VorDyn1.0 user manual - Boccelli Engineering
Contents
1. Mx My Mz generated by the whole configura tion e component_aerodynamic_forces the same but separating the wing horztail and verttail contribute Filename Calculated_ Component_Aerodynamic_Forces dat e panel aerodynamic_forces writes on a file the forces Fx Fy Fz generated by every single panel and also the relative Coefficient of Pressure Cp The panels coordinates are printed too 3 Component_Aerodynamics e neutral _point_computation calculates the position of the neu tral point by evaluating the pitching moment in two different ref erence points e aerodynamic_centers_lifting derivatives computes the aero dynamic center of wing and horizontal tail and the derivatives La and Ma of stand alone wing and tail The position of aero dynamic centers is plotted and printed on a file called Aerody namic_Centers dat while wing and tail a derivatives are available as internal variables 4 Stability_Derivatives e longitudinal derivatives longitudinal stability derivatives are evaluated around the linearization condition set in the nitial_ Conditions file The output is written to a file called Stabil ity_Derivatives_ Longitudinal dat e lateral_derivatives the same as for lateral derivatives 5 Longitudinal_Modes A dynamical system simplified to take only longitudinal variations into account is created and solved Inertial properties are stored in the Various_Properties m file Be careful bec2. lateral modes e etc Which geometries can I create process You can study airplane geometries composed by one wing one horizontal tail and one or two vertical tails Clearly tails can be canard surfaces if you like you just have to put them in the right place Every Lifting surface can be composed by more segments each one with control surfaces or flaps What if you don t want the tail Just put the tail somewhere far from your wings and set them to be very very very very small Numerical and model errors will do the rest Fuselage not implemented yet 2 Functionalities To tell the program what to do you set 1 or O flags in the What_To_Do m file See the Performing an Analisys Paragraph Let s now see what the code can do by analizing the variables in the What_To_Do file Open it and you will find the following 1 Geometry_Various e surfaces_and_aerodynamic_chords the surface of every wing horizontal tail and vertical tail section is calculated and printed on a file Mean aerodynamic chords of wing and tail are calculated too The file is called Surfaces_and_Chords dat e plot_normal_vectors geometry and panel normal vectors are plotted 2 Aerodynamic_Forces e plot_cp_vectors plots geometry and the Pressure Coefficient act ing on every panel e total_aerodynamic_forces writes on the file Calculated_Total_ Aerodynamic_Forces dat the aerodynamic forces Lift Drag Side force Fx Fy Fz
3. VorDyn1 0 user manual Stefano Boccelli February 2014 Fast presentation Hello everyone My name is Stefano Boccelli and I m a student of Aerospace actually Aeronautic Engineering at Politecnico di Milano Italy After the last exam session waiting for new lessons to start I ve written this Vortex Lattice code for MATLAB as a spare time project This software is surely buggy and odd written but I tried to make it as simple as possible and also to deeply comment strange lines of code You can calculate aerodynamic forces and stability derivatives with VorDyn and more There s plenty of software that does the same my softer does and does it better Tornado for example is one of them AVL is another There are also commercial codes etcetera The goal of my script is supposed to be providing a fast access to geometry modification in a hands on code style What else as I told you the code is probably full of bugs or mathematical mistakes so don t get angry with me if the numerical results cause you to be fired or to retrieve a bad mark at school Hope you enjoy Stefano Contents 8 9 Introduction to the software Functionalities Geometry Construction 325 Winglels fo ey pee ae fe Se pct ae Se Le hk ag ge Be gee OE gy Se RR AE et go 3 30 Horizontal Tall 2 22 4 ae 6 amar a hs BAL Vertical Taller i see ose Qe ae ne Ee le Ee Phe Performing an Analysis Program Structure Vortex Lattice Method Stabil
4. ause I haven t tested this module much e eigenvalue_plot_longitudinal plots the 4 eigenvalues of the lon gitudinal plane e eigenvectors_plot_longitudinal plots two of the longitudinal plane eigenvectors on an Argand diagram e state matrix export longitudinal you may be interested in the state matrix for various purposes like studying an automatic control system for example The matrix is written on a file named Longitudinal_State_Matrix dat 6 Lateral Modes the same as Longitudinal_Modes e eigenvalue_plot_lateral e eigenvectors_plot_lateral e state_matrix_export_lateral file Lateral State Matrix dat 7 Mesh_Esporting you may find useful to create a vortex mesh with VorDyn who knows you can export it a file called Generated_Mesh dat is created and it contains the position of control points where tangency condition is imposed the components of normal vectors for every control point the area of every panel and the position of the vertices of the vortex on a certain panel Note that the area of the panels is the area of the surface surrounded by the vortex for every panel except for those placed at the trailing edge Since trailing edge rings go to infinity the area of the lifting surface panel must be calculated in a different and fictitious way Every upper case variable causes a call to a certain MODULE called MOD ULE_UpperCaseVariableName The MODULE checks the lower case vari ables an
