Flux Behavior Research Articles

Inertial effects on free surface pumping with an undulating surface

Free surface flows driven by boundary undulations are observed in many biological phenomena, including the feeding and locomotion of water snails. To simulate the feeding strategy of apple snails, we develop a centimetric robotic undulator that drives a thin viscous film of liquid with the wave speed $V_w$ . Our experimental results demonstrate that the behaviour of the net fluid flux $Q$ strongly depends on the Reynolds number $Re$ . Specifically, in the limit of vanishing $Re$ , we observe that $Q$ varies non-monotonically with $V_w$ , which has been successfully rationalised by Pandey et al. (Nat. Commun., vol. 14, no. 1, 2023, p. 7735) with the lubrication model. By contrast, in the regime of finite inertia ( ${Re} \sim O(1)$ ), the fluid flux continues to increase with $V_w$ and completely deviates from the prediction of lubrication theory. To explain the inertia-enhanced pumping rate, we build a thin-film, two-dimensional model via the asymptotic expansion in which we linearise the effects of inertia. Our model results match the experimental data with no fitting parameters and also show the connection to the corresponding free surface shapes $h_2$ . Going beyond the experimental data, we derive analytical expressions of $Q$ and $h_2$ , which allow us to decouple the effects of inertia, gravity, viscosity and surface tension on free surface pumping over a wide range of parameter space.

Heat and mass flux dynamics of tangent hyperbolic nanofluid flow with unsteady rotatory stretching disk over Darcy-Forchheimerporous medium

Abstract The purpose of the research is to examine a tangent hyperbolic nanofluid flowing in three dimensions (3D) axisymmetrically on an unsteady rotatory stretching disk over a DarcyForchheimer porous medium. First order initial value problems (IVPs) are generated from the governing partial differential equations (PDEs) through the use of similarity transformation and linearization. The Runge-Kutta sixth order (RK6) is utilized to solve the IVP system using the shooting technique and the built-in Python software ”fsolve model10.” Articles that have already been published are used to validate the implemented approach. Graphs are used to examine how various parameters affect velocity, temperature, and concentration. Additionally, the behavior of heat, mass flux, and skin friction in response to different parameters is investigated. The study’s findings showed that as the Forchheimer number and velocity slip parameter increased, the nanofluid’s radial and tangential velocities decreased as well. As temperature and concentration slip parameters increase, correspondingly, thicker and thinner boundary layer structures are seen. Both the rates of heat and mass transfers are initiated for an increase Eckert and Prandtl numbers and demotivated for power-law index number.

Utilising Artificial Intelligence to Predict Membrane Behaviour in Water Purification and Desalination

Water scarcity is a critical global issue, necessitating efficient water purification and desalination methods. Membrane separation methods are environmentally friendly and consume less energy, making them more economical compared to other desalination and purification methods. This survey explores the application of artificial intelligence (AI) to predict membrane behaviour in water purification and desalination processes. Various AI platforms, including machine learning (ML) and artificial neural networks (ANNs), were utilised to model water flux, predict fouling behaviour, simulate micropollutant dynamics and optimise operational parameters. Specifically, models such as convolutional neural networks (CNNs), recurrent neural networks (RNNs) and support vector machines (SVMs) have demonstrated superior predictive capabilities in these applications. This review studies recent advancements, emphasising the superior predictive capabilities of AI models compared to traditional methods. Key findings include the development of AI models for various membrane separation techniques and the integration of AI concepts such as ML and ANNs to simulate membrane fouling, water flux and micropollutant behaviour, aiming to enhance wastewater treatment and optimise treatment and desalination processes. In conclusion, this review summarised the applications of AI in predicting the behaviour of membranes as well as their strengths, weaknesses and future directions of AI in membranes for water purification and desalination processes.

Flux and fouling behavior during constant pressure sterile filtration of nanoemulsions

