vsp high-lift modeling -...

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www.nasa.gov

National Aeronautics and Space Administration

VSP High-Lift Modeling

Erik D. OlsonNASA-Langley Research Center

OpenVSP Workshop 2015Aug. 12, 2015

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Transformational Tools and Technologies Project

Outline

• Motivation and Goal

• Modeling High-Lift Components

• Deflecting Flaps and Slats

• Gap, Overlap and Relative Deflection

• Current Shortcomings

• Recommendations

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Transformational Tools and Technologies Project

Motivation

• OpenVSP can model high-lift surfaces using simple shearing of the airfoil coordinates. This is an appropriate level of complexity for lower-order aerodynamic analysis methods, such as vortex-lattice.

• For higher-order analysis methods (panel and Euler codes), actual three-dimensional surfaces must be modeled, particularly for slats and slotted flaps.

• No direct method for controlling complex flap and slat motions parametrically or intuitively.

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Transformational Tools and Technologies Project

Goal

• Establish a set of best practices for modeling high-lift components in OpenVSP at a level of complexity suitable for higher-order analysis methods.

– Flaps and slats modeled as separate three-dimensional surfaces

– Controlling motion using simple parameters in the local frame of reference

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Transformational Tools and Technologies Project

Outline

• Motivation and Goals

• Modeling High-Lift Components

• Deflecting Flaps and Slats

• Gap, Overlap and Relative Deflection

• Current Shortcomings

• Recommendations

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Transformational Tools and Technologies Project

Modeling High-Lift Components

• Components of the high-lift configuration (main wing, slat, vane and flap) modeled as separate wings.

• Planform layout for components identical to the complete wing (same span, tip chord, root chord, sweep, dihedral and twist).

• Component airfoil coordinates use fractional chord but normalized by the chord of the full wing section.

• Transition segments allow for nearly-discontinuous change in cross section.

• Flap and slat surfaces can be assigned to separate sets to visualize and export independently.

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Fractional Airfoil Coordinates

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EET AR12 ExampleHigh-lift Configuration

(Stowed)

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EET AR12 Example

Cruise wing

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Transition Segments

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Transformational Tools and Technologies Project

Outline

• Motivation and Goals

• Modeling High-Lift Components

• Deflecting Flaps and Slats

• Gap, Overlap and Relative Deflection

• Current Shortcomings

• Recommendations

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Transformational Tools and Technologies Project

Deflecting Flaps and Slats

• Problem: VSP transformations (XForm) are defined relative to the 𝑥, 𝑦, and 𝑧 axes – whereas we want to specify flap and slat transformations relative to the hinge axis.

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Transformational Tools and Technologies Project

Deflecting Flaps and Slats

• Problem: VSP transformations (XForm) are defined relative to the 𝑥, 𝑦, and 𝑧 axes – whereas we want to specify flap and slat transformations relative to the hinge axis.

• Solution: derive method to allow the user to directly specify flap motions relative to the hinge axis.

• Approach: define User Parameters for flap transformation relative to hinge axis, and use Advanced Parameter Linking to calculate the equivalent transformation in the component’s XForm parameters.

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Transformational Tools and Technologies Project

Definition of Hinge Line

• Flap with semispan, 𝑏

• Hinge line between 𝑝𝑜 = 𝑥0, 0, 𝑧0 and 𝑝1 = 𝑥1, 𝑦1, 𝑧1 where

𝑦1 = 𝑏2 − 𝑧1 − 𝑧02

• Hinge axis dihedral, Γ = sin−1𝑧1−𝑧0

𝑏and sweep, Λ = tan−1

𝑥1−𝑥0

𝑏

𝑝1 = 𝑥1, 𝑦1, 𝑧1

𝑝0 = 𝑥0, 0, 𝑧0

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Transformational Tools and Technologies Project

Hinge Axis Coordinates

𝑛

𝑠

𝑐

• 𝑐-axis lies in the plane of the flap, orthogonal to the hinge axis (approx. chordwise).

• 𝑠-axis is aligned with hinge axis (approx. spanwise).

• 𝑛-axis is orthogonal to 𝑐 and 𝑠 (approx. vertical).

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Transformational Tools and Technologies Project

Deflection relative to hinge axis

• Inboard end of hinge axis translated by Δ𝑐0, 0, Δ𝑛0 .

