Correlations for the Onset of Instabilities of Spherical Laminar Premixed Flames

2005 ◽  
Vol 127 (12) ◽  
pp. 1410-1415 ◽  
Author(s):  
M. Z. Haq
Keyword(s):  
Coherent Structure ◽  
Critical Radius ◽  
Critical Size ◽  
Initial Conditions ◽  
Critical Value ◽  
Flame Surface ◽  
Flame Acceleration ◽  
Elapsed Time ◽  
Bifurcation Phenomenon ◽  
Spherical Flame Propagation

A spherically expanding flame in a quiescent premixture is a bifurcation phenomenon, in which the flame becomes unstable at a radius, greater than some critical value, while remaining stable below that critical radius. Beyond this critical radius, developing instabilities are initiated by propagating cracks to form a coherent structure covering the entire flame surface and the flame accelerates. The present paper reports a Schlieren photographic study of spherical flame propagation in methane—air, iso-octane—air and n-heptane—air premixtures at different initial conditions where the onset of instability and the flame acceleration are clearly perceived. Critical size and corresponding elapsed time for the development of such instability are measured and these values are correlated with the appropriate flame parameter.

Prediction of Instabilities of Spherically Propagating Flames in Laminar Premixture

2003 ◽  
Author(s):  
M. Z. Haq
Keyword(s):  
Large Scale ◽  
Critical Radius ◽  
Initial Conditions ◽  
Critical Time ◽  
Flame Surface ◽  
Flame Acceleration ◽  
Elapsed Time ◽  
Bifurcation Phenomenon ◽  
Spherical Flame Propagation ◽  
Good Agreement

A spherically expanding flame in a quiescent premixture is a bifurcation phenomenon, in which the flame becomes unstable at a radius, greater than some critical value, while remaining stable below that critical radius. Beyond this critical radius, developing instabilities are initiated by propagating cracks to form a coherent structure covering the entire flame surface and flame accelerates. The present paper reports a schlieren photographic study of spherical flame propagation in methane–air, iso-octane–air and n-heptane–air premixtures at different initial conditions where the onset of instability and the flame acceleration are clearly perceived. Hence, elapsed time and flame radius for onset of instability are correlated with the flame parameters. Predicted critical time and flame radius for the onset of instability are in good agreement with available experimental data obtained from a large-scale unconfined explosions in methane-air premixture.

An Investigation on the Profile of Microlens by the Thermal Reflow Process Due to Surface Tension and Gravity

2008 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Yong-Sung Hsu
Keyword(s):  
Surface Tension ◽  
Critical Radius ◽  
Critical Size ◽  
Liquid Droplet ◽  
Bond Number ◽  
Diameter Ratio ◽  
Experimental Result ◽  
Critical Number ◽  
Reflow Process ◽  
Thermal Reflow

Microlens and its mold fabricated by thermal reflow using photoresist have been widely used for forming patterns in different scales. When the photoresist solidifies from melting condition, for example by the reflow process, its profile is formed based on the balance between surface tension and gravity. This research is aimed to investigate the influence of surface tension and gravity on the profile of microlens in thermal reflow process. Theoretical analysis based on the interaction between surface tension and gravity of liquid droplet is first investigated. The result showed that the height to diameter ratio (h/D), or the sag ratio, of the liquid droplet is affected by the Bond number (Bo), a number defined as the ratio of gravity to surface tension. The sag ratio is not sensitive to Bo when Bo is small but the ratio decreases as Bo increases if Bo is over the critical number. Based on the analysis, the critical number for the AZ4620 photoresist on a silicon substrate is 1, corresponding to the critical radius of droplet R = 2,500μm. When the size of the droplet is less then the critical size, the profile is mainly controlled by the surface tension and thus the sag ratio is about the same regardless the size. The profile, in contrast, is highly affected by the gravity if the size of the droplet is larger then the critical size. The sag ratio decreases exponentially with respect to Bo in this case. Experiments are also designed and conducted to verify the analysis. Experimental result showed that the sag ratio of the photoresist reduces to 0.065 from 0.095 when Bo increases from 0.0048 to 0.192. The results showed that the trend is consistent to the theoretical model.

