Numerical simulation of non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes

Meburger, Stefanie; Niethammer, Matthias; Bothe, Dieter; Schäfer, Michael

doi:10.1016/j.jnnfm.2020.104451

Cited by 14 publications

(9 citation statements)

References 30 publications

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“…The non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes has been simulated numerically. They demonstrated the stability of the finite volume method in the experimentally relevant range of high Weissenberg numbers.their findings shows it was in good agreement with experimental data [9]. In this work numerical approximations to ODEs Initial value Problem using some selected methods [10] to solve a case study of gluconic acid frementation by Psuedonomas Ovalis has been presented to validate the adoption of numerical approximations for complex scientific systems studies.…”

Section: Introductionmentioning

confidence: 67%

“…In their numerical simulation Runge Kutta Lower order was most accurate and significantly approximates their analytical solution [8]. Meburgerac et al [9] demonstrated the stability of finite volume numerical method while studying thermorheological properties in Oldroyd-B type viscoelastic fluids. They found the results at different imposed wall temperatures, as well as Weissenberg numbers to be in good agreement with experimental data.…”

Section: Resultsmentioning

confidence: 99%

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Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

Ihoeghian

John

2021

JAMCS

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Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques. This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy. The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.

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Section: Introductionmentioning

confidence: 67%

Section: Resultsmentioning

confidence: 99%

Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

Ihoeghian

John

2021

JAMCS

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“…In the present work, we use the unified mathematical and numerical stabilization framework, proposed by Niethammer et al [46] for the general conformation tensor constitutive equations ( 20) and ( 22). This generic framework has been validated [46,36] and extended to non-isothermal [47] and two-phase flows [22]. For a detailed description of the generic stabilization framework and its validation in computational benchmarks, we refer to [46,35].…”

Section: Stabilizationmentioning

confidence: 99%

On the molecular mechanism behind the bubble rise velocity jump discontinuity in viscoelastic liquids

Bothe,

Niethammer,

Pilz

et al. 2021

Preprint

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Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. The phenomenon has been extensively investigated in the literature, both by means of experiments as well as via numerical simulations. The occurrence of the velocity jump has been associated with a change of the bubble shape under the formation of a pointed tip at the rear end and to the appearance of a so-called negative wake with the liquid velocity behind the bubble, pointing in the opposite direction to that in viscous Newtonian fluids. We revisit this topic, starting with a review of the state of knowledge on the interrelations between the mentioned characteristic features. In search for a convincing explanation of the jump phenomenon, we performed detailed numerical simulations of the transient rise of single bubbles in 3D, allowing for a local polymer molecular conformation tensor analysis. The latter shows that polymer molecules traveling along the upper bubble hemisphere are stretched in the circumferential direction, due to the flow kinematics. Then, depending on the relaxation time scale of the polymer, the stored elastic energy is either unloaded essentially above or below the bubble's equator. In the former case, this slows down the bubble, while the bubble gets accelerated otherwise. In this latter case, the relative velocity of the polymer molecules against the bubble is increased, giving rise to a self-amplification of the effect and thus causing the bubble rise velocity to jump to a higher level. Detailed experimental velocity measurements in the liquid field around the bubble confirmed the conclusion that the ratio of the time scale of the Lagrangian transport of polymer molecules along the bubble contour to the relaxation time scale of the polymer molecules determines the subor supercritical state of the bubble motion.

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“…The polymers’ processing techniques are predominantly non-isothermal, such as injection molding [ 1 , 2 , 3 ], heat exchange problems [ 4 , 5 ], or in plastication, including heating and cooling sequences [ 6 , 7 ]. The thermal conductivity and heat transfer are usually low in this processes; however, due to the heating or cooling of the machine’s operations, large temperature gradients arise in the fluid [ 4 , 8 ]. In addition, the viscoelastic behavior of polymers acts on the temperature field as well as on the fluid deformation [ 4 , 8 ].…”

Section: Introductionmentioning

confidence: 99%

“…The thermal conductivity and heat transfer are usually low in this processes; however, due to the heating or cooling of the machine’s operations, large temperature gradients arise in the fluid [ 4 , 8 ]. In addition, the viscoelastic behavior of polymers acts on the temperature field as well as on the fluid deformation [ 4 , 8 ]. Therefore, flow properties are strongly dependent on both rheology and temperature; and, thus, it is essential to understand and make predictions regarding non-isothermal viscoelastic fluid flows.…”

Section: Introductionmentioning

confidence: 99%

A Fully Implicit Log-Conformation Tensor Coupled Algorithm for the Solution of Incompressible Non-Isothermal Viscoelastic Flows

Fernandes

2022

Polymers

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In this work, a block-coupled algorithm is presented, which can compute laminar, incompressible, non-isothermal, viscoelastic flow problems based on the log-conformation tensor approach. The inter-equation coupling of the incompressible Cauchy linear momentum and mass conservation equations is obtained in a procedure based on the Rhie–Chow interpolation. The divergence of the log-conformation tensor term in the linear momentum equations is implicitly discretized in this work. In addition, the velocity field is considered implicitly in the log-conformation tensor constitutive equations by expanding the advection, rotation and the rate of deformation terms with a Taylor series expansion truncated at the second-order error term. Finally, the advection and diffusion terms in the energy equation are also implicitly discretized. The mass, linear momentum, log-conformation tensor constitutive model and energy-discretized linear equations are joined into a block-matrix following a monolithic framework. Validation of the newly developed algorithm is performed for the non-isothermal viscoelastic matrix-based Oldroyd-B fluid flow in the axisymmetric 4:1 planar sudden contraction benchmark problem.

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Numerical simulation of non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes

Cited by 14 publications

References 30 publications

Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

On the molecular mechanism behind the bubble rise velocity jump discontinuity in viscoelastic liquids

A Fully Implicit Log-Conformation Tensor Coupled Algorithm for the Solution of Incompressible Non-Isothermal Viscoelastic Flows

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