Complex Fluid Flow Research Articles

A novel transformation free nonuniform higher order compact finite difference scheme for solving incompressible flows on circular geometries

This paper presents a newly developed higher order compact scheme that is designed on a polar grid by using an implicit form of first order derivatives on nonuniform grids. These derivatives are formulated compactly and implicitly with a relationship of the coefficients in terms of the unknown variables. The proposed scheme is free from transformation technique and third order accurate in space. The objective is to solve Stokes equations and Navier–Stokes equations on curvilinear grids using the polar nature of the coordinate system. Our newly developed scheme is used to solve several problems namely, a problem having an analytical solution, Stokes flow with different orientations of the lids for the half filled annular and wedge cavity, the lid driven polar cavity flow and flow past an impulsively started circular cylinder. Our newly developed scheme is used to analyze the flow structures for the flow governed by different physical control parameters: the cavity radius ratio, the cavity angle and the ratio of the upper and lower lid speeds with rotating coaxial cylinders and Reynolds number for the impulsively started circular cylinder. The Stokes equations and the Navier–Stokes equations are efficiently solved with Dirichlet as well as Neumann boundary conditions. The efficacy and robustness of our proposed scheme are shown through its applicability in all the complex fluid flow problems.

Darcy-Brinkman Flow of a Micropolar Fluid through an Anisotropic Porous Channel

This study investigates the Darcy-Brinkman flow of micropolar fluid through an anisotropic porous channel, a configuration relevant to various industrial and natural processes involving complex fluid flow. The anisotropy of the porous medium is characterized by its permeability aligned along two principal axes, with one axis forming an angle with the horizontal direction. The model applies no-slip and no-spin boundary conditions at the channel’s impermeable walls. Using a combination of analytical techniques and graphical analysis, we explore how key parameters such as the Darcy number, anisotropy angle, permeability ratio, and micropolar material parameters affect the flow behavior. Results reveal that increasing the anisotropy angle and permeability ratio leads to a reduction in both fluid velocity and micro rotational velocity, while the Darcy number promotes an increase in flow velocity. Additionally, the study discusses the impact of these parameters on shear stress and couple stress at the channel walls. The findings contribute to a deeper understanding of micropolar fluid behavior in porous media, with potential applications in filtration, lubrication, and subsurface fluid dynamics.

Thermal profile modeling and microstructural evolution in laser processing of Inconel 625 plates by comparison of analytical and numerical methods

Microstructural evolution of materials under specified process conditions and parameters can be predicted by thermal modeling of additive manufacturing laser processes. The objective of this study was to develop, analyze and compare two methods for prediction: an analytical method and a numerical method for laser processing of Inconel 625 material. These methods were compared with experimental results for thermal profiling, and the effect of thermal profiles on microstructure of the experimental samples was explored. Maximum temperature and cooling rate of the numerical method were shown in good agreement, while the analytical method proved more challenging when compared to the experimental results for three laser parameters. Cooling curves were correlated with microstructure in terms of grain size, morphology, and orientation, with findings trending with parameter adjustments. This research supports the numerical modeling approach as a method for examining optimal laser processing conditions for Inconel 625 that is ideally suited for complex fluid flow analyses.

An artificial neural network approach to characterizing the behavior of bioconvective nanofluid model using backpropagation of Levenberg–Marquardt algorithm

