non-Newtonian Flow Model Research Articles

Nonlinear parametric models of viscoelastic fluid flows

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate W i , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

Numerical simulation and redesign of Kamar Kajang Levee against Mount Semeru lahar flood based on HEC-RAS 2D non-newtonian flow model

Mount Semeru is one of the most active volcanoes in Indonesia where the pyroclastic, debris, and mudflows from its activities have severely damaged its surrounding areas. On December 4, 2021, Mount Semeru erupted, followed by intense rainfall, and damaged the Kamar Kajang Levee after a lahar flood event. The collapsed Levee was located along the Leprak Lumajang River, one of the natural drainage systems for Mount Semeru. The dyke failure had led to severe economic loss. Thus, reconstruction of the training dyke is highly important. In response, this research aims to propose an improvement to the Kamar Kajang Levee. This study was done through field observation, numerical simulation, and levee design calculation. The Non-Newtonian algorithm in HEC-RAS 6.2 was employed to model the flood events. The 2D model has been verified using a Sentinel-2 image and has shown a 90.7% similarity of inundated area after flooded by at least 214 m3/s of flood discharge, equivalent to a 5-year design discharge. The engineering design analysis shows that an additional 3.5 m height is needed to anticipate future floods and mitigate events effectively.

Comparison of River Stability using 2D HEC-RAS Newtonian and Non-Newtonian Flow Modelling (Case Study: Design of Sabo Dam in the Namo River Basin, Sigi Regency, Indonesia)

River stability is a crucial factor in assessing and managing risks associated with natural disasters, such as debris flows. This study compares river stability using two-dimensional (2D) HEC-RAS modeling with both Newtonian and Non-Newtonian flow approaches. Typically, non-Newtonian flow models are used for modeling debris flows. However, this study examines how the differences in modeling using Newtonian and non-Newtonian flows affect the potential for debris and the stability of the river system. The study focuses on the Namo River located in Sigi Regency, Indonesia, which is prone to debris flow events. In order to mitigate debris flows in the Namo River, three Sabo Dams and one Consolidation Dam have been built. The conditions before and after the construction of the Sabo Dam and the Consolidation Dam will also be modeled in this study. By comparing the results obtained from these modeling techniques, the study aims to provide a comprehensive understanding of river stability and improve the accuracy of debris flow prediction. The findings from this study have significant implications for the management and planning of the Namo River and similar river systems, enabling effective measures to minimize the potential risks associated with debris flow events.

Influence of parent vessel feature on the risk of internal carotid artery aneurysm rupture via computational method

In this study, the role of sac section area and parent vessel diameter on the hemodynamic feature of the blood flow in selected internal carotid artery (ICA) aneurysms is comprehensively investigated. The changes of wall shear stress, pressure, and oscillatory shear index (OSI) of blood stream on the vessel for various aneurysms with coiling treatment. To attain hemodynamic factors, computational technique is used for the modeling of non-Newtonian transient blood flow inside the three different ICA aneurysms. Three different saccular models with various Parent vessel mean Diameter is investigated in this study. The achieved outcomes show that increasing the diameter of the parent vessel directly decreases the OSI value on the sac surface. In addition, the mean wall shear stress decreases with the increase of the parent vessel diameter.

Traveling wave solutions for a realistic non-Newtonian foam flow model

Due to several environmental and petroleum engineering applications, there is a renewed interest in studying foam flow in porous media, commonly described as shear-thinning non-Newtonian flow. Based on experiments reporting saturation profiles with an unchanging shape displacing through the medium, we investigate the solution of the model describing foam displacement as a traveling wave. For that, we consider a realistic non-Newtonian foam flow model, which successfully described several experimental studies found in the literature. The aimed traveling wave solution is equivalent to the existence of the solution of the corresponding ordinary differential equations connecting initial and injection conditions. We address this problem by proposing a semi-analytical technique for finding such a connection in the phase space using the explicit foam’s apparent viscosity. Our semi-analytical solution is validated with direct numerical simulations and also by comparing it to experimental data from the literature.

