Characteristics of Wave Propagation in The Saturated Thermoelastic Porous Medium

Took into consideration the coupling effect of thermo, hydraulics and mechanics, a set of thermo–hydro-mechanical coupled wave equations for fluid–saturated soil are developed. In these wave equations, the $P_{3}$ -wave in solid phase and $P_{4}$ -wave in fluid phase are coupled into $T$ -wave in fluid–saturated soil by the assumption that the temperature of the solid phase is equal to the temperature of liquid phase at the same position. The dispersion equations for the thermo-elastic wave, which can be degraded to the equations for elastic wave in fluid–saturated soil, are derived from the above equations by introducing four potential functions. Then, these equations are solved numerically. The characteristics of wave phase velocity, attenuation and the effect of thermal expansion, initial temperature and porosity, etc., on phase velocities of $P_{1}$ -, $P_{2}$ -, and $T$ -wave are discussed. As a reference, the characteristics of the propagation of elastic waves in fluid–saturated soil are also studied. The computation results show that (1) the phase velocity of $P_{1}$ -wave obtained by the theory of thermoporoelascity (THM) is faster than that by the theory of poroelasticity (HM); (2) the attenuation of $P_{1}$ -wave obtained by either the theory of THM or HM are consistent; (3) the dissemination characteristics of $P_{2}$ -wave are almost consistent; (4) the phase velocity of $T$ -wave is the slowest among the three compressional waves; and (5) The attenuation versus frequency characteristic of $T$ -wave is similar to that of $P_{2}$ -wave.     

Simultaneous measurement of fluctuating velocity and pressure in the near wake of a circular cylinder

Simultaneous measurement of fluctuating velocity and pressure by a static-pressure probe and a hot-wire probe was performed in the near wake of a circular cylinder, in order to strengthen reliability of the measurement technique. Effect of geometry of the static-pressure probe was systematically investigated, and validity of the measurement results was addressed by quantitative comparison with reference data by a large-eddy simulation. Interference between the probes was found to mainly depend on the diameter of the pressure probe and only weakly on the length. A certain time lag between the velocity and pressure signals was detected in the experiment, and the measurement results of velocity–pressure correlation $\overline{up}$ and $\overline{vp}$ obtained with the correction of the time lag were in good agreement with the computational results. It was also found that the measurement of $\overline{vp}$ is extremely sensitive to a small time lag between the velocity and pressure signals, while that of $\overline{up}$ is not.     

Comparative characteristics of strong shock and detonation waves in bubble media by an electrical wire explosion

Strong shock and detonation waves in inert and chemically active bubble media, which are generated by a wire explosion initiated by a capacitor with a stored energy $W_0 =12.3$ –1,600 J, is experimentally studied. The measurements are performed near the wire and far from the wire in a vertical shock tube 4.5 m long with a volume fraction of the gas in the medium $\beta _0 =1$ –4 %. It is shown that in inert bubble medium, a short intensely decaying shock wave (SW) with intense pressure oscillations is formed in the vicinity of wire explosion point; near the explosion point at $\beta _0 \le 2$  % the SW propagates with the velocity of sound in a liquid. In chemically active bubble medium, an unsteady detonation wave generated by a wire explosion is formed. The pressure amplitude and the velocity of this wave are greater and the length is smaller than those of SW in an inert bubble medium in the same range of explosion energy. It is found that in the interval of low energy explosion from ${\sim }12$ to 64 J, the formation of the bubble detonation wave occurs faster than that at high energies ( $3\times 10^{2}$ – $10^{3}$  J).     

