High-velocity Limit Research Articles

Spark ignition and stable flame of premixed methanol-ammonia gaseous jet at atmospheric surrounding

Ammonia, regarded as a zero-carbon fuel, presents significant challenges due to its notable combustion and chemical inertness. To mitigate these challenges, blending liquid ammonia with carbon-neutral methanol offers a promising avenue for creating an innovative, stable, and large-scale producible carbon-neutral fuel. This study investigates the impacts of xCH3OH (methanol mole ratio in methanol-ammonia mixture) and v (mean jet velocity at nozzle outlet) on forming stable flames of a premixed methanol-ammonia argon-oxygen (MA-AO) gaseous jet in the atmospheric surrounding. Results indicate that the pure ammonia argon-oxygen (A-AO) mixture can be ignited by an electrical spark with the energy of about 52.1 mJ, but it cannot grow to be a stable jet flame although the fire nucleus can form. Blending methanol is very helpful in forming a stable jet flame of the MA-AO mixture. When xCH3OH is lower than 49% at λ = 1.0, only the fire nucleus could be formed without a stable jet flame. When xCH3OH is more than 49%, there is a certain mean jet velocity range for different xCH3OH to form a stable flame. At the low-velocity limit, the flame would be quenching. While the flame would be blown off at the high-velocity limit. The velocity limits of quenching and blow-off become higher with higher xCH3OH, and the blow-off velocity limit increases more evident.

Inverse scattering for repulsive potential and strong singular interactions

In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder [J. Math. Phys. 36(8), 3902–3921 (1995)], the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.

Experimental study of the ignition chamber with accelerating cavity applying to methanol lean combustion

Owing to the high laminar flame velocity and broad flammability limit of methanol (CH3OH), it is ideal for lean burning. How to obtain high energy and reliable ignition is one of the biggest challenges with lean or ultra-low combustion. To gain good ultra-lean burn performance, one solution is utilizing an turbulent jet ignition (TJI)system. Moreover, the methanol can be directly used in the jet ignition chamber for its low vaporization temperature and volatile characteristics. To enhance the methanol jet ignition performance, the two-stage accelerating cavity was applied to accelerate the combustion and extend the lean-burn limit in this research. In a optical experimental apparatus, jet ignition and combustion process of premixed methanol in the main combustion chamber (MCC) were investigated using the shadowgraph and transient pressure data acquisition methods. The experiment results showed that the pressure of the MCC emerged an obvious two-stage rising process to use the two-stage accelerating cavity (SAC). In addition, when the SAC was applied in the ignition chamber (IC), the proportion and peak value of the first stage heat release in the MCC were clearly higher than those of the single straight hole (SSH). Moreover, the ignition chamber compounded with SAC exhibited a short ignition delay and long jet ignition duration. Compared to SSH, the methanol combustion duration in the MCC by using SAC shortened by approximately 28% under both stoichiometric and lean conditions. In other words, The SAC accelerated the combustion process of methanol. More significantly, it was found that the proper secondary acceleration hole diameter (SAHD) play an crucial role in the jet ignition and combustion process, especially under ultra-lean conditions. In addition, by utilizing SAC-3-4.5, the combustion duration of was shortened by 41.9% than that of using SAC-3-3 at the equivalence ratio of 0.6. Finally, the ultra-lean burn limit could be extended to 0.35 by using SAC-3-4.5, which greatly expanded the methanol lean combustion limit.

Performance Comparison of Wood, Plywood, and Oriented Strand Board under High- and Low-Velocity Impact Loadings

Abstract In this article, the behavior of wood, plywood, and oriented strand board (OSB) under high- and low-velocity impact loadings was investigated experimentally. For the high-velocity impact test, limit velocity (Vbl) and impact energy absorbed (Eab) were determined by subjecting the material to different impact loading by conical nose projectile. For the low-velocity impact test, the materials were subjected to four levels of energy—10, 39, 78, and 98 J—and the time history responses of velocity, energy, load, and displacement were obtained. Additionally, quantitative data for damage size are presented. The results show that in comparison with OSB and solid wood plates, plywood presents better characteristics in response to both high- and low-velocity impact loadings.

