Search Results (27)

Cardiovascular diseases represent one of the leading causes of mortality worldwide, underscoring the need for accurate simulations of blood flow to improve diagnosis and treatment. This study examines blood flow dynamics in two different vascular structures—the aorta and the right coronary artery (RCA)—using Computational Fluid Dynamics (CFD). Utilizing COMSOL Multiphysics^®, various mathematical models were applied to simulate blood flow under physiological conditions, assuming a steady-flow regime. These models include both Newtonian and non-Newtonian approaches, such as the Carreau and Casson models, as well as viscoelastic frameworks like Oldroyd-B, Giesekus, and FENE-P. Key metrics—such as velocity fields, pressure distributions, and error analysis—were evaluated to determine which model most accurately describes hemodynamic behavior in large vessels like the aorta and in smaller and more complex vessels like the RCA. The results highlight the importance of shear-thinning and viscoelastic properties in small vessels like the RCA, which contrasts with the predominantly Newtonian behavior observed in the aorta. While computational challenges remain, this study contributes to a deeper understanding of blood rheology, enhancing the accuracy of cardiovascular simulations and offering valuable insights for diagnosing and managing vascular diseases. Full article

The accurate estimation of the entry length required for a flow in a tube to transition from a uniform velocity profile to a fully developed state is crucial in many industrial processes. Although viscoelastic fluids are widely utilized in industrial processes, most studies have concentrated on inelastic fluids. This study employed computational fluid dynamics (CFD) to analyze the developing flow of viscoelastic fluids in a circular tube. An axisymmetric computational domain was employed along with the Giesekus model to represent the viscoelastic fluid flow. The Log Conformation Technique (LCT) was adopted to ensure numerical stability and accuracy at high Weissenberg numbers. The CFD model was first validated against published data for planar contraction flow. After validation and mesh sensitivity analysis for tube geometry, we systematically studied the influence of the Reynolds and Weissenberg numbers, solvent viscosity ratio, and mobility parameter on the entry length. Our results highlight the significant influence of fluid elasticity on flow development. For a constant Wi value, reducing inertia enhances the elastic effects, whereas at a fixed Re number, increasing Wi strongly impacts the developing flow region. Increased elasticity extends the entry length for both velocity and stress fields, with stress typically requiring a longer region to develop fully. Full article

In this study, the influence of the presence of a Newtonian solvent on the flow of a Giesekus fluid in a plane channel or fracture is investigated with a focus on the determination of the flow rate for an assigned external pressure gradient. The pressure field is nonlinear due to the presence of the normal transverse stress component. As expected, the flow rate per unit width $Q^{\prime }$ is larger than for a Newtonian fluid and decreases as the solvent increases. It is strongly dependent on the viscosity ratio $\epsilon$ ($0\le \epsilon \le 1$), the dimensionless mobility parameter $\beta$($0\le \beta \le 1$) and the Deborah number $De$, the dimensionless driving pressure gradient. The degree of dependency is notably strong in the low range of $\epsilon$. Furthermore, $Q^{\prime }$ increases with $De$ and tends to a constant asymptotic value for large $De$, subject to the limitation of laminar flow. When the mobility factor $\beta$ is in the range $\left[0.5÷1\right]$, there is a minimum value of $\epsilon$ to obtain an assigned value of $De$. The ratio $U_N/U$ between Newtonian and actual mean velocity depends only on the product $\sqrt{\beta }De$, as for other non-Newtonian fluids. Full article

A steady plane hydrodynamic problem of lubrication of a lightly loaded contact of two parallel cylinders lubricated by a non-Newtonian fluid with Giesekus rheology is considered. The advantage of this non-Newtonian rheology is its ability to properly describe the real behavior of formulated lubricants at high and low shear stresses. The problem is solved by using a modification of the regular perturbation method with respect to the small parameter $\alpha$, characterizing the degree to which the polymeric molecules of the additive to the lubricant follow the streamlines of the lubricant flow. It is assumed that the lubricant relaxation time and the value of $\alpha$ are of the order of the magnitude of the ratio of the characteristic gap between the contact surfaces and the contact length. The obtained analytical solution of the problem is analyzed numerically for the dependencies of the problem characteristics such as contact pressure, fluid flux, lubrication film thickness, friction force, energy loss in the lubricated contact, etc., on the problem input parameters. Full article