Nanoemulsions with droplet diameters from 20 to 200 nm have emerged as attractive adjuvants in the development of novel vaccines and as an advanced method of drug delivery for hydrophobic drugs. However, the large size of the nanoemulsion droplets leads to very low capacities during the final sterile filtration step used to ensure sterility of parenteral drug products. The objective of this study was to examine the sterile filtration of a model nanoemulsion made using squalene as the oil and Tween 20 and Span 85 as stabilizing surfactants. Data were obtained with different commercial sterile filters with different morphology and chemistry during constant pressure filtration. In each case, there was essentially no filtration until the transmembrane pressure exceeded a critical value related to the force required to push the deformable nanoemulsion droplets through the membrane pores. The filter capacity increased with increasing pressure, going from 700 g/m2 at 140 kPa to 1300 g/m2 at 280 kPa for a dual layer polyethersulfone sterile filter, with the flux decline well described by the complete pore blockage model. The dual layer asymmetric membranes showed much higher capacities than corresponding single layer filters due to the effectiveness of the upper layer in removing larger nanoemulsion droplets that would otherwise block the pores of the sterile filter. The capacity of the different sterile filters was also well-correlated with the initial filtrate flux, with both of these parameters governed by the pore size distribution and surface chemistry of the filters. These results provide important insights into factors controlling the sterile filtration of highly concentrated nanoemulsions used in the formulation of vaccines and drug products.

Critical flux-based fouling control method for forward osmosis during simultaneous thickening and digestion of waste activated sludge

The use of forward osmosis (FO) membranes for simultaneous thickening and digestion of waste activated sludge (WAS) (FO-MSTD) has recently garnered significant interest. However, a major challenge hindering the widespread adoption of the FO-MSTD process is severe membrane fouling, which results from increasing sludge concentrations and deteriorating sludge properties. In response, this study proposes a novel FO membrane fouling control strategy based on the critical flux concept, involving a variable draw solution (DS) operating mode. Two operating modes were examined based on the critical flux behavior of the FO membrane: a constant DS concentration mode (with a fixed DS concentration of 1.5 M, referred to as Constant DS1.5) and a variable DS concentration mode (with varying DS concentrations at different operational stages, referred to as Variable DS1.5-1.0 and Variable DS1.5-0.75). Over 21 days of operation, the MLSS concentrations of WAS in the Constant DS1.5, Variable DS1.5-1.0, and Variable DS1.5-0.75 reactors increased from initial values of 3.46, 3.88, and 4.20 g/L to 35.2, 31.5, and 29.2 g/L, respectively. Concurrently, the cumulative digestion rates of MLVSS in the three FO-MSTD processes reached 29.3 %, 29.0 %, and 36.3 %, respectively. After adjusting the DS concentration, the FO membrane flux decay rates for Constant DS1.5, Variable DS1.5-1.0, and Variable DS1.5-0.75 were 57.7 %, 49.4 %, and 13.8 %, respectively. In addition to experiencing a lower flux decline, the Variable DS1.5–0.75 mode achieved a significantly higher flux recovery rate of 98.5 % compared to the other two modes. Moreover, the biovolume of proteins and microorganisms in the membrane fouling layer decreased by 85.2 % and 72.7 %, respectively, in the Variable DS1.5–0.75 mode compared to the Constant DS1.5 mode. These findings indicate that operating with a DS below the critical concentration can significantly improve the reversibility of membrane fouling and reduce the presence of organic and biological foulants in the fouling layer, thereby mitigating membrane fouling in the FO-MSTD reactor.

Pore Engineering as a General Strategy to Improve Protein-Based Enzyme Nanoreactor Performance.

Enzyme nanoreactors are nanoscale compartments consisting of encapsulated enzymes and a selectively permeable barrier. Sequestration and colocalization of enzymes can increase catalytic activity, stability, and longevity, highly desirable features for many biotechnological and biomedical applications of enzyme catalysts. One promising strategy to construct enzyme nanoreactors is to repurpose protein nanocages found in nature. However, protein-based enzyme nanoreactors often exhibit decreased catalytic activity, partially caused by a mismatch of protein shell selectivity and the substrate requirements of encapsulated enzymes. No broadly applicable and modular protein-based nanoreactor platform is currently available. Here, we introduce a pore-engineered universal enzyme nanoreactor platform based on encapsulins-microbial self-assembling protein nanocompartments with programmable and selective enzyme packaging capabilities. We structurally characterize our protein shell designs via cryo-electron microscopy and highlight their polymorphic nature. Through fluorescence polarization assays, we show their improved molecular flux behavior and highlight their expanded substrate range via a number of proof-of-concept enzyme nanoreactor designs. This work lays the foundation for utilizing our encapsulin-based nanoreactor platform for diverse future biotechnological and biomedical applications.