Registry-Dependent Peeling of Layered Material Interfaces: The Case of Graphene Nanoribbons on Hexagonal Boron Nitride

Peeling of layered materials from supporting substrates, which is central for exfoliation and transfer processes, is found to be dominated by lattice commensurability effects in both low and high velocity limits. For a graphene nanoribbon atop a hexagonal boron nitride surface, the microscopic peeling behavior ranges from stick-slip, through smooth-sliding, to pure peeling regimes, depending on the relative orientation of the contacting surfaces and the peeling angle. The underlying mechanisms stem from the intimate relation between interfacial registry, interlayer interactions, and friction. This, in turn, allows for devising simple models for extracting the interfacial adhesion energy from the peeling force traces.

The checkerboard model for the eddy-dispersion in laminar flows through porous media. Part I: Theory and velocity field properties

The additivity assumption underlying Giddings' coupling model for the eddy-dispersion in laminar flows through heterogeneous media is critically analyzed and a potential solution for its non-additivity in the high velocity limit is presented. Whereas the unit cell in Giddings' model only consists of a single velocity bias step, the unit dispersion cell of the newly proposed model comprises two consecutive velocity bias steps. Consequently, the unit cell of this new model allows to account for the occurrence of an internal velocity bias rectification at high reduced velocities and is therefore additive in both the low and high velocity limit.First, a mathematical expression for the velocity- and diffusion-dependency of the model's dispersion characteristics has been established. Subsequently, the physical behavior of the model is discussed. It is shown the relation between the eddy-dispersion plate height h and the reduced velocity ν can be expected to display a local maximum in systems where the transversal dispersion purely occurs by molecular diffusion, as is the case in perfectly ordered flow-through media. In disordered media, where the transversal dispersion also contains a significant advective component, the model predicts a velocity-dependency that is qualitatively similar to that described by Giddings' coupling model but, all other conditions being equal, converges to a significantly smaller horizontal asymptote at high reduced velocity. The latter might shed new light on earlier eddy-dispersion studies pursuing a quantitative agreement between experimental data and the Giddings model.

Morphological stability diagram for slowly and rapidly solidifying binary systems

A linear morphological stability of the solid-liquid interface is analyzed for a binary alloy in the limit of low and high crystal growth velocities. Using the result of this analysis, a diagram of morphologies is derived for a whole range of solidification rates with indicating critical growth velocities for the transitions planar front ⇔ cellular/dendritic structure. It is specially noted that the speed of solute diffusion in the bulk liquid limits the absolute chemical stability velocity from the high-rate transition cells/dendrites ⇒ planar front.

A numerical study on premixed hydrogen/air flames in a narrow channel with thermally orthotropic walls

Premixed hydrogen/air micro-flame stabilizations in a narrow channel confined by two parallel plates with thermally isotropic and orthotropic wall materials are numerically studied using a OpenFOAM-based, reacting flow code. For a range of simulated equivalence ratios and inflow velocities, two modes of flame shapes (convex-shaped and concave-shaped) are observed, accompanying with variations of the number of heat release rate peaks in flame structures, which can be attributed to the appearance of some critical O-participating and H-participating elementary reactions. Flame stability limits are studied for three sets of wall thermal conductivities of k = 16 W/m K, k = 128 W/m K (isotropic) and kxx = 128 W/m K &kyy = 16 W/m K (orthotropic). The low velocity limits show invariant with wall thermal conductivities, while the high velocity limits in descending order are found to be: “k = 128 W/m K” > “kxx = 128 W/m K &kyy = 16 W/m K” > “k = 16 W/m K”. The logic behind is the competition between two mechanisms: the wall pre-heating effects and the transverse heat losses to the ambient. The critical convective heat transfer coefficients that reflect the combustor's ability to resist heat losses are also investigated among the three cases. The reduction of the transverse thermal conductivity can have a high critical coefficient value in the low-inflow velocity regime while makes negligible impacts on extending the critical coefficient in the high-inflow velocity regime. In summary, the use of thermally orthotropic wall materials leads to a slightly decreased high velocity limit (~3% lower) but a considerably increased critical convective heat transfer coefficient in the high-inflow velocity-regime (~25% higher), as compared to the thermally isotropic combustor of k = 128 W/m K.

Modified parameterization of the Li-Petrasso charged-particle stopping power theory

Charged-particle energy loss or “stopping power” in plasmas has been studied theoretically and experimentally, with important applications in modeling fusion experiments. Dense plasmas relevant to inertial fusion are theoretically challenging, but several models have been developed. Here, we report several physically motivated modifications to the parameterization of the Li-Petrasso stopping-power model. The new parameterization described in this work leads to larger discrepancies between the Li-Petrasso model and both other theories and experimental data near the Bragg peak for plasma stopping, corroborating recent conclusions that the Li-Petrasso model is not accurate in this regime [Frenje et al., Phys. Rev. Lett. 122, 015002 (2019)]. Conversely, our modified parameterization agrees better with other theories in the high-velocity limit.