5. better be careful with my results 15 9 Validation I shall now compare the results of my code with other data First of all a naif and very crude validation have been made comparing the lift computed on a finite wing geometry to the theoretical lift generated by a wing immerged into bidimensional current L i pV SCL CL is 2ra as stated by the small perturbances theory Creating four wings with increasing aspect ratios I ver ified that the relative error between numerical Lift and theoretical 2D Lift decreased Of course a real validation would have passed through Prandtl finite wing model 24 T T T 227 7 error o 0 5 10 15 20 25 30 35 40 45 50 Wing Aspect Ratio The software Tornado is the result of a Magistral Thesis work In one of the final chapters of the thesis stability derivatives of a Cessna 172 Skyhawk are calculated and compared with experimental data I add here my results calculated like Tornado in a reference point located at 31 9 of the wing mean aerodynamic chord 16 Derivative Experimental Tornado VorDyn Cr 0 386 0 386 0 3812 Cp 0 042 0 006 0 0212 Cra 4 41 5 21 5 019 Cpa 0 182 0 17 0 2409 Cina 0 0409 1 55 1 358 CyB 0 35 0 47 0 287 C 8 0 103 0 008 0 0233 Cn 0 0583 0 197 0 1159 Cyp 0 0925 1 87 0 1146 Cp 0 483 0 484 0 2567 Crp 0 035 0 846 0 0278 Cyr 0 175 0 091 0 2652 Cir 0 1 0 03 0 0129 Chr 0 086 0 038 0 0269 a c
6. d if they are set to 1 executes the operations 3 Geometry Construction You can create the geometry by editing the file Geometry m Let s now focus on tge wing the rest is the same The wing can be composed by many segments with different sweep angle dihedral root inclination trailing edge flaps ailerons or not different number of mesh vortices in the spanwise direction and variable pitch along the wing An example of wing geometry may look like this Nc_wing is the number of panels chordwise It is the same for every wing section xA_wing yA_wing zA_wing are the coordinates of the leading edge of the root section SYM if you set this flag to one the wing will be complete otherwise you will have only the right wing After setting those parameters you create the geometry the length of the following vectors is the number of the wing sections you create Each element is a wing section if you want your wing to have 57 hope you don t segments and the 56 to have an aileron you add 57 elements in the following vectors and put FCR zero to any of them and the right flap chord ratio on the 56 h element of the vector If you look at the vectors one upon the other each column of the matrix you created represents a wing segment 3 1 Aileron or Flap Once you have set the FCR of a segment you choose the deflection angle by placing in the vector its value in RADIANS Note that in the default Geometry m file th
7. e value between the brackets is in DEG dimensions but is converted to radians by multiplying to pi 180 If you flagged SYM 1 then the symmetric wing segment will be created To tell the software that your surface is an aileron for example you set the inversion flag to 1 the deflection of the symmetric flap will be inverted You can do that by simply compiling the inversion vector 3 2 Winglets If you want to create a vertical surface you make a segment with a 90 dihe dral Please note that wing geometry is created using an approsite function different from the one used for the vertical tail if you have a wing section with a huge dihedral say gt 45 you can t put flaps on that wing section Well you could but deflection won t be the expected because of geometry creation and rotation issues Also the generated vertical surface can t be rotated to have an inclination for the explained reasons 3 3 Horizontal Tail The same horizontal tail too is created using the function wing geometry function004 3 4 Vertical Tail The same philosophy behind wing creation stands for vertical tail too except a couple of things e SYM flag creates a tail which is symmetrical on the longitudinal aircraft plane F18 like twin tail configuration e lambdavect is still the sweep and deltavect the dihedral a O value means vertical tail really vertical perpendicular to the xy plane The Geometry m file is an i
