An exact solution for axial flow in cylindrically symmetric, steady‐state detonation in polytropic explosive with an arbitrary rate of decomposition

1994 ◽  
Vol 6 (3) ◽  
pp. 1357-1378 ◽  
Author(s):  
M. Cowperthwaite
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Axial Flow ◽  
Cylindrically Symmetric ◽  
Arbitrary Rate

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

scholarly journals Exact solution to the steady-state dynamics of a periodically modulated resonator

APL Photonics ◽  
2017 ◽  
Vol 2 (7) ◽  
pp. 076101 ◽  
Author(s):  
Momchil Minkov ◽  
Yu Shi ◽  
Shanhui Fan
Keyword(s):  
Exact Solution ◽  
Steady State

Drawing of Tubes

1980 ◽  
Vol 47 (4) ◽  
pp. 736-740 ◽  
Author(s):  
D. Durban
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Radial Flow ◽  
Material Behavior ◽  
Wall Friction ◽  
Flow Rule ◽  
Flow Conditions ◽  
Steady State Flow ◽  
Linear Hardening ◽  
Von Mises

The process of the tube drawing between two rough conical walls is analyzed within the framework of continuum plasticity. Material behavior is modeled as rigid/linear-hardening along with the von-Mises flow rule. Assuming a radial flow pattern and steady state flow conditions it becomes possible to obtain an exact solution for the stresses and velocity. Useful relations are derived for practical cases where the nonuniformity induced by wall friction is small. A few restrictions on the validity of the results are discussed.

Exact Dynamics in a Model of the Bimolecular Reaction A+B→ 0

1992 ◽  
Vol 290 ◽  
Author(s):  
Eric Clément ◽  
Patrick Leroux-Hugon ◽  
Leonard M. Sander
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Initial Conditions ◽  
Finite Size ◽  
Bimolecular Reaction ◽  
Reaction Model

AbstractWe have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.

The generalized Burgers and Zabolotskaya-Khokhlov equations

1994 ◽  
Vol 447 (1930) ◽  
pp. 253-270 ◽  
Keyword(s):  
Exact Solution ◽  
Plane Waves ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Compressive Wave ◽  
Similarity Reduction ◽  
Weakly Nonlinear ◽  
Cylindrically Symmetric ◽  
Generalized Burgers Equation ◽  
Long Time

A point transformation between forms of the generalized Burgers equation (g b e) first given by Cates (1989) is investigated. Applications include generalizations of Scott’s (1981) classification of long-time behaviour for compressive wave solutions of the GBE and the equivalence of the exponential and cylindrical forms of the GBE, yielding an exact solution for the exponential GBE. Applications to nonlinear diffractive acoustics are considered by using a similarity reduction of the dissipative Zabolotskaya-Khokhlov (dzk) equation (describing the evolution of nearly plane waves in a weakly nonlinear medium with allowance for transverse variation effects) onto the GBE. The result is that waves from parabolic sources may be described by the cylindrical GBE in the case of two dimensions, and by the spherical GBE in the three-dimensional, cylindrically symmetric case. Furthermore, results on the formation of shocks and caustics in the context of the ZK equation are presented, along with an exact solution to the DZK equation. Exact solutions with caustic singularities are studied, along with a possible mechanism for their control. Finally, results on the evolution of a shock approaching a caustic are given through the identification of a series of parameter regimes dependent on the diffusivity.

scholarly journals A type of Levi–Civita solution in modified Gauss–Bonnet gravity

2014 ◽  
Vol 92 (2) ◽  
pp. 173-176 ◽  
Author(s):  
M.E. Rodrigues ◽  
M.J.S. Houndjo ◽  
D. Momeni ◽  
R. Myrzakulov
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Perfect Fluid ◽  
Cosmic String ◽  
Coupling Parameter ◽  
Vacuum Solution ◽  
Einstein Gravity ◽  
Parameter Family ◽  
Bonnet Gravity ◽  
Cylindrically Symmetric

