Two-dimensional Numerical Simulations Research Articles

High-speed microactuation in a supersonic dual-stream jet flow

Supersonic shear layers experience instabilities that generate significant adverse effects; in complex configurations, these instabilities have global impacts as they foster compounding complications with other independent flow features. We consider the flow near the exit of a dual-stream rectangular nozzle. The supersonic core and sonic bypass streams mix downstream of a splitter plate trailing edge (SPTE) just above an adjacent deck. We perform two-dimensional direct numerical simulations with laminar inflow conditions to parametrically explore the influence of active flow control, considering various actuation angles and locations. The goal is to alleviate the prominent tone associated with vortices shed at the SPTE; these vortices initiate an unsteady shock system that affects the entire flow field through a shock-induced separation and the downstream evolution of plume shear layers. Resolvent analysis is performed on the baseline flow. The identified optimal response guides the placement of steady-blowing actuators. Since the resolvent analysis fundamentally investigates the input–output dynamics of a system, it is also utilized to uncover actuation-induced changes in the forcing–response dynamics. Spectral analysis shows that the baseline flow fluctuating energy is concentrated in the shedding instability. Actuating at optimal angles based on location disperses this energy into various flow features; this affects the shedding itself, and the structure and unsteadiness of the shock system, and thus the response of the deck and nozzle wall boundary layers and the plume. The resolvent analysis indicates, and Navier–Stokes solutions confirm, that favourable control is obtained by either indirectly or directly mitigating the baseline instability.

Unifying suspension and granular shear-induced self-diffusion

Shear-induced self-diffusion is a fundamental mode of transport in granular flows. Yet its critical behaviour and dependence on the particle solid fraction are still unclear. Here, we rationalize these dependencies by performing two-dimensional pressure-imposed numerical simulations of dense non-Brownian frictional suspensions. Our results, combined with existing numerical data on inertial granular flows, show that the shear-induced diffusion coefficients of both systems can be captured by a single function of the distance to jamming. They further show that the grain diffusive behaviour is underpinned by a specific random walk process, having a constant elementary step length driven at a frequency that increases with the solid fraction. The proposed scaling laws pave the way for a better understanding of mixing processes in granular media.

Dynamic interaction patterns of oblique detonation waves with boundary layers in hypersonic reactive flows

Due to their high thermal cycle efficiency and compact combustor, oblique detonation engines hold great promise for hypersonic propulsion. Previous numerical simulations of oblique detonation waves have predominantly solved the Euler equations, disregarding the influence of viscosity and boundary layers. This work aims to study how the interaction between the oblique detonation wave and the boundary layer influences the detonation wave structures in confined spaces. Two-dimensional numerical simulations considering detailed chemistry are performed in a stoichiometric H2/air mixture. The results indicate that the wedge-induced oblique detonation wave generates a strong adverse pressure gradient upon impacting the upper wall, leading to boundary layer separation. The separation zone subsequently induces an oblique shock wave near the upper wall, and an increase in separation angle will cause the transition from an oblique shock wave to an oblique detonation wave. The formation of the separation zone reduces the actual flow area and may even lead to flow choking; its obstructive effect is similar to that of the Mach stem in inviscid flow. To establish a connection between the viscous recirculation zone and the inviscid Mach stem, we introduce a dimensionless parameter, η, based on the inviscid assumption. It is defined as the ratio of the inviscid Mach stem height to the channel entrance height. This parameter can be used to identify three wave systems in a viscous flow field: separation shock-dominated wave systems, separation detonation-dominated wave systems, and unstable Mach stem-dominated wave systems. Among these, the appearance of detonation Mach stems leads to flow choking, and the shock-detonation wave system continually moves upstream, ultimately causing the failure of the oblique detonation combustion. The findings of this study provide new insights into the investigation of the influence of viscosity on the flow structure of oblique detonation waves.

