Modeling and Simulation of Pressure Control in High Pressure Fuel Engineering

In this paper, a special integrable negative-order Calogero–Bogoyavlenskii–Schiff equation (nCBS) in fluid mechanics is studied by means of the symmetry reduction method and consistent tanh expansion method. The Painlevé integrability is investigated to confirm the compatibility conditions. This integrable nCBS equation has been transformed into different reduction equations and the corresponding invariant solutions with arbitrary functions are obtained. The corresponding structures of the invariant solutions for the nCBS equation are also shown graphically. At last, new types of soliton–cnoidal interaction solutions for the nCBS equation are presented through the consistent tanh expansion method on the basis of the truncated Painlevé expansion.

We present a fluid---structure interaction (FSI) modeling method based on using the deforming-spatial-domain/stabilized space---time (DSD/SST) method for the fluid mechanics part and a finite difference (FD) method for the structural mechanics part. As the structural mechanics model, we focus on the thin-shell model. The fluid mechanics equations with moving boundaries are solved with the DSD/SST method and the thin-shell structural mechanics equation is solved with a FD method, with partitioned coupling between the two parts. The coupling of the DSD/SST and FD solvers makes sure that the boundary conditions on the fluid-structure interface at the end of each time step are matched between the fluid and the structure. A hanging plate in vacuum under gravitational force is performed to validate the structure solver. In addition, a pitching plate in a uniform flow is simulated to validate the FSI solver. The present results are in reasonable agreement with data predicted by other methods.

Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev–Petviashvili equation in fluid mechanics

The Euler-Taylor-Galerkin flux-corrected transport (ETG-FCT) algorithm for the numerical solution of particle transport equations is described, based on the method developed by Lohner to solve conservation equations in fluid mechanics, and its application is extended to gas discharge problems. To improve the efficiency of computing and reduce numerical error, the nonuniform triangular mesh method is introduced, and the continuity equation is solved by ETG-FCT. The new contributions in this paper include the development of the ETG scheme and its application to rod-plate gap streamer discharge in 50~50% SF6/N2gas mixtures problems. Results are obtained: the spatial distributions of electron densities, positive ion densities, negative ion densities, photoelectron densities, and the electric field, respectively. The velocities of streamer propagations and the radius of streamer obtained from the proposed model are in good agreement with experimental and simulation results in literature. The results also prove that the ETG-FCT method is valid.

Of current interest, the paper commented [i.e., Eur. Phys. J. Plus (2020) 135:272] has investigated the $$(3+1)$$ -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation in ocean dynamics, fluid mechanics and plasma physics. However, the story that the paper commented has caused could be made more complete. Hereby, for the same equation, via the Bell polynomials, we work out the same bilinear form as that in the paper commented, but the ways of derivation are different. With symbolic computation, we also construct two auto-Backlund transformations for the same equation with some solitons. Our results are with respect to the amplitude or elevation of the relevant wave in ocean dynamics, fluid mechanics and plasma physics.

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

Under investigation in this paper is the (2 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation, which can be utilized to describe certain nonlinear phenomena in fluid mechanics. We obtain the higher-order lump, breather and hybrid solutions, and analyze the effects of the constant coefficients $$h_1$$ , $$h_2$$ , $$h_4$$ and $$h_5$$ in that equation on those solutions, since the higher-order lump solutions are generalized via the long-wave limit method, and since the higher-order breather solutions and hybrid solutions composed of the solitons, breathers and lumps are derived. With the help of the analytic and graphic analysis, we get the following: (1) amplitudes of the humps and valleys of the first-order lumps are related to $$h_1$$ , $$h_2$$ , $$h_4$$ and $$h_5$$ , proportional to $$h_4$$ while inversely proportional to $$h_2$$ . Velocities of the first-order lumps are proportional to $$h_4$$ . The second-order lumps describe the interaction between the two first-order lumps, which is elastic since those lumps keep their shapes, velocities and amplitudes unchanged after the interaction. Effects of $$h_2$$ and $$h_4$$ on the second-order lumps are graphically illustrated. (2) Amplitudes of the first-order breathers are proportional to $$h_2$$ . Interaction between the breather waves is graphically presented. Effects of $$h_2$$ and $$h_1$$ on the amplitudes and shapes of the second-order breathers are graphically discussed. (3) Elastic interactions are graphically illustrated, between the first-order breathers and one solitons, the first-order lumps and one solitons, as well as the first-order breathers and first-order lumps. Also graphically illustrated, amplitudes of all those three kinds of hybrid solutions are inversely proportional to $$h_2$$ , and velocity of the one soliton is positively correlated to $$h_4$$ .