The motion of air bubbles within a liquid plays a crucial role in various aspects including heat transfer and material quality. In the context of non-Newtonian fluids, such as elastoviscoplastic fluids, the presence of air bubbles significantly influences the viscosity of the liquid. This study presents the development of an interface-capturing method for multiphase viscoelastic fluid flow simulations. The proposed algorithm utilizes a geometric volume of fluid (isoAdvector) approach and incorporates a reconstructed distance function (RDF) to determine interface curvature instead of relying on volume fraction gradients. Additionally, a piecewise linear interface construction (PLIC) scheme is employed in conjunction with the RDF-based interface reconstruction for improved accuracy and robustness. The validation of the multiphase viscoelastic PLIC-RDF isoAdvector (MVP-RIA) algorithm involved simulations of the buoyancy-driven rise of a bubble in fluids with varying degrees of rheological complexity. First, the newly developed algorithm was applied to investigate the buoyancy-driven rise of a bubble in a Newtonian fluid on an unbounded domain. The results show excellent agreement with experimental and theoretical findings, capturing the bubble shape and velocity accurately. Next, the algorithm was extended to simulate the buoyancy-driven rise of a bubble in a viscoelastic shear-thinning fluid described by the Giesekus constitutive model. As the influence of normal stress surpasses surface tension, the bubble shape undergoes a transition to a prolate or teardrop shape, often exhibiting a cusp at the bubble tail. This is in contrast to the spherical, ellipsoidal, or spherical-cap shapes observed in the first case study with a bubble in a Newtonian fluid. Lastly, the algorithm was employed to study the buoyancy-driven rise of a bubble in an unbounded elastoviscoplastic medium, modeled using the Saramito–Herschel–Bulkley constitutive equation. It was observed that in very small air bubbles within the elastoviscoplastic fluid, the dominance of elasticity and capillary forces restricts the degree of bubble deformation. As the bubble volume increases, lateral stretching becomes prominent, resulting in the emergence of two tails. Ultimately, a highly elongated bubble shape with sharper tails is observed. The results show that by applying the newly developed MVP-RIA algorithm, with a tangible coarser grid compared to the algebraic VOF method, an accurate solution is achieved. This will open doors to plenty of applications such as bubble columns in reactors, oil and gas mixtures, 3D printing, polymer processing, etc. Full article

A numerical study was conducted on the interaction of bubbles with different diameters and arrangements in shear-thinning viscoelastic fluids using OpenFOAM. The Volume of Fluid (VOF) method combined with the surface tension model was used to track the gas–liquid interface, and the rheological properties of the fluid were characterized with the Giesekus model. The numerical results are corresponded with the previous references, verifying the correctness of the simulation method. The influences of the initial bubble diameter, horizontal spacing, and arrangement on the motion state of three parallel bubbles were studied in detail. The flow pattern of the bubble rising was analyzed and compared with the motion state of parallel unequal double bubbles. As the diameter of the bubbles increases, the interaction among three equal size bubbles is changed from coalescence to detachment. Changing the diameter of one of the bubbles will significantly affect the movement of the larger diameter bubble, which is due to the enhancement in kinetic energy. The final state of some arrangement ways is consistent with the phenomenon of unequal double bubbles. The shear thinning effect, the velocity difference between bubbles, and the flow field around bubbles are considered the main reasons that decide the interaction between bubbles. Full article

The flow dynamics of wormlike micellar solutions around a sphere is a fundamental problem in particle-laden complex fluids but is still understood insufficiently. In this study, the flows of the wormlike micellar solution past a sphere in the creeping flow regime are investigated numerically with the two species, micelles scission/reforming, Vasquez–Cook–McKinley (VCM) and the single-species Giesekus constitutive equations. The two constitutive models both exhibit the shear thinning and the extension hardening rheological properties. There exists a region with a high velocity that exceeds the main stream velocity in the wake of the sphere, forming a stretched wake with a large velocity gradient, when the fluids flow past a sphere at very low Reynolds numbers. We found a quasi-periodic fluctuation of the velocity with the time in the wake of the sphere using the Giesekus model, which shows a qualitative similarity with the results found in present and previous numerical simulations with the VCM model. The results indicate that it is the elasticity of the fluid that causes the flow instability at low Reynolds numbers, and the increase in the elasticity enhances the chaos of the velocity fluctuation. This elastic-induced instability might be the reason for the oscillating falling behaviors of a sphere in wormlike micellar solutions in prior experiments. Full article

