Equations Of Fluid Dynamics Research Articles

MATHEMATICAL RANDOM GENERATION OF METAL FOAM AND NUMERICAL 3D SIMULATIONS OF HEAT TRANSFER IN A HYBRID SOLAR COLLECTOR

This study explores numerically the heat transfer of a hybrid solar collector. The collector is a Cartesian channel partially filled with randomly generated metal foam (MF). The channel is subjected to solar irradiation, and through it the air flows from the side due to natural convection or ventilation. To generate the MF, random Gaussian correlations are used. This technique allows spatial control of density, permeability, and porosity, whose values are also theoretically accessible. To solve the equations of fluid dynamics and heat transfer, a finite volume multigrid scheme is used. An energy equation is framed on the two-temperature model, and a momentum equation is that of the clear fluid case, since the pores' volumes are largely greater than the ver in the porous media. The velocity as well as temperature fields are discussed for different pertinent parameters, and mathematic correlations are given between the Nusselt, porosity, Richardson, and Reynolds numbers. It is found that heat transfer is improved with increasing metal foam blocks and with decreasing porosities for different Reynolds numbers, however it decreases with Richardson number. It is also found that the two-temperature model is more realistic than models with averaged properties, and gives a wide range of perspectives thanks to the possibility of carrying out numerical and experimental investigations on the same MF model: randomly generated and printable in 3D.

Density waves of vortex fluids on a sphere

We aim to find one highly nontrivial example of the solutions to the vortex fluid dynamical equation on the unit sphere (S 2) and compare it with the numerical simulation. Since the rigid rotating steady solution for vortex fluids on S 2 is already known to us, we consider the perturbations above it. After decomposing the perturbation of the vortex number density and vortex charge density into spherical harmonics, we find that the perturbations are propagating waves. To be precise, the velocities for different single-mode vortex number density waves are all the same, while the velocities for single-mode vortex charge density waves depend on the degree of the spherical harmonics l, which is a signal of the existence of dispersion. Meanwhile, we find that there is a beat phenomenon for the positive (or negative) vortex density wave. Numerical simulation based on the canonical equations for the point vortex model agrees perfectly with our theoretical calculations.

A Hybrid Model for Freight Train Air Brake Condition Monitoring

The Digital Freight Train is expected to revolutionise the rail freight industry. A critical aspect of this transformation is real-time condition monitoring of air brake systems, which are among the leading causes of train malfunctions. To achieve this goal, advanced algorithms for air brake modelling are required. This paper introduces a computationally efficient air brake model tailored for real-time diagnostic applications. A hybrid approach, integrating both empirical data and simplified fluid-dynamic equations, has been adopted. Compared to other air brake models found in the literature, the innovative contributions of the presented model are the reduction of the number of required parameters and the estimation of the brake cylinder pressure directly from the main brake pipe pressure using a feed-forward approach. Moreover, a new approach in the evaluation of the first braking phase and the brake cylinder pressure build-up as the saturation of the brake mode is presented. The model input includes the main brake pipe pressure, the weighing valve pressure, and the brake mode, and the output includes the pressure at the brake cylinder. The air brake model has been validated using data from a previous experimental campaign. The model’s accuracy in replicating the air brake system mechanism makes it well-suited for future development of model-based algorithms designed for air brake fault detection.

Analyzing the Dynamics and Friction Forces on Spheres in Fluid Flows: Applications Across Engineering and Sports Science

This study explores the dynamics and friction forces of spherical objects in fluid flows, emphasizing their applications across engineering and sports science. By examining key theoretical concepts such as drag coefficient, Reynolds number, and fluid dynamics equations, the research highlights how these principles influence the motion of spheres in various fluid environments. The analysis encompasses computational fluid dynamics (CFD) and experimental approaches, addressing applications in ocean, aerospace, and vehicle engineering, as well as sports science. The findings demonstrate the critical role of understanding drag and friction characteristics in optimizing designs, improving performance, and driving technological innovation. Challenges such as multi-scale phenomena, nonlinear dynamics, and measurement techniques are identified, suggesting future research directions to refine theoretical models and enhance practical applications. The study not only advances the theoretical understanding of fluid dynamics but also provides essential insights for engineering optimization and sports performance enhancement.

