Constrained Aero-elastic Multi-Point Optimization Using the Coupled Adjoint Approach
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1 Chart 1 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Aero-elastic Multi-Point Optimization Using the Coupled Adjoint Approach M. Abu-Zurayk MUSAF II Colloquium 20th Sept. 2013, Toulouse
2 Chart 2 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Table of Contents Motivation Formulation of the Coupled Adjoint Approach Test Case Description Unconstrained Single-Point Optimization Constrained Single- and Multi-Point Optimizations Future Work: Gradient Correction due to Trimming Conclusions
3 Chart 3 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Courtesy of Stefan Keye
4 Chart 4 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape The effect becomes more evident towards the wing tip Courtesy of Stefan Keye
5 Chart 5 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design
6 Chart 6 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects)
7 Chart 7 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects). BUT this increases the weight
8 Chart 8 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects). BUT this increases the weight 2. Design the Fight shape and inversely compute the Jig shape
9 Chart 9 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects). BUT this increases the weight 2. Design the Fight shape and inversely compute the Jig shape. Requires experience. What about multipoint? Aeroelastic deformation is dependent on the flow condition (Mach, lift, )
10 Chart 10 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects) 2. Design the Fight shape and inversely compute the Jig shape. BUT this increases the weight. Requires experience. What about multipoint? Aeroelastic deformation is dependent on the flow condition (Mach, lift, ) 3. Start with Jig shape and design Flight shape
11 Chart 11 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation During the flight, the wing deforms due to the aero-elastic effects. The aero-elastic deformation significantly modifies the wing shape (twist and bending) and impacts the aerodynamic coefficients => need to take them into account in the design phase. Flight Shape Jig Shape Several approaches for dealing with elasticity in wing design 1. Stiffer wing reduces the deformation (elastic effects) 2. Design the Fight shape and inversely compute the Jig shape. BUT this increases the weight. Requires experience. What about multipoint? Aeroelastic deformation is dependent on the flow condition (Mach, lift, ) 3. Start with Jig shape and design Flight shape. Works for multipoint. However, requires coupled CFD-CSM simulations
12 Chart 12 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation The aero-elastic equilibrium is obtained after several couplings between aerodynamics and structure and incurs high-computational cost => in case of optimization efficient strategies are required Aerodynamics Deformations Loads Structure
13 Chart 13 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation The aero-elastic equilibrium is obtained after several couplings between aerodynamics and structure and incurs high-computational cost => in case of optimization efficient strategies are required Gradient-based optimization algorithms are known to be efficient but computing the gradients is expensive with the standard finite differences approach. Traditional Finite Differences Approach Design Variables Loop over number of design variables Aerodynamics Deformations Loads Structure Gradients
14 Chart 14 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Motivation The aero-elastic equilibrium is obtained after several couplings between aerodynamics and structure and incurs high-computational cost => in case of optimization efficient strategies are required Gradient-based optimization algorithms are known to be efficient but computing the gradients is expensive with the standard finite differences approach. => need for an efficient approach to determine the gradients: the coupled aero-structural adjoint approach Traditional Finite Differences Approach Coupled Adjoint Approach Design Variables Design Variables Loop over number of design variables Aerodynamics Deformations Loads Structure Coupled Aero-Structural Adjoint computation Adjoint approach is independent on the number of design variables Gradients Gradients
15 Chart 15 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Formulation of the Coupled Adjoint Approach
16 Chart 16 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS
17 Chart 17 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS
18 Chart 18 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS
19 Chart 19 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
20 Chart 20 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
21 Chart 21 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR TAU ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
22 Chart 22 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR transfer deformation from CSM mesh to CFD mesh using : Radial Basis Function TAU ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
