From cec5f48ece82f6a769030705aa7272007a8b9101 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 09:53:07 +0100 Subject: [PATCH 01/25] Update tutorials.yml Added the unsteady fsi entry --- _data/tutorials.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/_data/tutorials.yml b/_data/tutorials.yml index e0f7787d..85806de3 100644 --- a/_data/tutorials.yml +++ b/_data/tutorials.yml @@ -37,6 +37,7 @@ - title: Multiphysics tutorials: - Static_FSI + - Unsteady_FSI_Python - title: Design Features tutorials: From c250bd55b2171a527461a0a041bd0621e23ad012 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 09:56:15 +0100 Subject: [PATCH 02/25] Initial commit unsteady_fsi --- _tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi | 1 + 1 file changed, 1 insertion(+) create mode 100644 _tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi b/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi new file mode 100644 index 00000000..bf0297b0 --- /dev/null +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi @@ -0,0 +1 @@ +## Test From 2028e55fa10585137968c0e52f75457ebcb37127 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 10:02:17 +0100 Subject: [PATCH 03/25] Renamed tutorial Dynamic_FSI_Python --- _data/tutorials.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_data/tutorials.yml b/_data/tutorials.yml index 85806de3..e69dbc6b 100644 --- a/_data/tutorials.yml +++ b/_data/tutorials.yml @@ -37,7 +37,7 @@ - title: Multiphysics tutorials: - Static_FSI - - Unsteady_FSI_Python + - Dynamic_FSI_Python - title: Design Features tutorials: From 67cda58a6bf6f08629d8894eb8f4123d89780bcb Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 12:12:08 +0100 Subject: [PATCH 04/25] Some modifications to .md file --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 368 ++++++++++++++++++ .../Unsteady_FSI_Python/unsteady_fsi | 1 - 2 files changed, 368 insertions(+), 1 deletion(-) create mode 100644 _tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md delete mode 100644 _tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md new file mode 100644 index 00000000..c3ad1452 --- /dev/null +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -0,0 +1,368 @@ +--- +title: Dynamic Fluid-Structure Interaction (FSI) using the Python wrapper and an external structural solver +permalink: /tutorials/Dynamic_FSI_Python/ +written_by: Nicola-Fonzi +for_version: 7.0.6 +revised_by: +revision_date: +revised_version: +solver: Multiphysics +requires: SU2_CFD, PYTHON WRAPPER +complexity: intermediate +follows: Static_FSI +--- +### Goals + +This tutorial shows how to exploit the capabilities of the Python wrapper to couple SU2 with an external strutural solver. The problem at hand consist in a NACA 0012 airfoil, +free to pitch and plunge, with given stiffnesses, immersed in a flow with varying Mach number. The two frequencies of the modes of the structure will vary as the speed is increased, reaching +a point when the aeroelastic system will be unstable. The classical pitch-plunge flutter will then be visible. + +The considered case has been presented in $$^1$$, the reader is encouraged to refer to that reference for further details on the problem. + +The structual solver used in this example loosely couples SU2 with the commercial code Nastran, keeping the results of general interest. Indeed, linear strctures of arbitrary +complexity can be analysed with the same workflow. + +Summarizing, this document will cover: +- Preparing a FSI analysis to be used with the python wrapper +- Using the strctural solver for Nastran models with SU2 +- Important keywords for the fsi and solid solver config files + +A sketch of the problem at hand is presented below: + +![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/Setup.png) + +### Resources + +You can find the resources for this tutorial in the folder [fsi/steady_state](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [FSI config file](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_fsi_steady.cfg) and two sub-config files for the [flow](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_channel.cfg) and [structural](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_cantilever.cfg) subproblems. + +Moreover, you will need two mesh files for the [flow domain](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/mesh_channel.su2) and the [cantilever](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/mesh_cantilever.su2). + +### Background + +The solution process will follow a very similar flow as the one explained in [this](https://su2code.github.io/tutorials/Static_FSI/) tutorial, +which you should complete before stepping to the present one. The fluid and structural solutions will be obtained separately, iterating between them until convergence. +Here, the difference is due to the fact that the simulation is unsteady. Thus, this inner iteration between fluid and struture will be repeated at each physical time step. + +The aerodynamic model is based on the compressible Reynolds-averaged Navier-Stokes equations. A central JST scheme is used for the convective fluxes, and a weighted least square +scheme is used for the gradients. The turbulence model is the SST and a CFL number of 20, for the psuedo time step, is used. + +The strctural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. +Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available +analytically and reads: + + + +The structural solver, instead of integrating +the equations of motions for this point, which are available analytically, is intended to solve a general strctural problem. For this reason, a preprocessing step in Nastran +will be performed, computing the mode shapes and modal frequencies of the model. Then, the structural solver will integrate a set of ODEs for the modes of the strcture. + +In this particular case, it may look excessively complicated, but it allows to solve an arbitrary aeroelastic problem with the same scheme. + +#### Mesh Description + +The fluid domain is discretised with 133k nodes, with refining close to the airfoil surface, in order to correctly represent the turbulent boundary layer. The first cell +is placed at a height of $y+\approx 1$. A close up view of the mesh is pictured below: + +![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/CFDmesh.png) + +As far as the strctural mesh is concerned, this is a finite element mesh prepared for the commercial code Nastram. In the context of this example, as only a 2D problem, with +only two degrees of freedom, is considered, the mesh is extremely simple; a set of rigid elements that connect all the nodes to the master node, positioned on the rotation axis. +The master node only has two degrees of freedom: pitch and plunge. + +Another slave node is added, in the position of the center of mass, that will house the mass and inertia of the airfoil. + +It should always be recalled that, if interpolation is needed +between the strctural and fluid meshes, RBF will be used. The limitation of this linear interpolation is due to the fact that, if a 2D problem is concerned, the strctural points +cannot all lie on the same line. Equivalently, if a 3D problem is tackled, the points cannot lie all in the same plane. For this reason, the thickness is represented in the +FEM mesh for Nastran as shown below: + +![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/FEMmesh.png) + +#### Configuration File Options + +We start the tutorial by definining the problem as a multiphysics case, + +``` +SOLVER = MULTIPHYSICS +``` + +We set the config files for each sub-problem using the command ```CONFIG_LIST```, and state that each sub-problem will use a different mesh file: + +``` +CONFIG_LIST = (config_channel.cfg, config_cantilever.cfg) +MULTIZONE_MESH = NO +``` + +Now, we define the outer iteration strategy to solve the FSI problem. We use a Block Gauss-Seidel iteration as defined in the background section with a maximum of 40 outer iterations + +``` +MULTIZONE_SOLVER = BLOCK_GAUSS_SEIDEL +OUTER_ITER = 40 +``` + +Then, the convergence criteria is set to evaluate the averaged residual of the flow state vector (zone 0) (```AVG_BGS_RES[0]```) and the structural state vector (zone 1) (```AVG_BGS_RES[1]```) in two consecutive outer iterations, $$\mathbf{w}^{n+1}-\mathbf{w}^{n}$$ and $$\mathbf{u}^{n+1}-\mathbf{u}^{n}$$ respectively. + +``` +CONV_FIELD = AVG_BGS_RES[0], AVG_BGS_RES[1] +CONV_RESIDUAL_MINVAL = -9 +``` + +Finally, we define the coupling conditions. In this case, the interface between the marker ```flowbound``` in the flow field, and ```feabound``` in the structural field, is defined as + +``` +MARKER_ZONE_INTERFACE = (flowbound, feabound) +``` + +The last step is defining our desired output. In this tutorial, we will use the following configuration for the screen output + +``` +SCREEN_OUTPUT = (OUTER_ITER, AVG_BGS_RES[0], AVG_BGS_RES[1], DEFORM_MIN_VOLUME[0], DEFORM_ITER[0]) +WRT_ZONE_CONV = NO +``` + +where the convergence magnitudes are plotted alongside the minimum volume obtained in the deformed mesh, and the number of iterations required by the linear solver that updates the mesh deformation. For clarity, the command ```WRT_ZONE_CONV``` limits the output to the outer iterations, while the convergence of the flow and structural sub-problems is not written to screen. + +The convergence output will be set using + +``` +HISTORY_OUTPUT = ITER, BGS_RES[0], AERO_COEFF[0], BGS_RES[1] + +WRT_ZONE_HIST = NO +CONV_FILENAME= history +``` + +where the individual components of the flow and structural outer-iteration residuals will be written, together with the convergence of the aerodynamic coefficients for the flow domain. In terms of result output, we use + +``` +OUTPUT_FILES = (RESTART, PARAVIEW) +RESTART_FILENAME = restart_fsi_steady +VOLUME_FILENAME = fsi_steady +``` + +where the volume files ```fsi_steady_*.vtu``` and restart files ```restart_fsi_steady_*.vtu``` will be appended the zone number. + +#### Applying coupling conditions to the individual domains + +Minor modifications are required for the flow and structural config files to be used in Fluid-Structure Interaction, as compared to a single-zone problem. As it is understood that the user will have a basic knowledge of the flow and structural solvers of SU2 before attempting this tutorial, only the specific commands for FSI will be discussed here. + +On the fluid domain (zone 0), it is necessary to indicate SU2 what is the boundary for which the flow loads will need to be computed and later applied to the structural domain, in [config_channel.cfg](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/config_channel.cfg). This is done using + +``` +MARKER_FLUID_LOAD = ( flowbound ) +``` + +Next, given that we are using an Arbitrary Lagrangian-Eulerian (ALE) formulation for the flow domain, the conditions for mesh deformation need to be set. We start by defining + +``` +DEFORM_MESH = YES +MARKER_DEFORM_MESH = ( flowbound ) +``` + +where the deforming boundary is set to ```flowbound```. Next, the mesh problem defined in the background section is set. We define the stiffness of the flow mesh as a function of the distance to the deformable wall, where volumes that are farther away from the boundary will be more flexible (thus, more prone to deform largely) + +``` +DEFORM_STIFFNESS_TYPE = WALL_DISTANCE +``` + +Next, we set the properties of the linear solver. This is a pseudo-linear-elastic problem and, therefore, the properties of the linear elastic solver will be similar as those used on the [Linear Elasticity Tutorial](../Linear_Elasticity/). As a result, for this case we use +``` +DEFORM_LINEAR_SOLVER = CONJUGATE_GRADIENT +DEFORM_LINEAR_SOLVER_PREC = ILU +DEFORM_LINEAR_SOLVER_ERROR = 1E-8 +DEFORM_LINEAR_SOLVER_ITER = 1000 +DEFORM_CONSOLE_OUTPUT = NO +``` + +As the structural side uses a Lagrangian formulation, and therefore no mesh deformation is carried out, only the wet boundary that receives the flow loads needs to be specified in [config_cantilever.cfg](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/config_cantilever.cfg) + +``` +MARKER_FLUID_LOAD = ( feabound ) +``` + +### Running SU2 + +Follow the links provided to download the [FSI config file](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/config_fsi_steady.cfg) and the [flow](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/config_channel.cfg) and [structural](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/config_cantilever.cfg) sub-config files. + +Also, you will need two files for the [channel mesh](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/mesh_channel.su2) and the [cantilever mesh](https://github.com/su2code/Tutorials/blob/master/fsi/steady_state/mesh_cantilever.su2). Please note that the latter is different from the structural mechanics tutorial due to a different definition of the boundary conditions. + +Execute the code with the standard command and using the multi-zone config file + +``` +$ SU2_CFD config_fsi_steady.cfg +``` + +which will show the following convergence history: + +``` ++----------------------------------------------------------------+ +| Multizone Summary | ++----------------------------------------------------------------+ +| Outer_Iter| avg[bgs][0]| avg[bgs][1]|MinVolume[0]|DeformIter[0| ++----------------------------------------------------------------+ +| 0| -0.298306| -2.048554| 8.8212e-10| 0| +| 1| -1.221569| -2.661506| 8.7196e-10| 44| +| 2| -2.176547| -3.088096| 8.7369e-10| 44| +| 3| -2.822207| -3.526246| 8.7331e-10| 44| +| 4| -3.479962| -3.962556| 8.7339e-10| 44| +| 5| -4.134404| -4.399315| 8.7337e-10| 44| +| 6| -4.789556| -4.835974| 8.7338e-10| 44| +| 7| -5.444539| -5.272643| 8.7338e-10| 44| +| 8| -6.099727| -5.709490| 8.7338e-10| 44| +| 9| -6.756832| -6.147703| 8.7338e-10| 44| +| 10| -7.393475| -6.578762| 8.7338e-10| 44| +| 11| -8.032563| -7.003230| 8.7338e-10| 44| +| 12| -8.670813| -7.426572| 8.7338e-10| 44| +| 13| -9.309448| -7.851164| 8.7338e-10| 44| +| 14| -9.949022| -8.277094| 8.7338e-10| 44| +| 15| -10.588983| -8.703770| 8.7338e-10| 44| +| 16| -11.228939| -9.130581| 8.7338e-10| 44| +``` + +The code is stopped as soon as the values of ```avg[bgs][0]``` and ```avg[bgs][1]``` are below the convergence criteria set in the config file. + +The displacement field on the structural domain and the velocity field on the flow domain obtained in ```fsi_steady_1.vtu```_and ```fsi_steady_0.vtu``` respectively are shown below: + +![FSI Results1](../../tutorials_files/multiphysics/steady_fsi/images/fsi2.png) + +![FSI Results2](../../tutorials_files/multiphysics/steady_fsi/images/fsi3.png) + +#### Relaxing the computation + +In order to increase the speed of convergence, it is normally a good option to apply a relaxation + + +to the sub-iterations of the FSI problem. This is done by adding the following commands + +``` +BGS_RELAXATION= FIXED_PARAMETER +STAT_RELAX_PARAMETER= 0.8 +``` + +to the FSI master config file. Running SU2 now would result in the following convergence history + +``` ++----------------------------------------------------------------+ +| Multizone Summary | ++----------------------------------------------------------------+ +| Outer_Iter| avg[bgs][0]| avg[bgs][1]|MinVolume[0]|DeformIter[0| ++----------------------------------------------------------------+ +| 0| -0.298306| -2.048554| 8.8212e-10| 0| +| 1| -1.316281| -2.740561| 8.4063e-10| 44| +| 2| -2.215592| -3.528252| 8.6618e-10| 44| +| 3| -3.014938| -4.639836| 8.7192e-10| 44| +| 4| -3.732471| -5.402349| 8.7309e-10| 44| +| 5| -4.436227| -5.790750| 8.7332e-10| 44| +| 6| -5.137723| -6.263485| 8.7337e-10| 44| +| 7| -5.840368| -6.711814| 8.7338e-10| 44| +| 8| -6.536232| -7.339662| 8.7338e-10| 44| +| 9| -7.247336| -7.555240| 8.7338e-10| 44| +| 10| -7.946736| -8.297281| 8.7338e-10| 44| +| 11| -8.648240| -8.586354| 8.7338e-10| 44| +| 12| -9.353917| -9.043231| 8.7338e-10| 44| +``` + +where the -9 convergence parameter is reached in almost half the iterations as per the non-relaxed case. + +#### Printing the inner convergence + +Sometimes, especially when things don't work as expected, it's interesting to visualize the convergence of each of the subproblems. This can be achieved enabling + +``` +WRT_ZONE_CONV = YES +``` + +in the main config file of the multizone problem, ```config_fsi_steady.cfg```. In most cases we will not be interested on every single inner iteration of the fluid domain; we can use + +``` +SCREEN_WRT_FREQ_INNER = 10 +``` + +in ```config_channel.cfg``` to limit the printout to every 10 iterations. The resulting screen output is the following: + + +``` ++----------------------------------------------------------------+ +| Zone 0 (Incomp. Fluid) | ++----------------------------------------------------------------+ +| Outer_Iter| Inner_Iter| rms[P]| rms[U]| rms[V]| ++----------------------------------------------------------------+ +| 0| 0| -4.799717| -19.870540| -32.000000| +| 0| 10| -5.421646| -4.859176| -5.558343| +| 0| 20| -6.200459| -5.584293| -6.120761| +| 0| 30| -6.852188| -6.205093| -6.958953| +| 0| 40| -7.502751| -6.854100| -8.034484| +| 0| 50| -8.316190| -7.662838| -8.492639| +| 0| 60| -9.153994| -8.509430| -9.696622| +| 0| 70| -10.119472| -9.498203| -10.117162| +| 0| 80| -11.035958| -10.448171| -11.143732| +| 