Simulating groundwater flow and contaminant transport

This study presents a comprehensive simulation of groundwater flow and contaminant transport using advanced numerical modeling techniques. The research focuses on understanding the complex interactions between groundwater movement and pollutant dispersion across various geological settings. By applying the governing equations of fluid dynamics and solute transport, the model incorporates essential parameters such as hydraulic conductivity, porosity, and dispersivity, enabling the accurate prediction of contaminant behavior over time. Simulations were carried out under a range of scenarios to assess the effects of differing recharge rates and contaminant source configurations on groundwater quality. The results provide critical insights into the mechanisms governing contaminant migration, highlighting the importance of soil properties, boundary conditions, and flow dynamics in influencing transport behavior. Moreover, the study demonstrates how variations in geological features and pollutant sources can significantly alter contaminant dispersal patterns. This work contributes to the development of robust groundwater management strategies and emphasizes the role of simulation tools in assessing environmental risks tied to groundwater contamination.

Gyrotactic micro-organism dusty fluid flow over an extended surface

The conventional magnetohydrodynamics (MHD) equations are modeled for the dusty fluid flow past a stretching sheet embedded in a porous medium. These equations are coupled with motile microorganisms, temperature and concentration equations for both fluid and dust particles dynamical equations. The two-phase dusty fluid flow is subjected to magnetic effect, porosity factor, 2nd order chemical reaction, Brownian diffusion, thermophoretic effect and Arrhenius activation energy. An appropriate transformation is used to reset the system of partial differential equations (PDEs) into non-linear system of ODEs (ordinary differential equations). The flow equations are numerically solved by using the parametric continuation method (PCM). For validity of the applied methodology, the results are compared using numerical and graphical results of Matlab built-in package “BVP4c”. Both results show accuracy up to four decimal places. Furthermore, from graphical results, it can be noticed that the fluid particles interaction parameter causes an attractive force among fluid particles which prevents the dust particles phase flow. This technique can be used for biological separations, filters, fluid dust separators and crude oil purification.

On the Equations of Compressible Fluid Dynamics With Cattaneo‐Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure

ABSTRACTThe aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid dynamics with Cattaneo‐type extensions for the heat flux. In contrast, the linearizations of such system around constant equilibrium solutions have Friedrichs symmetrizers. Then, from a physical perspective, we aim to understand the relaxation term appearing in this system. By noticing the violation of the Kawashima–Shizuta condition, locally and smoothly, with respect to the Fourier frequencies, we construct persistent waves, that is, solutions preserving the norm for all times that are not dissipated by the relaxation terms.

Understanding Shunt Currents in Flow Batteries: A Multiphysics Approach to Analysis and Mitigation