Investigation on the integrated characteristics of n-decane/air rotating detonation combustor and supersonic turbine

In this study, the two-dimensional numerical simulations are conducted to study the flow field characteristics, turbine performance and loss mechanism of integrated system of rotating detonation combustor and supersonic turbine under two different directions of detonation wave propagation. The results indicate that the propagation direction of RDW affects the incident angle between OSW and guide vanes, resulting in different operating modes for aligned and unaligned modes. OSW in the turbine cascade undergoes the leading-edge shock, blade surface reflection and trailing edge diffraction. The backward-propagating rake-type shock envelope is formed due to leading-edge shock of the rotor. In misaligned mode, the stator has higher damping of both pressure and temperature. The stator significantly improves the circumferential uniformity of both velocity and pressure, particularly when operating in aligned mode. The total pressure loss in aligned mode is less, therefore the turbine achieves higher rim work and efficiency. The viscosity is one of the main sources of loss in the flow field. The reflected shock waves at the leading edge of the rotor and in the stator cascade are the primary factors contributing to the leading-edge vortices on the stator vanes.

On the Complex Flow Dynamics of Shear Thickening Fluids Entry Flows

Due to their nature, using shear thickening fluids (STFs) in engineering applications has sparked an interest in developing energy-dissipating systems, such as damping devices or shock absorbers. The Rheinforce technology allows the design of customized energy dissipative composites by embedding microfluidic channels filled with STFs in a scaffold material. One of the reasons for using microfluidic channels is that their shape can be numerically optimized to control pressure drop (also known as rectifiers); thus, by controlling the pressure drop, it is possible to control the energy dissipated by the viscous effect. Upon impact, the fluid is forced to flow through the microchannel, experiencing the typical entry flow until it reaches the fully developed flow. It is well-known for Newtonian fluid that the entrance flow is responsible for a non-negligible percentage of the total pressure drop in the fluid; therefore, an analysis of the fluid flow at the entry region for STFs is of paramount importance for an accurate design of the Rheinforce composites. This analysis has been numerically performed before for shear-thickening fluids modeled by a power-law model; however, as this constitutive model represents a continuously growing viscosity between end-viscosity plateau values, it is not representative of the characteristic viscosity curve of shear-thickening fluids, which typically exhibit a three-region shape (thinning-thickening-thinning). For the first time, the influence of these three regions on the entry flow on an axisymmetric pipe is analyzed. Two-dimensional numerical simulations have been performed for four STFs consisting of four dispersions of fumed silica nanoparticles in polypropylene glycol varying concentrations (7.5–20 wt%).

Flow-field analysis and performance assessment of rotating detonation engines under different number of discrete inlet nozzles

This study explores in depth rotating detonation engines (RDEs) fueled by premixed stoichiometric hydrogen/air mixtures through two-dimensional numerical simulations including a detailed chemical kinetic mechanism. To model the spatial reactant non-uniformities observed in practical RDE combustors, the referred simulations incorporate different numbers of discrete inlet nozzles. The primary focus here is to analyze the influence of reactant non-uniformities on detonation combustion dynamics in RDEs. By systematically varying the number of reactant injection nozzles (from 15 to 240), while maintaining a constant total injection area, the study delves into how this variation influences the behavior of rotating detonation waves (RDWs) and the associated overall flow field structure. The numerical results obtained here reveal significant effects of the number of inlets employed on both RDE stability (self-sustaining detonation wave) and performance. RDE configurations with a lower number of inlets exhibit a detonation front with chaotic behavior (pressure oscillations) due to an increased amount of unburned gas ahead of the detonation wave. This chaotic behavior can lead to the flame extinguishing or decreasing in intensity, ultimately diminishing the engine's overall performance. Conversely, RDE configurations with a higher number of inlets feature smoother detonation propagations without chaotic transients, leading to more stable and reliable performance metrics. This study uses high-fidelity numerical techniques such as adaptive mesh refinement (AMR) and the PeleC compressible reacting flow solver. This comprehensive approach enables a thorough evaluation of critical RDE characteristics including detonation velocity, fuel mass flow rate, impulse, thrust, and reverse pressure waves under varying reactant injection conditions. The insights derived from the numerical simulations carried out here enhance the understanding of the fundamental processes governing the performance of RDE concepts.

