http://www.cfd-online.com/W/index.php?title=Special:Contributions/Dmitry&feed=atom&limit=50&target=Dmitry&year=&month=CFD-Wiki - User contributions [en]2016-10-24T21:14:40ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/2-D_Mach_3_Wind_Tunnel_With_a_Step2-D Mach 3 Wind Tunnel With a Step2007-07-19T12:15:24Z<p>Dmitry: New page: '''Preface.''' 2D test problem was introduced more then fifty years ago in the paper by Emery [1], but it overall public acknowledgement was taken place after paper by Woodward and Colella...</p>
<hr />
<div>'''Preface.''' 2D test problem was introduced more then fifty years ago in the paper by Emery [1], but it overall public acknowledgement was taken place after paper by Woodward and Colella was published in 1984 [2]. This problem has proven to be useful test for a large number of numerical methods, schemes and algorithms during large number of years. <br />
<br />
'''Geometry.''' The wind tunnel is 1 length unit wide and 3 length unit long. The step is 0.2 length units high and is located 0.6 length units from the left-hand end of the tunnel. We assume here that tunnel has an infinity width, or in other words we consider two-dimensional planar base flow. <br />
<br />
'''Boundary and initial conditions.''' The test has the following boundary conditions: flow inlet conditions at the felt (basically so-called pressure-inlet conditions are used) and at the right all gradients are assumed to vanish. Since the exit velocity is always supersonic the exit boundary conditions has no effect on the flow. Along the walls of the tunnel reflecting boundary conditions are applied. Initially wind tunnel is filled with a inviscid gamma-law gas (<math>\gamma</math> = 1.4), which everywhere has density 1.4, pressure 1.0 and velocity 3. Gas with such properties is continually fed in from the left-hand boundary. <br />
<br />
'''Singular point.''' The corner of the step is the center of rarefaction fan and hence is a singular point of the flow. Frankly speaking the flow is seriously affected by large numerical errors generated just in the neighborhood of this singular point if nothing special is not undertaken. The modern study shown that the presence of such point in flow may lead to phase – time delay [3]. Generally there are two ways to reduce or eliminate this point. The original idea was proposed by Woodward [2] and consisted of applying special boundary conditions near the corner of the step, which is based on the assumption of a nearly steady flow in this region. The density was reset here so that the entropy has the same value as in the zone just to the left and below the corner of the step. The magnitudes of velocities (but no their directions) were reset also, so that the sum of enthalpy and kinetic energy per unit mass has the same value as in the same zone to set the entropy. More sophisticated and accurate approach may be applied to solve this problem at present. One can make a little fillet to avoid the straight angle in the step corner. Robust unstructured meshes allow additionally preparing some grid refinement in this region.<br />
<br />
'''Numerical solution.''' The time evolution, up to time 4 in the wind tunnel may be found in [2]. Since the flow at time 4 is still unsteady and steady flow develops by time 12, it’s accepted in general to focus on the flow structure at time 4. Typical state-of-the-art solution obtained in one the commercial CFD codes based on dynamic local grid refinement is displayed in Fig1: (a) – unstructured triangular mesh, contours of log density, contours of the quantity <math>A=p/\rho^\gamma</math> (or numerical noise), which is a function of entropy. Main discordance, which should be underlined - Kelvin-Helmholtz instability development starting from the trinity point - intersection of the main strong shock wave and upper Mach disk. Such instabilities evolution is amplified by numeric errors generated in the trinity point while shock waves interaction independently of mesh density. Increasing the dissipation of the numeric scheme near such a shock-waves interaction can eliminate this effect. <br />
