Dimensionless Phase Research Articles

Experimental study of crossflow instability in a Mach 6 delta wing flow

In this paper, the traveling crossflow instability in the boundary layer on the windward side of a delta wing is studied. The experiments are carried out in a Mach 6 low-noise wind tunnel, with the angles of attack of the model being 5° and 10°, and the Reynolds number being in a range of 2.43 × 10<sup>6</sup>–14.21 × 10<sup>6</sup> m<sup>–1</sup>. The wall fluctuation pressure is measured by fast-response Kulite pressure transducers. The power spectrum density (PSD) analysis is conducted to obtain the disturbance waves' development process in the boundary layer. The temperature-sensitive paints (TSPs) and nano-tracer based planar laser scattering (NPLS) technique are also used. From the TSP results, the boundary layer transition near the leading edge of the delta wing is smooth and parallel to the leading edge. A peak around 10 kHz in power spectrum density is detected by the fast-response pressure sensor, which may be caused by the traveling crossflow waves. To verify this dominant mode, an NPLS image in the plane of <i>n</i> = 36 mm is obtained. The shapes of vortex structures correspond to the shapes of the crossflow vortices from the numerical simulation. Only when the boundary layer is laminar can the traveling crossflow wave signal be observed from the PSD curves. When the boundary layer is at a transitional or turbulent phase, the low-frequency component is dominant in the PSD curve. With the increase of Reynolds number, the characteristic frequency of the crossflow wave increases, and the wave’s amplitude first increases and then decreases. Moreover, the angle of attack effect is obtained. The increasing of the angle of attack can make the traveling crossflow wave grow faster and saturate, attenuate at the position closer to the leading edge of the delta wing or at a lower Reynolds number. By sensor pairs composed of three Kulite transducers, the phase velocity and the propagation angle of the traveling crossflow wave are investigated. The dimensionless phase velocities of the traveling wave are in ranges of 0.24–0.26 and 0.26–0.32 at 5° and 10° angles of attack, respectively. The propagation angles are at 50°–60° and 40°–55° at the angles of attack of 5° and 10°, respectively. At a larger angle of attack, the traveling wave’s propagation angel is smaller, but the phase velocity is bigger. It may be because the spanwise pressure gradient is higher at a larger angle of attack, and then the crossflow velocity is stronger.

Constraining Hadron-quark Phase Transition Parameters within the Quark-mean-field Model Using Multimessenger Observations of Neutron Stars

Abstract We extend the quark mean-field (QMF) model for nuclear matter and study the possible presence of quark matter inside the cores of neutron stars. A sharp first-order hadron-quark phase transition is implemented combining the QMF for the hadronic phase with “constant-speed-of-sound” parameterization for the high-density quark phase. The interplay of the nuclear symmetry energy slope parameter, L, and the dimensionless phase transition parameters (the transition density n trans/n 0, the transition strength Δε/ε trans, and the sound speed squared in quark matter ) are then systematically explored for the hybrid star properties, especially the maximum mass M max and the radius and the tidal deformability of a typical 1.4 M ⊙ star. We show the strong correlation between the symmetry energy slope L and the typical stellar radius R 1.4, similar to that previously found for neutron stars without a phase transition. With the inclusion of phase transition, we obtain robust limits on the maximum mass (M max < 3.6 M ⊙) and the radius of 1.4 M ⊙ stars (R 1.4 ≳ 9.6 km), and we find that a phase transition that is too weak (Δε/ε trans ≲ 0.2) taking place at low densities ≲1.3–1.5 n 0 is strongly disfavored. We also demonstrate that future measurements of the radius and tidal deformability of ∼1.4 M ⊙ stars, as well as the mass measurement of very massive pulsars, can help reveal the presence and amount of quark matter in compact objects.