An analytical I-V model of SiC double-gate junctionless MOSFETs

Silicon carbide(SiC) double gate junctionless metal oxide semiconductor field-effect transistors(DG JL MOSFETs) have attracted significant attention due to their ideal high temperature characteristics and radiation resistance. Therefore, it is meaningful to exploit an I-V model for SiC DG JL MOSFETs. In this article, we make a linear approximation to describe the relationship between the surface mobile charge density and the surface electron concentration of the device. Based on this approximation and using the one-dimensional Poisson’s equation, we solve for the potential distribution of a SiC DG JL MOSFET in the subthreshold region. From this solution, we derived a functional relationship between the surface mobile charge density in the channel and the channel quasi-Fermi potential. Then we successfully developed a unified I-V model for the SiC DG JL MOSFETs. Based on the drain to source current calculation formula, the calculation expressions for the device’s transconductance and output conductance are derived. By comparing our model with the results from the two-dimensional numerical simulation software Silvaco Atlas, our model’s calculations closely match the two-dimensional numerical simulation results from the subthreshold region to the accumulation region. This model has reference significance for SiC DG JL MOSFETs in the high temperature electronic circuit application field.

Analysis of diversion ratio and study of sediment transport in the first canal station of an irrigation area based on Mike21 hydrodynamic model

Abstract Based on MIKE21 hydrodynamic model, the change of diversion ratio and sediment transport at the first canal station in an irrigation area are analyzed. Two-dimensional numerical simulation is carried out by using MIKE21 FM hydrodynamic module, and the split ratio is studied. In the aspect of sediment transport, the transport path and deposition distribution of different sediment particle sizes are simulated by simulating sediment transport. The results show that under the lowest daily average water level, the diversion canal flow can meet the irrigation demand; The particle size of sediment has a great influence on the deposition distribution and thickness of the approach channel at the first station of the canal, and then affects the water diversion capacity of the pumping station.

Sustenance of hydrogen–oxygen cellular detonation with ozone additions in confined space

The sustenance of cellular detonation under weak confinement is studied through two-dimensional (2D) numerical simulations of hydrogen–oxygen mixtures surrounded by inert gas. The results show that in the weakly confined space, the cellular detonation with Chapman-Jouguet velocity can survive by increasing the width of the reactant layer and enhancing the reactivity of reactants, which ensures enough triple points and high reactivity in the reactant layer for detonation sustenance since transverse shocks cannot be regenerated and reinforced by boundary reflection. By adding ozone into the system and changing the width of the reactant layer, the relationship between induction length and detonation sustenance is established. It is found that the sustenance of cellular detonation in the weakly confined space is related to the ratio of the reactant layer width to the induction length. Ozone reactions can reduce the induction length and enhance reactivity, thereby promoting the generation of new transverse shocks and significantly improving the sustenance of cellular detonation in weakly confined space.

Effect of a longitudinal magnetic field on streamer propagation in air: Numerical simulation

Two-dimensional numerical simulation of the negative streamer propagation in external electric and magnetic fields is performed for the case when applied electric and magnetic field vectors are parallel to the symmetry axis of the problem. The calculations are performed for air (a mixture of 80% N2 and 20% O2) with a concentration of gas molecules equal to Loshmidt's number. It is shown that the presence of a longitudinal field leads to a noticeable increase in the streamer propagation velocity associated with a decrease in its radius, which agrees with the known analytical estimates.

Numerical studies of hydrodynamic relativistic astrophysical jet: The modification of vorticity transport equation

In this Letter, we have carried out the two-dimensional numerical simulation of axisymmetric relativistic jet in cylindrical coordinates by employing higher order finite volume method in PLUTO [Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] solver. The modified vorticity transport equation has been proposed for relativistic flow by taking the curl of the momentum equation, which shows significant change in the baroclinic vorticity production term due to relativistic effect. Both mathematical analysis and numerical results show that the vorticity production term due to baroclinic torque is heavily influenced due to the presence of specific enthalpy gradient and square of Lorentz factor gradient in a relativistic fluid flow.

Numerical simulation of the effects of pulsed injection on combustion and flow processes in a supersonic combustor

This paper describes two-dimensional numerical simulations of pulsed injection to a hydrogen-fueled air-breathing ramjet using the Reynolds-averaged Navier–Stokes method. We analyze the effects of sinusoidal pulsed injection on the start-up ignition time, start-up ignition range, combustion efficiency, and flow field evolution of the ramjet and compare the performance with that of steady injection. The results show that pulsed injection shortens the ignition time and optimizes the ignition equivalence ratio of hydrogen. Pulsed injection also improves the combustion efficiency of hydrogen, increasing the thrust of the engine by 7.79% compared with steady injection under the same equivalence ratio. We find that pulsed injection can cause oscillations in the ramjet combustion flow field, and show that the oscillation frequency is affected by the pulsed injection frequency.