The study of the behavior of bioconvective nanofluid model (BC-NFM) was explored using bioconvection properties in the computational analysis of magnetized nanofluid flow that was convectively heated, which is critical for applications in energy systems and biomedical devices. We implemented a backpropagated Levenberg–Marquardt neural network approach (BLMNNA) to enhance the analysis and prediction accuracy of such fluid flows. Using the Adams numerical technique, we generated a comprehensive dataset for eight distinct scenarios by variation of thermophoresis parameter, Rayleigh number, Deborah parameter, Hartman number, Prandtl number, bioconvection Lewis number, and Schmidt number to train and test our model. The results demonstrate significant improvements in prediction accuracy and computational efficiency compared to traditional numerical solvers. The steps of training, testing, and validating the developed BLMNNA are used to get the desired numerical solutions of BC-NFM for various instances. The worth and accuracy of the stochastic numerical solutions of BC-NFM are established and authenticated by the outputs of the designed methodology BLMNNA through Adaptation graphs of Mean Square Error, regression studies, plots of error histogram and index of state transition. Excellent measurements of performance in terms of MEAN SQUARE ERROR are achieved at level 9.76E[Formula: see text], 1.41E[Formula: see text], 1.79E[Formula: see text], 1.22E[Formula: see text], 8.49E[Formula: see text], 7.19E[Formula: see text], 9.72E[Formula: see text], and 9.35E[Formula: see text] against 69, 73, 96, 76, 237, 86, 120, and 33 epochs. The significant connection between the proposed and reference findings demonstrates the validity of the BLMNNA based on error analysis, which ranges from E[Formula: see text] to E[Formula: see text] for all situations. The results show that the proposed neural network approach achieves a high level of accuracy, closely matching the outcomes obtained from the numerical solver. The method provides an efficient and precise solution for the analysis of complex fluid flow problems, representing a significant advancement over traditional numerical techniques.

Algorithm for the treatment of boundary conditions in NMM-SPH coupling models: Interface element-wise boundary particle scheme

Large deformation and complex fluid flow interactions, known as the fluid–structure interaction (FSI), are common in geotechnical and coastal projects. To address FSI problems involving crack development, block contact and large movement, a numerical model that utilises smoothed particle hydrodynamics for fluid field spatial discretisation and numerical manifold method for solid block domain solution is proposed in the present study. Specifically, to restore the particle inconsistency near the interface and the overflow issue around the sharp corner in traditional coupled methods, a recommended boundary particle approach is designed to provide full support for particles near the interface, regardless of the interface’s geometry. Moreover, this approach enables the choice of different spatial resolutions tailored to requirements of solid and fluid domains. Six numerical examples were conducted to verify the reliability, accuracy and robustness of the new method. Results showed that relative errors around the sharp corner are lower than those in previous studies. Furthermore, the new model performs well in dealing with the motion of blocks with arbitrary shapes, including large movements, block contacts, crack propagations, and large deformations. Additionally, various inner-variable field evolutions between fluids and solids were visualised, which is beneficial for the prediction of multi-hazard scenario outcomes.

Stochastic neuro-swarming intelligence paradigm for the analysis of magneto-hydrodynamic Prandtl–Eyring fluid flow with diffusive magnetic layers effect over an elongated surface

In recent years, the integration of stochastic techniques, especially those based on artificial neural networks, has emerged as a pivotal advancement in the field of computational fluid dynamics. These techniques offer a powerful framework for the analysis of complex fluid flow phenomena and address the uncertainties inherent in fluid dynamics systems. Following this trend, the current investigation portrays the design and construction of an important technique named swarming optimized neuro-heuristic intelligence with the competency of artificial neural networks to analyze nonlinear viscoelastic magneto-hydrodynamic Prandtl–Eyring fluid flow model, with diffusive magnetic layers effect along an extended sheet. The currently designed computational technique is established using inverse multiquadric radial basis activation function through the hybridization of a well-known global searching technique of particle swarm optimization and sequential quadratic programming, a technique capable of rapid convergence locally. The most appropriate scaling group involved transformations that are implemented on governing equations of the suggested fluidic model to convert it from a system of nonlinear partial differential equations into a dimensionless form of a third-order nonlinear ordinary differential equation. The transformed/reduced fluid flow model is solved for sundry variations of physical quantities using the designed scheme and outcomes are matched consistently with Adam's numerical technique with negligible magnitude of absolute errors and mean square errors. Moreover, it is revealed that the velocity of the fluid depreciates in the presence of a strong magnetic field effect. The efficacy of the designed solver is depicted evidently through rigorous statistical observations via exhaustive numerical experimentation of the fluidic problem.