Super-equilibrium increase of chemical reaction rate in the detonation front and other effects in the detonation wave initiated by a shock wave

In the present work the problem of detonation wave formation in a shock tube was considered in one-dimensional formulation. The Monte Carlo non-stationary method of statistical simulation (MCNMSS), also known as DSMC, was used for simulation. The method automatically takes into account all details of mass and heat transfer. At an initial moment, the low-pressure channel (LPC) of the shock tube was filled with gas A while the high-pressure chamber (HPC) was filled with gas C. The cross-sections of the HPC and LPC, as well as the temperatures of gases A and C were equal to each other. At the beginning of the simulation the ratio of pressures in the HPC and LPC was equal to 100. It was assumed that chemical reactions $\mathrm{{A}}+\mathrm{{M}} \rightarrow \mathrm{{B}}+\mathrm{{M}}$ ( $\mathrm{{M}}=\mathrm{{A}},\, \mathrm{{B}}$ and $\mathrm{{C}}$ ) took place. The ratio of molecular masses of gases $\mathrm{{A}},\, \mathrm{{B}}$ and $\mathrm{{C}}$ was taken as 20:20:1. Different reaction thresholds were considered. For the case of a low reaction threshold, the velocity of the resulting detonation wave was found to be higher than the Chapman–Jouguet velocity. A region with constant values of flow parameters inside product was observed. An increase of the reaction threshold led to disappearance of this region and gave rise to something similar to an expansion wave, with peaks of flow parameters at the leading part of the detonation wave. The values of these peaks were found to be constant in time. The velocity of the detonation wave became appreciably lower than the Chapman–Jouguet velocity. Further increase of the reaction threshold led to disappearance of detonation. The reactions $\mathrm{{A}}+\mathrm{{B}} \rightarrow \mathrm{{B}}+\mathrm{{B}}$ and $\mathrm{{A}}+\mathrm{{C}}\rightarrow \mathrm{{B}}+\mathrm{{C}}$ turned out to be very important for initiation of detonation.     

Singular Perturbation of Reduced Wave Equation and Scattering from an Embedded Obstacle

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain ${\Omega \subset \mathbb{R}^N}$ (N ≥?2). In a subregion ${D \Subset \Omega}$ , the medium is supposed to be lossy and have a large mass density. We study the asymptotic development of the wave field as the mass density ρ → +?∞ and show that the wave field inside D will decay exponentially while the wave filed outside the medium will converge to the one corresponding to a sound-hard obstacle ${D \Subset \Omega}$ buried in the medium supported in ${\Omega \backslash \overline{D}}$ . Moreover, the normal velocity of the wave field on ? D from outside D is shown to be vanishing as ρ → +?∞. We derive very accurate estimates for the wave field inside and outside D and on ? D in terms of ρ, and show that the asymptotic estimates are sharp. The implication of the obtained results is given for an inverse scattering problem of reconstructing a complex scatterer.     

Influence of \text{ CF }_{3}\text{ H } and \text{ CCl }_{4} additives on acetylene detonation

The influence of $\text{ CF }_{3}\text{ H }$ and $\text{ CCl }_{4}$ admixtures (known as detonation suppressors for combustible mixtures) on the development of acetylene detonation was experimentally investigated in a shock tube. The time-resolved images of detonation wave development and propagation were registered using a high-speed streak camera. Shock wave velocity and pressure profiles were measured by five calibrated piezoelectric gauges and the formation of condensed particles was detected by laser light extinction. The induction time of detonation development was determined as the moment of a pressure rise at the end plate of the shock tube. It was shown that $\text{ CF }_{3}\text{ H }$ additive had no influence on the induction time. For $\text{ CCl }_{4}$ , a significant promoting effect was observed. A simplified kinetic model was suggested and characteristic rates of diacetylene $\text{ C }_{4}\text{ H }_{2}$ formation were estimated as the limiting stage of acetylene polymerisation. An analysis of the obtained data indicated that the promoting species is atomic chlorine formed by $\text{ CCl }_{4}$ pyrolysis, which interacts with acetylene and produces $\text{ C }_{2}\text{ H }$ radical, initiating a chain mechanism of acetylene decomposition. The results of kinetic modelling agree well with the experimental data.     