Comparative experimental and numerical study of mixing efficiency in 3D-printed microfluidic droplet generators: T junction, cross junction, and asymmetric junctions with varying angles

In droplet-based microfluidics, rapid mixing during droplet formation enhances reaction uniformity, eliminating the need for micromixers. In this research, we conducted a comprehensive study by first employing a series of two-dimensional (2D) numerical simulations, followed by experimental investigations using 3D-printed microfluidic chips. We compared the mixing efficiency, droplet diameter, and droplet eccentricity of three different types of droplet generators: T junction, cross junction, and asymmetric droplet generators with various angles. Regarding mixing efficiency, we observed that the asymmetric droplet generators outperformed the cross junction by 30 % but fell slightly short of the mixing efficiency achieved by the T junction (1 %). Additionally, while the mixing index in the asymmetric generators closely matched that of the T junction, these asymmetric generators produced smaller droplets by 72 %. Increasing the angle in asymmetric droplet generators resulted in enhanced mixing efficiencies and an increase in droplet diameters. The asymmetric junction with a 30° angle could achieve a mixing efficiency of up to 80 %. Additionally, an analysis of the dispersed phase flow rate revealed that higher flow rates lead to larger droplet sizes and reduced mixing efficiencies. The asymmetric droplet generators improve mixing efficiency facilitating rapid reagent mixing, all while maintaining a small droplet diameter.

The effect of ice shelf rheology on shelf edge bending

Abstract. The distribution of pressure on the vertical seaward front of an ice shelf has been shown to cause downward bending of the shelf if the ice is assumed to have vertically uniform viscosity. Satellite lidar observations show that many shelf edges bend upward and that the amplitude of upward deflections depends systematically on ice shelf thickness. A simple analysis is presented showing that upward bending of shelf edges can result from vertical variations in ice viscosity that are consistent with field observations and laboratory measurements. Resultant vertical variations in horizontal stress produce an internal bending moment that can counter the bending moment due to the shelf-front water pressure. Assuming a linear profile of ice temperature with depth and an Arrhenius relation between temperature and strain rate allows derivation of an analytic expression for internal bending moments as a function of shelf surface temperatures, shelf thickness and ice rheologic parameters. The effect of a power-law relation between stress difference and strain rate can also be included analytically. The key ice rheologic parameter affecting shelf edge bending is the ratio of the activation energy, Q, and the power-law exponent, n. For cold ice surface temperatures and large values of Q/n, upward bending is expected, while for warm surface temperatures and small values of Q/n downward bending is expected. The amplitude of bending should scale with the ice shelf thickness to the power 3/2, and this is approximately consistent with a recent analysis of shelf edge deflections for the Ross Ice Shelf. These scaling relations should help guide fully two-dimensional numerical simulations of shelf bending.

FGM modeling considering preferential diffusion, flame stretch, and non-adiabatic effects for hydrogen-air premixed flame wall flashback

Preferential diffusion plays an important role especially in hydrogen flames. Flame stretch significantly affects the flame structure and induces preferential diffusion. A problematic phenomenon occurring in real combustion devices is flashback, which is influenced by non-adiabatic effects, such as wall heat loss. In this paper, an extended flamelet-generated manifold (FGM) method that explicitly considers the preferential diffusion, flame stretch, and non-adiabatic effects is proposed. In this method, the diffusion terms in the transport equations of scalars, viz. the progress variable, mixture fraction, and enthalpy, are formulated employing non-unity Lewis numbers that are variable in space and different for each chemical species. The applicability of the extended FGM method to hydrogen flames is investigated using two- and three-dimensional numerical simulations of hydrogen-air flame flashback in channel flows. The results of the extended FGM method are compared with those of detailed calculations and other FGM methods. The two-dimensional numerical simulations show that considering both preferential diffusion and flame stretch improves the prediction accuracy of the mixture fraction distribution and flashback speed. The three-dimensional numerical simulations show that the prediction accuracy of the flashback speed, backflow region, and distributions of physical quantities near the flame front is improved by employing the extended FGM method, compared with the FGM method that considers only the heat loss effect. In particular, the extended FGM method successfully reproduced the relationship between the reaction rate and curvature. These results demonstrate the effectiveness of the extended FGM method.Novelty and Significance Statement The novelty of this research is the development of a flamelet-generated mani-fold (FGM) method that explicitly considers preferential diffusion, flame stretch, and non-adiabatic effects. To the best of the authors’ knowledge, no studies have performed numerical simulations of pure hydrogen flames using such an FGM method. The developed FGM method was applied to numerical simula- tions of hydrogen-air premixed flame flashback at an equivalence ratio of 0.5 and reproduced the flashback speed of lean hydrogen-air premixed flame. The applicability of the FGM method to the numerical simulation of hydrogen-air flashback is reported first. This research is significant because the FGM method is one of the most widely used combustion models for premixed combustion, and the development of an accurate FGM method will contribute to the engineering field. The accurate prediction of the flame flashback attempted in this study is particularly important for the development of hydrogen-fueled combustion devices.