Reconstruction of particle distribution for tomographic particle image velocimetry based on unsupervised learning method

The development of deep learning has inspired some new methods to solve the 3D reconstruction problem for Tomographic Particle Image Velocimetry (Tomo-PIV). However, the supervised learning method requires a large number of data with ground truth as training information, which is very difficult to gather from experiments. Although synthetic datasets can be used as alternatives, they are still not exactly the same with the real-world experimental data. In this paper, an Unsupervised Reconstruction Technique based on U-net (UnRTU) is proposed to reconstruct volume particle distribution explicitly. Instead of using ground truth data, a projection function is used as an unsupervised loss function for network training to reconstruct particle distribution. The UnRTU was compared with some traditional algebraic reconstruction algorithms and supervised learning method using synthetic data under different particle density and noise level. The results indicate that UnRTU outperforms these traditional approaches in both reconstruction quality and noise robustness, and is comparable to the supervised learning methods AI-PR. For experimental tests, particles dispersed in cured epoxy resin are moved by an electric rail with a certain speed to obtain the ground truth data of particle velocity. Compared with other algorithms, the reconstructed particle distribution by UnRTU has the best reconstruction fidelity. And the accuracy of the 3D velocity field estimated by UnRTU is 12.9% higher than that from the traditional MLOS-MART algorithm. It demonstrates significant potential and advantages for UnRTU in 3D reconstruction of particle distribution. Finally, UnRTU was successfully applied to the high-speed planar cascade airflow field, demonstrating its applicability for measuring complex fluid flow fields at higher particle density.

Moving control surfaces in a geometry-resolved CFD model of an airborne wind energy system

Properly understanding the unsteady interaction of the wind with the aircraft is critical to develop reliable airborne wind energy (AWE) systems. High-fidelity simulation tools are needed to accurately predict these interactions, providing insights into the design and operation of efficient and safe AWE systems. In this work, we present a computational fluid dynamics (CFD) framework of an airborne wind system which resolves all lifting surfaces and includes moving control surfaces. This work considers a reference multi-megawatt ground-gen pumping system. To simulate complex fluid flow problems, with large rigid-body motion and deflecting control surfaces using CFD, we opt for the Chimera/overset technique. The goal of this contribution is to demonstrate the effect of the control surfaces in the CFD framework. This work is a major milestone in the ongoing development of high-fidelity aero-servo-elastic simulation models for airborne wind energy systems.

A modified cell-centered nodal integral scheme for the convection-diffusion equation

The nodal integral methods (NIMs) are very efficient and accurate coarse-mesh methods for solving partial differential equations. The cell-centered NIM (CCNIM) is a simplified variant of the NIMs that has recently shown its efficiency in solving fluid flow problems but has been hampered by issues such as inapplicability to one-dimensional problems, complexities in handling Neumann boundary conditions and the formulation of a system of differential-algebraic equations (DAEs) for discrete unknowns. Here, we present a modified version of the CCNIM designed to overcome the challenges associated with its previous version. Our novel development retains the essence of CCNIM while resolving these issues. The proposed scheme, grounded in the nodal framework, achieves second-order accuracy in both spatial and temporal dimensions. Unlike its precursor, the proposed method formulates algebraic equations for discrete variables per node, eliminating the cumbersome DAE system. Neumann boundary conditions are seamlessly incorporated through a straightforward flux definition, and applicability to one-dimensional problems is now feasible. We successfully apply our approach to one and two-dimensional convection-diffusion problems with known analytical solutions to validate our approach. The simplicity and robustness of the approach lay the foundation for its seamless extension to more complex fluid flow problems.

Numerical investigation of fluid flow behavior in steel cord with lattice Boltzmann methodology: The impacts of microstructure and loading force.

