Dimensionless Model Research Articles

Burning behavior of hydrogen jet flame inhibited by a wire mesh screen

Hydrogen is recognized as a promising energy source and the potential risks associated with leakage and jet fire accidents should be considered. The objective of this study is to explore the feasibility of utilizing wire mesh to suppress hydrogen jet flames. The experiments of hydrogen jet fire with ignitors below and above the wire mesh were performed to explore the effect of wire mesh on the burning behaviors at different mesh numbers, mesh-to-nozzle distances, and fuel flow rates. Compared to the free jet flame, the length of jet flame under the action of wire mesh is decreased by 50–90 %. The flame with topside ignition fails to pass through the mire mesh due to the cooling effect of the fuel jet. Experimental results reveal that the state of the flow field in the impingement area plays an important role in determining the upper flame height. Both the upper flame height and the flame extension length beneath the screen decrease with mesh-to-nozzle distance. As the mesh porosity decreases, the flame extension length increases, however, the upper flame height decreases. Based on the classical theory of flow resistance through porous media, a new dimensionless model was developed to predict the characteristic flame lengths of the jet flame inhibited by wire mesh. The findings presented in this paper offer fresh insight into the safeguarding of jet fires.

Optimizing pipeline systems with surge tanks using a dimensionless transient model

Optimizing pipeline systems with surge tanks using a dimensionless transient model

Intelligent predictions for flow pattern and phase fraction of a horizontal gas-liquid flow

In-situ measurement of phase fraction of a gas-liquid flow is closely related to the production efficiency in natural gas extraction. However, the measurement accuracy can be affected by the co-existed multiple flow patterns. This study proposes an intelligent strategy that identifies the flow pattern followed by a phase fraction prediction. For flow pattern recognition, we establish a bidirectional long short-term memory (BI-LSTM) network whose inputs are time-series phases of a Radio Frequency Sensor (RFS). The accuracy is 92.4 % over four classical flow patterns. The time-series phases of RFS are agreed well with the axial imaging from a Wire-Mesh Sensor (WMS). Two predictive models are developed for gas fraction: dimensionless analysis model (DAM) based on RFS and gas Froude number, and neural network model (NNM) with the phases of RFS and the recognized flow pattern. The mean absolute errors (MAE) are 3.2 % and 1.5 % for DAM and NNM, respectively. It is concluded that a NNM, incorporated with RFS and flow pattern by BI-LSTM, can intelligently predict gas fraction with high-accuracy. As the present strategy decouples the pattern recognition and gas fraction prediction into two networks, the complexity of a NNM is reduced which benefits the in-situ measurement practice.

Novel method for measuring surface residual stress using flat-ended cylindrical indentation

Instrumented indentation is a promising technique for estimating surface residual stresses and mechanical properties in engineering components. The relative difference between the indentation loads for unstressed and stressed specimens was selected as the key parameter for measuring surface residual stresses in flat-ended cylindrical indentations. Based on the equivalent material method and finite element simulations, a dimensionless mapping model with six constants was established between the relative load difference, constitutive model parameters, and normalized residual stress. A novel method for measuring the surface residual stress and constitutive model parameters of metallic material through flat-ended cylindrical indentations was proposed using this model and a mechanical properties determination method. Numerical simulations were conducted using numerous elastoplastic materials with different residual stresses to verify the proposed model; good agreements were observed between the predicted residual stresses and those previously applied in finite element analysis. Flat-ended cylindrical indentation tests were performed on four metallic materials using cruciform specimens subjected to various equibiaxial stresses. The results exhibited good conformance between the stress–strain curves obtained using the proposed method and those from traditional tensile tests, and the absolute differences between the predicted residual stresses and applied stresses were within 40 MPa in most cases.

Prediction of slug length distribution in horizontal large-diameter gas/liquid pipeline systems

Large-diameter (ID ≥ 0.1524 m) pipeline network systems are widely used in the food industry for grain transportation, in the chemical and nuclear industries for steam/water thermal distribution systems, in the oil and gas industry for crude oil transportation and exploitation, and in urban water supply and drainage systems. Due to the favorable operational and geometrical conditions in surface gas/liquid pipelines, slug flow often prevails, dominating the horizontal and slightly inclined flow pattern map. Formed liquid slugs at large-diameter pipeline entrances and dip can grow, accelerate, and overtake other slugs, resulting in high-momentum and long slugs ranging in length from a few meters to a few hundred meters. The discrepancy of current mechanistic models to predict slug length in large diameter pipes, and the scarcity of large diameter slug length data motivated this work to propose a combined mechanistic and empirical approach to predict full slug length distribution in large diameter surface pipeline systems. A first-principle mechanistic mean slug length model is improved by optimizing its closure relationships using a large-diameter lab and field slug length database. Furthermore, an empirical large-diameter slug length standard deviation dimensionless model is proposed and statistically validated. The proposed mean and standard deviation slug length models are combined to construct a probability distribution and maximum slug length models. Validation of the proposed model revealed an absolute average error of 27% and 31% for the mean and maximum slug lengths, respectively, vastly outperforming all existing models.