Robust mixed H_2 /H_\infty active control for offshore steel jacket platform

This paper presents a robust mixed \(H_2 /H_\infty \) control method for wave-excited offshore jacket platforms. Its objective was to design a controller that minimizes the upper bound of the \(H_2 \) performance measure on platform dynamics satisfying some \(H_\infty \) norm bound constraint simultaneously. Based on mixed \(H_2 /H_\infty \) control theory and linear matrix inequality techniques, a novel approach to stabilize offshore platform vibration with constrained \(H_2 /H_\infty \) performances is proposed. Uncertainties of the wave excitation are considered in dynamic performance analysis of offshore platforms. A reduced mode offshore platform structure under wave excitation is analyzed, and simulations are used to verify the effectiveness of the proposed approach. Compared with existing \(H_\infty \) control methods, the proposed approach makes a significant improvement for dynamic performances of offshore platforms under random wave excitation.     

Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations

This paper is concerned with the existence and qualitative property of standing wave solutions for the nonlinear Schrödinger equation with E being a critical frequency in the sense that . We show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of V and whose amplitude goes to 0 as . Moreover, depending upon the local behaviour of the potential function V(x) near the minimum points, the limiting profile of the standing-wave solutions will be shown to exhibit quite different characteristic features. This is in striking contrast with the non-critical frequency case which has been extensively studied in recent years.     

On solutions of two coupled fractional time derivative Hirota equations

We consider the well-known nonlinear Hirota equation (NLH) with fractional time derivative and derive its periodic wave solution and approximate analytic solitary wave solution using the homotopy analysis method (HAM). We also apply HAM to two coupled time fractional NLHs and construct their periodic wave solution and approximate solitary wave solution. We observe that the obtained periodic wave solution in both cases can be written in terms of the Mittag–Leffler function when the convergence control parameter \({c}_0\) equals \(-1\) . Convergence of the obtained solution is discussed. The derived approximate analytic solution and the effect of time-fractional order \(\alpha \) are shown graphically.     

Statistical behavior of post-shock overpressure past grid turbulence

When a shock wave ejected from the exit of a 5.4-mm inner diameter, stainless steel tube propagated through grid turbulence across a distance of 215 mm, which is 5–15 times larger than its integral length scale \(L_{u}\) , and was normally incident onto a flat surface; the peak value of post-shock overpressure, \(\Delta P_{\mathrm{peak}}\) , at a shock Mach number of 1.0009 on the flat surface experienced a standard deviation of up to about 9 % of its ensemble average. This value was more than 40 times larger than the dynamic pressure fluctuation corresponding to the maximum value of the root-mean-square velocity fluctuation, \(u^{\prime }= 1.2~\hbox {m}/\hbox {s}\) . By varying \(u^{\prime }\) and \(L_{u}\) , the statistical behavior of \(\Delta P_{\mathrm{peak}}\) was obtained after at least 500 runs were performed for each condition. The standard deviation of \(\Delta P_{\mathrm{peak}}\) due to the turbulence was almost proportional to \(u^{{\prime }}\) . Although the overpressure modulations at two points 200 mm apart were independent of each other, we observed a weak positive correlation between the peak overpressure difference and the relative arrival time difference.     

Integrability with symbolic computation on the Bogoyavlensky–Konoplechenko model: Bell-polynomial manipulation,bilinear representation,and Wronskian solution

With symbolic computation, this paper investigates some integrable properties of a two-dimensional generalization of the Korteweg-de Vries equation, i.e., the Bogoyavlensky–Konoplechenko model, which can govern the interaction of a Riemann wave propagating along the \(y\) -axis and a long wave propagating along the \(x\) -axis. Within the framework of Bell-polynomial manipulations, Bell-polynomial expressions are firstly given, which then are cast into bilinear forms. The \(N\) -soliton solutions in the form of an \(N\) th-order polynomial in the \(N\) exponentials and in terms of the Wronskian determinant are, respectively, constructed with the Hirota bilinear method and Wronskian technique. Bilinear Bäcklund transformation is also derived with the achievement of a family of explicit solutions.     