8. ity Derivatives 7 1 Angle Derivatives mia is ab ds 7 2 Roll Pitch Yaw Rate Derivatives ES TO DENVER A id e id a ee oY 7 4 Adimensionalization a RA OL Rs iO USES Le amp tes ye 0 Gis Ae age Date A hh eh Flight Dynamics modes Validation 10 Thanks to 10 11 12 14 14 14 14 14 14 15 16 18 1 Introduction to the software Vordyn is basically a vortex lattice method actually a vortex ring method that can evaluate aerodynamic properties of a given aircraft geometry The reference conditions are stored in the Initial_Conditions m file Why the name VorDyn Because my idea was originally to implement a vortex lattice method to obtain stability derivatives and solve the aircraft dynamical system Then since it always takes longer than you expected I ran out of time and havn t tested the dynamical part very much This is a Vortex Lattice method which gives a solution of the potential flow that s why the initial linearization condition must be in the linear aerodynamics field the method won t take stall or any kind of flow separation into account A Prandtl Glauert correction is still not implemented LOW SUBSONIC CODE If you like you can do it by hand The code can return some different outputs see functionalities para graph mainly e aerodynamic forces e control surfaces deflection e stability derivatives e mesh exporting e longitudinal and
9. m I set this lone arm at 300 chords away iv locating control points one for each panel placed in the middle of the 3 4 chord line As a result the control point will be situated in the middle of the vortex ring v creating normal vectors and surfaces Unfortunately a quadrilat eral one of our panels is not necessarily a planar surface finding the normal vector of a skew quadrilateral is mostly a question of inventing the normal vectors Several methods are available I use the cross product of the quadrilateral diagonals This also allows me to compute an approximated panel surface The points i to v are implemented in the functions wing_geometry_function004 and vtail_geometry_function004 The vectors xcv yev zcv are filled with coordinates of the control points in global axis xnv ynv znv are the xyz normals vector components of the normal vectors in the x y and z direction Clearly numel xnv numel xcv LA Vortices are stored in the xvortic yvortic zvortic matrices the size of them is 4 x numel xcv Every column is a vortex ring the four rows are the coordinates of every vortex corner IMPORTANT the vortex must be percurred in a certain direction al ways the same for every section of every lifting surface of any wing tail or the result will be a complete mess Induced Velocity Calculation For every control point the velocity induced by the vortices is calcu lated usi
10. n a flag is found to be 1 a MODULE is called I call MODULE a script that collects the operation of the same type For example the MODULE_Aerodynamic_Forces contains the following operations e print on a file the total forces e print on a file the forces generated by every aircraft component e print forces generated by every single panel How do I activate those sub tasks By setting the relative sub flag in the What_To_Do file In the MODULEs you can find some more if statements to check that 11 6 Vortex Lattice Method First of all I strongly suggest the book Low Speed Aerodynamics by Joseph Katz and Allen Plotkin It s basically a text about numerical panel meth ods for solving the incompressible flow and it s a kind of holy textbook for aerodynamics students Ok let s talk about VorDyn As you can see the created geometry is not thick at all as a matter of fact the code is a lifting surface method The implemented method consists in some steps 1 Preparing the geometry i dividing the surface into panels ii finding the quarter chord line and the 3 4 line of every panel iii placing a vortex ring of unknown intensity T on the panels start ing from the quarter chord line of a panel and ending to the quarter chord of the next panel in chordwise direction The vortex of the trailing edge panels is a horseshow vortex a ring vortex with an arm placed at infinity running in the direction of the strea
11. nce of the tail to vary of 1 14 8 Flight Dynamics modes The flying aircraft is subject to different aerodynamic forces as a first ap proximation some are almost proportional to an angular position like angle of attack or sideslip we can see them as stiffnesses others to the velocity and in the end we have inertial terms As a result the aircraft is a dynamical system subject to well known flight modes Phugoid short period and the third mode are linked to the longitudinal plane while the roll mode the spiral mode and the dutch roll mode are latero directional modes Knowing the damping ratio and the natural frequency of those modes is important to ensure proper flight qualities ensuring the modes are stable or not too much unstable is a fundamental requirement for succesful and safe flight By filling a couple of matrices with proper stability derivatives VorDyn accepts the Hypothesis of small perturbations and studies separately the longitudinal and the latero directional planes solving two separated linear systems Eigenvalues are plotted on the Gauss plane and Figenvectors on the Ar gand Diagram a plot of the magnitude and the phase of the states involved in a certain mode ATTENTION The results are clearly strongly affected by the inertial properties to be set in the Various_Geometry m file and by the CG position static margin Also I m not that sure of having well compiled matrices and all so you
