Viscoelasticity: Mathematical Modeling, Numerical Simulations, and Experimental Work

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Fluid Science and Technology".

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 24920

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1. Department of Mechanical Engineering (Section of Mathematics), FEUP, University of Porto, 4200-465 Porto, Portugal
2. Center for Mathematics, University of Minho, 4710-057 Braga, Portugal
Interests: numerical analysis; integro-differential equations; mathematical modelling; viscoelastic flows; anomalous diffusion; machine learning
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CEFT-Transport Phenomena Research Center, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
Interests: theoretical and computational rheology; complex flows of complex fluids; electrokinetics; multiphase flow; micro-combustion
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to gather new developments on the different areas of viscous and viscoelastic fluid flows, ranging from mathematical modeling to experimental work.

All researchers working in these areas are encouraged to submit their works. All submissions will be subject to rapid and thorough review.

Prof. Dr. Luís L. Ferrás
Prof. Dr. Alexandre M. Afonso
Guest Editors

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Keywords

  • viscoelasticity
  • mathematical models for viscous-viscoelastic fluids
  • computational fluid dynamics
  • computational rheology
  • numerical methods for complex viscous-viscoelastic flows
  • analytical solutions
  • boundary conditions
  • experimental work

Published Papers (12 papers)

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Editorial

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2 pages, 203 KiB  
Editorial
Viscoelasticity: Mathematical Modelling, Numerical Simulations, and Experimental Work
by Luís L. Ferrás and Alexandre M. Afonso
Appl. Sci. 2023, 13(2), 1022; https://doi.org/10.3390/app13021022 - 12 Jan 2023
Viewed by 935
Abstract
Viscoelastic materials are abundant in nature and present in our daily lives [...] Full article