This paper investigates the quasi-periodic breathers of the (2+1)-dimensional Hirota equation, which can describe the wave phenomena in nonlinear optics and fluid mechanics. By combining the theta function and Hirota bilinear method, the quasi-periodic breather solutions are constructed. The solvability problem of the quasi-periodic breathers is transformed into a least squares problem, which can be solved via a new algorithm called the global Levenberg-Marquardt (LM) method. Different types of quasi-periodic breathers are obtained, including quasi-periodic Kuznetsov-Ma breather, quasi-periodic Akhmediev breather as well as regular quasi-periodic breather. By introducing an analysis method related to the characteristic line, the dynamical characteristics of the quasi-periodic breathers are derived. In addition, the data-driven quasi-periodic breathers are studied by using the physics-informed neural network-adaptive residual distribution optimization (PINN-ARDO) method.

Traffic flow analysis was considered as one of the main steps in transportation planning and engineering. Various methods have been developed for this purpose. Most of these methods are based on available equations in traffic engineering. Mathematical methods used for analyzing traffic flow has always been very complicated and resource consuming. In 1995, using finite elements method for analyzing traffic flow was first introduced and developed over the few years. Hence it is a new look at traffic flow analysis which still needs lots of complex equations to be solved. In 2007, for the first time, it was suggested to simulate traffic flow as a fluid; using finite elements equations in fluid mechanics (i.e. model the vehicles in the road as a fluid in a canal). Results were considerably matching the real world case studies data. In this paper which is a part of study on the finite elements methods in transportation modeling and planning, ten different routes (e.g. bridge, intersection, roundabout) in Shiraz city (one of large scale cities of Iran) have been modeled in one of fluid mechanics modeling platform. Outputs compared with real world data by some adjustment and calibration which have been made to make it possible to match data and calculate the errors. Results show acceptable errors regarding modeling traffic flow by fluid mechanics simulation platforms. Additionally, a sensitivity analysis has been performed for acquisition of each element’s role (e.g. number of lanes, maximum allowed speed and AADT) in model accuracy in Neural Network Algorithm platform.

In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain Bäcklund transformation associated with truncated Painlevé expansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.

