External Pressure Field Research Articles

Vibration characteristics of dual-rotor system with staggered-type double elastic ring squeeze film dampers under maneuvering flight

The vibration of the rotor system is significantly intensified during maneuvering flight, rendering traditional elastic ring squeeze film dampers (ERSFDs) insufficient or unstable. To improve the applicability of dampers, a novel structure of staggered-type double elastic ring squeeze film dampers (SDERSFD) is proposed in this paper. Through the synergistic effect of double elastic rings, the damping effect is significantly enhanced, and the circumferential stiffness anisotropy of the damper is improved, which is more suitable for vibration reduction requirements under complex working conditions. Utilizing the Reynolds equation, the internal and external pressure field control equations of the double elastic rings are established. The finite difference method is then employed to solve the dynamic characteristics of the damper. Additionally, a finite element model of the dual-rotor system with SDERSFDs considering complex dynamic factors such as unbalanced force, oil film force, gravity, and additional inertial force caused by maneuvering flight is established for the study of nonlinear rotor dynamic characteristics and the analysis of SDERSFDs vibration reduction effect. Based on the model, the influence of various factors such as maneuvering speed, maneuvering radius, rotor speed and unbalance on the transient response of dive-pull up condition is analyzed. The results reveal that during dive-pull up, the vibration of the rotor system intensifies significantly. When compared with the ERSFDs, the SDERSFDs effectively reduce the vibration amplitudes of the rotor system under maneuvering flight condition, achieving the maximum vibration reduction ratio of 48.9%. Furthermore, the SDERSFD exhibits robustness against large maneuvering loads, enhancing the stability of the rotor system under extreme conditions.

Effect of Acoustics on Droplet Grouping Behaviour in a Single Stream of Droplets

Droplet and particle grouping can be influenced by applying an acoustic field and have practical applications such as particle scavenging and aerosol filters of engine exhaust and air purifiers. The present work experimentally investigates the influence of a standing acoustic wave on a single stream of droplets. The experimental setup consists of an acoustic transducer and a reflector plate through which the droplet stream passes in the presence or absence of an external pressure field generated by a standing acoustic wave. A droplet stream is generated with the help of a nozzle connected to a pressurized working fluid supply and piezoelectric transducer to control the spacing between droplets. The effect of the acoustic pressure field on the droplet stream generated by the nozzle operated at different piezoelectric excitation frequencies and fluid pressures is investigated. Droplet stream characteristics at every nozzle excitation frequency are observed with a high-speed camera when the acoustic field is switched OFF and ON. The competing effect of nozzle excitation frequency and acoustic field is observed. At lower nozzle frequencies, the nozzle generates an unstable stream of droplets having different sizes and spacings between them. When the acoustic field is applied at these lower frequencies, the stream of droplets becomes organized, and in some cases, it becomes equispaced and of the same size. However, an opposite behavior is observed at higher frequencies. In these cases, as the acoustic field is applied, an equispaced mono-disperse droplet stream becomes unstable due to the coalescence of droplets within the stream.

Rayleigh–Plesset-based Eulerian mixture model for cavitating flows

The homogeneous mixture model (HMM) is widely in use for simulation of cavitating flows. The mass transfer is typically ruled by simplified models whose efficiency is strictly dependent on the empirical choice of vaporization/condensation constants. In the present paper, we formulate a physically based mass-transfer model relying on the solution of the complete Rayleigh–Plesset (RP) equation. The latter can model the elasticity of the bubbles and non-linear interaction with the external pressure field. The model is tested in different configurations, also considering comparisons with the Schnerr–Sauer model (SSm) and the linearized version of the RP equation. The preliminary simplified tests show that the SS model responds statically to pressure variations and thus in not able to reproduce the actual dynamics of cavitation, under certain circumstances. On the other hand, the linearized RP model (RPl), although dynamically responsive to pressure variations, produces unrealistic small-amplitude bubble fluctuations, whereas the complete RP model (RPc) gives more realistic results. Tests on the performance of the SSm and RP models were carried out considering the turbulent flow in a convergent–divergent Venturi channel, already tested in numerical and experimental reference research. Here, we use the incompressible HMM. The study highlights various crucial aspects of the RPc model, emphasizing its own ability in replicating the shedding cycle as a three-dimensional, and non-stationary phenomenon. On the other hand, the SSm model results as a valid approximation for initial growth stages but fails to capture complex dynamics during the collapse phase. The results are consistent with recent literature findings, and refinements in grid resolution enhance accuracy in capturing the non-stationary sheet-to-cloud vapor dynamics. Neglecting compressibility may account for disparities between numerical and experimental outcomes, especially concerning shock waves generation and propagation. The RPc model emerges as a good candidate in reproducing bubble cloud dynamics and, in the next future, can be implemented in compressible HMM.

