An approach to predict gust effects by means of hybrid ROM/CFD simulations M. Bergmann 1, A. Ferrero 1, A. Iollo 1, H. Telib 2 1 Inria Bordeaux Sud-Ouest and Université de Bordeaux, Talence, France 2 Optimad Engineering, Torino, Italy
POD-CFD coupling POD can identify the main structures in a flow field by extracting the information from a database of snapshots Need for a robust POD model: ability to predict flows with parameter s values not present in the database Possible approach: POD-CFD coupling The POD model is used to define the boundary conditions for a reduced CFD domain The non linearities which are difficult to describe by POD and the phenomena not included in the database are directly taken into account by the CFD
Proper Orthogonal Decomposition F = XN s k=1 Snapshots from CFD simulation: U j s 1 apple j apple N s U POD (x,t)= i = XN s j=1 b j i U j s NX i=1 a i (t) i (x) (Sirovich approach) (Us k ) 2 ( 1) => @F @b j =0 [A] b = b Constrained minimisation problem Eigenvalue problem A mn = U m s U n s Correlation matrix
U ROM = U avg + NX i=1 a i i POD-CFD coupling with ai obtained at each time step by min No=number of points in the overlapping zone XN o l=1 (U l CFD U l ROM) 2! Uavg fixes the far field value The modes are zero in the far field The far field values which characterise the working condition (e.g. Reynolds number) are automatically satisfied Two completely independent models, one for velocity and one for pressure
G = min XN o POD-CFD coupling! 0 XN o (UCFD l UROM) l 2 = min @ (UCFD l Uavg l l=1 l=1 1 NX l a j j ) 2 A j=1 @G @a j =0 1apple j apple N [C] {a} = {d} {a} =[C] 1 {d} (Inverse matrix computed and stored) C ij = XN o l=1 l i l j d i = XN o l=1 l i(u l CFD U l avg)
The gust problem The evaluation of the load induced by a gust is a critical issue in the design of wind turbines and aircraft wings. There are two possible approaches to the description of the gust: If Lgust>>Lbody, the gust can be seen as a change in the far field velocity (IEC gust definition for wind turbines) otherwise the gust is described as a structure in the flow field which travels and interacts with the body
Example: cylinder (Re=200) and Rankine vortex (Ux field)
Original and reduced computational domains On uniform meshes, the reduction in the computational cost is approximately equal to the ratio between the areas of the original and reduced domain
POD-CFD: how to attract the gust? CLASSICAL POD U ROM (x,t)=u avg (x)+ If the gust is not in the small domain at the beginning of the simulation the calibration will never select the modes related to the gust POD+ FORCING TERM Ug (control function) NX a i (t) i (x) Introduction of a time dependent forcing term Ug: the POD describes the difference between the flow field and the forcing term i=1 U ROM (x,t)=u avg (x)+u g (x,t)+ NX a i (t) i (x) i=1
t t ECCOMAS Congress POD with forcing term The forcing term Ug should approximately describe the translation of the gust profile or the increase in the free stream velocity Ug is approximated, but the POD will introduce the corrections: NX U ROM (x,t)=u avg (x)+u g (x,t)+ a i (t) i (x) u Classical POD u i=1 POD+forcing term POD Ug POD
Forcing term Ug: translation of the vortex Simple and cheap description No decay of the vortex No interaction with the body POD will introduce the corrections 11
Convergence analysis: number of POD modes 12
Robust POD basis The coupled POD/CFD simulation requires a preliminary database of full CFD (expensive) simulations to build the POD model The POD is useful only if it is robust: it must be able to predict a configuration not in the database A possible approach is to use a Voronoi tesselation to sample the space of parameters
Prediction of a configuration not in the database 14
Prediction of a configuration not in the database 15
Prediction of a configuration not in the database 16
Phase problems related to the presence of large structures in the wake: POD creates a correlation between the position of the Rankine vortex and the position of the vortexes in the von Karman wake. Spatial scales in the wake are very similar to the Rankine vortex scale. Further investigations will be done for improve the robustness of the procedure when the database contains snapshots related to vortexes with a different phase
NACA0012 (Re=1000, α=5 ) and Rankine vortex (Ux field)
Full and reduced CFD domain ECCOMAS Congress
Interaction between NACA0012 airfoil and Rankine vortex: lift coefficient ECCOMAS Congress
Interaction between NACA0012 airfoil and Rankine vortex: lift coefficient POD model describes 86.5% of the energy
Interaction between NACA0012 airfoil and Rankine vortex: lift coefficient POD model describes 96.9% of the energy
Interaction between NACA0012 airfoil and Rankine vortex: lift coefficient POD model describes 99.4% of the energy
Interaction between NACA0012 airfoil and Rankine vortex: lift coefficient POD model describes 99.9% of the energy
Far field velocity increase for NACA0012 airfoil at Re=1000 and α=5 Ug(x,y,t) is a uniform field which describes the change of U
Far field velocity increase for NACA0012 airfoil: lift coefficient ECCOMAS Congress
Far field velocity increase for NACA0012 airfoil: lift coefficient POD model describes 91.4% of the energy
Far field velocity increase for NACA0012 airfoil: lift coefficient POD model describes 98.7% of the energy
Far field velocity increase for NACA0012 airfoil: lift coefficient POD model describes 99.8% of the energy
Far field velocity increase for NACA0012 airfoil: lift coefficient POD model describes 99.9% of the energy
Far field velocity increase for NACA0012 airfoil: lift coefficient POD model describes 99.99% of the energy
Future work Investigation of more general forcing functions Ug Robustness test for problems with several design parameters Evaluation of different calibration procedures (choice of overlapping region, function which is minimised, ) Further investigations for phase problem related to the coupling between the gust and the structures in the wake
Acknowledgments This work has been funded by the European Commission through the AeroGust Project (grant agreement number 636053).
Thank you for your attention ECCOMAS Congress