In this work, we present our progress on high-temperature water splitting (HTWS) and hydrogen production at elevated pressure using proton-conducting ceramics. The electrochemical performance of the proton-conducting electrolyzer unit-cell stack is analyzed at 550 °C and pressures up to 12 bar.Proton-conducting ceramics are a promising new class of electrochemical cells due to their high proton conductivity at intermediate temperatures in comparison to more-conventional solid-oxide or molten-carbonate counterparts. Materials exploration continues for fabricating proton conducting cells to achieve better electrochemical performance during operation. Recently, lower ohmic resistance and degradation rates have been observed using the highly proton-conductive and chemically stable perovskite BaCe0.4 Zr0.4 Y0.1 Yb0.1 O3−δ (BCZYYb4411). In this study we work with a composite of Ni–BZCYYb4411 as the fuel electrode (cathode), BCZYYb4411 as the electrolyte and BCFZY as the steam electrode (anode). The cathode and electrolyte layers of the membrane-electrode assemblies used in this study are synthetized using the solid-state reactive sintering (SSRS) method. SSRS is an attractive MEA-fabrication method, as it greatly reduces the number of costly and time-consuming high-temperature sintering processes. During SSRS, single-phase protonic-ceramic perovskite is formed from parent oxides during high-temperature co-sintering of the anode-electrolyte layers. This is in contrast to more-traditional processing, in which the desired phase is first formed in powder form through calcination of parent oxides, while MEA formation is executed in follow-on high-temperature sintering steps.The cathode support is formed by dry-pressing to produce a 57-mm-dia x 1.5-mm-thick disc. The electrolyte (~ 10 mm) layer is deposited using an ultrasonic spray atomizer. The process control and narrow particle size distribution delivered by the ultrasonic atomizer consistently produces a high-density electrolyte, while minimizing thickness. We are now extending the use of ultrasonic spray deposition to other critical components such as the air-steam electrode and interfacial layers.As shown in Figure 1a, the protonic-ceramic membrane-electrode assembly (MEA) is bonded to a composite ceramic frame and assembled into a sealed cell stack with metallic interconnects, current collectors, sealing gaskets and end plates. The stack is placed in a preloaded spring-based mechanical compression system that axially compresses the electrolyzer stack while avoiding any direct compression of the MEA. The assembly is placed in a sealed vessel (Figure 1b); anode and cathode gas pressures are balanced across the MEA, and with the surrounding inert vessel gas (N2). Downstream back-pressure regulators maintain electrolyzer and vessel pressures to minimize the risk of cell fracture.Despite the challenges associated with high pressure operation, this technology is key to address some of the main issues associated with proton conducting ceramics. Higher pressure operation should lead to higher efficiencies by decreasing the electron hole concentration in the electrolyte usually associated with the electron leakage problem. Also, electrode activity can be enhanced at higher pressures, enabling higher currents at lower driving voltages. Figure 1c shows an increased electrolyzer performance of almost 50% when the operating pressure is raised to 12.5 bar. This is evidence of the better kinetics and lower power required to electrolyze at higher pressures.In parallel, the high-pressure protonic-ceramic electrolyzer delivers a pure, dry, pressurized hydrogen product stream that does not require downstream separation processes. Pressurized operation reduces downstream compression needs. Elevated-pressure operation is also beneficial for the synthesis of electrofuels, where green hydrogen is transformed into higher-value chemical. These chemistries often require high temperatures and pressures to achieve meaningful production rates. Ammonia serves as an example, the second-most-produced global chemical that contributes nearly 1.5% of global annual CO2 emissions. We are currently integrating our high-pressure electrolysis operation with ruthenium-based catalysts for electrochemical ammonia synthesis. In this talk, our progress in electrochemical energy storage with proton-conducting ceramics will be reviewed. Figure 1

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to non-linear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing.

This paper continues our study of vortices in Ginzburg-Landau theories with special attention to applications in superconductivity. In another paper, we derived asymptotic equations governing the dynamics of interacting vortices. Here, we study the hydrodynamic limit of these vortices. For vortices in the solutions of the nonlinear Schr\"odinger equation, the hydrodynamic equation is the incompressible Euler's equation in fluid mechanics. For vortices in the time-dependent Ginzburg-Landau equations, the hydrodynamic equations can be thought of as being the complement of the Euler equations. Preliminary results on the numerical studies of the hydrodynamic equations are presented. As applications of the hydrodynamic formalism, we study the pinning of vortex liquids by periodic potentials, and the propagation of magnetic fields into type-II superconductors. The hydrodynamic formalism suggests that to leading order, the vortex liquids are pinned even at small but positive temperature.

In this paper, we introduce a new nonlinear evolution equation, which is ([Formula: see text])-dimensional variable-coefficient Kadomtsev–Petviashvili equation. First, according to the Hirota bilinear method, we get some exact solutions of the equation, including lump solution, lump-soliton solution, rogue-soliton solution and lump-kink solution. Then, we obtain some new exact solutions by generalizing the form of the lump solution on a further solution. Finally, based on the symbolic calculation method with Mathematica, the characteristics of the interaction solutions are shown in the graphs and we analyze the dynamic change of the solutions. Furthermore, we discuss the applications of these solutions in physics via the analysis.

The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of the variable considered (velocity, scalar, and position). A study of the implications of entrance and exit conditions is performed, showing that a new term should be added to the PDF transport equation to preserve normalization in some nonstationary processes. In practice, this term is taken into account naturally in particle methods. Finally, the existence of discontinuities at the limits is also investigated.