Size scale effect on mass burning flux and flame behavior of solid fuels

The study investigates the horizontal fuel size effect on free-burning fires for PMMA plates and wood cribs. The fuel size effect on mass burning flux and flame behavior is mainly discussed and compared with typical pool fires. For the PMMA plate and liquid pool, when the fuel size is small (< 10 cm), either the 3D sidewall burning of PMMA or the container wall heated by flame can promote the burning flux at the horizontal projection area. As the fuel size increases, these side wall burning or heating effects decrease, causing the drop in burning flux with fuel scale for both the PMMA plate and liquid pool. For small-scale wood cribs, fire cannot self-sustain due to the large airflow cooling. With the increase in wood crib size, the burning rate first remains constant and then gradually increases, driven by the enhanced internal radiation. As the fuel size increases above 20–30 cm, the flame radiation dominates the burning flux for all fuel types. Fire dynamics simulator (FDS) was adopted to simulate the horizontal size effect by setting a varied fire source (horizontal projection) area. First, the flame geometry and heat release rate (HRR) of simulations were validated against experimental results. Subsequently, the validated fire model generates cases covering a broad range of fire scales. Finally, a new correlation of flame height with the fire heat release rate and fuel size is proposed, and its prediction capability is validated in the numerical fire modeling. This study quantifies the size effect on the burning rate for common solid fuels and provides valuable information for the numerical modeling of multi-scale fires.

Thermal rectification in segmented Frenkel–Kontorova lattices with asymmetric next-nearest-neighbor interactions

In this work, we conduct an extensive study of the asymmetric heat flow, i.e. thermal rectification, present in the two-segment Frenkel Kontorova model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. We have considered systems with both high and low asymmetry and determined that, in the weak-coupling limit, thermal rectification is larger when NNN interactions are relevant. The behavior of the heat fluxes as a function of the coupling strength between the two segments is largely consistent with a well-defined rectification for larger system sizes. The local heat fluxes present a very different behavior for systems with high and low asymmetry. The results of this work may help in the design of molecular bridges, which have recently been shown to be able to function as thermal rectification devices.

Purification of crude glycerol derived from biodiesel production process using ceramic membranes: Experimental studies and modeling of flux behavior

Large-scale biodiesel production generates large quantities of glycerol with high impurities levels, and new purification processes are needed to add value to this by-product of biodiesel production. Thus, this study evaluated the application of ceramic membranes for glycerol purification from biodiesel production and the influence of the mean pore diameter of the membrane, pressure, temperature, and the addition of acidified water to the mixture to be purified. The experiments were carried out in a tangential filtration module with ceramic membranes of 5 kDa, 20 kDa, 0.05 μm, and 0.2 μm, varying the pressure by 1, 2, and 3 bar and the temperature by 25, 40, and 60 °C. The results showed that increasing the pressure, average pore diameter and temperature caused an increase in the permeate flux. Furthermore, adding acidified water increased permeate fluxes and glycerol concentrations for all membranes and pressures used. A higher glycerol content (91.13 %) was obtained with the 5 kDa membrane at 3 bar and 60 °C. The traditional fouling mechanism models failed to fit most of the experimental data. On the other hand, the proposed generalized model adequately predicted the experimental permeate flux data for the different types of fouling mechanisms observed.

Viscosity, Density, Surface Tension, and Crystallization Behavior of Commercial Mold Fluxes

This study investigates the viscosity, density, surface tension, and crystallization behavior of two commercial mold fluxes that are utilized to cast ultralow‐carbon, low‐carbon, and medium‐carbon steel grades, as well as electric steels (high‐B magnetic and grain‐oriented steels). Experiments are performed in the temperature range of 1073–1673 K using the rotating bob method, maximum bubble pressure method, buoyancy method, and single hot thermocouple technique. The phase structure is investigated via scanning electron microscopy and X‐ray powder diffraction. The results indicate that viscosity and density exhibit nonlinear temperature dependence. Increased basicity (CaO/SiO2) results in reduced viscosity and elevates the break temperature of the mold fluxes. Furthermore, the incubation time required for phase formation decreases with increasing basicity. Finally, time–temperature transformation and continuous cooling transformation diagrams are constructed.