Migration of a particle in a confined shear flow of Giesekus fluids is investigated numerically with the method of direct forcing/fictitious domain. We focus on the migration direction for the particle with initial lateral position y₀ and determination of critical point y_c of a particle moving towards the center line or wall. The effect of viscosity ratio μ_r, shear-thinning parameter α, Weissenberg number Wi, and blocking rate β on the value y_c is analyzed. The results showed that when μ_r ≤ 0.5, the particle will migrate towards the wall regardless of the value of y₀. When μ_r > 0.5, y_c increases with increasing μ_r, and some particles will migrate towards the center line with the increase in μ_r. The particle is more likely to migrate towards the center line at small values of Wi and α but at large values of μ_r. The impact of Wi and β on the particle migration direction is more obvious. The particle will migrate towards the wall for β = 0.3 and is more likely to migrate towards the wall with increasing β. α and Wi have little influence on the pressure distribution in the case of the same β and μ_r. The particle near the wall will migrate faster because large positive pressure and negative pressure appear around the particle. Full article

Growth of the microfluidics field has triggered numerous advances in focusing and separating microparticles, with such systems rapidly finding applications in biomedical, chemical, and environmental fields. The use of shear-thinning viscoelastic fluids in microfluidic channels is leading to evolution of elasto-inertial focusing. Herein, we showed that the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference, lead to different particle focusing patterns in the elasto-inertial regime. Experiments and 3D simulations were performed to study the effects of flowrate, particle size, and the shear-thinning extent of the fluid on the focusing patterns. The Giesekus constitutive equation was used in the simulations to capture the shear-thinning and viscoelastic behaviors of the solution used in the experiments. At low flowrate, with Weissenberg number Wi ~ O(1), both the elastic force and secondary flow effects push particles towards the channel center. However, at a high flowrate, Wi ~ O(10), the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at the high flowrate, pushes particles away from the channel center. Additionally, a precise prediction of the focusing position can only be made when the shear-thinning extent of the fluid is correctly estimated in the modeling. The shear-thinning also gives rise to the unique behavior of the inertial forces near the channel walls which is linked with the ‘warped’ velocity profile in such fluids. Full article

This study computationally investigates the heat transfer characteristics in a double-pipe counter-flow heat-exchanger. A heated viscoelastic fluid occupies the inner core region, and the outer annulus is filled with a colder Newtonian-Fluid-Based Nanofluid (NFBN). A mathematical model is developed to study the conjugate heat transfer characteristics and heat exchange properties from the hot viscoelastic fluid to the colder NFBN. The mathematical modelling and formulation of the given problem comprises of a system of coupled nonlinear partial differential Equations (PDEs) governing the flow, heat transfer, and stress characteristics. The viscoelastic stress behaviour of the core fluid is modelled via the Giesekus constitutive equations. The mathematical complexity arising from the coupled system of transient and nonlinear PDEs makes them analytically intractable, and hence, a recourse to numerical and computational methodologies is unavoidable. A numerical methodology based on the finite volume methods (FVM) is employed. The FVM algorithms are computationally implemented on the OpenFOAM software platform. The dependence of the field variables, namely the velocity, temperature, pressure, and polymeric stresses on the embedded flow parameters, are explored in detail. In particular, the results illustrate that an increase in the nanoparticle volume-fraction, in the NFBN, leads to enhanced heat-exchange characteristics from the hot core fluid to the colder shell NFBN. Specifically, the results illustrate that the use of NFBN as the coolant fluid leads to enhanced cooling of the hot core-fluid as compared to using an ordinary (nanoparticle free) Newtonian coolant. Full article

The friction factor and heat transfer of Giesekus-fluid-based nanofluids in a pipe flow were studied in the ranges of 0.5 ≤ Reynolds number (Re) ≤ 500, 1 ≤ Weissenberg number (Wi) ≤ 8, 0.5% ≤ particle volume concentration (Φ) ≤ 3.0%, 0 ≤ viscosity ratio (β₀) ≤ 1, and 0 ≤ mobility parameter (α) ≤ 0.5. Our numerical method was validated by comparing the results with available ones in the literature. The effects of Wi, Φ, β₀, Re, and α on the relative friction factor (C_f/C_fNew), Nusselt number (Nu), and ratio (PEC_nf/PEC_f) of energy performance evaluation criterion for Giesekus-fluid-based nanofluids to those for Giesekus fluid were discussed. The results showed that the values for the C_f/C_fNew and Nu of Giesekus-fluid-based nanofluids were larger than those for Newtonian fluid-based nanofluids and those for pure Giesekus fluid. The values for C_f/C_fNew increased with increasing Φ and Re, but they increased with decreasing β₀ and α. As Wi increased, the values of C_f/C_fNew first increased and then decreased. The values of Nu and PEC_nf/PEC_f were enhanced with increasing Wi, Φ, Re, and α, but with decreasing β₀. It is more effective to use Giesekus-fluid-based nanofluids to improve heat transfer with the conditions of a larger Wi, Φ, Re, and α and a smaller β₀. Finally, the correlation formula for PEC_nf/PEC_f as a function of Wi, Φ, β₀, Re, and α was derived. Full article

