Update for LM2015 transition model

_docs_v7/Physical-Definition.md

@@ -158,3 +158,25 @@ The following modifications are allowed:
   - Curvature corrections are currently not implemented.
 
 Modifications from each of these three groups can be combined, for example `SST_OPTIONS= V2003m, VORTICITY, SUSTAINING`
+
+## Transition Models ##
+
+| Solver | Version |
+| --- | --- |
+| `*_RANS` | 7.5.0 |
+
+This section describes how to setup transition models for RANS simulations. Transition is activated using the option `KIND_SOLVER= RANS`, or `KIND_SOLVER= INC_RANS` together with a choice of `KIND_TRANS_MODEL` (different from `NONE`).
+Currently, the only valid option for `KIND_TRANS_MODEL` is `LM`, for Langtry-Menter transition models.
+Different submodels and correlations are then specified via `LM_OPTIONS` (for example `LM_OPTIONS= LM2015, MENTER_LANGTRY`).
+
+The following modifications are allowed:
+- Versions:
+  - `LM2015` - Correction to include stationary crossflow instabilities. It has to be used only in 3D problems. The RMS of roughness used in this model has to be set through the separate option `HROUGHNESS`.
+- Correlations (only one can be specified):
+  - `MALAN` - This is the default correlation when the LM model is coupled with the `SA` turbulence model.
+  - `SULUKSNA` - This should be used only if the `SST` model is used. It should require a formulation of the Re_theta_t correlation that omits the pressure gradient parameter, however it is not clear. 
+  - `KRAUSE` - This correlation should be used for hypersonic flows. Its implementation at the moment is unclear due to inconsistencies in the literature.
+  - `KRAUSE_HYPER` - This correlation should be used for hypersonic flows. Its implementation at the moment is unclear due to inconsistencies in the literature.
+  - `MEDIDA` - Designed for `SA` turbulence model. Has problems when dealing with separation induced transition.
+  - `MEDIDA_BAEDER` - Designed for `SA` turbulence model. Has problems when dealing with separation induced transition.
+  - `MENTER_LANGTRY` - This is the default correlation when the LM model is coupled with the `SST` turbulence model.

_vandv/LM_transition.md

@@ -15,23 +15,24 @@ To validate the LM model, the simulation results of SU2 are compared with the re
 
 Flow conditions are the reference from : https://doi.org/10.2514/6.2022-3679 and [AIAA Transition modeling workshop-I](https://transitionmodeling.larc.nasa.gov).
 
-| Case | T3A | T3B | T3Am | NLF0416|
-| --- | --- | --- | --- | --- |
-|Inlet Velocity (m/s)| 69.44 | 69.44 | 19.8 | 34.72 |
-|Density (kg/m^3) | 0.053 | 0.053 | 1.2 | 2.13 |
-|Viscosity (kg/ms) | 1.85E-5 | 1.85E-5 | 1.79E-5 | Sutherland's Law |
-|Freestream Temperature (K) | 300 | 300 | 300 | 300 |
-|Unit Reynolds number (1/m) | 2.0E5 | 2.0E5 | 1.328E6 | 4.0E6 | 
-|Mach Number | 0.2 | 0.2 | 0.058 | 0.1 |
-|AoA | 0.0 | 0.0 | 0.0 | 0.0 |
-|Viscosity Ratio| 11.9 | 99.0 | 9.0 | 1.0 |
-|Freestream Turbulence Intensity (%) | 5.855 | 7.216 | 1.0 | 0.15 |
+| Case | T3A | T3B | T3Am | NLF0416 | E387|
+| --- | --- | --- | --- | --- | --- |
+|Inlet Velocity (m/s)| 69.44 | 69.44 | 19.8 | 34.72 | 20.42 |
+|Density (kg/m^3) | 0.053 | 0.053 | 1.2 | 2.13 | 0.175 |
+|Viscosity (kg/ms) | 1.85E-5 | 1.85E-5 | 1.79E-5 | Sutherland's Law | Sutherland's Law |
+|Freestream Temperature (K) | 300 | 300 | 300 | 300 | 288.15 |
+|Unit Reynolds number (1/m) | 2.0E5 | 2.0E5 | 1.328E6 | 4.0E6 | 2.0E5 |
+|Mach Number | 0.2 | 0.2 | 0.058 | 0.1 | 0.06 |
+|AoA | 0.0 | 0.0 | 0.0 | 0.0 | 0,2,4,6 |
+|Viscosity Ratio| 11.9 | 99.0 | 9.0 | 1.0 | 1.0 |
+|Freestream Turbulence Intensity (%) | 5.855 | 7.216 | 1.0 | 0.15 | 0.001 |
+|Turbulence Problem | SST | SST | SST | SST | SA/SST |
 