<br />
[[Image:figure11.jpg]]<br />
<br />
'''References'''<br />
<br />
[1] Emery A.E. An evaluation of several differencing methods for inviscid fluid flow problems// Journal of Computational Physics, Vol. 2 (1968). 306-331.<br />
<br />
[2] Woodward P., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks // Journal of Computational Physics. 1984. V.54, PP.115-173.<br />
<br />
[3] Lysenko D.A., Isaev S.A. Testing of the FLUENT package in calculations of supersonic flow in a step channel// Journal of Engineering Physics and Thermophysics. 2004. Vol:77(4). PP. 857-860.</div>Dmitryhttp://www.cfd-online.com/Wiki/File:Figure11.jpgFile:Figure11.jpg2007-07-19T12:10:48Z<p>Dmitry: </p>
<hr />
<div></div>Dmitryhttp://www.cfd-online.com/Wiki/Validation_and_test_casesValidation and test cases2007-07-19T12:03:44Z<p>Dmitry: /* 2-D test cases */</p>
<hr />
<div>Suitable cases for the validation and benchmarking of CFD codes. Articles should include a description of the case, data to compare with, and possibly contributed solutions. We could definitely use more three dimensional cases (only one has an article currently).<br />
<br />
== Introduction ==<br />
A common issue that arises in CFD is the validation and testing of the code to be used for a computation. The code can be a newly written one (the testing then is to determine if the code works properly), or it can be a commercial code (the testing then is to determine if the code is suitable for the task at hand). Some of the cases described in the article below are easy to solve, while others are more difficult.<br />
<br />
<br />
<br />
When choosing a case for validation purposes, keep the following in mind:<br />
<br />
* Don't try to do too much. If you have written a code, try the 2-D cases first. If you are testing a commercial code, it is probably best to try (vendor supplied) tutorial cases, and then move on to a test case that is like what the code will be expected to do.<br />
* Some of these cases are still active areas of research, particularly for LES and the like. <br />
* Don't rely just on the information here. The authoritative source is always the literature, so look at the references cited in the articles for definitive details.<br />
<br />
== 1-D test cases ==<br />
<br />
*[[Shock tube problem]]<br />
<br />
== 2-D test cases ==<br />
<br />
*[[2-D vortex in isentropic flow]]<br />
*[[2-D Riemann problem]]<br />
*[[2-D laminar/turbulent driven square cavity flow]]<br />
*[[Circular advection]]<br />
*[[Explosion test in 2-D]]<br />
*[[Lid-driven cavity problem]]<br />
*[[Jeffery-Hamel flow]]<br />
*[[Laminar flow over backward facing step]]<br />
*[[Turbulent flow over backward facing step]]<br />
*[[Flow around a circular cylinder]]<br />
*[[Flow across a square cylinder]]<br />
*[[NACA0012 airfoil]]<br />
*[[RAE2822 airfoil]]<br />
*[[Ringleb flow]]<br />
*[[Scramjet intake]]<br />
*[[Suddhoo-Hall airfoil]]<br />
*[[Turbulent flat-plate]]<br />
*[[Viscous diffusion of multiple vortex system]]<br />
*[[Williams airfoil]]<br />
*[[2-D ramp in channel problem]]<br />
*[[2-D Single Mode Rayleigh-Taylor Instability]]<br />
*[[2-D Single Mode Richtmyer-Meshkov Instability]]<br />
*[[2-D Mach 3 Wind Tunnel With a Step]]<br />
<br />
== 3-D test cases ==<br />
<br />
*[[Ahmed body]]<br />
*[[Flow in the 180 degree U-bend square duct]]<br />
*[[DARPA SUBOFF model]]<br />
*[[Hypersonic blunt body flow]]<br />
*[[Onera M6 wing]]<br />
*[[Turbomachinery]]<br />
*[[Eckardt Centrifugal Compressor]]<br />
*[[NASA Rotor 37 for axial rotors]]<br />
*[[NASA Rotor 67 for axial fans]]<br />
*[[3-D Single Mode Rayleigh-Taylor Instability]]<br />
*[[3-D Single Mode Richtmyer-Meshkov Instability]]<br />
<br />
== Transition test cases ==<br />
*[[2D Cascade]]<br />