0| 90| -11.613994| -10.982943| -11.842820| +| 0| 100| -12.264740| -11.616077| -12.556728| +| 0| 104| -12.684964| -12.046580| -12.778620| ++-----------------------------------------------------------------------------+ +| Zone 1 (Structure) | ++-----------------------------------------------------------------------------+ +| Outer_Iter| Inner_Iter| rms[U]| rms[R]| rms[E]| VonMises| ++-----------------------------------------------------------------------------+ +| 0| 0| -1.121561| -2.706864| -4.419338| 2.2876e+03| +| 0| 1| -1.708123| 1.269382| -1.716845| 2.2429e+03| +| 0| 2| -2.583705| 0.631041| -3.175890| 2.2237e+03| +| 0| 3| -2.508726| -0.795411| -5.686295| 2.0701e+03| +| 0| 4| -2.751613| -1.306797| -6.550284| 2.0544e+03| +| 0| 5| -3.147799| -1.271416| -6.914834| 2.0364e+03| +| 0| 6| -2.962716| -2.664273| -7.800357| 2.0171e+03| +| 0| 7| -4.083257| -2.080066| -8.553973| 2.0155e+03| +| 0| 8| -4.522566| -4.400710| -11.005428| 2.0149e+03| +| 0| 9| -7.252524| -5.240218| -14.876499| 2.0149e+03| +| 0| 10| -10.834476| -10.711888| -23.634504| 2.0149e+03| ++----------------------------------------------------------------+ +| Multizone Summary | ++----------------------------------------------------------------+ +| Outer_Iter| avg[bgs][0]| avg[bgs][1]|MinVolume[0]|DeformIter[0| ++----------------------------------------------------------------+ +| 0| -0.298306| -2.048554| 8.8212e-10| 0| +... + ++----------------------------------------------------------------+ +| Zone 0 (Incomp. Fluid) | ++----------------------------------------------------------------+ +| Outer_Iter| Inner_Iter| rms[P]| rms[U]| rms[V]| ++----------------------------------------------------------------+ +| 16| 0| -15.808168| -15.358431| -15.769282| +| 16| 10| -16.714759| -16.074145| -17.174991| ++-----------------------------------------------------------------------------+ +| Zone 1 (Structure) | ++-----------------------------------------------------------------------------+ +| Outer_Iter| Inner_Iter| rms[U]| rms[R]| rms[E]| VonMises| ++-----------------------------------------------------------------------------+ +| 16| 0| -11.937375| -11.637725| -25.999458| 1.8531e+03| +| 16| 1| -15.794016| -11.636749| -28.541279| 1.8531e+03| +| 16| 2| -16.165350| -11.621837| -28.528692| 1.8531e+03| +| 16| 3| -16.056047| -11.608302| -28.544055| 1.8531e+03| +| 16| 4| -16.156344| -11.627675| -28.565975| 1.8531e+03| +| 16| 5| -16.204699| -11.633976| -28.581277| 1.8531e+03| ++----------------------------------------------------------------+ +| Multizone Summary | ++----------------------------------------------------------------+ +| Outer_Iter| avg[bgs][0]| avg[bgs][1]|MinVolume[0]|DeformIter[0| ++----------------------------------------------------------------+ +| 16| -11.228939| -9.130581| 8.7338e-10| 44| +``` + +where it can be observed that the multizone summary corresponds to the non-relaxed case presented first, and each of the subproblems are converged to a very high accuracy level. + +### References +$$^1$$ Sanchez, R. (2018), A coupled adjoint method for optimal design in fluid-structure interaction problems with large displacements, _PhD thesis, Imperial College London_, DOI: [10.25560/58882](https://doi.org/10.25560/58882) + +$$^2$$ Matthies H. G. and Steindorf J. (2002), Partitioned but strongly coupled iteration schemes fornonlinear fluid–structure interaction, _Computers & Structures, 80(27–30):199–1999_. + +### Attribution + +If you are using this content for your research, please kindly cite the following reference in your derived works: + +Sanchez, R. _et al._ (2018), [Coupled Adjoint-Based Sensitivities in Large-Displacement Fluid-Structure Interaction using Algorithmic Differentiation](https://spiral.imperial.ac.uk/handle/10044/1/51023), _Int J Numer Meth Engng, Vol 111, Issue 7, pp 1081-1107_. DOI: [10.1002/nme.5700](https://doi.org/10.1002/nme.5700) + +
+This work is licensed under a Creative Commons Attribution 4.0 International License +
+Creative Commons Licence +
diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi b/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi deleted file mode 100644 index bf0297b0..00000000 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/unsteady_fsi +++ /dev/null @@ -1 +0,0 @@ -## Test From 5c81c63115af2ad831daf2492cda4de8ed5adc1d Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 13:08:09 +0100 Subject: [PATCH 05/25] Description of cfg files --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 237 +++++++++++++----- 1 file changed, 172 insertions(+), 65 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index c3ad1452..ca97c562 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -1,5 +1,5 @@ --- -title: Dynamic Fluid-Structure Interaction (FSI) using the Python wrapper and an external structural solver +title: Dynamic Fluid-Structure Interaction (FSI) using the Python wrapper and a Nastran structural model permalink: /tutorials/Dynamic_FSI_Python/ written_by: Nicola-Fonzi for_version: 7.0.6 @@ -46,15 +46,60 @@ Here, the difference is due to the fact that the simulation is unsteady. Thus, t The aerodynamic model is based on the compressible Reynolds-averaged Navier-Stokes equations. A central JST scheme is used for the convective fluxes, and a weighted least square scheme is used for the gradients. The turbulence model is the SST and a CFL number of 20, for the psuedo time step, is used. +Different Mach numbers will be considered, namely $M=[0.1, 0.2, 0.3, 0.357, 0.364]$. The Reynolds number is fixed at 4 millions, and the temperature is equal to 273K. + The strctural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available analytically and reads: +$m\ddot{h} + S\ddot{\alpha} + C_{h}\dot{h} + K_{h}h = -L$ +$S\ddot{h} + I\ddot{\alpha} + C_{\alpha}\dot{\alpha} + K_{\alpha}\alpha = M$ + +Where $m$ is the mass of the airfoil, $I$ the inertia around the center of mass, $S$ the static moment of inertia at the rotation axis, $C$ and $K$ the dampings and stiffnesses respectively. $L$ and $M$ are the lift and pitching up moment. + +These equations are usually adimensionalised to obtain results independent from the free-stream density of the flow. +Indeed, we can define the following parameters: + +$\Csi=\frac{S}{mb}$, $r_{\alpha}^2=\frac{I_f}{mb^2}$, $\bar{\omega}=\frac{\omega_h}{\omega_{\alpha}}$, $\mu=\frac{m}{\pi \rho_{\inf} b^2}$ + +Where $b$ is the semi chord of the airfoil, $\omega_h = \sqrt{\frac{K_h}{m}}$ $\omega_{\alpha} = \sqrt{\frac{K_{\alpha}}{I_f}}. If we fix them, the structure will behave always the same regardless of $\rho_{\inf}$. + +In this context $\Csi=0.25$, $r_{\alpha}^2=0.5$, $\bar{\omega}=0.3185$ and $\mu=100$. + +Note that, as we will vary the Mach number, the density will also change accordingly. Thus, with given nondimensional parameters, the inertias and stiffnesses must be +varied accordingly. + +No strunctural damping is included and a time step of 1ms is used. + +The structural solver, instead of integrating the equations of motions for this point, which are available analytically, is intended to solve a general strctural problem. +For this reason, a preprocessing step in Nastran will be performed, computing the mode shapes and modal frequencies of the model. Then, the structural solver will +integrate a set of ODEs for the modes of the structure. + +To perform the preprocessing step, in the case control section of the Nastran model (i.e. at the very beginning of +the file), the following lines must be added: + +ECHO = SORT +DISPLACEMENT(PRINT,PUNCH)=ALL +A real egeinvalue analysis will then be performed. +This will produce, in the f06 file, an equivalent, ordered, model that will +eventually be read by the python script to create the interface. Further, it will +be created a punch file where all the mode shapes, together with their stiffness, +are stored. -The structural solver, instead of integrating -the equations of motions for this point, which are available analytically, is intended to solve a general strctural problem. For this reason, a preprocessing step in Nastran -will be performed, computing the mode shapes and modal frequencies of the model. Then, the structural solver will integrate a set of ODEs for the modes of the strcture. +IMPORTANT: The modes should be normalised to unit mass. + +Further, in the Nastran model, a SET1 card must be added that contains all the +nodes to be interfaced with aerodynamics. Note that, as of now, only one SET1 card +is allowed. However, this should be sufficiently general not to create issues. + +The input and output reference systems of the interface nodes can be defined as +local, but