ADJOINT BASED AEROELASTIC SHAPE OPTIMIZATION OF A SLENDER WING MOUNTED ON A LOITERING MUNITION

5^th Annual SU2 Conference

1 October 2024

Ongoing MSc Study By:

Emirhan Evin

Supervisor : Prof. Dr. İsmail H. Tuncer

OUTLINE

• INTRODUCTION
• PROBLEM DEFINITION
• FLUID DOMAIN PROPERTIES
• FLOW SOLUTION
• STRUCTURAL PROPERTIES
• STRUCTURAL SOLUTION
• FSI ANALYSIS
• ADJOINT SOLUTION
• AN ODD PROBLEM
• FUTURE WORK

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INTRODUCTION

Tube/Air launched munitions face difficulties while opening their wings or control surfaces due to the excessive final deflection and root bending moments. This problem became more important with the increased popularity of loitering munitions.

Altius 700 – An example of Air Launch

Hero 30 – An example of Tube/Ground Launch

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PROBLEM DEFINITON

Conceptual Configuration

• Airfoil : SD7037
• Span : 2000 mm

The main objective of the study is to optimize the wing geometry of a tube/air launched munition to minimize;

• Drag

While;

• Keeping the lift fixed
• Reducing the amount of tip deflection
• Reducing the bending moment at the wing root
• Keeping the span fixed
• Preventing the wings colliding during the opening phase

• Chord : 200 mm
• Length : 1630 mm

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PROBLEM DEFINITON

Simple thinplate is chosen to model wing structure. Although more complex wing structure models have been tried none of them converged / deformed successfully.

Clamped boundary condition is assigned to the blue part on the figure. �Wing structure model starting from 11.25% of the chord length. The distance is approximately 22.5mm

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PROBLEM DEFINITON

Placement of the thinplate structure inside the wing

Following structural models were tried but failed.

Thick, hollow shell

Rib – Spar formation

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FLUID DOMAIN PROPERTIES

Farfield :: L=30m, D=20m

Farfield and all sources are in the form of cylinder.�

Fluid domain mesh is unstructred. All the sources are used to cluster mesh close to the body and refine the expansion of the cells to the farfield.

Source1 :: L=16.5m, D=11m

Source2 :: L=9m, D=6m

Source3 :: L=3.6m, D=2.4m

Geometry

4.5 m

2.5 m

1.8 m

3.6 m

5.0 m

9.0 m

Alignment of the sources can be seen in this figure.

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FLUID DOMAIN PROPERTIES

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FLOW SOLUTION

With the given setup, 4 different fluid meshes are obtained, here the results of the wings only.

Solver : RANS

Turb. Model : SST – V2003m

Mach : 0.1

Alpha : 0°

Beta : 0°

Density : 1.11164 kg/m³

Viscosity : 1.758e-5

Speed of Sound: 336.434 m/s

Temperature : 281.65 K

Pressure : 89874.56 Pa

Re : 4.255e5

First cell height to achieve y+ ~1: 1.0405e-5 m

Required layer amount: 27

Altitude : 1000 m

Conv Criteria : RMS<1e-10

Num. Method : JST

The 19.5 million mesh is chosen considering accuracy and speed

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FLOW SOLUTION

Y+ Distribution [19.5m mesh]

Pressure Distribution [19.5m mesh]

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STRUCTURAL PROPERTIES

T

L

H

Solid domain’s mesh is prepared structred. By changing the shown named parameters, different solid meshes are created.

​

These parameters stating the number of nodes used in that direction.