The transition to renewable energy systems is critically dependent on the development and optimization of large-scale energy storage technologies, among which Vanadium Redox Flow Batteries (VRFBs) stand out for their scalability, flexibility, and long cycle life. However, the operational efficiency and lifespan of VRFBs are significantly undermined by shunt currents—unwanted internal currents that bypass the electrochemical reaction zones, leading to energy losses and accelerated degradation. Previous studies have predominantly employed lumped electrical circuit models to investigate these currents, a method that, while providing initial insights, substantially oversimplifies the complex interplay of ionic and electronic transport mechanisms within the VRFB electrolytes.This study proposes a novel multiphysics modeling framework that eschews the simplifications of previous models in favor of a detailed representation that captures the coupled dynamics of ionic conduction, electronic conduction, and fluid flow within the VRFB. By integrating the Navier-Stokes equations for fluid dynamics with the Nernst-Planck equation for ionic transport, and the Poisson equation for electric fields, this model aims to provide a holistic view of the factors contributing to shunt currents. This approach not only facilitates a deeper understanding of the underlying physical phenomena but also opens new avenues for identifying effective mitigation strategies.The superiority of this multiphysics approach lies in its ability to accurately simulate the complex interdependencies within the VRFB system, which are overlooked by simpler models. This enables the identification of specific structural and operational factors that contribute to shunt currents, facilitating the development of targeted optimization strategies. Through the application of this advanced modeling framework, the research can precisely quantify the impact of various physical parameters, such as membrane permeability, electrode porosity, and flow channel design, on the magnitude and distribution of shunt currents, guiding the engineering of VRFB components for minimal energy loss and enhanced efficiency.Moreover, the multiphysics model paves the way for innovative optimization techniques, such as the strategic placement of barriers or the adjustment of flow patterns, to disrupt or redirect shunt pathways effectively. These strategies, informed by a deep understanding of the underlying physics, promise to significantly improve VRFB performance, offering a path to more reliable, durable, and efficient energy storage systems.The implications of this research extend beyond academic interest, offering practical insights for the design and operation of more efficient and sustainable VRFBs. As the demand for reliable large-scale energy storage solutions grows in the context of global renewable energy integration, the findings of this study promise to contribute significantly to the advancement of VRFB technology, aligning with the broader goals of energy sustainability and environmental stewardship. References Tang, J. McCann, J. Bao, M. Skyllas-Kazacos, Investigation of the effect of shunt current on battery efficiency and stack temperature in vanadium redox flow battery, J. Power Sources, 242, (2013) 349 - 356, doi: 10.1016/j.jpowsour.2013.05.079.Viswanathan, A. Crawford, D. Stephenson, S. Kim, W. Wang, B. Li, G. Coffey, E. Thomsen, G. Graff, P. Balducci, M. Kintner-Meyer, V. Sprenkle, Cost and performance model for redox flow batteries, J. Power Sources, 247, (2014) 1040 – 1051. doi: 10.1016/j.jpowsour.2012.12.023Skyllas-Kazacos, J. McCann, Y. Li, J. Bao, A. Tang, The Mechanism and Modelling of Shunt Current in the Vanadium Redox Flow Battery, ChemistrySelect, 1(10), (2016) 2249–2256. doi: 10.1002/slct.201600432. Moro, A. Trovò, S. Bortolin, D. Del Col, M. Guarnieri, An alternative low-loss stack architecture for vanadium redox flow battery: comparative assessment, J. Power Sources, 340, (2017) 229-241.doi:10.1016/j.jpowsour.2016.11.042.Trovò, G. Marini, A. Sutto, P. Alotto, M. Giomo, F. Moro, M. Guarnieri, Standby thermal model of a vanadium redox flow battery stack with crossover and shunt-current effects, Appl Energy, 240, (2019) 893-906. doi: 10.1016/j.apenergy.2019.02.067. Trovò, F. Picano, M. Guarnieri, Comparison of energy losses in a 9 kW vanadium redox flow battery, J. Power Sources, 440, (2019) 227144. doi: 10.1016/j.jpowsour.2019.227144. Figure 1

Numerical Analysis of the Vehicle Damping Performance of a Magnetorheological Damper with an Additional Flow Energy Path

Vehicles experience various frequency excitations from road surfaces. Recent research has focused on active dampers that adapt their damping forces according to these conditions. However, traditional magnetorheological (MR) dampers face a “block-up phenomenon” that limits their effectiveness. To address this, additional flow-type MR dampers have been proposed, although revised designs are required to accommodate changes in damping force characteristics. This study investigates the damping performance of MR dampers with an additional flow path to enhance the vehicle ride quality. An optimization model was developed based on fluid dynamics equations and analyzed using electromagnetic simulations in ANSYS Maxwell software. Vibration analysis was conducted using AMESim by applying a sinusoidal road surface model with various frequencies. Results show that the optimized diameter of the additional flow path obtained from the analysis was 1.1 mm, and it was shown that the total damping force variation at low piston velocities decreased by approximately 56% compared to conventional MR dampers. Additionally, vibration analysis of the MR damper with the optimized additional flow path diameter revealed that at 30 km/h, 37.9% acceleration control was achievable, at 60 km/h, 18.7%, and at 90 km/h, 7.73%. This demonstrated the resolution of the block-up phenomenon through the additional flow path and confirmed that the vehicle with the applied damper could control a wider range of vehicle upper displacement, velocity, and acceleration compared to conventional vehicles.

Conservation laws for a perturbed resonant nonlinear Schrödinger equation in quantum fluid dynamics and quantum optics

The current paper retrieves the conservation laws for the extended version of the resonant nonlinear Schrödinger's equation for description of physical processes in quantum fluid dynamics and quantum optics. The method of multipliers recovers three fundamental conservation laws. Analytical solutions of equation are found taking into account traveling wave reduction. The conserved quantities are subsequently computed from the soliton solution of the model equation that is derived in this work too.

