Multigrid accelerated numerical methods based on implicit scheme for moving control volumes for WT flows simulatingE.Kazhan, I.Kursakov, A.Lysenkov
Explicit approximation – convective & diffusion fluxes • convection: Godunov-Kolgan-Rodionov(Russian TVD) • diffusion: central-difference approximation • sources: local-implicit scheme • stable only with CFL ≤ 1 – turbulent model source terms
Implicit scheme. Smoother «explicit» part Roe linearization Linear system: Next step value:
Localization Example: 1-D Euler (for simplification) Gauss-Zeidel
Zonal approach Explicit scheme area Implicit scheme: • Large computation time per step • CFL can be larger than 1 • Effective only with huge CFL • Results: incorrect description of global-scale processes Zonal approach: • Ignoring small-scale processes in boundary layer, assuming them as quasi-steady • Correct global-scale processes description • Global-scale processes predominate the behavior of boundary layer Implicit scheme area P0 Zone separation: • main (inviscid) area - explicit scheme • thin layer near wall - implicit scheme
Explicit-implicit combination Explicit Implicit
Calculation speed-up: multigrid Fine grid High solution accuracy Low convergence speed Coarse grid Low solution accuracy High convergence speed
RANS in rotating frame No change of flows Additional terms appear in the sources - rotating rate - axis of rotation This system can be solved, but there are difficulties in the calculation of the far field at long distance to the axis of rotation
RANS on rotating mesh Special thanks to Dr. V.Titarev The flow through the rotating mesh faces An amendment to the Coriolis force For rotation around the axis X: Additional terms are entered into the calculation of flows associated with the flow due to the grid rotation. In the source term is the correction to the Coriolis force.
Solver modifications for solutions on rotating mesh • The solution of the Riemann problem of the discontinuity decay on moving mesh • Modification of the boundary conditions: • slip condition - given by the rotation rate • impermeability condition – condition is stated for • the "Riemann" condition – mesh rotation rate is taken into account in determining the flow direction • Time step correction for the explicit scheme • Roe matrixes are modified for implicit scheme
Features of the implicit scheme on rotating meshes The matrix of the Roe matrix eigenvalues: Rotating rate is accounted in the stabilizing matrixes
Implicit smoother test case Boundary layer on plateM = 0.8 Re = 22.8×106 NACA 0012 M = 0.8 α = 0° Re = 9×106 CPU time CPU time Acceleration: 27 times Acceleration: 20 times COMGLEI (Combination of Global and Local tau type with Explicit and Implicit schemes)
Multigrid test case Friction drag coefficient Onera M6 wing M = 0.8395 α = 3.06° Re = 11.72×106 Residual Lift coefficient Fivefold solution convergence acceleration
Rotating mesh test case Computation PSP Precision on most considered regimes – 3 - 4 %
The thrust reverser impact on aircraft aerodynamics Lift velocity “Jump” in Lift magnitude due to the flow structure reconfiguration
The thrust reverser impact on aircraft aerodynamics Higher pressure zones • Landing devices impacts on the reversed jets propagation • Calculations considered landing devices allow determining the high loads zones
WT modeling Brand new estimation of corrections for CL_max caused by the WT walls are obtained
Propeller characteristics calculation approach application WTТ-104 • Obtaining the integral characteristics of propeller: thrust, torque • Propeller and airframe interference • Experimental data corrections : • Calculation of the shaftcone and propeller blades interference • Calculation of the influence of the experimental setup elements on the propeller characteristics • Reynolds number influence Propeller test rig VP-107
Propellers calculation features Flow separation Mesh refinement at the blade end is required The maximum propeller thrust mode is alike the flow separation regime. Separation from the propeller blades should be well predicted.
Conclusion • Combined method based on the Godunov-Kolgan-Rodionov is proposed. • Acceleration: • «Boundary layer on plate» ‑ 27 times; • «Profile NACA0012» – up to 20 times; • 3. Use of the multigrid approach demonstrates that the convergence of the solution is fivefold accelerated. • 4. The solvers developed in this work allow to solving the wide class of stationary problems of computational aerodynamics.