Using the Buckingham π Theorem for Multi-System Transfer Learning: A Case-Study with 3 Vehicles Sharing a Database

Many advanced driver assistance schemes or autonomous vehicle controllers are based on a motion model of the vehicle behavior, i.e., a function predicting how the vehicle will react to a given control input. Data-driven models, based on experimental or simulated data, are very useful, especially for vehicles difficult to model analytically, for instance, ground vehicles for which the ground-tire interaction is hard to model from first principles. However, learning schemes are limited by the difficulty of collecting large amounts of experimental data or having to rely on high-fidelity simulations. This paper explores the potential of an approach that uses dimensionless numbers based on Buckingham’s π theorem to improve the efficiency of data for learning models, with the goal of facilitating knowledge sharing between similar systems. A case study using car-like vehicles compares traditional and dimensionless models on simulated and experimental data to validate the benefits of the new dimensionless learning approach. Preliminary results from the case study presented show that this new dimensionless approach could accelerate the learning rate and improve the accuracy of the model prediction when transferring the learned model between various similar vehicles. Prediction accuracy improvements with the dimensionless scheme when using a shared database, that is, predicting the motion of a vehicle based on data from various different vehicles was found to be 480% more accurate for predicting a simple no-slip maneuver based on simulated data and 11% more accurate to predict a highly dynamic braking maneuver based on experimental data. A modified physics-informed learning scheme with hand-crafted dimensionless features was also shown to increase the improvement to precision gains of 917% and 28% respectively. A comparative study also shows that using Buckingham’s π theorem is a much more effective preprocessing step for this task than principal component analysis (PCA) or simply normalizing the data. These results show that the use of dimensionless variables is a promising tool to help in the task of learning a more generalizable motion model for vehicles, and hence potentially taking advantage of the data generated by fleets of vehicles on the road even though they are not identical.

Local non-similar solution for MHD mixed convection flow of a power law fluid along a permeable wedge with non-linear radiation

In this study, a novel investigation for the effects of non-linear thermal radiation and magnetic field is conducted on mixed convection flow of non-Newtonian fluid along a permeable wedge. Power-law model is used as a non-Newtonian fluid model that predicts shear thinning/thickening effects. For theoretical analysis, a mathematical model in terms of nonlinear PDEs are transformed into a dimensionless non-similar model which is treated as a non-linear ODE when streamwise coordinate is assumed as a constant. The obtained system is solved numerically using the built-in ‘bvp4c’ technique, and the effects of the pertinent parameters is examined through plots illustrating the velocity profiles, temperature distributions, Nusselt number, and skin friction coefficients. From the results, it is revealed that heat transfer rate accelerates in occurrence of assisting flow as compared to opposing flow and further in the existence of thermal radiation, heat transfer rate becomes higher which is crucial in industry because more enhancement in heat transfer rate is required. Skin friction coefficient reduces in the occurrence of opposing flow as compared to assisting flow and further reduction is noted by taking thermal radiation.

Inclined magnetic field and joule heat on unsteady ternary nanofluidic flow impinging over a convectively heated cylinder

The present analysis considered the condition of unsteady stagnation point flow on ternary nanofluid [Formula: see text] through the regularly affecting and convective heated stretchable cylinder by the effect on inclining Lorentz force. This influence on thermal radiation, velocity slip, viscous dissipation, and Joule dissipation were again integrated by the analysis. The suitable thermo-physical relationship in the hybrid nanofluid is cultivated into followed Xue form. With the help of appropriate comparison alterations, the controlling dimensional numerical equations were transformed by the dimensionless models. The governing equations are transformed through comparison transformation and mathematically tackled in MATLAB with a boundary value problem algorithm. These mathematical solutions were validated with the presented material. Tabular and graphical descriptions of mathematical information were utilized to analyze the physical effect on different relevant parameters in the ternary nanofluid temperature and velocity. This thermal buoyancy force hikes the fluid flow although the opposite direction was noted in magnetic parameters and velocity slips. This heat transport rate in the surface was enhanced by an improvement in thermal radiation, Biot number, and solid fraction of nanoparticles. Moreover, a 44.9754% enhanced decreased skin friction is observed by triple nanoparticle nanofluid it signifies its best behavior as related to both other nanofluids.

