Viscous fingering phenomena in the early stage of polymer membrane formation

2019 ◽  
Vol 864 ◽  
pp. 97-140 ◽  
Author(s):  
Manuel Hopp-Hirschler ◽  
Mostafa Safdari Shadloo ◽  
Ulrich Nieken
Keyword(s):  
Pore Formation ◽  
Stokes Equations ◽  
Early Stage ◽  
Polymer Membranes ◽  
Viscous Fingering ◽  
Porous Polymer ◽  
Navier Stokes ◽  
Time Resolved ◽  
Liesegang Rings ◽  
Fingering Phenomena

Currently, the most important preparation process for porous polymer membranes is the phase inversion process. While applied for several decades in industry, the mechanism that leads to diverse morphology is not fully understood today. In this work, we present time resolved experiments using light microscopy that indicate viscous fingering during the early stage of pore formation in porous polymer membranes. Numerical simulations using the smoothed particle hydrodynamics method are also performed based on Cahn–Hilliard and Navier–Stokes equations to investigate the formation of viscous fingers in miscible and immiscible systems. The comparison of pore formation characteristics in the experiment and simulation shows that immiscible viscous fingering is present; however, it is only relevant in specific preparation set-ups similar to Hele-Shaw cells. In experiments, we also observe the formation of Liesegang rings. Enabling diffusive mass transport across the immiscible interface leads to Liesegang rings in the simulation. We conclude that further investigations of Liesegang pattern as a relevant mechanism in the formation of morphology in porous polymer membranes are necessary.

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based on PIV Data

2021 ◽  
Author(s):  
Jens Satria Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Flow Instability ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response

Abstract In order to determine the flame transfer function of a combustion system only based on isothermal flow field data, three governing mechanisms have been identified which need to be modeled: swirl fluctuations, equivalence fluctuations and velocity fluctuations excited by planar acoustic waves. This study focuses on the generation and propagation of swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms the recent theoretical work of Albayrak et al. (Journal of Fluid Mechanics, 879). However, the contribution of these inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the amplification of shear-driven modes which are expected to be much more influential for this type of swirler. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Modeling and simulation of membrane process

2017 ◽  
Vol 2 (6) ◽  
Author(s):  
Maciej Staszak
Keyword(s):  
Fluid Dynamics ◽  
Stokes Equations ◽  
Polymer Membranes ◽  
Lattice Models ◽  
Network Models ◽  
Navier Stokes ◽  
Neural Network Models ◽  
Navier Stokes Equations ◽  
Different Types ◽  
Boltzmann Lattice

AbstractThe article presents the different approaches to polymer membrane mathematical modeling. Traditional models based on experimental physicochemical correlations and balance models are presented in the first part. Quantum and molecular mechanics models are presented as they are more popular for polymer membranes in fuel cells. The initial part is enclosed by neural network models which found their use for different types of processes in polymer membranes. The second part is devoted to models of fluid dynamics. The computational fluid dynamics technique can be divided into solving of Navier-Stokes equations and into Boltzmann lattice models. Both approaches are presented focusing on membrane processes.

Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements

1985 ◽  
Vol 160 ◽  
pp. 93-117 ◽  
Author(s):  
Ta Phuoc Loc ◽  
R. Bouard
Keyword(s):  
Circular Cylinder ◽  
Flow Structure ◽  
Stokes Equations ◽  
Early Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Unsteady Viscous Flow ◽  
Vorticity Transport ◽  
New Phenomena

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.

Sound generation by shock–vortex interactions

1999 ◽  
Vol 380 ◽  
pp. 81-116 ◽  
Author(s):  
OSAMU INOUE ◽  
YUJI HATTORI
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Early Stage ◽  
Near Field ◽  
Time Integration ◽  
Flow Fields ◽  
Navier Stokes ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Reflected Shock

Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier–Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based On PIV Data

2021 ◽  
Author(s):  
Jens S. Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Stokes Equations ◽  
Flow Instability ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Navier Stokes Equations ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response ◽  
Measured Flow

Abstract In order to determine the flame transfer function of a combustion system, different mechanisms have been identified that need to be modeled. This study focuses on the generation and propagation of one of these mechanisms, namely the swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms recent theoretical works on inertial waves. However, the contribution of the identified inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the additional amplification of shear-driven modes. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

scholarly journals Solving Galbrun's Equation with a Discontinuous galerkin Finite Element Method