• Outboard translated by Δ𝑐1, Δ𝑠1, Δ𝑛1 , where

Δ𝑠1 =𝑏

cos Λ

2

− Δ𝑐0 − Δ𝑐12 − Δ𝑛0 − Δ𝑛1

2 −𝑏

cos Λ

• Component rotated around hinge axis by 𝜃𝑓.

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Transformational Tools and Technologies Project

Translation in 𝑥𝑦𝑧 Coordinates

• In 𝑥𝑦𝑧 coordinate system, deflection of inboard end of hinge axis is

Δ𝑝0 =

Δ𝑥0Δ𝑦0Δ𝑧0

=

Δ𝑐0 cos Λ−Δ𝑐0 cos Γ sin Λ − Δ𝑛0 sin Γ−Δ𝑐0 sin Γ sin Λ + Δ𝑛0 cos Γ

• Outboard deflection is

Δ𝑝1 =

Δ𝑥1Δ𝑦1Δ𝑧1

=Δ𝑐1 cos Λ + Δ𝑠1 sin Λ

−Δ𝑐1 cos Γ sin Λ + Δ𝑠1 cos Γ cosΛ − Δ𝑛1 sin Γ−Δ𝑐1 sin Γ sin Λ + Δ𝑠1 sin Γ cos Λ + Δ𝑛1 cos Γ

• New semispan, dihedral, and sweep:

𝑏′ = 𝑦1 + Δ𝑦1 − 𝑦0 − Δ𝑦02 + 𝑧1 + Δ𝑧1 − 𝑧0 − Δ𝑧0

2

Γ′ = sin−1𝑧1+Δ𝑧1−𝑧0−Δ𝑧0

𝑏′, Λ′ = cos−1

𝑥1+𝑥1−𝑥0−Δ𝑥0

𝑏′

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Transformational Tools and Technologies Project

Flap Transformation Steps

1. Translate the flap by −𝑝0 so that the inboard end of the hinge axis coincides with the flap origin.

2. Rotate about the 𝑥-axis by the negative of the dihedral angle (−Γ) so that the hinge axis lies in the 𝑧 = 0 plane.

3. Rotate about the 𝑧-axis by the sweep angle (Λ) so that the hinge axis coincides with the 𝑦-axis.

4. Rotate about 𝑦-axis by the flap rotation angle (𝜃𝑓).

5. Rotate about the 𝑧-axis by the negative of the new sweep angle (−Λ′).

6. Rotate about the 𝑥-axis by the new dihedral angle (Γ′).

7. Translate by 𝑝0 + Δ𝑝0 so that the inboard end of the hinge axis coincides with its new location.

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Transformational Tools and Technologies Project

Transformation Matrix

𝐴 =

𝐴11 𝐴12 𝐴13 𝑋𝐴21 𝐴22 𝐴23 𝑌𝐴31 𝐴32 𝐴33 𝑍0 0 0 1

Where𝐴12 = −sin Γ sin 𝜃𝑓 cos Λ

′ − cos Γ cos 𝜃𝑓 sin Λ cos Λ′ + cos Γ cos Λ sinΛ′

𝐴13 = cos Γ sin 𝜃𝑓 cos Λ′ − sin Γ cos 𝜃𝑓 sinΛ cos Λ

′ + sin Γ cos Λ sinΛ′

𝐴23 =

sin Γ cos Λ cos Λ′ cos Γ′ − cos Γ sin 𝜃𝑓 sin Λ′ cos Γ′ + cos 𝜃𝑓 sin Γ

′

− sin Γ sinΛ sin 𝜃𝑓 sin Γ′ − cos 𝜃𝑓 sin Λ

′ cos Γ′

⋮

(etc.)

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Transformational Tools and Technologies Project

OpenVSP Transformation Steps

1. Rotate around the 𝑧-axis by angle .

2. Rotate around the 𝑦-axis by angle .

3. Rotate around the 𝑥-axis by angle .

4. Translate along the vector (Δ𝑥, Δ𝑦, Δ𝑧).𝐵 =

cos 𝛽 cos 𝛾 − cos𝛽 sin 𝛾 sin 𝛽 Δ𝑥sin 𝛼 sin 𝛽 cos 𝛾 + cos 𝛼 sin 𝛾 cos𝛼 cos 𝛾 − sin 𝛼 sin 𝛽 sin 𝛾 − sin 𝛼 cos 𝛽 Δ𝑦sin 𝛼 sin 𝛾 − cos𝛼 sin 𝛽 cos 𝛾 sin 𝛼 cos 𝛾 + cos 𝛼 sin 𝛽 sin 𝛾 cos 𝛼 cos𝛽 Δ𝑧

0 0 0 1

If these transformations are equivalent, then 𝐴 = 𝐵.