Enhancing efficiency in a-Si:H/μc-Si micromorph tandem solar cells through advanced light-trapping techniques using ARC, TRJ, and DBR

In this study, the performance of a-Si:H/μc-Si:H tandem solar cells was comprehensively assessed through two-dimensional numerical simulations. Our work involved optimizing the layer thicknesses and exploring advanced light-trapping techniques to enhance photogenerated current in both sub-cells. To reduce surface reflections on the top cell, we proposed a two-layer antireflection coating, composed of SiO2/Si3N4. Additionally, we implemented a 1D photonic crystal as a broadband back reflector within the solar cell. In order to balance the current density between the sub-cells and prevent carrier accumulation at the interface, we introduced a tunnel recombination junction (TRJ). This TRJ consisted of n-μc-Si:H/p-μc-Si:H layers with a thickness of 10 nm. Under global AM 1.5G conditions, our proposed cell structure exhibited impressive electrical characteristics, including an open-circuit voltage of 1.38 V, a short-circuit current density of 12.51 mA/cm2, and a fill factor of 80.82%. These attributes culminated in a remarkable total area conversion efficiency of 14%.

Three-dimensional numerical simulations and experimental studies on the viscoelastic rheological and deformation behavior of polymer catheter in gas-assisted extrusion processing

Gas-assisted extrusion is an effective method for improving the deformation behavior of polymer catheters during extrusion. However, the underlying mechanisms that dictate how geometrical and constitutive models influence the complex rheological behavior of the melt are not yet fully understood, which hinders further utilization and optimization. In this study, the three-dimensional (3D) gas–liquid–gas model for catheter gas-assisted extrusion was constructed. Subsequently, the Bird–Carreau model and the Phan–Thien–Tanner (PTT) model were employed in finite element numerical simulations to analyze the complex behavior. For comparative analysis, simplified two-dimensional (2D) model numerical simulations were also conducted. Additionally, experiments on catheter gas-assisted extrusion and parameterization studies of key constitutive model parameters were performed. The findings indicate that the 3D model, when integrated with the PTT constitutive model, demonstrates superior predictability and aligns more closely with experimental results. Furthermore, as the flow rate increases, discrepancies among different models diminish, and the distance required for the melt and gas to achieve motion equilibrium decreases. The internal mechanisms behind these phenomena are elucidated through the analysis of velocity and stress field distributions. This research enhances our understanding of the complex rheological behavior in polymer catheter gas-assisted extrusion, providing valuable insights for both academic research and industrial production in this field.

Numerical simulations of wedge-induced oblique detonation waves in ammonia/hydrogen/air mixtures