Mixed Convection Boundary-Layer Flow Over a Vertical Surface Embedded in a Porous Material Subject to a Convective Boundary Condition

The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature $T_\mathrm{{f}}$ . The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter $\epsilon $ and a surface heat transfer parameter $\gamma $ . The results indicate that dual solutions exist for opposing flow, $\epsilon <0$ , with the dependence of the critical values $\epsilon _\mathrm{{c}}$ on $\gamma $ being determined, whereas for the assisting flow $\epsilon >0$ , the solution is unique. Limiting asymptotic forms for both $\gamma $ small and large and $\epsilon $ large are also discussed.     

The influence of gas phase velocity fluctuations on primary atomization and droplet deformation

The effects of grid-generated velocity fluctuations on the primary atomization and subsequent droplet deformation of a range of laminar liquid jets are examined using microscopic high-speed backlit imaging of the break-up zone and laser Doppler anemometry of the gas phase separately. This is done for fixed gas mean flow conditions in a miniature wind tunnel experiment utilizing a selection of fuels, turbulence-generating grids and two syringe sizes. The constant mean flow allows for an isolated study of velocity fluctuation effects on primary atomization in a close approximation to homogeneous decaying turbulence. The qualitative morphology of the primary break-up region is examined over a range of turbulence intensities, and spectral analysis is performed in order to ascertain the break-up frequency which, for a case of no grid, compares well with the existing literature. The addition of velocity fluctuations tends to randomize the break-up process. Slightly downstream of the break-up region, image processing is conducted in order to extract a number of metrics, which do not depend on droplet sphericity, and these include droplet aspect ratio and orientation, the latter quantity being somewhat unconventional in spray characterization. A turbulent Weber number $We^{\prime}$ which takes into account gas phase fluctuations is utilized to characterize the resulting droplet shapes, in addition to a mean Weber number <We _d>. Above a $We^{\prime}>0.05$ a clear positive relationship exists between the mean aspect ratio of droplets and the turbulent Weber number where $We^{\prime}$ is varied by altering all relevant variables including the velocity root mean square, the initial droplet diameter, the surface tension and the density.     

A New Insight into the Convective Boundary Condition

The steady mixed convection boundary layer flows over a vertical surface adjacent to a Darcy porous medium and subject respectively to (i) a prescribed constant wall temperature, (ii) a prescribed variable heat flux, $q_\mathrm{w} =q_0 x^{-1/2}$ q w = q 0 x ? 1 / 2 , and (iii) a convective boundary condition are compared to each other in this article. It is shown that, in the characteristic plane spanned by the dimensionless flow velocity at the wall ${f}^{\prime }(0)\equiv \lambda $ f ′ ( 0 ) ≡ λ and the dimensionless wall shear stress $f^{\prime \prime }(0)\equiv S$ f ′ ′ ( 0 ) ≡ S , every solution $(\lambda , S)$ ( λ , S ) of one of these three flow problems at the same time is also a solution of the other two ones. There also turns out that with respect to the governing mixed convection and surface heat transfer parameters $\varepsilon $ ε and $\gamma $ γ , every solution $(\lambda , S)$ ( λ , S ) of the flow problem (iii) is infinitely degenerate. Specifically, to the very same flow solution $(\lambda , S)$ ( λ , S ) there corresponds a whole continuous set of values of $\varepsilon $ ε and $\gamma $ γ which satisfy the equation $S=-\gamma (1+\varepsilon -\lambda )$ S = ? γ ( 1 + ε ? λ ) . For the temperature solutions, however, the infinite degeneracy of the velocity solutions becomes lifted. These and further outstanding features of the convective problem (iii) are discussed in the article in some detail.     