Research

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22 pages, 7946 KiB  
Article
An MHD Marangoni Boundary Layer Flow and Heat Transfer with Mass Transpiration and Radiation: An Analytical Study
by Thippeswamy Anusha, Rudraiah Mahesh, Ulavathi Shettar Mahabaleshwar and David Laroze
Appl. Sci. 2022, 12(15), 7527; https://doi.org/10.3390/app12157527 - 27 Jul 2022
Cited by 4 | Viewed by 1356
Abstract
This examination is carried out on the two-dimensional magnetohydrodynamic problem for a steady incompressible flow over a porous medium. The CuAl2O3 nanoparticles are added to the water base fluid in order to improve thermal efficiency. The [...] Read more.
This examination is carried out on the two-dimensional magnetohydrodynamic problem for a steady incompressible flow over a porous medium. The CuAl2O3 nanoparticles are added to the water base fluid in order to improve thermal efficiency. The transverse magnetic field with strength B0 is applied. The governing equations formed for the defined flow form a system of partial differential equations that are then converted to a system of ordinary differential equations upon applying the suitable similarity transformations. On analytically solving the obtained system, the solutions for velocity profile and temperature distribution are obtained in terms of exponential and Gamma functions, respectively. In addition, the physical parameter of interest, the local Nusselt number, is obtained. The results are analyzed through plotting graphs, and the effect of different parameters is analyzed. Furthermore, we observe that the suction/injection parameter enhances the axial velocity. The porous and radiation parameters enhance the temperature distribution, and the suction/injection parameter suppresses the temperature distribution. Full article
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14 pages, 5030 KiB  
Article
An Effect of MHD on Non-Newtonian Fluid Flow over a Porous Stretching/Shrinking Sheet with Heat Transfer
by Angadi Basettappa Vishalakshi, Thippaiah Maranna, Ulavathi Shettar Mahabaleshwar and David Laroze
Appl. Sci. 2022, 12(10), 4937; https://doi.org/10.3390/app12104937 - 13 May 2022
Cited by 20 | Viewed by 1610
Abstract
The current article explains the 3-D MHD fluid flow under the impact of a magnetic field with an inclined angle. The porous sheet is embedded in the flow of a fluid to yield the better results of the problem. The governing PDEs are [...] Read more.
The current article explains the 3-D MHD fluid flow under the impact of a magnetic field with an inclined angle. The porous sheet is embedded in the flow of a fluid to yield the better results of the problem. The governing PDEs are mapped using various transformations to convert in the form of ODEs. The yielded ODEs momentum equation is examined analytically to derive the mass transpiration and then it is used in the energy equation and solved exactly by using various controlling parameters. In the case of multiple solutions, the closed-form exact solutions of highly non-linear differential equations of the flow are presented as viscoelastic fluid, which is classified as two classes, namely the second order liquid and Walters’ liquid B fluid. The results can be obtained by using graphical arrangements. The current work is utilized in many real-life applications, such as automotive cooling systems, microelectronics, heat exchangers, and so on. At the end of the analysis, we concluded that velocity and mass transpiration was more for Chandrasekhar’s number for both the stretching and shrinking case. Full article
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17 pages, 2143 KiB  
Article
Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
by Juliana Bertoco, Rosalía T. Leiva, Luís L. Ferrás, Alexandre M. Afonso and Antonio Castelo
Appl. Sci. 2021, 11(21), 10352; https://doi.org/10.3390/app112110352 - 04 Nov 2021
Cited by 2 | Viewed by 1254
Abstract
In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised [...] Read more.
In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number. Full article
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23 pages, 2286 KiB  
Article
Different Formulations to Solve the Giesekus Model for Flow between Two Parallel Plates
by Laison Junio da Silva Furlan, Matheus Tozo de Araujo, Analice Costacurta Brandi, Daniel Onofre de Almeida Cruz and Leandro Franco de Souza
Appl. Sci. 2021, 11(21), 10115; https://doi.org/10.3390/app112110115 - 28 Oct 2021
Cited by 5 | Viewed by 2179
Abstract
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 [...] Read more.
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
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18 pages, 2990 KiB  
Article
Effects of Viscoelasticity on the Stress Evolution over the Lifetime of Filament-Wound Composite Flywheel Rotors for Energy Storage
by Miles Skinner and Pierre Mertiny
Appl. Sci. 2021, 11(20), 9544; https://doi.org/10.3390/app11209544 - 14 Oct 2021
Cited by 3 | Viewed by 1489
Abstract
High-velocity and long-lifetime operating conditions of modern high-speed energy storage flywheel rotors may create the necessary conditions for failure modes not included in current quasi-static failure analyses. In the present study, a computational algorithm based on an accepted analytical model was developed to [...] Read more.
High-velocity and long-lifetime operating conditions of modern high-speed energy storage flywheel rotors may create the necessary conditions for failure modes not included in current quasi-static failure analyses. In the present study, a computational algorithm based on an accepted analytical model was developed to investigate the viscoelastic behavior of carbon fiber reinforced polymer composite flywheel rotors with an aluminum hub assembled via a press-fit. The Tsai-Wu failure criterion was applied to assess failure. Two simulation cases were developed to explore the effects of viscoelasticity on composite flywheel rotors, i.e., a worst-case operating condition and a case akin to realistic flywheel operations. The simulations indicate that viscoelastic effects are likely to reduce peak stresses in the composite rim over time. However, viscoelasticity also affects stresses in the hub and the hub-rim interface in ways that may cause rotor failure. It was further found that charge-discharge cycles of the flywheel energy storage device may create significant fatigue loading conditions. It was therefore concluded that the design of composite flywheel rotors should include viscoelastic and fatigue analyses to ensure safe operation. Full article
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17 pages, 896 KiB  
Article
Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity
by Jie Liu, Martin Oberlack and Yongqi Wang
Appl. Sci. 2021, 11(15), 6931; https://doi.org/10.3390/app11156931 - 28 Jul 2021
Cited by 1 | Viewed by 1484
Abstract
Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions [...] Read more.
Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution. Full article
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19 pages, 8389 KiB  
Article
The Role of Elasticity in the Vortex Formation in Polymeric Flow around a Sharp Bend
by Brian Wojcik, Jason LaRuez, Michael Cromer and Larry A. Villasmil Urdaneta
Appl. Sci. 2021, 11(14), 6588; https://doi.org/10.3390/app11146588 - 17 Jul 2021
Cited by 4 | Viewed by 2143
Abstract
Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges [...] Read more.
Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works. Full article
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16 pages, 2999 KiB  
Article
Numerical Simulation of KBKZ Integral Constitutive Equations in Hierarchical Grids
by Juliana Bertoco, Manoel S. B. de Araújo, Rosalía T. Leiva, Hugo A. C. Sánchez and Antonio Castelo
Appl. Sci. 2021, 11(11), 4875; https://doi.org/10.3390/app11114875 - 26 May 2021
Cited by 6 | Viewed by 1969
Abstract
In this work, we present the implementation and verification of HiGTree-HiGFlow solver (see for numerical simulation of the KBKZ integral constitutive equation. The numerical method proposed herein is a finite difference technique using tree-based grids. The advantage of using hierarchical grids is that [...] Read more.
In this work, we present the implementation and verification of HiGTree-HiGFlow solver (see for numerical simulation of the KBKZ integral constitutive equation. The numerical method proposed herein is a finite difference technique using tree-based grids. The advantage of using hierarchical grids is that they allow us to achieve great accuracy in local mesh refinements. A moving least squares (MLS) interpolation technique is used to adapt the discretization stencil near the interfaces between grid elements of different sizes. The momentum and mass conservation equations are solved by an implicit method and the Chorin projection method is used for decoupling the velocity and pressure. The Finger tensor is calculated using the deformation fields method and a three-node quadrature formula is used to derive an expression for the integral tensor. The results of velocity and stress fields in channel and contraction-flow problems obtained in our simulations show good agreement with numerical and experimental results found in the literature. Full article
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25 pages, 1166 KiB  
Article
A Backwards-Tracking Lagrangian-Eulerian Method for Viscoelastic Two-Fluid Flows
by Simon Ingelsten, Andreas Mark, Roland Kádár and Fredrik Edelvik
Appl. Sci. 2021, 11(1), 439; https://doi.org/10.3390/app11010439 - 05 Jan 2021
Cited by 4 | Viewed by 2171
Abstract
A new Lagrangian–Eulerian method for the simulation of viscoelastic free surface flow is proposed. The approach is developed from a method in which the constitutive equation for viscoelastic stress is solved at Lagrangian nodes, which are convected by the flow, and interpolated to [...] Read more.
A new Lagrangian–Eulerian method for the simulation of viscoelastic free surface flow is proposed. The approach is developed from a method in which the constitutive equation for viscoelastic stress is solved at Lagrangian nodes, which are convected by the flow, and interpolated to the Eulerian grid with radial basis functions. In the new method, a backwards-tracking methodology is employed, allowing for fixed locations for the Lagrangian nodes to be chosen a priori. The proposed method is also extended to the simulation of viscoelastic free surface flow with the volume of fluid method. No unstructured interpolation or node redistribution is required with the new approach. Furthermore, the total amount of Lagrangian nodes is significantly reduced when compared to the original Lagrangian–Eulerian method. Consequently, the method is more computationally efficient and robust. No additional stabilization technique, such as both-sides diffusion or reformulation of the constitutive equation, is necessary. A validation is performed with the analytic solution for transient and steady planar Poiseuille flow, with excellent results. Furthermore, the proposed method agrees well with numerical data from the literature for the viscoelastic die swell flow of an Oldroyd-B model. The capabilities to simulate viscoelastic free surface flow are also demonstrated through the simulation of a jet buckling case. Full article
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21 pages, 2205 KiB  
Article
A FENE-P kε Viscoelastic Turbulence Model Valid up to High Drag Reduction without Friction Velocity Dependence
by Michael McDermott, Pedro Resende, Thibaut Charpentier, Mark Wilson, Alexandre Afonso, David Harbottle and Gregory de Boer
Appl. Sci. 2020, 10(22), 8140; https://doi.org/10.3390/app10228140 - 17 Nov 2020
Cited by 5 | Viewed by 2453
Abstract
A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a kε representation, along with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. The model performance is evaluated against [...] Read more.
A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a kε representation, along with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. The model performance is evaluated against a wide variety of direct numerical simulation data, described by different combinations of rheological parameters, which is able to predict all drag reduction (low, intermediate and high) regimes with good accuracy. Three main contributions are proposed: one with a simplified viscoelastic closure for the NLTij term (which accounts for the interactions between the fluctuating components of the conformation tensor and the velocity gradient tensor), by removing additional damping functions and reducing complexity compared with previous models; second through a reformulation for the closure of the viscoelastic destruction term, Eτp, which removes all friction velocity dependence; lastly by an improved modified damping function capable of predicting the reduction in the eddy viscosity and thus accurately capturing the turbulent kinetic energy throughout the channel. The main advantage is the capacity to predict all flow fields for low, intermediate and high friction Reynolds numbers, up to high drag reduction without friction velocity dependence. Full article
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Review