Mechanics of 2D Elastic Stress Waves Propagation Impacted by Concentrated Point Source Disturbance in Composite Material Bars

Green’s function, an analytical approach in inhomogeneous linear differential equations, is the impulse response, which is applied for deriving the wave equation solution in composite materials mediums. This paper investigates the study of SH wave’s transmission influenced by concentrated point source disturbance in piezomagnetic material resting over heterogeneous half-space. Green function approach is used to solve differential equation and obtain the dispersion relation in determinant form and match with existing classical Love wave equation for the authenticity for the article. The properties of SH wave throughout the considered framework and their state of relying on varied geometrical and physical parameters are scrutinized. The simulated outcomes of disparate physical quantities viz., dimensionless phase velocity, elastic parameter, group velocity, initial stress, piezomagnetic/heterogeneity parameter and stress distribution of SH wave in the considered structure are investigated and used to regulate the behavior of dispersion characteristics of smart material waveguides.

Influence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformations. The dimensionless phase velocity is plotted against dimensionless wave number for the different size of ratios of depth of rectangular irregularity with the height of the layer and anisotropy parameters with the help of MATLAB graphical routines in presence and absence of initial stress. From the graphical results, it has been seen that the phase velocity is significantly influenced by the wave number, the depth of the irregularity, rigid boundary and initial stress. The acquired outcomes can be valuable for the investigation of geophysical prospecting and understanding the cause and evaluating of damage due to earthquakes.

Confinement Effect of Graphene Interface on Phase Transition of n-Eicosane: Molecular Dynamics Simulations.

Phase change materials (PCMs) are widely used in thermal management and energy storage systems. Investigations on the thermophysical properties enhancement of organic PCMs by introducing carbon-based frameworks have received much attention in recent years. Studies of the phase transition in nanoconfinement are still in controversy with divergent opinions among researchers. In this article, the phase transition behavior of n-eicosane in slit-shaped pores between sheets of graphene is investigated by molecular dynamics simulation. It is found that the graphene interface makes the phase transition temperature of n-eicosane increase, under the initial slit widths of 1.5-5.3 nm. Impacted by interaction and size effects, the distribution and orientation of n-eicosane molecules are quite different from those of the bulk state. In the confinement of graphene, the molecules turn to a reversible layered distribution parallel to the graphene sheets after solidification. The contact layers are found in all the confined systems, which is harder to melt and easier to solidify compared with the main part of the systems. The melting points of different systems are obtained by analysis of the liquid ratio. Finally, the relationship between the dimensionless phase transition point and slit width is discussed.

Influence of periodic pressure on dendritic morphology and sidebranching

The influence of periodic pressure with low and high frequencies on microstructure and dendritic sidebranching was studied by using 3-D phase field method. In both low and high frequency cases, the variation trend of SDAS (secondary dendritic arm spacing) with increasing pressure frequency is opposite to that of sidebranching frequency, while the variation trend of the average length of secondary arms is consistent with that of sidebranching frequency. The high sidebranching frequency indicates that more secondary arms share the whole driving force of dendrite growth, resulting in lower driving force for each one and leading to less developed secondary arms. The smallest SDAS is obtained when perturbed by the periodic pressure with the frequency of 0.157/τ0 (τ0 is the physical unit of time in the dimensionless phase field model) and 2.200/τ0 in low and high frequency cases, respectively. Comparisons of dendritic morphology and secondary arms are made between the low and high frequency cases. Firstly, in the low frequency case, secondary arms are luxuriant especially when pressure frequency is low, with many high-order side branches stretching out. Secondly, the average length of secondary arms in primary dendrite is longer in the low frequency case than that without pressure, and much longer than that in the high frequency case. Thirdly, the dendrite tip without side branches in the high frequency case is much longer than that in the low frequency case. All of the differences in dendritic morphology and sidebranching in the two cases can be attributed to the different modulation mechanism. In the low frequency case, periodic pressure determines tip velocity and then modulates sidebranching directly. While in the high frequency case, periodic pressure cannot determine sidebranching directly, but via modulating tiny protuberances in dendrite tip, part of which evolves into side branch. In this case, the tiny protuberances take part of the whole driving force, leading to less developed secondary arms.

