Radial Flow of Compressible Fluids Between Discs

1965 ◽  
Vol 16 (3) ◽  
pp. 282-288
Author(s):  
Tsung Yen Na
Keyword(s):  
Compressible Fluid ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Supersonic Flows ◽  
Compressible Fluids ◽  
One Dimensional ◽  
The One

SummaryNumerical solutions are obtained for the one-dimensional radial flow of a compressible fluid between parallel discs. A general discussion of the variations of pressure, density, velocity and temperature along the radius of the disc is then given. The present investigation covers both subsonic and supersonic flows, a range not previously covered in the literature.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

scholarly journals Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

1999 ◽  
Vol 396 ◽  
pp. 223-256 ◽  
Author(s):  
B. S. BROOK ◽  
S. A. E. G. FALLE ◽  
T. J. PEDLEY
Keyword(s):  
Shallow Water ◽  
Numerical Solutions ◽  
Godunov Method ◽  
Test Case ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
Collapsible Tubes ◽  
Highly Nonlinear ◽  
Pressure Area ◽  
The One

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

scholarly journals Two-dimensional oscillations in divergent jets of compressible fluid

1934 ◽  
Vol 145 (854) ◽  
pp. 52-71 ◽  
Keyword(s):  
Compressible Fluid ◽  
Radial Flow ◽  
Fluid Motion ◽  
Radial Distance ◽  
Two Dimensions ◽  
Common Point ◽  
Compressible Fluids ◽  
Fluid Density ◽  
Straight Lines ◽  
Steady Velocity

1. The problem of determining the possible modes of stationary oscillation for a compressible fluid, moving with a steady velocity which is not constant, usually presents great difficulties. One case which is to some extent amenable to analysis is that of uniform radial flow in two dimensions, where the undisturbed paths of the fluid particles are straight lines radiating from a common point or source. The term “source” is here used somewhat loosely, for in the solution which will be given it is found that the fluid density attains unreal values inside a certain circle having its centre at this common point. It is well known that in radial flow two systems of velocity are possible to a compressible fluid—namely, either (i) zero velocity at r = ∞, and an increasing but limited velocity as the radial distance from the source decreases ( i. e. , a modified “perfect fluid” motion); or (ii) the maximum possible velocity at infinity (corresponding with zero pressure and density), and a decreasing speed—also limited—as r decreases. This type of flow is peculiar to compressible fluids.

Verification of a One-Dimensional Two-Phase Flow Model of the Frontal Gap in Electrochemical Machining

1976 ◽  
Vol 98 (2) ◽  
pp. 431-437 ◽  
Author(s):  
F. Fluerenbrock ◽  
R. D. Zerkle ◽  
J. F. Thorpe
Keyword(s):  
Flow Model ◽  
Radial Flow ◽  
Electrochemical Machining ◽  
Equilibrium Conditions ◽  
Two Phase ◽  
One Dimensional ◽  
Supply Pressure ◽  
Theoretical Predictions ◽  
The One ◽  
Experimental Pressure

A set of six equations, which are based on the ECM model developed by Thorpe and Zerkle, can be solved numerically to yield the one-dimensional distributions of pressure, temperature, gas density, gap thickness, void fraction, and electrolyte velocity in the rectilinear ECM frontal gap under equilibrium conditions. The validity of the model, which also applies to radial flow geometries, is confirmed by comparing experimental pressure and gap profiles with theoretical predictions. It is shown that for a given set of operating parameters there is a minimum supply pressure below which no machining is possible. When machining steel with an aqueous NaCl electrolyte the deposition of a black smut (Fe(OH)2) occurs beyond a certain smut-free entrance length, which was experimentally found to be proportional to the inlet gap thickness.

scholarly journals FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

2007 ◽  
Vol 17 (04) ◽  
pp. 567-591 ◽  
Author(s):  
LIVIU I. IGNAT
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Continuous Model ◽  
Local Smoothing ◽  
Euler Approximation ◽  
One Dimensional ◽  
Fully Discrete ◽  
Backward Euler ◽  
The One

We consider fully discrete schemes for the one-dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular, Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent scheme for the nonlinear Schrödinger equation with nonlinearities which cannot be treated by energy methods.

General Solutions for Pistonlike Displacement of Compressible Fluids in Porous Media

1985 ◽  
Vol 107 (4) ◽  
pp. 523-526 ◽  
Author(s):  
S. H. Advani ◽  
J. S. Torok ◽  
J. K. Lee
Keyword(s):  
Coal Gasification ◽  
Compressible Fluids ◽  
Fracture Face ◽  
Underground Coal Gasification ◽  
Interface Motion ◽  
One Dimensional ◽  
Special Solutions ◽  
The One ◽  
Step Step ◽  
Constant Slope

Exact solutions for the one-dimensional problem of a compressible fluid having a time-dependent pressure at the source (fracture face) and displacing a compressible reservoir fluid are generated. Special solutions for various cases represented by step, step with constant slope front, and sinusoidal pressure variations at the fracture face are derived. Numerical results and trends for fluid interface motion are revealed for selected cases. The applicability of the presented solutions to hydraulic fracturing is discussed. In addition, response solutions for problems in reservoir mechanics, underground coal gasification, and nuclear waste management can be similarly investigated.

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