23 Chart 23 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR transfer deformation from CSM mesh to CFD mesh using : Radial Basis Function TAU ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
24 Chart 24 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Components of the Coupled System Loose aero-structural coupling is employed at DLR transfer deformation from CSM mesh to CFD mesh using : Radial Basis Function 5 Couplings Flight Shape TAU Jig Shape ANSYS transfer loads from CFD mesh to CSM mesh using : Linear Interpolation Tool
25 Chart 25 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Formulation of the Coupled Adjoint Equations Motivation: Efficient computation of the gradient of a cost function (I) w.r.t the design parameters (D). The aero-structural coupled system is defined by: = u w W = Rs Ra R D = T A Aerodynamic residual Structural residual Shape design variables Structural deformation Flow variables Structural thickness State variables Vector Design variables Vector Residual Vector I=I (W,D) ; R=R (W,D)=0 Where and are the aerodynamic and the structure Lagrange multipliers. ψa The Coupled Adjoint Equation The Gradients = u w ψs ψa u Rs w Rs u Ra w Ra I I T T T T + = = T Rs A Rs T Ra A Ra ψs ψa T A D D T T T T I I d dl d di ψs R I L Ψ + = Define the Lagrange:
26 Chart 26 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test case description
27 Chart 27 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. Reynolds number : 21e06 Lift is kept constant by varying angle of attack (implicit lift constraint à requires gradient correction) CFD One-Equation turbulence model Spalart-Allmaras
28 Chart 28 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. Reynolds number : 21e06 Lift is kept constant by varying angle of attack (implicit lift constraint à requires gradient correction) CFD One-Equation turbulence model Spalart-Allmaras CFD structured mesh; 1.2 Million nodes
29 Chart 29 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. Reynolds number : 21e06 Lift is kept constant by varying angle of attack (implicit lift constraint à requires gradient correction) CFD One-Equation turbulence model Spalart-Allmaras CFD structured mesh; 1.2 Million nodes Parameterization: 30 parameters fixing the body 150/2 FFD parameters on the wing (implicit thickness constraint)
30 Chart 30 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. Reynolds number : 21e06 Lift is kept constant by varying angle of attack (implicit lift constraint à requires gradient correction) CFD One-Equation turbulence model Spalart-Allmaras CFD structured mesh; 1.2 Million nodes Parameterization: 30 parameters fixing the body 150/2 FFD parameters on the wing (implicit thickness constraint) d( C )@ constant Lift dc = da da dcd dcl ( / dα dα D D ) dcl da
31 Chart 31 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. The Structure model: 27 Ribs 2 Spars Lower & Upper Skin
32 Chart 32 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Test Case Description Wing-Body configuration based on the DO728 geometry used as a test case. The Structure model: 27 Ribs 2 Spars Lower & Upper Skin CSM The CSM mesh: 4000 nodes. Modeled using rectangular shell elements, each node has 6 DOFs.
33 Chart 33 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations
34 Chart 34 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations Three optimizations were performed
35 Chart 35 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations Three optimizations were performed 1. Unconstrained Single-point optimization at the design point CL Mach
36 Chart 36 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations Three optimizations were performed 1. Unconstrained Single-point optimization at the design point 2. Constrained Single-point optimization at the design point CL Mach
37 Chart 37 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations Three optimizations were performed 1. Unconstrained Single-point optimization at the design point CL 2. Constrained Single-point optimization at the design point 3. Constrained Multi-Point Optimization Mach
38 Chart 38 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Optimizations Three optimizations were performed 1. Unconstrained Single-point optimization at the design point CL 2. Constrained Single-point optimization at the design point 3. Constrained Multi-Point Optimization The objective is drag reduction at constant CL and wing thickness. (Aerodynamic objective with elastic effects taken into account) Mach
39 Chart 39 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization The optimization employed a quasi-newton gradient-based algorithm.
40 Chart 40 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization The optimization employed a quasi-newton gradient-based algorithm. Optimization converged after 41 aero-structural couplings and 25 coupled adjoint computations. The optimization reduced the drag by 15 drag counts while keeping the lift and the thickness constant.