Coupling mechanism of mass transport and electrochemical reaction within patterned anode of solid oxide fuel cell

Patterned electrodes are widely used in the development of novel electrodes of solid oxide fuel cells (SOFCs) because of their well-controlled geometries, distinguishable catalytically active sites and simple transport paths. In the existing studies the patterned electrodes are usually adopted to reveal relevant reaction mechanisms and to investigate the electrochemical characteristics of new materials of SOFCs, however, the effects of electrode geometry are not taken into consideration. In the present paper, a lattice Boltzmann model for simulating the charge transport and electrochemical reaction in an SOFC patterned anode is established, and the key dimensionless parameters governing the above electrode process are deduced. This model is then used to investigate the effects of the key dimensionless parameters on the electrochemical performance of a patterned anode. More importantly, the influences of the patterned anode geometry on the coupling of the charge transport and electrochemical reaction are unraveled. According to the sensitivity of the electrode performance to the dimensionless parameters, a dimensionless phase map, which is divided into maximum area, transition area and minimum area, is built. It is concluded that the transition area, in which the electrode performance varies dramatically with the parameters of design and operation, is regarded as the optimal range for studying the relevant reaction mechanism. Meanwhile, it is found that although the electron transport does not restrict the electrode performance, the moderate decrease of the height-to-width ratio of electronic conductor is capable of enlarging the transition area, which is beneficial to revealing the relevant reaction mechanism. Conversely, the ion transport is the rate-limiting step, however, the transition area remains unchanged under different ionic conductor geometries. The present numerical method and conclusions could offer guidance for rationally designing and operating the patterned electrodes.

Rigidity and Irregularity Effect on Surface Wave Propagation in a Fluid Saturated Porous Layer

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations. It can be seen that the phase velocity is strongly influenced by the wave number, the depth of the irregularity, homogeneity parameter and the rigid boundary. The dimensionless phase velocity is plotted against dimensionless wave number graphically for different size of rectangular irregularities and homogeneity parameter with the help of MATLAB graphical routines for both free and rigid boundaries for several cases. The numerical analysis of dispersion equation indicates that the phase velocity of surface waves decreases with the increase in dimensionless wave number. The obtained results can be useful to the study of geophysical prospecting and understanding the cause and estimating of damage due to earthquakes.

Dispersion of Torsional Surface Wave in a Pre-Stressed Heterogeneous Layer Sandwiched Between Anisotropic Porous Half-Spaces Under Gravity

The study of surface waves in a layered media has their viable application in geophysical prospecting. This paper presents an analytical study on the dispersion of torsional surface wave in a pre-stressed heterogeneous layer sandwiched between a pre-stressed anisotropic porous semi-infinite medium and gravitating anisotropic porous half-space. The non-homogeneity within the intermediate layer and upper semi-infinite medium is assumed to rise up, because of quadratic variation and exponential variation in directional rigidity, pre-stress, and density respectively. The displacement dispersion equation for the torsional wave velocity has been expressed in the term of Whitaker function and their derivatives. Dispersion relation and the closed-form solutions have been obtained analytically for the displacement in the layer and the half-spaces. It is determined that the existing geometry allows torsional surface waves to propagate and the observe exhibits that the layer width, layer inhomogeneity, frequency of heterogeneity in the heterogeneous medium has a great impact on the propagation of the torsional surface wave. The influence of inhomogeneities on torsional wave velocity is also mentioned graphically by means plotting the dimensionless phase velocity against non-dimensional wave number for distinct values of inhomogeneity parameters.

Rivalry in Bacillus subtilis colonies: enemy or family?

Two colonies of Bacillus subtilis of identical strains growing adjacent to each other on an agar plate exhibit two distinct types of interactions: they either merge as they grow or demarcation occurs leading to formation of a line of demarcation at the colony fronts. The nature of this interaction depends on the agar concentration in the growth medium and the initial separation between the colonies. When the agar concentration was 0.67% or lower, the two sibling colonies were found to always merge. At 1% or higher concentrations, the colonies formed a demarcation line only when their initial separation was 20 mm or higher. Interactions of a colony with solid structures and liquid drops have indicated that biochemical factors rather than the presence of physical obstacles are responsible for the demarcation line formation. A reaction diffusion model has been formulated to predict if two sibling colonies will form a demarcation line under given agar concentration and initial separation. The model prediction agrees well with experimental findings and generates a dimensionless phase diagram containing merging and demarcation regimes. The phase diagram is in terms of a dimensionless initial separation, d[combining macron], and a dimensionless diffusion coefficient, D[combining macron], of the colonies. The phase boundary between the two interaction regimes can be described by a power law relation between d[combining macron] and D[combining macron].