X-ray variability of the triplet star system LTT1445 and evaporation history of the planets around its A component

Context. The high-energy environments of host stars could prove deleterious for their planets. It is crucial to ascertain this contextual information to characterize the atmospheres of terrestrial exoplanets. Aims. We aim to fully characterize a unique triple system, LTT1445, with three known rocky planets around LTT 1445A. Methods. We studied the X-ray irradiation and flaring of this system based on a new 50 ks Chandra observation, which is divided into 10 ks, 10 ks, and 30 ks segments conducted two days apart, and two months apart, respectively. These data were complemented by an archival Chandra observation approximately 1 yr earlier and repeated observations with extended ROentgen Survey with an Imaging Telescope Array (eROSITA), the soft X-ray instrument on the Spectrum-Roentgen-Gamma (SRG) mission. This enabled the investigation of X-ray flux behavior across multiple time scales. With the observed X-ray flux from the exoplanet host star A, we estimated the photo-evaporation mass loss of each exoplanet. With the planet modeling package, VPLanet, we predicted the evolution and anticipated current atmospheric conditions. Results. Our Chandra observations indicate that LTT 1445C is the dominant X-ray source, with additional contribution from LTT 1445B. We find that LTT 1445A, a slowly rotating star, exhibits no significant flare activity in the new Chandra dataset. Comparing the flux incident occuring on the exoplanets, we find that LTT 1445BC components do not pose a greater threat to the planets orbiting LTT 1445A than the emission from A itself. According to the results from the simulation, LTT 1445Ad could have the capacity to retain its water surface.

First observation of edge impurity behavior with n = 1 RMP application in EAST L-mode plasma

High-Z impurity accumulation suppression and mitigation in core plasma is frequently observed in EAST edge localized mode mitigation experiments by using resonant magnetic perturbations (RMP) coils. To study the individual effects of the RMP field on impurity transport, based on high-performance extreme ultraviolet impurity spectroscopic diagnostics, the effect of the n = 1 (n is the toroidal mode number) RMP field on the behavior of intrinsic impurity ions at the plasma edge, e.g. He+, Li2+, C2+–C5+, O5+, Fe8+, Fe15+, Fe17+, Fe22+, Cu17+, Mo12+, Mo13+ and W27+, is analyzed for the first time in L-mode discharges. Based on the evaluation of the location of these impurity ions, it is found that with the increase in RMP current (I RMP), an impurity screening layer inside the last closed flux surface is formed, e.g. at ρ = 0.74–0.96, which is also the region that the RMP field affects. Outside this screening layer, the impurity ion flux of He+, Li2+, C2+, C3+, O5+, Fe8+, Mo12+ and Mo13+ ions increases gradually, while inside this screening layer, the impurity ion flux of C4+, C5+, Cu17+, W27+, Fe15+, Fe17+ and Fe22+ ions decreases gradually. When I RMP is higher than a threshold value, RMP field penetration occurs, accompanied with m/n = 2/1 mode locking, and the position of this screening layer moves to the plasma core region, i.e. ρ = 0.66–0.76, close to the q = 2 surface, and the opposite behavior of the impurity ion flux at two sides of the screening layer is strengthened dramatically. As a result, significant decontamination effects in the plasma core region, indicated by the factor of ((Γ Imp Z+)w/o–(Γ Imp Z+))/(Γ Imp Z+)w/o (where (Γ Imp Z+)/(Γ Imp Z+)w/o denotes the impurity ion flux ratio with and without RMP), is observed, i.e. 30%–60% for heavy impurity (Fe, Cu, Mo, W), and ∼27% for light impurity of C. In addition, the analysis of the decontamination effects of C and Fe impurities under four different RMP phase configurations shows that it may be related to the strength of the response of the plasma to RMP. These results enhance the understanding of impurity accumulation suppression by the n = 1 RMP field and demonstrate a candidate approach using RMP coils for W control in magnetic confinement devices.

Prediction of boundary heat flux in mold by inverse problem method

This study utilizes inverse heat transfer techniques to analyze heat flux distribution within a mold. By collecting temperature data from thermocouples, a two-dimensional heat transfer model of the mold’s cross section is developed to investigate the transverse heat flux behavior, temperature distribution, relationship between heat flux and height, and three-dimensional heat flux within the mold. The direct problem model is solved using the finite volume method, while the inverse problem is tackled with the Levenberg-Marquardt Method (LMM) in conjunction with the Broyden method (BM). The model’s validity is confirmed through experimentation, which includes assessing the impact of initial parameter estimations, thermocouple placements and quantities, and measurement inaccuracies.

