glass fiber wick, the maximum heat transports is calculated by one-dimensional steady governing equations. Experimental testing is performed for the fabricated micro heat pipe in vacuum. The testing results is presented and analyzed.

Two-point similarity in temporally evolving plane wakes

2007 ◽  
Vol 577 ◽  
pp. 287-307 ◽  
Author(s):  
D. EWING ◽  
W. K. GEORGE ◽  
M. M. ROGERS ◽  
R. D. MOSER
Keyword(s):  
Large Scale ◽  
Single Point ◽  
Similarity Solutions ◽  
Similarity Analysis ◽  
Governing Equations ◽  
Large Scale Structures ◽  
Rate Dependent ◽  
Dependent Parameter ◽  
Scale Structures ◽  
Point Velocity

The governing equations for the two-point correlations of the turbulent fluctuating velocity in the temporally evolving wake were analysed to determine whether they could have equilibrium similarity solutions. It was found that these equations could have such solutions for a finite-Reynolds-number wake, where the two-point velocity correlations could be written as a product of a time-dependent scale and a function dependent only on similarity variables. It is therefore possible to collapse the two-point measures of all the scales of motions in the temporally evolving wake using a single set of similarity variables. As in an earlier single-point analysis, it was found that the governing equations for the equilibrium similarity solutions could not be reduced to a form that was independent of a growth-rate dependent parameter. Thus, there is not a single ‘universal’ solution that describes the state of the large-scale structures, so that the large-scale structures in the far field may depend on how the flow is generated.The predictions of the similarity analysis were compared to the data from two direct numerical simulations of the temporally evolving wakes examined previously. It was found that the two-point velocity spectra of these temporally evolving wakes collapsed reasonably well over the entire range of scales when they were scaled in the manner deduced from the equilibrium similarity analysis. Thus, actual flows do seem to evolve in a manner consistent with the equilibrium similarity solutions.

Radioecological studies at the Kraton-3 underground nuclear explosion site in 1978–2007: a review

2009 ◽  
Vol 100 (12) ◽  
pp. 1092-1099 ◽  
Author(s):  
V. Ramzaev ◽  
A. Mishin ◽  
V. Golikov ◽  
T. Argunova ◽  
V. Ushnitski ◽  
...  
Keyword(s):  
Nuclear Explosion ◽  
Underground Nuclear Explosion

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

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