A Comment on the Flow and Heat Transfer Past a Permeable Stretching/Shrinking Surface in a Porous Medium: Brinkman Model

An analytical solution is presented for the boundary-layer flow and heat transfer over a permeable stretching/shrinking surface embedded in a porous medium using the Brinkman model. The problem is seen to be characterized by the Prandtl number $Pr$ , a mass flux parameter $s$ , with $s>0$ for suction, $s=0$ for an impermeable surface, and $s<0$ for blowing, a viscosity ratio parameter $M$ , the porous medium parameter $\Lambda $ and a wall velocity parameter $\lambda $ . The analytical solution identifies critical values which agree with those previously determined numerically (Bachok et al. Proceedings of the fifth International Conference on Applications of Porous Media, 2013) and shows that these critical values, and the consequent dual solutions, can arise only when there is suction through the wall, $s>0$ .     

Microsize and initial pressure effects on shock wave propagation in a tube

In this paper, the shock wave propagation in a channel with a micrometric hydraulic diameter is numerically simulated for an initial Mach number \(M_{s}=2.61\) . The obtained values of the Mach number along the tube are compared to experimental and numerical data given in the literature. The microscale effects on the flow behavior, such as shock wave attenuation and pressure increase behind the shock wave, are amplified by further reducing the scaling ratio (or Reynolds number) of the flow. This reduction is obtained by either decreasing the hydraulic diameter \(D_\mathrm{H}\) or the initial driven gas pressure \(P_1\) . Under these conditions, the flow behavior changes drastically.     

Development of a feedback model for the high-speed impinging planar jet

This article experimentally investigates the self-excited impinging planar jet flow, specifically the development and propagation of large-scale coherent flow structures convecting between the nozzle lip and the downstream impingement surface. The investigation uses phase-locked particle image velocimetry measurements and a new structure-tracking scheme to measure convection velocity and characterize the impingement mechanism near the plate, in order to develop a new feedback model that can be used to predict the oscillation frequency as a function of flow velocity ( $U_o$ ), impingement distance ( $x_o$ ) and nozzle thickness ( $h$ ). The resulting model prediction shows a good agreement with experimental tone frequency data.     

Spatiotemporal complexity of a three-species ratio-dependent food chain model

In this paper, we investigate the complex dynamics of a ratio-dependent spatially extended food chain model. Through a detailed analytical study of the reaction–diffusion model, we obtain some conditions for global stability. On the basis of bifurcation analysis, we present the evolutionary process of pattern formation near the coexistence equilibrium point $(N^*,P^*,Z^*)$ via numerical simulation. And the sequence cold spots $\rightarrow $ stripe–spots mixtures $\rightarrow $ stripes $\rightarrow $ hot stripe–spots mixtures $\rightarrow $ hot spots $\rightarrow $ chaotic wave patterns controlled by parameters $a_1$ or $c_1$ in the model are presented. These results indicate that the reaction–diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics.     

On the neutralization of bacterial spores in post-detonation flows

In multiple operational scenarios, explosive charges are used to neutralize confined or unconfined stores of bacterial spores. The spore destruction is achieved by post-detonation combustion and mixing of hot detonation product gases with the ambient flow and spore clouds. In this work, blast wave interaction with bacterial spore clouds and the effect of post-detonation combustion on spore neutralization are investigated using numerical simulations. Spherical explosive charges (radius, \(R_\mathrm{C}\) = 5.9 cm) comprising of nitromethane are modeled in the vicinity of a spore cloud, and the spore kill in the post-detonation flow is quantified. The effect of the mass of the spores and the initial distance, \(d^0\) , of the spore cloud from the explosive charge on the percentage of spores neutralized is investigated. When the spores are initially placed within a distance of 3.0 \(R_\mathrm{C}\) , within 0.1 ms after detonation of the charge, all the spores are neutralized by the blast wave and the hot detonation product gases. In contrast, almost all the spores survived the explosion when \(d^0\) is greater than 8.0 \(R_\mathrm{C}\) . The percentage of intact spores varied from 0 to 100 for 3.0 \(R_\mathrm{C}\) \( 8.0 \(R_\mathrm{C}\) with spore neutralization dependent on time spent by the spores in the post-detonation mixing/combustion zone.