scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

Coherent Structures and Correlation Fields in the Mixing Transition of a Turbulent Round Free Jet

2018 ◽  
Author(s):  
Benedikt Krohn ◽  
Sunming Qin ◽  
Victor Petrov ◽  
Annalisa Manera
Keyword(s):  
Coherent Structures ◽  
High Speed ◽  
Near Field ◽  
The Self ◽  
Turbulent Shear ◽  
Past Century ◽  
Self Similarity ◽  
Free Jet ◽  
Similar Region ◽  
Self Similar

Turbulent free jets attracted the focus of many scientists within the past century regarding the understanding of mass- and momentum transport in the turbulent shear field, especially in the near-field and the self-similar region. Recent investigations attempt to understand the intermediate fields, called the mixing transition or ‘the route to self-similarity’. An apparent gap is recognized in light of this mixing transition, with two main conjectures being put forth. Firstly the flow will always asymptotically reach a fully self-similar state if boundary conditions permit. The second proposes partial and local self-similarity within the mixing transition. We address the later with an experimental investigation of the intermediate field turbulence dynamics in a non-confined free jet with a nozzle diameter of 12.7 mm and an outer scale Reynolds number of 15,000. High speed Particle Image Velocimetry (PIV) is used to record the velocity fields with a final spatial resolution of 194 × 194 μm2. The analysis focuses on higher order moments and two-point correlations of velocity variances in space and time. We observed local self-similarity in the measured correlation fields. Coherent structures are present within the near-field where the turbulent energy spectrum cascades along a dissipative slope. Towards the transition region, the spectrum smoothly transforms to a viscous cascade, as it is commonly observed in the self-similar region.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

Identification of Chaos-Periodic Transitions, Band Merging, and Internal Crisis Using Wavelet-DFA Method

2016 ◽  
Vol 26 (04) ◽  
pp. 1650065 ◽  
Author(s):  
Mahsa Vaghefi ◽  
Ali Motie Nasrabadi ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Mohammad Reza Mohammadi ◽  
Shahriar Gharibzadeh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Period Doubling ◽  
Nonstationary Time Series ◽  
The Self ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Analysis Method ◽  
Self Similarity ◽  
Self Similar ◽  
Detrended Fluctuation

Detrended Fluctuation Analysis (DFA) is a scaling analysis method that can identify intrinsic self-similarity in any nonstationary time series. In contrast, Wavelet Transform (WT) method is widely used to investigate the self-similar processes, as the self-similarity properties exist within the subbands. Therefore, a combination of these two approaches, DFA and WPT, is promising for rigorous investigation of such a system. In this paper a new methodology, so-called wavelet DFA, is introduced and interpreted to evaluate this idea. This approach, further than identifying self-similarity properties, enable us to detect and capture the chaos-periodic transitions, band merging, and internal crisis in systems that become chaotic through period-doubling phenomena. Changes of wavelet DFA exponent have been compared with that of Lyapunov and DFA through Logistic, Sine, Gaussian, Cubic, and Quartic Maps. Furthermore, the potential capabilities of this new exponent have been presented.

Direct numerical simulation of axisymmetric wakes embedded in turbulence

2012 ◽  
Vol 710 ◽  
pp. 482-504 ◽  
Author(s):  
Elad Rind ◽  
Ian P. Castro
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Decay Rate ◽  
Relative Strength ◽  
Decay Rates ◽  
The Self ◽  
Self Similarity ◽  
Self Similar ◽  
External Turbulence ◽  
Different Levels

AbstractDirect numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the former.

scholarly journals On the self-similarity problem for smooth flows on orientable surfaces

2011 ◽  
Vol 32 (5) ◽  
pp. 1615-1660 ◽  
Author(s):  
JOANNA KUŁAGA
Keyword(s):  
Orientable Surface ◽  
The Self ◽  
Self Similarity ◽  
Similarity Problem ◽  
Orientable Surfaces

AbstractOn each compact connected orientable surface of genus greater than one we construct a class of flows without self-similarities.

The persistence of regular reflection during strong shock diffraction over rigid ramps

2001 ◽  
Vol 431 ◽  
pp. 273-296 ◽  
Author(s):  
L. F. HENDERSON ◽  
K. TAKAYAMA ◽  
W. Y. CRUTCHFIELD ◽  
S. ITABASHI
Keyword(s):  
Stokes Equations ◽  
Mach Reflection ◽  
Strong Shock ◽  
Navier Stokes ◽  
Regular Reflection ◽  
Navier Stokes Equations ◽  
Von Neumann ◽  
Initial Appearance ◽  
Self Similar ◽  
Initial Shock

We report on calculations and experiments with strong shocks diffracting over rigid ramps in argon. The numerical results were obtained by integrating the conservation equations that included the Navier–Stokes equations. The results predict that if the ramp angle θ is less than the angle θe that corresponds to the detachment of a shock, θ < θe, then the onset of Mach reflection (MR) will be delayed by the initial appearance of a precursor regular reflection (PRR). The PRR is subsequently swept away by an overtaking corner signal (cs) that forces the eruption of the MR which then rapidly evolves into a self-similar state. An objective was to make an experimental test of the predictions. These were confirmed by twice photographing the diffracting shock as it travelled along the ramp. We could get a PRR with the first exposure and an MR with the second. According to the von Neumann perfect gas theory, a PRR does not exist when θ < θe. A viscous length scale xint is a measure of the position on the ramp where the dynamic transition PRR → MR takes place. It is significantly larger in the experiments than in the calculations. This is attributed to the fact that fluctuations from turbulence and surface roughness were not modelled in the calculations. It was found that xint → ∞ as θ → θe. Experiments were done to find out how xint depended on the initial shock tube pressure p0. The dependence was strong but could be greatly reduced by forming a Reynolds number based on xint. Finally by definition, regular reflection (RR) never interacts with a boundary layer, while PRR always interacts; so they are different phenomena.

A parametric study of Mach reflection in steady flows

1997 ◽  
Vol 341 ◽  
pp. 101-125 ◽  
Author(s):  
H. LI ◽  
G. BEN-DOR
Keyword(s):  
Present Model ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Incoming Flow ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Set Up

The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. It is shown that the point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumann's three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated. Predictions based on the present model are found to agree well both with experimental and numerical results.

Non-self-similar characteristics of weak Mach reflection: the von Neumann paradox

2004 ◽  
Vol 35 (4) ◽  
pp. 275-286 ◽  
Author(s):  
Susumu Kobayashi ◽  
Takashi Adachi ◽  
Tateyuki Suzuki
Keyword(s):  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Self Similar

scholarly journals On the self-similarity of wind turbine wakes in complex terrain using large-eddy simulation

2019 ◽  
Author(s):  
Arslan Salim Dar ◽  
Jacob Berg ◽  
Niels Troldborg ◽  
Edward G. Patton
Keyword(s):  
Large Eddy Simulation ◽  
Complex Terrain ◽  
The Self ◽  
Self Similarity ◽  
Flat Terrain ◽  
Eddy Simulation ◽  
Atmospheric Stratification ◽  
Large Eddy ◽  
Self Similar ◽  
Turbine Wake

Abstract. We perform large-eddy simulation of flow in complex terrain under neutral atmospheric stratification. We study the self-similar behavior of a turbine wake as a function of varying terrain complexity and perform comparison with a flat terrain. By plotting normalized velocity deficit profiles in different complex terrain cases, we verify that self-similarity is preserved as we move downstream from the turbine. We find that this preservation is valid for a shorter distance downstream compared to what is observed in flat terrain. A larger spread of the profiles toward the tails due to varying levels of shear is also observed.

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