12. ng the well known Biot Savart law There are mainly two ways to do that matricial operation of for cycles I ve implemented the sec ond one which is reeeeeally slower I implemented also the first but it was not working properly and unfortunately my spare time is almost over The induced velocity calculation is performed by the Vorter_Lattice_ INDUCEDVELOCITYFUNCTION function The function internally imports the geometry and returns the MAT matrix Only the constant term is now needed to solve the linear system and find the circulations MAT Dj ff The Constant Term The constant term is where the main variables come in ff is basically the dot product of the free stream velocity and the normal vector of every panel By modifying the 8 and a angles we can calculate the results in that a 6 condition We can find the stability derivatives by solving two times the main linear system the first time with a certain ff and the second one with a constant term ff evaluated with incremented angles Forces and Moments From T we can easily obtain aerodynamic loads thanks to the Kutta Joukowski theorem Moments are obtained multiplying the forces for the distance from the center of mass of the vehicle Lift Drag and Sideforce are calculated as geometrical projection of the total Force in wind axis 13 7 Stability Derivatives 7 1 Angle Derivatives Calculating an estimation of a and f derivatives is pretty easy
13. nput for other scripts like Geometry_Creator m but just let it do the job for you Performing an Analysis Create the Geometry by editing the default Geometry m file or if you already have call your Geometry file Geometry m and replace the original Set inertial properties in the Various_Properties m file Tell the program what to do set the flags in the What_To_Do m file Do you want to perform some aerodynamic force analysis Then set the upper case variable ON 1 Now which one of the available analysis do you want to perform Set the lower case variable You can perform more simulations at once Oh I forgot set the initial conditions Edit the Initial Conditions m file Set Ving rho alphaO and beta0 betal is the sideslip angle positive when the aircraft velocity has a component in the positive Y body direction Run VorDyn m And possibly yell Go Go Gadget VorDyn 10 5 Program Structure Everything starts from VorDyn which imports the geometry Geometry m file and the flight conditions Initial_Conditions m file then the geometry is created Geoemtry_Creator calls some functions wing_geometry_function004 for every single lifting segment of the wing and tails collecting data and building big vectors and matrices These are the infos needed for plotting mesh exporting or further processing Then a sequence of if statements starts checking the flags set in the What_To_Do m file Whe
14. onvention is clearly different And now a figure of the Skyhawk geometry created Vortex rings are displayed in green 17 I m afraid something s wrong in my code 10 Thanks to Special thanks to Politecnico di Milano that inter alia provided some of the electric current that powered my laptop Thanks to all the scientists and engineers who discovered and built the aerodynamic knowledge we have today 18
15. the software performs a couple of force and moment evaluations with 2 different angles the stability derivative is simply Force Force angle angle Attention stability derivatives are evaluated in the linearization condi tions so the angle is in reality an increment 7 2 Roll Pitch Yaw Rate Derivatives The computation of angular rate derivatives is easy too although requiring some small adjustment by you if the calculated derivative values are odd or the flow velocity is much different from the default 50m s see Adjustments paragraph a triangular velocity profile centered in the CG is added to the stream velocity 7 3 Derivatives For the derivatives my ideas weren t that fast implementing so I decided to exploit an analitic expression involving Cia tay and 0 Sth data that VorDyn can easily calculate 7 4 Adimensionalization To provide adimensional coefficientsm forces and angular rates are divided by the following factors p 2 d io S z where p q and r are the roll pitch and yaw rate 7 5 Adjustments Angular derivatives are easy to be found you just set an increment of few degrees 1 in my case in the MODULE_Stability_Derivatives but angular rate derivatives are a little more touchy A nice way to set them would be starting from the stream velocity composing a velocity triangle and setting the angular rate increment so that tan 1 a the angular rate causing the incide
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