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2094
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Improvement of an unbaffled stirred tank mixing characteristics using variable speed impeller
Gebouský, Ondřej; Haidl, Jan; Bodnár, J.; Pivokonský, Martin
2024 - English
Unbaffled mixing tanks with magnetically driven impellers are increasingly used in biotechnological and pharmaceutical industries, combining the benefits of a closed, sterile environment with easy equipment cleanability. On the other hand, missing internals, such as baffles or cooling coils, have an adverse effect on the equipment mixing characteristics, namely the batch\nhomogenization time. In our previous research, we uncovered that the eccentricity and inclination of the impeller – both employed routinely to enhance the mixing characteristics of unbaffled vessels – are not fully effective in the suppression of central vortex formation resulting in the increase in the homogenization time. In this work, we propose a simple solution to counteract the central vortex formation – a periodical variation of impeller rotational speed. This approach destabilizes the central vortex, significantly reducing homogenization time while maintaining the benefits of the original unbaffled setup. This innovation can seamlessly integrate into existing industrial setups, promising efficiency gains for biotech and pharmaceutical production.
Keywords:
unbaffled mixing tanks; variable rotational speed; vortex destabilization; mixing time improvement
Available in digital repository of the ASCR
Improvement of an unbaffled stirred tank mixing characteristics using variable speed impeller
Unbaffled mixing tanks with magnetically driven impellers are increasingly used in biotechnological and pharmaceutical industries, combining the benefits of a closed, sterile environment with easy ...
Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements
Vacek, Karel; Sváček, P.
2024 - English
This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible Navier-Stokes equations written in the arbitrary Eulerian-Lagrangian (ALE) formulation. The ALE mapping is constructed with the use of a pseudo-elastic approach. The flow problem is numerically approximated by the finite element method (FEM). For discretization of the fluid flow, the results obtained by both the Taylor-Hood (TH) element and the Scott-Vogelius (SV) finite element are compared. The TH element satisfies the Babuška-Brezzi inf-sup condition, which guarantees the stability of the scheme. In the case of the SV element the mesh, that is created as a barycentric refinement of regular triangulation, is used to satisfy the Babuška-Brezzi condition. The numerical results for two benchmark problems are shown.
Keywords:
finite element method; arbitrary Lagrangian-Eulerian method; Scott-Vogelius element; Taylor-Hood element
Available in digital repository of the ASCR
Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements
This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible ...
Flow simulations approach for flocculation tanks
Idžakovičová, Kristýna; Bílek, Vojtěch; Haidl, Jan; Isoz, M.; Pivokonský, Martin
2024 - English
Flocculation in water treatment facilities plays a key role in the separation of colloidal inorganic and organic substances. Its optimization leads to a significant increase in its efficiency and savings of operational costs. However, it is currently based on trial-and-error experimental approaches. In this contribution, we focus on flow modeling in stirred flocculation tanks that would, after coupling with a calibrated model of particle aggregation, enable simulationbased flocculation optimization. Despite the abundance of literature on stirred tank modeling, there is no universal agreement on the methodology used to describe turbulence nor on the approach to the computational mesh creation. Consequently, there is no unified methodology for simulations and their validation. To address this, we present a best-practice methodology for economical, yet reliable flow simulations in the said device. This methodology includes the choice of the turbulence model, the approach to the design of a high quality mesh suitable for arbitrary geometries, and results evaluation. It is developed based on an extensive literature review, a multitude of flow simulations using several meshes of progressively higher quality and resolution, and various strategies to converge to steady-state flow conditions. The simulation quality indicators used here involve comparison with the experimental data on fluid velocity, stirrer power output, and flow rate through the impeller zone. Additionally, the resulting flow simulation models are compared using tracer transport simulations, hinting at their potential for coupling with particle aggregation models.
Keywords:
flocculation tank; stirring; MRF; CFD; OpenFOAM
Available in digital repository of the ASCR
Flow simulations approach for flocculation tanks
Flocculation in water treatment facilities plays a key role in the separation of colloidal inorganic and organic substances. Its optimization leads to a significant increase in its efficiency and ...
Numerical study of the steady airflow in the human respiratory system during inhaling and exhaling
Lancmanová, Anna; Bodnár, Tomáš
2024 - English
This paper presents some of the initial results of the numerical simulations of a steady turbulent flow in human upper airways during inhalation and exhalation. The mathematical model is based on the system of Reynolds-Averaged incompressible Navier-Stokes equations complemented by the SST k − ω turbulence model. The simulations were performed using finite-volume open source solver OpenFOAM on a realistic three-dimensional geometry. The main aim of this particular study is to verify the computational setup with special focus on appropriate choice and implementation of boundary conditions. The prescribed boundary conditions are chosen to mimic the physiological conditions during normal breathing cycle. This study aims to gain an insight into the airflow behavior during the inhalation and exhalation process by comparing the results of two distinct simulations corresponding to two different (opposite) flow rates . The obtained local flow rates and flow fields for both cases are presented and mutually compared. This initial work should serve as a foundation for future more complex simulations that will include the time-dependent and compressible effects.
