Turbulence Modelling for Aerospace January 2007 Alistair Revell

1. Turbulence Modelling for Aerospace January 2007 Alistair Revell 1

2. Outline • Review of EU Project work • An Outline of recent research • Derivation of a URANS model for stress-strain misalignment • Application to industrial cases • Future Work • Further model development • Application to aerospace 2

3. Increasing cost CFD in Aerospace: A comparison of methods • There is a range of numerical methods applicable to prediction of turbulent flow. • trade-off between calculation cost and accuracy/detail • the suitability of a method is dependent upon the application and the required results • Spalart (2000) compared these methods based upon the complete calculation of flow around a typical commercial jet aircraft at cruise conditions • DES was put forward as a compromise between URANS and LES URANS : Unsteady Reynolds Averaged Navier-Stokes DES : Detached Eddy Simulation LES : Large Eddy Simulation DNS : Direct Numerical Simulation 3

4. DESider • DESider(2004-07), has looked at improved URANS and hybrid LES-RANS approaches. • Aims to overcome deficiencies in RANS whilst retaining realistic computational requirements. • Objectives include: • Improved URANS modelling • Improved and standardised DES • Novel approaches (eg. SAS, Hybrid RANS-LES) • Embedded LES-RANS (inlet methods) Involved in all activities Detached Eddy Simulation for Industrial Aerodynamics • Previous EU project, FLOMANIA(2002-04), attempted to identify if any one turbulence modelling scheme was capable of tackling the range of challenges in an industrial case. (separation, reattachment, vortex shedding) • - the answer was NO 4

5. Wing in deep stall Full aircraft EFA Expt DES URANS Landing Gear Ducted Cylinder Testcase examples 5

6. Reynolds Averaged Navier Stokes equations are unclosed; require turbulence models • Turbulent models predict evolution of one or more quantities in order to approximate the Reynolds Stresses (-) or the turbulent viscosity () Increasing complexity 1 eqn. Eg. Spalart Almaras 3 eqns. 7 eqns. RSM uiuj - e 2 eqns. Eg. k-e, k-w SST SST-Cas • The parameter, Cas, provides a measure of the misalignment of the tensors of stress anisotropy, and strain, (Revell, Craft, Laurence 2006) • New SST-Casmodel reproduces some effects of the Reynolds Stress Model (RSM) Derivation of new 3-equation model: SST-Cas Objective: develop a turbulence model for industry that is able to accurately predict transient flow effects without compromising cost and stability 6

7. Advantages of SST-Cas model • The widespread success of two equation turbulence models is due in part to their compromise between complexity and numerical stability • But, in standard 2 equation Eddy viscosity models, the stresses are directly linked to the strains. • When strain Sij= 0 , stress anisotropy aij= 0 • No transport or history effects • This is not the case with a 7 equation RSM, where transport equations are solved for the six individual stress components. • In some cases, the additional equations have caused convergence problems • The SST-Cas model inherits stability advantages of eddy viscosity while accounting for some of the stress transport effects 7

8. Implementation in Code_Saturne • The misalignment parameter is defined as: Which will be zero when aij and Sij are mutually perpendicular (for 2D) • Where the implemented form of the transport equation is: • Which fits easily into the SST implementation with a modification of viscosity as: 8

9. Model implemented into Code_Saturne • - 3D unstructured finite volume code • Validated for simple 1D and 2D unsteady flows: • - homogenous cyclic strain, oscillating channel • extra equation found to add a 10-15% cost compared to a 2-equation model. • RSM is around 80-100% more expensive than a 2-equation model • Reproduces similar results to RSM: (7-eqns) (3-eqns) (2-eqns) • Flowfield around NACA0012 at 20o, Re= 105 • Contour plots of long-time averaged Pressure with mean flow streamlines Implementation of SST_Cas model 9

10. 1 3 2 1 2 3 • Unsteady flow in wake of aerofoil: • misalignment of stress and strain is shown by eigenvectors, and elements are coloured by values of Cas NACA0012 @ 20o • Phase averaged velocity profiles <U> • Good agreement of SST_Caswith RSM (SSG) 10

11. Cylinder in Square Duct • Experimental setup showing location of PIV data planes • work done at IMFT • Re = 1.4x106 • 3D Calculations with ~2x106 cells, where long-time averaged solutions obtained after: e.g. 5.6 ~ 2 weeks calculation on 16 processors 11

12. Cylinder in Square Duct <U> Streamlines Iso-Q contours SST SST-Cas SST-DES • In Streamlines and <U>, top half is experimental data: bottom half is numerical results • ‘Q’ criterion: a parameter used to visualise structures in the flow = (Sij2-Wij2) 12

13. Results from Linear and Non-linear EVM are found to exhibit a far too rapid decay of the vortex core. • A Reynolds stress transport model (RSM) reproduces the principal features found in the experimental measurements. (Craft et al 2006) Wingtip Vortex CTR Summer Program 2006 • Since standard RANS models over-predict the levels of turbulence in a vortex, they also tend to over-predict the decay rate of the axial velocity of a vortex. 13

14. Uq Ux • On the graph to the right, the black lines are DNS data (reference) at fixed time intervals after the start of the calculation. (Numerical results are in red) • The RSM and new SST-Cas are able to capture correctly this behaviour, while the SST model over-predicts the decay-rate as expected. Isolated Vortex CTR Summer Program 2006 • The case of an isolated decaying vortex was studied, using DNS data for initial conditions, to study the response of RANS models in closer detail. 14

15. This presents an opportunity for the use of unstructured meshes, which have the potential to reduce grid sizes by over 90%. • Initial results are encouraging Hanging Nodes: Total Mesh ~ 750 000 cells Fully Structured: Total Mesh ~ 10 000 000 cells Wingtip Vortex CTR Summer Program 2006 • Many cells are required to correctly resolve both the very thin boundary layer over the wing, and the core of the vortex behind the wingtip (Re=4.35x106). • Both regions are crucial in order to correctly model the flow. 15

16. Conclusions 1 • Equation derived to allow for stress-strain misalignment in URANS • Only solving 3 equations • Only small additional expense compared to EVM (additional ~15%) • Remains ~40% cheaper than a full RSM • Retains stability advantages of eddy viscosity over individual stress components. • Fully implemented into Code_Saturne • Good practise is to start the SST-Cas calculation from a converged SST flow field. • Further work • The possibility to use the SST-Cas model in a Detached Eddy Simulation (DES) framework should be explored • Development required for near-wall effects • Investigate inclusion of Reynolds stresses in momentum eqn. • Secondary flow effects 17

17. Code_Saturne is now an open source code University of Manchester will aim to become the hub for development We will benefit from the implementation of further capabilities from 3rd parties New version has ‘Chimera’ moving-grid feature allowing for calculation of Fluid-Structure Interactions Conclusions 2 • Aerospaceapplications • Ongoing work on wingtip vortex (paper for TSFP5) • Transient calculations can be used to study aeroacoustics • Investigate noise reduction e.g. jagged flap edges, casing around landing gear, cavities • Develop cross-discipline topics in aerospace areas • Fluid-Structure interactions: eq. aeroelasticity • Combustion in complex cases: eg. Entire jet engine flow • Drag reduction calculations can examine effect of bumps, grooves, dimples… • Unstructured code used to tackle complex geometries. 18