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STRUCTURAL SOLUTION

1kPa pressure difference is created between the top and bottom surfaces of the wing and displacement values obtained. The 270-35-4 [27438 cells] mesh is chosen considering speed and accuracy

SOLVER = ELASTICITY

GEOMETRIC_CONDITIONS = SMALL_DEFORMATIONS

MATERIAL_MODEL = LINEAR_ELASTIC

MATERIAL_COMPRESSIBILITY= COMPRESSIBLE

MATERIAL_DENSITY= 2700.0

ELASTICITY_MODULUS = 70E9

POISSON_RATIO = 0.33

FORMULATION_ELASTICITY_2D = PLANE_STRAIN

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STRUCTURAL SOLUTION

Displacement Magnitude [m]

VonMises Stress [Pa]

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FSI ANALYSIS

Fluid and structural solver settings are held similar to the previously shown analysis. Coupling is done throught the following configuration files:

coupled.cfg

SOLVER = MULTIPHYSICS CONFIG_LIST = (fluid.cfg, solid1.cfg, solid2.cfg)�MULTIZONE_SOLVER = BLOCK_GAUSS_SEIDEL OUTER_ITER = 20�KIND_INTERPOLATION = ISOPARAMETRIC CONSERVATIVE_INTERPOLATION = YES

DEFORM_STIFFNESS_TYPE = INVERSE_VOLUME DEFORM_LINEAR_SOLVER = CONJUGATE_GRADIENT

DEFORM_LINEAR_SOLVER_PREC = ILU DEFORM_NONLINEAR_ITER = 1

DEFORM_LINEAR_SOLVER_ITER = 10000 DEFORM_LINEAR_SOLVER_ERROR = 1E-14

DEFORM_CONSOLE_OUTPUT = YES MARKER_ZONE_INTERFACE = (wing1, wing1S_solid , wing2 , wing2S_solid)

​

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FSI ANALYSIS

At the FSI equilibrium, change in the aerodynamic coefficients is observed.

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FSI ANALYSIS

Wing2 – [Orange] Original Geom – [Grey] Position after the FSI analysis

Displacement magnitude of the wings [m] / Top view

Wing1 – [Orange] Original Geom – [Grey] Position after the FSI analysis

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FFD BOX SETTINGS

FFD_TOLERANCE = 1E-10 DV_KIND = FFD_SETTING

FFD_ITERATIONS = 500 DV_MARKER = ( wing1 , wing2)

FFD_DEFINITION = (WINGBOX, -0.126, -1.03, -0.0577, 0.134, -1.03, … DV_VALUE = 0.0

DEFINITION_DV = ( 11, 1.0 | wing2 | WINGBOX, 0, 0, 0, 0.0 … FFD_DEGREE = (5, 21, 1)

DV_PARAM =( WINGBOX, 0, 0, 0, 0.0, 0.0, 1.0 ) FFD_CONTINUITY = 2ND_DERIVATIVE

Red points are fixed

To generate FFD Box, SU2DEF used with the modified config file, which has following additional settings

# Total Design Points = 264

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ADJOINT SOLUTION

The configuration file:

​

MATH_PROBLEM= CONTINUOUS_ADJOINT

OBJECTIVE_FUNCTION= DRAG

CONV_NUM_METHOD_ADJFLOW= JST

SLOPE_LIMITER_ADJFLOW= VENKATAKRISHNAN

ADJ_JST_SENSOR_COEFF= ( 0.0, 0.02 )

TIME_DISCRE_ADJFLOW= EULER_IMPLICIT

CFL_REDUCTION_ADJFLOW= 0.8

LIMIT_ADJFLOW= 1E6

SENS_REMOVE_SHARP = NO

​

SU2_CFD is used for solution.

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AN ODD PROBLEM

Oddly deformed fluid surface after mapping structural deformation with RBF

​

Changing settings did not solve the problem…

In between every rib surface, trailing edge become step like structure with ‘Y’ shape and every mid points between ribs and spars, surface becomed crippled/wavy with ISOPARAMETRIC.

​

Changing settings did not solve the problem…

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FUTURE WORK

• Define objective function for optimization in configuration file
• Define constraints for optimization in configuration file
• Complete optimization and evaluate the results
• Try new objective functions and compare the results

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ADJOINT BASED AEROELASTIC SHAPE OPTIMIZATION OF A SLENDER WING MOUNTED ON A LOITERING MUNITION

Thank you for your attention…

Presented By : Emirhan Evin

E-mail : emirhan.evin@metu.edu.tr