Aerodynamics of 3D Lifting Surfacesthrough Vortex Lattice Methods (3)

Two implementations of the VLM

Outline• Basic Concepts

– Boundary conditions on the mean surface

– Vortex Theorems, Biot-Savart Law

– The Horseshoe Vortex

– Selection of Control Point and Vortex Location

– The Classical Vortex Lattice Method

• Two implementations of the VLM– VLM program

– TORNADO

• Application Examples of VLM

• Insights into wing and wing-canard aerodynamics

Using VLM Program

Xiongqing Yu

Under the Guidance of Prof. Stephen Batillat the University of Notre Dame

Notre Dame, Indiana, USAFebruary, 1998

Introduction• Objectives

– VLM is a FORTRAN computer program estimating the subsonic aerodynamic characteristics of complex planforms.

• Predicting lift and pitch moment coefficients, maximum lift coefficient, induced drag coefficient and distributions of span load for the complex configurations.

• Background– VLM is a modified version of the NASA-Langley Vortex Lattice

Computer Program that had been used at the Langley Research Center and in industry.

– The original program has been modified to provide a useful tool for the aircraft design class in the university level.

• To simplify the input and output file for the fixed wing configuration.

• To display the panel arrangement presenting the platforms

Program Description

• The VLM consists of three subroutines:– geomtr– matxso– aerody

Program Description• Geomtr

– When the total approximate panel number is specified• it is used to determine the number of chordwise horseshoe

vortices

• the number of spanwise rows at which chordwise horseshoe vortices

• the panel aspect ratio is kept between 0.5 and 4

– When two planforms are used to describe a wing-tail configuration, this subroutine is used to handle with panel match between two planforms.

Program Description

• matxso – It is used to calculate the circulations which is

required to satisfy the tangent flow boundary condition.

– The circulations is determined by solving a matrix equation.

Program Description

• aerody – To obtain the lift and pitching moment data

for configurations by using Kutta-Loukowskitheorem.

– The final form of the output data is computed and printed by this subroutine.

Modeling the configuration

• Modeling planforms– The planforms can be modeled with one or two lifting surfaces

• where wing planform can consists of up to three segments, that is in-board, mid-board and out-board segments, and tail planform is modeled with a trapezoid.

• Modeling dihedrals– The wing can have up to three dihedral angles corresponding to

three segments of the wing.

– Winglets can be modeled, but the dihedral angle must be greater than -90.0 degrees or less than 90.0 degrees. The dihedral of the horizontal tail can be modeled with one dihedral angle.

• Modeling twist– The wing can have up to three twist angles corresponding

to three segments of the wing. • For inboard segment, the angle of its tip section with respect to its

root section is used to define the twist of the inboard segment

– The twists are assumed to be small and can have effect on the local angle of attack of lifting surfaces, but no effect on displacements of control points.

• Modeling camber – When the airfoil of the wing is specified, its camber can

be modeled with a curve determined based on tabulated data by least-square-distance curve fit

• coordinates of ten points on mean camber line of the airfoil

• Modeling elevator– It is assumed that the elevator can have effect on local angle of

attack of the control point on the horizontal tail

– the effect on displacements of control points is neglected when

the elevator is up or down.

• Definition of axis system

Running VLM program• The input data setup

– A include file (input.f) is used to set up the input data. The following is the input data required to be specified.

• Group one:– mach Mach number

– alpd Angle of attack at root section of main wing (degree)

– plan The number of lifting surface (1 or 2)

– nseg The number of wing segments(1,2 or3)

– cg Center of gravity location with respect to the origin of the coordinate system. Pitch moment computation is referenced to this location.

Group two: wing external definition – b1 Span of in-board segment of the wing– b2 Span of mid-board segment of the wing– b3 Span of out-board segment of the wing– cr Root chord of the wing – ct1 Tip chord of inboard segment of the wing– ct2 Tip chord of mid-board segment of the wing– ct3 Tip chord of outboard segment of the wing– sweep1 Sweep angle of inboard segment (leading line, in degree)– sweep2 Sweep angle of mid-board segment (leading line, in degree)– sweep3 Sweep angle of out-board segment (leading line, in degree)– theta1 Twist angle of inboard segment ( positive for washout, in deg. )– theta2 Twist angle of mid-board segment ( positive for washout, in deg. )– theta3 Twist angle of out-board segment ( positive for washout, in deg. )– dih1 Dihedral angle of inboard segment (in degree)– dih2 Dihedral angle of mid-board segment (in degree) – dih3 Dihedral angle of out-board segment (in degree) – alp_wing Wing incidence angle at root section – clmax2d Max. lift coefficient of wing airfoil

