COMPARISON OF AERODYNAMIC MODELS FOR 1-COSINE …...Nastran coupled to external aerodynamic solvers through the OpenFSI interface Strong coupling used Displacements Forces Nastran

Funded by the European Union

COMPARISON OF AERODYNAMIC MODELS FOR1-COSINE GUST LOADS PREDICTION

IFASD 201725th - 28th June 2017, Como

C. Wales, R. G. Cook, D. P. Jones, A. L. GaitondeUniversity of Bristol, Faculty of Engineering


Outline• Background

• Aerodynamic models• DLM• UVLM• CFD

• Correction Matrices

• Aeroelastic Coupling

• Results• UAV wing• NASA CRM Wing


Background

• Aerogust project researching methods for gust loads prediction• Speeding up calculations

• Include more nonlinearities in model

• UVLM aerodynamic model can be coupled with non linear structural model


DLM

• MSC.NASTRAN used for DLM calculations gust calculations

• Sol 146

• Aeroelastic frequency response analysis in modal coordinates formulation:

Mode Deformation Rigid Gust


UVLM code

• 3 Parts• Vortex ring elements on body

• Layer of buffer panels in the wake

• Vortex particles in the wake

• Box method to speed up wake influence calculations

• Rigid body motions

• Deformations

• Gust interactions


CFD - Split Velocity Method

• Velocities are split into the prescribed gust components and the remaining velocity components

• Substituting into the Navier-Stokes equations and rearranging in terms of remaining velocity components leads to a set of equations similar to a moving mesh formulation plus source terms

• There are only gradients of the prescribed velocity in the source terms.

• Includes the interaction with the body

• Implemented in the Tau CFD solver

6

𝑢 = 𝑢 + 𝑢𝑔𝑣 = 𝑣 + 𝑣𝑔𝑤 = 𝑤 + 𝑤𝑔

Prescribed gust velocities

Remaining velocity components

Huntley, S., Jones, D., and Gaitonde, A. (2016). 2d and 3d gust response using a prescribed velocity method in viscous flows. In 46th AIAA Fluid Dynamics Conference, AIAA 2016-425


Corrections

• Apply corrections to the DLM and UVLM to match the sectional lift and moment from CFD or experimental data


DLM correction

The loads on each DLM strip can be written as

The aim is to correct the DLM so that it matches the loads from CFD

Rewriting as

The difference between the uncorrected DLM and CFD can be written as

Correction matrices can be solved for using a least squares approach

𝑭𝐷𝐿𝑀 = 𝑺𝑨−1𝒘

𝑭𝐶𝐹𝐷 = 𝑺𝑨−1𝑪𝒘+ 𝑪0

𝑭𝐶𝐹𝐷 = 𝑺𝑨−1⋱

𝑰 + 𝝐⋱

𝒘 + 𝑪0

∆𝑭 = 𝑺𝑨−1𝒘𝝐 + 𝑪0

Giesing, J., Kalman, T., and Rodden, W. P. (1976). Correction factory techniques for improving aerodynamic prediction methods. NASA CR-144967.


UVLM correction

The UVLM equations can be written as

The loads on each UVLM strip can be written as

Appling the following correction matrices to the ULVM

And equating the corrected UVLM to the CFD loads gives

This lead to the following equation for the correction factors

𝑭𝐶𝐹𝐷 = 𝑺𝒁𝑨−1𝑪𝒘+ 𝑺𝒁𝑨−1𝑪0

𝑭𝐶𝐹𝐷 = 𝑺𝒁𝑨−1⋱

𝑰 + 𝝐⋱

𝒘 + 𝑺𝒁𝑨−1𝑪0

∆𝑭 = 𝑺𝒁𝑨−1𝒘𝝐 + 𝑺𝒁𝑪0

𝑭𝑈𝑉𝐿𝑀 = 𝑺𝒁𝚪

𝚪 = 𝑨𝒘

𝚪 = 𝑨(𝑪𝒘 + 𝑪𝟎)


UVLM correction process

The corrected UVLM solves the following equations

Where the downwash has two components

𝒘 = 𝒘𝑏𝑜𝑑𝑦 +𝒘𝑤𝑎𝑘𝑒

The wake downwash depends on the strength of the shed vortex panels/particles. So the wake downwash changes with the correction matrices so the correction procedure has to be iterated