Application extension of the meshless local Petrov-Galerkin method: Non-Newtonian fluid flow implementations

A computer code is developed to enhance the meshless local Petrov-Galerkin method capability to solve non-Newtonian fluid flow problems. In particular, the mesh-free method here, is to be empowered to simulate and solve the two-dimensional laminar incompressible power-law cases for the first time. The newly developed computer code expresses the appropriate governing equations in terms of the vorticity-stream function formulation and sustains a weighting function of unity. The local quadrature domain integrated by parts over the appropriate control volumes provides the local weak form of the considered governing equations. The extended scheme implements the moving least square interpolation technique to approximate the obtained field variables. The ability of the developed code to handle the Ostwald-de Waele (also known as the power-law) fluid flow occurrences were assessed through comparing the obtained results of the extended method to those of the conventional mesh-based methods for some benchmarking cases available in the paper. Based on this comparison, the extended code demonstrates a good capability to address the power-law fluid flow problems for different indices for one of the most popular non-Newtonian fluid flow models.

Research on the Internal Flow Field of Left Atrial Appendage and Stroke Risk Assessment with Different Blood Models.

Extant clinical research has underscored that patients suffering from atrial fibrillation (AF) bear an elevated risk for stroke, predominantly driven by the formation of thrombus in the left atrial appendage (LAA). As such, accurately identifying those at an increased risk of thrombosis becomes paramount to facilitate timely and effective treatment. This study was designed to shed light on the mechanisms underlying thrombus formation in the LAA by employing three-dimensional (3D) left atrium (LA) models of AF patients, which were constructed based on Computed Tomography (CT) imaging. The distinct benefits of Computational Fluid Dynamics (CFD) were leveraged to simulate the blood flow field within the LA, using three distinct blood flow models, both under AF and sinus rhythm (SR) conditions. The potential risk of thrombus formation was evaluated by analyzing the Relative Residence Time (RRT) and Endothelial Cell Activation Potential (ECAP) values. The results gleaned from this study affirm that all three blood flow models align with extant clinical guidelines, thereby enabling an effective prediction of thrombosis risk. However, noteworthy differences emerged when comparing the intricacies of the flow field and thrombosis risk across the three models. The single-phase non-Newtonian blood flow model resulted in comparatively lower residence times for blood within the LA and lower values for the Oscillatory Shear Index (OSI), RRT, and ECAP within the LAA. These findings suggest a reduced thrombosis risk. Conversely, the two-phase non-Newtonian blood flow model exhibited a higher residence time for blood and elevated RRT value within the LAA, suggesting an increased risk for thrombosis.

Stability Analysis of Dual Solutions of Convective Flow of Casson Nanofluid past a Shrinking/Stretching Slippery Sheet with Thermophoresis and Brownian Motion in Porous Media

This article considered the steady two-dimensional boundary layer flow of incompressible viscous Casson nanofluids over a permeable, convectively heated, shrinking/stretching slippery sheet surface. The achievements of this work are extremely relevant, both theoretically with respect to the mathematical modeling of non-Newtonian nanofluid flow with heat transfer in engineering systems and with respect to engineering cooling applications. The combined impacts of suction/injection, viscous dissipation, convective heating, and chemical reactions were considered. The governing modeled partial differential equations with boundary conditions are transformed into nonlinear ordinary differential equations using similarity transformations and finally converted to the first-order initial value problem. Then, the technique of the fourth-fifth order Runge–Kutta–Fehlberg with the shooting method is used to obtain numerical solutions. Moreover, the effects of different involving parameters on the dimensionless temperature, velocity, and concentration, as well as, from an engineering viewpoint, local Nusselt number, the skin friction, and local Sherwood number are illustrated and presented in graphs and tabular forms. For critical shrinking parameter λ c , the existence of a dual solution within the interval λ c < λ < 0 is revealed, and this range escalates with the suction and slipperiness parameters; hence, both control the flow stability. The increment in the values of the porous media, Casson, Forchheimer, slipperiness, and convective heating parameters reduces the local skin friction and intensifies the rates of mass and heat transfer. For the Newtonian flow (that is, as the Casson parameter β gets to infinity ∞ ), the thermal boundary layer thickness, temperature profile, and skin friction diminish, whereas the concentration profile, mass, and heat transfer rates increase compared to the non-Newtonian Casson nanofluid. These results excellently agree with the existing ones.