Application of strongly charged porous additives to enhance dewatering of clay dispersions

The main mechanisms of dewatering of model dispersions based on natural kaolin using external pressure and electric field have been considered. The factors which affect the studied process were analyzed, with a primary focus on the control of the electrokinetic potential of dispersion particles through varying the pH value of the pore solution. Optimal dewatering conditions for single-component model dispersions were selected. To intensify moisture removal, it is proposed to use an additional dispersion component, namely: charged particles in the form of bulk diaphragms or their mix with the main dispersion. Characteristics of single- and two-component dispersion, as well as the mechanisms which govern the impact of an additional dispersed component on dewatering, were analyzed. Conditions were determined under which the use of porous charged additives could enhance both the hydrodynamic and electroosmotic components of liquid removal. Experimental studies of dewatering were performed using bulk diaphragms formed from porous materials of different nature and size (coal and sand). Alternatively, highly charged electroconductive particles of finely dispersed coal were directly introduced into the model dispersion. The obtained results confirmed the validity of the concept about a significant intensification of dewatering when using additives that not only increase the porosity of the disperse system but also exhibit high values of electrical conductivity and electrokinetic potential, which greatly enhance the electroosmotic component of water removal.

Numerical Simulation of Heat and Moisture Transfer in Corrugated Walls Dryer

The primary goal of the current work is to model heat and mass transfer during mango drying in a wavy airflow dryer. By modifying the dryer walls, we were able to produce the undulating airflow (with V-shaped obstacles). With convective boundary conditions applied to all product surfaces, the explicit finite difference approach was used to study heat and mass exchanges in two dimensions during the drying of mango slices. During drying, the transfer coefficients are thought to fluctuate. Using EasyCFD software, the external flow, temperature, velocity, and pressure fields were then analyzed. This provided the profile of the heat transfer coefficient. These profiles were then utilized to calculate the mass transfer coefficient using the Shilton-Colburn analogy. Moreover, the code created to determine the heat and mass transfer coefficients in the product was used to derive the evolution of temperature and moisture content over time. The results allowed for the discovery of a new air flow in dryers called an undular flow and demonstrated how modifying the drying air stream enhanced heat transfer efficiency. By changing the air flow in the dryer, it was possible to achieve heat transfer coefficients ranging from 47.55 W/m²K to 357.38 W/m²K and mass transfer coefficients of 3.21 x 10-5 to 3.21 x 10-4 m²/s. When the outcomes of this investigation were compared to experimental results from the literature (under identical drying circumstances), a reasonable level of adequacy was discovered.

In‐situ generation of biodegradable poly(lactic acid)/poly(butylene succinate) nanofibrillar composites via a facile and cost‐effective strategy of pressure‐induced flow processing

AbstractInspired by the fact that the in‐situ fibrillation structure can enhance the polymer's macroscopic mechanical performance, a facile and cost‐effective strategy based on the pressure‐induced flow (PIF) processing was developed to produce ultra‐strong and super‐tough biodegradable poly(lactic acid)/poly(butylene succinate) (PLA/PBS) blends. Under the action of external pressure field, the ductile and flexible PBS droplets deformed along the flow direction (FD) and shifted from spheroid to ellipsoid, eventually to nanofiber as the compression ratio (CR) increased. From the scanning electron microscopy (SEM) results, it was found that the PBS droplets did not in‐situ take shape into nanofibrils until the CR reached to 4, and the PBS nanofibrils served as the central shish to induce the PLA molecular chain to crystallize in the perpendicular direction, resulting in nanohybrid shish‐kebab superstructures. The Raman spectra and differential scanning calorimetry results confirmed the enhancement effect of the CR on the orientation degree, lamellar thickness, and crystallization properties. Benefiting from the abundant interlocked hybrid shish‐kebabs, the tensile strength, tensile modulus, and impact strength of the PIF processing PLA/PBS blend (CR = 4) reached the maximum value of 106.4 MPa, 2332.4 MPa, and 87.4 kJ/m2, respectively, which were 116.7%, 40.1%, and 20.8‐folds higher than those of the common PLA/PBS blend. Overall, it is believed that the proposed methodology put forward a facile and cost‐effective way to produce PLA‐based in‐situ fibrillation reinforced composites for engineering applications.