Effect of photons and electrons on the over-response of optical fiber X-ray sensors

Optical fiber X-ray sensors are prone to over-response compared to ionization chambers (ICs) when used to measure the percentage depth dose (PDD) curves and off axis ratio (OAR) curves. Investigating this phenomenon is crucial for the successful adoption of these sensors in clinical radiotherapy. Compared with ion chambers and other water equivalent dosimeters, the fiber X-ray sensors using high Zeff scintillators (Gd2O2S:Tb) have generally higher mass attenuation coefficients. In this case, the response of scintillators to photons needs to be considered. In this article, a Monte-Carlo (MC) software package BEAMnrc was used to simulate the distribution of photon and electron fluxes in a clinical based water phantom, besides the energy deposition of air and Gd2O2S:Tb in varying energy was also simulated. The distribution of the photon and electron fluxes in the horizontal (radial) direction at a fixed 10 cm water depth was studied, as well as the fluxes in the vertical (depth) direction. An embedded-structure fiber X-ray sensor was used for the experimental measurements. The simulation results indicate that, in the horizontal direction, there are many photons remain outside the radiation field. In the vertical direction, as the size of the radiation field increases, the maximum point of the photon flux shifts towards a deeper water depth. These behavior of photon flux is consistent with the fiber X-ray sensors measurement. However, the maximum point of the electron flux remains unchanged in the vertical direction. In the horizontal direction, the electron flux decreases rapidly, and this scenario is similar to the case when using the ion chamber. Results of analyzing the spectra inside and outside the radiation field show that there is a large number of photons with energy below 0.2 MeV outside the radiation field, and the proportion of these low-energy photons is greater than 60 %. The findings indicate that the fiber X-ray sensors' over-response can be primarily attributed to the lower energy scattered photons.

Filtration performance of biofilm membrane bioreactor: Fouling control by threshold flux operation

Membrane fouling is the major factor that restricts the furtherly widespread use of membrane bioreactor (MBR). As a new generation of MBR, biofilm membrane bioreactor (BF-MBR) demonstrates high treatment efficiency and low sludge growth rate, however the filtration performance improvement and membrane fouling control are still the challenges for its further development. This work investigated the filtration performance using resistance in series model and membrane fouling control via threshold flux for BF-MBR. At first, the flux behavior and filtration resistance under various operating conditions, including agitation speed, membrane and TMP, were explored by resistance in series model. Because of the desirable anti-fouling capacity, UP100 and UP030 had the high threshold flux (100 and 90 L m−2 h−1) and low irreversible fouling resistance (1 and 1.3 × 10−10 m-1). Higher shear stress produced by higher agitation speed could reduce membrane fouling, while greatly promote the threshold flux (138 L m−2 h−1) and membrane cleaning efficiency (96%). Moreover, increasing shear stress or selecting membrane with large pore size could decrease the fouling rate and raise the threshold flux. As for TMP, high TMP reduced the removal rate for organic and nutrient, and enhanced the irreversible fouling. Besides, the aerobic-BF-MBR (101 L m−2 h−1 and 1.3 × 10−10 m-1) with lower foulant concentration had a better filtration performance than anoxic-BF-MBR (90 L m−2 h−1 and 1.5 × 10−10 m-1). Additionally, the long-term tests with 10 cycles were conducted to evaluate the industrial application value of BF-MBR (45–58 L m−2 h−1). This work provides the technical support for sustainable filtration performance of BF-MBR.

A chelation process by an amino alcohol electrolyte additive to capture Zn2+ and realize parallel Zn deposition for aqueous Zn batteries

Zn anode experiences dendrite issues in aqueous Zn batteries. They result from uneven Zn2+ flux and Sand behavior depending on the current density. Herein, the amino alcohol of 2,2′,2′′-nitrilotriethanol (NTE) additive with chelation ability is introduced to achieve stable and parallel Zn deposition. NTE preferentially adsorbs on Zn surface, which chelates with Zn2+ at interface upon geometry transformation. It not only homogenizes Zn2+ flux to inhibit dendrites at low current densities, but also supply sufficient Zn2+ to delay Sand behavior at high current densities. Parallel growth of Zn hexagonal plates is realized. Thus, Zn plating/stripping in symmetric cells at 10 mA cm−2 reaches >1600 h cycle life with the addition of 2.5% NTE in the ZnSO4 electrolyte, corresponding to a high cumulative plated capacity of 8.5 Ah cm−2. At the conditions of 5 °C or 70% depth of discharge, the lifespans of symmetric cells also extend to 6977 h and 230 h, respectively. In anode free full cells, a Zn2+ pre-inserted V6O13·H2O cathode retains 250 mAh g−1 capacity after 300 cycles at 6 A g−1, superior to 83 mAh g−1 with NTE free electrolyte.