Steel cord materials were found to have internal porous microstructures and complex fluid flow properties. However, current studies have rarely reported the transport behavior of steel cord materials from a microscopic viewpoint. The computed tomography (CT) scanning technology and lattice Boltzmann method (LBM) were used in this study to reconstruct and compare the real three-dimensional (3D) pore structures and fluid flow in the original and tensile (by loading 800 N force) steel cord samples. The pore-scale LBM results showed that fluid velocities increased as displacement differential pressure increased in both the original and tensile steel cord samples, but with two different critical values of 3.3273 Pa and 2.6122 Pa, respectively. The original steel cord sample had higher maximal and average seepage velocities at the 1/2 sections of 3D construction images than the tensile steel cord sample. These phenomena should be attributed to the fact that when the original steel cord sample was stretched, its porosity decreased, pore radius increased, flow channel connectivity improved, and thus flow velocity increased. Moreover, when the internal porosity of tensile steel cord sample was increased by 1 time, lead the maximum velocity to increase by 1.52 times, and the average velocity was increased by 1.66 times. Furthermore, when the density range was determined to be 0-38, the pore phase showed the best consistency with the segmentation area. Depending on the Zou-He Boundary and Regularized Boundary, the relative error of simulated average velocities was only 0.2602 percent.

Numerical treatment for radiative hybrid nanofluid flow over a stretching sheet

Artificial neural networks (ANNs) have brought a huge transformation to the machine learning regime by furnishing unparalleled abilities for modeling intricate phenomena and coping with a variety of challenges. In the oneiric field of ANNs, the essential approach for training ANNs is backpropagation. However, optimization is crucial when handling the complex fluid flow phenomenon through backpropagation. The current article implements the Levenberg Marquardt Technique with ANN backpropagation (LMT-BP-ANN) to investigate the radiative flow of a hybrid nanofluid (RHNF) addressing a Cattaneo-Christov flux system past a stretching sheet (SS). Fe2O3 with single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) hybrid nanofluid is considered. The base fluid is ethylene glycol. Physical parameters of nanofluidic system, including the magnetic parameter M, the solid volume fractions φ1 and φ2, the velocity slip parameter λ, the relaxation time parameter Ω, the Biot number ϒ, and the thermal radiation parameter Gr are evaluated through appropriate variations that effectively accomplish the dynamics of the fluid model. These are utilized to create the dataset for LMT-BP-ANNs using the renowned deterministic Adam's numerical technique in Mathematica software. In MATLAB software, 70 % of data is kept for preparing, 15 % for checking, and 15 % for validating the neural network. The performance plot, regression graphs, and error histograms are constructed to demonstrate the suggested LMT-BP neural network scheme's high efficiency, efficacy, and exactness. When ANN performs, a mean squared error (MSE) of order 10−11 is observed. The observed R squared value is 1. As the magnetic parameter estimate grows, the fluid velocity declines, although the thermal profile shows increasing behavior. As the velocity slip parameter increases, the velocity of the fluid drops. Key findings of this study are anticipated to have a noteworthy bearing on sectors that require local refrigeration and heating by contravention.

On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid

The theoretical development of the complex fluid flows such as more than one obstacle with different shapes have great interest for scientists to understand flow phenomena and verify the model or approximate solution. The complex physical properties due to a uniform streaming motion past two fixed spheres is investigated having one with shear stress and another being shear stress-free. This study concerns analytical technique of a steady incompressible viscous fluid past to two fixed spheres. The Gegenbaur function and associated Legendre polynomials is used to derive the solution that simplify the process of the theoretical calculations. The mathematical expression for the flow fields are obtained in terms of stream functions by Gegenbaur function and associated Legendre polynomials. The physical properties of interest such as the Stokes stream function, the stress and its drag are calculated. It is understandable that for the uniform streaming motion around a sphere with the stress and its drag are affected owing to the presence of another stress-free are analyzed. The present result can be considered as a generalized by making other established results as a corollary of this solution. This theoretical study helps to the numerical or computational work for the verification of their approximated results of interest.