 
 ## Mesh Description
 
-The grids of T3A, T3B, and NLF cases are provided by [TMW](https://transitionmodeling.larc.nasa.gov/workshop_i/)(Transition Model Workshop). And, The grid of T3Am was made with reference to https://doi.org/10.2514/6.2022-3679.
-If you want to run the above cases, you can use only the fine-level grid files available in the [SU2 V&V repository](https://github.com/su2code/Tutorials/tree/master/compressible_flow/Transitional_Flat_Plate/).
+The grids of T3A, T3B, and NLF cases are provided by [TMW](https://transitionmodeling.larc.nasa.gov/workshop_i/)(Transition Model Workshop). The grid of T3Am was made with reference to https://doi.org/10.2514/6.2022-3679. At the moment, no mesh convergence study has been performed on E387 case. The grid of Eppler E387 was made with reference to https://doi.org/10.1177/0954406217743537.
+If you want to run the above cases (Flat plate), you can use only the fine-level grid files available in the [SU2 V&V repository](https://github.com/su2code/Tutorials/tree/master/compressible_flow/Transitional_Flat_Plate/). If you want to run the E387 test case you can use the mesh file available in the [SU2 V&V repository](https://github.com/su2code/Tutorials/tree/master/compressible_flow/Transitional_Airfoil/)
 
 
 ## Numerical Scheme 
@@ -51,10 +52,18 @@ If you want to run the above cases, you can use only the fine-level grid files a
 | Spatial Discretization Flow | second-order Upwind | MUSCL_FLOW |
 | Spatial Discretization Turbulence | second-order Upwind | MUSCL_YES |
 
+| E387 | SU2 |
+| --- | --- |
+| Flux | L2ROE/ROE |
+| Gradient | WEIGHTED_LEAST_SQUARES |
+| Spatial Discretization Flow | MUSCL_FLOW |
+| Spatial Discretization Turbulence | UPWIND |
+
 ## Results
 
-Present results of all grid resolutions and then plot the results of the fine-level grid separately. If you want to see other results of the gird level, you can see them at "vandv_files/LMmodel".
-All of the flat plate results(= attached flow) are in good agreement with the Fluent results. But, the Airfoil results have the oscillation near the separation region both Fluent and SU2. 
+Present results of all grid resolutions and then plot the results of the fine-level grid separately. If you want to see other results of the grid level, you can see them at "vandv_files/LMmodel".
+All of the flat plate results(= attached flow) are in good agreement with the Fluent results. But, the NLF0416 results have the oscillation near the separation region both Fluent and SU2. 
+All of the E387 results are in good agreement with respect to experimental results. Only the combination SST_v2003m-LM seems to predict early transition at higher angles of attack.
 
 
 
@@ -135,3 +144,38 @@ Instantaneous result is :
 <img src="/vandv_files/LM_model/NLF/Inst_All_Cf.png" alt="Fine level result comparsion of Cf distribution on NLF-0416" />
 <img src="/vandv_files/LM_model/NLF/Inst_Fine_Cp.png" alt="Fine level result comparsion of Cp distribution on NLF-0416" />
 <img src="/vandv_files/LM_model/NLF/Inst_Fine_Cf.png" alt="Fine level result comparsion of Cf distribution on NLF-0416" />
+
+
+### E387
+Experimental results are available. The pressure coefficient distribution has been compared for 4 angles of attack, namely 0deg, 2deg, 4deg, and 6deg. Cl-alpha and polar curves are also avaliable for comparison.
+
+Pressure coefficient distribution obtained through ROE scheme.
+
+<p align="center">
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_0_Roe.png" alt="-Cp distribution for AoA = 0deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_2_Roe.png" alt="-Cp distribution for AoA = 2deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_4_Roe.png" alt="-Cp distribution for AoA = 4deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_6_Roe.png" alt="-Cp distribution for AoA = 6deg" />
+
+
+Cl-alpha and polar curve obtained through ROE scheme.
+
+<p align="center">
+<img src="/vandv_files/LM_model/Eppler/CLAlpha_ROE.png" alt="Cl-alpha curve" />
+<img src="/vandv_files/LM_model/Eppler/Polar_ROE.png" alt="Polar curve" />
+
+
+Pressure coefficient distribution obtained through L2ROE scheme.
+
+<p align="center">
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_0_L2Roe.png" alt="-Cp distribution for AoA = 0deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_2_L2Roe.png" alt="-Cp distribution for AoA = 2deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_4_L2Roe.png" alt="-Cp distribution for AoA = 4deg" />
+<img src="/vandv_files/LM_model/Eppler/CPPlots/AoA_6_L2Roe.png" alt="-Cp distribution for AoA = 6deg" />
+
+
+Cl-alpha and polar curve obtained through L2ROE scheme.
+
+<p align="center">
+<img src="/vandv_files/LM_model/Eppler/CLAlpha_L2ROE.png" alt="Cl-alpha curve" />
+<img src="/vandv_files/LM_model/Eppler/Polar_L2ROE.png" alt="Polar curve" />