Inverse scattering in the Stark effect

We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder (1995 J. Math. Phys. 36 3902–21), we prove that the high-velocity limit of the scattering operator uniquely determines the short-range interaction potentials. Moreover, we prove that, when a long-range interaction potential is given, the high-velocity limit of the Dollard-type modified scattering operator uniquely determines the short-range part of the interactions. We allow the potential functions to belong to very broad classes. These results are improvements on the previous results obtained by Adachi and Maehara (2007 J. Math. Phys. 48 042101; Adachi et al 2013 Inverse Problems 29 085012).

Time-dependent methods in inverse scattering problems for the Hartree-Fock equation

The major purpose of this paper is to establish a reconstruction procedure of two-body interactions from scattering solutions for a Hartree-Fock equation. We give a uniqueness theorem and propose a new reconstruction procedure of the short-range and two-body interactions from a high-velocity limit of the scattering operator for the Hartree-Fock equation. Moreover, it will be found that the high-velocity limit of the scattering operator is equal to a small-amplitude limit of the scattering operator.

High-velocity runaway binaries from supernovae in triple systems

Recent studies on hypervelocity stars (HVSs) have generated a need to understand the high velocity limits of binary systems. If runaway binary systems with high movement speeds well in excess of 200km/s were to exist, it would have implications on how HVS candidates are selected, and our current understanding of how they form needs to be reinforced. In this paper, we explore the possibility that such high velocity runaway binaries (HVRBs) can be engendered by supernova explosions of the tertiary in close hierarchical triple systems. We find that such explosions can lead to significant remnant binary velocities, and demonstrate via constraining the velocity distribution of such HVRBs that this mechanism can lead to binaries with centre of mass velocities of 350 km/s or more, relative to the original centre of mass of the progenitor triple system. This translates into potential observations of binaries with velocities high enough to escape the Galaxy, once the Galactic rotational velocity and objects of Large Magellanic Cloud origins are considered.

Experimental investigation of flame stability limits of a mesoscale combustor with thermally orthotropic walls

Flame stability limits were experimentally investigated for a parallel plate mesoscale combustor with orthotropic walls. The combustor walls were made of pyrolytic graphite, which has orthotropic thermal conductivity of 350 W/m-K in ab-plane and 3.5 W/m-K in the c-plane at room temperature. Infrared images of the combustor walls showed that the pyrolytic graphite plates had uniform temperature distributions at all operating conditions tested. Compared to an isotropic material (stainless steel), pyrolytic graphite showed a greater high velocity limit (HVL) and thereby wider flame stability limit. Thermal performance of the combustor was also evaluated via an energy balance, wherein, heat losses were found to dominate the thermal fluxes. The uniform temperature profile and the lack of a distinctive “hot spot” in the thermal images of the pyrolytic graphite indicate that it is a suitable combustor material for thermoelectric and thermophotovoltaic power conversion applications. Future work should focus on the thermal management so as to avoid excessive heat losses leading to an improvement in the thermal performance of the combustor.

On inverse scattering problem for the Schrödinger equation with repulsive potentials

We study multidimensional inverse scattering for Hamiltonians with repulsive potentials. Assuming short-range conditions for the interaction potential, the high velocity limit of the scattering operator determines uniquely the short-range part, using the Enss-Weder time-dependent method (1995). This work improves on a previous result obtained by Nicoleau (2006). We can allow interaction potentials to have not only slower decays but also Coulomb-like singularities.

High-speed monodisperse droplet generation by ultrasonically controlled micro-jet breakup