<br />
== Aeroacoustics == <br />
<br />
=== Workshops ===<br />
<br />
*[[ICASE/LaRC workshop on benchmark problems in computational aeroacoustics]]<br />
<br />
=== 1-D test cases === <br />
*[[Linear wave propagation]]<br />
*[[Non linear wave propagation]]<br />
*[[Burgers equation]]<br />
<br />
=== 2-D test cases ===<br />
*[[2-D linearised Euler equation]]<br />
*[[2-D scattering from a cylinder]] <br />
*[[Driven cavity with feedback]]<br />
<br />
=== 3-D test cases === <br />
*[[Driven cavity with feedback]]<br />
*[[3-D Scattering from a cylinder]]<br />
<br />
== External links ==<br />
<br />
*[http://www.cfd-online.com/Links/refs.html#validation CFD Online links to validation cases]<br />
*[http://www.grc.nasa.gov/WWW/wind/valid/tutorial/tutorial.html Tutorial on CFD verification and validation]<br />
*[http://journaltool.asme.org/Templates/JFENumAccuracy.pdf Statement on the content of numerical accuracy] of [http://scitation.aip.org/ASMEJournals/Fluids/ Journal of Fluids Engineering]<br />
*[http://cfl3d.larc.nasa.gov/Cfl3dv6/cfl3dv6_testcases.html CFL3D test cases]<br />
*[http://ad-www.larc.nasa.gov/tsab/usm3d/TESTCASES.html USM3D test cases]<br />
*[http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw AIAA CFD drag prediction workshop]<br />
*[http://www.grc.nasa.gov/WWW/wind/valid/validation.html NPARC Alliance CFD verification and validation web-site]<br />
*[http://www.aero.gla.ac.uk/Research/CFD/projects/cfdval/TN02-016/TN02-016.html Test case validation database] at CFD Lab, University of Glasgow<br />
*[http://www.csar.uiuc.edu/F_viz/gallery/VnV/SAND2002-0529.pdf Verification and validation in computational fluid dynamics]<br />
*[http://flowlab.fluent.com/exercise/index.htm Many of the standard cfd excercises are validated using Fluent, the files are available here. The case/data files can be found inside each template library.]</div>Dmitryhttp://www.cfd-online.com/Wiki/2-D_laminar/turbulent_driven_square_cavity_flow2-D laminar/turbulent driven square cavity flow2007-03-22T10:45:16Z<p>Dmitry: </p>
<hr />
<div>== Itroduction ==<br />
<br />
A classical test problem is numerical simulation of a laminar/turbulent flow of an incompressible viscous fluid in a square cavity with the upper moving boundary. It has long since been a "testing area" for approbation of approximation schemes for terms in initial equations as well as of computational models and methods. A large number of calculation data concerning this problem have been accumulated. Therefore, it makes sense to return periodically to the solution of the indicated problem at different levels of development of computer systems and software for verification and analysis of the computational codes developed. <br />
<br />
[[Image:Cavity2d.jpg]]<br />
<br />
The interest shown by researchers in the problem on a circulation flow in a cavity was stimulated in the past by the relatively low level of computational resources required for solving it because, in this case, the computational region is limited and, therefore, a small number of grid nodes are selected and simple boundary conditions are set. For this problem, the first solutions of Navier–Stokes equations written, for economy of computational resources, in transformed vorticity–stream function variables were obtained. The calculations were performed not even on a computer but by brigades of specialists. <br />
<br />
When computers appeared, the indicated problem remained, as before, the focus of attention of specialists developing computational methods. A detailed analysis of methods concerning the problem considered that appeared in the period from the 1960s to the late 1980s is given in a set of monographs (for example 1, 2, 3). One of the first works in the area of numerical investigation of a viscous-fluid flow in a square cavity began thirty years ago [1] on a BESM-4 computer containing 21 × 21 grid nodes in one memory cube. At that time, in the mid-1970s, high-accuracy Arakava schemes of the second and fourth order of approximation and nonuniform grids were used for the first time for solving Navier–Stokes equations. <br />