Asymmetric Contact Loss Dynamics during Plating and Stripping in Solid‐State Batteries

AbstractSolid‐state batteries (SSBs) hold the potential to improve energy density and offer enhanced safety when compared to lithium‐ion batteries. However, the development of practical SSBs faces major challenges, such as filament growth and void formation, which necessitate a comprehensive understanding of the intrinsic solid–solid interfaces and limiting mechanisms. In this work, the underpinning asymmetry in the mechanistic interplay and resulting interface dynamics during Li plating and stripping is demonstrated, illustrating the critical effect of reaction heterogeneity on the contact loss behavior. With increasing stripping rates, the manifestation of solid–solid point contacts is identified as a key descriptor that signifies a transition in electrochemical response from a regime of continuous contact decay to current constriction. It is revealed that contact loss can also occur during plating at the Li/Li6PS5Cl interface; this severity scales with the reaction heterogeneity and is identified as an important challenge toward achieving faster charging rates in SSBs. The distinct nature of competing electrochemical–mechanical interactions that govern void formation during plating/stripping are delineated in this work. Coupled with these intrinsic mechanisms, non‐uniformities in external pressure and temperature fields drastically alter the contact dynamics, resulting in disparate void localization patterns.

Pickering emulsion strategy for high compressive carbon aerogel for use as insulation material and dual-mode pressure/magnetic sensor

Dual-mode pressure/magnetic sensors have recently become of great interest to the research community. The sensors can provide real-time monitoring of the surrounding environment through contact mode, non-contact mode, or a combination of both. However, straightforward construction a pressure/magnetic dual mode sensor remains a great challenge. In this study, carbon/reduced graphene oxide/Fe3O4 (CRF) carbon composite aerogel was facilely and innovatively prepared via a Pickering emulsion method using freeze drying and thermal annealing techniques. The effects of the concentration ratio of cellulose nanofibers (CNF) to graphene oxide (GO) and the concentration of Fe3O4 were studied against the mechanical, insulate and sensing performances of carbon aerogels. Due to its electrically conductive pathways and highly elastic deformation capacity as well as the successful composite of Fe3O4 nanoparticles, the flexible pressure/magnetic sensor based on C2R3F1 has a sensitivity of 8.6 kPa−1 and 3.9 kPa−1 for the ranges of 0–400 Pa and 400–1600 Pa, respectively, and a magnetic field sensitivity of 2.8 T-1 in the 0–50 mT range. Thus, utilizing the responding of the CRF to both the external pressure and magnetic field, by recording current signal or controlling the current switch on-off, the CRF as a double model sensor can realize the monitoring for movement of bodies and the remote control.

Bifurcation analysis of residually stressed neo-Hookean and Ogden electroelastic tubes.

The conditions for bifurcation of a circular cylindrical tube of elastic material subjected to combined axial loading and internal pressure are well known and are frequently used as a reference in related works. The present paper takes the theory further by considering a residually stressed circular cylindrical dielectric tube subjected to a combination of internal or external pressure, axial load and radial electric field. We examine axisymmetric incremental deformations and increments in the electric displacement superimposed on a known finitely deformed and residually stressed configuration in the presence of an electric field. The governing equations and boundary conditions are first obtained in general form and then specialized for the neo-Hookean and Ogden electroelastic models. The system of equations is solved numerically for different values of charge density and radial and circumferential residual stresses, and the results are compared with the purely elastic case. The bifurcation curves are presented as the azimuthal stretch on the inner surface versus the axial stretch together with the corresponding zero pressure curves. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

The effect of external pressure & magnetic field in star formation: The critical mass model

Theoretical work addressing the role of external pressure with magnetic fields in collapsing molecular clouds is important in building a comprehensive theory of star formation(SF). In many SF studies turbulence, magnetic fields, and self-gravity are described as the key dynamical processes involved in SF. However, the importance of external pressure in collapsing strongly magnetized clouds has not yet been particularly explained. Magnetic fields transport excess angular momentum from the central core while external pressure compresses the cloud. Thus the outflow of angular momentum, and on the other hand, the compression made by external pressure are the cause for matter falling onto the central core from the envelope. Therefore, external pressure facilitates the collapse of gas and the inflow of matter. In this work, we show theoretically how the strong magnetic field is dragged inward by the external pressure during the core collapse and formulate the critical mass of the core in the presence of external pressure.