Optimizing energy generation in power-law nanofluid flow through curved arteries with gold nanoparticles

The investigation of blood flow into curved arteries is fascinating and essential to prevent the advancement of vascular disease. Motivated by electro-kinetic manipulation, gold nanoparticles, and their size applications, a mathematical model is developed to explain blood flow, entropy generation, and electro-kinetic energy conversion (EKEC) efficiency in curved arterial flow. To make this study more realistic, a patient-specific overlapped stenosis condition and non-Newtonian (power-law fluid) blood flow model have been considered. The effects of a magnetic field, external heating, and chemical reactions are also included. The Stone’s strongly implicit scheme has been considered to solve the system of non-linear partial differential equations (PDE’s) in the” MATLAB” software. In this numerical investigation, an error tolerance of 10 − 6 has been considered for every iteration step under Stone’s scheme. The significance of various physical parameters, such as nanoparticle volume fraction (m), their size (dp), magnetic field intensity (M), inverse Debye length ( κ ¯ ), flow behavior index (Sc), heat source (H), and chemical reaction parameter (ξ) on the blood flow velocity, temperature, concentration, EKEC efficiency, and entropy generation have been explained graphically. This study also developed stream function contours to describe flow trapping patterns. The findings of this study conclude that the blood flow EKEC efficiency reduces with the presence of nanoparticles and stenosis in the artery. In addition, both flow velocity and entropy enhance by adopting large-size nanoparticles instead of small diametric nanoparticles. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries with WSS profiles, by which the severity of these conditions can be reduced.

Numerical computation of pulsatile hemodynamics and diagnostic concern of coronary bifurcated artery flow for Newtonian and non-Newtonian fluid

Atherosclerotic with the high occurrence of plaque formation due to stenosis has attracted wide attention among researchers. The left coronary artery has been studied in two-dimensional and in three-dimensional (3D) bifurcation as the models of blood flow through Newtonian and non-Newtonian fluids to better understand the physical mechanism. The computational Fluid Dynamics (CFD) technique is incorporated in COMSOL Multiphysics and then it is justified by satisfactory validation. It is found that the Newtonian model shows larger recirculation zones than non-Newtonian does. The present study also focuses on the evaluations of the lesion of diagnostic and the coefficient of pressure drop assessments on the basis of the diagnostic parameter’s critical values affected by the rheological model. Nevertheless, the leading concentration of the subsisting investigation works is confined to the change of importance factor (IFc) affected by arterial blockage. But the IFc of non-Newtonian fluid for 3D left coronary artery bifurcation model decreases with increasing bifurcation angle and the time-averaged inlet pressure is the least for smaller bifurcation angles. The current research further concentrates that the flow separation length reduces with developing bifurcation angle in bifurcated geometry. It is significant to mention that non-Newtonian blood flow model incorporating hemodynamic and diagnostic parameters has great impacts on instantaneous flow systems.

Modeling and simulation of non-Newtonian fluid flows and heat transfer in a non-isothermal coiled tubing to oil well operations

The coiled tubing system has become an attractive option for oil industry operations in deep-water environments. Composed of a long, continuous, and flexible steel pipe, the coiled tubing provides a quick and safe intervention in active wells reducing the process time and cost. The fluid flow in curved pipes is characterized by centrifugal forces that significantly affect the frictional head loss and fluid heat transfer. The temperature variation affects the fluid physicochemical properties, such as rheology, density, thermal properties, and the cement setting time. To avoid the risk of the cement slurry setting before reaching the desired location, set retarders are added to its formulation. Therefore, it is essential to predict the temperature profile in coiled tubing to optimize the fluid formulation and process control, avoiding increased process time and cost. This research aimed to develop a mathematical model to simulate the heat transfer in coiled tubing fluid flow based on momentum, energy, and mass conservation. The mathematical model is composed of a set of partial differential equations spatially discretized using the finite volume technique. A case study was used, providing actual oilfield data to simulate the non-isothermic flow through the coiled tubing. Temperature data from a Brazilian offshore oil well abandonment process in two different operating conditions were used to validate the mathematical model. The results obtained in this paper indicated a good agreement between the model predictions and the oil well experimental data, with average relative errors of up to 2.5%.

