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Numerical simulation of unsteady low-Mach number viscous flow in a channel
Punčochářová, P. ; Kozel, Karel ; Horáček, Jaromír ; Fürst, J.
This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds to the human vocal tract. The flow is described by a system of Navier-Stokes equations for laminar flows. The numerical solution is implemented using a grid of quadrilateral cells. Due the motion of the grid, the basic equations are considered in the Arbitrary Lagrangian-Eulerian form. Numerical results are presented for Mach number 0,012m, Reynolds number 5000 and vibration frequency 100 Hz.
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Dual-time stepping method applied to a numerical solution of unsteady incompressible flow with a vibrating profile
Honzátko, R. ; Horáček, Jaromír ; Kozel, K.
The paper presents numerical solution of two-dimensional incompressible flow in the interaction with a vibrating profile. The profile has two degrees of freedom. Mathematical model is represented either by the Euler equations in the case of inviscid flow or the Navier-Stokes equations in the case of viscous flow. Finite volume method is used as a discretization method. The dual-time stepping method is applied to unsteady simulations. This method provides a possibility to develop a time-accurate time-marching scheme for unsteady incompressible flows. Computational domain deformation due to the profile motion are treated using the Arbitrary Lagrangian-Eulerian method (ALE). Numerical schemes used for unsteady flow calculations are implemented in a form satisfying the geometric conservation law (GCL).
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Numerické simulace interakce neviskozního a viskozního proudění nestlačitelné tekutiny s vibrujícím profilem
Honzátko, R. ; Horáček, Jaromír ; Kozel, Karel
The work deals with a numerical solution of the interaction of 2D incompressible flows and a freely vibrating profile with large amplitudes. The profile can oscillate around an elastic axis and in the vertical direction. The motion of the profile is described by two nonlinear ordinary differential equations solved numerically using four-order Runge-Kutta method. The Euler or Navier-Stokes equations represent the inviscid or viscous flows. Numerical schemes of the finite volume method are applied on a structured quadrilateral C-mesh. The method of artificial compressibility and dual-time stepping method are employed for numerical solution. Deformations of the computational domain due to the profile motion are treated using the ALE method.
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Numerická simulace stlačitelného proudění s nízkým Machovým číslem skrz oscilující štěrbinu
Punčochářová, Petra ; Fürst, J. ; Kozel, Karel ; Horáček, Jaromír
The work deals with the numerical solution of 2D unsteady compressible viscous flows in a symmetric channel for a low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during the oscillations. The flow in the channel can represent a simplified model of airflow coming from the trachea, through the glottal region with periodically vibratin vocal folds to the human vocal tract. The numerical solution is realized by finite volume method and the explicit predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. The moved grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method.
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Numerické řešení stacionárního a nestacionárního proudění kolem profilu v kanálu
Furmánek, P. ; Horáček, Jaromír ; Kozel, Karel
The work deals with steady and unsteady solution of subsonic flow over a profile DCA 18%in a channel. For the computation the predictor-correstor MacCormack scheme with modified TVD Cousonś artificial dissipation is used. Firstly, the steady state solution compared to the experimental results is presented. Than a simple unsteady model based on pressure change at the outlet area of the computational domain and finaly an unsteady model obtained with the use of ALE method (moving mesh) are presented.
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Numerické řešení stacionárního a nestacionárního stlačitelného viskozního proudění v kanále
Punčochářová, P. ; Kozel, Karel ; Horáček, Jaromír ; Fürst, J.
This study deals with numerical solution of 2D unsteady flow of compressible viscous fluid in channel for a low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes. The channel is harmonically opening and nearly closing. When closing the airlow velocity is becoming much higher in the narrowest part of the airways, where also the viscous forces play important role. Therefore for a correct modelling of a real flow the compressible, viscous and unsteady fluid-flow model decribed by Navire-Stokes equations should be considered. The authors present the simulations of the flow field by the expecially developed program.
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Numerické řešení proudění kolem profilu vibrujícího s dvěma stupni volnosti
Honzátko, R. ; Horáček, Jaromír ; Kozel, K.
The work deals with a numerical solution of two-dimensional inviscid incompressible flow over a profile NACA 0012 with two degrees of freedom. the profile can rotate around an elastic axis and oscillate in the vertical direction. The finite volume method in a form of a cell-centered scheme at qaudrilateral C-mesh is considered. The mathematical model of the fluid flow is represented by a modified system of unsteady Euler equations. The motion of the profile is described by a system of two ordinary differential equations. The numerical simulation of flow induced vibrations of the profile consists in a couling of the two systems of equations. An arbitrary Lagrangian-Eulerian method is employed to solve unsteady flows on a moving grid.
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Numerické řešení vybraných problémů vnější a vnitřní aerodynamiky
Furmánek, P. ; Fürst, J. ; Horáček, Jaromír ; Kozel, Karel
The work deals with numerical solution of transonic flows around a DCA 18% profile and over a wing (modified NACA 0012) in the wall. The numerical solution is based on MacCormack finite volumes prdictor-corrector scheme with Jameson's artifficial dissipation. We present several results of subsonic and transonic flow over DCA 18% in the channel compared to the experimental results of Institute of Thermomechanics. Next simulation considers 3D transonic flow over a wing with two different angles of attack.
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Numerické řešení nestacionárního proudění stlačitelné viskozní tekutiny v kanále
Punčochářová, Petra ; Kozel, Karel ; Fürst, J. ; Horáček, Jaromír
This work deals with numerical solutin of viscous laminar flows in a channel with time-changing wall. MacCormack scheme and Jameson artificial viscosity are used for numerical solution in the form of finite volume method with grid of quadrilateral cells. Mathematical model is unsteady system of 2D laminar Navier-Stokes equations. Unsteady behavior is caused by time dependent-boundary of lower. The channel represents a simple case of vocal tract. an unsteady domain is presented using Arbitrary Lagrangian-Eulerian method. In the work several numerical results of flows in two different channels are presented.
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Numerické modelování nestacionárního proudění viskozní tekutiny ve 2D kanále pro nízká Machova čísla
Punčochářová, Petra ; Kozel, Karel ; Fürst, J. ; Horáček, Jaromír
The work presents an unsteady viscous flow for low upstream Mach number (M =0.012) in a 2D channel. Unsteady flow is caused by a moving part of the channel wall as a given function of time. The problem is described by the system of Navier-Stokes equations for compressible leminar flows. It is numerically solved by the explicit central finite volume version of MacCormack scheme on a grid of quadrilateral cells. Moved grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method. Physically the flow in the symmetrical channel can present some very simple model of flow in a human vocal tract. The aim is to compare two different cases of this problem of the flowfield.
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