2D analysis of sputtered species transport in high-power impulse magnetron sputtering (HiPIMS) discharge

Among the numerous advantages of the high-power impulse magnetron sputtering (HiPIMS) technique, the most important is the enhanced ionization degree of sputtered species contributing to the film growth. Consequently, the quality of deposited thin films is highly improved. Still, the optimization process is challenging due to the complexity associated with the intricate transport of the sputtered species, ionized or neutrals. The scarce knowledge available on the spatial distribution of these species when operating a HiPIMS discharge makes the quantitative prediction of any deposition feature particularly difficult. In this paper, we discuss the influence of experimentally controllable quantities, such as gas pressure and target current density, on the transport of sputtered titanium in non-reactive (argon) HiPIMS, namely, on the behavior of metal atoms and metal ion fluxes intercepting the substrate. Systematic quantitative measurements were performed in a diameter normal plane on a circular planar target. Hence, the 2D spatial distribution of the ionized flux fraction (IFF) and the total flux of titanium sputtered particles (deposition rate) are evaluated by biasing a quartz crystal microbalance equipped with an electron magnetic filter. The wide range of parameters we examined allows us to predict and optimize the flux of sputtered species based on complete mapping of the IFF of sputtered particles.

Evaluation of isothermal and isofield designs of a temperature sensor using magnetic phase transition

Digitalisation and related concepts such as cyber-physical systems and Industry 4.0 have gained focus in the past few decades with the increasing need for real-time data acquisition methods for large-scale use. This study investigates the magnetic flux change throughout a magnetic phase transition and the potential of changing the magnetic moment in a temperature sensor. Magnetothermal properties are experimentally measured using gadolinium to examine characteristics that have strong implications for the proposed temperature sensor. The results are used to propose different device designs for changing magnetic flux. The magnetothermal characteristics identified in the previous investigation are also reconsidered under the scope of these device designs. The results show that while certain characteristics need to be carefully considered throughout material development and the actual device designing process, the magnetic flux behaviour shows potential for temperature sensor application.

Plasma-assisted aerogel interface engineering enables uniform Zn2+ flux and fast desolvation kinetics toward zinc metal batteries

The poor reversibility of Zn anodes induced by dendrite growth, surface passivation, and corrosion, severely hinders the practical applicability of Zn metal batteries. To address these issues, a plasma-assisted aerogel (PAG) interface engineering was proposed as efficient ion transport modulator that can simultaneously regulate uniform Zn2+ flux and desolvation behavior during battery operation. The PAG with ordered mesopores acted as an ion sieve to homogenize Zn deposition and accelerate Zn2+ flux, which is favorable for corrosion resistance and dendrite suppression. Importantly, the plasma-assisted aerogel with abundant hydrophilic groups can facilitate the desolvation kinetics of Zn2+ due to the multiple hydrogen-bonding interaction with the activated water molecules, thus accelerating the Zn2+ migration kinetics. Consequently, the Zn/Zn cell assembled with PAG-modified separator demonstrates stable plating and stripping behavior (over 1400 h at 1 mA cm−2) and high Coulombic efficiency (99.8% at 1 mA cm−2 after 1100 cycles), and the Zn||MnO2 full cell shows excellent long-term cycling stability and maintains a high capacity of 154.9 mA h g−1 after 1000 cycles at 1 A g−1. This study provides a feasible approach for the large-scale fabrication of aerogel functionalized separators to realize ultra-stable Zn metal batteries.

Mathematical Analysis of the Electromotive Induced Force in a Magnetically Damped Suspension

This study explores the advanced mathematical modeling of electromagnetic energy harvesting in vehicle suspension systems, addressing the pressing need for sustainable transportation and improved energy efficiency. We focus on the complex challenge posed by the non-linear behavior of magnetic flux in relation to displacement, a critical aspect often overlooked in conventional approaches. Utilizing Taylor expansion and Fourier analysis, we dissect the intricate relationship between oscillation and electromagnetic damping, crucial for optimizing energy recovery. Our rigorous mathematical methodology enables the precise calculation of the average power per cycle and unit mass, providing a robust metric for evaluating the effectiveness of energy harvesting. Further, the study extends to the practical application in a combined system of passive and electromagnetic suspension, demonstrating the real-world viability of our theoretical findings. This research not only offers a comprehensive solution for enhancing vehicle efficiency through advanced suspension systems but also sets a precedent for the integration of complex mathematical techniques in solving real-world engineering challenges, contributing significantly to the future of energy-efficient automotive technologies. The cases reviewed in this article and listed as references are those commonly found in the literature.