Merge pull request #137 from KratosMultiphysics/fsi/embedded-membrane…

…-example

[FSI] Update readme of flexible membrane example

fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md

@@ -1,34 +1,43 @@
-# Mixer with flexible blades
+# Flexible membrane airfoil
 
 **Author:** [Rubén Zorrilla](https://github.com/rubenzorrilla)
 
-**Kratos version:** 9.1
+**Kratos version:** 9.5
 
-**Source files:** [Mixer with flexible blades](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/source)
+**Source files:** [Flexible membrane airfoil](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source)
 
 ## Case Specification
-This example is specifically conceived to prove the extended scope of applicatoin of embedded mesh methods. Hence, it involves extremely large rotations, which would be impossible to solve by using a body fitted ALE based approach.
+This example reproduces the experimental study of the aerodynamics of a simplified two-dimensional membrane airfoil described in [1]. For doing so, the embedded FSI solver for thin-walled bodies is used [2]. This makes possible to avoid the common preprocessing and mesh entangling issues arising when dealing with volume meshes around membrane-like structures.
 
-The problem is set up as a 2D idealization of a turbine mixer with clockwise-anticlockwise alternate rotation. The problem geometry is a unit diameter circle with three embedded flexible blades. An imposed rotation is enforced in the blades axis to emulate the spin of the rotor. Such rotation changes the direction (anticlockwise to clockwise and viceversa) after More details on the dimensions, material settings and boundary conditions can be found in [here](https://doi.org/10.1016/j.cma.2020.113179).
+The airfoil measures 0.15m and is placed with an angle of attack of 4º. Its material properties are a Young modulus of 250e3Pa and null Poisson ratio. The inlet characteristic velocity is 2.5833m/s and the material properties are set such that the Re is 2500. The structure and fluid density ratio is 441.75.
 
 ## Results
-The fluid domain is meshed with a 45 and 540 radial and perimeter subdivisions Q1P1 elements centered structured mesh. Each one of the flexible blades is meshed with an 8x39 subdivisions structured mesh made with Total Lagrangian quadrilateral elements. The problem is run for 20s so three complete rotations (anticlockwise - clockwise - anticlockwise) are simulated.
+The fluid domain is meshed with 144k P1P1 elements. For the structure, 128 line elements implementing a simplified 2D nonlinear membrane model are used. The problem is run for 2s, with a ramp-up period of 1s, so to ensure that the steady state is reached.
 
-The obtained velocity and pressure fields, together with the level set zero isosurface representing the deformed geometry, are shown below.
+The obtained fluid velocity and pressure contour fields as well as the deformed structure displacement vector field are shown below.
 
 <p align="center">
 <figure>
-  <img src="data/embedded_fsi_mixer_Y_v.gif" alt="Velocity field and level set isosurface." style="width: 600px;"/>
+  <img src="data/embedded_fsi_membrane_airfoil_fluid_v.gif" alt="Fluid velocity contour field." style="width: 600px;"/>
   <figcaption>Velocity field and level set isosurface.</figcaption>
 </figure>
 </p>
 
 <p align="center">
 <figure>
-  <img src="data/embedded_fsi_mixer_Y_p.gif" alt="Pressure field and level set isosurface." style="width: 600px;"/>
+  <img src="data/embedded_fsi_membrane_airfoil_fluid_p.gif" alt="Fluid pressure contour field." style="width: 600px;"/>
+  <figcaption>Pressure field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_membrane_airfoil_structure_u.gif" alt="Structure displacement vector field." style="width: 600px;"/>
   <figcaption>Pressure field and level set isosurface.</figcaption>
 </figure>
 </p>
 
 ## References
-R. Zorrilla, R. Rossi, R. Wüchner and E. Oñate, An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures, Computer Methods in Applied Mechanics and Engineering (368), [10.1016/j.cma.2020.113179](https://doi.org/10.1016/j.cma.2020.113179)
+[1] P. Rojratsirikul, Z. Wang and I. Gursul, Unsteady Aerodynamics of Membrane Airfoils, AIAA 2008-613. 46th AIAA Aerospace Sciences Meeting and Exhibit, 2008 [10.2514/6.2008-613](https://doi.org/10.2514/6.2008-613).
+
+[2] R. Zorrilla, R. Rossi, R. Wüchner and E. Oñate, An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures, Computer Methods in Applied Mechanics and Engineering (368), 2020 [10.1016/j.cma.2020.113179](https://doi.org/10.1016/j.cma.2020.113179)