Vortex breakdown in a three-dimensional swirling flow

2002 ◽  
Vol 459 ◽  
pp. 347-370 ◽  
Author(s):  
E. SERRE ◽  
P. BONTOUX
Keyword(s):  
Stokes Equations ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Rotation Speed ◽  
Three Dimensional ◽  
Time Dependent ◽  
Computational Time ◽  
Oscillatory Regime ◽  
Axisymmetric Mode ◽  
Centrifugal Instability

Time-dependent swirling flows inside an enclosed cylindrical rotor–stator cavity with aspect ratio H/R = 4, larger than the ones usually considered in the literature, are studied. Within a certain range of governing parameters, vortex breakdown phenomena can arise along the axis. Very recent papers exhibiting some particular three-dimensional effects have stimulated new interest in this topic. The study is carried out by a numerical resolution of the three-dimensional Navier–Stokes equations, based on high-order spectral approximations in order to ensure very high accuracy of the solutions.The first transition to an oscillatory regime occurs through an axisymmetric bifurcation (a supercritical Hopf bifurcation) at Re = 3500. The oscillatory regime is caused by an axisymmetric mode of centrifugal instability of the vertical boundary layer and the vortex breakdown is axisymmetric, being composed of two stationary bubbles. For Reynolds numbers up to Re = 3500, different three-dimensional solutions are identified. At Re = 4000, the flow supports the k = 5 mode of centrifugal instability. By increasing the rotation speed to Re = 4500, the vortex breakdown evolves to an S-shaped type after a long computational time. The structure is asymmetric and gyrates around the axis inducing a new time-dependent regime. At Re = 5500, the structure of the vortex breakdown is more complex: the upper part of the structure takes a spiral form. The maximum rotation speed is reached at Re = 10000 and the flow behaviour is now chaotic. The upper structure of the breakdown can be related to the spiral-type. Asymmetric flow separation on the container wall in the form of spiral arms of different angles is also prominent.

Modulated rotating waves in an enclosed swirling flow

2002 ◽  
Vol 465 ◽  
pp. 33-58 ◽  
Author(s):  
H. M. BLACKBURN ◽  
J. M. LOPEZ
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Low Frequency ◽  
Rotating Waves ◽  
Axisymmetric Solution ◽  
Axisymmetric Mode ◽  
Very Low Frequency

The loss of axisymmetry in a swirling flow that is generated inside an enclosed cylindrical container by the steady rotation of one endwall is examined numerically. The two dimensionless parameters that govern these flows are the cylinder aspect ratio and a Reynolds number associated with the rotation of the endwall. This study deals with a fixed aspect ratio, height/radius = 2.5. At low Reynolds numbers the basic flow is steady and axisymmetric; as the Reynolds number increases the basic state develops a double recirculation zone on the axis, so-called vortex breakdown bubbles. On further increase in the Reynolds number the flow becomes unsteady through a supercritical Hopf bifurcation but remains axisymmetric. After the onset of unsteadiness, another two unsteady axisymmetric solution branches appear with further increase in Reynolds number, each with its own temporal characteristic: one is periodic and the other is quasi-periodic with a very low frequency modulation. Solutions on these additional branches are unstable to three-dimensional perturbations, leading to nonlinear modulated rotating wave states, but with the flow still dominated by the corresponding underlying axisymmetric mode. A study of the flow behaviour on and bifurcations between these solution branches is presented, both for axisymmetric and for fully three-dimensional flows. The presence of modulated rotating waves alters the structure of the bifurcation diagram and gives rise to its own dynamics, such as a truncated cascade of period doublings of very-low-frequency modulated states.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

scholarly journals PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

scholarly journals METHOD OF PARALLELIZATION OF NUMERICAL ALGORITHMOF NAVIER-STOKES EQUATIONS COMPLETE SYSTEM

2016 ◽  
pp. 92-98
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Thermal Conductivity ◽  
Gas Flow ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Computation Time ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Comparison Of The Results

The article considers the features of numerical construction of solutions of the Navier-Stokes equations full system describing a three-dimensional flow of compressible viscous heat-conducting gas under the action of gravity and Coriolis forces. It is shown that accounting of dissipative properties of viscosity and thermal conductivity of the moving continuum, even with constant coefficients of viscosity and thermal conductivity, as well as the use of explicit difference scheme calculation imposes significant restrictions on numerical experiments aimed at studying the arising complex flows of gas or liquid. First of all, it is associated with a signifi- cant complication of the system of equations, the restrictions on the value of the calculated steps in space and time, increasing the total computation time. One of the options is proposed of algorithm parallelization of numerical solution of the complete Navier - Stokes equations system in the vertical spatial coordinate. This parallelization option can significantly increase the computing performance and reduce the overall time of counting. A comparison of the results of calculation of one of options of gas flow in the upward swirling flow obtained by serial and parallel programs is presented.

