Aerodynamics of 3D Lifting Surfaces through Vortex Lattice Methods (3) Two implementations of the VLM

Transcription

1 Aerodynamics of 3D Lifting Surfaces through Vortex Lattice Methods (3) Two implementations of the VLM

2 Basic Concepts Outline 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

3 Using VLM Program Xiongqing Yu Under the Guidance of Prof. Stephen Batill at the University of Notre Dame Notre Dame, Indiana, USA February, 1998

4 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

5 Program Description The VLM consists of three subroutines: geomtr matxso aerody

6 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.

7 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.

8 Program Description aerody To obtain the lift and pitching moment data for configurations by using Kutta-Loukowski theorem. The final form of the output data is computed and printed by this subroutine.

9 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 inboard, 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 degrees or less than 90.0 degrees. The dihedral of the horizontal tail can be modeled with one dihedral angle.

10 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

11 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

12 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.

13 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

14 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)

15 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.

16 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

17 Running VLM program Run the executable file "vlm"

18 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.

19 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.

20 The output file Two options brief output total panel layout aerodynamic characteristics of total configuration detail output each panel information

21 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, c av, true configuration area divided by true span

22 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

23 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

24 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

25 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

26 Verifications (1) Result comparisons between VLM and Wing Design VLM Wing Design discrepancy Lift coef. Cl % Pitch moment coef. Cm % Induced drag coef. Cdi %

27 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 % % Cm % % Cdi % %

28 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.

29 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.

30 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., 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.

31 Application to EPUAV Design

32 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)

33 TORNADO Wing features Sweep. Dihedral. Twist. Taper. TE control surface Camber (NACA 4D)

34 TORNADO Design features Multiple wings Full 3D orientation Multiple control surfaces Cranked wings

35 Solver features TORNADO Explicit forces in Newtons. Stability derivatives with respect to: Pitch Roll Yaw Angular rates Control surface power derivatives. Parameter sweep.

36 3-D wing configuration

37 Cp Distribution

38 Local CL on Main Wing

39 Result Summary

40 Stability Analysis

41 An Application in My Research work Jointed-Wing Stability Analysis

42 Jointed-Wing Stability Analysis

43 Jointed-Wing Stability Analysis

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

45 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

46 界面

47

48

49 实例一

50 实例二

51 实例三