<br />
One of the most important scientific achievements of the CFD in the 1980s was a numerical solution of the diffusion problem, since this problem is associated with errors in approximation of convective terms of equations. In simulation of separation flows, a necessary condition for obtaining an exact result is the use of schemes with a low numerical viscosity (upwind schemes of the second and higher orders of approximation of the type of the Leonard scheme with quadratic interpolation, the Agarval scheme, and others) for representation of convective terms in transfer equations. At the same time, it has been established that the first-order schemes give erroneous solutions at high Reynolds numbers even in the case where multigrid methods are used. <br />
<br />
Progress in computational engineering and, especially, widespread use of personal computers in the 1980s and subsequent years have made it possible, first of all, to develop universal first-wave codes of applied programs, such as the PHOENIX, FLOW3D, and FIDAP, and then more modern information products/commercial CFD codes such as FLUENT, StarCD, and CFX. When computers with a large memory and a high CPU speed appeared, instead of the Navier–Stokes equations in transformed variables, Navier–Stokes equations written in physical variables — Cartesian velocity or pressure components — began to be predominantly used. Moreover, this made it possible to substantially (by an order of magnitude and more) increase the number of computational cells and increase the resolution of nearwall region for this problem.<br />
<br />
References <br />
<br />
[1] I. A. Belov, I. P. Ginzburg, and S. A. Isaev, Motion and heat transfer in a closed region with moving boundaries, Vestn. LGU, No. 13, 41–50 (1976).<br />
<br />
[2] I. A. Belov and N. A. Kudryavtsev, Heat Transfer and Resistance of Tube Bundles [in Russian], Energoatomizdat, Leningrad (1987).<br />
<br />
[3] I. A. Belov, S. A. Isaev, and V. A. Korobkov, Problems and Methods of Calculation of Separation Incompressible-Fluid Flows [in Russian], Sudostroenie, Leningrad (1989).<br />
<br />
== Literature == <br />
<br />
[1] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
SIMULATION OF A CIRCULATION LAMINAR FLOW AROUND A SQUARE CAVITY WITH A MOBILE BOUNDARY AT HIGH REYNOLDS NUMBERS WITH THE USE OF VP2/3 AND THE FLUENT PACKAGE. Journal of Engineering Physics and Thermophysics, Vol. 78, No. 4, 2005<br />
<br />
[2] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
Complex Analysis of turbulence models, algorithms, and grid structures at the computation of recirculating flow in a cavity by means of VP2/3 and FLUENT packages. Part 1. Scheme factors influence. Thermophysics and Aeromechanics, 2005, Vol: 12, No 4. <br />
<br />
[3] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
Complex Analysis of turbulence models, algorithms, and grid structures at the computation of recirculating flow in a cavity by means of VP2/3 and FLUENT packages. Part 2. Estimation of models adequacy. Thermophysics and Aeromechanics, 2006 , Vol 13, No 1.</div>Dmitryhttp://www.cfd-online.com/Wiki/2-D_laminar/turbulent_driven_square_cavity_flow2-D laminar/turbulent driven square cavity flow2007-03-22T10:41:31Z<p>Dmitry: </p>
<hr />
<div>A classical test problem is numerical simulation of a laminar/turbulent flow of an incompressible viscous fluid in a square cavity with the upper moving boundary. It has long since been a "testing area" for approbation of approximation schemes for terms in initial equations as well as of computational models and methods. A large number of calculation data concerning this problem have been accumulated. Therefore, it makes sense to return periodically to the solution of the indicated problem at different levels of development of computer systems and software for verification and analysis of the computational codes developed. <br />