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25 pages, 6717 KiB  
Review
A Critical Review of Supersonic Flow Control for High-Speed Applications
by Abdul Aabid, Sher Afghan Khan and Muneer Baig
Appl. Sci. 2021, 11(15), 6899; https://doi.org/10.3390/app11156899 - 27 Jul 2021
Cited by 7 | Viewed by 4312
Abstract
In high-speed fluid dynamics, base pressure controls find many engineering applications, such as in the automobile and defense industries. Several studies have been reported on flow control with sudden expansion duct. Passive control was found to be more beneficial in the last four [...] Read more.
In high-speed fluid dynamics, base pressure controls find many engineering applications, such as in the automobile and defense industries. Several studies have been reported on flow control with sudden expansion duct. Passive control was found to be more beneficial in the last four decades and is used in devices such as cavities, ribs, aerospikes, etc., but these need additional control mechanics and objects to control the flow. Therefore, in the last two decades, the active control method has been used via a microjet controller at the base region of the suddenly expanded duct of the convergent–divergent (CD) nozzle to control the flow, which was found to be a cost-efficient and energy-saving method. Hence, in this paper, a systemic literature review is conducted to investigate the research gap by reviewing the exhaustive work on the active control of high-speed aerodynamic flows from the nozzle as the major focus. Additionally, a basic idea about the nozzle and its configuration is discussed, and the passive control method for the control of flow, jet and noise are represented in order to investigate the existing contributions in supersonic speed applications. A critical review of the last two decades considering the challenges and limitations in this field is expressed. As a contribution, some major and minor gaps are introduced, and we plot the research trends in this field. As a result, this review can serve as guidance and an opportunity for scholars who want to use an active control approach via microjets for supersonic flow problems. Full article
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