Course control in a self-consistent model of cuttlefish movement

We developed a simulation model to mimic cuttlefish movement. We developed a simulation model to mimic cuttlefish movement, representing an elongated body with two undulatory fins that generate propulsive forces for underwater movement. Our mathematical model concurrently solved equations for both body mechanics and fluid dynamics, using the Navier–Stokes equations to describe the latter. To implement this self-consistent model, we utilized deformable mesh techniques. This enabled us to compute both the apparatus’s movement performance characteristics and hydrodynamic flow parameters, such as vorticity and pressure fields. Our study focused on examining how oscillations of the left and right fins, each with different parameters, impact the apparatus’s maneuverability. We found that differences in frequencies between the left and right fins resulted in a peak turning angle velocity. We also explored how the interplay between hydrodynamic forces influences the apparatus’s course control.

Calculation and analysis of wet clutch sliding torque based on fluid-solid coupling dynamic behavior

The fluid dynamics equations of groove cavity and non-grooved gap are established and combined to obtain fluid load bearing model. Considering the chain effect among local deformation, the deformation equation of friction surface under fluid-solid coupling load is developed to characterize reconstructed friction gap. The internal pressure and external load are used to iteratively solve the distribution of film thickness and contact area. An improved sliding torque calculation model is established by the microscopic state of fluid motion and solid deformation instead of fitting friction coefficient by multiple conditions. The accuracy of torque model is proved by sliding test. The influence of applied pressure, relative speed and lubricant flow on torque is weakened in turn according to fluid-solid state analysis.

Evolution of CFD numerical methods and physical models towards a full discrete approach

The physical models and numerical methodologies of Computational Fluid Dynamics (CFD) are historically linked to the concept of continuous medium and to analysis where continuity, derivation and integration are defined as limits at a point. The first consequence is the need to extend these notions in a multidimensional space by establishing a global inertial frame of reference in order to project the variables there. In recent decades, the emergence of methodologies based on differential geometry or exterior calculus has changed the point of view by starting with the creation of entangled polygonal and polyhedral structures where the variables are located. Mimetic methods and Discrete Exterior Calculus, notably, have intrinsic conservation properties which make them very efficient for solving fluid dynamics equations. The natural extension of this discrete vision relates to the derivation of the equations of mechanics by abandoning the notion of continuous medium. The Galilean frame of reference is replaced by a local frame of reference composed of an oriented segment where the acceleration of the material medium or of a particle is defined. The extension to a higher dimensional space is carried from cause to effect, from one local structure to another. The conservation of acceleration over a segment and the Helmholtz–Hodge decomposition are two essential principles adopted for the derivation of a discrete law of motion. As the fields covered by CFD are increasingly broad, it is natural to return to the deeper meaning of physical phenomena to try a new research or new path which would preserve the properties of current formulations.

Physics-Guided Neural Networks for Intraventricular Vector Flow Mapping.

Intraventricular vector flow mapping (iVFM) seeks to enhance and quantify color Doppler in cardiac imaging. In this study, we propose novel alternatives to the traditional iVFM optimization scheme by utilizing physics-informed neural networks (PINNs) and a physics-guided nnU-Net-based supervised approach. When evaluated on simulated color Doppler images derived from a patient-specific computational fluid dynamics model and in vivo Doppler acquisitions, both approaches demonstrate comparable reconstruction performance to the original iVFM algorithm. The efficiency of PINNs is boosted through dual-stage optimization and pre-optimized weights. On the other hand, the nnU-Net method excels in generalizability and real-time capabilities. Notably, nnU-Net shows superior robustness on sparse and truncated Doppler data while maintaining independence from explicit boundary conditions. Overall, our results highlight the effectiveness of these methods in reconstructing intraventricular vector blood flow. The study also suggests potential applications of PINNs in ultrafast color Doppler imaging and the incorporation of fluid dynamics equations to derive biomarkers for cardiovascular diseases based on blood flow.

Fokker-Planck Central Moment Lattice Boltzmann Method for Effective Simulations of Fluid Dynamics

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory.

