Karthikeyan Duraiswamy James D. Baeder James D. Baeder Alfred Gessow Rotorcraft Center University of Maryland College Park, MD Mar Case-3 Validation using RANS and DES tools.

Introduction Boundary layer flows with separation and downstream re- attachment can be classified as non-equilibrium.  Generally, production and dissipation of TKE are not balanced. Difficult to characterize since multiple length scales present.  Can expect RANS to struggle. Objective: to assess RANS capabilities and explore higher level approximations.  Preliminary Detached Eddy Simulation of the baseline uncontrolled case attempted.

Solution Methodology Codes used: OVERFLOW and TURNS (Originally Transonic Unsteady Rotor Navier-Stokes). Unsteady Compressible RANS. Turbulence Models: Spalart-Allmaras / Menter-SST (Overflow). Spatial discretization: Inviscid: Roe-upwinding (3 rd /5 th order) / 2 nd order central. Viscous: 2 nd order central. Time Integration: 2 nd order BDF (unsteady), Implicit Euler (steady). Both codes generate identical results for RANS. DES computations with TURNS.

Grids 4-Block structured grid provided by organizers. 2D computations: fine grid (Grid 1): points, coarse grid (Grid 2): every other point. y+ 80 points in boundary layer. Further coarsening of grids (y+<2.5) showed grid independence. Alternate hyperbolic grids with clustering in shear layer did not affect RANS solution significantly. 3D and DES grids explained later in the presentation.

Boundary Conditions Suction/Blowing: Extrapolate ρ and p from interior and specify momentum. ( ρ v)/(ρ inf v inf )= (steady). ( ρ v)/(ρ inf v inf )= sin(2 π f t) (unsteady).  Extrapolating T o instead of ρ gave identical results. Viscous (Inviscid) Walls: No-slip (Tangency) and extrapolation of p and ρ. Inlet: Characteristic BC with Riemann invariants. Outflow: Specified pressure with extrapolation of ρ, V. Block Interface: Average solution from interior of both grids.

Results For a non-equilibrium flow, turbulence model can be expected to dominate the RANS solution. Modeling the various mixing scales is bound to cause errors in solution. Before evaluating the turbulence model or RANS in general, necessary to look at other procedures in the solution. Evaluation of following are made:  Normal spacing and Grid adaptation/refinement in separated region.  Extent of outflow region.  Inviscid differencing: Upwind/Central diff.  Turbulence model: SA (with different production terms) and Menter-SST.  3D effects: Extruded Grid 2 with 51 points (z+ ~ 2) in half- span. Viscous wall BC on one end along entire length (No end plate) and span-wise symmetry. Single grid.

Cp: Upwind/Central diff. No flow Suction

Comparison of SA/Menter-SST Cp Cf

Comparison of 2D/3D Cp Cf

U-velocity – SA/SST 2D (No Flow) x/c=0.65 x/c=0.80 x/c=1.0 x/c=1.3

Reynolds shear stress - SA/SST 2D (No-Flow) x/c=0.65 x/c=0.80 x/c=1.0 x/c=1.3

SA 2D/3D u’v’ x/c=0.65 U x/c=0.80 U x/c=0.65 u’v’ x/c=0.80

Suction

Zero-mass Jet (612 steps per cycle) Normal Velocity at slot exit Mass flow co-efficient at slot exit

Comparison of No-flow, Steady suction and Zero-mass jets Cp Cf

RANS Summary Grid resolution seems to be adequate – orders of magnitude less than DES/LES/DNS. Turbulence model dominates solution. Under-predicts suction peak. Larger adverse pressure. Poor prediction of separation and re-attachment regions (especially Reynolds-stress). Size of re-circulating bubble over-predicted. All the above carried over to prediction of steady suction and zero-mass cases also. Good prediction of momentum co-efficient and peak velocity at slot exit for control cases – useful insight in developing a surface boundary condition.

Possible causes of discrepancy due to RANS. Isotropic eddy viscosity  Unreliable for turbulent normal stress prediction.  Hence cannot model rotation and curvature effects inherently. Need empiricism (SA-RC).  Since non-equilibrium, production (and dissipation) terms become important.  Bradshaw: Eddy viscosity is like a mongrel dog on a leash – It generally follows the master, but it will also be up to some mischief along the way. Reynolds Stress Models can help cure the above (at least conceptually), but more constants and higher cost. Any RANS model can be expected to struggle with such flows because flow is inherently unsteady.  Almost impossible to correctly model mixing due to eddies of various length scales.

Other factors. 3D effects  Experimental results are 2D, but what about CFD modeling?. Blockage effects. Boundary conditions. Experimental uncertainty?.

DES-details. Idea of DES: Single turbulence model that functions as RANS model near the wall and a Smagorinsky-type sub-grid scale model away from it.  Achieved by the approximate balance of production and destruction terms. The S-A model: distance function d=min (d wall, 0.65 Δ), Δ =max(δ x, δ y,δ z ) To expect meaningful solutions, spatial and temporal discretization should be fine enough in the LES region. Spatial discretization: Δ much smaller than local eddy length scale. Temporal discretization: Time-step should be small enough to resolve eddy convection. CFL ~ 1.

DES – Grid spacing Grid dim: 400x130x61~3x10^6 points. Normal spacing: y+=2.0 Target spacing: δ/15= c Spanwise spacing: c. Periodic spanwise length : 4 δ = 0.24 c Single grid, no slot, baseline case only.

DES Grid plane Hyperbolic grid

Evolving DES solution Started from an extruded RANS solution superimposed with random 3D disturbances. Δt = a ∞ / c Dominant shedding frequency ~ 36 Hz. A B

RANS Spanwise Vorticity Contours

DES – Instant A Spanwise Vorticity Contours

DES – Instant B Spanwise Vorticity Contours

Instant A: Q=0.05

Instant A: Q=3

Instant B: Q=3

Instantaneous Cp Instant A Instant B