We investigated the shear banding phenomena in the non-isothermal simple-shear flow of a viscoelastic-fluid-based nanofluid (VFBN) subject to exothermic reactions. The polymeric (viscoelastic) behavior of the VFBN was modeled via the Giesekus constitutive equation, with appropriate adjustments to incorporate both the non-isothermal and nanoparticle effects. Nahme-type laws were employed to describe the temperature dependence of the VFBN viscosities and relaxation times. The Arrhenius theory was used for the modeling and incorporation of exothermic reactions. The VFBN was modeled as a single-phase homogeneous-mixture and, hence, the effects of the nanoparticles were based on the volume fraction parameter. Efficient numerical schemes based on semi-implicit finite-difference-methods were employed in MATLAB for the computational solution of the governing systems of partial differential equations. The fundamental fluid-dynamical and thermodynamical phenomena, such as shear banding, thermal runaway, and heat transfer rate (HTR) enhancement, were explored under relevant conditions. Important novel results of industrial significance were observed and demonstrated. Firstly, under shear banding conditions of the Giesekus-type VFBN model, we observed remarkable HTR and Therm-C enhancement in the VFBN as compared to, say, NFBN. Specifically, the results demonstrate that the VFBN are less susceptible to thermal runaway than are NFBN. Additionally, the results illustrate that the reduced susceptibility of the Giesekus-type VFBN to the thermal runaway phenomena is further enhanced under shear banding conditions, in particular when the nanofluid becomes increasingly polymeric. Increased polymer viscosity is used as the most direct proxy for measuring the increase in the polymeric nature of the fluid. Full article

This study presents a framework based on Machine Learning (ML) models to predict the drag coefficient of a spherical particle translating in viscoelastic fluids. For the purpose of training and testing the ML models, two datasets were generated using direct numerical simulations (DNSs) for the viscoelastic unbounded flow of Oldroyd-B (OB-set containing 12,120 data points) and Giesekus (GI-set containing 4950 data points) fluids past a spherical particle. The kinematic input features were selected to be Reynolds number, $0<Re\le 50$, Weissenberg number, $0\le Wi\le 10$, polymeric retardation ratio, $0<\zeta <1$, and shear thinning mobility parameter, $0<\alpha <1$. The ML models, specifically Random Forest (RF), Deep Neural Network (DNN) and Extreme Gradient Boosting (XGBoost), were all trained, validated, and tested, and their best architecture was obtained using a 10-Fold cross-validation method. All the ML models presented remarkable accuracy on these datasets; however the XGBoost model resulted in the highest $R^2$ and the lowest root mean square error (RMSE) and mean absolute percentage error (MAPE) measures. Additionally, a blind dataset was generated using DNSs, where the input feature coverage was outside the scope of the training set or interpolated within the training sets. The ML models were tested against this blind dataset, to further assess their generalization capability. The DNN model achieved the highest $R^2$ and the lowest RMSE and MAPE measures when inferred on this blind dataset. Finally, we developed a meta-model using stacking technique to ensemble RF, XGBoost and DNN models and output a prediction based on the individual learner’s predictions and a DNN meta-regressor. The meta-model consistently outperformed the individual models on all datasets. Full article

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model. Full article

This work presents different formulations to obtain the solution for the Giesekus constitutive model for a flow between two parallel plates. The first one is the formulation based on work by Schleiniger, G; Weinacht, R.J., [Journal of Non-Newtonian Fluid Mechanics, 40, 79–102 (1991)]. The second formulation is based on the concept of changing the independent variable to obtain the solution of the fluid flow components in terms of this variable. This change allows the flow components to be obtained analytically, with the exception of the velocity profile, which is obtained using a high-order numerical integration method. The last formulation is based on the numerical simulation of the governing equations using high-order approximations. The results show that each formulation presented has advantages and disadvantages, and it was investigated different viscoelastic fluid flows by varying the dimensionless parameters, considering purely polymeric fluid flow, closer to purely polymeric fluid flow, solvent contribution on the mixture of fluid, and high Weissenberg numbers. Full article