<br />
[[Image:Cavity2d.jpg]]<br />
<br />
The interest shown by researchers in the problem on a circulation flow in a cavity was stimulated in the past by the relatively low level of computational resources required for solving it because, in this case, the computational region is limited and, therefore, a small number of grid nodes are selected and simple boundary conditions are set. For this problem, the first solutions of Navier–Stokes equations written, for economy of computational resources, in transformed vorticity–stream function variables were obtained. The calculations were performed not even on a computer but by brigades of specialists. <br />
<br />
When computers appeared, the indicated problem remained, as before, the focus of attention of specialists developing computational methods. A detailed analysis of methods concerning the problem considered that appeared in the period from the 1960s to the late 1980s is given in a set of monographs (for example 1, 2, 3). One of the first works in the area of numerical investigation of a viscous-fluid flow in a square cavity began thirty years ago [1] on a BESM-4 computer containing 21 × 21 grid nodes in one memory cube. At that time, in the mid-1970s, high-accuracy Arakava schemes of the second and fourth order of approximation and nonuniform grids were used for the first time for solving Navier–Stokes equations. <br />
<br />
One of the most important scientific achievements of the CFD in the 1980s was a numerical solution of the diffusion problem, since this problem is associated with errors in approximation of convective terms of equations. In simulation of separation flows, a necessary condition for obtaining an exact result is the use of schemes with a low numerical viscosity (upwind schemes of the second and higher orders of approximation of the type of the Leonard scheme with quadratic interpolation, the Agarval scheme, and others) for representation of convective terms in transfer equations. At the same time, it has been established that the first-order schemes give erroneous solutions at high Reynolds numbers even in the case where multigrid methods are used. <br />
<br />
Progress in computational engineering and, especially, widespread use of personal computers in the 1980s and subsequent years have made it possible, first of all, to develop universal first-wave codes of applied programs, such as the PHOENIX, FLOW3D, and FIDAP, and then more modern information products/commercial CFD codes such as FLUENT, StarCD, and CFX. When computers with a large memory and a high CPU speed appeared, instead of the Navier–Stokes equations in transformed variables, Navier–Stokes equations written in physical variables — Cartesian velocity or pressure components — began to be predominantly used. Moreover, this made it possible to substantially (by an order of magnitude and more) increase the number of computational cells and increase the resolution of nearwall region for this problem.<br />
<br />
References <br />
<br />
[1] I. A. Belov, I. P. Ginzburg, and S. A. Isaev, Motion and heat transfer in a closed region with moving boundaries, Vestn. LGU, No. 13, 41–50 (1976).<br />
<br />
[2] I. A. Belov and N. A. Kudryavtsev, Heat Transfer and Resistance of Tube Bundles [in Russian], Energoatomizdat, Leningrad (1987).<br />
<br />
[3] I. A. Belov, S. A. Isaev, and V. A. Korobkov, Problems and Methods of Calculation of Separation Incompressible-Fluid Flows [in Russian], Sudostroenie, Leningrad (1989).<br />
<br />
[4] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
SIMULATION OF A CIRCULATION LAMINAR FLOW AROUND A SQUARE CAVITY WITH A MOBILE BOUNDARY AT HIGH REYNOLDS NUMBERS WITH THE USE OF VP2/3 AND THE FLUENT PACKAGE. Journal of Engineering Physics and Thermophysics, Vol. 78, No. 4, 2005<br />