𝚪 = 𝑨(𝑪𝒘 + 𝑪𝟎)


Fluid Structure Coupling

Structure - Nastran Aerodynamics – Tau/UVLM

Splines

Nastran coupled to external aerodynamic solvers through the OpenFSI interfaceStrong coupling used

Displacements

Forces

Nastran splining matrices used for the transfer of forces and displacements between the aerodynamic and structural meshes

Valente, C., Jones, D., Gaitonde, A., et al. (2015). Openfsi interface for strongly coupled steady and unsteady aeroelasticity. IFASD 2015, IFASD 2013-178


UAV Wing

• Unswept, untapered wing• Span 25m

• Chord 2m

• Aerofoil NASA LRN 1015

• Beam stick model for Structure

• Aircraft mass 8000kg


UAV test cases

• Flight conditions

• Altitude 55000ft

• Mach 0.55

• Rigid response

• Aeroelastic response, wing clamped at root

Gust Length(m)

Gust velocity(m/s)

Equivalent AoA(degrees)

18.29 11.71 4.12

91.44 15.31 5.39

213.36 17.63 6.20

The main goal is to focus on the gust response analysis of interest in a design process:

With a design gust velocity given by :


UAV static correction

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Cl

Angle of attack (degrees)

UVLM DLM CFD

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 1 2 3 4 5 6

Cm

Angle of Attack (degrees)

UVLM corrected DLM corrected CFD

DLM and UVLM corrected to match CFD at 2°, 4° and 6°


UAV gust response rigid

30ft 150ft 350ft


UAV gust response aeroelastic

30ft 150ft 350ft


NASA Common Research Model• NASA Common Research model, is a generic wide body aircraft[1]

• Span 58.764• MAC 7m

• Structural model is a condensed beam stick version of the FERMAT structural model develop based on the NCRM[2]

[1] J. C. Vassberg, M. A. DeHaan, S. M. Rivers, and R. A. Wahls. Development of a

common research model for applied CFD validation studies, 2008. DPW4 website:

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaadpw/Workshop4/workshop4.html .

[2] T. Klimmek. Development of a Structural Model of the CRM Configuration for Aeroelastic

and Loads Analysis. In IFASD 2011 16th International Forum on Aeroelasticity and Structural

Dynamics, 24-25 June 2013, Bristol, United Kingdom, 2013.


• Flight conditions• Altitude 29995ft

• Mach 0.86

• Rigid response

• Aeroelastic response, wing clamped at root

Case H

Gust Length(m)

Gust velocity(m/s)

Equivalent AoA(degrees)

18.29 11.24 2.47

91.44 14.70 3.23

213.36 16.94 3.72

0

2

4

6

8

10

12

14

16

18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Gu

st v

elo

city

(m

/s)

Time (s)

The main goal is to focus on the gust response analysis of interest in a design process:

With a design gust velocity given by :


NCRM static correction

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Cl

Angle of attack (deg)

DLM_corrected UVLM_corrected CFD

-5.00E+00

-4.50E+00

-4.00E+00

-3.50E+00

-3.00E+00

-2.50E+00

-2.00E+00

-1.50E+00

-1.00E+00

-5.00E-01

0.00E+00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Cm

Angle of attack (deg)

DLM_corrected UVLM_corrected CFD

DLM and UVLM corrected to match CFD at 0°, 1° and 2°


NCRM rigid gust response

30ft 150ft 350ft


NCRM aeroelastic response

30ft 150ft 350ft


Conclusions

• UVLM methods can be corrected using steady CFD strip loads in the same way as DLM

• Correction improves prediction of 1-cosine gusts specified in CS-25

• Tends to under predict gust loads compared to DLM especially for shorter gust

• Geometrically non-linear version of UAV wing

• Full aircraft version of NCRM

• Free-Free

Future Work


The research leading to this work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 636053.

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COMPARISON OF AERODYNAMIC MODELS FOR 1-COSINE …...Nastran coupled to external aerodynamic solvers through the OpenFSI interface Strong coupling used Displacements Forces Nastran