these reference systems must be directly defined with respect to the +global one. Thus, if node x is referring to reference system y, y must be defined +with respect to the global one. + +In the structural input file the keyword NMODES must then be defined to select which, +of all the modes in the punch file, to be used. In this particular case, it may look excessively complicated, but it allows to solve an arbitrary aeroelastic problem with the same scheme. @@ -78,107 +123,169 @@ FEM mesh for Nastran as shown below: ![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/FEMmesh.png) -#### Configuration File Options +#### Configuration File for the fluid zone -We start the tutorial by definining the problem as a multiphysics case, +First of all, the users should know that three configuarions file are required for this case: one for the fluid zone, one for the solid zone and one for the interface. +The configuration file for the fluid zone is very similar to a configuration file for a simple single zone simulation. Indeed, SU2 does not know about the external strctural +solver, it will only see the points on the aerodynamic mesh changing positions. + +For this reason, the solver keyword is set as: ``` -SOLVER = MULTIPHYSICS +SOLVER = RANS ``` -We set the config files for each sub-problem using the command ```CONFIG_LIST```, and state that each sub-problem will use a different mesh file: +A new marker is introduced, MARKER_MATCH_DEFORM_MESH. This marker is effectively +a symmetry marker for the mesh deformation only. It may be useful in cases where +symmetry in the mesh is required, but not in the fluid simulation. An example may +be the simulation of a plane half-model, in wind tunnel, where the effect of boundary +layer on the tunnel walls must be studied, but a pitch movement of the model is +also allowed. Fluid symmetry cannot be used, but at the same time the mesh should +move on the tunnel wall to match the deformation given by the pitch motion. However, in the context of this example, this marker is not required. + +The only difference from a common single zone configuration file is the addition of the following lines: ``` -CONFIG_LIST = (config_channel.cfg, config_cantilever.cfg) -MULTIZONE_MESH = NO +%-------------- Coupling conditions -------------------------------------------% +DEFORM_MESH = YES +MARKER_DEFORM_MESH = ( airfoil ) +DEFORM_STIFFNESS_TYPE = WALL_DISTANCE +DEFORM_LINEAR_SOLVER_ITER= 200 +MARKER_FLUID_LOAD = ( airfoil ) ``` -Now, we define the outer iteration strategy to solve the FSI problem. We use a Block Gauss-Seidel iteration as defined in the background section with a maximum of 40 outer iterations +Where we selected the airfoil as our marker for coupling. + +The simulation is unsteady with a physical time step of 1ms: ``` -MULTIZONE_SOLVER = BLOCK_GAUSS_SEIDEL -OUTER_ITER = 40 +TIME_DOMAIN = YES +TIME_STEP= 1e-3 ``` -Then, the convergence criteria is set to evaluate the averaged residual of the flow state vector (zone 0) (```AVG_BGS_RES[0]```) and the structural state vector (zone 1) (```AVG_BGS_RES[1]```) in two consecutive outer iterations, $$\mathbf{w}^{n+1}-\mathbf{w}^{n}$$ and $$\mathbf{u}^{n+1}-\mathbf{u}^{n}$$ respectively. +#### Configuration File for the solid zone -``` -CONV_FIELD = AVG_BGS_RES[0], AVG_BGS_RES[1] -CONV_RESIDUAL_MINVAL = -9 -``` +This configuration file will be read by the structural python solver included in SU2, that will read the preprocessed Nastran model. -Finally, we define the coupling conditions. In this case, the interface between the marker ```flowbound``` in the flow field, and ```feabound``` in the structural field, is defined as +The solver can work in two ways: -``` -MARKER_ZONE_INTERFACE = (flowbound, feabound) -``` +1) It can impose the movement of a mode, with prescribed law, to provide forced +response analysis -The last step is defining our desired output. In this tutorial, we will use the following configuration for the screen output +2) It can integrate in time the modal equation of motions to study the linearised +structural deformations when the body is surrounded by the flow -``` -SCREEN_OUTPUT = (OUTER_ITER, AVG_BGS_RES[0], AVG_BGS_RES[1], DEFORM_MIN_VOLUME[0], DEFORM_ITER[0]) -WRT_ZONE_CONV = NO -``` +Available keyword for the config file: -where the convergence magnitudes are plotted alongside the minimum volume obtained in the deformed mesh, and the number of iterations required by the linear solver that updates the mesh deformation. For clarity, the command ```WRT_ZONE_CONV``` limits the output to the outer iterations, while the convergence of the flow and structural sub-problems is not written to screen. +NMODES (int): number of modes to use in the analysis -> if n modes are available in + the punch file, but only the first m Date: Mon, 7 Dec 2020 15:42:06 +0100 Subject: [PATCH 06/25] Update Dynamic_FSI_Python.md --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 221 ++++-------------- 1 file changed, 48 insertions(+), 173 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index ca97c562..fa5cde44 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -33,9 +33,9 @@ A sketch of the problem at hand is presented below: ### Resources -You can find the resources for this tutorial in the folder [fsi/steady_state](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [FSI config file](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_fsi_steady.cfg) and two sub-config files for the [flow](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_channel.cfg) and [structural](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/config_cantilever.cfg) subproblems. +You can find the resources for this tutorial in [this folder] (https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [matlab file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/FlatPlateModel.m) that can be used to produce validation data with Theodorsen theory and the [mesh file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/airfoil.su2). -Moreover, you will need two mesh files for the [flow domain](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/mesh_channel.su2) and the [cantilever](https://github.com/su2code/Tutorials/tree/master/multiphysics/steady_fsi/mesh_cantilever.su2). +In the [main directory] (https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python), there are other 5 subdirectories containing the configuration files and structural models for the different Mach numbers. Please do not mix those files as the structural models and configurations are different at the different aerodynamic conditions. ### Background @@ -163,6 +163,18 @@ TIME_DOMAIN = YES TIME_STEP= 1e-3 ``` +It is important to set an appropriate convergence criteria for the fluid zone. Indeed, while the structural part is linear and requires no interations, it is important that +the fluid zone correcly converges for accurate results. + +The relative residual cannot be used as this is reset at each inner iteration. Thus, aver the first inner loop, it would be difficult to obtain convergence as the absolute +residuals are already quite low. For this reason we will use: + +``` +CONV_CRITERIA = RESIDUAL +CONV_FIELD= RMS_DENSITY +CONV_RESIDUAL_MINVAL= -9.0 +``` + #### Configuration File for the solid zone This configuration file will be read by the structural python solver included in SU2, that will read the preprocessed Nastran model. @@ -177,7 +189,7 @@ structural deformations when the body is surrounded by the flow Available keyword for the config file: -NMODES (int): number of modes to use in the analysis -> if n modes are available in +NMODES (int): number of modes to use in the analysis. If n modes are available in the punch file, but only the first m This work is licensed under a Creative Commons Attribution 4.0 International License From e8496480f8aa44f193d485fb78a6e4a940d8c6e3 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 16:20:00 +0100 Subject: [PATCH 07/25] Update Dynamic_FSI_Python.md --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 24 ++++++++++--------- 1 file changed, 13 insertions(+), 11 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index fa5cde44..7d348c0d 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -6,7 +6,7 @@ for_version: 7.0.6 revised_by: revision_date: revised_version: -solver: Multiphysics +solver: RANS requires: SU2_CFD, PYTHON WRAPPER complexity: intermediate follows: Static_FSI @@ -33,9 +33,9 @@ A sketch of the problem at hand is presented below: ### Resources -You can find the resources for this tutorial in [this folder] (https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [matlab