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Transformational Tools and Technologies Project

Solve by Inspection𝐴 =

𝐴11 𝐴12 𝐴13 𝑋𝐴21 𝐴22 𝐴23 𝑌𝐴31 𝐴32 𝐴33 𝑍0 0 0 1

𝐵 =cos 𝛽 cos 𝛾 − cos𝛽 sin 𝛾 sin 𝛽 Δ𝑥

sin 𝛼 sin 𝛽 cos 𝛾 + cos 𝛼 sin 𝛾 cos𝛼 cos 𝛾 − sin 𝛼 sin 𝛽 sin 𝛾 − sin 𝛼 cos 𝛽 Δ𝑦sin 𝛼 sin 𝛾 − cos𝛼 sin 𝛽 cos 𝛾 sin 𝛼 cos 𝛾 + cos 𝛼 sin 𝛽 sin 𝛾 cos 𝛼 cos𝛽 Δ𝑧

0 0 0 1

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Transformational Tools and Technologies Project

Equivalent Transformations

𝛽 = sin−1 𝐴13

𝛼 = −sin−1𝐴23cos 𝛽

𝛾 = −sin−1𝐴12cos 𝛽

Δ𝑥 = XΔ𝑦 = YΔ𝑧 = Z

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Implementation

Inboard vane hinge axis

Inboard vane translation/rotation

Calculate X_Location, Y_Location, Z_Location,X_Rotation, Y_Rotation, Z_Rotation

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Transformational Tools and Technologies Project

Example

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Transformational Tools and Technologies Project

Outline

• Motivation and Goals

• Modeling High-Lift Components

• Deflecting Flaps and Slats

• Gap, Overlap and Relative Deflection

• Current Shortcomings

• Recommendations

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Transformational Tools and Technologies Project

Gap, Overlap, Rel. Deflection

• Problem: flap and slat translation and rotation tends to be specified in terms of Gap, Overlap, and Relative Deflection (𝛿𝑣).

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Transformational Tools and Technologies Project

Gap, Overlap, Rel. Deflection

• Problem: flap and slat translation and rotation tends to be specified in terms of Gap, Overlap, and Relative Deflection (𝛿𝑣).

• Solution: determine Δ𝑐0 , Δ𝑛0, Δ𝑐1, and Δ𝑛1that correspond to the desired gap, overlap and 𝛿𝑣.

• Approach: post-process OpenVSP geometry to calculate gap, overlap and 𝛿𝑣. Use constrained optimization to solve for Δ𝑐0 , Δ𝑛0, Δ𝑐1, and Δ𝑛1.

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Transformational Tools and Technologies Project

EET AR12 Flap SettingsConfiguration Component Gap/c Overlap/c Deflection, deg

Takeoff Slat 0.02 0.02 50

Vane 0.015 0.04 15

Flap 0.01 0.01 15

Landing Slat 0.02 0.02 50

Vane 0.02 0.03 30

Flap 0.01 0.005 30

Outboard vane Outboard flap

takeoff

landing

landing

takeofflanding

takeoff

landing

takeoff

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Transformational Tools and Technologies Project

EET AR12 Flap Settings

Takeoff

Landing

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Transformational Tools and Technologies Project

Outline

• Motivation and Goals

• Modeling High-Lift Components

• Deflecting Flaps and Slats

• Gap, Overlap and Relative Deflection

• Current Shortcomings

• Recommendations

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Current Shortcomings

• Discontinuous Airfoils in Cove Region

– VSP w-lofting (chordwise) is always continuous.

• Spanwise Lofting of Discontinuities

– When “discontinuities” are at different arc lengths, u-lofting does not connect them to each other.

cove

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Transformational Tools and Technologies Project

Recommendations

1. Add rotation about an arbitrary axis.

2. Add a method for introducing discontinuities to airfoils (repeated point?).

3. Automatically connect discontinuities during spanwise lofting (in conjunction with #2) .

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Transformational Tools and Technologies Project

Acknowledgements

• This work was conducted as part of the NASA Transformational Tools and Technologies Project, led by James D. Heidmann, within the Multi-Disciplinary Design, Analysis and Optimization element, led by Jeffrey K. Viken.