Wave propagation analysis in viscoelastic thick composite plates resting on Visco-Pasternak foundation by means of quasi-3D sinusoidal shear deformation theory

In this research, the wave propagation in a viscoelastic composite thick plate resting on a Visco-Pasternak foundation is analyzed by means of sinusoidal shear deformation theory (SSDT). The viscoelastic properties of the plate are considered by using Kelvin-Voigt model. The material properties of composite plate are assumed viscoelastic based on Kelvin-Voigt model. The governing equations of motion are derived by Hamilton's principle. The analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the viscoelastic composite plate including the dimensionless phase velocity, cut-off and escape frequencies. The obtained results indicate that the dimensionless phase velocity and natural frequency decrease with increasing the damping coefficient. Also, it is observed that the effect of layups on the phase velocity becomes more sensible for small wave numbers. However, the effect of the damping coefficient on the dimensionless phase velocity and natural frequency is only observed at large dimensionless wave numbers.

Controls on microstructural features during solidification of colloidal suspensions

We present a mathematical model of the directional freezing of colloidal suspensions. Key ingredients of the model are the disjoining forces between the colloidal particles and the solidified suspending fluid, flow of the suspending fluid towards the solidification front through an accumulating layer of particles, and flow through microscopic films of unfrozen liquid separating particles from the freezing front. Our model predicts three different modes of solidification leading to different microstructures: dendritic formations; laddered structures of ice spears and lenses; a frozen fringe, from which transverse ice lenses can form. It explains why different researchers have reported the existence of ice lensing with and without the pre-existence of frozen fringes. Our quantitative predictions are encapsulated within a universal, dimensionless phase diagram showing which microstructure is to be expected under which operating conditions, and we show that these predictions are consistent with previous experimental studies as well as new experiments that we present here.

Influence of Stress on Propagation of Shear Wave in Piezoelectric-Piezoelectric (PE-PE) Composite Layered Structure

Shear waves (SH) propagation in piezoelectric composite under the influence of initial stress is investigated analytically and numerically. The dispersion equation of shear waves propagation in direction normal to the layering is obtained in presence of initial stress. Numerical solutions were obtained for evaluating the effect of stress on dimensionless frequency and phase velocity. The effect of stress on stop band is discussed in this study. It can be concluded from the results that initial stress has significant effect on propagation characteristics of shear waves. The variation of initial stress has small effect on the phase velocity of shear waves. This study provides insight for development of piezoelectric composite structure under the influence of initial stress.

Dispersion and non-reciprocal elastic wave propagation in a membrane coupled with a uniform flow

In this paper, we carry out an analytical study to investigate the dispersive and non-reciprocal properties of harmonic elastic wave propagation in a membrane on an elastic foundation. One side of the membrane is in contact with a uniform inviscid and incompressible flow. The analysis shows that the frequency spectrum and the dispersion curve are not symmetric, therefore breaking the principle of reciprocity. We show that the dynamics of the wave propagation of the system depends on the dimensionless phase velocity of the membrane and the dimensionless stiffness of the elastic foundation. The system possesses one region where the phase velocity of the propagating waves in opposite directions is different, and another where the waves travel only in one direction (directional band gap). There also exist regions in which only evanescent and spatially growing waves are excited.

Phase structural ordering kinetics of second-phase formation in the vicinity of a crack

The formation of a second phase in presence of a crack in a crystalline material is modelled and studied for different prevailing conditions in order to predict and a posteriori prevent failure, e.g. by delayed hydride cracking. To this end, the phase field formulation of Ginzburg–Landau is selected to describe the phase transformation, and simulations using the finite volume method are performed for a wide range of material properties. A sixth order Landau potential for a single structural order parameter is adopted because it allows the modeling of both first and second order transitions and its corresponding phase diagram can be outlined analytically. The elastic stress field induced by the crack is found to cause a space-dependent shift in the transition temperature, which promotes a second-phase precipitation in vicinity of the crack tip. The spatio-temporal evolution during nucleation and growth is successfully monitored for different combinations of material properties and applied loads. Results for the second-phase shape and size evolution are presented and discussed for a number of selected characteristic cases. The numerical results at steady state are compared to mean-field equilibrium solutions and a good agreement is achieved. For materials applicable to the model, the results can be used to predict the evolution of an eventual second-phase formation through a dimensionless phase transformation in the crack-tip vicinity for given conditions.