file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/FlatPlateModel.m) that can be used to produce validation data with Theodorsen theory and the [mesh file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/airfoil.su2). +You can find the resources for this tutorial in [this folder](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [matlab file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/FlatPlateModel.m) that can be used to produce validation data with Theodorsen theory and the [mesh file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/airfoil.su2). -In the [main directory] (https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python), there are other 5 subdirectories containing the configuration files and structural models for the different Mach numbers. Please do not mix those files as the structural models and configurations are different at the different aerodynamic conditions. +In the [main directory](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python), there are other 5 subdirectories containing the configuration files and structural models for the different Mach numbers. Please do not mix those files as the structural models and configurations are different at the different aerodynamic conditions. ### Background @@ -52,19 +52,19 @@ The strctural model is made by a single point, positioned at the rotation axis, Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available analytically and reads: -$m\ddot{h} + S\ddot{\alpha} + C_{h}\dot{h} + K_{h}h = -L$ -$S\ddot{h} + I\ddot{\alpha} + C_{\alpha}\dot{\alpha} + K_{\alpha}\alpha = M$ +$$m\ddot{h} + S\ddot{\alpha} + C_{h}\dot{h} + K_{h}h = -L$$ +$$S\ddot{h} + I\ddot{\alpha} + C_{\alpha}\dot{\alpha} + K_{\alpha}\alpha = M$$ -Where $m$ is the mass of the airfoil, $I$ the inertia around the center of mass, $S$ the static moment of inertia at the rotation axis, $C$ and $K$ the dampings and stiffnesses respectively. $L$ and $M$ are the lift and pitching up moment. +Where $$m$$ is the mass of the airfoil, $$I$$ the inertia around the center of mass, $$S$$ the static moment of inertia at the rotation axis, $$C$$ and $$K$$ the dampings and stiffnesses respectively. $$L$$ and $$M$$ are the lift and pitching up moment. These equations are usually adimensionalised to obtain results independent from the free-stream density of the flow. Indeed, we can define the following parameters: -$\Csi=\frac{S}{mb}$, $r_{\alpha}^2=\frac{I_f}{mb^2}$, $\bar{\omega}=\frac{\omega_h}{\omega_{\alpha}}$, $\mu=\frac{m}{\pi \rho_{\inf} b^2}$ +$$\Csi=\frac{S}{mb}$$, $$r_{\alpha}^2=\frac{I_f}{mb^2}$$, $$\bar{\omega}=\frac{\omega_h}{\omega_{\alpha}}$$, $$\mu=\frac{m}{\pi \rho_{\inf} b^2}$$ -Where $b$ is the semi chord of the airfoil, $\omega_h = \sqrt{\frac{K_h}{m}}$ $\omega_{\alpha} = \sqrt{\frac{K_{\alpha}}{I_f}}. If we fix them, the structure will behave always the same regardless of $\rho_{\inf}$. +Where $$b$$ is the semi chord of the airfoil, $$\omega_h = \sqrt{\frac{K_h}{m}}$$ $$\omega_{\alpha} = \sqrt{\frac{K_{\alpha}}{I_f}}$$. If we fix them, the structure will behave always the same regardless of $$\rho_{\inf}$$. -In this context $\Csi=0.25$, $r_{\alpha}^2=0.5$, $\bar{\omega}=0.3185$ and $\mu=100$. +In this context $$\Csi=0.25$$, $$r_{\alpha}^2=0.5$$, $$\bar{\omega}=0.3185$$ and $$\mu=100$$. Note that, as we will vary the Mach number, the density will also change accordingly. Thus, with given nondimensional parameters, the inertias and stiffnesses must be varied accordingly. @@ -106,7 +106,7 @@ In this particular case, it may look excessively complicated, but it allows to s #### Mesh Description The fluid domain is discretised with 133k nodes, with refining close to the airfoil surface, in order to correctly represent the turbulent boundary layer. The first cell -is placed at a height of $y+\approx 1$. A close up view of the mesh is pictured below: +is placed at a height of $$y+\approx 1$$. A close up view of the mesh is pictured below: ![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/CFDmesh.png) @@ -317,7 +317,9 @@ TIME_MARCHING = YES ``` ### Running SU2 -Follow the links provided to download the [main directory] (https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python). +Follow the links provided to download the [main directory](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python). + +The preprocessing step in Nastran has already been performed, thus you will directly find the required structural model. Copy the mesh file in each subdirectory, then run the following command from inside each subdirectory: From 8926caca57bd9ac18ff5db62c3d3ad049707f45b Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 17:13:51 +0100 Subject: [PATCH 08/25] Create dummy --- tutorials_files/multiphysics/unsteady_fsi_python/images/dummy | 1 + 1 file changed, 1 insertion(+) create mode 100644 tutorials_files/multiphysics/unsteady_fsi_python/images/dummy diff --git a/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy b/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy @@ -0,0 +1 @@ + From 48ab04b6b8cff715e3a62caadeeb6b71f6f401dc Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 17:14:23 +0100 Subject: [PATCH 09/25] Add files via 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HcmV?d00001 From 0e68b091f92ab58e1a691050a7334e3cf54a1420 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 17:14:47 +0100 Subject: [PATCH 10/25] Delete dummy --- tutorials_files/multiphysics/unsteady_fsi_python/images/dummy | 1 - 1 file changed, 1 deletion(-) delete mode 100644 tutorials_files/multiphysics/unsteady_fsi_python/images/dummy diff --git a/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy b/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy deleted file mode 100644 index 8b137891..00000000 --- a/tutorials_files/multiphysics/unsteady_fsi_python/images/dummy +++ /dev/null @@ -1 +0,0 @@ - From cb05d1580b886c6a69e025f579b9cd452dd851b2 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Mon, 7 Dec 2020 22:42:31 +0100 Subject: [PATCH 11/25] Update Dynamic_FSI_Python.md --- .../multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index 7d348c0d..8971ae30 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -46,7 +46,7 @@ Here, the difference is due to the fact that the simulation is unsteady. Thus, t The aerodynamic model is based on the compressible Reynolds-averaged Navier-Stokes equations. A central JST scheme is used for the convective fluxes, and a weighted least square scheme is used for the gradients. The turbulence model is the SST and a CFL number of 20, for the psuedo time step, is used. -Different Mach numbers will be considered, namely $M=[0.1, 0.2, 0.3, 0.357, 0.364]$. The Reynolds number is fixed at 4 millions, and the temperature is equal to 273K. +Different Mach numbers will be considered, namely $$M=[0.1, 0.2, 0.3, 0.357, 0.364]$$. The Reynolds number is fixed at 4 millions, and the temperature is equal to 273K. The strctural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available @@ -64,7 +64,7 @@ $$\Csi=\frac{S}{mb}$$, $$r_{\alpha}^2=\frac{I_f}{mb^2}$$, $$\bar{\omega}=\frac{\ Where $$b$$ is the semi chord of the airfoil, $$\omega_h = \sqrt{\frac{K_h}{m}}$$ $$\omega_{\alpha} = \sqrt{\frac{K_{\alpha}}{I_f}}$$. If we fix them, the structure will behave always the same regardless of $$\rho_{\inf}$$. -In this context $$\Csi=0.25$$, $$r_{\alpha}^2=0.5$$, $$\bar{\omega}=0.3185$$ and $$\mu=100$$. +In this context $$\Csi=0.25$$, $$r_{\alpha}=0.5$$, $$\bar{\omega}=0.3185$$ and $$\mu=100$$. Note that, as we will vary the Mach number, the density will also change accordingly. Thus, with given nondimensional parameters, the inertias and stiffnesses must be varied accordingly. @@ -135,7 +135,7 @@ For this reason, the solver keyword is set as: SOLVER = RANS ``` -A new marker is introduced, MARKER_MATCH_DEFORM_MESH. This marker is effectively +A new marker is introduced, MARKER_DEFORM_MESH_SYM_PLANE. This marker is effectively a symmetry marker for the mesh deformation only. It may be useful in cases where symmetry in the mesh is required, but not in the fluid simulation. 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ztk13H8IKI>vQe>O8qE=46tm&LN!5xn+8qR^y=rw1!DczpY!iEINEweE;x6}V^@`ga z6L>5>QhOnzz|maUaj!hS#9v}J?An99)4DLb34;CE4j<(UA%0^xqp_ipx+>%?&XE}l z4IlO%=d4T1U!B&ifBe+qAsDx=F%3bqnMHk1WUD@*>kp{ZSeQUsb^R;OrJP zba73+rZV-Aq*EPJWRKD#yVA|Yp?