scholarly journals Three-dimensional modeling of Ge₁₋xSix by the traveling solvent method to study the effect of gravity orientations under different rotational speed

2021 ◽  
Author(s):  
Mahwish Sohail
Keyword(s):  
Crystal Growth ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Computational Time ◽  
Solvent Method ◽  
Continuity Equations ◽  
Element Technique

This thesis presents a 3-D numerical simulation study for the growth of germanium-silicon (Ge₁₋xSix) under different gravity orientation and axial rotation. The process use for crystal growth of Ge₁₋xSix is traveling solvent method known as TSM. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. In this model a mesh sensitivity analysis his been carried out to find an optimum mesh which provides accurate results while saving computational time. The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of gravity orientation and crucible rotation to the traveling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation showed to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three-dimensional modeling of Ge₁₋xSix by the traveling solvent method to study the effect of gravity orientations under different rotational speed

2021 ◽  
Author(s):  
Mahwish Sohail
Keyword(s):  
Crystal Growth ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Computational Time ◽  
Solvent Method ◽  
Continuity Equations ◽  
Element Technique

This thesis presents a 3-D numerical simulation study for the growth of germanium-silicon (Ge₁₋xSix) under different gravity orientation and axial rotation. The process use for crystal growth of Ge₁₋xSix is traveling solvent method known as TSM. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. In this model a mesh sensitivity analysis his been carried out to find an optimum mesh which provides accurate results while saving computational time. The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of gravity orientation and crucible rotation to the traveling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation showed to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three-Dimensional Modeling of the Rotation Effect on the Growth of Ge₁₋ˣSiˣ, by the Traveling Solvent Method

2021 ◽  
Author(s):  
Theodore Jason Makriyannis
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Navier Stokes ◽  
Computational Time ◽  
Solvent Method ◽  
Three Dimensional Modeling ◽  
Continuity Equations ◽  
Element Technique

The travelling solvent method known as TSM is a process used to produce pure and homogeneous crystals. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. A three-dimensional numerical simulation for the growth of Ge1-xSix by the travelling solvent method under axial rotation has been modelled. In this model a mesh sensitivity analysis has been carried out to find an optimum mesh which provides accurate results while saving computational time, The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of crucible rotation to the travelling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. The application of different rotational speeds on the solvent has also been investigated. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation was found to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

Three-Dimensional Laminar Flow in a Rotating Multiple-Pass Square Channel With Sharp 180-Deg Turns

1998 ◽  
Vol 120 (3) ◽  
pp. 488-495 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Dong-Yuo Lai
Keyword(s):  
Fluid Flow ◽  
Laminar Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rotation Speed ◽  
Three Dimensional ◽  
Elliptic Type ◽  
Straight Channel ◽  
Through Flow ◽  
Sharp Turn

This paper presents a study of three-dimensional laminar flow in a rotating multiplepass channel connected with 180-deg sharp bends. Fluid-flow fields are calculated for the entire domain via the Navier-Stokes equations through a finite-difference scheme. For closure of this elliptic-type problem, periodical fully developed conditions are employed between the entrance and exit of the two-pass module. Experiments for the stationary two-pass channel are conducted to validate the numerical procedure and data. The emphasis of the present prediction is on the rotating and through-flow rate effects on the fluid-flow and friction characteristics in the straight channel as well as in the turn region. It is found that the rotation-induced Coriolis force significantly raises the wall-friction losses in the straight channel. However, the head loss of the sharp turn is decreased with increasing rotation speed, because the flow discrepancy between the inlet and outlet of the sharp turn is less significant for the higher rotation speed. Moreover, overall pressure-drop penalty across the two-pass channel is found to be enhanced by the rotation speed as well as the duct through-flow rate.

A computational study of the topology of vortex breakdown

1991 ◽  
Vol 435 (1894) ◽  
pp. 321-337 ◽  
Keyword(s):  
Topological Structure ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Computational Study ◽  
Double Helix ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Streamwise Direction ◽  
Navier Stokes Equations ◽  
Axial Velocity Distribution

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier–Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

scholarly journals ACCOUNTING INFLUENCE OF CENTRIFUGAL FORCE IN THE NUMERICAL MODELING OF RISING SWIRLED GAS FLOW

2015 ◽  
pp. 92-97
Author(s):  
S. P. Bautin ◽  
A. G. Obukhov
Keyword(s):  
Centrifugal Force ◽  
Gas Flow ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Power Characteristics ◽  
Gas Dynamic

In work the consistent inclusion of centrifugal force in the numerical calculations of three-dimensional gas-dynamic characteristics of the unsteady flow of compressible viscous heat-conducting gas in an upward swirling flow caused by the vertical cold blowing. Provides detailed conversion of the complete system of Navier-Stokes equations associated with consistent view of the centrifugal force. Results of thermodynamic calculations and comparisons, speed and power characteristics of emerging upward swirling flows. There was a slight influence of the centrifugal force on the basic parameters of the gas-dynamic study of complex flows of gas.

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