Effect of external magnetic field on realistic bifurcated right coronary artery hemodynamics

Diagnostic technology based on magnetic fields is commonly used in medicine for diagnosis and therapy. However, the exposure to strong electromagnetic fields has adverse outcomes in patients. Thus, the objective of the current study is to investigate the effect of applying external uniform magnetic fields on the blood flow in both healthy and diseased cases of right coronary artery and determine the safe values of the applied magnetic field strengths. The diseased cases include a 40% stenosed artery along with two blood disorder cases with a hematocrit level of 20% and 60%. A comprehensive three-dimensional steady non-Newtonian flow model is developed using the Casson model to investigate the effect of the magnetic field on both shear rate and hematocrits. The model is numerically simulated at different values of magnetic field strengths and its orientation. The results indicated that the magnetic field in the Y-direction has a dominant effect compared to other directions. Moreover, the maximum increase in the main branch mass flow rate fraction is about 6.2%. Another interesting finding is that the wall shear stress is slightly affected by the magnetic field strength. For the stenosed case, it is found that the high magnetic field strengths can reduce the formulation of the vortices and hence reduce the risk of thrombosis, which agrees with published works. Additionally, the obtained results confirm that using a magnetic field up to 11.7 T, which is used in magnetic resonance imaging devices, is safe, and has a slight effect on blood flow parameters such as the wall shear stress.

Intraluminal Thrombus Characteristics in AAA Patients: Non-Invasive Diagnosis Using CFD.

Abdominal aortic aneurysms (AAA) continue to pose a high mortality risk despite advances in medical imaging and surgery. Intraluminal thrombus (ILT) is detected in most AAAs and may critically impact their development. Therefore, understanding ILT deposition and growth is of practical importance. To assist in managing these patients, the scientific community has been researching the relationship between intraluminal thrombus (ILT) and hemodynamic parameters wall shear stress (WSS) derivatives. This study analyzed three patient-specific AAA models reconstructed from CT scans using computational fluid dynamics (CFD) simulations and a pulsatile non-Newtonian blood flow model. The co-localization and relationship between WSS-based hemodynamic parameters and ILT deposition were examined. The results show that ILT tends to occur in regions of low velocity and time-averaged WSS (TAWSS) and high oscillation shear index (OSI), endothelial cell activation potential (ECAP), and relative residence time (RRT) values. ILT deposition areas were found in regions of low TAWSS and high OSI independently of the nature of flow near the wall characterized by transversal WSS (TransWSS). A new approach is suggested which is based on the estimation of CFD-based WSS indices specifically in the thinnest and thickest ILT areas of AAA patients; this approach is promising and supports the effectiveness of CFD as a decision-making tool for clinicians. Further research with a larger patient cohort and follow-up data are needed to confirm these findings.

Modeling and numerical simulation of non-Newtonian arterial blood flow for mild to severe stenosis

The fundamental cause of coronary heart disease is thought to be atherosclerosis. Blood flow in arteries under plaque formation is widely studied using both experimental and theoretical methods in literature. This paper presents a comprehensive study on the mathematical modelling and numerical simulation of non-Newtonian blood flow in an idealized stenosed artery. Non-Newtonian behavior of blood flow is assumed by Casson and Quemada fluid models. An analysis is performed for four forms of stenosis, 50%, 60%, 70%, and 80%, which are defined by a narrowing of the artery's diameter. The mathematical model for non-Newtonian fluid transport is presented in the form of highly nonlinear coupled partial differential equations. A finite-volume approach is used to solve the system of equations numerically. The solutions are obtained using a hybrid mesh with hexahedron and tetrahedron control volumes. Numerical solutions are validated first with experimental results from the literature for a Newtonian fluid, and then the results are extended to non-Newtonian fluid models. It can be observed that the non-Newtonian nature of the fluid model influences flow dynamics and is a significant aspect to consider for arteries with small diameter. The velocity and pressure drop rise as the degree of stenosis develops. Wall shear is substantially larger in stenotic passages and severity of stenosis is directly related with this increasing behavior.