_Rr22E@;9K4{j8Gp?z7V};&v$g7py8flHq#s74 z=%d<1#g3U+jrZk6%^~LsgLrDE-{U6 z>5gAo1IW$pllOJMj}6)Z%Fxo%v{;Df{;UiV0sBr zCcIte1bYWAR*`J^SBGdSID7|1L<7z3tIvBcz5Ua#tT~3%GT_f#?9QC~!y~h+5{gLU kLE0BB0G^W@S((dr_}U<8P*&318t^-D3=v%Y^$*wo55*ZB&;S4c literal 0 HcmV?d00001 From c04005d982a40f931d11f5b53b283ccaff9efeed Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Wed, 9 Dec 2020 15:38:37 +0100 Subject: [PATCH 15/25] Update Dynamic_FSI_Python.md --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 89 +++++++++++++++++-- 1 file changed, 82 insertions(+), 7 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index 8971ae30..e4d05429 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -19,7 +19,7 @@ a point when the aeroelastic system will be unstable. The classical pitch-plunge The considered case has been presented in $$^1$$, the reader is encouraged to refer to that reference for further details on the problem. -The structual solver used in this example loosely couples SU2 with the commercial code Nastran, keeping the results of general interest. Indeed, linear strctures of arbitrary +The structual solver used in this example couples SU2 with the commercial code Nastran, keeping the results of general interest. Indeed, linear strctures of arbitrary complexity can be analysed with the same workflow. Summarizing, this document will cover: @@ -29,11 +29,11 @@ Summarizing, this document will cover: A sketch of the problem at hand is presented below: -![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/Setup.png) +![Problem_Setup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/Setup.png) ### Resources -You can find the resources for this tutorial in [this folder](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [matlab file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/FlatPlateModel.m) that can be used to produce validation data with Theodorsen theory and the [mesh file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/airfoil.su2). +You can find the resources for this tutorial in [this folder](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python) of the [Tutorials repository](https://github.com/su2code/Tutorials). There is a [matlab file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/Main_Compare.m) that can be used to produce validation data with Theodorsen theory and the [mesh file](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python/airfoil.su2). In the [main directory](https://github.com/su2code/Tutorials/tree/master/multiphysics/unsteady_fsi_python), there are other 5 subdirectories containing the configuration files and structural models for the different Mach numbers. Please do not mix those files as the structural models and configurations are different at the different aerodynamic conditions. @@ -50,7 +50,7 @@ Different Mach numbers will be considered, namely $$M=[0.1, 0.2, 0.3, 0.357, 0.3 The strctural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available -analytically and reads: +analytically and read: $$m\ddot{h} + S\ddot{\alpha} + C_{h}\dot{h} + K_{h}h = -L$$ $$S\ddot{h} + I\ddot{\alpha} + C_{\alpha}\dot{\alpha} + K_{\alpha}\alpha = M$$ @@ -108,7 +108,7 @@ In this particular case, it may look excessively complicated, but it allows to s The fluid domain is discretised with 133k nodes, with refining close to the airfoil surface, in order to correctly represent the turbulent boundary layer. The first cell is placed at a height of $$y+\approx 1$$. A close up view of the mesh is pictured below: -![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/CFDmesh.png) +![CFD_Mesh](../../tutorials_files/multiphysics/unsteady_fsi_python/images/CFD_Mesh.png) As far as the strctural mesh is concerned, this is a finite element mesh prepared for the commercial code Nastram. In the context of this example, as only a 2D problem, with only two degrees of freedom, is considered, the mesh is extremely simple; a set of rigid elements that connect all the nodes to the master node, positioned on the rotation axis. @@ -121,7 +121,9 @@ between the strctural and fluid meshes, RBF will be used. The limitation of this cannot all lie on the same line. Equivalently, if a 3D problem is tackled, the points cannot lie all in the same plane. For this reason, the thickness is represented in the FEM mesh for Nastran as shown below: -![ProblemSetup](../../tutorials_files/multiphysics/unsteady_fsi_python/images/FEMmesh.png) +![FEM_Mesh](../../tutorials_files/multiphysics/unsteady_fsi_python/images/nastran_model.png) + +As you can see, then exact profile is not required. The interpolation will take care of displacing correctly the fluid mesh. However, thickness must somehow be represented. #### Configuration File for the fluid zone @@ -335,8 +337,81 @@ $ mpirun -np X python3 /your/path/to/fsi_computation.py --parallel -f fsi.cfg Substituting X with the appropriate number of cores. -Generate validation data running the matlab script. This will produce the required database containing the time history of angle of attack and vertical displacement. +You will see, after the ussual preprocessing steps, the following output: + +``` +********************************** +* Begin unsteady FSI computation * +********************************** + +Setting FSI initial conditions +Checking f/s interface conservation... +Solid side (Wx, Wy, Wz) = (0.0, 0.0, 0.0) +Fluid side (Wx, Wy, Wz) = (0.0, 0.0, 0.0) + +Performing static mesh deformation (ALE) of initial mesh... + + +FSI initial conditions are set +Beginning time integration +``` + +In these steps, an initial deformation is imposed, if required, and the mesh is deformed accordingly. Afterwords, the computation can start: + +``` +>>>> Time iteration 0 / FSI iteration 0 <<<< +Checking f/s interface conservation... +Solid side (Wx, Wy, Wz) = (0.0, 0.0, 0.0) +Fluid side (Wx, Wy, Wz) = (0.0, 0.0, 0.0) + +Performing dynamic mesh deformation (ALE)... + +CSysSolve::FGMRES(): system solved by initial guess. + +Launching fluid solver for one single dual-time iteration... ++-----------------------------------------------------------------------------+ +| Time_Iter| Inner_Iter| CD| CL| rms[Rho]| relrms[Rho]| ++-----------------------------------------------------------------------------+ +| 0| 0| 2.925114| -5.650014| -2.772504| 0.000000| +| 0| 1| 2.419387| -4.707503| -3.257713| -0.485209| +| 0| 2| 2.039722| -3.799496| -3.346967| -0.574463| +| 0| 3| 1.887042| -3.439476| -3.470247| -0.697743| +| 0| 4| 1.831439| -3.346855| -3.558842| -0.786338| +| 0| 5| 1.800010| -3.330105| -3.595711| -0.823207| +| 0| 6| 1.769099| -3.325896| -3.588726| -0.816222| +| 0| 7| 1.732970| -3.321408| -3.551232| -0.778728| +``` + +This is the typical output that you will see. There was no initial deformation imposed and for this reason you can see that the mesh deformation system was solved by the initial guess. FSI iteration is the inner iteration index, and it will keep inccreasing untile the inner convergence if found. Then, this index will be set to zero and the time iteration will be increased. + +Please do not confuse Inner_Iter with FSI iteration. The former is the iteration, in the fluid zone only, using the pseudo time; the latter is the iteration index between fluid and structure. + +After all the computations are completed (i.e. for all the Mach numbers), in each case folder yuo will see a file called StructHistoryModal.dat. The first rows of this file, for Mach number 0.1, are reported below. + +``` +Time Time Iteration FSI Iteration q1 qdot1 qddot1 q2 qdot2 qddot2 +0.099 99 1 -0.1501 0.0000 30.0116 -0.2343 0.0 649.9362 +0.100 100 2 -0.1500 0.0505 66.9711 -0.2339 0.6319 617.5777 +0.101 101 1 -0.1499 0.1133 63.2111 -0.2330 1.2470 609.8225 +0.102 102 1 -0.1498 0.1754 60.8115 -0.2314 1.8549 605.5686 +0.103 103 1 -0.1496 0.2352 58.7621 -0.2293 2.4576 599.9707 +0.104 104 1 -0.1493 0.2931 56.9690 -0.2265 3.0535 592.1878 +0.105 105 1 -0.1490 0.3493 55.3371 -0.2232 3.6407 582.3177 +``` +The first column contains the physical time (please note that we started the fluid-structure coupling after 99 time iterations), the second one contains the time iteration, the third one the number of FSI iterations required for convergence, then we have the time histories of the modes. + +For many applications this may be already the desired output. However, in this case, we actually want the physical rotation and displacement of the point at the rotation axis. A post processing step must be performed to multiply the mode shapes for their amplitude. This can be done with the provided matlab file. You only need to run the Main_compare.m file and it will take care of all the required operations. + +Please note that those files are absolutely general. Thus, feel free to reuse them for other models. + +At the end of the matlab run, you will see outputs as the ones reported