Dept Seminar : Jan 2007 Slide 1 Turbulence Modelling for Aerospace January 2007 Alistair Revell.

1Dept Seminar: Jan 2007 Slide

Turbulence Modelling for Aerospace

January 2007

Alistair Revell


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


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

Incr

easi

ng

co

st


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)

• 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

- the answer was NO


Testcase examples

Landing Gear

Full aircraft EFA

DES

Expt

URANS

Wing in deep stall

Ducted Cylinder


Derivation of new 3-equation model: SST-Cas

Increasing complexity

1 eqn.

Eg. Spalart Almaras

2 eqns.

Eg. k-

kSST

7 eqns.

RSM

uiuj -

3 eqns.

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-Cas model reproduces some effects of the Reynolds Stress Model (RSM)

Objective: develop a turbulence model for industry that is able to accurately predict transient flow effects without compromising cost and stability

• 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 ( )


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


• 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:

Implementation in Code_Saturne


Implementation of SST_Cas model

• 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

– Flowfield around NACA0012 at 20o, Re= 105

– Contour plots of long-time averaged Pressure with mean flow streamlines

(2-eqns) (3-eqns) (7-eqns)

• Reproduces similar results to RSM:


NACA0012 @ 20o

1 2 3

12 3

• Phase averaged velocity profiles <U>

• Good agreement of SST_Cas with RSM (SSG)

• Unsteady flow in wake of aerofoil:

misalignment of stress and strain is shown by eigenvectors, and elements are coloured by values of Cas


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


Cylinder in Square Duct

SST

SST-Cas

SST-DES

Streamlines Iso-Q contours

• 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-ij

2)

<U>


Wingtip VortexCTR 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.

EXPT NLEVM RSMEVMEXPT NLEVM RSMEVM

• 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)


Isolated Vortex

• 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.

CTR Summer Program 2006

U 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.


• 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

Wingtip VortexCTR Summer Program 2006

Hanging Nodes: Total Mesh ~ 750 000 cells Fully Structured: Total Mesh ~ 10 000 000 cells

• 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.


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


Conclusions 2

• 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

• Aerospace applications– 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.

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Dept Seminar : Jan 2007 Slide 1 Turbulence Modelling for Aerospace January 2007 Alistair Revell.

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