Keywords:
human airways; incompressible Navier-Stokes; OpenFOAM
Available in digital repository of the ASCR
Numerical study of the steady airflow in the human respiratory system during inhaling and exhaling
This paper presents some of the initial results of the numerical simulations of a steady turbulent flow in human upper airways during inhalation and exhalation. The mathematical model is based on the ...
Numerical evaluation of mass-diffusive compressible fluids flows models
Bodnár, Tomáš; Fraunié, P.
2024 - English
This contribution presents first numerical tests of some recently published alternative models for solution of viscous compressible and nearly incompressible models. All models are solved by high resolution compact finite difference scheme with strong stability preserving RungeKutta time stepping. The two simple but challenging computational test cases are presented, based on the double-periodic shear layer and the Kelvin-Helmholtz instability. The obtained time-dependent flow fields are showing pronounced shear and vorticity layers being resolved by the standard as well as by the new mass-diffusive modified models. The preliminary results show that the new models are viable alternative to the well established classical models.
Keywords:
compressible Navier-Stokes; nearly incompressible flow; mass diffusion; compact finite-difference
Available in digital repository of the ASCR
Numerical evaluation of mass-diffusive compressible fluids flows models
This contribution presents first numerical tests of some recently published alternative models for solution of viscous compressible and nearly incompressible models. All models are solved by high ...
Motion of fluids in the moving domain
Nečasová, Šárka
2024 - English
It is a survay paper where the problem of the existence of weak solutions of compressible barotropic solutions in a moving bounded domain is studied.
Keywords:
compressible fluid; moving domain; weak solutions
Available in digital repository of the ASCR
Motion of fluids in the moving domain
It is a survay paper where the problem of the existence of weak solutions of compressible barotropic solutions in a moving bounded domain is studied.
Some modifications of the limited-memory variable metric optimization methods
Vlček, Jan; Lukšan, Ladislav
2023 - English
Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modified to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new efficient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
Keywords:
unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; arithmetic operations reduction; global convergence
Available in a digital repository NRGL
Some modifications of the limited-memory variable metric optimization methods
Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric ...
GA 19-07635S: Outputs and Results
Rehák, Branislav
2023 - English
This manuscript aims to deliver a survey of results obtained during the solution of the project No. GA19-07635S of the Czech Science Foundation. The timespan dedicated to the work on this project was 1.3.2019 - 30.6.2022. The main area dealt with were\nnonlinear multi-agent systems and their synchronization, further, attention was paid to some auxiliary results in the area of nonlinear observers. This Report briefly introduces the Project, provides a summary of the results obtained and also sketches an outline how these results will be applied and extended in future.
Keywords:
multi-agent systems; nonlinear multi-agent systems; synchronization
Fulltext is available at external website.
GA 19-07635S: Outputs and Results
This manuscript aims to deliver a survey of results obtained during the solution of the project No. GA19-07635S of the Czech Science Foundation. The timespan dedicated to the work on this project was ...
On the structure and values of betweenness centrality in dense betweenness-uniform graphs
Ghanbari, B.; Hartman, David; Jelínek, V.; Pokorná, Aneta; Šámal, R.; Valtr, P.
2023 - English
Betweenness centrality is a network centrality measure based on the amount of shortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of betweenness centrality. In this contribution, we focus on betweenness-uniform graphs with betweenness centrality below one. We disprove a conjecture about the existence of a BUG with betweenness value α for any rational numberαfrom the interval (3/4,∞) by showing that only very few betweenness centrality values below 6/7 are attained for at least one BUG. Furthermore, among graphs with diameter at least three, there are no betweenness-uniform graphs with a betweenness centrality smaller than one. In graphs of smaller diameter, the same can be shown under a uniformity condition on the components of the complement.
Keywords:
betweenness; graphs
Available in digital repository of the ASCR
On the structure and values of betweenness centrality in dense betweenness-uniform graphs
Betweenness centrality is a network centrality measure based on the amount of shortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of ...
On the development of a numerical model for the simulation of air flow in the human airways
Lancmanová, Anna; Bodnár, Tomáš; Sequeira, A.
2023 - English
This contribution reports on an ongoing study focusing on reduced order models for incompressible viscous fluid flow in two dimensional channels. A finite difference solver was developed using a simple implementation of the immersed boundary method to represent the channel geometry. The solver was validated for unsteady flow by comparing the obtained two-dimensional numerical solutions with analytical profiles computed from the Womersley solution. Finally the 2D model was coupled to a simple 1D extension simulating the flow in axisymmetric elastic vessel (tube). Some of the coupling principles and implementation issues are discussed in detail.
Keywords:
reduced order model; incompressible Navier-Stokes equations; finite difference approximation; coupling method
Available in digital repository of the ASCR
On the development of a numerical model for the simulation of air flow in the human airways
This contribution reports on an ongoing study focusing on reduced order models for incompressible viscous fluid flow in two dimensional channels. A finite difference solver was developed using a ...
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