Numerical comparison of unsteady compressible viscous flow in convergent channel

summary:This study deals with a numerical solution of a 2D flows of a compressible viscous fluids in a convergent channel for low inlet airflow velocity. Three governing systems -- Full system, Adiabatic system, Iso-energetic system$based on the Navier-Stokes equations for laminar flow are tested. The numerical solution is realized by finite volume method and the predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method. The numerical results, acquired from a developed program, are presented for inlet velocity$\hat u_{\infty}=4.12 {\rm ms^{-1}}$and Reynolds number Re =$4 \times 10^3$.

The comparison of different acoustic approaches in the simulation of human phonation

This contribution deals with mathematical modelling and numerical simula- tion of the human phonation process. This phenomena is described as a coupled problem composed of the three mutually coupled physical fields: the deformation of elastic body, the fluid flow and the acoustics. For the sake of simplicity only a two-dimensional model problems is considered in this paper. The fluid-structure interaction problem is described by the incompressible Navier-Stokes equations, by the linear elasticity theory and by the interface conditions. In order to capture the motion of the fluid domain the arbitrary Lagrangian-Eulerian method is used. The strongly coupled partitioned scheme is used for solution of the coupled fluid-structure problem. For solution of acoustics the acoustic analogies are used. Two analogies are compared - the Lighthill analogy and convected perturbation wave equation. The influence of acoustic field back to fluid as well as to structure is neglected. The numerical approximation of all three physical domains is per- foremd with the aid of the finite element method. The numerical results present sound propagation through the model of the vocal tract

Modeling of flow generated sound in a constricted duct at low Mach number flow

Modelling flow and acoustics in a constricted duct at low Mach numbers is important for investigating many physiological phenomena such as phonation, generation of arterial murmurs, and pulmonary conditions involving airway obstruction. The objective of this study is to validate computational fluid dynamics (CFD) and computational aero-acoustics (CAA) simulations in a constricted tube at low Mach numbers. Different turbulence models were employed to simulate the flow field. Models included Reynolds Average Navier-Stokes (RANS), Detached eddy simulation (DES) and Large eddy simulation (LES). The models were validated by comparing study results with laser doppler anemometry (LDA) velocity measurements. The comparison showed that experimental data agreed best with the LES model results. Although RANS Reynolds stress transport (RST) model showed good agreement with mean velocity measurements, it was unable to capture velocity fluctuations. RANS shear stress transport (SST) k-{\omega} model and DES models were unable to predict the location of high fluctuating flow region accurately. CAA simulation was performed in parallel with LES using Acoustic Perturbation Equation (APE) based hybrid CAA method. CAA simulation results agreed well with measured wall sound pressure spectra. The APE acoustic sources were found in jet core breakdown region downstream of the constriction, which was also characterized by high flow fluctuations. Proper Orthogonal Decomposition (POD) is used to study the coherent flow structures at the different frequencies corresponding to the peaks of the measured sound pressure spectra. The study results will help enhance our understanding of sound generation mechanisms in constricted tubes including biomedical applications

Modeling of flow generated sound in a constricted duct at low Mach number flow

Modelling flow and acoustics in a constricted duct at low Mach numbers is important for investigating many physiological phenomena such as phonation, generation of arterial murmurs, and pulmonary conditions involving airway obstruction. The objective of this study is to validate computational fluid dynamics (CFD) and computational aero-acoustics (CAA) simulations in a constricted tube at low Mach numbers. Different turbulence models were employed to simulate the flow field. Models included Reynolds Average Navier-Stokes (RANS), Detached eddy simulation (DES) and Large eddy simulation (LES). The models were validated by comparing study results with laser doppler anemometry (LDA) velocity measurements. The comparison showed that experimental data agreed best with the LES model results. Although RANS Reynolds stress transport (RST) model showed good agreement with mean velocity measurements, it was unable to capture velocity fluctuations. RANS shear stress transport (SST) k-ω model and DES models were unable to predict the location of high fluctuating flow region accurately. CAA simulation was performed in parallel with LES using Acoustic Perturbation Equation (APE) based hybrid CAA method. CAA simulation results agreed well with measured wall sound pressure spectra. The APE acoustic sources were found in jet core breakdown region downstream of the constriction, which was also characterized by high flow fluctuations. Proper Orthogonal Decomposition (POD) is used to study the coherent flow structures at the different frequencies corresponding to the peaks of the measured sound pressure spectra. The study results will help enhance our understanding of sound generation mechanisms in constricted tubes including biomedical applications