scholarly journals New Solution of a Spherically Symmetric Static Problem of General Relativity

2017 ◽  
Vol 9 (5) ◽  
pp. 29
Author(s):  
Valery Vasiliev
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Classical Solution ◽  
Critical Radius ◽  
Static Problem ◽  
Critical Value ◽  
Relativity Theory ◽  
Spherically Symmetric ◽  
General Relativity Theory ◽  
Gravitational Radius

The paper is concerned with the spherically symmetric static problem of the General Relativity Theory. The classical solution of this problem found in 1916 by K. Schwarzschild for a particular metric form results in singular space metric coefficient and provides the basis of the objects referred to as Black Holes. A more general metric form applied in the paper allows us to obtain the solution which is not singular. The critical radius of the fluid sphere, following from this solution does not coincide with the traditional gravitational radius. For the spheres with radii that are less than the critical value, the solution of GRT problem does not exist.

scholarly journals Bifurcation and global dynamical behavior of the f(T) theory

2014 ◽  
Vol 29 (07) ◽  
pp. 1450033 ◽  
Author(s):  
Chao-Jun Feng ◽  
Xin-Zhou Li ◽  
Li-Yan Liu
Keyword(s):  
Dynamical System ◽  
Critical Points ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Nonlinear Effects ◽  
Local Analysis ◽  
Local Method ◽  
Initial Values ◽  
Bifurcation Phenomenon

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

Critical size of newborn homeotherms

1978 ◽  
Vol 44 (6) ◽  
pp. 1002-1002
Author(s):  
R. T. Balmer ◽  
A. D. Strobusch
Keyword(s):  
Critical Radius ◽  
Critical Size ◽  
Correct Form ◽  
Pass Through

Page 571: R. T. Balmer and A. D. Strobusch. “Critical size of newborn homeotherms.” Page 574: Eq. 31 has the wrong final exponent. It should read (See PDF) This error results in Eqs. 37, 39, 40, 41, and 42 also being wrong. Equation 37 now has the form (See PDF) where (See PDF and (See PDF) Equations 39, 40, and 41 are the algebraic manipulations required in using the new Eq. 37 (given above) in Eq. 38 of the paper. Equation 42 is the final result, which in its correct form is now (See PDF) where, for T0 – T∞ = 5°C, rocc = 0.80 cm. Thus, even though the error in Eq. 31 was rather significant, it had remarkably little effect on the final result, Eq. 42. Page 577: the line labeled cylinder in Fig. 5 should be raised slightly (it should pass through the point critical radius = 0.8 cm, T0 – T∞ = 5°C) bringing it closer to the line labeled sphere. (See PDF)

Critical size of newborn homeotherms

1977 ◽  
Vol 42 (4) ◽  
pp. 571-577 ◽  
Author(s):  
R. T. Balmer ◽  
A. D. Strobusch
Keyword(s):  
Heat Transfer ◽  
Body Size ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Critical Radius ◽  
Critical Size ◽  
The Body ◽  
Birth Size ◽  
Critical Weight

It is shown that for cylindrical and spherical bodies there is a critical radius below which the addition of any form of insulation to the body will increase rather than decrease the cooling of the body. It is proposed, therefore, that it would be thermally detrimental to newborn homeotherms to be born with a protective covering (fur or down) if their body size were less than this critical size, and consequently that the degree of natal covering is not necessarily related to the overall development of the species when the birth size is less than this critical size. A critical weight is derived from the critical radius for basically spherical animals which compares favorably with typical birth weights of various altricial homeotherms. The effect of the overall conductive-convective heat transfer caused by a basically cylindrical animal rolling up into a ball is also discussed.

scholarly journals TIMELIKE GEODESIC MOTION IN HORAVA–LIFSHITZ SPACE–TIME

2010 ◽  
Vol 25 (07) ◽  
pp. 1439-1448 ◽  
Author(s):  
JUHUA CHEN ◽  
YONGJIU WANG
Keyword(s):  
Initial Conditions ◽  
Detailed Balance ◽  
Critical Value ◽  
Space Time ◽  
Three Dimensions ◽  
Geodesic Motion ◽  
Timelike Geodesic ◽  
Particle Orbit ◽  
Renormalizable Theory ◽  
Finite Distance