<br />
[5] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
Complex Analysis of turbulence models, algorithms, and grid structures at the computation of recirculating flow in a cavity by means of VP2/3 and FLUENT packages. Part 1. Scheme factors influence. Thermophysics and Aeromechanics, 2005, Vol: 12, No 4. <br />
<br />
[6] Isaev S. A., Baranov P. A., Kudryavtsev N. A., Lysenko D. A., and Usachov A. E.<br />
Complex Analysis of turbulence models, algorithms, and grid structures at the computation of recirculating flow in a cavity by means of VP2/3 and FLUENT packages. Part 2. Estimation of models adequacy. Thermophysics and Aeromechanics, 2006 , Vol 13, No 1.</div>Dmitryhttp://www.cfd-online.com/Wiki/File:Cavity2d.jpgFile:Cavity2d.jpg2007-03-22T10:36:09Z<p>Dmitry: </p>
<hr />
<div></div>Dmitryhttp://www.cfd-online.com/Wiki/Validation_and_test_casesValidation and test cases2007-03-22T10:27:05Z<p>Dmitry: /* 2-D test cases */</p>
<hr />
<div>Suitable cases for the validation and benchmarking of CFD codes. Articles should include a description of the case, data to compare with, and possibly contributed solutions. We could definitely use more three dimensional cases (only one has an article currently).<br />
<br />
== Introduction ==<br />
A common issue that arises in CFD is the validation and testing of the code to be used for a computation. The code can be a newly written one (the testing then is to determine if the code works properly), or it can be a commercial code (the testing then is to determine if the code is suitable for the task at hand). Some of the cases described in the article below are easy to solve, while others are more difficult.<br />
<br />
<br />
<br />
When choosing a case for validation purposes, keep the following in mind:<br />
<br />
* Don't try to do too much. If you have written a code, try the 2-D cases first. If you are testing a commercial code, it is probably best to try (vendor supplied) tutorial cases, and then move on to a test case that is like what the code will be expected to do.<br />
* Some of these cases are still active areas of research, particularly for LES and the like. <br />
* Don't rely just on the information here. The authoritative source is always the literature, so look at the references cited in the articles for definitive details.<br />
<br />
== 1-D test cases ==<br />
<br />
*[[Shock tube problem]]<br />
<br />
== 2-D test cases ==<br />
<br />
*[[2-D vortex in isentropic flow]]<br />
*[[2-D Riemann problem]]<br />
*[[2-D Laminar/Turbulent driven square cavity flow]]<br />
*[[Circular advection]]<br />
*[[Explosion test in 2-D]]<br />
*[[Lid-driven cavity problem]]<br />
*[[Jeffery-Hamel flow]]<br />
*[[Laminar Flow over backward facing step]]<br />
*[[Turbulent Flow over backward facing step]]<br />
*[[Flow around a circular cylinder]]<br />
*[[Flow across a square cylinder]]<br />
*[[NACA0012 airfoil]]<br />
*[[RAE2822 airfoil]]<br />
*[[Ringleb flow]]<br />
*[[Scramjet intake]]<br />
*[[Suddhoo-Hall airfoil]]<br />
*[[Turbulent flat-plate]]<br />
*[[Viscous diffusion of multiple vortex system]]<br />
*[[Williams airfoil]]<br />
*[[2d ramp in channel problem]]<br />
<br />
== 3-D test cases ==<br />
<br />
*[[Ahmed body]]<br />
*[[Flow in the 180 degree U-bend square duct]]<br />
*[[DARPA SUBOFF model]]<br />
*[[Hypersonic blunt body flow]]<br />
*[[Onera M6 wing]]<br />
*[[Turbomachinery]]<br />
*[[Eckardt Centrifugal Compressor]]<br />
*[[NASA Rotor 37 for axial rotors]]<br />
*[[NASA Rotor 67 for axial fans]]<br />
<br />
== Transition test cases ==<br />
*[[2D Cascade]]<br />
<br />
== Aeroacoustics == <br />
<br />
=== Workshops ===<br />
<br />
*[[ICASE/LaRC workshop on benchmark problems in computational aeroacoustics]]<br />
<br />
=== 1-D test cases === <br />
*[[Linear wave propagation]]<br />
*[[Non linear wave propagation]]<br />
*[[Burgers equation]]<br />
<br />
=== 2-D test cases ===<br />