Shear Wave Propagation Due to a Point Source

The present paper is concerned with the propagation of shear waves in a heterogeneous isotropic layer lying over a semi-infinite homogeneous isotropic half-space due to a point source. The dispersion equation of shear waves has been established with the help of Green's function technique and Fourier transform. The deduced dispersion equation for this study agrees well with the classical Love wave equation in the absence of heterogeneity. Significant effect of heterogeneity on the phase velocity of shear wave has been observed. The dimensionless phase velocity against dimensionless wave number has been plotted and the influence of heterogeneity parameter is also revealed graphically through numerical computation.

Shear Wave Propagation in a Cylindrical Earth Model

In the present paper the study of shear wave propagation in a cylindrical fibre-reinforced earth model has been discussed in the presence of radial inhomogeneity. The dispersion equation of shear wave propagation has been derived by using Debye asymptotic expansion for upper layer and lower layer to be heterogeneous and homogeneous respectively. The oncoming results are verified with the classical result of Love wave in the absence of reinforcement and inhomogeneity parameter. The variation of dimensionless phase velocity has been plotted against dimensionless wave number to show the effect of inhomogeneity parameter, reinforcement and the ratio of radii.

The propagation of surface waves in a double layered medium over an anisotropic liquid saturated porous half space

A model of surface wave propagation in a transversely isotropic elastic solid layer lying between a homogeneous liquid layer and liquid saturated porous anisotropic half space has been considered. This appears to be a realistic model of interest as the bottom of ocean is likely to be anisotropic homogeneous to some kilometers. The frequency equation has been obtained in the form of ninth order determinant and gives complex velocities representing the attenuated waves when the liquidsaturated porous solid is dissipative. Some special cases have been discussed and numerical computations have been done by Symbolab Solutions with mathematical approximation method. The dimensionless phase velocity ratios have been plotted against the dimensionless wave number for different values of density and different values of ratio of anisotropy parameters C/F with the help of MATLAB graphical routines. Finally, conclusions have been drawn on the basis of analysis of results and graphs.

On rare metal separation by counter-current extraction in chromatography mode

Computational studies using special software have shown by the example of lanthanide salts that the use of counter-current multistep extraction in chromatography mode provides efficient separation of metals from solutions of their mixtures. Fractions with prescribed purity of separated metals can be obtained by changing the number of stages and cycles of counter-current process and varying the value of dimensionless phase movement time.

Experimental and numerical investigation of natural circulation stability of the SHUNCL thermal-hydraulic loop

Nowadays, the application of natural circulation due to safety margins that provide for cooling the nuclear reactor cores has drawn the attention of researchers and designers in this context. Employing the benefits of natural circulation demands a thorough study of various phenomena such as thermo-fluid dynamics of steam-liquid interaction with the associated challenges that the most significant one is instabilities due to the severe dependency of mass flow rate on the applied heat flux. For this purpose, SHUNCL1 thermal hydraulic loop has been designed and constructed under atmospheric conditions and an experimental scenario has been arranged to investigate the mass flow rate variation due to heat flux. It is observed that the system behavior particularly the mass flow rate shows a considerable sensitivity to the heat flux variation such that in specific limit of heat flux implementation, the system behavior undergoes severe fluctuations and never attains to a stable condition. In addition to the experimental study, a numerical simulation of the SHUNCL loop has been prepared using the RELAP5 code in order to more investigate the effect of thermal hydraulic parameters on the instability of the operating system. System pressure, inlet subcooling, chimney length, orificing diameter and the heat section length are analyzed. Also, stability boundary is obtained based on two dimensionless numbers, phase change (Npch) and subcooling (Nsub) and it was observed that the occurred instability in the SHUNCL thermal hydraulic loop is of the type-1 dynamic instability.