Brinkman equation in reactive flow: Contribution of each term in carbonate acidification simulations

Ferreira, Leandro de Paulo; Oliveira, T. D. S.; Surmas, Rodrigo; Silva, Mônica Antunes Pereira da; Peçanha, Ricardo Pires

doi:10.1016/j.advwatres.2020.103696

Cited by 11 publications

(4 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Brinkman equation [ 59 ] not only considers the viscous shear stress term of fluid in the Navier–Stokes equation, but also considers Darcy’s law [ 60 ]. This equation can well explain the rapid flow of fluid in porous media.…”

Section: Methodsmentioning

confidence: 99%

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

Liang

2021

Polymers

View full text Add to dashboard Cite

In situ injection molding of continuous fiber reinforced thermoplastic composites is challenged by unbalanced dual-scale infiltration flow due to the pronounced capillary effect. In this paper, a general and efficient approach was proposed for dual-scale infiltration flow balancing based on numerical simulation. Specifically, Stokes and Brinkman equations were used to describe the infiltration flow in inter- and intra-fiber bundles. In particular, capillary pressure drop was integrated in the Brinkmann equation to consider the capillary effect. The infiltration flow front is tracked by the level set method. Numerical simulation and experimental results indicate that the numerical model can accurately demonstrate the unbalanced infiltration flow in inter- and intra-fiber bundles caused by the changes of the injection rate, the resin viscosity, the injection rate, the fiber volume fraction and the capillary number. In addition, the infiltration flow velocity in inter- and intra-fiber bundles can be efficiently tuned by the capillary number, which is mainly determined by the injection rate for a specified resin system. The optimal capillary numbers obtained by simulation and experiment are 0.022 and 0.026, which are very close to each other. Finally, one-dimensional in situ injection molding experiments with constant injection pressure were conducted to prepare fiber reinforced polymerized cyclic butylene terephthalate composite laminate with various flow rates along the infiltration direction. The experimental results confirmed that the lowest porosity and the highest interlaminar shear strength of the composite can only be obtained with the optimized capillary number, which is basically consistent with the simulation results.

show abstract

Section: Methodsmentioning

confidence: 99%

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

Liang

2021

Polymers

View full text Add to dashboard Cite

show abstract

“…The Brinkman equations (1.1)-(1.3) can be seen as a modified version of Darcy's law obtained by adding viscous forces to the Navier-Stokes equations [5]. This model has been applied in many fields, such as power engineering, petroleum industry, geology, geophysics, and so on [4,9,10,20]. Mathematically speaking, the Brinkman equations have different properties due to the varying permeability tensor κ.…”

Section: Introductionmentioning

confidence: 99%

A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations

Dang,

Zhai,

null

et al. 2025

JCM

View full text Add to dashboard Cite

We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkman equations. The main idea is to use high order polynomials to compute the discrete weak gradient and then the stabilizing term is removed from the numerical formulation. The SFWG scheme is very simple and easy to implement on polygonal meshes. We prove the well-posedness of the scheme and derive optimal order error estimates in energy and L 2 norm. The error results are independent of the permeability tensor, hence the SFWG method is stable and accurate for both the Stokes and Darcy dominated problems. Finally, we present some numerical experiments to verify the efficiency and stability of the SFWG method.

show abstract

“…These equations extend Darcy's law to describe the dissipation of kinetic energy caused by viscous forces, similarly to the Navier-Stokes equations [5]. Brinkman equations are also applied in many other fields, such as environmental science, geophysics, petroleum engineering, biotechnology, and so on [3,9,10,14,18].…”

Section: Introductionmentioning

confidence: 99%

A conforming discontinuous Galerkin finite element method for Brinkman equations

Dang¹,

Zhai²,

Zhao³

2023

Preprint

View full text Add to dashboard Cite

In this paper, we present a conforming discontinuous Galerkin (CDG) finite element method for Brinkman equations. The velocity stabilizer is removed by employing the higher degree polynomials to compute the weak gradient. The theoretical analysis shows that the CDG method is actually stable and accurate for the Brinkman equations. Optimal order error estimates are established in H 1 and L 2 norm. Finally, numerical experiments verify the stability and accuracy of the CDG numerical scheme.

show abstract

Brinkman equation in reactive flow: Contribution of each term in carbonate acidification simulations

Cited by 11 publications

References 44 publications

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations

A conforming discontinuous Galerkin finite element method for Brinkman equations

Contact Info

Product

Resources

About