Recently a nonrelativistic renormalizable theory of gravitation has been proposed by P. Horava. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value λ = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates xi as well as t, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Horava–Lifshitz space–time. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are three different cases due to the energy of radial particle: (i) when the energy of radial particle is higher than a critical value EC, the particle will fall directly from infinity to the singularity; (ii) when the energy of radial particle equals to the critical value EC, the particle orbit at r = rC is unstable, i.e. the particle will escape from r = rC to the infinity or to the singularity, depending on the initial conditions of the particle; (iii) when the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, depending on the initial conditions of the particle.

STABILITY OF AN EXCITON BOUND TO AN IONIZED ACCEPTOR IN QUANTUM DOTS

2003 ◽  
Vol 17 (11) ◽  
pp. 2273-2279 ◽  
Author(s):  
S. BASKOUTAS ◽  
A. F. TERZIS ◽  
C. POLITIS
Keyword(s):  
Quantum Dots ◽  
Binding Energy ◽  
Quantum Dot ◽  
Numerical Method ◽  
Schrodinger Equation ◽  
Critical Radius ◽  
Critical Value ◽  
Two Dimensional ◽  
Mass Ratio ◽  
Acceptor Impurity

Binding energy for an exciton (X) bound in a parabolic two-dimensional quantum dot by an acceptor impurity A- located on the z-axis at a distance d from the dot plane, are calculated using the Hartree formalism with a recently developed numerical method (PMM) for the solution of the Schrödinger equation. As our analysis indicates there is a critical dot radius Rc such that for R < Rc the complex (A-, X) is unstable and with an increase of the impurity distance this critical radius increases. Furthermore, there is a critical value σc of the mass ratio [Formula: see text] such that for σ > σc the complex is stable.

On the direct initiation of gaseous detonations by an energy source

1994 ◽  
Vol 277 ◽  
pp. 227-248 ◽  
Author(s):  
Longting He ◽  
Paul Clavin
Keyword(s):  
Energy Source ◽  
Critical Radius ◽  
Critical Value ◽  
Blast Waves ◽  
Initiation Energy ◽  
Point Energy ◽  
Gaseous Detonations ◽  
Curvature Effects ◽  
Direct Initiation ◽  
Steady Solutions

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.

The Effect of Intrinsic Instabilities on Effective Flame Speeds in Under-Resolved Simulations of Lean Hydrogen–Air Flames

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Peter Katzy ◽  
Josef Hasslberger ◽  
Lorenz R. Boeck ◽  
Thomas Sattelmayer
Keyword(s):  
Flame Front ◽  
Optical Measurement ◽  
Initial Conditions ◽  
Measurement Techniques ◽  
Evaluation Methods ◽  
Line Of Sight ◽  
Flame Surface ◽  
Validation Data ◽  
Time Resolved ◽  
The Impact

The presented work aims to improve computational fluid dynamics (CFD) explosion modeling for lean hydrogen–air mixtures on under-resolved grids. Validation data are obtained from an entirely closed laboratory-scale explosion channel (GraVent facility). Investigated hydrogen–air concentrations range from 6 to 19 vol %. Initial conditions are p = 0.1 MPa and T = 293 K. Two highly time-resolved optical measurement techniques are applied simultaneously: (1) 10 kHz shadowgraphy captures line-of-sight integrated macroscopic flame propagation and (2) 20 kHz planar laser-induced fluorescence of the OH radical (OH-PLIF) resolves microscopic flame topology without line-of-sight integration. This paper presents the experiment, measurement techniques, data evaluation methods, and simulation results. The evaluation methods encompass the determination of flame tip velocity over distance and a detailed time-resolved quantification of the flame topology based on OH-PLIF images. One parameter is the length of wrinkled flame fronts in the OH-PLIF plane obtained through automated postprocessing. It reveals the expected enlargement of flame surface area by instabilities on a microscopic level. A strong effect of mixture composition is observed. Simulations based on the new model formulation, incorporating the microscopic enlargement of the flame front, show a promising behavior, where the impact of the augmented flame front on the observed flame front velocities can be detected.

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