Study on the flame radiative heat transfer and near-field radiation heat flux predictive model of vehicle fires in a tunnel

As a major form of heat transfer, flame thermal radiation has an important effect on the ignition of adjacent energy, fire spread and environmental damage. Forecasting the flame radiation heat flux can provide theoretical basis for fire hazard assessment, fire extinguishing and salvation. Meanwhile, the distinctive structure of the arc tunnel can result in significant variations in the local heat and mass transfer processes during tunnel fires compared to those in rectangular tunnels, leading to different fire characteristics parameters. In this study, experiments and theoretical analyses were conducted to investigate the flame length scale and near-field radiation heat flux on the lower surface of an arc-shaped ceiling induced by vehicle fires in a tunnel. The findings reveal that the flame length scale in the transverse direction beneath the arc-shaped ceiling decreases with an increasing burner aspect ratio and increases with the increasing heat release rate. A dimensionless model of the flame length scale under the arced ceiling with various burner aspect ratios was proposed based on the amount of remaining unburned fuel after flame impingement and the buoyancy component along the arc-shaped ceiling. Simultaneously, radiative heat fluxes on the lower surface also increase with rising heat release rate. The flame geometry beneath the arc-shaped ceiling is assumed to be a combination of a cuboid and an arc plate model based on the actual flame length scale. Subsequently, the view factor, radiative fraction, and flame surface area are analyzed to predict the radiative heat fluxes on the lower surface. The predictions of the cuboid and arc plate flame model show good agreement with the current experimental data. This work presents a dimensionless correlation of the flame length scale and calculates the view factor between the target and the arc plate to predict the near-field radiative heat flux more accurately. This approach also facilitates the understanding of flame spreading behavior and thermal hazards impacted by arced ceiling.

Vibration control by using active electromagnetic shunt damper

It is well-known that the traditional electromagnetic shunt damping (EMSD) techniques are limited by the damping force of electronic components and require a negative resistance (NR) shunt circuit to enhance performance. However, the NR shunt circuit could lead to the EMSD system being unstable. Addressing this, this study proposes an advanced control system that employs active control technology combined with EMSD for vibration control. We first developed a dimensionless mathematical model of the control system, which was then finely tuned using an adaptive simulated annealing particle swarm optimization algorithm. Subsequently, the relationship between control gain and optimal shunt circuit parameters was predicted using a BP neural network. Finally, the proposed Active-EMSD (AEMSD) was experimentally verified. The experimental results demonstrate that the proposed AEMSD not only surpasses traditional thresholds but also excels in isolating low-frequency vibrations. Compared to traditional EMSD, the proposed AEMSD showed improved effectiveness.

Experimental study on hydrogen-enriched natural gas jet fire hazards: Assessment of the flame geometrical parameters

In the future, hydrogen will be more frequently injected into natural gas networks for storage and transportation purposes. A diffusion jet flame forms when gaseous fuel leakage occurs during the transportation or utilization of hydrogen-enriched natural gas, and the fuel is ignited by an ignition source in still air. In the study, methane was chosen to simulate natural gas. Experiments with the hydrogen addition fraction reaching up to 20% were performed to study the effects of the initial flame angle (θ = 90°, 60°, 30°, 0°, and −30°), variable nozzle diameter (de = 3.15, 4, 4.94, 5.65, and 6 mm) and a multitude of fuel flow rates (10, 20, 30, 40, 50, and 60 L/min) on the morphological parameters of the gas jet flames. The geometrical features of the jet flame were determined via video processing for each experiment. The geometrical parameters of hydrogen-enriched natural gas were quantified under different conditions. The experimental results indicate that a dimensionless prediction model was established for the flame height of hydrogen-enriched natural gas by modifying the flame Froude number (Frf) for vertical jet flames. For upward jet flames, the normalized flame horizontal projection length (Lx) of hydrogen-enriched natural gas is well correlated with Q∗. A global prediction model for inclination angles of 0° ≤ θ ≤ 60° and 2000 < Q∗<20,000 was proposed based on the experimental data. For downward jet flames, the normalized horizontal projection length and downward extension length (Ld) of the hydrogen-enriched natural gas jet flame are correlated with Q∗, with powers of 2/5 and 3/5, respectively. Dimensionless prediction models for the horizontal projection length and downward extension length are given by modifying the flame Froude number. Quantitative results were proposed in order to gain insight into the development of the key parameters and the effects on the environment, from which extinguishing concepts and safety areas can be directly derived.