Group 3: Horizontal tail external definition – b0 Semi-span of the horizontal tail or canard

– cr0 Root chord of the horizontal tail or canard

– ct0 Tip chord of the horizontal tail or canard

– sweep0 Sweep angle of leading edge

– dihtail Dihedral angle of the horizontal tail

– alp_tail Horizontal tail incidence angle

– ielevator Control variable: set 1 if elevator is up or down; otherwise set 0

– be Elevator span

– cer Elevator root chord

– cet Elevator tip chord

– delta_e Rotate angle of elevator (positive when it is up)

Group 4: Relative position definition between the wing and the horizontal tail

– distx Distance between leading edge of the root section of the wing and leading edge of the root section of the horizontal tail in X-axis;

» Use 0 if only wing is specified (i.e. plan = 1)

» If canard is specified, distx should be negative;

– distz Vertical distance of the horizotal tail planform with respect the wing planform root chord height (in Z direction)

» use 0 if only wing is specified.

Group 5 : Specify camber of wing airfoil – iairfoil Control variable

» use 1 for camber airfoil;

» use 0 for symmetric airfoil

– stat Chordwise station location; range from 0 to 100

– yupper Upper surface coordinates of the specified airfoil

– ylower Lower surface coordinates of the specified airfoil

Running VLM program

• Run the executable file "vlm"

Running VLM program

• The interface options – Input the name of input data file:

– Input the approximate panel numbers of semi-wing.• Note: generally, this number ranges from 40 to 190 for single

wing, and from 40 to 120 for wing-tail configuration.

– Enter name of output file:

– Enter 0 for brief output. Usually use this option.

Enter 1 for detail output. This option is rarely used.

Displaying panel arrangement• You can check input file to verify its correction by displaying

panel arrangement.

• Under the MATLAB environment, run M-file "panelshow", and the panel arrangement will be displayed on a window.

The output file

• Two options– brief output

• total panel layout

• aerodynamic characteristics of total configuration

– detail output• each panel information

• All the items of output data for detail output– x c/4 X location of quarter-chord at the horseshoe vortex midspan.– x 3c/4 X location of three-quarter-chord at the horseshoe vortex midspan.

This is location of the control point.– y Y location of the horseshoe vortex midspan. – z Z location of the horseshoe vortex midspan.– s Semiwidth of horseshoe vortex– c/4 sweep angle Sweep angle of the quarter-chord of the elemental panel and

horseshoe vortex.– dihedral angle Dihedral angle of elemental panel– local alpha in radians Local angle of attack in radians at control point. – delta cp ∆Cp normal to the surface at dihedral for each elemental panel

under the flight condition. This is located across the panel as an average. It corresponds to the incremental lift associated with the bound vortex strength of the particular panel

– ref.chord Reference chord of the configuration

– c average Average chord, cav, true configuration area divided by true span

– total area Total area computed from the configuration listed.– reference area User input reference area ( wing area )– b/2 Maximum semispan of all planforms listed in second group of

geometry data – ref. ar Reference aspect ratio computed from the reference planform area

and wing span. – mach number Mach number

– CL Lift coefficient under the flight condition / ( q • reference area )– angle of attack Angle of attack ( input data )– CL (wing only) That portion of desired lift coefficient developed by the

planform with the maximum span when multiple planforms are specified. When one planform is specified, this is the desired lift coefficient

– CL alpha Lift-curve slope per radian, and per degree– CM Pitching-moment coefficient about the reference point (cg)

= Pitching-moment / ( q • reference area • ref. chord )– alpha at CL=0 Angle of attack at zero lift in degrees; nonzero only when

twist and/or camber and/or elevator is specified

– y cp Spanwise distance in fraction of semispan from root chord to center of pressure on the left wing panel

– CM/CL Longitudinal stability parameter based on a moment center about the reference point

– CM0 Pitching-moment coefficient at CL=0

For each spanwise station, the following data are presented; from the left tip towards the root:

– 2y/b Location of midpoint of each spanwise station in fraction of wing semispan. – c/cav Ratio of local chord to average chord– cl c/cav Distribution of span-load coefficients at the computed CL– cl Section life coefficients = lift per unit length of span / ( q • c)– x location The X location of the local center of pressure for the resulting span load

at cl , as a function of 2y/b– cdi induced drag coefficient– clmax maximum lift coefficient of complete configuration

Example• Step 1: Set up input data:

– See Appendix A.