Comparative Analysis of Surface Pressure Fluctuations of High-Speed Train Running in Open-Field and Tunnel Using LES and Wavenumber-Frequency Analysis

The interior noise of a high-speed train due to the external flow disturbance is more than ever a major problem for product developers to consider during a design state. Since the external surface pressure field induces wall panel vibration of a high-speed train, which in turn generates the interior sound, the first step for low interior noise design is to characterize the surface pressure fluctuations due to external disturbance. In this study, the external flow field of a high-speed train cruising at a speed of 300 km/h in open-field and tunnel are numerically investigated using high-resolution compressible LES (large eddy simulation) techniques, with a focus on characterizing fluctuating surface pressure field according to surrounding conditions of the cruising train, i.e., open-field and tunnel. First, compressible LES schemes with high-resolution grids were employed to accurately predict the exterior flow and acoustic fields around a high-speed train simultaneously. Then, the predicted fluctuating pressure field on the wall panel surface of a train was decomposed into incompressible and compressible ones using the wavenumber-frequency transform, given that the incompressible pressure wave induced by the turbulent eddies within the boundary layer is transported approximately at the mean flow and the compressible pressure wave propagated at the vector sum of the sound speed and the mean flow velocity. Lastly, the power levels due to each pressure field were computed and compared between open-field and tunnel. It was found that there is no significant difference in the power levels of incompressible surface pressure fluctuations between the two cases. However, the decomposed compressible one in the tunnel case is higher by about 2~10 dB than in the open-field case. This result reveals that the increased interior sound of the high-speed train running in a tunnel is due to the compressible surface pressure field.

Influence of Coolant Density on Turbine Blade Tip Film Cooling at Transonic Cascade Flow Conditions Using the Pressure-Sensitive Paint Technique

Abstract This work is an experimental study of film cooling effectiveness on a blade tip in a stationary, linear cascade. The cascade is mounted in a blowdown facility with controlled inlet and exit Mach numbers of 0.29 and 0.75, respectively. The freestream turbulence intensity is measured to be 13.5% upstream of the blade’s leading edge. A flat tip design is studied, having a tip gap of 1.6%. The blade tip is designed to have 15 shaped film cooling holes along the near-tip pressure side (PS) surface. Fifteen vertical film cooling holes are placed on the tip near the pressure side. The cooling holes are divided into a two-zone plenum to locally maintain the desired blowing ratios based on the external pressure field. Two coolant injection scenarios are considered by injecting coolant through the tip holes only and both tip and PS surface holes together. The blowing ratio (M) and density ratio (DR) effects are studied by testing at blowing ratios of 0.5, 1.0, and 1.5 and three density ratios of 1.0, 1.5, and 2.0. Three different foreign gases are used to create density ratio effect. Over-tip flow leakage is also studied by measuring the static pressure distributions on the blade tip using the pressure-sensitive paint (PSP) measurement technique. In addition, detailed film cooling effectiveness is acquired to quantify the parametric effect of blowing ratio and density ratio on a plane tip design. Increasing the blowing ratio and density ratio resulted in increased film cooling effectiveness at all injection scenarios. Injecting coolant on the PS and the tip surface also resulted in reduced leakage over the tip. The conclusions from this study will provide the gas turbine designer with additional insight on controlling different parameters and strategically placing the holes during the design process.

Numerical Simulation of Continuous Extraction of Li+ from High Mg2+/Li+ Ratio Brines Based on Free Flow Ion Concentration Polarization Microfluidic System.

Ion concentration polarization (ICP) is a promising mechanism for concentrating and/or separating charged molecules. This work simulates the extraction of Li+ ions in a diluted high Mg2+/Li+ ratio salt lake brines based on free flow ICP focusing (FF-ICPF). The model solution of diluted brine continuously flows through the system with Li+ slightly concentrated and Mg2+ significantly removed by ICP driven by external pressure and perpendicular electric field. In a typical case, our results showed that this system could focus Li+ concentration by ~1.28 times while decreasing the Mg2+/Li+ ratio by about 85% (from 40 to 5.85). Although Li+ and Mg2+ ions are not separated as an end product, which is preferably required by the lithium industry, this method is capable of decreasing the Mg2+/Li+ ratio significantly and has great potential as a preprocessing technology for lithium extraction from salt lake brines.