One-dimensional nonlinear rheological consolidation analysis of soft ground under continuous drainage boundary conditions

This work presents an upgraded one-dimensional (1D) nonlinear rheological system of soft ground consolidation. In the system, the boundaries are characterized by the time-dependent drainage boundary conditions at the surface and bottom of the layer. Meanwhile, the modified UH relationship and non-Newtonian index flow model are used to simulate the viscous effect of clay and the flow of excess pore-water during consolidation, respectively. Then, two numerical discretization formats of the system, namely the finite volume method (FDM) and finite difference method (FVM), are given, and corresponding calculation programs are compiled. The model solutions have been validated by degraded analytical solutions, FDM and FVM comparison solutions, and available laboratory data. Further, the consolidation behaviour under different model parameters is illustrated. The calculated results indicate that the change of interface parameters and flow mode does not influence the final foundation settlement, but both significantly affect the overall dissipation process of EPWP of soils. At last, an efficient method for determining CDB parameters is proposed and verified by available test data.

Influence of Rigid-Elastic Artery Wall of Carotid and Coronary Stenosis on Hemodynamics.

Cardiovascular system abnormalities can result in serious health complications. By using the fluid-structure interaction (FSI) procedure, a comprehensive realistic approach can be employed to accurately investigate blood flow coupled with arterial wall response. The hemodynamics was investigated in both the coronary and carotid arteries based on the arterial wall response. The hemodynamics was estimated based on the numerical simulation of a comprehensive three-dimensional non-Newtonian blood flow model in elastic and rigid arteries. For stenotic right coronary artery (RCA), it was found that the maximum value of wall shear stress (WSS) for the FSI case is higher than the rigid wall. On the other hand, for the stenotic carotid artery (CA), it was found that the maximum value of WSS for the FSI case is lower than the rigid wall. Moreover, at the peak systole of the cardiac cycle (0.38 s), the maximum percentage of arterial wall deformation was found to be 1.9%. On the other hand, for the stenotic carotid artery, the maximum percentage of arterial wall deformation was found to be 0.46%. A comparison between FSI results and those obtained by rigid wall arteries is carried out. Findings indicate slight differences in results for large-diameter arteries such as the carotid artery. Accordingly, the rigid wall assumption is plausible in flow modeling for relatively large diameters such as the carotid artery. Additionally, the FSI approach is essential in flow modeling in small diameters.

A cell-based smoothed finite element model for non-Newtonian blood flow

Smoothed Finite Element Method (S-FEM) has drawn increasing attention in the field of computational fluid dynamics (CFD) and the present work seeks to make further contribution to this growing field of S-FEM by simulating for the non-Newtonian blood flow. This investigation took the form of Streamline Upwind Petrov-Galerkin in conjunction with Stabilized Pressure Gradient Projection (SUPG/SPGP) to alleviate the spatial oscillation and instability problems. The validation of the cell-based S-FEM (CS-FEM) combined with SUPG/SPGP was carried out by the blood flow over a backward-facing step. The performances of the presented method were explored by the blood flow in the carotid bifurcation and blood flow in the intracranial segment of internal carotid artery. Impressively, the results exhibit good features of the CS-FEM on solving severely distorted mesh vis-a-vis the standard finite element method (FEM). The presented method could realize the accurate prediction in the mentioned complex blood flows as the same as Finite Volume Method software STAR-CCM+.