• Step 2: run “vlm”

• Sept 3: The interface options– Input the approximate panel number of semi-wing.

– Note: generally, this number ranges from 40 to 190 for single wing, and from 40 to 120 for wing-tail configuration.

• 100

– Enter name of output file:

• example.out

Example– Enter 0 for brief output. Usually use this option.

– Enter 1 for detail output. This option is rare used.• 0

• Step 4: Displaying panel arrangement– Under the MATLAB environment, run M-file

"panelshow"

• Step 5: Opening output file– See Appendix B

Verifications (1)

Result comparisons between VLM and Wing Design

VLM Wing Design discrepancy

Lift coef. Cl 0.4923 0.4860 1.28 %

Pitch moment coef. Cm -0.106 -0.107 0.94 %

Induced drag coef. Cdi 0.0111 0.0110 0.90 %

Verifications (2)

Result comparisons between VLM and LinAir

case 1 twist=4 dihedral =3 case 2 twist=0 dihedral=0

VLM LinAir discrepancy VLM LinAir discrepancy

Cl 0.6286 0.6186 1.59 % 0.7652 0.7544 1.41 %

Cm -0.5627 -0.5602 0.44 % -0.6375 -0.6313 0.97 %

Cdi 0.02023 0.01948 1.85 % 0.02737 0.02644 3.4 %

Limitations• A maximum of two planforms may be specified.

• A maximum of three segments with different twists and dihedrals may be used to define the wing of a configuration, but only one segment with one dihedral can be used to define the horizontal tail of the configuration.

• The maximum number of the panels on the left side the configuration plan of symmetry is 200. when you input the panel number more than 200, an error information will display on monitor.

• The variation in local chord must be continuous from the tip chord to the root chord of each planform specified.

• The panel number in each chordwise row must be at least two.

Convergence

• You may use different panel number to run VLM, and make sure that the computed results reach the convergence.

• Some common rules of thumb may be used in selecting the panel number as indication in the interface when you run VLM.

References

• Margason, R.J., and Lamar, J.E., Vortex-Lattice FORTRAN Program for Estimating Subsonic Aerodynamic Characteristics of Complex Planforms, NASA TN D-6142, Feb., 1971.

• Lamar, J.E.and Gloss, B.B., Subsonic Aerodynamic Characteristic of Interacting Lifting Surfaces with Separated Flow around Sharp Edges Predicted by a Vortex-Lattice Method, NASA TN D-7921, Sept., 1975.

Application to EPUAV Design

TORNADO

• Background– Tornado is a vortex lattice program developed by

Tomas Melin at the Royal Institute of Technology.

– It was developed as a part of a masters thesis

– Tornado allows a user to define most types of aircraft designs

– The method is implemented in MATLAB (R12)

TORNADO

• Wing features– Sweep.

– Dihedral.

– Twist.

– Taper.

– TE control surface

– Camber (NACA 4D)

TORNADO

• Design features– Multiple wings

– Full 3D orientation

– Multiple control surfaces

– Cranked wings

TORNADO• Solver features

– Explicit forces in Newtons.

– Stability derivatives with respect to: • Pitch

• Roll

• Yaw

• Angular rates

– Control surface power derivatives.

– Parameter sweep.

3-D wing configuration

Cp Distribution

Local CL on Main Wing

Result Summary

Stability Analysis

An Application in My Research workJointed-Wing Stability Analysis

Jointed-Wing Stability Analysis

Jointed-Wing Stability Analysis

•Both VLM and TORNADO were applied to the design of EPUAV projects at NUAA

STRVLM

数据的输入及修改都较以前直观、方便

考虑了机身的影响

翼型的计算不再仅限于NACA四位翼型

图像的输出也可完全根据用户的需要

界面

实例一

实例二

实例三