The initiation of detonation from general non-uniformly distributed initial conditions

1995 ◽  
Vol 353 (1702) ◽  
pp. 173-203 ◽  
Keyword(s):  
Initial Velocity ◽  
High Speed ◽  
Mass Concentration ◽  
Initial Conditions ◽  
Fluid Particle ◽  
Time Dependent ◽  
Hot Gas ◽  
Velocity Pressure ◽  
Reaction Wave ◽  
Particle Paths

The chemical evolution of a hot gas subject to initial non-uniformities in velocity, pressure, temperature and reactant mass concentration is studied for moderate activation energies. It is demonstrated that such initial non-uniformities generate gradients in the distribution of chemical ignition times for each fluid particle, resulting in the creation of a high-speed, shockless reaction wave. If these gradients are sufficiently large, a transition from the high speed reaction wave to a strong detonation occurs. Time-dependent generalizations of the spontaneous flame concept, where the evolution of each fluid particle is determined by integration along particle paths only, are derived for initial velocity and pressure disturbances under the assumption of slowly varying initial disturbances. The unsteady structure of the high-speed reaction wave arising due to reaction from initial non-uniformities is investigated for the moderate activation energy used.

Stability of one-dimensional systems of colliding particles

1976 ◽  
Vol 13 (1) ◽  
pp. 155-158
Author(s):  
Alan F. Karr
Keyword(s):  
Initial Velocity ◽  
Initial Conditions ◽  
Random Measure ◽  
Initial Position ◽  
Dimensional System ◽  
Poisson Random Measure ◽  
Initial Particle ◽  
One Dimensional ◽  
Stability Theorems ◽  
Particle Paths

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.

Stability of one-dimensional systems of colliding particles

1976 ◽  
Vol 13 (01) ◽  
pp. 155-158
Author(s):  
Alan F. Karr
Keyword(s):  
Initial Velocity ◽  
Initial Conditions ◽  
Random Measure ◽  
Initial Position ◽  
Dimensional System ◽  
Poisson Random Measure ◽  
Initial Particle ◽  
One Dimensional ◽  
Stability Theorems ◽  
Particle Paths

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals High-Speed Video Analysis of the Process Stability in Plasma Spraying

2021 ◽  
Author(s):  
K. Bobzin ◽  
M. Öte ◽  
M. A. Knoch ◽  
I. Alkhasli ◽  
H. Heinemann
Keyword(s):  
Plasma Spraying ◽  
High Speed ◽  
Plasma Jet ◽  
Plasma Jets ◽  
Time Dependent ◽  
Acquisition Time ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Dependent Signal ◽  
The Stability

AbstractIn plasma spraying, instabilities and fluctuations of the plasma jet have a significant influence on the particle in-flight temperatures and velocities, thus affecting the coating properties. This work introduces a new method to analyze the stability of plasma jets using high-speed videography. An approach is presented, which digitally examines the images to determine the size of the plasma jet core. By correlating this jet size with the acquisition time, a time-dependent signal of the plasma jet size is generated. In order to evaluate the stability of the plasma jet, this signal is analyzed by calculating its coefficient of variation cv. The method is validated by measuring the known difference in stability between a single-cathode and a cascaded multi-cathode plasma generator. For this purpose, a design of experiment, covering a variety of parameters, is conducted. To identify the cause of the plasma jet fluctuations, the frequency spectra are obtained and subsequently interpreted by means of the fast Fourier transformation. To quantify the significance of the fluctuations on the particle in-flight properties, a new single numerical parameter is introduced. This parameter is based on the fraction of the time-dependent signal of the plasma jet in the relevant frequency range.

High-Speed Imaging to Study an Auto-Oscillating Vocal Fold Replica for Different Initial Conditions

2017 ◽  
Vol 09 (05) ◽  
pp. 1750064 ◽  
Author(s):  
A. Van Hirtum ◽  
X. Pelorson
Keyword(s):  
Vocal Fold ◽  
High Speed ◽  
Initial Conditions ◽  
Vocal Folds ◽  
High Speed Imaging ◽  
Human Voice ◽  
Manual Intervention ◽  
Geometrical Features ◽  
Upstream Pressure

Experiments on mechanical deformable vocal folds replicas are important in physical studies of human voice production to understand the underlying fluid–structure interaction. At current date, most experiments are performed for constant initial conditions with respect to structural as well as geometrical features. Varying those conditions requires manual intervention, which might affect reproducibility and hence the quality of experimental results. In this work, a setup is described which allows setting elastic and geometrical initial conditions in an automated way for a deformable vocal fold replica. High-speed imaging is integrated in the setup in order to decorrelate elastic and geometrical features. This way, reproducible, accurate and systematic measurements can be performed for prescribed initial conditions of glottal area, mean upstream pressure and vocal fold elasticity. Moreover, quantification of geometrical features during auto-oscillation is shown to contribute to the experimental characterization and understanding.

scholarly journals Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 35 ◽  
Author(s):  
Anshul Sharma ◽  
Irvine Lian Hao Ong ◽  
Anupam Sengupta
Keyword(s):  
Phase Transition ◽  
Aspect Ratio ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Medical Diagnostics ◽  
Time Dependent ◽  
Disodium Cromoglycate ◽  
M Phase ◽  
Static Conditions

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

Dynamic characteristics of a drill in the drilling process

2003 ◽  
Vol 217 (2) ◽  
pp. 161-167 ◽  
Author(s):  
B W Huang
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Thrust Force ◽  
Time Dependent ◽  
Drilling Process ◽  
Improve Quality ◽  
Vibration Model ◽  
High Speed Drilling ◽  
Spinning Speed ◽  
Twisted Beam

The dynamic characteristics of high-speed drilling were investigated in this study. To improve quality and produce a higher production rate, the dynamic characteristics of the drilling process need to be studied. A pre-twisted beam is used to simulate the drill. The moving Winkler-type elastic foundation is used to approximate the drilling process. A time-dependent vibration model for drilling is presented. The spinning speed, pre-twisted angle and thrust force effects of the drill are considered. The numerical analysis indicates that the natural frequency is suddenly reduced as the drill moves into a workpiece.

High-Performance Motion Control With Slosh: A Constrained Sliding Mode Approach

2008 ◽  
Author(s):  
Hanz Richter ◽  
Kedar B. Karnik
Keyword(s):  
High Speed ◽  
High Performance ◽  
Design Methodology ◽  
Closed Loop ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Rectilinear Motion ◽  
Industrial Setting ◽  
Open Container ◽  
Nominal Performance

The problem of controlling the rectilinear motion of an open container without exceeding a prescribed liquid level and other constraints is considered using a recently-developed constrained sliding mode control design methodology based on invariant cylinders. A conventional sliding mode regulator is designed first to address nominal performance in the sliding mode. Then an robustly-invariant cylinder is constructed and used to describe the set of safe initial conditions from which the closed-loop controller can be operated without constraint violation. Simulations of a typical transfer illustrate the usefulness of the method in an industrial setting. Experimental results corresponding to a high-speed transfer validate the theory.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

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