41 Chart 41 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization The optimization employed a quasi-newton gradient-based algorithm. Optimization converged after 41 aero-structural couplings and 25 coupled adjoint computations. The optimization reduced the drag by 15 drag counts while keeping the lift and the thickness constant. Baseline Optimized
42 Chart 42 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization The optimization employed a quasi-newton gradient-based algorithm. Optimization converged after 41 aero-structural couplings and 25 coupled adjoint computations. The optimization reduced the drag by 15 drag counts while keeping the lift and the thickness constant. Baseline Optimized
43 Chart 43 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization η=0.25 η=0.45 η=0.55 η=0.75 Baseline Op+mized
44 Chart 44 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization
45 Chart 45 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Unconstrained Single-point Optimization This (at constant lift) increases the bending moment at the Wing s root Keep CMx constant during the aero-elastic optimization
46 Chart 46 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Single-point Optimization The optimization employed SQP gradient-based algorithm. Optimization converged after 31 aero-structural couplings and 19 coupled adjoint computations. The optimization reduced the drag by 13 drag counts while keeping the lift and the thickness constant.
47 Chart 47 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Single-point Optimization The optimization employed SQP gradient-based algorithm. Optimization converged after 31 aero-structural couplings and 19 coupled adjoint computations. The optimization reduced the drag by 13 drag counts while keeping the lift and the thickness constant.
48 Chart 48 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Single-point Optimization The optimization employed SQP gradient-based algorithm.
49 Chart 49 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di CL Mach
50 Chart 50 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di CL Mach
51 Chart 51 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di CL Constraint applied on design point only Mach
52 Chart 52 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di 25 design iterations 20 gradient computations 260 hrs on 48 processors Highest gradients bring highest change (drag reduction) CL Mach
53 Chart 53 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di 25 design iterations 20 gradient computations 260 hrs on 48 processors Highest gradients bring highest change (drag reduction) CL drag counts Mach
54 Chart 54 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization The points were equally weighted. Cost_Function = 5 i= 1 0.2* C Di 25 design iterations 20 gradient computations 260 hrs on 48 processors Highest gradients bring highest change (drag reduction)
55 Chart 55 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization
56 Chart 56 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Constrained Multi-point Optimization
57 Chart 57 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Future Work: Gradient Correction due to Trimming Trimming the flight with a horizontal tailplane (to reach a target pitching moment) will be considered during the Optimization. The gradients of our cost function need to be corrected if the flight is trimmed using horizontal tailplane. (similar to correcting gradients of drag when running for target lift). Use the Lagrange formulation to predict the correction term in the gradients.
58 Chart 58 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Future Work: Gradient Correction due to Trimming Trimming the flight with a horizontal tailplane (to reach a target pitching moment) will be considered during the Optimization. The gradients of our cost function need to be corrected if the flight is trimmed using horizontal tailplane. (similar to correcting gradients of drag when running for target lift). Use the Lagrange formulation to predict the correction term in the gradients. If our cost function is drag then: Correction Term " $ : far-field angle of attack " & : tail s angle of incidence
59 Chart 59 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Future Work: Gradient Correction due to Trimming Tested on 2D Euler case
60 Chart 60 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Future Work: Gradient Correction due to Trimming Tested on 2D Euler case
61 Chart 61 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, Conclusions The coupled aero-structural adjoint approach was employed to efficiently obtain the gradients employed in single- and multi-point aero-elastic optimizations. The approach employs DLR s TAU code to solve the flow equations and ANSYS Mechanical to solve the structure equations, and deals with inviscid as well as viscous turbulent flows. The coupled adjoint approach could save around 75% of computational time, which makes it now possible to perform aero-elastic optimizations using the gradient-based techniques, even for multipoint optimizations. A single- and multi-point optimizations with constrained rolling moment were performed and expected to have better effect on the structure (less weight). Future optimizations will include aerodynamic to structure cross sensitivities Future optimizations will include (horizontal tail) trimming effect
62 Chart 62 Aero-elastic Multi-point Optimization, M.Abu-Zurayk, MUSAF II, THANK YOU FOR YOUR ATTENTION
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