Electroacoustic analysis of a directional moving-coil microphone using combined lumped-parameter models and BEM

This article presents a lumped-parameter model combined with external sound pressure field simulation, based on the boundary element method (BEM) for utilization in a directional microphone. A study about microphone capsule of a typical handheld moving-coil microphone with hyper-cardioid pattern has been conducted. In the BEM simulation, a simplified 3D model of the capsule that met sound waves which radiated from a point sound source has been taken into account. The blocked average pressure at the openings of the capsule is used to drive the lumped element equivalent circuit model. Through the model, the sensitivity, directivity, and impedance of the microphone were analyzed. Hence, the proximity effect is observed and discussed. To verify our simulation, the microphone characteristics were experimentally measured by B&K devices with SoundCheck software in an anechoic chamber. The simulation data are in good agreement with the measurement data at low and medium frequencies below 13 kHz, and there were larger errors at higher frequencies, which may indicate that the lumped parameters is less applicable at higher frequencies. The proposed method gains more precise and comprehensive prediction for the microphone characteristics, which therefore could be utilized in optimizing the choice of materials and size of the microphone capsule design.

Optical absorption computation of a [formula omitted] artificial molecule in GaAs/Ga[formula omitted]Al[formula omitted]As nanometer-scale rings

The linear and non-linear optical absorption coefficients of a D2+ artificial molecule confined in GaAs nano-scaled rings under a threading magnetic field were calculated. The results showed that by varying the position and the angle formed by the double-donor system, the total optical absorption can be enhanced, quenched, or even totally nullified. On the other hand, small changes of the optical response close to 2% due to external hydrostatic pressure fields or sample temperature variations within the ranges 0–30 kbar and 4–400 K, respectively, were obtained. In addition, reducing the aluminum concentration in the surrounding matrix significantly enhanced the optical absorption. A careful analysis was carried out in order to determine the conditions that will avoid an overflow of the wavefunction and that complement the previously obtained results. Furthermore, oscillatory behavior of the optical absorption with the magnetic field was observed. By increasing the QR’s radius, a red-shift of the total optical absorption spectra was observed, allowing the tuning of the resonance peaks below 20 meV (also known as the THz band).

Universal scaling of charge-order melting in the magnetic field–pressure–temperature landscape

Dc magnetic measurements across the charge ordering (CO) transition temperature (T$_{CO}$) in polycrystalline Pr$_{0.5}$Ca$_{0.5}$Mn$_{0.975}$Al$_{0.025}$O$_3$ have been performed under simultaneous influence of external hydrostatic pressure (P) and magnetic field (H). We show the first experimental evidence that the melting of charge order instability obey an interesting scaling function, $\delta$T$_{CO}$/P$^\alpha$ = $f$(H/P$^\beta$) in H-P-T landscape, where $\delta$T$_{CO}$ is the suppression of T$_{CO}$ by P and H. Corresponding values of the exponents, $\alpha$ = 1.63 and $\beta$ = 0.33 have been extracted from data collapsing phenomena. Possible origin of such a scaling behavior has been discussed.

Investigation of a Liquid-Phase Electrode for Micro-Electro-Discharge Machining.

Micro-electro-discharge machining (μEDM) plays a significant role in miniaturization. Complex electrode manufacturing and a high wear ratio are bottlenecks for μEDM and seriously restrict the manufacturing of microcomponents. To solve the electrode problems in traditional EDM, a µEDM method using liquid metal as the machining electrode was developed. Briefly, a liquid-metal tip was suspended at the end of a capillary nozzle and used as the discharge electrode for sparking the workpiece and removing workpiece material. During discharge, the liquid electrode was continuously supplied to the nozzle to eliminate the effects of liquid consumption on the erosion process. The forming process of a liquid-metal electrode tip and the influence of an applied external pressure and electric field on the electrode shape were theoretically analyzed. The effects of external pressure and electric field on the material removal rate (MRR), liquid-metal consumption rate (LMCR), and groove width were experimentally analyzed. Simulation results showed that the external pressure and electric field had a large influence on the electrode shape. Experimental results showed that the geometry and shape of the liquid-metal electrode could be controlled and constrained; furthermore, liquid consumption could be well compensated, which was very suitable for µEDM.