In this study, two-dimensional numerical simulations of oblique detonation waves (ODWs) under a flight altitude of 10 km were performed. Because of their high importance in a zero-carbon economy, ammonia and hydrogen are considered as the fuel for aircrafts. Six cases with various hydrogen addition ratios in the fuel mixture were considered to explore the effects of hydrogen addition on the ignition structure, surface instability and NO emission of ODWs. It was found that as the hydrogen addition ratio decreases, the ODWs become more difficult to initiate with increased ignition length, and more complicated multi-wave system emerges with a second oblique detonation wave (SODW). The oblique wave angle is rarely influenced by hydrogen addition ratio. Two types of reaction surfaces, i.e. “saw-tooth” and “key-stone”, along with a series of transverse waves and vortices can be observed for the case with a hydrogen addition ratio of 20% by volume in the fuel mixture. The oscillation amplitude of the reaction zone length, which quantifies the surface instability, increases with decreasing hydrogen addition ratios. The mass fraction of NO is the highest in the case with a hydrogen addition ratio of 40%. NO concentration is higher in detonation compared to that in deflagration in all cases. The pathway analysis of NO indicates that the thermal NO is the primary contributor to NO production in the cases with high hydrogen addition ratios, while the HNO pathway becomes more significant in the cases with low hydrogen addition ratios.

Spontaneous ignition and flame propagation in hydrogen/methane wrinkled laminar flames at reheat conditions: Effect of pressure and hydrogen fraction

Direct numerical simulations (DNS) with detailed chemical kinetics and chemical explosive mode analysis (CEMA) are performed to investigate the effect of operating pressure and hydrogen–methane blending on laminar wrinkled flames at reheat combustion conditions. Building upon previous three-dimensional DNS datasets of reheat hydrogen flames, the present work considers two-dimensional configurations that render computationally-feasible simulations of high-pressure combustion and significantly more complex hydrocarbon chemistry. A geometrically-simplified representation of the reheat combustor is adopted and the thermodynamic states considered in the simulations are carefully chosen to mimic gas turbine operation conditions, which are constrained to achieve a target flame position and flame temperature. The two-dimensional DNS results are first assessed against the available three-dimensional data and then analyzed to extract the main trends exhibited by the reheat combustion process with respect to the fraction of the fuel consumed by spontaneous ignition and flame propagation, for increasing pressures and hydrogen fractions. Due to significant differences in the characteristic features of the velocity and thermal boundary layers between the three-dimensional and the two-dimensional configurations, a different global flame shape is observed (V-shaped flame vs W-shape flame) together with a ∼10% bias in the fraction of fuel consumed by spontaneous ignition. Crucially, results from the scaling studies reveal very clear trends with a significant decrease in the fuel consumption by spontaneous ignition for increasing pressures and hydrogen fractions, at the conditions investigated. Finally, this study highlights the important role that first-principle direct numerical simulations, even when conducted in computationally affordable two-dimensional simplified geometrical configurations, can play in obtaining detailed insights and quantitative trends useful for the characterization of complex reactive flows.Novelty and significanceThe reheat burners of the two-stage sequential gas turbine combustors are designed to stabilize flames primarily due to spontaneous ignition. However, prior numerical simulations revealed the presence of an additional assisted-ignition mode aided by recirculation zones. In this study, we used practically feasible two-dimensional direct numerical simulations of premixed hydrogen–air mixtures under lean conditions to quantify the roles of the two flame stabilization modes at different operating pressures. Achieving fundamental understanding of the effect of pressure and hydrogen fraction on flame stabilization is crucial to the development of two-stage sequential combustion and the present two-dimensional calculations provide important new insights. We show that at high pressures, both modes consume fuel to a similar extent. We also investigated the effect of methane blending on flame stabilization. This study also discusses how two-dimensional direct numerical simulations can be leveraged in the design optimization of reheat burners at low technology readiness levels.

Numerical Simulation of Corona Discharge Plasma Affecting the Surface Behavior of Polymer Insulators

Corona discharge is a significant problem in the operation of high-voltage transmission and distribution systems, particularly for polymer insulators. Numerical simulation has become an effective tool for investigating the underlying physical mechanisms and optimizing the design of insulators. In this paper, we present a two-dimensional numerical simulation study on corona discharge plasma affecting the surface behavior of polymer insulators. The simulation was performed with the Comsol Multiphysic software and is based on the finite element method and the fluid plasma model, which considers ionization, recombination, and the transport of plasma species. The numerical results are analyzed to study the spatial and temporal characteristics of the corona discharge and its effect on the surface behavior of polymer insulators. The results show that the electric field is affected not only by the volume charge density but also by the surface charge density, which in turn depends on the densities of the charge carriers migrating on the insulator surface. However, the electric field drops drastically when one or two grading rings are installed. But one grading ring is not enough to limit the discharge.