MODELING OF FLOW AND PARTICLE DYNAMICS HUMAN RESPIRATORY SYSTEM USING FLUID DYNAMICS

The aim of this research is to study numerically the flow characteristics and particle transport within a human respiratory system, including the human nasal cavity and the bifurcation. Various flow rates and particle sizes are main parameters varied in order to analyze the effects on particle movements and deposition on the human respiratory system. There are three main systems considered in this research: flow around a blockage in a channel, flow in the Final particle deposition with Stokes number, St = 0.12 for inlet flow rates of: (a) 30 L/min; (b) 60 L/min in human nasal cavity, and flow in the double bifurcation. Computational Fluid Dynamics (CFD) is used to solve gas-particle flow equations using a commercial software, FLUENT. Flow around a blockage in a channel was performed to gain confidence in the CFD model that has recirculation zone behind the block. The unsteady vortices flow around this blockage is investigated for Reynolds numbers, Re = 150, 300, 600, 900, and 1200 and Stokes numbers, St = 0.01, 0.1, 0.5, 1.0 and 2.0 by solving momentum and particle model equations. A detailed airflow structures such as vortices, flow distribution are obtained. It was found that the particle distribution depends on vortical structures and Stokes number. A model of real human nasal cavity is reconstructed from computerized tomography (CT) scans. The flow structure is validated with experimental data for flowrates of 7.5 L/min (Re = 1500) and 15 L/min (Re = 3000). The total particle deposition in nasal cavity is also validated with experimental data using inertial parameter. Then the model is further investigated the effect of turbulence on particle deposition with flowrates of 20, 30 and 40 L/min. Deposition was found to increase with Stoke number for the same Reynolds number. vii Three-dimensional double bifurcations with coplanar configurations are employed to investigate the flow. Results of laminar flow (Re = 500, Re = 1036, and Re = 2000) are used to compare with experimental and numerical solution for validation. The model is further used to investigate the turbulent flow and particle deposition for heavy breathing with flowrates of 30 L/min (Re = 7300) and 60 L/min (Re = 14600). It was found that the deposition efficiency is dependent on Reynolds number and Stokes numbers. This research outcome will guide to improve the injection particle drugs to human lungs and to develop nasal mask to protect the lungs from hazardous particles

Direct numerical simulation of human phonation

The generation and propagation of the human voice is studied using direct numerical simulation. A full body domain is employed for the purpose of directly computing the sound in the region past the speaker's mouth. The air in the vocal tract is modeled as a compressible and viscous fluid interacting with the vocal folds (VFs). The vocal fold tissue material properties are multi-layered, with varying stiffness, and a finite-strain model is utilized and implemented in a quadratic finite element code. The fluid-solid domains are coupled through a boundary-fitted interface and utilize a Poisson equation-based mesh deformation method. The domain includes an anatomically relevant vocal tract geometry, either in two dimensions or in three dimensions. Adult and two-year-old child anatomy inspired simulations are performed. Phonation simulations using a non-linear hyper elastic, linear elastic and viscoelastic models of the VFs are performed and compared. The sensitivity of phonation to the VF Poisson's ratio is also evaluated. Simulations are employed to investigate voice disorders related to vocal fold stiffness asymmetry and unilateral vocal fold paralysis (UVFP). Additionally, an analysis is performed for medialization laryngoplasty, a well known surgical treatment for UVFP. Phonation onset is determined from all the simulations as a measure of degree of voice disorder with phonation threshold pressure (PTP) as a key parameter for the quantification. The computational model developed is demonstrated to be consistent with prior measurements and sufficiently sensitive to be used in future studies involving VF pathologies, surgical procedures to restore voice, and/or closed loop models of voice, speech and perception.Ope