below. + +![Freq](../../tutorials_files/multiphysics/unsteady_fsi_python/images/Freq.png) +![H_Ma01](../../tutorials_files/multiphysics/unsteady_fsi_python/images/h_Ma=0.1.png) +![Alpha_Ma01](../../tutorials_files/multiphysics/unsteady_fsi_python/images/alpha_Ma=0.1.png) +You can see how the frquency merging is nicely captured; after the flutter point the two frequencies are coincident and nonlinear effects are presents. Thus, comparing the Theodorsen theory and SU2 is not fully meaningful. +The time histories also match nicely. ### References $$^1$$ Sanchez, R. (2018), A coupled adjoint method for optimal design in fluid-structure interaction problems with large displacements, _PhD thesis, Imperial College London_, DOI: [10.25560/58882](https://doi.org/10.25560/58882) From ad963fab8fb3049f96407167c116f43568b541b1 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Wed, 9 Dec 2020 15:52:59 +0100 Subject: [PATCH 16/25] Update Dynamic_FSI_Python.md --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index e4d05429..f43a60f1 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -389,14 +389,14 @@ Please do not confuse Inner_Iter with FSI iteration. The former is the iteration After all the computations are completed (i.e. for all the Mach numbers), in each case folder yuo will see a file called StructHistoryModal.dat. The first rows of this file, for Mach number 0.1, are reported below. ``` -Time Time Iteration FSI Iteration q1 qdot1 qddot1 q2 qdot2 qddot2 -0.099 99 1 -0.1501 0.0000 30.0116 -0.2343 0.0 649.9362 -0.100 100 2 -0.1500 0.0505 66.9711 -0.2339 0.6319 617.5777 -0.101 101 1 -0.1499 0.1133 63.2111 -0.2330 1.2470 609.8225 -0.102 102 1 -0.1498 0.1754 60.8115 -0.2314 1.8549 605.5686 -0.103 103 1 -0.1496 0.2352 58.7621 -0.2293 2.4576 599.9707 -0.104 104 1 -0.1493 0.2931 56.9690 -0.2265 3.0535 592.1878 -0.105 105 1 -0.1490 0.3493 55.3371 -0.2232 3.6407 582.3177 +Time Time Iteration FSI Iteration q1 qdot1 qddot1 q2 qdot2 qddot2 +0.099 99 1 -0.1501 0.0000 30.0116 -0.2343 0.0000 649.9362 +0.100 100 2 -0.1500 0.0505 66.9711 -0.2339 0.6319 617.5777 +0.101 101 1 -0.1499 0.1133 63.2111 -0.2330 1.2470 609.8225 +0.102 102 1 -0.1498 0.1754 60.8115 -0.2314 1.8549 605.5686 +0.103 103 1 -0.1496 0.2352 58.7621 -0.2293 2.4576 599.9707 +0.104 104 1 -0.1493 0.2931 56.9690 -0.2265 3.0535 592.1878 +0.105 105 1 -0.1490 0.3493 55.3371 -0.2232 3.6407 582.3177 ``` The first column contains the physical time (please note that we started the fluid-structure coupling after 99 time iterations), the second one contains the time iteration, the third one the number of FSI iterations required for convergence, then we have the time histories of the modes. From 0bd84ef4ce65b47c22b99708ade8cd24adc377e9 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Wed, 9 Dec 2020 18:00:45 +0100 Subject: [PATCH 17/25] Typos --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 56 +++++++++---------- 1 file changed, 28 insertions(+), 28 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index f43a60f1..51a0c1b8 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -13,7 +13,7 @@ follows: Static_FSI --- ### Goals -This tutorial shows how to exploit the capabilities of the Python wrapper to couple SU2 with an external strutural solver. The problem at hand consist in a NACA 0012 airfoil, +This tutorial shows how to exploit the capabilities of the Python wrapper to couple SU2 with an external structural solver. The problem at hand consists in a NACA 0012 airfoil, free to pitch and plunge, with given stiffnesses, immersed in a flow with varying Mach number. The two frequencies of the modes of the structure will vary as the speed is increased, reaching a point when the aeroelastic system will be unstable. The classical pitch-plunge flutter will then be visible. @@ -24,7 +24,7 @@ complexity can be analysed with the same workflow. Summarizing, this document will cover: - Preparing a FSI analysis to be used with the python wrapper -- Using the strctural solver for Nastran models with SU2 +- Using the structural solver for Nastran models with SU2 - Important keywords for the fsi and solid solver config files A sketch of the problem at hand is presented below: @@ -48,7 +48,7 @@ scheme is used for the gradients. The turbulence model is the SST and a CFL numb Different Mach numbers will be considered, namely $$M=[0.1, 0.2, 0.3, 0.357, 0.364]$$. The Reynolds number is fixed at 4 millions, and the temperature is equal to 273K. -The strctural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. +The structural model is made by a single point, positioned at the rotation axis, with two degrees of freedom, pitch and plunge. Inertia and mass of the airfoil are concentrated at the center of mass of the profile, at a certain distance from the rotation axis. The equations of motions are available analytically and read: @@ -69,9 +69,9 @@ In this context $$\Csi=0.25$$, $$r_{\alpha}=0.5$$, $$\bar{\omega}=0.3185$$ and $ Note that, as we will vary the Mach number, the density will also change accordingly. Thus, with given nondimensional parameters, the inertias and stiffnesses must be varied accordingly. -No strunctural damping is included and a time step of 1ms is used. +No structural damping is included and a time step of 1ms is used. -The structural solver, instead of integrating the equations of motions for this point, which are available analytically, is intended to solve a general strctural problem. +The structural solver, instead of integrating the equations of motions for this point, which are available analytically, is intended to solve a general structural problem. For this reason, a preprocessing step in Nastran will be performed, computing the mode shapes and modal frequencies of the model. Then, the structural solver will integrate a set of ODEs for the modes of the structure. @@ -84,7 +84,7 @@ DISPLACEMENT(PRINT,PUNCH)=ALL A real egeinvalue analysis will then be performed. This will produce, in the f06 file, an equivalent, ordered, model that will eventually be read by the python script to create the interface. Further, it will -be created a punch file where all the mode shapes, together with their stiffness, +be created a punch file where all the mode shapes, together with modal stiffnesses, are stored. IMPORTANT: The modes should be normalised to unit mass. @@ -110,25 +110,25 @@ is placed at a height of $$y+\approx 1$$. A close up view of the mesh is picture ![CFD_Mesh](../../tutorials_files/multiphysics/unsteady_fsi_python/images/CFD_Mesh.png) -As far as the strctural mesh is concerned, this is a finite element mesh prepared for the commercial code Nastram. In the context of this example, as only a 2D problem, with -only two degrees of freedom, is considered, the mesh is extremely simple; a set of rigid elements that connect all the nodes to the master node, positioned on the rotation axis. +As far as the structural mesh is concerned, this is a finite element mesh prepared for the commercial code Nastran. In the context of this example, as only a 2D problem, with +only two degrees of freedom, is considered, the mesh is extremely simple; a set of rigid elements that connect several slave nodes to the only master node, positioned on the rotation axis. The master node only has two degrees of freedom: pitch and plunge. -Another slave node is added, in the position of the center of mass, that will house the mass and inertia of the airfoil. +One of the slave nodes, at the position of the center of mass, houses the mass and inertia of the airfoil. It should always be recalled that, if interpolation is needed -between the strctural and fluid meshes, RBF will be used. The limitation of this linear interpolation is due to the fact that, if a 2D problem is concerned, the strctural points +between the structural and fluid meshes, RBF will be used. The limitation of this linear interpolation is due to the fact that, if a 2D problem is concerned, the structural points cannot all lie on the same line. Equivalently, if a 3D problem is tackled, the points cannot lie all in the same plane. For this reason, the thickness is represented in the FEM mesh for Nastran as shown below: ![FEM_Mesh](../../tutorials_files/multiphysics/unsteady_fsi_python/images/nastran_model.png) -As you can see, then exact profile is not required. The interpolation will take care of displacing correctly the fluid mesh. However, thickness must somehow be represented. +As you can see, the exact profile is not required. The interpolation will take care of displacing correctly the fluid mesh. However, thickness must somehow be represented. #### Configuration File for the fluid zone -First of all, the users should know that