Drag Coefficient of Emergent Vegetation in a Shallow Nonuniform Flow Over a Mobile Sand Bed

AbstractWidely distributed in natural rivers and coasts, vegetation interacts with fluid flows and sediments in a variable and complicated manner. Such interactions make it difficult to predict associated drag forces during sediment transport. This paper investigates the drag coefficient for an emergent vegetated patch area under nonuniform flow and mobile bed conditions, based on an analytical model solving the momentum equation following our previous work (Zhang et al., 2020, https://doi.org/10.1029/2020WR027613). Emergent vegetation was modeled with rigid cylinders arranged in staggered arrays of different vegetation coverage ∅. Laboratory flume tests were conducted to measure variations in both the water and bed surfaces along a vegetated patch on a sand bed. Based on the experimental and theoretical analyses, a dimensionless drag model integrating both terms of flow properties and bed effects is proposed to predict the drag coefficient Cd over a mobile bed. The calculated values of Cd exhibit two different trends, that is, nonmonotonically or monotonically increasing along the streamwise direction, due to the combined effect of water surface gradient and bed slope. The morphodynamic response of the mobile bed to nonuniform flow manifests as an evolution in the bed slope within the vegetated patch. Ongoing scouring directs the flow's energy toward overcoming the rising Cd and bed slope, leading to a relatively stable stage with a low sediment transport rate. This study advances the existing understanding of the drag coefficient's role over a mobile bed within nonuniform flows. It also enhances the applicability of vegetation drag models in riverine restoration.

Experimental study of the dynamics and mass transfer of single CO2 bubble accompanied by reactions in Hele-Shaw cell

The reduction of carbon emissions has become a critical global issue, and the use of monoethanolamine (MEA) solution for CO2 absorption is prevalent in industry. To elucidate the mass transfer mechanisms in reactive multiphase flow, we employed high-speed photography and digital image processing to examine the dynamics and mass transfer behavior of CO2 bubbles in a Hele-Shaw cell. The results indicate that as the MEA solution concentration increases, oscillations during bubble ascent diminish, and the terminal velocity decreases. Based on changes in the mass transfer coefficient, the reaction process can be segmented into a phase of intensified mass transfer, marked by a rapid decrease in bubble equivalent diameter, and a phase of deteriorating mass transfer, where the diameter stabilizes. Additionally, we introduced a dimensionless mathematical model for the Sherwood number based on experimental findings, and its reliability was confirmed.

Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems.

This article proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theories, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler-Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e-3 % error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space-time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.

Dynamics of inclined simply supported piping system subjected to slug flow

In this paper, the linear and nonlinear dynamics of a simply supported inclined piping system conveying slug flow are investigated, by using a dimensionless approach. A method is proposed for constructing equivalent flow parameters in order to achieve a dimensionless model equation. The validity of this method has been verified through the literature data. The effects of superficial velocities and inclined angle on the stability of the system, as well as post-instability nonlinear dynamical behaviors, are investigated. The linear analysis results showed that the superficial gas velocity stabilized the system at lower values, but had a destabilizing effect at higher values. The main reason is the reduction in system mass resulting from the increase in superficial gas velocity. The superficial liquid velocity negatively impacted the system's stability, necessitating evaluation through the critical pipe length. The nonlinear analysis results showed that the inclined system, in the absence of modal coupling occurrence, may exhibit chaotic behavior due to its inherent nonlinearity. The system stability could be regained as the superficial gas velocity increased following self-weight instability under low superficial gas velocity conditions. This work is helpful for the design of operating parameters to ensure the safety of the piping system.