Mathematical Analysis of a Model of Blood Flow Through a Channel with Flexible Walls

The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls. The walls of the vessel conveying fluid are subject to traveling waves. Experimental data shows that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), which induces “traveling wave flutter.” The problem of stability of fluid-structure interaction splits into two parts: (i) stability of fluid flow in the channel with harmonically moving walls and (ii) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow is the main focus of the research. It is shown that using the mass conservation and the incompressibility condition one can obtain the initial boundary value problem for the stream function. The boundary conditions reflect the facts that (i) for the axisymmetrical flow, there is no movement in the vertical direction along the axis of symmetry, and (ii) there is no relative movement between the near-boundary flow and the structure (“no-slip” condition). The closed form solution is derived and is represented in the form of an infinite functional series

Parallel Lagrangian particle transport : application to respiratory system airways

This thesis is focused on particle transport in the context of high computing performance (HPC) in its widest range, from the numerical modeling to the physics involved, including its parallelization and post-process. The main goal is to obtain a general framework that enables understanding all the requirements and characteristics of particle transport using the Lagrangian frame of reference. Although the idea is to provide a suitable model for any engineering application that involves particle transport simulation, this thesis uses the respiratory system framework. This means that all the simulations are focused on this topic, including the benchmarks for testing, verifying and optimizing the results. Other applications, such as combustion, ocean residuals, or automotive, have also been simulated by other researchers using the same numerical model proposed here. However, they have not been included here in the interest of allowing the project to advance in a specific direction, and facilitate the structure and comprehension of this work. Human airways and respiratory system simulations are of special interest for medical purposes. Indeed, human airways can be significantly different in every individual. This complicates the study of drug delivery efficiency, deposition of polluted particles, etc., using classic in-vivo or in-vitro techniques. In other words, flow and deposition results may vary depending on the geometry of the patient and simulations allow customized studies using specific geometries. With the help of the new computational techniques, in the near future it may be possible to optimize nasal drugs delivery, surgery or other medical studies for each individual patient though a more personalized medicine. In summary, this thesis prioritizes numerical modeling, wide usability, performance, parallelization, and the study of the physics that affects particle transport. In addition, the simulation of the respiratory system should carry out interesting biological and medical results. However, the interpretation of these results will be only done from a pure numerical point of view.Aquesta tesi se centra en el transport de partícules dins el context de la computació d'alt rendiment (HPC), en el seu ventall més ampli; des del model numèric fins a la física involucrada, incloent-hi la part de paral·lelització del codi i de post-procés. L'objectiu principal és obtenir un esquema general que permeti entendre tant els requeriments com les característiques del transport de partícules fent servir el marc de referència Lagrangià. Encara que la idea sigui definir un model capaç¸ de simular qualsevol aplicació en el camp de l'enginyeria que involucri el transport de partícules, aquesta tesi utilitza el sistema respiratori com a temàtica de referència. Això significa que totes les simulacions estan emmarcades en aquest camp d'estudi, incloent-hi els tests de referència, verificacions i optimitzacions de resultats. L'estudi d'altres aplicacions, com ara la combustió, els residus oceànics, l'automoció o l'aeronàutica també han estat dutes a terme per altres investigadors utilitzant el mateix model numèric proposat aquí. Tot i així, aquests resultats no han estat inclosos en aquesta tesi per simplificar-la i avançar en una sola direcció; facilitant així l'estructura i millor comprensió d'aquest treball. Pel que fa al sistema respiratori humà i les seves simulacions, tenen especial interès per a propòsits mèdics. Particularment, la geometria dels conductes respiratoris pot variar de manera considerable en cada persona. Això complica l'estudi en aspectes com el subministrament de medicaments o la deposició de partícules contaminants, per exemple, utilitzant les tècniques clàssiques de laboratori (in-vivo o in-vitro). En altres paraules, tant el flux com la deposició poden canviar en funció de la geometria del pacient i aquí és on les simulacions permeten estudis adaptats a geometries concretes. Gràcies a les noves tècniques de computació, en un futur proper és probable que puguem optimitzar el subministrament de medicaments per via nasal, la cirurgia o altres estudis mèdics per a cada pacient mitjançant una medicina més personalitzada. En resum, aquesta tesi prioritza el model numèric, l'amplitud d'usos, el rendiment, la paral·lelització i l'estudi de la física que afecta directament a les partícules. A més, el fet de basar les nostres simulacions en el sistema respiratori dota aquesta tesi d'un interès biològic i mèdic pel que fa als resultats