2019 ◽  
Vol 105 (6) ◽  
pp. 1149-1163 ◽  
Author(s):  
Marcus Maeder ◽  
Andrew Peplow ◽  
Maximilian Meindl ◽  
Steffen Marburg
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Early Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linearized Euler Equations ◽  
Displacement Based ◽  
Spurious Modes

Over many years, scientists and engineers have developed a broad variety of mathematical formulations to investigate the propagation and interactions with flow of flow-induced noise in early-stage of product design and development. Beside established theories such as the linearized Euler equations (LEE), the linearized Navier–Stokes equations (LNSE) and the acoustic perturbation equations (APE) which are described in an Eulerian framework, Galbrun utilized a mixed Lagrange–Eulerian framework to reduce the number of unknowns by representing perturbations by means of particle displacement only. Despite the advantages of fewer degrees of freedom and the reduced effort to solve the system equations, a computational approach using standard continuous finite element methods (FEM) suff ers from instabilities called spurious modes that pollute the solution. In this work, the authors employ a discontinuous Galerkin approach to overcome the difficulties related to spurious modes while solving Galbrun's equation in a mixed and pure displacement based formulation. The results achieved with the proposed approach are compared with results from previous attempts to solve Galbrun's equation. The numerical determination of acoustic modes and the identification of vortical modes is discussed. Furthermore, case studies for a lined-duct and an annulus supporting a rotating shear-flow are investigated.

Unsteady Vortices and Blade Loading in a High-Pressure Turbine

2009 ◽  
Author(s):  
Dongil Chang ◽  
Stavros Tavoularis
Keyword(s):  
High Pressure ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Blade Loading ◽  
Pressure Losses ◽  
Horseshoe Vortices

Unsteady flow in a transonic, single-stage, high-pressure, axial turbine has been investigated numerically by solving the URANS (Unsteady Reynolds-Averaged Navier-Stokes) equations with the SST (Shear Stress Transport) turbulence model. Interest has focused on the identification and effects of the quasi-stationary vane and blade horseshoe vortices, vane and blade passage vortices, vane and blade trailing edge vortices, and blade tip leakage vortices. Moreover, two types of unsteady vortices, not discussed explicitly in the previous literature, have been identified and termed “axial gap vortices” and “crown vortices”. All vortices have been clearly and distinctly identified using a modified form of the Q criterion, which is less sensitive to the set threshold than the original version. The use of pathlines and iso-contours of static pressure, axial vorticity and entropy has been further exploited to distinguish the different types of vortices from each other and to mark their senses of rotation and strengths. The influence of these vortices on the entropy distribution at the outlet has been investigated. The observed high total pressure losses in the turbine at blade midspan have been connected to the action of passage vortices. The formation and disappearance processes of unsteady vortices located in the spacing between the stator and the rotor have been time-resolved. These vortices are roughly aligned with the leading edges of the rotor blades and their existence depends on the position of the blade with respect to the upstream vanes. In addition, the present study focuses on the unsteady blade loading that influences vibratory stresses. Contours of the time-dependent surface pressure on the rotor blade have demonstrated the presence of large pressure fluctuations near the front of the blade suction sides; these pressure fluctuations have been associated with the periodic passages of shock waves originating at the vane trailing edges.

Numerical Simulation Analysis on the Flow Mechanism of Passive Containment Cooling System

2013 ◽  
Author(s):  
Yang Song ◽  
Wei-Hua Li ◽  
Sheng-Qiang Li
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Simulation Analysis ◽  
Cooling System ◽  
Early Stage ◽  
Three Dimensional ◽  
Cooling Water ◽  
Navier Stokes ◽  
Flow Mechanism ◽  
Three Dimensional Model

In the third generation PWR, passive containment cooling system was one of the key security parts. If accident happened, the blasting valves in the containment would automatically open and the steam would be injected into the containment. When the pressure reached a certain value, the tank on the top of containment would automatically spray. Driven by gravity, the cooling water would flow along outer surface of containment. Steam inside the containment would condense on inner wall and the pressure in the containment would decrease. A numerical simulation of steam jet in the passive containment cooling system was carried out using computational fluid dynamics methods. Flow mechanism in the process was studied. A simplified three-dimensional model of the passive containment cooling system was built. The hexahedral structured mesh was made. The RNG k-epsilon turbulence model was used in solving the transient Reynolds Navier-Stokes equations by the Fluent. The distributions of velocity in containment at different time were acquired. Reference would be provided for understanding of flow mechanism of gas jet-flow in containment during the early stage of accident.

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