Effect of unpowered ventilation caps and shaft parameters on fire smoke spread in the natural ventilation tunnel with shafts

Shaft-type natural ventilation offer a sustainable and cost-effective alternative to mechanical systems for the mitigation of smoke hazards. This study investigated the behavior of smoke with the application of unpowered ventilation caps in 1/15 scale shallow-buried urban road tunnels with shafts, and analyzed parameters such as the shaft axis wheelbase, shaft width, shaft width-to-height ratio, and heat release rate (HRR). The results show that the dimensionless HRR as an independent relationship with the dimensionless ceiling temperature rise in both the presence and absence of the unpowered ventilation cap. According to the experimental results, dimensionless length of smoke backlayering increases significantly with the increase of the HRR. In addition, the smoke backlayering length is positively correlated with the shaft width, and the backlayering length decreases and then increases with increases of the axis wheelbase. Moreover, the chimney effect is facilitated with the shaft height increase, which enhances exhaust effect, and the backlayering length decreases with the increase in the shaft height when the aspect ratio is greater than 0.5. Once the critical shaft width-to-height ratio is reached, the change in the shaft height no longer has an effect on the backlayering length. Finally, a dimensionless backlayering length calculation model based on the shaft parameters with different shaft exhaust effects is developed by combining the discriminant factors. The findings have crucial implications for fire prevention and safety management, and provide a valuable reference for future studies and engineering applications.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

Entropy Generation and Thermal Radiation Impact on Magneto-Convective Flow of Heat-Generating Hybrid Nano-Liquid in a Non-Darcy Porous Medium with Non-Uniform Heat Flux

The principal objective of the study is to examine the impact of thermal radiation and entropy generation on the magnetohydrodynamic hybrid nano-fluid, Al2O3/H2O, flow in a Darcy–Forchheimer porous medium with variable heat flux when subjected to an electric field. Investigating the impact of thermal radiation and non-uniform heat flux on the hybrid nano-liquid magnetohydrodynamic flow in a non-Darcy porous environment produces novel and insightful findings. Thus, the goal of the current study is to investigate this. The non-linear governing equation can be viewed as a set of ordinary differential equations by applying the proper transformations. The resultant dimensionless model is numerically solved in Matlab using the bvp4c command. We obtain numerical results for the temperature and velocity distributions, skin friction, and local Nusselt number across a broad range of controlling parameters. We found a significant degree of agreement with other research that has been compared with the literature. The results show that an increase in the Reynolds and Brinckmann numbers corresponds to an increase in entropy production. Furthermore, a high electric field accelerates fluid velocity, whereas the unsteadiness parameter and the presence of a magnetic field slow it down. This study is beneficial to other researchers as well as technical applications in thermal science because it discusses the factors that lead to the working hybrid nano-liquid thermal enhancement.

Nonlinear dynamics of cavity optomechanical-thermal systems.

Cavity optomechanics is concerned with the interaction between optical cavities and mechanical resonators. Here, we present systematic research on the dynamic behaviors of cavity optomechanical systems incorporating the influence of thermal nonlinearity. A dimensionless theoretical model was established to describe the system and numerical simulations were performed to study the dynamic behaviors. We theoretically identify the staircase effect, which can abruptly alter the system parameters when adiabatically sweeping the pump laser frequency across the optical cavity resonance and driving the mechanical resonator into oscillation. Moreover, we found bistability effects in several detuning intervals when sweeping the laser forward and backward. Both effects are analyzed theoretically and the roots lie in the thermal instability between averaged cavity energy and laser detuning. Our study shows the dynamic behaviors in an optomechanical-thermal system and provides guidance in leveraging the systems for applications in optical frequency comb, phonon laser, etc.

Contact-line bending energy controls phospholipid vesicle adhesion

Phospholipid bilayer bending energy is often discarded in the analysis of vesicle adhesion on the basis of a dimensionless parameter w = − Δ U R 0 2 / κ b ≫ 1 (interaction energy Δ U , spherical radius R 0 , bending rigidity κ b ), considered a regime of strong adhesion. In this study, we propose a model by which bending energy in a singular proximity of the contact line balances the adhesion energy. This is developed for a regime in which the membrane correlation length ξ is small compared with the vesicle radius R 0 , so a spherical cap with circular footprint presents an effective contact angle θ . Experiments are conducted in which the adhesion of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) vesicles to hyaluronic acid hydrogel substrates is controlled by tuning the van der Waals attraction with systematic change in the hydrogel concentration. Theoretical interpretation of the data furnishes a dimensionless model parameter α ≈ 2 – 10 for contact angles θ ≈ 20 – 80 ∘ , beyond which vesicles collapse into discs. We show that the van der Waals interaction energy varies in the range − Δ U ≈ 0.14 – 0.68 μ J m − 2 in response to varying the hydrogel concentration in a range c ha ≈ 2 – 10 %. The analysis provides a foundation for exploring vesicle–hydrogel interactions with electro-steric influences; these are poorly understood but pertinent in a wide variety of biological and technological applications.