MODELING OF FLOW AND PARTICLE DYNAMICS HUMAN RESPIRATORY SYSTEM USING FLUID DYNAMICS

The aim of this research is to study numerically the flow characteristics and particle transport within a human respiratory system, including the human nasal cavity and the bifurcation. Various flow rates and particle sizes are main parameters varied in order to analyze the effects on particle movements and deposition on the human respiratory system. There are three main systems considered in this research: flow around a blockage in a channel, flow in the Final particle deposition with Stokes number, St = 0.12 for inlet flow rates of: (a) 30 L/min; (b) 60 L/min in human nasal cavity, and flow in the double bifurcation. Computational Fluid Dynamics (CFD) is used to solve gas-particle flow equations using a commercial software, FLUENT. Flow around a blockage in a channel was performed to gain confidence in the CFD model that has recirculation zone behind the block. The unsteady vortices flow around this blockage is investigated for Reynolds numbers, Re = 150, 300, 600, 900, and 1200 and Stokes numbers, St = 0.01, 0.1, 0.5, 1.0 and 2.0 by solving momentum and particle model equations. A detailed airflow structures such as vortices, flow distribution are obtained. It was found that the particle distribution depends on vortical structures and Stokes number. A model of real human nasal cavity is reconstructed from computerized tomography (CT) scans. The flow structure is validated with experimental data for flowrates of 7.5 L/min (Re = 1500) and 15 L/min (Re = 3000). The total particle deposition in nasal cavity is also validated with experimental data using inertial parameter. Then the model is further investigated the effect of turbulence on particle deposition with flowrates of 20, 30 and 40 L/min. Deposition was found to increase with Stoke number for the same Reynolds number. vii Three-dimensional double bifurcations with coplanar configurations are employed to investigate the flow. Results of laminar flow (Re = 500, Re = 1036, and Re = 2000) are used to compare with experimental and numerical solution for validation. The model is further used to investigate the turbulent flow and particle deposition for heavy breathing with flowrates of 30 L/min (Re = 7300) and 60 L/min (Re = 14600). It was found that the deposition efficiency is dependent on Reynolds number and Stokes numbers. This research outcome will guide to improve the injection particle drugs to human lungs and to develop nasal mask to protect the lungs from hazardous particles

Fluid-structure interaction of compressible flow

The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L^2(L^2)-norm and in DG-norm formed by the L^2(H^1)-seminorm and penalty terms. The second part of the thesis deals with the realization of fluid-structure interaction problem of the compressible viscous flow with the elastic structure. The time-dependence of the domain occupied by the fluid is treated by the ALE (Arbitrary Lagrangian-Eulerian) method, when the compressible Navier-Stokes equations are formulated in the ALE formulation. The deformation of the elastic body, caused by the aeroelastic forces, is described by the dynamical elasticity equations. Both these systems are coupled by the transmission conditions. For the space discretization of the flow problem the DGFE method is used. The time-discretization is realized by the backward difference formula. The structural problem is discretized by conforming finite element method and the Newmark method. The fluid-structure interaction is realized via weak or strong coupling algorithms. The developed technique is tested by numerical experiments and applied to the simulation of vibrations of vocal folds during phonation onset