Macroscopic model for unsteady generalized Newtonian fluid flow in homogeneous porous media

A macroscopic model for unsteady incompressible isothermal non-Newtonian flow in homogeneous porous media, taking into account inertial and slip effects at solid–fluid interfaces, is derived in this work. The development is carried out considering a general Newton’s law of viscosity for the fluid phase. Using the classical volume averaging method, the seepage velocity is shown to be solenoidal. The macroscopic momentum equation is derived in the Laplace domain, employing a simplified version of the volume averaging method, which calls upon Green’s formulas and adjoint problems for Green’s function pairs for the velocity and pressure. In the Laplace domain, the macroscopic momentum equation takes the form of Darcy’s law corrected by a term that accounts for the initial flow condition. Once transformed back into the time domain, this equation provides the macroscopic velocity that depends on two terms. The first one is under the form of a time convolution between the macroscopic pressure gradient and the time derivative of an apparent permeability tensor. The second one is a memory term that accounts for the effect of the initial flow conditions. These two effective quantities are determined from the solution of a single closure problem that naturally results from the derivations. The model is consistent with the unsteady model in the Newtonian case and simplifies to the steady versions of some non-Newtonian macroscopic flow models. The macroscopic model is validated with pore-scale simulations performed in 2D model porous structures, considering a Carreau fluid. The impact of inertia and non-Newtonian effects on the dynamics of the macroscopic coefficients is highlighted.

Fluid structure interaction versus rigid-wall approach in the study of the symptomatic stenosed carotid artery: Importance of wall compliance and resilience of loose connective tissue.

The purpose of this paper is to demonstrate the importance of a compliant wall approach in modeling of non‐Newtonian and non‐physiological blood flows. A case study of a stenosed and symptomatic carotid bifurcation was considered to show the influence of the wall‐resilience assumption on the flow parameters obtained with numerical simulations. Patient‐specific data concerning the geometry and flow conditions were collected and used to carry out two‐way coupled fluid structure interaction simulations of the pulsatile blood flow through carotid artery. The wall compliance was considered separately as related to the wall‐elasticity and as associated with the reaction of the loose connective tissue surrounding the carotid bifurcation. The obtained hemodynamic parameters were compared to those which were found in rigid‐wall simulations. The difference between the results obtained for rigid‐wall and compliant‐wall approaches for the peak‐systolic area‐averaged wall shear stress achieved 35%, whereas the difference between the time‐averaged local vorticity and shear strain reached, respectively, 42% and 43%. The influence of the highly resilient wall on the monitored hemodynamic parameters was significant even if time‐averaged values are compared, which suggests that these metrics are considerably overestimated if the wall compliance is not considered. Moreover, the findings show that the mechanical response of the loose connective tissue cannot be neglected in blood flow simulations. Additionally, this study indicates that stiffening of the arterial wall due to atherosclerosis significantly rises hemodynamic parameters. This explains the therapeutic benefits of surgical removal of plaque lesions formed in the carotid bifurcation (endarterectomy).

Investigation of Non-Newtonian Characteristics of Water Flow in Micro-/Nanochannels and Tight Reservoirs

The characteristic scale of pore flow in tight reservoirs is generally in the range of 0.1 μm to 1 μm, which shows the obvious micro- and nanoscale effect. The traditional oil and gas seepage theory cannot accurately describe the flow law of liquid in the micro- and nanopores. The determination of seepage characteristics is crucial to the development, layout, and prediction of tight oil. Therefore, a non-Newtonian fluid model is established to discuss the flow characteristics of confined liquid in the heterogeneous pores of microtubules and reveal the nonlinear seepage law of water in micro- and nanochannels and tight reservoirs. Based on the characteristics of non-Newtonian fluid of confined fluid in micro- and nanospace, the flow model of non-Newtonian fluid under the action of shear stress was deduced. The flow velocity variation of liquid in micro- and nanochannel and dense core was analyzed, and the flow rate of water was less than that predicted by macro theory. According to the flow experiment of water in micro- and nanochannels, the flow model of power-law non-Newtonian fluid was verified. At the same time, through the flow experiment of water in the dense rock core, the non-Newtonian model was used for nonlinear fitting, and the non-Newtonian power-law parameters and average pore radius were obtained, which verified the effectiveness of the non-Newtonian flow model.