Tilted magnetic micropillars enabled dual-mode sensor for tactile/touchless perceptions

The smart flexible devices that can implement both tactile and touchless sensing in real-time have attracted abundant interest due to the high demand for human-machine interaction (HMI), internet of things (IoT) and virtual reality (VR) system. However, obtaining the sensor that can precisely monitor signals via contact/non-contact modes without overlapping while in a facile and cost-effective methodology is still a challenge. Herein, we introduce a flexible dual-mode capacitive sensor for pressure (contact) and magnetic field (non-contact) detection based on magnetic tilted micropillar array (MTMPA) via a facile and tunable methodology. The MTMPA sandwiched in AgNW/PDMS electrodes can response to the external pressure and magnetic field with bidirectional deflection, allowing the sensor to precisely distinguish different stimuli in real-time without overlapping. With the optimal structure, the sensor exhibits high performance of magnetic response with sensitivity of −0.69 T-1, detection limit of 25 mT and excellent recoverability. The sensor also exhibits high pressure sensitivity of 0.301 kPa−1 (0–2 kPa) with the ultra-low detection limit of 1.2 Pa with excellent repeatability and mechanical robustness. As a proof of concept, practical wearable tactile applications (e.g. pulse-sensing, voice recognition, finger touching, pressure mapping and dynamic tracking) and touchless demonstrations such as magnetic field identification and trajectory tracking have been presented. The sensitive response of the sensor to external magnetic fields also enables us to customize the non-contact Braille recognition system through arranging specific magnet patterns, where the characters such as ‘a’, ‘b’, ‘c’, and ‘d’ have been well distinguished without direct contact. The results experimentally prove the profound significance of the methodology for potential uses towards health monitoring, body motion feedback, and human-machine interface, etc.

Effective Utilization of Limonitic Nickel Laterite via Pressurized Densification Process and Its Relevant Mechanism

Limonitic laterite contains low iron and nickel grades and much high smelting minerals and loss on ignition (LOI), identified as refractory iron ore for sintering. Thus, sinter pot tests of limonitic laterite via pressurized densification sintering and its intensification mechanism were conducted, and the industrial application prospect was explored. The results indicate that the sintering performance of the limonitic laterite of the new process is significantly improved with the tumble index and productivity increased by 19.2% and 18.6%, respectively, and solid fuel rate lowered by 10.3%. The external pressure field promotes the synchronization of heat front velocity and combustion front velocity for better sintering heat and mass transfer conditions, which also greatly improves the mineral compositions and microstructure of the product sinter. The microstructure is converted from large thin-wall pores into small thin-wall or large thick-wall pores with the sinter porosity decreased by 42.4%. Much close interlocking texture between hercynite and silico-ferrite of calcium and alumina (SFCA) is formed with hercynite grains aggregation and growth, and SFCA amount substantially increased. The better sintering performance will bring about a remarkable economic benefit of 282.78 million RMB/a if the industrial application is implemented. The pressurized densification sintering process is considered as one of the effective technologies for improving limonitic laterite sintering.

Pressure and electric field dependence of quasicrystalline electronic states in 30∘ twisted bilayer graphene

30$^{\circ}$ twisted bilayer graphene demonstrates the quasicrystalline electronic states with 12-fold symmetry. These states are however far away from the Fermi level, which makes conventional Dirac fermion behavior dominating the low energy spectrum in this system. By using tight-binding approximation, we study the effect of external pressure and electric field on the quasicrystalline electronic states. Our results show that by applying the pressure perpendicular to graphene plane one can push the quasicrystalline electronic states towards the Fermi level. Then, the electron or hole doping of the order of $\sim$ $4\times10^{14}$ $cm^{-2}$ is sufficient for the coincidence of the Fermi level with these quasicrystalline states. Moreover, our study indicates that applying the electric field perpendicular to the graphene plane can destroy the 12-fold symmetry of these states and break the energy degeneracy of the 12-wave states, and it is easier to reach this in the conduction band than in the valence band. Importantly, the application of the pressure can recover the 12-fold symmetry of these states to some extent against the electric field. We propose a hybridization picture which can explain all these phenomena.