Modeling of rapid solidification in Laser Powder Bed Fusion processes

This paper addresses a numerical framework for modeling site-specific microstructure evolution in Laser Powder Bed Fusion (LPBF), where rapid solidification significantly influences the microstructure and properties of manufactured components. The fine microstructure and rapid solidification can enhance mechanical properties in final parts, yet pose challenges in controlling microstructure and addressing potential defects. In this study, an in-house developed free surface thermo-fluidic Computational Fluid Dynamics (CFD) model is coupled with a binary alloy phase-field model characterized by rapid solidification kinetics. The CFD model considers complex fluid flows related to Marangoni and recoil pressure, laser-material interactions, and rapid melting and solidification of the melt pool. A convergence study for the phase-field model is conducted, comparing simulated partition coefficients with the Continuous Growth Model (CGM) theory. The study investigates the individual effects of temperature gradients and solidification rates on simulated microstructure. Results indicate that, for the same order of magnitude change, the solidification rate has a more pronounced effect on microstructure than temperature gradients. The paper concludes with the simulation of site-specific microstructure evolution within the melt pool, comparing the results with experiments conducted at varied scanning speeds. The predicted microstructure aligns well with experimental measurements, suggesting the potential utility of the developed phase-field model in quantitative microstructural modeling. Overall, this work contributes to understanding microstructure evolution under rapid solidification conditions, providing a fundamental basis for optimizing the LPBF process.

The Gordon–Schowalter/Johnson–Segalman model in parallel and orthogonal superposition rheometry and its application in the study of worm-like micellular systems

Parallel and Orthogonal Superposition experiments may be employed to probe a material’s non-linear rheological properties through the rate-dependent parallel and orthogonal superposition moduli, G∥∗(ω,γ̇) and G⊥∗(ω,γ̇), respectively. In a recent series of publications, we have considered the problem of interconversion between parallel and orthogonal superposition moduli as a means of probing flow induced anisotropy. However, as noted by Yamomoto (1971) superposition flows may be used to assess the ability of a particular constitutive model to describe the flow of complex fluids. Herein, we derive expressions for the superposition moduli of the Gordon–Schowalter (or Johnson–Segalman) fluid. This model contains, as special cases, the corotational Maxwell model, the upper (and lower) convected Maxwell models, the corotational Jeffreys model, and the Oldroyd-B model. We also consider the conditions under which the superposition moduli may take negative values before studying a specific, non shear banding, worm like micellular system of cetylpyridinium chloride and sodium salicylate. We find that, using a weakly non-linear analysis (in which the model parameters are rate independent) the Gordon–Schowalter/Johnson–Segalman (GS/JS) model is unable to describe the superposition moduli. However, by permitting strong non-linearity (allowing the GS/JS parameters to become shear rate dependent), the superposition moduli, at all rates studied, are described well by the model. Based on this strongly non-linear analysis, the shear rate dependency of the GS/JS ‘slip parameter’, a, suggests that the onset of shear thinning in the specific worm-like micellular system studied herein is driven by a combination of microstructural modification and a transition from rotation dominated (as in the corotational Jeffreys model) to shear dominated (as in the Oldroyd-B model) deformation of the microstructural elements.

An energy estimate and a stabilized Lagrange–Galerkin scheme for a multiphase flow model

Multiphase flow models are commonly employed for understanding complex fluid flows, while few mathematical discussions exist. For a general multiphase flow model in Gidaspow (1994), an energy decay property is proved. A stabilized Lagrange–Galerkin scheme for the model and its stability property are presented. Here, a hyperbolic tangent transformation is employed to preserve the boundedness of the volume fraction. A novel artificial term is added to obtain the stability property. Two-dimensional numerical examples exhibit the experimental order of convergence and applicability in modelling sedimentation phenomena.

Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control

This paper provides a novel approach to studying the chaos control and synchronization of fractional-order hybrid Darcy–Brinkman systems (FOHDBs). We use the truncated Galerkin method to transform the system of partial differential equations (PDEs) into ordinary differential equations (ODEs) based on Fourier modes in a nonlinear low-dimensional Brinkman model. In the nonlinear complex system, hybrid nanoparticles and fluid flow physical characteristics are considered to be external disturbances. As a result, the implications of model uncertainty and external disruptions are fully absorbed into the problem, further complicating it and resulting in highly complex and unpredictable behaviors. In addition, To assure the occurrence of the sliding motion in a finite amount of time, an appropriate robust fractional sliding mode technique is proposed. Sliding motion is shown to occur in finite time using the fractional Lyapunov stability. Following that, we discussed control techniques for achieving infinitesimally close to an equilibrium of chaotic states and tracking errors. It is important to note that FOHDBs and external stochastic disturbances can be controlled using the proposed fractional nonsingular terminal sliding mode control technique. Finally, the effectiveness and applicability of the suggested finite-time control technique are graphically illustrated by the analytical and numerical simulations.