Deciphering postoperative hemodynamics in pediatric intensive care: insights from patient-specific computational fluid dynamics models for congenital heart disease

Abstract Purpose Precise hemodynamic control is imperative for optimizing outcomes in children undergoing cardiac surgery, particularly in the pediatric intensive care unit (PICU). Computational fluid dynamic (CFD) models tailored to individual pediatric patients following definitive repairs for congenital heart disease hold the potential to discern and analyze the intricacies of their hemodynamic systems. This study aims to explore the applicability of patient-specific CFD models in determining optimal treatment strategies to enhance patient hemodynamics. Methods Ten postoperative pediatric patients (6 females and 4 males, median age 4.5±3.6 months, median height 62.5±5.3 cm, and median weight 6.2±1.3 kg) diagnosed with ventricular septal defect (VSD, n=5), atrial septal defect (ASD, n=2), and atrioventricular septal defect (AVSD, n=3) were enrolled. Continuous radial arterial waveforms and sporadic arterial blood draws, including lactate levels, were recorded in the PICU postoperatively. Fluid dynamics equations were employed to model major and peripheral blood vessels, utilizing a 0–1-dimensional hemodynamic model validated in previous studies and refined for this investigation. Sensitivity analysis based on correlation coefficients identified significant parameters, adjusted for replicating pressure waveforms. Comparison and re-approximation was made with actual radial artery pressure waveforms from 78 arterial waveforms and blood draws. Updated parameters were then correlated with postoperative time and lactate levels in the ICU. Results Replicated waveforms demonstrated high agreement with original arterial waveforms, with mean, maximal, and minimal blood pressure percentages of 96.7±1.8%, 96.7±2.4%, and 95.8±2.4%, respectively. Notably, systemic vascular resistance and compliance exhibited a substantial relationship with time elapsed after admission to the PICU, with correlation coefficients (R) of 0.26 and 0.43, respectively. Lactate levels demonstrated a decrease with reduced peripheral vascular resistance and an increase in vascular compliance, with R of 0.23 and 0.32, respectively, aligning with expected clinical improvement and stability. Conclusion This study successfully attained precise replication of radial artery blood pressures and intricate pressure waveforms using patient-specific CFD models in pediatric patients following congenital heart disease repairs. The insights gained shed light on the pivotal hemodynamic parameters that impact both stability and instability. This research sets the stage for theoretically informed treatments by amalgamating real-time biological information with patient-specific CFD models.Re-approximation of arterial waveformCorrelation of hemodynamic parameters

Optimal decay of the Boltzmann equation

The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high‐low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity‐weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time‐weighted dissipation estimates via the time‐weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.

Closed-Boundary Reflections of Shallow Water Waves as an Open Challenge for Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or time discretization. However, PINNs often exhibit slow or incomplete convergence, depending on the architecture, optimization algorithms, and complexity of the PDEs. To address these difficulties, a variety of novel and repurposed techniques have been introduced to improve convergence. Despite these efforts, their effectiveness is difficult to assess due to the wide range of problems and network architectures. As a novel test case for PINNs, we propose one-dimensional shallow water equations with closed boundaries, where the solutions exhibit repeated boundary wave reflections. After carefully constructing a reference solution, we evaluate the performance of PINNs across different architectures, optimizers, and special training techniques. Despite the simplicity of the problem for classical methods, PINNs only achieve accurate results after prohibitively long training times. While some techniques provide modest improvements in stability and accuracy, this problem remains an open challenge for PINNs, suggesting that it could serve as a valuable testbed for future research on PINN training techniques and optimization strategies.

Algebraic calming for the 2D Kuramoto-Sivashinsky equations

Abstract We propose an approximate model for the 2D Kuramoto–Sivashinsky equations (KSE) of flame fronts and crystal growth. We prove that this new ‘calmed’ version of the KSE is globally well-posed, and moreover, its solutions converge to solutions of the KSE on the time interval of existence and uniqueness of the KSE at an algebraic rate. In addition, we provide simulations of the calmed KSE, illuminating its dynamics. These simulations also indicate that our analytical predictions of the convergence rates are sharp. We also discuss analogies with the 3D Navier–Stokes equations of fluid dynamics.

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality and symmetry, a weak formulation of differential equations and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics – the Navier–Stokes equation, the continuity equation and the boundary conditions – as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well suited for analysis of experimental data.