Herein we obtain an exact solution for cylindrically symmetric modified Gauss–Bonnet gravity. This metric is a generalization of the vacuum solution of Levi–Civita in general relativity. It describes an isotropic perfect fluid one-parameter family of the gravitational configurations, which can be interpreted as the exterior metric of a cosmic string. By setting the Gauss–Bonnet coupling parameter to zero, we recover the vacuum solution in the Einstein gravity as well.

scholarly journals Simulation of steady-state cuttings transport through a horizontal annulus channel

2019 ◽  
Vol 196 ◽  
pp. 00011 ◽  
Author(s):  
Yaroslav Ignatenko ◽  
Andrey Gavrilov ◽  
Oleg Bocharov ◽  
Roland May
Keyword(s):  
Steady State ◽  
Pressure Gradient ◽  
Yield Stress ◽  
Cross Section ◽  
Drilling Fluid ◽  
Drill Pipe ◽  
Axial Flow ◽  
Cuttings Transport ◽  
Rigid Spheres ◽  
Pipe Rotation

The current study is devoted to simulating cuttings transport by drilling fluid through a horizontal section of borehole with an annular cross section. Drill pipe rotates in fixed eccentric position. Steady-state flow is considered. Cuttings are rigid spheres with equal diameters. The carrying fluid is drilling mud with Herschel-Bulkley rheology. Suspension rheology depends on local shear rate and particles concentration. Continuous mixture model with algebraic equation for particles slipping velocity is used. Two hydrodynamic regimes are considered: axial flow without drill pipe rotation and with drill pipe rotation. In the case of axial flow was shown that increasing of power index n and consistency factor k increases pressure gradient and decreases cuttings concentration. Increasing of yield stress leads to increasing of pressure gradient and cuttings concentration. Cuttings concentration achieves constant value for high yield stress and not depends on it. Rotation of the drill pipe significantly changes the flow structure: pressure loss occurs and particles concentration decreases in the cross section. Two basic regimes of rotational flow are observed: domination of primary vortex around drill pipe and domination secondary vorticity structures. Transition between regimes leads to significant changes of flow integral parameters.

A Numerical Method for Heat Conduction Problems

1974 ◽  
Vol 96 (3) ◽  
pp. 307-312 ◽  
Author(s):  
M. J. Reiser ◽  
F. J. Appl
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Steady State ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Singular Integral ◽  
Integral Method ◽  
Two Dimensional ◽  
Convection Boundary ◽  
Steady State Heat

A singular integral method of numerical analysis for two-dimensional steady-state heat conduction problems with any combination of temperature, gradient, or convection boundary conditions is presented. Excellent agreement with the exact solution is illustrated for an example problem. The method is used to determine the solution for a fin bank with convection.

Casing Convective Heat Transfer Coefficient and Reference Freestream Temperature Determination Near an Axial Flow Turbine Rotor

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
C. Camci ◽  
B. Gumusel
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Transfer Coefficient ◽  
Axial Flow ◽  
Reference Temperature ◽  
Steady State Heat Transfer

The present study explains a steady-state method of measuring convective heat transfer coefficient on the casing of an axial flow turbine. The goal is to develop an accurate steady-state heat transfer method for the comparison of various casing surface and tip designs used for turbine performance improvements. The freestream reference temperature, especially in the tip gap region of the casing, varies monotonically from the rotor inlet to rotor exit due to work extraction in the stage. In a heat transfer problem of this nature, the definition of the freestream temperature is not as straightforward as constant freestream temperature type problems. The accurate determination of the convective heat transfer coefficient depends on the magnitude of the local freestream reference temperature varying in axial direction, from the rotor inlet to exit. The current study explains a strategy for the simultaneous determination of the steady-state heat transfer coefficient and freestream reference temperature on the smooth casing of a single stage rotating turbine facility. The heat transfer approach is also applicable to casing surfaces that have surface treatments for tip leakage control. The overall uncertainty of the method developed is between 5% and 8% of the convective heat transfer coefficient.

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