A multiscale framework for polymer modeling applied in a complex fluid flow

A multiscale framework for polymer modeling applied in a complex fluid flow

Rheology-based wall function approach for wall-bounded turbulent flows of Herschel–Bulkley fluids

Modeling fully developed turbulent flow for Herschel–Bulkley (HB) fluids in pipes is a long-standing challenge. Existing semi-empirical, theoretical, and numerical methods are either inconsistent with experimental data or are validated for low Reynolds numbers. This study focuses on validating a novel approach using rheology-based wall functions within Reynolds-averaged Navier–Stokes solvers. Simulations of wall shear stress and velocity profiles were conducted across a wide range of Reynolds numbers using a single-phase HB fluid, with measurements taken both upstream and downstream of a 90° pipe bend. Two turbulence closure models, the k–ε model and the Reynolds stress model, were employed with the wall function implemented as a specified shear boundary condition. Results demonstrate significant improvements over the Newtonian-based models, such as standard wall function by Launder–Spalding or with available semi-empirical models, achieving strong statistical correlations and minimal deviation (from the experimental findings) at high Reynolds numbers. The study also examines the utility of the wall viscosity Reynolds number and assesses the reliability of semi-empirical models for HB fluids. These findings offer valuable insights for enhancing modeling accuracy in complex fluid flow scenarios, with potential applications spanning industries like mining, chemical processing, petroleum transportation, and sanitation systems, providing practical alternatives to costly experimental procedures in pipe systems.

Elastoviscoplasticity intensifies the unstable flows through a micro-contraction geometry

This study focuses on the two-dimensional numerical investigation of complex fluid flows through a micro-contraction geometry in the creeping flow regime, specifically examining elastoviscoplastic (EVP) fluids. These fluids exhibit a combination of viscous, elastic, and plastic behaviors. The governing equations, including mass and momentum, are solved using a finite volume method-based discretization technique. Saramito’s constitutive model is utilized to accurately represent the viscous, elastic, and plastic responses of the EVP fluid. The present results demonstrate significant differences in flow dynamics, such as vortex dynamics and transitions between flow regimes (e.g., steady to unsteady), when compared to simple Newtonian and non-Newtonian viscoelastic (VE) or viscoplastic (VP) fluids. This study reveals that when the yield strain (ϵy) exceeds a critical value, approximately ranging from 0.79 to 0.89, the flow transits from a steady to an unsteady state for the EVP fluids. Importantly, the present study shows that EVP fluids exhibit intensified chaotic flow dynamics and increased instability compared to VE and VP fluids under similar flow conditions. However, the presence of shear-thinning behavior in EVP fluids suppresses this instability. The analysis of local velocity fields and flow deformation in this study highlights the impact on the stretching of fluid microstructure and elastic stresses, which ultimately contribute to the origin of this intensified unstable flow condition for EVP fluids. The finding from this study holds significant potential for enhancing heat or mass transfer rates and mixing efficiency in micro-scale systems, where the prevailing steady and laminar flow conditions often hinder these transport processes.

MHD Casson Fluid Flow in Stagnation-Point over an Inclined Porous Surface

Motivated by the need to comprehend and optimize complex fluid flow phenomena in various engineering and industrial applications, this paper investigates the magnetohydrodynamic (MHD) Casson fluid flow characteristics in the vicinity of a stagnation point over an inclined porous surface. The study addresses the interplay of permeability, viscous dissipation, buoyancy, and volumetric heat source, chemical reaction of the diffusion species, thermal slip, and obliqueness at the bounding surface. The governing equations are transformed into a dimensionless form using appropriate similarity transformations. The resulting nonlinear ordinary differential equations are solved numerically using the fourth-order Runge-Kutta method, coupled with the shooting technique as coded into the bvp4c solver of MATLAB 2021a. Findings from this study show that instability arises due to reduced velocity at low permeability, and Biot number enhances the Newtonian cooling at the surface, a requirement for the design of heat exchangers.