*[[2-D linearised Euler equation]]<br />
*[[2-D scattering from a cylinder]] <br />
*[[Driven cavity with feedback]]<br />
<br />
=== 3-D test cases === <br />
*[[Driven cavity with feedback]]<br />
*[[3-D Scattering from a cylinder]]<br />
<br />
== External links ==<br />
<br />
*[http://www.cfd-online.com/Links/refs.html#validation CFD Online links to validation cases]<br />
*[http://www.grc.nasa.gov/WWW/wind/valid/tutorial/tutorial.html Tutorial on CFD verification and validation]<br />
*[http://journaltool.asme.org/Templates/JFENumAccuracy.pdf Statement on the content of numerical accuracy] of [http://scitation.aip.org/ASMEJournals/Fluids/ Journal of Fluids Engineering]<br />
*[http://cfl3d.larc.nasa.gov/Cfl3dv6/cfl3dv6_testcases.html CFL3D test cases]<br />
*[http://ad-www.larc.nasa.gov/tsab/usm3d/TESTCASES.html USM3D test cases]<br />
*[http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw AIAA CFD drag prediction workshop]<br />
*[http://www.grc.nasa.gov/WWW/wind/valid/validation.html NPARC Alliance CFD verification and validation web-site]<br />
*[http://www.aero.gla.ac.uk/Research/CFD/projects/cfdval/TN02-016/TN02-016.html Test case validation database] at CFD Lab, University of Glasgow<br />
*[http://www.csar.uiuc.edu/F_viz/gallery/VnV/SAND2002-0529.pdf Verification and validation in computational fluid dynamics]</div>Dmitryhttp://www.cfd-online.com/Wiki/Flow_around_a_circular_cylinderFlow around a circular cylinder2007-03-21T10:45:00Z<p>Dmitry: /* Literature */</p>
<hr />
<div>== Introduction ==<br />
The flow around a (geometrically) two-dimensional circular cylinder is case that has been used both as a validation case and as a legitimate research case. At very low Reynolds numbers, the flow is steady and symmetrical. As the Reynolds number is increased, asymmetries and time-dependence develop, eventually resulting the famous Von Karmann vortex street, and then on to turbulence. The problem geometry is two-dimensional and there is some variation in the details (both geometry and boundary conditions) that can be used. A typical geometry is shown below (not to scale).<br />
<br />
[[Image:VTC_circularcyl_geometry.png]]<br />
<br />
The exterior boundaries are generally placed very far from the cylinder surface to avoid interaction between the boundary conditions. Grid generation is not especially difficult, though care must be taken to properly resolve the near-wall region as the Reynolds number is increased.<br />
<br />
This problem has been solved as both a laminar flow and a turbulent flow. The DNS, LES, and the transitional cases are still considered a research cases. Many different numerical techniques have been used to solve this problem, but one usual comparison is the the resulting Strouhal frequency (if the simulation is in the proper Reynolds number range.<br />
<br />
Many variations on the geometry are possible. One can impose symmetry by cutting the solution domain in half (along the x-direction). This will reduce the computational burden, but will reduce the range of physical applicability of the simulations (asymmetries develop at rather moderate Reynolds numbers). Another variation it to impose periodic conditions in the y-direction - which gives us an array of cylinders rather than just one cylinder. There has also been work done simulating the response of spinning cylinders both in a free stream and near walls.<br />
<br />
==Literature==<br />
<br />
There are a tremendous number of references for that problem. Here is a selection of some:<br />
<br />
[1] Ahmad, R.A., 1996, Steady-state numerical solution of the Navier-Stokes and energy equations around a horizontal cylinder at moderate Reynolds numbers from 100 to 500, Heat Transfer Engg., 17: 31-81.<br />
<br />
[2] Chakraborty, J., Verma, N. and Chhabra, R. P., 2004, Wall effects in the flow past a circular cylinder in a plane channel: a numerical study, Chem. Engng. Processing, 43: 1529-1537.<br />