three configuarions file are required for this case: one for the fluid zone, one for the solid zone and one for the interface. -The configuration file for the fluid zone is very similar to a configuration file for a simple single zone simulation. Indeed, SU2 does not know about the external strctural +First of all, the users should know that three configuration files are required for this case: one for the fluid zone, one for the solid zone and one for the interface. +The configuration file for the fluid zone is very similar to a configuration file for a simple single zone simulation. Indeed, SU2 does not know about the external structural solver, it will only see the points on the aerodynamic mesh changing positions. For this reason, the solver keyword is set as: @@ -165,10 +165,10 @@ TIME_DOMAIN = YES TIME_STEP= 1e-3 ``` -It is important to set an appropriate convergence criteria for the fluid zone. Indeed, while the structural part is linear and requires no interations, it is important that -the fluid zone correcly converges for accurate results. +It is important to set an appropriate convergence criteria for the fluid zone. Indeed, while the structural part is linear and requires no iterations, it is important that +the fluid zone correctly converges for accurate results. -The relative residual cannot be used as this is reset at each inner iteration. Thus, aver the first inner loop, it would be difficult to obtain convergence as the absolute +The relative residual cannot be used as this is reset at each inner iteration. Thus, after the first inner loop, it would be difficult to obtain convergence as the absolute residuals are already quite low. For this reason we will use: ``` @@ -186,7 +186,7 @@ The solver can work in two ways: 1) It can impose the movement of a mode, with prescribed law, to provide forced response analysis -2) It can integrate in time the modal equation of motions to study the linearised +2) It can integrate in time the modal equations of motion to study the linearised structural deformations when the body is surrounded by the flow Available keyword for the config file: @@ -194,7 +194,7 @@ Available keyword for the config file: NMODES (int): number of modes to use in the analysis. If n modes are available in the punch file, but only the first m>>> Time iteration 0 / FSI iteration 0 <<<< @@ -382,11 +382,11 @@ Launching fluid solver for one single dual-time iteration... | 0| 7| 1.732970| -3.321408| -3.551232| -0.778728| ``` -This is the typical output that you will see. There was no initial deformation imposed and for this reason you can see that the mesh deformation system was solved by the initial guess. FSI iteration is the inner iteration index, and it will keep inccreasing untile the inner convergence if found. Then, this index will be set to zero and the time iteration will be increased. +This is the typical output that you will see. There was no initial deformation imposed and for this reason you can see that the mesh deformation system was solved by the initial guess. FSI iteration is the inner iteration index, and it will keep increasing until the inner convergence is found. Then, this index will be set to zero and the time iteration will be increased. Please do not confuse Inner_Iter with FSI iteration. The former is the iteration, in the fluid zone only, using the pseudo time; the latter is the iteration index between fluid and structure. -After all the computations are completed (i.e. for all the Mach numbers), in each case folder yuo will see a file called StructHistoryModal.dat. The first rows of this file, for Mach number 0.1, are reported below. +After all the computations are completed (i.e. for all the Mach numbers), in each case folder you will see a file called StructHistoryModal.dat. The first rows of this file, for Mach number 0.1, are reported below. ``` Time Time Iteration FSI Iteration q1 qdot1 qddot1 q2 qdot2 qddot2 @@ -398,7 +398,7 @@ Time Time Iteration FSI Iteration q1 qdot1 qddot1 q2 qdo 0.104 104 1 -0.1493 0.2931 56.9690 -0.2265 3.0535 592.1878 0.105 105 1 -0.1490 0.3493 55.3371 -0.2232 3.6407 582.3177 ``` -The first column contains the physical time (please note that we started the fluid-structure coupling after 99 time iterations), the second one contains the time iteration, the third one the number of FSI iterations required for convergence, then we have the time histories of the modes. +The first column contains the physical time (please note that we started the fluid-structure coupling after 99 time iterations), the second one contains the time iteration, the third one the number of FSI iterations required for convergence, then we have the time histories of the modes and their derivatives. For many applications this may be already the desired output. However, in this case, we actually want the physical rotation and displacement of the point at the rotation axis. A post processing step must be performed to multiply the mode shapes for their amplitude. This can be done with the provided matlab file. You only need to run the Main_compare.m file and it will take care of all the required operations. @@ -410,7 +410,7 @@ At the end of the matlab run, you will see outputs as the ones reported below. ![H_Ma01](../../tutorials_files/multiphysics/unsteady_fsi_python/images/h_Ma=0.1.png) ![Alpha_Ma01](../../tutorials_files/multiphysics/unsteady_fsi_python/images/alpha_Ma=0.1.png) -You can see how the frquency merging is nicely captured; after the flutter point the two frequencies are coincident and nonlinear effects are presents. Thus, comparing the Theodorsen theory and SU2 is not fully meaningful. +You can see how the frequency merging is well captured; after the flutter point the two frequencies are coincident and nonlinear effects are present. Thus, comparing the Theodorsen theory and SU2 is not fully meaningful. 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zp-xc)2A$Yf^I;$|NtQLBeTq~%;$3g=|J8So fa@@z3R$Nl3&CAq1^d631|3P!#;h&TDn)>}Ol}k-D literal 0 HcmV?d00001 From f3092ae96086bc9a2a84f890e8f76b6ffb9d69a9 Mon Sep 17 00:00:00 2001 From: Nicola-Fonzi <60700515+Nicola-Fonzi@users.noreply.github.com> Date: Thu, 10 Dec 2020 11:46:08 +0100 Subject: [PATCH 20/25] Update Dynamic_FSI_Python.md --- .../multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index 51a0c1b8..57bc12ad 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -64,7 +64,7 @@ $$\Csi=\frac{S}{mb}$$, $$r_{\alpha}^2=\frac{I_f}{mb^2}$$, $$\bar{\omega}=\frac{\ Where $$b$$ is the semi chord of the airfoil, $$\omega_h = \sqrt{\frac{K_h}{m}}$$ $$\omega_{\alpha} = \sqrt{\frac{K_{\alpha}}{I_f}}$$. If we fix them, the structure will behave always the same regardless of $$\rho_{\inf}$$. -In this context $$\Csi=0.25$$, $$r_{\alpha}=0.5$$, $$\bar{\omega}=0.3185$$ and $$\mu=100$$. +In this context $$\Csi=0.25$$, $$r_{\alpha}=0.5$$, $$\omega_{\alpha} = 45 rad/s$$ ,$$\bar{\omega}=0.3185$$ and $$\mu=100$$. Note that, as we will vary the Mach number, the density will also change accordingly. Thus, with given nondimensional parameters, the inertias and stiffnesses must be varied accordingly. 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zK2_L23sQM=^GS%C?0znsnVA_bvmhrTQdU=|!C~<%M*OLu2@(=0BAVXV1)@;BpXosC zrscw9^714`QV_xNB=Z|FD$E2Kq`!UbSbEfmzgN;IFkpZGH8Nr}wQv-*t#$avp%LVz zf`zZ1a{tr8mGjj{aw_U5%AW>#+^+&atfWgF2|#kV?}u;Qx@F1*TZRY`SBOBre#H~{ d`F|Gt2Za86S2qQZ;cp{fQ&H5!;xAi<{|62 Date: Thu, 10 Dec 2020 18:36:06 +0100 Subject: [PATCH 25/25] Updated fonts --- .../Unsteady_FSI_Python/Dynamic_FSI_Python.md | 91 ++++++++----------- 1 file changed, 36 insertions(+), 55 deletions(-) diff --git a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md index 57bc12ad..885bc3f4 100644 --- a/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md +++ b/_tutorials/multiphysics/Unsteady_FSI_Python/Dynamic_FSI_Python.md @@ -183,50 +183,41 @@ This configuration file will be read by the structural python solver included in The solver can work in two ways: -1) It can impose the movement of a mode, with prescribed law, to provide forced -response analysis +1. It can impose the movement of a mode, with prescribed law, to provide forced response analysis -2) It can integrate in time the modal equations of motion to study the linearised -structural deformations when the body is surrounded by the flow +2. It can integrate in time the modal equations of motion to study the linearised structural deformations when the body is surrounded by the flow Available keyword for the config file: -NMODES (int): number of modes to use in the analysis. If n modes are available in - the punch file, but only the first m