A liquid jet that is ejected from a nozzle into air will disintegrate into drops via the well-known Plateau–Rayleigh instability within a certain range of Ohnesorge and Reynolds numbers. With the focus on the micrometer scale, we investigate the control of this process by superimposing a suitable ultrasonic signal, which causes the jet to break up into a very precise train of monodisperse droplets. The jet leaves a pressurized container of liquid via a small orifice of about 20 μm diameter. The break-up process and the emerging droplets are recorded via high-speed imaging. An extended parameter study of exit speed and ultrasonic frequency is carried out for deionized water to evaluate the jet’s state and the subsequent generation of monodisperse droplets. Maximum exit velocities obtained reach almost 120 m s−1, and frequencies have been applied up to 1.8 MHz. Functionality of the method is confirmed for five additional liquids for moderate jet velocities \(\lesssim\)38 m s−1. For the uncontrolled jet disintegration, the drop size spectra revealed broad distributions and downstream drop growth by collision, while the acoustic control generated monodisperse droplets with a standard deviation less than 0.5 %. By adjustment of the acoustic excitation frequency, drop diameters could be tuned continuously from about 30 to 50 μm for all exit speeds. Good agreement to former experiments and theoretical approaches is found for the relation of overpressure and jet exit speed, and for the observed stability regions of monodisperse droplet generation in the parameter plane of jet speed and acoustic excitation frequency. Fitting of two free parameters of the general theory to the liquids and nozzles used is found to yield an even higher precision. Furthermore, the high-velocity instability limit of regular jet breakup described by von Ohnesorge has been superseded by more than a factor of two without entering the wind-induced instability regime, and monodisperse droplet generation was always achievable. Thus, the reliable and robust realization of tunable high-speed monodisperse micro-droplet trains is demonstrated. Some implication for applications is discussed.

A finite parallel zone model to interpret and extend Giddings’ coupling theory for the eddy-dispersion in porous chromatographic media

The finite length parallel zone (FPZ)-model is proposed as an alternative model for the axial- or eddy-dispersion caused by the occurrence of local velocity biases or flow heterogeneities in porous media such as those used in liquid chromatography columns. The mathematical plate height expression evolving from the model shows that the A- and C-term band broadening effects that can originate from a given velocity bias should be coupled in an exponentially decaying way instead of harmonically as proposed in Giddings’ coupling theory. In the low and high velocity limit both models converge, while a 12% difference can be observed in the (practically most relevant) intermediate range of reduced velocities. Explicit expressions for the A- and C-constants appearing in the exponential decay-based plate height expression have been derived for each of the different possible velocity bias levels (single through-pore and particle level, multi-particle level and trans-column level). These expressions allow to directly relate the band broadening originating from these different levels to the local fundamental transport parameters, hence offering the possibility to include a velocity-dependent and, if, needed retention factor-dependent transversal dispersion coefficient. Having developed the mathematics for the general case wherein a difference in retention equilibrium establishes between the two parallel zones, the effect of any possible local variations in packing density and/or retention capacity on the eddy-dispersion can be explicitly accounted for as well. It is furthermore also shown that, whereas the lumped transport parameter model used in the basic variant of the FPZ-model only provides a first approximation of the true decay constant, the model can be extended by introducing a constant correction factor to correctly account for the continuous transversal dispersion transport in the velocity bias zones.

On multidimensional inverse scattering in time-dependent electric fields

We study one of the multidimensional inverse scattering problems for quantum systems in time-dependent electric fields E(t), which is represented as E0(1 + |t|)−μ with 0 ⩽ μ < 1, based on the Enss–Weder time-dependent method. We show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the short-range part like |x|−γ with γ > 1/(2 − μ) of the potential belonging to the class rather wider than the one given by Adachi, Kamada, Kazuno and Toratani. Our method can also improve previous results in the case where E(t) is periodic in t with non-zero mean E0.

High-velocity estimates and inverse scattering for quantum N-body systems with Stark effect

In an N–body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials and long-range potentials, from the high-velocity limit of the Dollard scattering operator. We give a reconstruction formula with an error term.

Bright matter-wave soliton collisions at narrow barriers

We study fast-moving bright solitons in the focusing nonlinear Schr\"odinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons collide at the location of the barrier. In the limiting case of a $\ensuremath{\delta}$-function barrier, we use an analytic method to show that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and to determine whether one, or both, of the outgoing waves are bright solitons. We show using numerical simulations that this analytic result is valid in the high velocity limit: outside this limit nonlinear effects introduce a skew to the phase dependence, which we quantify. Finally, we numerically explore the effects of introducing a finite-width Gaussian barrier. Our results are particularly relevant, as they can be used to describe a range of interferometry experiments using bright solitary matter-waves.

On multidimensional inverse scattering in an external electric field asymptotically zero in time

Based on the Enss–Weder time-dependent method, we study one of the multidimensional inverse scattering problems for quantum systems in an external electric field asymptotically zero in time as E0(1 + |t|)−μ with 0 < μ < 1, where E0 is a non-zero constant electric field. We show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the short-range potential like |x|−γ with γ > 1/(2 − μ). Moreover, we prove that the high velocity limit of any one of the Dollard-type modified scattering operators determines uniquely the total potential.Dedicated to the memory of Professor Tetsuro Miyakawa.