<br />
[3] Coutanceau, M. and Bouard, R., 1977, Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1: Steady flow, J. Fluid Mech., 79: 231-256.<br />
<br />
[4] Coutanceau, M. and Defaye, J.-R., 1991 Circular cylinder wake configurations: a flow visualization survey, Appl. Mech. Rev., 44: 255-305.<br />
<br />
[5] D'Alessio, S. J. D. and Dennis, S. C. R., 1994, A vorticity model for viscous flow past a cylinder, Comp. Fluids, 23: 279-293.<br />
<br />
[6] Dennis, S. C. R. and Chang, G.-Z., 1970, Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100, J. Fluid Mech., 42: 471-489.<br />
<br />
[7] Dennis, S. C. R. and Hudson, J. D., 1995, An $h^4$ accurate vorticity-velocity formulation for calculating flow past circular cylinder, Int. J. Numer. Meth. Fluids, 21: 489-497.<br />
<br />
[8]Dennis, S. C. R., Hudson, J. D. and Smith, N., 1968, Steady laminar forced convection from a circular cylinder at low Reynolds numbers, Phys. Fluids, 11: 933-940.<br />
<br />
[9]Fornberg, B., 1980, A numerical study of steady viscous flow past a circular cylinder, J. Fluid Mech., 98: 819-855.<br />
<br />
[10] Fornberg, B., 1985, Steady viscous flow past a circular cylinder up to Reynolds number 600, J. Comp. Phys., 61: 297-320.<br />
<br />
[11] Ding, H., Shu, C., Yeo, K. S. and Xu, D., 2004, Simulations of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference scheme, Comput. Methods Appl. Mech. Engng., 193: 727-744.<br />
<br />
[12] Hamielec, A. E. and Raal, J. D., 1969, Numerical studies of viscous flow around circular cylinders, Phys. Fluids, 12: 11-17.<br />
<br />
[13] Kawaguti, M. and Jain, P., 1966, Numerical study of a viscous flow past a circular cylinder, J. Phys. Soc. Jpn., 21: 2055-2062.<br />
<br />
[14] Sucker, D. and Brauer, H., 1975, Fluiddynamik bie quer angestromten Zylindern, Warme- and Stoffubertagung, 8: 149-158.<br />
<br />
[15] Takami, H. and Keller, H. B., 1969, Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder, High-Speed Computing in Fluid Dynamics The Phys. Fluids Supplement II, 12: 51-56. <br />
<br />
M.M. Zdravkovich, Flow Around Circular Cylinders, Vol. 1 Fundamentals, Oxford University Press, 1997<br />
<br />
[2] M.M. Zdravkovich, Flow Around Circular Cylinders, Vol. 2 Applications, Oxford University Press, 2003 <br />
<br />
[1] Norberg, C. (2003). Fluctuating lift on a circular cylinder: Review and new measurements, Journal of Fluids and Structures 17 (1), pp. 57-96 29<br />
<br />
[2] Norberg, C. (2001). Flow around a circular cylinder: Aspects of fluctuating lift, Journal of Fluids and Structures 15 (3-4), pp. 459-469<br />
<br />
[3]Norberg, C. (1994). Experimental investigation of the flow around a circular cylinder: influence of aspect ratio, Journal of Fluid Mechanics 258, pp. 287-316 96<br />
<br />
[4] Norberg, C., Sunden, B. J. (1987). Turbulence and Reynolds number effects on the flow and fluid forces on a single cylinder in cross flow, FLUIDS & STRUCT. 1 (3 , Jul. 1987), pp. 337-357 9<br />
<br />
[5] Norberg, C. (1985). INTERACTION BETWEEN FREESTREAM TURBULENCE AND VORTEX SHEDDING FOR A SINGLE TUBE IN CROSS-FLOW, Journal of Wind Engineering and Industrial Aerodynamics 23 (1-3), pp. 501-514<br />
<br />
[16] Isaev S. A., Leontiev A. I., Kudryavtsev N. A., Baranova T. A., Lysenko D. A. (2005).<br />
Numerical Simulation of Unsteady-State Heat Transfer under Conditions of Laminar Transverse Flow past a Circular Cylinder, High Temperature. Vol. 43, No. 5, pp. 746–759<br />
<br />
[17] Isaev S.A., Baranov P.A., Kudryavtsev N.A., Lysenko D.A., Usachov A.E. (2005). <br />
Comparative analysis of the calculation data on an unsteady flow around a circular cylinder obtained using the VP2/3 and Fluent packages and the Spalart-Allmaras and Menter turbulence models // J. Engineering Physics and Thermophysics. Vol.78. No.6. pp. 1199-2013.<br />
<br />
== Laminar Simulations ==<br />
<br />
== Turbulent Simulations ==</div>Dmitry